Logical Matters: Essays in Ancient Philosophy II 0199577528, 9780199577521

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LO GIC AL MATTERS

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Logical Matters Essays in Ancient Philosophy II JONATHAN BARNES edited by

Maddalena Bonelli

CLARENDON PRESS _ OXFORD

CLARENDON PRESS _ OXFORD Great Clarendon Street, Oxford, OX2 6DP, United Kingdom

Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide. Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries q in this volume Jonathan Barnes 2012 The moral rights of the authors have been asserted First Edition published in 2012 Impression: 1 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, by licence or under terms agreed with the appropriate reprographics rights organization. Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this work in any other form and you must impose this same condition on any acquirer British Library Cataloguing in Publication Data Data available Library of Congress Cataloging in Publication Data Data available ISBN 978–0–19–957752–1 Printed in Great Britain by MPG Books Group, Bodmin and King’s Lynn Links to third party websites are provided by Oxford in good faith and for information only. Oxford disclaims any responsibility for the materials contained in any third party website referenced in this work.

Contents Acknowledgements Preface 1. Galen, Christians, logic

vii xi 1

2. Cicero on logic

22

3. Logical form and logical matter

43

4. Grammar on Aristotle’s terms

147

5. Peripatetic negations

172

6. Aristotle’s Categories and Aristotle’s ‘categories’

187

7. Syllogistic and the classification of predicates

266

8. Speusippus and Aristotle on homonymy

284

9. Property in Aristotle’s Topics

312

10. ‘Sheep have four legs’

346

11. The law of contradiction

353

12. Proofs and the syllogistic figures

364

13. Aristotle and Stoic logic

382

14. Theophrastus and Stoic logic

413

15. Terms and sentences

433

16. Logic and the dialecticians

479

17. The Logical Investigations of Chrysippus

485

18. —ØŁÆ
a ı

Å
Æ

499

19. What is a disjunction?

512

20. Medicine, experience, and logic

538

21. Meaning, saying, and thinking

582

22. Epicurus: meaning and thinking

602

23. Ammonius and adverbs

621

vi

Contents

24. Priscian and connectors

639

25. Late Greek syllogistic

659

26. Boethius and the study of logic

666

27. Syllogistic in the anon Heiberg

683

Bibliography Index of Passages General Index

729 751 775

Acknowledgements The papers of which the chapters in this volume are revised and sometimes translated versions first appeared in the following places. The editor and the author are grateful to those publishing houses who generously gave permission to use material which is in their copyright. 1. ‘Galen, Christians, logic’: T.P. Wiseman (ed), Classics in Progress: essays on ancient Greece and Rome (Clarendon Press, Oxford, 2002), pp.399–417. 2. ‘Cicero on logic’: B. Inwood and J. Mansfeld (eds), Assent and Argument: studies in Cicero’s Academic Books, Philosophia Antiqua 76 (Brill, Leiden, 1997), pp.140–160. 3. ‘Logical form and logical matter’: A. Alberti (ed), Logica Mente e Persona (Olschki, Florence, 1990), pp.7–119. 4. ‘Grammar on Aristotle’s terms’: M. Frede and G. Striker (eds), Rationality in Greek Thought (Clarendon Press, Oxford, 1996), pp.175–202. 5. ‘Peripatetic negations’: Oxford Studies in Ancient Philosophy 4, 1986, 201–214. 6. ‘Aristotle’s Categories and Aristotle’s ‘‘categories’’’: O. Bruun and L. Corti (eds), Les Cate´gories et leur histoire (Vrin, Paris, 2005), pp.11–80. 8. ‘Aristotle and Speusippus on homonymy’: Classical Quarterly 21, 1971, 65–80. 9. ‘Property in Aristotle’s Topics’: Archiv fu¨r Geschichte der Philosophie 52, 1970, 136–155, and (for the final section) R. Brague and J.-F. Courtine (eds), Herme´neutique et ontologie: hommage a` Pierre Aubenque (Vrin, Paris, 1990), pp.79–96. 10. ‘Sheep have four legs’: Proceedings of the World Congress on Aristotle (Ministry of Culture, Athens, 1982), volume III, pp.113–119. 11. ‘The law of contradiction’: Philosophical Quarterly 19, 1969, 302–309.

viii

Acknowledgements

12. ‘Proofs and the syllogistic figures’: H.-C. Gu¨nther and A. Rengakos (eds), Beitra¨ge zur antiken Philosophie: Festschrift fu¨r Wolfgang Kullmann (Franz Steiner Verlag, Stuttgart, 1997), pp.153–166. 13. ‘Aristotle and Stoic logic’: K. Ierodiakonou (ed), Topics in Stoic Philosophy (Clarendon Press, Oxford, 1999), pp.23–53. 14. ‘Theophrastus and Stoic logic’: J. Wiesner (ed), Aristoteles Werk und Wirkung—Paul Moraux gewidmet I (Walter de Gruyter, Berlin, 1985), pp.557–576. 15. ‘Terms and sentences: Proceedings of the British Academy 69, 1983, 279–326. 16. ‘Logic and the dialecticians’: Classical Review 43, 1993, 304–306. 17. ‘The Logical Investigations of Chrysippus’: Jahrbuch des Wissenschaftskolleg zu Berlin 1984/5, pp.19–29. 18. ‘—ØŁÆ
a ı

Å
Æ’: Elenchos 6, 1985, 453–467. 19. ‘What is a disjunction?’: D. Frede and B. Inwood (eds), Language and Learning (Cambridge University Press, Cambridge, 2005), pp.274–298. 20. ‘Medicine, experience and logic’: J. Barnes, J. Brunschwig, M.F. Burnyeat, and M. Schofield (eds), Science and Speculation (Cambridge University Press, Cambridge, 1982), pp.24–68. 21. ‘Meaning, saying and thinking’: K. Do¨ring and T. Ebert (eds), Dialektiker und Stoiker (Franz Steiner Verlag, Stuttgart, 1993), pp.47–61. 22. ‘Epicurus: meaning and thinking’: G. Giannantoni and M. Gigante (eds), Epicureismo greco e romano (Bibliopolis, Naples, 1996), pp.197–220. 23. ‘Ammonius and adverbs’: Oxford Studies in Ancient Philosophy, supplementary volume 1991, pp.145–163. 24. ‘Priscian and connectors’: M. Baratin, B. Colombat, and L. Holtz (eds), Priscien: transmission et refondation de la grammaire de l’Antiquite´ aux modernes, Studia Artistarum 21 (Brepols, Turnhout, 2009), pp.365–383. 25. ‘Late Greek syllogistic’: Phronesis 30, 1985, 92–98.

Acknowledgements

ix

26. ‘Boethius and the study of logic’: M. Gibson (ed), Boethius (Blackwell, Oxford, 1981), pp.73–89. 27. ‘Syllogistic in the anon Heiberg’: in K. Ierodiakonou (ed), Byzantine Philosophy and its ancient sources (Clarendon Press, Oxford, 2002), pp.97–137.

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Preface This is the second of four volumes which, taken together, contain most of the papers I have published on ancient philosophy over the last forty years or so. Short reviews of books have, almost all, been excluded; so have pieces which were written for encyclopaedias and companions and the like; and I have left out one or two items which repeat or anticipate what I have written elsewhere — and one or two items which even to my partial eye do not deserve a reappearance in public. The organization of the chapters is, in general, thematic rather than chronological. Of course, the thematic character of a paper is, often enough, plural or indeterminate, and its attribution to this volume rather than to that may be fairly arbitrary. Similarly with the arrangement of the papers within each volume — although there chronology has something to say in the matter. None of the volumes purports to form a unity or to constitute a book. Nonetheless, the things do hang together in an informal sort of fashion; and no other way of arranging them — no other way that I could dream up — would have been any more useful or agreeable. Some of the chapters were originally published in French: they have all been done into English — the translations are usually free. All the chapters have been retouched. Misprints and other itching errors have been corrected (where I have noticed them). Certain infelicities of style have been removed — and others, no doubt, introduced in their stead. Some harmonization has been done — for example, in the manner of references to the ancient texts and to the modern literature. In addition, passages from the ancient authors, which were originally cited sometimes in Greek (or in Latin) and sometimes in English, are now more often than not quoted both in the dead langauge (at the foot of the page) and in the living (in the body of the text). Several of the chapters have been revised, one or two of them substantially: sometimes some new material has been incorporated; often, new references — both to the ancient and to the modern literature — have been pasted in; and occasionally propositions and arguments have been added and subtracted, and expanded or contracted or transmuted. These revisions have not been carried out systematically; and I should confess that I have only a

xii

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haphazard acquaintance with the literature which has come out since the essays were first printed. The original page-numbers are indicated within square brackets and in a lighter type. Some of the original footnotes have been suppressed or incorporated into the text: those — the large majority — which survive carry their original numbers. New notes are signalled by an asterisk or two. As a result, the sequence of footnote signals is sometimes engagingly eccentric. References to ancient texts use abbreviations which I hope are perspicuous — and which in any event are explained in the Index of Passages. References to modern literature are given in full on their first occurrence within a chapter, and thereafter in a truncated form. The few abbreviations which are used throughout the volume are explained at the start of the Bibliography. ***** I owe many things to many people, and most of the individual papers acknowledge their individual debts. The collection as a whole owes a vast amount to two people. Peter Momtchiloff first suggested to me that I should put together some of my ancient stuff. He chivvied me when I dragged my feet. From the start to the finish he offered sympathy and advice. But for his encouragement the business would never have been undertaken. Maddalena Bonelli has acted as general editor of the volumes. She too was good at chivvying when chivvying was needed; and she too offered constant advice and sympathy — as well as undertaking the several ungrateful tasks which fall to an editor. But for her support the business would never have been finished. ***** This second volume contains papers on logic, the word ‘logic’ being understood in a broad and Oxonian sense. The first few items are of a general nature; then a group of pieces deals with various Aristotelian issues; next come three papers on the connection, or lack of connection, between Peripatetic logic and Stoic logic; and thereafter the order of events is (with a hiccup or two) chronological, running from Chrysippus down to an anonymous logician of the eleventh century. Chapter 1 is primarily concerned with the attitudes which different Fathers of the Christian Church displayed towards the study of logic; and so it looks indirectly at the place which antiquity assigned to logic within the domain of intellectual inquiry. Chapter 2 is primarily concerned with Cicero’s

Preface

xiii

understanding of the nature and scope of logic; and so it looks indirectly at the status and significance of the discipline as a ‘part’ of philosophy. A distinction is often made between ‘formal’ logic and other kinds of informal reasoning. Chapter 3, ‘Logical form and logical matter’, discusses the ancient origins of the distinction, and investigates some of the ancient disputes and disagreements which hovered around it. Chapter 4, the first of the Aristotelian group of papers, treats some of the grammatical and syntactical considerations which underlie Peripatetic syllogistic — in particular, ideas about subjects and predicates and the ‘copula’. Chapter 5 turns around a passage in Alexander of Aphrodisias which examines the notion of negation and which defends a Peripatetic account of the thing against a rival, or at any rate a different account. The next two papers turn to the Aristotelian theory of the ten ‘categories’ which came to be seen within the Peripatetic tradition as the starting-point of logical inquiry. Chapter 6 is a historical survey of the topic, from Aristotle to late antiquity — and beyond. Chapter 7 argues, against the tradition, that the theory of the ‘categories’, whatever its other merits may be, is of no pertinence to the theory of inference — not even to the theory of Aristotelian syllogistic. Aristotle’s Categories opens with a brief section on homonymy, synonymy, and paronymy, phenomena which assume a considerable importance in various parts of Aristotle’s philosophy. Chapter 8 contemplates an influential thesis about the origins and the nature of the Aristotelian onymies. Aristotle’s Topics is organized about the four ‘predicables’ or styles of predication, one of them being the predicable of ‘property’. Chapter 9 analyses Aristotle’s account of the nature of properties and of some of the uses to which he put that account. Some predicates hold of their subjects ‘for the most part’: men go grey — not all men, nor just some men, but men for the most part. Such predications have a vast importance in Aristotle’s physics (and in his ethics), but they sit uneasily with his logic. Chapter 10 sets out some of the problems. A long and strong tradition has held that the Law (or Principle) of Contradiction (or of Non-Contradiction) is a foundation-stone of logic, and a ‘law of thought’. Chapter 11 dissects an argument presented by Aristotle in Book Gamma of the Metaphysics which would prove that it is impossible to believe that the Law does not hold. An equally long (but less strong) tradition has held that Aristotle’s syllogistic is a logic adequate to all scientific needs. Chapter 12 dissects the chapter in the Prior Analytics in which Aristotle would demonstrate the truth of that audacious claim.

xiv

Preface

Did the Stoics know about Aristotle’s logical inquiries? and if they did, were they influenced by them? Chapter 13 examines a number of ancient texts which say or imply that Chrysippus knew his Analytics, and it examines them with a sceptical eye. Stoic logic deals with ‘hypothetical’ syllogisms — that is to say, it is (roughly speaking) a part of the logic of propositions. Theophrastus also dealt with ‘hypothetical’ arguments: Chapters 14 and 15 consider the most important of the Theophrastean texts, and offer some account of the Peripatetic version of ‘hypothetical’ logic, comparing it both to Stoic logic and also to Aristotelian syllogistic. The next papers are chiefly concerned with the Stoics. Chapter 16 discusses the so-called ‘Dialectical’ School of logically minded philosophers, who — it has been claimed — anticipated some of the fundamental features of Stoic logic. Chapter 17 scrutinizes a passage in Chrysippus’ Logical Investigations which concerns complex imperatives. Chapter 18 asks what the Stoics were up to when they spoke about ØŁÆ
a ı

Å
Æ or ‘persuasive conditionals’. The Stoic logicians were accused of attending too much to words and too little to things: Chapter 19 examines the accusation insofar as it attaches to disjunctive propositions, asking how the Stoics defined disjunctions and how they should have defined them. ‘Medicine, experience and logic’, Chapter 20, collects ancient comments upon and allusions to the paradox of the sorites. Its main concerns are, first, to determine as clearly as possible just what a soritical argument was supposed to be, and secondly, to reconstruct and assess the only ancient answer to the paradox which has survived, namely the answer produced by Chrysippus. Chapters 21 and 22 form a pair and discuss three ancient theories of meaning — or rather, three different notions of what it is for an expression to mean something. Chapter 21 looks at the Peripatetic notion, according to which an expression means what its utterer is thinking, and the Stoic notion, according to which an expression means what its utterer may say by uttering it. Chapter 22 sets out — and defends — the Epicurean notion that expressions mean things, that the word ‘cow’, say, means cows (or is true of an item if and only if that item is a cow). The modal operators (for example, ‘possibly’ in ‘This is possibly the last time you’ll see me’) were construed by ancient logicians as adverbs: in Chapter 23, which circles about a few pages in Ammonius’ commentary on the de Interpretatione, I characterize that construal and consider some of its drawbacks. Ancient theorists supposed that connectors — roughly, what we

Preface

xv

think of as propositional connectives — were expressions which tied one word to another (‘Tom and Jerry’, ‘Wenn Wagner, dann Oskar’): Chapter 24 attempts to make some sense of the notion, on the basis of what Priscian has to say about connectors in his Latin grammar. ‘Late Greek syllogistic’, Chapter 25, touches on some of the issues which exercised John Philoponus and his contemporaries when they came to teach Aristotelian logic. Chapter 26 surveys Boethius’ contribution to logic, addressing in particular his puzzling account of conditional propositions. And the last chapter analyses half a dozen issues raised by an anonymous introduction to logic which was written towards the end of the year 1007.

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1 Galen, Christians, logic* I Galen was ‘first among physicians and unique among philosophers’ (so said the emperor Marcus Aurelius — as Galen himself tells us). He was born in Pergamum in ad 129, son of an architect. He enjoyed the best provincial education. Then, guided by a divine dream, his father decided that he should become a physician. He read indefatigably; he served as doctor to a gladiatorial school (it was a pleasure to be able to see the inside of living bodies); he travelled widely — and he went, of course, to Rome, where luck, good connections, and his own undeniable talents brought him success. He came to the emperor’s attention, and was appointed doctor-in-waiting to Marcus’ son Commodus. He worked like the devil; and he still found time to write — on pharmacology and anatomy, on diagnostics and therapeutics; commentaries on the works of Hippocrates and essays in the history of medicine; works of philosophy — and of logic. The surviving œuvre runs to some ten thousand Greek pages, which are supplemented by several items which have been preserved in Arabic translation. Much is lost. In particular, the fifteen books of On Demonstration (Galen’s major work on logic) are known only from a handful of references. But the Introduction to Logic survives, in a single Greek manuscript; and although it is elementary in intention, it expounds Galen’s own great logical invention — of which more anon.1 [400] * First published in T. P. Wiseman (ed), Classics in Progress: essays on ancient Greece and Rome (Oxford, 2002), pp.399–417. 1 On Galen in general and in particular, see R.J. Hankinson (ed), The Cambridge Companion to Galen (Cambridge, 2008). — The standard edition of the works of Galen (Greek text and Latin translation) was prepared, for the use of doctors, by C.G. Ku¨hn and published in Leipzig between 1821 and 1833. From a philological point of view, Ku¨hn’s edition leaves almost everything to be desired; it contains several late forgeries; and it is incomplete. (The last failing is not to be laid at Ku¨hn’s door: several Galenic texts have been rediscovered since his time.) The series Corpus Medicorum Graecorum will eventually replace Ku¨hn (but in its first century of existence it has not reached the half-way point); so too will the Bude´ editions (but they have only just started to appear); and there are, of course, other modern editions of certain texts. The Introduction to Logic, absent from Ku¨hn, is available in a Teubner edition (edited by K. Kalbfleisch: Leipzig, 1896). The ¨ ber Galens Werk testimonies to On Demonstration are collected and discussed by I. von Mu¨ller, U

2

Logical Matters

By the time of Galen’s death, in about 210, Christianity had rooted itself in most parts of the empire. It was still a minority interest, unloved by the authorities. But it was no longer a Jewish splinter group: there were cultivated Greeks and Romans among its adherents; and it was beginning to gather a learned literature. During Galen’s lifetime a number of Christians wrote addresses to their emperor, and they strove to present the new religion as a philosophy, a system of thought which might be compared — to its own advantage — with Stoicism or Platonism. The Apology of Justin and the Embassy of Athenagoras demonstrate a certain culture and a certain capacity to write. In the early years of the third century, Clement of Alexandria wrote his Stromateis or Miscellanies, an endlessly digressive and exuberantly erudite work, in order to show that the Christian religion was the one true philosophy. And thenceforth to the end of antiquity the Church Fathers never ceased to scribble.2 As for logic, the modern term — like its ancient counterparts — is elastic. I use it here in a narrow sense, to denote the theory of argument and proof. In the second century ad, the schools taught logic in two parts: there was ‘categorical syllogistic’ — essentially a simplified version of the logic found in Aristotle’s Prior Analytics; and there was ‘hypothetical syllogistic’, which is associated with the Stoics and in particular with Chrysippus. Galen was dissatisfied with the bipartite version of the discipline; for he found that it could not account for the proofs which scientists — and in particular mathematicians — habitually provide for their theorems. So he discovered what he termed ‘a third class of syllogism’, the class of relational arguments.3 [401] vom wissenschaftlichen Beweis, Abhandlungen der Bayerischen Akademie 1895.2 (Munich, 1897). On dem, and on Galen’s logic in general, see J. Barnes, ‘Galen on logic and therapy’, in F. Kudlien and R. Durling (eds), Galen’s Method of Healing (Leiden, 1991), pp.50–102 [reprinted in volume III], with the bibliographical references in n.19 (dem) and n.21 (logic). — The compliment paid to Galen by Marcus Aurelius may be found in Galen, praecogn XIV 660: Marcus ØºØ ... æd K F ºªø
Id ... H
b
NÆæH
æH
r
ÆØ, H
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. (For this work there is a splendid edition, with English translation and commentary, by Vivian Nutton in the Corpus Medicorum Graecorum, Berlin, 1979). 2 Biographical and bibliographical facts about the several Church Fathers mentioned in this chapter may be found in any of the standard handbooks — e.g. J. Quasten, Patrology (Utrecht, 1960). 3 See inst log xvi 1; for bibliographical references see J. Barnes, ‘Galen and the utility of logic’, in J. Kollesch and D. Nickel (eds), Galen und das hellenistische Erbe (Stuttgart, 1993), pp.33–52, on p.37 n.24 [reprinted in volume III].

Galen, Christians, logic

3

Three examples should make the matter sufficiently clear. First, a categorical syllogism: Everyone we invited has come, and we invited some francophones — so some francophones have come. Secondly, a hypothetical argument: He can’t both be in Geneva and be at the conference, and he’s in Geneva — so he’s not at the conference. Thirdly, from the logic of relations: Marie’s boots are smaller than mine, and mine are smaller than Ben’s — so Marie’s are smaller than Ben’s. The examples are valid deductions — that is to say, their conclusion (marked by the word ‘so’) follows from their premisses. And their validity depends on the force of certain logical elements in them, different types of element in the three different types of case: in the first example, the validity depends on the terms ‘everyone’ and ‘some’; in the second, on the words ‘not’ and ‘and’; in the third, on the expression ‘smaller than’. For example, every argument of the same form as the second argument — that is to say, every argument of the form Not both A and B, and A — so not B is valid; and the validity of every argument of that form is underwritten by the sense or force of the words ‘and’ and ‘not’. The three subjects of this paper — Galen, Christians, logic — have two things in common. First, they are major aspects of the ancient world: Galen was one of the three most influential scientists of antiquity (alongside Aristotle and Ptolemy); the Christians eventually kidnapped the empire; logic is one of the few ancient sciences which is not entirely out of date. Secondly, they are of marginal interest to classical scholarship. Galen has his votaries; but there is too much of him, and his case exemplifies one of the iron laws of philology: the more of an author survives, the less he is read. The miserable remains of Heraclitus have spilled more scholarly ink than all the works of Galen. The Christians were yet more voluminous. Who on contemplating the Greek and Latin Patrologiae has not groaned: What, will they stretch on to the crack of doom? In any event, that’s not our department — there are theologians, church historians, patristic scholars to look after the stuff. As for logic, it has rarely been loved. It is repulsively technical — or else frivolous and trifling. In any event, it is dry as dust. In Martianus Capella’s Wedding of Philology and Mercury, a droll introduction to the seven ‘liberal arts’ written in the early fifth century ad, Dame Dialectic makes an appearance: ‘her body was wizened, her clothes were grim, she was unkempt [402]

4

Logical Matters

(her hair was like a thicket), and she was muttering something — I don’t know what, but something quite unintelligible to any ordinary person’ (IV 329).4

II Why put the three subjects under one hat? Galen and logic make a pair. But Galen and Christians? Christians and logic? A Galenic text makes the tie. In his work On the Difference of Pulses Galen thwacks the theories of Archigenes — whom he had already walloped in a separate work, eight books long (lib prop XIX 33). Archigenes, he says, is wrong from the start: he lists the primary qualities, but he thinks that it is not worth proving why there are just so many of them — he is content with a mere assertion. (diff puls VIII 578)

No man of science should be so cavalier: he ought to have added to his assertion about the eight qualities a proof — or at least an argument — in order to avoid the impression that the reader, just as if he had entered a school of Moses or of Christ, was going to hear undemonstrated laws. (ibid, 579)*

The side-swipe at Jews and Christians is unexpected. Galen does not distinguish between Jews and Christians, and his reference is no more than a polemical aside. The claim that Christians have no time for proofs and arguments, which became one of the platitudes of anti-Christian propaganda, was made by two of Galen’s contemporaries — Lucian waves at it in his Peregrinus, and it is a major theme in the True Account of Celsus, which was the first pagan rebuttal of the new religion.5 Perhaps Galen was casually echoing a current commonplace? 4 ipsa autem femina contractioris videbatur corporis habitusque furvum verum dumalibus hirta setis nescio quid vulgo inexplanabile loquebatur. * PŁf ŒÆ Iæåa æÅÆØ fiH æåت
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x  lŒØÆ åæ. 5 For Lucian, see M.J. Edwards, ‘Satire and verisimilitude: Christianity in Lucian’s Peregrinus’, Historia 38, 1989, 89–98. All that remains of Celsus’ True Account comes from the long criticism which Origen wrote some eighty years later: see the annotated translation by H. Chadwick, Origen: contra Celsum (Cambridge, 19652).

Galen, Christians, logic

5

But later in On the Difference of Pulses, Galen returns to the Jews and Christians: You will more readily convert the followers of Moses and of Christ than those doctors and philosophers who are stuck to their sects. (diff puls VIII 657)* [403]

And elsewhere he refers to ‘the doctrine of Moses’ about nature and the divine Demiurge: Moses may be no worse than Epicurus, but insofar as ‘he deems that everything is possible for God — so that he could make a horse or an ox out of ashes if he wanted to’, he is greatly inferior as a theologian to Galen, to Plato, and to all right-thinking Greeks (us part III 904–905).** The text alludes to the Book of Genesis. Further references to Christianity are found in the Arabic tradition. Two texts echo On the Difference of Pulses. One is a fragment from Galen’s lost treatise On the Anatomy of Hippocrates: Those who practise medicine without any scientific knowledge they compare to Moses, the Jewish lawgiver; for in his books his method is to write without giving any proofs, saying: God commanded, God spoke.

The second text comes from an anti-Aristotelian essay, Against the First Unmoved Mover : Were I thinking of those who teach pupils in the manner of the followers of Moses and Christ, ordering them to accept everything on trust, I should not have given you a definition.

Finally, in a passage from his synopsis of Plato’s Republic (or perhaps of the Phaedo) Galen offered the Christians a bouquet: to be sure, they ‘are unable to follow any demonstrative argument’; to be sure, they give credence to stories and parables; yet nevertheless they face death with an admirable resolution, they are properly self-controlled (even their womenfolk) in sexual matters, they eat and drink modestly, they love justice — in short, in practical life ‘they are not at all inferior to genuine philosophers’.6 If Galen was contemptuous of Christian logic, he admired Christian ethics — and he * ŁA
... ¼
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. 6 The texts are printed, translated, and discussed in R. Walzer, Galen on Jews and Christians (Oxford, 1949); see also e.g. S. Pines, An Arabic Version of the Testimonium Flavianum and its Implications (Jerusalem, 1971), pp.73–82; S. Gero, ‘Galen on the Christians: a reappraisal of the Arabic evidence’, Orientalia Christiana Periodica 56, 1990, 371–411.

6

Logical Matters

implicitly defended Christianity against the twin charges of cannibalism and incest which were frequently brought against it.7 It has been inferred from all this that Galen was rather well informed about the followers of Moses and of Christ; that he had some first-hand acquaintance with the Bible; and that his observations ‘reflect a discussion which had been going on for [404] some time in the higher strata of Roman society and of which we know merely because Galen inserted these chance remarks into some of his philosophical and medical works’.8 We might then look again at the Greek corpus. For example, Galen tells a story about the emperor Hadrian: he once struck a slave in anger and blinded him in one eye; asked to name his compensation, the slave ‘boldly asked for nothing else but an eye — for what gift could be worth the loss of an eye?’ (aff dig V 17–18). Has Hadrian — or Galen — not heard it said: ‘An eye for an eye, and a tooth for a tooth’?* All very seductive — but the evidence had better be set in its context. From other Arabic texts we learn that St Paul was Galen’s nephew; that Galen heard from Mary Magdalene of the miracles of Jesus; that he went to Palestine to interview the surviving disciples; that he foretold the Second Coming; that, a devout Christian himself, his dying wish was that his pupils should follow his own religious example.9 All that is wild fantasy; and some have supposed — to my mind, not implausibly — that Galen’s admiration for Christian morals belongs to the same branch of literature. Nor do any of the surviving texts prove that Galen had read the Bible; for although On the Use of Parts 7 On cannibalism and incest, Thyestean feasts and Oedipodean intercourse, see e.g. Fronto, in Minucius Felix, Oct ix 6 (cf viii 4; xxviii 2; xxxi 31.2); Justin, apol 1 xxvi 7; Athenagoras, leg iii 1; the letter from the church of Vienne and Lyons in Eusebius, HE V i 14–15; Origen, c Cels VI 27, 40 (compare Lucian, merc cong 41, on choice items of Roman pornography). On the whole matter, see A. Henrichs, ‘Pagan ritual and the alleged crimes of the early Christians’, in P. Granfield and J. A. Jungmann (eds), Kyriakon: Festschrift Johannes Quasten (Mu¨nster, 1971), pp.18–35. 8 Walzer, Jews and Christians, p.2 (to which there is a brisk application of scepticism by A.D. Nock, review of Walzer, Gnomon 23, 1951, 48–52). The view that Galen had read some of the Christian scriptures seems to go back at least to E. Norden, Die antike Kunstprosa (Leipzig, 19092), pp.518–519 (‘It is at least probable — though not certain — that Galen had read in the Gospels’). Norden appeals only to the fragment from syn Rep which neither states nor implies anything about reading. * Mt v 38 (MŒ Æ ‹Ø KææŁÅ OçŁÆºe
I
d OçŁÆº F ŒÆd O
Æ I
d O
 ), alluding to Ex xxi 24; Levit xxiv 20; Deut xix 21. Hadrian’s slave asks:  ªaæ i
ŒÆd ª
Ø Hæ
I
Ø
IøºÆ OçŁÆº F. 9 I take these examples from Gero, ‘Galen on the Christians’, pp.389, 391 n.61, 397 n.76, 398 n.78. See also [Galen], ren affect XIX 679: ‘Because these remedies generally fail, we Christians [ A  f æØØÆ
] must go to our greatest and truly mysterious items’ — and our Christian cures never fail. The work on the diseases of the kidneys is a late forgery.

Galen, Christians, logic

7

shows that he knew how the God of Genesis created the world, it does not show that he had read Genesis; and no other text suggests that he had read anything Scriptural. According to Tertullian, ‘only Christians read our books’ (test an i 1). Tertullian exaggerates, as he always does: Celsus, the declared foe of all things Christian, had read much of the Scriptures, and so had his contemporary, the Platonico-Pythagorean philosopher Numenius — and Numenius read with an approving eye. Yet Tertullian’s exaggeration is not far from the truth.10 Nonetheless, it is certain that Galen said once, and probable that he said three times, that Christians do not prove their doctrines; and it is likely that the accusation was based on some passing acquaintance with some Christians and with their religious notions and practices. [405]

I II Whether any Christians had a passing acquaintance with Galen is another question, to which I shall later turn. Before that, some words about the common accusation that Christianity despised and rejected logic. It must be allowed that innumerable Christian texts appear to give substance to the accusation. Had not St Paul denounced those who are ‘doting about questions and strifes of words’ (I Tim vi 4)? And was he not there referring to ‘the Greek art of logic, which he calls a disease’ (Clement, strom I viii 40.2)?* Many learned Christians thought so. From the Latin part of the empire and the late third century you might cite Arnobius, who affirms that Christians have no need of ‘syllogisms and enthymemes and definitions and other decorations of that sort’ (adv nat I 58); or Lactantius, according to whom divine learning has no need of logic, since wisdom is not in the tongue but in the heart, and it is of no account what style you use — it is things, not words, which we seek. (div inst III xiii) 10 For Numenius and the Bible, see e.g. M.J. Edwards, ‘Atticizing Moses? Numenius, the Fathers and the Jews’, Vigiliae Christianae 44, 1990, 64–75 (but his scepticism is unconvincing). For pagan citations of the Scriptures, see G. Rinaldi, Biblia Gentium (Rome, 1989), with pp.103–116, for a general survey of the evidence. (The celebrated citation of Genesis in [Longinus] ix 9 is surely an interpolation.) * Paul:
H
æd ÇÅØ ŒÆd º ª ÆåÆ; Clement: ›æfi A ‹ø æe ÆP f ŒŒ
ÅÆØ,

O
Çø
c
º ªØŒc
å
Å
ÆPH
.

8

Logical Matters

And a pair of Greek examples from the fourth century. Gregory of Nazianzus asserts that Christians should express their views ‘dogmatically, not antilogically; in a fishermanly fashion, not a` la Aristotle’ (orat xxiii [PG XXXV 1164]).11 And Gregory of Nyssa: As for confirming our doctrines by way of the dialectical art, through syllogisms and analytical science, we abjure that form of discourse as rotten and suspect with regard to the demonstration of the truth.

After all, dialectic has ‘equal strength in both directions’ and is as likely to subvert as to support the truth. A theologian who makes use of logic will only make his doctrines seem dubious (an et res [PG XLVI 52B]). In spurning logic, the Christians had pagan predecessors.12 They adopted the pagan objections. But they also had an objection of their own: logic was the seed-bed of heresy. Heresy, after all, was grown on the soil of Greek philosophy. The Refutation of all Heresies compiled by Hippolytus in the early third century is a sustained essay on the topic (and the one best known to classical scholars);13 but it [406] elaborates a commonplace. Tertullian, for example, knew that heretics associate with ‘magicians, mountebanks, astrologers and philosophers’ (praescr xliii 1). Logic in particular pleases their perverted palates: they love ‘wretched Aristotle, who taught them dialectic, the art of proving and refuting’ (ibid, vii 6).14 Jerome agreed with Tertullian: the heretics ‘seek a place and a refuge for themselves amid the thickets of Aristotle and Chrysippus’ (in Naum ii 15 [PL XXV 1269C]). The arch-heretic of the second century, Marcion, called his major work ‘Antitheses ’ — a technical term in logic. Apelles, a renegade pupil of Marcion, wrote a work in at least 38 books ‘which he entitled Syllogisms and in which he hopes to prove that everything which Moses wrote about God is not true 11 ÆFÆ ‰ K
æÆåØ çغ  çÅÆØ æe A  ªÆØŒH Iºº PŒ I
غ ªØŒH, ±ºØıØŒH Iºº PŒ `æØ ºØŒH. — Fishermen vs. philosophers: on this favourite trope, see H. Hagendahl, ‘Piscatorie et non aristotelice: zu einem Schlagwort bei den Kirchenvatern’, in AA. VV., Septentrionalia et Orientalia: studia Bernhardo Kalgren dedicata (Stockholm, 1959), pp.184–193. 12 See e.g. J. Barnes, Logic and the Imperial Stoa, Philosophia Antiqua 75 (Leiden, 1997) pp.1–11. 13 See J. Mansfeld, Heresiography in Context, Philosophia Antiqua 56 (Leiden, 1992); and cf J. Barnes, ‘The Presocratics in context’, Phronesis 33, 1988, 327–344 [reprinted in volume I, pp.125–142]. 14 See also e.g. praescr vii 3; adv Marc i 13. Elsewhere Tertullian calls the pagan philosophers the ‘patriarchs of the heretics’, a phrase which he repeats and which Jerome adopts (an iii 1; c Hermog viii 3; Jerome, ep cxxxiii 2).

Galen, Christians, logic

9

but false’ ([Tertullian], adv haer 6). At about the same time, an adherent of the Valentinian heresy, Alexander, produced a book full of heretical syllogisms.15 The fourth-century heretics were worse. Arius was ‘a man not unacquainted with logical quibbling’ (Socrates, HE I 5). In the nice phrase of Faustinus, Aristotle was ‘the bishop of the Arians’ (trin 12 [PL XIII 60B]). Ae¨tius loved ‘the matters set out technically by Aristotle’ (Socrates, HE II 35): he learned ‘the teachings of Aristotle’ in Alexandria, and rapidly became ‘a dialectician, good at syllogizing, practised in captious argumentation and wholly devoted to such things’ (Sozomenus, HE III 15). His Syntagmation or Pamphlet was copied out by the Catholic bishop of Salamis, Epiphanius, in the course of his exhausting denunciation of every hideous heterodoxy. In the Panarion or Bread-Basket Epiphanius affirms that Ae¨tius wrote ‘dialectically’; his work was ‘a dialectical error’ (pan III 351); it was nothing but a ‘dialectical ostentation and a syllogistic waste of labour’ (ibid, 361).16 [407] Eunomius likewise was ‘a technician of arguments, given to captiousness, rejoicing in syllogisms’ (Sozomenus, HE VI 26). Gregory of Nazianzus wonders why he ‘ties up the weak in spiders’ webs, as though that were something grand and clever’ (orat xxvii 9). According to Jerome, who refers disparagingly to ‘those who are trained in the art of dialectic and the arguments of the philosophers’, Eutychius and Eunomius ... attempt with syllogisms and enthymemes — with sophisms and Liars and Sorites — to confirm the errors which others have invented. (in Amos I i 4)

(It may be noted that Eunomius reversed the charges: the Catholics, he insisted, were ‘led astray by the sophisms of the Greeks’: apol 22; cf 27.)17 15 On Marcion, see A. von Harnack, Neue Studien zur Marcion, Texte und Untersuchungen zur Geschichte der altchristlichen Literatur 44 (Leipzig, 1923); id, Marcion: das Evangelium vom fremden Gott, Texte und Untersuchungen zur Geschichte der altchristlichen Literatur 45 (Leipzig, 19242); on Apelles: von Harnack, Marcion, pp.177–196 and 404–420 (testimonia); R.M. Grant, Heresy and Criticism: the search for authenticity in early Christian literature (Louisville KY, 1993), pp.75–88; on Alexander: Tertullian, de carne xvii 1, with J.-P. Mahe´ (ed), Tertullien: La Chair du Christ, Sources chre´tiennes 216 (Paris, 1975), pp.58–68. 16 ØƺŒØŒH ªæçø
... ØƺŒØŒ
Ø
Æ  çÆ
Ø
º
Å
... B ØƺŒØŒB  ı Œ Æ ŒÆd ıºº ªØØŒB ÆÆØ 
Æ. Ae¨tius’ Syntagmation: text, translation, and notes in L.R. Wickham, ‘The Syntagmation of Ae¨tius the Anomoean’, Journal of Theological Studies 19, 1968, 532–569. Ae¨tius was exiled in the 350s for his heretical opinions — and recalled by the pagan emperor Julian who remembered their ‘old acquaintance and intercourse’ (ep 46 [404C]). 17 On Eunomius and logic, see E. Vandenbussche, ‘La part de la dialectique dans la the´ologie d’Eunomius ‘‘le technologue’’ ’, Revue d’histoire eccle´siastique 40, 1944/5, 47–72, with a generous

10

Logical Matters

IV A diverting text refers to heretics, to logic — and to Galen. In his History of the Church Eusebius transcribes some pages from an attack on the followers of an heretical tanner, Theodotus by name. A part of the transcription is repeated by Theodoretus, who says that it comes from the Little Labyrinth, a work which some falsely ascribed to Origen. Other ancient authorities attributed the work to Gaius, of whom we know next to nothing; and some modern scholars have proposed Hippolytus.18 However that may be, Theodotus is dated to the papacy of Victor, bishop of Rome from 189 to about 200, and his followers had trouble with Victor’s successor Zephyrinus. [408] The Theodotians were charged with several sins. They tampered with the text of the Scriptures, a practice for which heretics (and Jews) were notorious — Celsus was delighted to report that ‘some of the believers’ altered the text of the Gospels three or four or more times in order to escape refutation (Origen, c Cels II 27).19 A second sin was equally heinous. The Theodotians do not inquire what the divine Scripture says. Rather, they diligently practise whatever syllogistic figure can be found to establish their atheism, and if you present them with a text of divine Scripture they investigate whether it can make a conditional or a disjunctive syllogistic figure. Abandoning the holy Scriptures of God, they study geometry — for they are of the earth and speak of the earth and they do not know Him that cometh from above [John iii 31]. Some of them diligently geometrize Euclid; Aristotle and Theophrastus are admired; and Galen no doubt is actually worshipped by some of them. (Eusebius, HE V xxviii 13–14)*

citation of texts. The texts of Eunomius: R.P. Vaggione, Eunomius: the extant works (Oxford, 1987). On logic and the fourth-century controversies, see J. de Ghellinck, Patristique et moyen aˆge: ´etudes d’histoire litte´raire et doctrinale III, Museum Lessianum section historique 7 (Brussels, 1961), pp.256–270. 18 The text: Eusebius, HE V xxviii 3–19; Theodoretus, haer fab II 5 (note that Theodoretus is independent of Eusebius); Methodius, symp viii 10. For title and authorship of the Labyrinth, see e.g. J. Schamp, Photios historien des lettres (Lie`ge, 1987) pp.109–115. On Theodotus, see D.A. Bertrand, ‘L’argument scripturaire de The´odore le Corroyeur (E´piphane, Panarion 54)’ in AA.VV., Lectures anciennes de la Bible, Cahiers de Biblia Patristica 1 (Strasbourg, 1987), pp.153–168. 19 For tampering with the Scriptures, see e.g. Justin, dial 72–73 (the Jews); Eusebius, HE IV xxix 6 (Tatian); Tertullian, adv Marc IV v 5–6 (the Gnostics); Augustine, retract I viii 6, II xxxiii 1 (Manicheans); Julian, c Gal 253E. See A. Bludau, Die Schriftfa¨lschungen der Ha¨retiker, Neutestamentlische Abhandlungen 11.5 (Mu¨nster, 1925). * ... P  ƃ ŁEÆØ ºª ıØ
ªæÆçÆd ÇÅ F
, Iºº › E
åBÆ ıºº ªØ F N c
B IŁ Å  ÆØ
æŁfiB çغ 
ø IŒ F
. Œi
ÆP E æ 
fiÅ Ø ÞÅe
ªæÆçB Ł€ØŒB,

Galen, Christians, logic

11

The Theodotians took refuge in logic — and they went to the best pagan authorities.20 Among those authorities was Galen, their contemporary, whom they worshipped. The verb is strong — Galen himself refers to intellectual idols whom you will not only emulate but worship — Socrates is among them, and Homer, and Hippocrates, and Plato, men whom we revere equally with the gods. (protr I 8)*

It has been inferred that the Theodotians knew Galen in person; that it was from him that they learned the geometry of Euclid and the logic of Aristotle and Theophrastus; and that their penchant for meddling with texts — in other words, for textual criticism — was encouraged by Galen’s scholarly work on the text of Hippocrates.21 The inferences are fragile. The Labyrinth implies no personal contact between the Theodotians and Galen — whose books were readily accessible. It does not suggest that Galen had anything to do with their philological [409] investigations — and there was a horde of pagan commentators from whom they might have sought inspiration. Nor does the text indicate that Galen was the source for all the Theodotians’ logical competence: on the contrary, its author, who later insists on the numerous schisms within the heresy, insinuates that one groupuscule ran to Euclid, another to the Peripatetic logicians, and a third to Galen. The Labyrinth is a piece of rude polemic, not a history of logic. Indeed, a solid sceptic might wonder if the reference to Galen was not the author’s own invention — does not the qualification ‘no doubt’ suggest as much? Perhaps it does; but I think that such scepticism is excessive. Later Fathers of the KÇ ıØ
 æ
ı
Å

j ØÇıª


ÆÆØ  ØBÆØ åBÆ ıºº ªØ F
ŒÆƺØ
 b a ±ªÆ  F Ł F ªæÆç, ªøæÆ
KØÅ ıØ
, ‰ i
KŒ B ªB Z
 ŒÆd KŒ B ªB ºÆº F
 ήd e
¼
øŁ
Kæå 

Iª
F
. ¯PŒºÅ ª F
Ææ ØØ
ÆPH
çغ 
ø ªøæEÆØ, `æØ ºÅ b ŒÆd ¨ çæÆ  ŁÆıÇ
ÆØ
ˆÆºÅ
e ªaæ Yø 

Ø
ø
ŒÆd æ Œı
EÆØ. 20 The passage has amassed a literature: see e.g. E. Schwartz, Zwei Predigten Hippolyts, Sitzungsberichte der bayerischen Akademie der Wissenschaften, phil-hist. Ableitung 1936.3 (Munich, 1936); H. Scho¨ne, ‘Ein Einbruch der antiken Logik und Textkritik in die altchristliche Theologie’, in T. Klauser and A. Ru¨cker (eds), Pisciculi: Studien zur Religion und Kultur des Altertums Franz Joseph Do¨lger dargeboten (Mu¨nster, 1939); Walzer, Jews and Christians, pp.75–86; de Ghellinck, Patristique, pp.288–296; Grant, Heresy and Criticism, pp.59–72. *  F
b
s
ܼ
r ÆØ e
å æe

Æ › E  KØ
P 

ÇźØ Iººa ŒÆd æ Œı
Ø. øŒæÅ ªæ KØ
K
ÆPfiH ŒÆd  …Åæ  ŒÆd   ŒæÅ ŒÆd —ºø
ŒÆd ƒ  ø
KæÆÆ, R YÆ ŒÆd  E Ł E  
. 21 So Walzer, Jews and Christians, pp.75–86.

12

Logical Matters

Church knew Galen; but they knew him as a physician. Efforts to find Galenic influence on earlier Christian authors — on Athenagoras, or on Clement, or Origen — fail.22 Nor is Galen often alluded to by pagans. The text of the Labyrinth is one of remarkably few early references to Galen. Moreover, it is the only text I know — outside the pages of Galen himself — which celebrates him as a logician. It is improbable that the reference was a pure invention. What of the other pagan logicians to whom the Theodotians applied themselves? Euclid is a surprise; and since geometry is in the text for the sake of the punning allusion to John’s Gospel (‘geo-metry’ is earth-measurement, and the Theodotians are of the earth), a sceptic might suspect that Euclid had been imported by the polemicist. At the other extreme, it has been supposed that the Theodotians made use of the Pseudaria — a lost work in which Euclid offered a sequence of exercises to guard students against logical fallacies.23 But neither scepticism nor subtlety is required: geometrical proofs were, after all, the very paradigms of logical demonstration, and the Theodotians will have conned their Euclid in order to hone their demonstrative prowess.24 [410] The name of Aristotle, on the other hand, is expected — who did not know that Aristotle had ‘turned philosophy into an expertise and was given to logic’ (Hippolytus, ref haer I xx 1)?25 Theophrastus might be there as his master’s dog; but he was still known at the end of the second century — at any rate, Galen wrote commentaries on his logical writings, and Alexander of

22 Galen has been found behind Athenagoras (with reference to the Ilkley Moor argument at res 5–8) by e.g. L.W. Barnard, Athenagoras: a study in second century Christian apologetic, The´ologie historique 18 (Paris, 1972), pp.53–59 — but see contra, and incontrovertibly, B. Pouderon, D’Athe`nes a` Alexandrie: ´etudes sur Athe´nagore et les origines de la philosophie chre´tienne, Bibliothe`que copte de Nag Hammadi, section E´tudes 4 (Quebec, 1997), pp.238–244. The best attempt to find Galen in Origen (not in itself an improbable notion) is R.M. Grant, ‘Paul, Galen, and Origen’, Journal of Theological Studies 34, 1983, 533–536 — but his arguments do not stand up. Later Jerome, for example, knows some Galen: A. Lu¨beck, Hieronymus quos noverit scriptores et ex quibus hauserit (Leipzig, 1872), pp.100–104; A.S. Pease, ‘Medical allusions in the works of St. Jerome’, Harvard Studies in Classical Philology 25, 1914, 73–86, on pp.81–82. 23 So Scho¨ne, ‘Einbruch der Logik’, pp.259–260. 24 See e.g. Gregory of Nazianzus, orat xxviii 25, for a Christian reference to Euclid as a celebrated proof-monger. 25 `æØ ºÅ ... N å
Å
c
çغ  çÆ
XªÆª
ŒÆd º ªØŒæ  Kª
 . — On Aristotle among the early Christians, see A.J. Festugie`re, L’Ide´al religieux des grecs et l’e´vangile (Paris, 19322), pp.221–263; D. T. Runia, ‘Festugie`re revisited: Aristotle in the Greek Patres’, Vigiliae Christianae 43, 1989, 1–34. — Runia finds fewer than 200 references to Aristotle in the Greek Fathers, scarcely any of which suggest a first-hand acquaintance with the texts.

Galen, Christians, logic

13

Aphrodisias discussed his contribution to hypothetical syllogistic.26 We may wonder if the old Peripatetics were read in the original — then as now, pagans and Christians got their logic (and most other items) from digests and handbooks. But the use of such conveniences is compatible with study of the original texts; and in truth we have no idea what Theodotus read in his tannery. There is a startling omission: no Chrysippus — no Stoics at all. At the end of the second century, the Stoic sun still shone bright enough. Hippolytus, for example, remarks casually that the Stoics — not Aristotle — ‘made philosophy more syllogistic’ (ref haer I xxi 1).27 Moreover, the one logical detail in the text suggests Stoic rather than Peripatetic logic: I mean the reference to conditionals and disjunctions. It is true that conditional propositions (‘If ... , then ... ’) and disjunctive propositions (‘Either ... or ... ’) had been discussed by Theophrastus; and of course the Theodotians could have learned of them from Galen — or from any textbook — without going back to the Stoic originals. But the Labyrinth uses the Stoic terminology rather than the Peripatetic; and it would have been peculiar to go to town on such items without knowing anything about the Stoics. I suspect that the absence of the Stoics from our text is an accident — its author, after all, does not profess to give a comprehensive account of the Theodotians’ logical studies. What he does say about conditionals and disjunctions has puzzled historians of logic: ... if you present them with a text of divine Scripture they investigate whether it can make a conditional or a disjunctive syllogistic figure. [411]

There are no such things as conditional or disjunctive ‘figures’ or forms of syllogism — it is propositions, not argument-forms, which are conditional and disjunctive. 26 See Galen, lib prop XIX 47; Alexander, in APr 262.28–264.31, 389.31–390.9. (See J. Barnes, ‘Terms and sentences’, Proceedings of the British Academy, 69, 1983, 279–326; id, ‘Theophrastus and hypothetical syllogistic’, in J. Wiesner (ed), Aristoteles Werk und Wirkung — Paul Moraux gewidmet (Berlin, 1985), pp.557–576 [both articles reprinted below, pp.433–478 and 413–432]). 27 ø€ØŒ d ŒÆd ÆP d b
Kd e ıºº ªØØŒæ
c
çغ  çÆ
ÅhÅÆ
... — Early Christian references to Stoic logic are collected by de Ghellinck, Patristique, pp.282–296. His general thesis is this: ‘The way in which they speak of Stoic logic does not point to a first hand acquaintance: it does not go beyond the small change of schoolboy learning characteristic of the culture of the time, or beyond the doxographies or collections of opinions of the philosophers’ (p.284). An exaggeration — Origen, at least, had pretty clearly read the stuff in the original.

14

Logical Matters

Scholars have therefore canvassed alternative translations.28 But they are implausible. And they are also superfluous. The Labyrinth has no interest in logical niceties, and we should not expect terminological precision from it. What the text means to say is plain enough. The Theodotians asked whether an argument which they found in the Bible should be formalized as a syllogism with a conditional premiss or as a syllogism with a disjunctive premiss. In short, they worried about the logical form of sacred arguments. Did Moses argue by modus ponens? Did St Paul syllogize in Barbara?

V Logic was tainted with heresy, and it was therefore to be rejected by Catholics. But what exactly were they to reject? What exactly were the logical sins of the heretics? There is no reason to think that the Theodotians theorized about logic or developed any logical techniques of their own. Rather, they applied to the Bible a technique used by commentators on pagan philosophical texts. Neither the Labyrinth nor any other of the sparse texts on the Theodotians actually cites one of their syllogisms; but it is easy enough to see what they must have been like. A Platonic commentator, for example, would identify an argument in a patch of Platonic text; he would set out the argument in a clear and explicit fashion; and he would perhaps refer it to one or another syllogistic form or figure.29 The Theodotians doubtless did the same thing. Something similar was probably true of Alexander, and certainly true of Apelles.30 Apelles’ Syllogisms was a collection of little arguments, each of them self-consciously dressed in the garb of school-logic. But in Apelles’ case the arguments were critical rather than exegetical: his syllogisms did not formalize the reasoning of the Prophets; they deduced absurd consequences from the Old Testament. (There was, for example, a detailed criticism of the story of Noah’s ark: if we take the scriptural [412] dimensions seriously, the ark could hardly have accommodated four elephants, let alone animals of every 28 See Scho¨ne, ‘Einbruch der Logik’, pp.257–258 (‘ ... they investigate whether as a conditional or a disjunctive it can make a syllogistic figure’). 29 See, e.g., Galen, inst log xv 9–10, xviii 2–3; Alcinous, didask vi [158–159]); cf D.J. O’Meara, Pythagoras Revived (Oxford, 1989), pp.41–42. 30 For Alexander and Apelles, see above, n.15.

Galen, Christians, logic

15

species. The Catholics replied that cubits were longer in Noah’s day.) And at the end of each syllogism, according to Origen, ‘he adds the words: ‘‘The story is therefore false; the scripture therefore does not come from God’’ ’ (hom in Gen 28.14).31 Apelles and the Theodotians had different aims; but their writings must have had a similar style. The case of the fourth-century heretics is in some respects rather different. A scrutiny of the surviving fragments of Eunomius will reveal no remark about logic. What is more, it will scarcely reveal an argument. Ae¨tius’ pamphlet at first blush makes a similar impression: it consists of a dozen and a half brief remarks on the unbegotten God. Here is a typical example: If the unbegotten nature is cause of the generated nature, and the unbegotten were nothing, how could nothing be cause of the generated? (Epiphanius, pan III 357)*

Now that is not a syllogism, even in the loosest of senses; it is not even an argument — it is a question, a conditional question.32 Was Epiphanius muddled when he accused Ae¨tius’ pamphlet of being a nest of logical vipers (pan III 351)? Well, Ae¨tius alleges that an early version of the work had been put abroad by his enemies in a corrupted form: they ‘ruined it with interpolations and excisions and altered the run of the implications’ (ibid, 352). He therefore prepared a revised version in which, he says, I have distinguished question from question and solution from solution in the form of verses so that the arguments may be easy to grasp and clear. (ibid)

There is indeed a run of implications, or of conditional sentences; and they are questions. But where are the solutions, and where the arguments? Those are obtuse interrogations. Ae¨tius’ questions are rhetorical questions — they are conditional assertions in interrogative form. And the conditional assertions are abridged or condensed arguments — the text I have quoted is to be reconstrued as an argument to the conclusion that the unbegotten nature is not nothing. Nonetheless, there are no explicit syllogisms in Ae¨tius’ pamphlet, and to that extent he is unlike Apelles and unlike the Theodotians. And yet all these 31 KØçæØ e łıc ¼æÆ › FŁ 
PŒ ¼æÆ KŒ Ł F ªæÆç. — I take the reference from von Harnack, Marcion, p.413*. * N B ª

Å Iª

Å  çØ Kd
ÆNÆ, e b Iª

Å
Åb
YÅ, H i
YÅ ÆYØ
e Åb
 F ªª
 ; 32 For Ae¨tius and Eunomius, see above, n.16 and n.17.

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heretics do have something in common — a certain address and style. It is a dry and abstract style, in which propositions are set down with no attention to [413] literary elegance; it is a spare and abrupt style, in which nothing is decked in rhetorical frippery; it is a pedantic style, in which everything pertinent to the argument and nothing superfluous is laid out as precisely and as plainly as possible. In short, it is a logical style — a style adopted in antiquity by the Stoic masters and affected today by certain logically minded philosophers.33 I think that it was this common style, as much as anything of a more strictly logical nature, which roused the ire of the orthodox. Arnobius urges us to do without syllogisms and the like ornaments; Lactantius links a rejection of logic with a recommendation of unadorned speech; Gregory contrasts ‘syllogisms and enthymemes’ with the plain language of fishermen.34 Again, Jerome observes of the apostles that the grandeur of their saintliness excused their simplicity of speech, while the Dead Man, resurrected, confuted the syllogisms of Aristotle and the twists and spikes of Chrysippus. (ep lvii 12)

According to Theodoretus, it would have been easy for the Source of all wisdom to make his heralds ‘more sweet-tongued than Plato, more clever than Demosthenes’, and to have them ‘surpass Thucydides in weight and Aristotle and Chrysippus in the insoluble binding of their syllogisms’ (cur VIII 2). Isidore of Pelusium remarks that the clever Greeks ‘preen themselves for their style and pride themselves on their logic’ (ep IV 27). Arnobius and his fellows want to defend plain speaking and to warn against the wiles of clever Greeks. Those wiles include cunning ratiocinations as well as mellifluous periods. Conversely, the praise of plain speaking recommends not only humdrum prose but also informal argumentation. It is not the use of argument which the enemies of logic deplored: it is the display of syllogistical technology; it is the logical style of writing. Better imitate the Persians, who are an ‘extremely syllogistic’ people — not because they have read the mazes of Chrysippus and of Aristotle, nor because Socrates and Plato have educated them in this area; for they have not been fed on

33 Grant, Heresy and Criticism, pp.80–81, well compares Apelles’ argument in Ambrose, parad vi 30 with Gellius, II vii (probably of Stoic origin). On the Stoic style, see M. Schofield, ‘The syllogisms of Zeno of Citium’, Phronesis 28, 1983, pp.31–58; Barnes, Logic, pp.12–23. 34 See the texts cited above, p.[405].

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rhetorical and philosophical arguments — their only teacher is nature. (Theodoretus, cur V 72)

John Locke would have nodded his accord. The attitude is intelligible enough. The logical style is meretricious, at once attractive and repugnant: its rapid patter seduces — and yet fails to [414] persuade; it leaves the mind stunned and the heart untouched. Many pagans disliked it for such reasons; and the Christians had a further motive: their Christian message was to be delivered to the masses, for whom such clevernesses are either dangerous or disgusting.

VI And yet the Christian attitude was humbug. There were no more selfconscious stylists than those Christian writers who most affected to scorn style; there were no more pedantic quibblers than those Christians who objected to heretical logic-chopping. Tertullian, for example, ‘attacked dialectic with a tenacious hatred — yet, as we know, he used it himself from the first line of his writings to the last. In the whole history of the early Church there is no more determined dialectician’.35 Or again, there is a close parallel to Ae¨tius’ Syntagmation in the ‘Proofs by way of syllogisms’, a short pamphlet ascribed to Theodoretus: the text consists of forty arguments, in the style of Ae¨tius, which purport to offer formal proofs of the points for which Theodoretus had argued conversationally in his Eranistes.36 Theodoretus sailed close to the wind of heresy; but this pamphlet, for all its technical form and its dialectical structure, is thoroughly Catholic. Gregory of Nyssa lambasts logic — he also lauds his brother Basil for ‘offering profane culture as a gift to the Church of God’, and the gift is expressly said to include ‘the discipline of logic’ (vit Mos ii 115). Gregory of Nazianzus scorns logic — he also says admiringly of Basil that he was supreme in rhetoric, in grammar, and in that philosophy which is really sublime and ascends on high — the practical and the theoretical and also that which concerns logical proofs and antitheses and tricks, 35 A. Labhardt, ‘Tertullien et la philosophie, ou la recherche d’une ‘position pure’’, Museum Helveticum 7, 1950, 159–180, on p.168. 36 See G.H. Ettlinger (ed), Theodoret of Cyrus: Eranistes (Oxford, 1975) — the syllogisms are printed on pp.254–265.

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so that it was easier to escape from a maze than to evade the toils of his arguments, should that prove necessary. (orat xliii 23)

To be sure, Basil’s writings scarcely suggest such eulogies. Jerome affected to despise logic. Yet he was sharp enough with an upstart young deacon: [415] You say that ... this dialectician, a pillar of your family and of the family of the Plautii, has not even read the Categories of Aristotle, nor his de Interpretatione, nor the Analytics, nor even Cicero’s Topics; but in the circles of the ignorant and at the tea-parties of little women he weaves his unsyllogistic syllogisms and by cunning argumentation unravels my so-called sophisms. ... In vain did I turn the pages of Alexander’s commentaries, in vain did my learned teacher introduce me to logic by way of Porphyry’s Isagoge, ... (ep 50 1)

Sir Have-it-both-ways was a familiar character in the early Church. But humbug and hypocrisy were not universal. Clement argues that the study of logic is indispensable to the intelligent Christian.38 It is childish to fear pagan logic: Most people fear pagan philosophy as children fear the bogeyman — they are afraid it will lead them astray. But if their faith — I will not call it knowledge — is such as to be dissolved by plausibilities, then let it be dissolved. (strom VI x 80.5–81.1)

An intelligent Christian will readily separate rhetoric, which is pernicious, from dialectic, which is useful (ibid I viii 44.2); and he will equally separate the sophistical and eristical use of logic from its honourable employment (ibid I x 47.2). Origen was another such: he mastered logic himself, and in his school — as one of his parting pupils described it — ‘he trained logically that part of the soul which judges concerning phrases and arguments’ (Gregory Thaumaturge, ad Orig vii; cf Eusebius, HE VI xviii 3). Origen flaunted his logical expertise, and his texts show that this was not mere vanity.39 Or consider Augustine, who was described by his enemy Julianus as the Carthaginian Aristotle (see Augustine, c Iul iii 199). He read Aristotle’s Categories when he was twenty, and his youthful studies of the liberal arts 38 See e.g. strom I xxviii 176.3–177.3; VI x 4–81.1. On Clement and logic, see J. Pe´pin, ‘La vraie dialectique selon Clement’, in J. Fontaine and C. Kannengieser (eds), Epektasis: me´langes patristiques offerts au Cardinal Jean Danie´lou (Paris, 1972), pp.375–383. 39 See e.g. H. Chadwick, ‘Origen, Celsus and the Stoa’, Journal of Theological Studies 48, 1947, 34–49.

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included logic: he found the stuff easy, his only puzzle (so he later avowed) being whether it helped him to adore God (conf IV xvi 28–29). However that may be, he acknowledged that ‘I have learned more from dialectic than from any other part of philosophy’ (c Acad III xiii 29); he once set out to write a book on the subject, of which ‘only the beginning has survived — and even that I have [416] lost though I think that some people have a copy’ (retract i 5);40 and he frequently defends the study of logic.41 His enemies exploited this weakness. Petilianus, a heretic of the Donatist variety who detested logic, accused him of being a vile and slippery dialectician (see c litt Petil iii 16); and Cresconius seconded the case (see c Crescon i 13; ii 18). At the end of Augustine’s life, the heretics of the day took an opposite tack, the Pelagians alleging the indispensability of logic for an understanding of the Word of God (e.g. c Iul vi 20). Augustine must have been tempted to change sides and reject logic as the devil’s game — and some scholars have argued that that is just what the old man did.42 But his reply to the Pelagians follows a different line: he does not argue that logic should be left to the infidels — rather, he urges that Julianus is an incompetent logician (c Iul iii 7), who shoots himself in the foot (ibid vi 18). What did these logical Fathers make of Paul and the Greek disease?43 Well, a Scriptural score lets you whistle any tune you like. Clement thinks that Paul is rejecting only rhetoric and sophistic, not logic in its entirety; and Eusebius remarks that Paul ‘rejects deceptive and sophistical plausibilities and employs plain proofs’ (PE I iii 5). Origen affirms that Paul used ‘sound syllogisms, brought to their conclusions by the art of dialectic’ (in Rom VI xiii [PG XIV 1098A]). After all, the Son of Man was the Word, the Logos; Jesus Christ was Reason Incarnate. How could He not have been a logician? And, as Augustine pertinently demands, with what if not logic did Jesus confute the Jews?44 [417] 40 The opening part of On Dialectic, perhaps all that Augustine wrote, has survived — on the question of authenticity, see B.D. Jackson, Augustine: de dialectica, Synthese Historical Library 16 (Dordrecht, 1975), pp.2–5, 26–28, 43–75; J. Pe´pin, Saint Augustin et la dialectique (Villanova PA, 1976), pp.21–60. 41 e.g. ord II xiii 38; solil II xi 19–21; doct Christ II xxxi 48–xxxvi 54; c Crescon i.14–16; c Iul 6. 42 See Pe´pin, Saint Augustin, pp.243–255. The texts which Pe´pin adduces are at best guarded. The clearest is this: Julian tries to teach dialectic, non cogitans quomodo abiciat Christi ecclesia dialecticum quem censet haereticum (op imperf iii 31). Pe´pin takes that to mean that the Church rejects dialecticians, whom it takes to be heretical; but I think that Augustine rather means that the Church rejects any dialectician whom it takes to be heretical. In written English, a comma makes all the difference; in Latin, the phrase is ambiguous, but the context favours the latter interpretation. 43 See the texts cited above, p.[405]. 44 See c Crescon I xvii 21–xviii 22, referring to Mt xxii 21.

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VII Galen was wrong about the Christians — like most pagans who troubled to notice them. They did not reject proof and argument. Carried away by the sacred duty to refute pagans and heretics, carried along to the rhetorical beat of divine inspiration, carried aloft far above the worldly virtue of selfconsistency, they sometimes sneered or snarled at logic. But they could not, and they did not, abjure ratiocination. On the contrary, they literally worshipped Reason. Christians and logic fit snugly together. And Galen? Did the Christians learn their logic from Galen, the third logician of antiquity after Aristotle and Chrysippus? It would be agreeable to think that they were particularly charmed by his ‘third class of syllogism’. After all, the logic of relations is of apparent pertinence to many of the theological controversies which divided the early Church. The concepts of Father and of Son are relational concepts; the concept of identity, which underlay the long and lacerating dispute over the doctrine of the Trinity, is a relational concept par excellence. Now identity, paternity, and sonship are each noticed in Galen’s discussion of relational syllogisms (inst log xvi). Admittedly, in all the vast patristic library, only one short text associates Christians with Galen the logician. Moreover, the Christians in question are a small and insignificant group of heretics; and the text gives no reason to think that they were especially interested in Galen’s logic of relations. But such reticence is unremarkable. Christians took their logic from the pagan authorities — whence else? Origen had read Chrysippus, Jerome says that he had read Aristotle; but in general, the Christians, like their pagan contemporaries, did not imbibe their logic from those original and distant sources — they drank in derivative streams, their logic came from manuals and handbooks. They do not say so; still less do they name the authors of such little works — whoever would expect them to do so? One of the few such manuals to survive from antiquity is Galen’s Introduction to Logic. No ancient author — not even Galen himself — ever refers to the Introduction. But it would be an error to infer that the work dropped still-born from the press: for all we know, the thing was sometimes used; for all we know, the thing was sometimes used in Christian schools.

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But let me not end on a note of speculative optimism. No surviving text from antiquity, Galen’s Introduction to Logic apart, ever refers to a logic of relations. Whatever may have been the fortune of the Introduction and of his other logical works, his great logical invention was neither admired nor copied.

2 Cicero on logic* I consider first the conception of logic which Cicero manifests in his Academic books; then I look at the attack on logic which he delivers in the Lucullus. I use the English word ‘logic’ as a rough translation of the Latin ‘dialectica ’ and the Greek ‘ØƺŒØŒ . I am interested in the views which Cicero expresses: I do not discuss the sources of those views or the extent to which they are original to Cicero; nor do I offer any opinion as to whether Cicero himself accepted all or any of the views he expressed.

I ˜ØƺŒØŒ was standardly conceived of as a part of º ªØŒ, the other part being rhetoric. ¸ ªØŒ was itself one of the three parts into which philosophy was standardly divided. The tripartition was the site of two famous battles: a battle over the proper ordering of the three parts; and a battle over the status of º ªØŒ — is it really a part of philosophy or should it rather be regarded as a philosophical tool or instrument? At Acad v 19 Cicero introduces the ‘threefold account of philosophizing’,1 which he ascribes to Plato.2 The parts are listed in an unusual order: ethics, physics, º ªØŒ.3 Cicero thus implicitly takes sides in the first battle.4 By listing º ªØŒ as a part of philosophy, he also implicitly takes sides in the second battle — which was neither a trivial skirmish nor irrelevant to sceptical concerns. But Cicero gives no hint that he knows of any fighting, * First published in B. Inwood and J. Mansfeld (eds), Assent and Argument: studies in Cicero’s Academic Books, Philosophia Antiqua 76 (Leiden, 1997), pp.140–160. 1 philosophandi ratio triplex : ‘ratio ’ presumably represents ‘º ª ’; but it would be an error to detect a subtle distinction between a division of the º ª  of philosophy and a division of philosophy herself — a little later, at Acad viii 30, Cicero writes ‘tertia ... philosophiae pars ’. 2 See e.g. Diogenes Laertius III 56; cf Sextus, M VII l6. 3 The ordering is marked, if not stressed: note primum (Acad v 19), sequebatur (vi 22), tertia (viii 30). The same order in e.g. Eudorus, apud Stobaeus, ecl II vii 2 [42.11–13]; Seneca, ep xcix 9; Augustine, CD VIII 4. 4 But in the Lucullus we get, without comment, the order: physics, ethics, º ªØŒ (xxxvi 114).

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nor does he indicate [141] that there is anything controversial about the thoughts he expresses. Perhaps the second battle had not been joined when Cicero wrote? ‘˜ØƺŒØŒ’ was Latinized as ‘dialectica ’;5 but neither in Cicero nor elsewhere in classical Latin do we find the word ‘logica ’. At fat i 1 Cicero offers ‘ratio disserendi ’ as a translation of ‘º ªØŒ ’;6 and at Acad v 19 he characterizes the third part of philosophy as being de disserendo.7 The characterization is surprising. For ‘disserere ’ usually represents the Greek ‘ØƺªŁÆØ’, so that ‘ratio disserendi ’ ought to refer to ØƺŒØŒ rather than to º ªØŒ as a whole.8 There are other indications that Cicero was sometimes inclined to assimilate º ªØŒ to ØƺŒØŒ. Thus at Luc xxxvi 114, in a brief account of the three parts of philosophy, he describes º ªØŒ by the phrase ‘disputandi et intellegendi iudicium ... et artificium ’. No smell of rhetoric here. Again, the discussion of the third part of philosophy at Luc xlvi 142–xlvii 146 does not mention rhetoric; and it is introduced by the words ‘iudicia ista dialecticae’, which suggest that dialectica, or logic (as I am calling it), constitutes on its own the third part of philosophy.9 It is tempting to suppose that Cicero, for good Ciceronian reasons, was unwilling to regard rhetoric as a part — let alone a subpart — of philosophy;10 and we might infer that Cicero’s characterization of º ªØŒ was deliberately done with the intention of intimating a theoretical stance of his own. But if that was his intention, he did not stick by it. Outside the Academic writings, º ªØŒ is characterized by the formula ‘vis loquendi ’ and divided into logic and rhetoric.11 And at Acad ii 4–7 the rude description of the ideas of the Latin Epicureans is [142] divided into three 5 See below, pp.[143–144]. 6 cf fin IV iv 8. 7 See e.g. Acad viii 30; Luc vii 21; fin I vii 22. 8 For ‘disserere’ used to characterize dialectica, see e.g. Brutus xxxi 120; leg I xxiv 62; top ii 6, fin IV iv 10. But note also e.g. de orat II xxxviii157 (where ‘disserere’ characterizes a subpart of logic); orat xxxii 113 (where ‘dicere ’ marks off rhetoric, ‘loqui ’ logic, and ‘disserere ’ is used generically to cover º ªØŒ as a whole — as also at de orat I xv 68). At the beginning of the de Interpretatione Apuleius (?) characterizes º ªØŒ as the pars rationalis of philosophy qua continetur ars disserendi (i [189.3–4]): ‘in which is contained the art of disserere [¼ dialectica]’ or ‘which is constituted by the art of disserere [¼ º ªØŒ]’? The phrase is ambiguous: the context perhaps favours the second interpretation. — In his specimen translation of Plato, symp 180E, Aulus Gellius turns ‘ØƺªŁÆØ’ by ‘disserere ’. 9 cf Tusc V xxv 72. 10 But note div II i 4, where Cicero — claiming the precedent of Aristotle and Theophrastus — urges that (some of) his rhetorical works be counted as part of his philosophical œuvre. 11 fin II vi 17; cf orat xxxii 113–114.

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parts, a correspondence with the three parts of philosophy being evident if not explicitly marked. Of º ªØŒ Cicero there says that ‘they think there is no art either of speaking or of reasoning [nullam ... artem esse nec dicendi nec disserendi putant]’ (ii 5): ‘dicendi ’ refers to rhetoric, ‘disserendi ’ to logic; the two together constitute º ªØŒ; and so here, at least, º ªØŒ is not reduced to logic. Moreover, the characterization of º ªØŒ at Acad v 19 reads in full like this: ... and the third about reasoning and judging what is true and what false, what is correct in speech and what incorrect, what is in agreement and what in conflict.12

I suppose that the ‘and’ after ‘reasoning’ is epexegetic, so that the content of º ªØŒ is given generically by ‘reasoning’ or ‘disserendo’ and specified by the three conjoined clauses after the ‘and’. The first conjunct, ‘quid verum quid falsum ’, must allude to the account of the criterion of truth. Perhaps it also covers other items — preconceptions, signs, proofs? If so, then it corresponds roughly to epistemology. The third conjunct, ‘quid consentiens quid repugnet ’, represents the Greek words ‘IŒ º ıŁÆ’ and ‘åÅ’, which refer to the logical relations of implication and exclusion, and which together frequently serve to indicate the content of logic.13 The second conjunct, ‘quid rectum in oratione pravumque ’, is more puzzling; and I find no close or helpful parallels. With little conviction, I incline to the orthodox view that the phrase is intended to characterize rhetoric. At Acad v 19, then, º ªØŒ is itself tripartite. It consists of (A) epistemology, (B) rhetoric, and (C) logic.14 Ancient texts offer us various divisions of º ªØŒ. There is no precise parallel to the division implicit in our passage. Acad viii 30–33 offers an outline of the Old Academic teachings on º ªØŒ. (The account is explicitly ascribed to the Peripatetics as well as to the early Academy.15) It begins with (1) the criterion of truth, iudicium veritatis. There then follows a reference to (2) definitions — definitiones rerum. After that, (3) etymology or verborum explicatio. [143] Next, (4) proofs

12 ... tertia de disserendo et quid verum quid falsum quid rectum in oratione pravumque quid consentiens quid repugnet iudicando. — The (minor) textual problems in the last phrase concern the Latinity, not the content, of the remark. 13 See also Luc vii 22; leg I xxiv 62 (where ‘ratio disserendi ’ is glossed by the phrase ‘veri et falsi iudicandi scientia et ars quaedam intellegendi quid quamque rem sequatur et quid sit cuique contrarium ’). 14 And so ‘disserere ’ must have a generic sense here, as at orat xxxii 113 (above, n.8). 15 See ‘ab utrisque ’ at Acad viii 30 (with vi 22); and also Acad viii 33.

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and signs (argumenta and notae). ‘In which is handed down (5) the whole discipline of logic’. To which is adjoined (6) rhetoric. Item (6) corresponds to item (B) of Acad v 19. Item (1) is included in item (A). The sentence which gives item (2) starts with the phrase ‘qua de causa ’, so that we may reasonably place (2) within (A). Item (3) is introduced by the particle ‘etiam ’; and this perhaps suggests that (3) may also be placed in (A). Item (4) — arguments and signs — is prefixed by the neutral word ‘post ’. And then comes item (5) and the sentence which refers to logic. The received text is this: in qua tradebatur omnis dialecticae disciplina id est orationis ratione conclusae.

The feminine ‘qua ’ is not easy to understand, and ‘quo ’ was long ago proposed (by Manutius); but ‘qua ’ or ‘quo ’, the relative pronoun seems to refer to the content of the preceding sentence — that is to say, Cicero seems to report that the whole of logic was somehow handed down in the context of a discussion of proofs and signs. In that case item (C) of Acad v 19 includes (4), arguments and signs, and also (5), the whole of logic. That is not particularly satisfactory; for it is not evident that proofs and signs should be thus separated from the epistemological issues of (1)–(3), and it is far from evident that the whole of logic is involved in the account of signs and proofs. (The discussion of paradoxes and sophisms was certainly a part of logic: it has nothing to do with proofs and signs.) Hence it is tempting to detach the sentence about logic from its predecessor: either ‘in qua ’ means, vaguely, ‘in this area’ and does not refer explicitly to what has just preceded, or else we should emend the text to ‘denique ’ (with Mu¨ller) or something similar. Then item (4) can be linked with items (1)–(3) and included in (A). Thus item (A) will be given a detailed analysis at Acad viii 30–33 (as we should expect, in the context), while items (B) and (C) have merely a phrase apiece. But perhaps that is too scholastic? After all, it is not evident that Acad v 19 offers a formal tripartition, or that the items at viii 30–32 must be distributed among its three parts. Perhaps v 19 offers a brief characterization of the contents of º ªØŒ while viii 30–32 offers a more extended characterization, stressing those aspects of the subject which are of most concern to the Academica. However that may be, what of the content of logic itself ? Cicero’s word for logic is ‘dialectica ’. He followed the prudent policy of accepting transliterations of Greek words when (and only [144] when) they were already established in Latin. Thus he says — he has Varro say —

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I shall try to speak in Latin — except in the case of words such as ‘philosophia ’ or ‘rhetorica ’ or ‘physica ’ or ‘dialectica ’ which, like so many others, custom has already treated as Latin. (Acad vii 25)*

In fact, ‘dialectica ’ is attested for Varro himself (Isidore, II xxiii 1) — but it would be rash to infer that Varro had domesticated it and that Cicero is paying him a subtle compliment.16 What objects does the word designate? At Acad viii 32 Cicero writes ‘ ... omnis dialecticae disciplina, id est orationis ratione conclusae ’. He thus apparently identifies logic with the theory of inference. At Luc xxviii 91 he remarks that ‘you say that logic was discovered as a sort of arbiter and judge of the true and the false’, thus apparently limiting the scope of logic to a study of the criterion of truth.17 But the apparent identification in Acad need not be taken seriously, and the apparent limitation in Luc is denied in the sentences which follow: Then what will logic judge? — It will judge which implications and disjunctions are true,18 what remarks are ambiguous, what follows what and what conflicts with what. ... The art at first progressed happily enough and explained the parts of speech,19 the understanding of ambiguities, the theory of inference; and then, a little later, it arrived at the sorites. ... (Luc xxviii 91–92)**

The initial characterization at Luc xxviii 91 was misleading. At Acad ii 5 it is said of the Epicureans that ‘they define nothing, divide nothing, infer nothing by appropriate argument’.20 Hence, by implication, logic covers definition, division and inference. Varro continues by observing that [145] * enitar ut Latine loquar nisi in huiusce modi verbis ut philosophiam aut rhetoricam aut physicam aut dialecticam appellem quibus ut aliis multis consuetudo iam utitur pro Latinis. 16 ‘philosophia ’ is found in Cassius Hermina; neither ‘physica ’ nor ‘rhetorica ’ happens to appear in a pre-Ciceronian text — but the adjectives ‘physicus ’ and ‘rhetoricus ’ are found in Lucilius and Ennius. 17 And therefore including item (A) of Acad v 19 under the rubric of logic — something which is also done at de orat II xxxviii 158. 18 See Luc xlvii 143, where the dialecticians are said to teach in elementis ‘how we should judge whether something connected in the fashion of ‘If it is day, it is light’ is true or false’. 19 elementa loquendi: this has nothing to do with rhetoric. ** quid igitur iudicabit? quae coniunctio quae disiunctio vera sit, quid ambigue dictum sit, quid sequatur quamque rem quid repugnet ... primo progressa festive tradit elementa loquendi et ambiguorum intelligentiam concludendique rationem, tum paucis additis venit ad soritas ... 20 nihil definiunt, nihil partiuntur, nihil apta interrogatione concludunt : I am not sure what ‘aptus ’ means in this context, but the phrase should not be confounded with ‘argumenti conclusio ’ at Luc viii 26, which Cicero uses to represent ‘I ØØ’ (cf xiv 44): not all inferences are proofs; and if logic studies inference as such, it is not clear (see above) that it also studies proof.

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we, on the other hand, observe the precepts of the logicians and the orators as though they were laws, since our people take each of these capacities to be a virtue. (Acad ii 5)

‘Our people’ are the Old Academics, to whom Varro ascribes the standard Stoic view that rhetoric and logic are virtues. The contrast between nostri and the Epicureans might suggest that, according to Varro, the Epicureans do not use logic — or even that they flout the precepts of the logicians. But I doubt if the accusation need be read into the text. However that may be, it seems that logic will start from a treatment of sentential connectives; that it will include a study of forms of inference; and that it will end in an examination of the logical paradoxes. Along the way it will deal with the parts of speech and ambiguity and definition and division.21 There is little remarkable about all that. But two features, from which an interesting conclusion might be inferred, are worth noting. First, logic in Cicero is essentially Stoic logic. Or rather, and more specifically, Ciceronian logic contains nothing which is peculiar to Aristotle (or, come to that, to Plato). I incline to believe that Cicero knew nothing about Aristotelian logic save what he had learned from the rhetorical tradition: he knew something about ‘topics’, nothing about syllogistic. But in any event, Acad and Luc betray no interest in or acquaintance with Peripatetic theories.22 Secondly, Cicero ascribes — or has Varro ascribe — all this logic to Plato. At Acad viii 33, immediately after his description of º ªØŒ has rounded off the discussion of the ratio triplex, he observes that ‘this was the original form of these things, handed down by Plato’. And when Varro turns to catalogue the changes which Zeno later introduced into the Old Academic philosophy, the only items he mentions under the third part of the subject concern the criterion of truth (Acad xi 40–42). The logic which Cicero depicts in the Academic writings appears to be presented as the doctrine of Plato himself. Thus Cicero describes Stoic logic, and he attributes what he describes to Plato. Hence — and this is the interesting conclusion I mentioned a moment ago — Cicero attributes Stoic logic to Plato.23 [146]

21 cf e.g. orat iv 16; xxxii 115; fin IV iv 8–9; part orat xl 139. 22 Recall the remarkable ascription of ignorantia dialecticae to the Peripatetics: fin III xii 41. 23 cf, with qualifications, fin IV iv 8–9.

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Of course, he does not do so explicitly. Of course, some of the lost parts of the Academic writings may have contained a modification — or even a rejection — of the attribution. But as matters stand Cicero gives us to suppose that Plato had anticipated Chrysippus. Did Cicero intend to give that impression, or is it a carelessness? I suppose that it was intentional. I suppose that Cicero — shall I for once mention Antiochus? — is intimating the sort of view which is familiar from later texts (from Atticus and Alcinous and others). According to this view, Plato invented the whole of philosophy: everything which later developed is to be found, at any rate in the seed or in the bud, in Plato’s writings. In particular, Stoic logic is to be found there.24 The view is, of course, either grossly muddled or else flatly false.

II The main assault on logic is made at Luc xxviii 91–xxx 98. First, Cicero plays down the importance of logic (91); then he adduces the paradox of the sorites, which supposedly demonstrates the debility of logic (92–94); and finally he considers the foundation of logic and the thesis that every statement — or rather, every ‘assertible’ — is either true or false (95–98). (But the articulation of 92–98 is not particularly clear.)

II. 1: Luc xxviii 91 The argument, which is modelled on a passage in the Gorgias,25 characterizes logic as ‘arbiter and judge of the true and the false’ — and proceeds to ask in what area logic can adjudicate. Not in geometry; nor in general in any of the special sciences. Nor even in physics and ethics. What is left? Only logic itself. Thus ‘it judges about itself.26 But it promised more’. The argument hardly deserves detailed scrutiny. Evidently, Cicero is right to reject the claim that logic is ‘arbiter and judge of the true and the false’ — if the claim means that logical expertise is [147] sufficient (and necessary) to 24 Aristotelian syllogistic too, and the theory of categories, according to later authors. 25 Note also div II iii 9–iv 12 (from Carneades). 26 According to Epictetus, the fact that logic can judge itself marks it out as the supreme 
ÆØ: diss I i 1–6.

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determine the answer to any factual question.27 Evidently, Cicero is wrong to conclude that the only area in which logical expertise has a utility is the study of logic itself.

II.2: Luc xxviii 92–xxix 94 The passage introduces the sorites28 — in soritical fashion. ‘Dialectic begins happily enough [primo progressa festive]’; and then, paucis additis, it reaches the sorites, ‘a slippery and dangerous area’. You start logic with the elements, which seem perfectly innocuous.29 You proceed by small and innocuous steps; and you end with the ¼ æÆ, and in particular with the sorites, where everything goes to pieces. The argument could be presented in formal soritical garb; and perhaps it was once so presented. I shall not here examine the content of the passage. Rather, I ask what the paragraphs purport to show. Cicero begins with a grave warning: ‘Since you place such weight on the art of logic, take care that it has not been born wholly to confute you’ (92). He ends with the following conclusion: ‘this art of yours does not give you any help against the sorites’ (94). The former sentence presumably alludes to the fact that the sceptical opponents of the Stoa used soritical arguments against central Stoic doctrines: the Stoics develop an art which is then used to destroy them. The latter sentence remarks, truly enough, that the art of logic has not yet resolved the paradox of the sorites. Those points are serious enough; but we might have expected something a little more startling. In particular, we might have expected that soritical predicates would have been used to throw doubt on ‘the foundation of logic, namely the thesis that whatever is asserted ... is either true or false’.30 In uttering sentences of the form ‘x is bald’ or ‘x is a heap of sand’, we can always, or so it seems, assert something; and yet in some cases it is at least tempting to imagine that what we assert is neither true nor false. (I assert that deepbrowed Homer is bald; but he still has a few tufts of greying hair on his head, and it is neither (‘really’) true [148] nor (‘really’) false that he is bald.) Again, 27 But surely no logician ever made so absurd a claim? 28 See also Luc xvi 49; xlviii 147. — On the sorites, see J. Barnes, ‘Medicine, experience and logic’, in J. Barnes, J. Brunschwig, M.F. Burnyeat, and M. Schofield (eds), Science and Speculation (Cambridge, 1982), pp.24–68 [reprinted below, pp.538–581]. 29 Of course, they are not as innocuous as they seem, being rent with discord: Luc xlvi 143. 30 Luc xxix 95: below, pp.[148–155].

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soritical paradoxes are readily represented as a sequence of modus ponens arguments. (‘One grain of sand is not a heap. If one grain is not a heap, then two grains are not a heap. Therefore two grains are not a heap. If two grains are not a heap, then three grains are not a heap. Therefore three grains are not a heap ... ’) And the sorites might thus be used to cast doubt on the acceptability of modus ponens, which is surely a ‘fundamental’ form of reasoning and which was the first of the five Stoic unproved syllogisms or ‘indemonstrables’. In such ways the sorites might indeed seem to unseat the whole of logic; for soritical arguments threaten to show that a fundamental thesis of logic is untenable and that a fundamental argument form is unacceptable. Now precisely those two threats are raised in Luc xxix 95–xxx 98, so that it is tempting to think that our text does not divide at 95 and that the sorites determines the course of the argument up to 98. But no sorites is mentioned in sections 95–98; and I am unable to construct a continuous and coherent train of thought which starts in 92 and ends in 98. I conclude, lamely, that Cicero has not made of the sorites all that he might have done.

II.3: Luc xxix 95 ‘This same art of yours, as though it were weaving Penelope’s cloth, ends by destroying its first parts’. The simile may not be pressed too hard; but the strategy it implies is clear enough (and identical with the strategy in Luc xxix 92–94).31 The art begins with certain elements, here characterized as the foundation (‘fundamentum ’) of logic, and it ends with a problem or paradox which shows that the foundation is unsound. It is surely the foundation of logic that whatever is asserted (they call such things IØÆÆ — which are as it were assertions) is either true or false. (Luc xxix 95)*

[149] An IøÆ is a complete ºŒ
of a particular type: it is a ºŒ
such that, if you say it, you may thereby assert something. (I shall use the unlovely

31 There is a close parallel at de orat II xxxviii 158 (weaving and unweaving — but no Penelope); cf the simile at Hort frag 25 Grilli (apud Nonius, p.81 M). * nempe fundamentum dialecticae est quidquid enuntietur (id autem appellant IøÆ quod est quasi ecfatum) aut verum esse aut falsum. — cf Tusc I vii 14: quasi non necesse sit quidquid isto modo pronunties, id aut aut esse aut non esse. an tu dialecticis ne imbutus quidem es? in primis enim hoc traditur: ... id est pronuntiatum quod est verum aut falsum.

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term ‘assertible’ to English ‘IøÆ’.33) In the thesis that every IøÆ or assertible is either true or false, the disjunction is exclusive: if ‘Either A or B’ is true, then exactly one of ‘A’ and ‘B’ is true. Thus the fundamental thesis of logic might initially be expressed in the following way: If it is possible to assert that P, then either it is true (and not also false) that P or it is false (and not also true) that P. Numerous texts ascribe that thesis to the (Stoic) logicians.34 It is worth remarking that the thesis seems, at first blush, to lie open to various sorts of counterexample. Thus, as I have already noticed, vague predicates appear to generate plausible counterexamples. (For if I assert that Homer is bald or that France is hexagonal, what I assert is perhaps not either true or false.) Certain types of assertion about the future have sometimes been held to be neither true nor false. (I assert that England will lose the Test series; but what I assert is not — ‘not yet’ — either true or false.) Assertions on moral or aesthetical matters have often been denied a truth value. (I assert that Strauss, R., is a more subtle composer than Wagner, R., — but is that either true or false?) And so on.35 Some at least of these apparent counterexamples were familiar to ancient philosophers; and it is therefore improbable that the logicians presented their fundamental thesis as a self-evident truth. Cicero refers to the thesis as a definition: ‘what becomes of that definition of yours, according to which an assertion is what is either true or false?’ (Luc xxx 95).36 That has caused some clucking in the hen-run. It has been observed that the thesis is not usually presented as a definition: an IøÆ is defined as a ºŒ
saying which we may assert something; and the thesis purports to offer additional information about the nature of IØÆÆ. Worse, if the thesis is presented as a definition, then it must, [150] trivially,

33 There is no good English translation — just as there was no good Latin translation — for ‘IøÆ’: the original version of this piece used ‘statement’; but a statement, or an assertion, is either an act of stating, or of asserting, or something which is stated, or asserted; and IØÆÆ are neither acts of asserting nor things (actually) asserted. 34 e.g. Cicero, fat ix 20 (ascribing the thesis to Chrysippus); Gellius, XVI viii 8; [Plutarch], fat 574F. 35 The putative counterexamples all suggest cases in which an assertion is neither true nor false. It is less easy to find counterexamples offering assertions which apparently are both true and false. (Is it raining? — Well, yes and no.) 36 cf Tusc I vii 14, above p. [418] n.*.

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be true. Cicero misrepresents the fundamental thesis, and in doing so he shoots himself in the foot. But that is a misunderstanding. Of course, the thesis is not a definition in the standard modern sense of the word ‘definition’; that is to say, it does not analyse the meaning of the word ‘IøÆ’. (It is neither a stipulative definition, announcing how the word will henceforth be used, nor a descriptive definition, reporting how the word in fact is used.) But the thesis may for all that be a definitio;37 that is to say, it may define or determine the boundaries of the concept. In effect, the word ‘definitio ’ indicates that the fundamental thesis is an equivalence rather than a one-way conditional; and it should be written in the following form: It is possible to assert that P if and only if either it is true (and not also false) that P or else it is false (and not also true) that P.38 No misrepresentation by Cicero, and no self-mutilation. According to Cicero, ‘Chrysippus strains every nerve to persuade us that every IøÆ is either true or false’; and he does so because he fears that if he is not granted that everything which is asserted is either true or false, then he will not be able to maintain that everything occurs by fate and from the eternal causes of future items. (fat x 21)*

Cicero claims to give Chrysippus’ motive for upholding the fundamental thesis; but there is no reason to think that the same motive pushed every logician who accepted the thesis; and in any event the motive does not supply us with an argument for the thesis. As far as I am aware, none of the nerve-straining arguments of Chrysippus has survived. Indeed, I know of only one ancient argument for the thesis.** It is given by Cicero (who does not ascribe it to Chrysippus): If something which is asserted is neither true nor false, then certainly it is not true; but how can what is not true fail to be false, and what is not false fail to be true? (fat xvi 38)*** 37 A ‘real definition’ if you like: cf ‘definitiones rerum ’, Acad viii 32. 38 But I suppose that Chrysippus was concerned only to defend the left–right half of the equivalence. Indeed, it is hard to imagine why anyone should want to defend the right–left half. * metuit ne si non obtinuerit omne quod enuntietur aut verum esse aut falsum, non teneat omnia fato fieri et ex causis aeternis rerum futurarum. ** But see Simplicius, in Cat 406.6–28, discussed by J. Barnes, Truth, etc. (Oxford, 2007), pp. 76–83. *** si ... aliquid in eloquendo nec verum nec falsum est, certe id verum non est; quod autem verum non est, qui potest non falsum esse, aut quod falsum non est qui potest non verum esse?

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The argument is, alas, infantile. Nevertheless, and despite the putative counterexamples, the fundamental thesis must seem plausible; and it is not difficult to dream up arguments in its favour which are constructed from [151] ancient material. For example: if it is possible to assert that P, then it is surely possible to assert that not-P. And hence it is possible to assert that either P or not-P. Now if you can assert that either P or not-P, it is surely true that either P or not-P. But, in general, if it is true that either A or B, then either it is true that A and false that B or else it is false that A and true that B. Hence either it is true that P and false that not-P or it is false that P and true that not-P. Hence either it is true that P or it is false that P.39 In general, if it is possible to assert that P, then we can produce any number of functions, ‘f()’, such that (i) it is true — or false — that f(P), and (ii) if it is true or false that f(P) then it is true or false that P. Such arguments do not prove the fundamental thesis; but they indicate the price which must be paid if the thesis is not accepted. In my example (where ‘f()’ is ‘either  or not-’), the conclusion may be avoided either by maintaining that in some cases it is possible to assert that P even though it is not true that either P or not-P, or by maintaining that ‘Either A or B’ may be true when neither ‘A’ nor ‘B’ is true. And those are not easy things to maintain. The fundamental thesis, in short, is something we might well wish to uphold.40 What, next, of Cicero’s objection to the fundamental thesis? He first produces examples of items which the logicians call inexplicabilia (that is, ¼ æÆ); and he asks: if these items cannot be explained and if no criterion for them can be found such that you can say whether they are true or false, then where is that definition of yours according to which an assertion is that which is either true or false? (Luc xxx 95)*

That seems to miss the mark. The fundamental thesis claims that every assertible is either true or false. Cicero apparently takes that to mean, or to imply, that, for every assertible, we can determine whether it is true or false. But that is not so; and the logicians may, with perfect consistency — indeed, with considerable plausibility — maintain the fundamental thesis while 39 See Luc xxx 97; nd I xxv 70. 40 And it is fundamental — fundamental to the logic of assertions — in the sense that if it is rejected then the rest of logic will have to be revamped. * si ista explicari non possunt nec eorum ullum iudicium invenitur ut respondere possitis verane an falsa sint, ubi est illa definitio, effatum esse id quod aut verum aut falsum sit?

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allowing that, in some cases, they have no idea how to determine whether an assertible is true or false. However that may be, it is plain what Cicero needs: he needs a case in which it is possible to assert that P and yet it is not either true [151] or false that P; he needs a sentence  such that in uttering  you may assert that P even though it is not either true or false that P. I suppose that — despite his words in Luc xxx 95 — Cicero imagined that he had produced some sentences of that sort. The sentences are evidently related to the Liar paradox — or rather, to that family of paradoxes which sports the sobriquet of ‘The Liar’. Now it is easy to produce a sentence related to the family which appears to fit Cicero’s bill. Take the sentence: ‘This assertion is false’. In uttering it I may apparently assert something — namely, that what I am asserting is false; but what I assert is not either true or false.41 But Cicero does not produce this example — nor is it clear what example he does produce. Having stated the fundamental thesis, he continues: ‘Well then — are these items true or false? [quid igitur? haec vera an falsa sunt ?’] The question is rhetorical; that is to say, Cicero suggests that ‘these items’ are not either true or false. The plural intimates that more than one example will follow.42 What, then, are the examples? The received text (there is no interesting variant reading) is this: si te mentiri dicis idque verum dicis mentiris verum dicis. The final two words have no visible connexion to the rest of the sentence; and it is generally supposed that the received text is corrupt: the offending words have been deleted; an ‘et ’ or an ‘an ’ has been inserted in order to tie them to what precedes them; and more audacious remedies have been proposed. Deletion leaves a text which offers a single example, namely the assertible expressed by the sentence: si te mentiri dicis idque verum dicis, mentiris. (That sentence certainly appears a little later on, in an example in Luc xxx 96.) Adding an ‘et ’ we presumably get the single example: si te mentiri dicis idque verum dicis, mentiris verum dicis. 41 If it is true, it is false; and if it is false, it is true. Hence it is either both true and false or neither true nor false. In either case it is not either true or false (where the disjunction is, as always, exclusive). 42 But see e.g. Acad xi 41, where ‘haec ’ (if it is the right reading) must be glossed by ‘talia qualia hoc ’; and in Greek texts a plural demonstrative will not infrequently introduce a single example. Nevertheless, I think that the plural form here at least intimates a plurality.

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The addition of ‘an ’ is said to be supported by a passage in Aulus Gellius.44 It is not quite clear what the resulting text offers — perhaps the single example: [153] te mentiri dicis idque verum dicis.45 None of those reconstructions produces a plurality of examples.46 If we desire a plurality we must resort to more showy methods. One possible textual intervention will yield: si te mentiri dicis idque verum dicis, mentiris verum dicis. Then Cicero gives us a matching pair of examples, namely: (A) si te mentiri dicis idque verum dicis, mentiris, and (B) si te mentiri dicis idque verum dicis, verum dicis. I am far from confident that (A) and (B) are the examples which Cicero actually gave; but I find this reconstruction of the text as plausible as any other, and I hope that it is worth a short run. Then why might (A) and (B) be offered as putative counterexamples to the fundamental thesis? Well, we might imagine the following simple consideration. (A) and (B) cannot both be true, since they draw conflicting consequents from the same antecedent. Yet (A) appears to be true; for in general if you state that P and state truly, then P. And (B) appears to be true; for, in general, if P and Q, then Q. Thus (A) and (B), taken as a pair, are perplexing: on the one hand, each seems to be true; on the other hand, both cannot be true. But that simple consideration is not good enough. Allow that both (A) and (B) are true: what is perplexing about that? In general, if it is not possible that both Q and R, then from ‘If P, then Q’ and ‘If P, then R’ we may infer ‘notP’. In particular, from (A) and (B) we may infer (C) non (te mentiri dicis idque verum dicis). 44 XVIII ii 10: cum mentior et mentiri me dico, mentior an verum dico? — But Gellius is not drawing on our text. 45 That is to say, the text would paraphrase like this: ‘Is the following example true or false? You say that you lie and say so truly — is that true or false? (I wonder if the received text cannot bear the same interpretation, if we punctuate: ‘verum dicis, mentiris? verum dicis? ’.) 46 Unless the second text, which adds ‘et ’, could be construed as offering, in a violent brachylogy, the pair of examples: si te mentiri dicis idque verum dicis, mentiris, and si te mentiri dicis idque verum dicis, verum dicis.

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That is to say, you cannot truly say that you are lying.47 Is that conclusion paradoxical? In a weak sense of ‘paradoxical’, [154] no doubt it is; for we might vaguely imagine, before falling in with the Liar, that it is easy enough to avow your own mendacity. Moreover, a little further reflection seems to lead us to something even more ‘paradoxical’. From (C) we may immediately infer: (D) si te mentiri dicis, non verum dicis. And from (D) we may like to infer: (E) If in uttering sentence  you assert te mentiri, non verum dicis. (Let the macaroni be pardoned.) Now it seems a plausible enough principle that: (P1) If in uttering  you assert that P and non verum dicis, mentiris. Hence in particular: (F) If in uttering  you assert te mentiri and non verum dicis, mentiris. Then from (E) and (F) we might conclude to: (G) If in uttering  you assert te mentiri, mentiris. Take, next, another plausible principle, namely: (P2) If (if in uttering  you assert that P, then P), then (if in uttering  you assert that P, then you assert truly). An instance of the general principle is: (H) If (if in uttering  you assert te mentiri, mentiris), then (if in uttering  you assert te mentiri, verum dicis). From (G) and (H) we reach: (I) If in uttering  you assert te mentiri, verum dicis. Finally, from (E) and (I), (J) It is not the case that in uttering  you assert te mentiri. That is to say, whatever you may care to utter, you cannot thereby say that you are lying. That conclusion may seem seriously paradoxical. After all, it is easy enough to utter the sentence ‘I’m lying’; with such an utterance you plainly seem to be asserting something and what could you be asserting other than that you are lying? Well, you can, of course, utter the sentence ‘I’m lying’; but, if the argument is sound, whatever else you may do in uttering the sentence there is one thing you certainly do not do — you do not thereby assert that you are 47 I follow tradition in using the English verb ‘to lie’ in connexion with the Liar. But the paradoxes concern false-telling, not lying; and ‘mentior ’ (like ‘łŁÆØ’) means ‘to speak falsely’, not ‘to lie’.

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lying. That is perhaps interesting enough to warrant a closer consideration of the argument which I have just sketched. But it is scarcely pertinent to Cicero’s present task; for nowhere in the course of the argument have we yet sniffed the beast for which [155] Cicero is searching — nowhere is there yet any trace of an assertion which is not either true or false. Or has my nose failed me? After all, the complex sentences which express the several parts of the argument all contain as one of their components the sentence ‘mentiris ’ (or its translation into oratio obliqua). Now that sentence has a perfectly non-paradoxical use (as does the firstperson sentence ‘mentior ’); but in the present context we are evidently entitled to look for a paradoxical twist. And we shall quickly imagine someone who utters the sentence ‘mentior ’ with the intention of asserting that he is thereby lying. ‘mentior ’, in other words, is strictly comparable to ‘This assertion is false’. And (A), for example, may be paraphrased roughly as follows: If you say ‘I am hereby saying something false’ and you speak truly, then what you say is false.

Cicero’s examples thus contain potentially troublesome components. Suppose we now introduce the following principle: if f(A) is a complex assertible containing the assertible A as a component, then if A is not either true or false, f(A) is not either true or false. I hope that this principle has — or could be given — some plausibility; for I shall invoke it again in what follows. But I must confess that I have not found it expressed in any ancient text. Nevertheless, given the principle, it will follow that (A) and (B) do, after all, meet Cicero’s needs; or rather, this conclusion will follow if it is the case that the assertible expressed by ‘mentior ’ is not either true or false. It might still be asked why Cicero did not stick to the simplest case: why did he not simply wheel out ‘mentior ’ itself? Well, if you restrict your attention to the simple ‘mentior ’, the Liar paradox may appear to be a small and isolated phenomenon, a phenomenon which does not endanger the whole of logic. But — or so the choice of complex examples may intimate — that is not so. Nothing, you might think, could be plainer than the plain truth of a statement of the form ‘If P and Q, then Q’. But the paradoxes related to the Liar — and in particular, example (B) — seem to show that even that plain truth is perplexing.

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II.4: Luc xxx 96–98 Cicero’s argument does not stop with the rhetorical question at the end of xxx 95. After a connecting sentence, to which I shall return, the discussion follows a relatively clear course. [156] In Luc xxx 96 Cicero adduces two arguments which involve lying premisses, namely: (I) If you say that you lie and say so truly, then you lie. You say that you lie and say so truly. —————————— You lie. And: (II) If you lie, you lie. You lie. ——— You lie. Chrysippus, according to Cicero, must accept both arguments as valid. For he certainly accepts: If you say that it is now light and you say so truly, then it is now light. You say that it is now light and you say so truly. ——————————— It is now light.48 But that argument is pertinently parallel to argument (I) — indeed, it is an instance of what Cicero calls the first mode (primus concludendi modus) or the first unproved. Hence Chrysippus must accept argument (I). Again, he accepts: If it is light, it is light. It is light. ———— It is light. But that argument is pertinently parallel to argument (II) — indeed, ‘the very sense of a conditional [ratio conexi] compels you to concede the consequent once you have conceded the antecedent’. Hence Chrysippus must accept argument (II).

48 The received text is corrupt; but the restoration (Manutius, Davis) is certain.

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That is not quite clean; for each argument is an instance of the ‘first mode’, and each argument may be underwritten by the ratio conexi. Nonetheless, Cicero has a case. Arguments (I) and (II) seem to be formally valid, and they seem to be formally valid in virtue of facts which lie at the heart of Chrysippus’ logic. Yet Chrysippus, it appears, would accept neither argument. Of argument (I) Cicero asks: [157] How can you refuse to accept this argument when you have accepted the earlier argument of the same kind? These are Chrysippus’ examples — and not even he has solved them. (Luc xxx 96)*

Of argument (II) he says: You deny that you can either accept it or reject it. Then how can you accept the earlier argument? (ibid.)**

(Cicero thus appears to make a subtle distinction: Chrysippus rejects argument (I); he neither accepts nor rejects argument (II). But I can see no explanation for such a subtlety, and I suppose that its appearance in the text is unintentional.) Next, in Luc xxx 97, Cicero records the logicians’ last throw: ‘They demand that these inexplicabilia be treated as exceptions’.*** Cicero will not cede the demand. After all, when Epicurus demands an exception to the law of excluded middle, ‘the logicians — I mean Antiochus and the Stoics — ’ will have none of it. Epicurus is represented as suggesting that there are exceptional assertibles of the form ‘Either P or not-P’: assertibles of this form which refer to contingent facts about the future are not either true or false. The logicians reply that he overthrows the whole of logic. For if a disjunction composed of contradictories — I call propositions contradictories when one of them affirms and the other denies — if such a disjunction can be false, then no disjunction is true. (Luc xxx 97)****

Taught by such stern masters — so Cicero concludes in xxx 98 — he will insist that if ‘If it is light, it is light’ is true, then so too is ‘If you lie, you lie’. After all, every assertible of the form ‘If P, then P’ is true. * qui potes hanc non probare cum probaveris eiusdem generis superiorem? haec Chrysippea sunt nec ab ipso quidem dissoluta. ** hoc negas te posse nec adprobare nec inprobare. *** postulant ut excipiantur haec inexplicabilia. **** totam ... evertit dialecticam; nam si e contrariis disiunctio — contraria autem ea dico cum altera ait altera negat — si talis disiunctio false potest esse, nulla vera est.

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By Luc xxx 98 Cicero has returned to assertibles; and although he does not explicitly say so, it is plausible to suppose that he offers si mentiris, mentiris as a further counterexample to the fundamental thesis of the logicians. Is it a counterexample? What is the connexion between the fundamental thesis and arguments (I) and (II)? Why should Chrysippus have felt uneasy about arguments (I) and (II)? Cicero implies that the logicians themselves did not accept that si mentiris, mentiris was true. But he does not explain what difficulty or danger they found in it. I suppose that the principle which I aired a few pages ago lies beneath the text: if we can assign no truth-value to ‘mentiris ’, [158] then we can assign no truth-value to ‘si mentiris, mentiris ’; for if the compound is true or false, then its components must be true or false. The disease which infects the simple ‘mentiris ’ obliges the logicians to reject si mentiris, mentiris, and hence to deny an apparently undeniable truth. They must deny that every assertible of the form ‘If P, then P’ is true; and yet the very sense of the connective ‘if ’ appears to guarantee the truth of every such compound. (All that needs no little refinement; for, as I have already remarked, there are perfectly unproblematical uses of the sentence ‘mentiris ’. But the general line of thought is clear enough: find a problematical Liar sentence , and the conditional ‘If ,  ’ will inherit the problem.) As for the two arguments, Cicero does not explain why Chrysippus could not accept them. But perhaps he did at least explain their pertinence to his theme. The sentence which connects Luc xxx 95 and 96 is transmitted in a corrupt form: rebus sumptis adiungam ex iis sequendas esse alias improbandas quae sint in genere contrario. A common remedy inserts a second ‘alias ’ after the existing ‘alias ’; and translates somewhat as follows: Taking certain premisses, I shall infer from them that certain things are to be accepted, others to be rejected, which things come from contradictory classes.

That is to say, from premisses A1, A2, ... , An Cicero will infer both B1, B2, ... , Bj, and also C1, C2, ... , Ck — where the Bis are to be accepted and the Cis are to be rejected.

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Perhaps he will. But so what? Why should such a thing upset a logician? And what has it got to do with the present context? I cannot find decent answers to these questions; and I can find no honest employment for a text with two aliases. I doubt if Cicero means to make a general remark about the assumption of ‘certain premisses’: surely he means to talk about the consequences of assuming as premisses the problematical examples which he has just given? In fact, argument (I) does take one of the problematical examples as a premiss. Perhaps, then, we should read ‘ rebus sumptis ’ (or ‘ rebus sumptis ’). That would tie the ensuing argument to its context. Given such assumptions, what follows? I guess that Cicero meant [159] to say something along the following lines: ‘Taking these assertibles as premisses, I will infer something which is both to be accepted and to be rejected’. Suppose that, after ‘alias ’, we add not a second ‘alias ’ but the word ‘et ’:49 Taking these items as premisses, I will infer that certain other items50 are both to be accepted and to be rejected — which properties are contradictory.

And we might construe that as a loose statement of the following claim: ‘With the help of (A) and (B) as premisses, I can construct arguments which yield conclusions which must be both accepted and rejected.’51 What, then, is wrong with argument (I)? Well, the conclusion, ‘mentiris ’, follows from the premisses and yet must be both accepted and rejected. It must be accepted because it follows from the premisses. It must be rejected because from the very same premisses we can infer ‘verum dicis ’, which is incompatible with it. At least, that, I suspect, is what Cicero implies is wrong with the argument. But of course (for reasons which I have already given) Cicero’s position here is frail. Indeed, we might think that Cicero’s position is hopeless — after all, why should not Chrysippus accept argument (I)? Why should he not simply say: ‘Argument (I) is indeed valid — it is a straightforward example of the first unproved. But of course it is not and cannot be a sound argument; for its premisses, as we have already seen, cannot be true.’

49 Again, I have no confidence that this suggestion is correct — other scholars have proposed to insert extra clauses into the text. 50 alias : i.e. ‘other than the premisses’. 51 In fact, my text says not quite that but rather this: ‘ ... I will draw a conclusion to the effect that we must accept that P and also reject that P.’

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Cicero’s text gives us no hint at all as to why Chrysippus was unhappy with the two arguments. But it is not difficult to dream up some plausible reasons. Here is one dream. According to Chrysippus and his logicians, an argument is valid only if its corresponding conditional is true. That is to say, the argument ‘A1, A2, ... , An: therefore B’ is valid only if the conditional assertible ‘If A1 and A2 and ... and An), then B’ is true. Now (by the principle which I have already twice invoked) a conditional statement — like any other compound statement — is only true if each of its constituents possesses a truth-value. Hence if the conditional statement [160] ‘If A1 and A2 and ... and An), then B’ is true, then each ‘Ai’ is either true or false and ‘B’ is either true or false. But in arguments (I) and (II), that is not so. Hence the corresponding conditionals are not true. Hence the arguments are not valid.

II.5: Conclusion Cicero’s argument in Luc xxix 95–xxx 98 is not easy to follow. There are textual difficulties; and in any case the subject is intrinsically baffling. Nonetheless, some things emerge with reasonable clarity. It is clear, for example, that Cicero’s argument is ad hominem — and none the worse for that. It is clear that he is trying not merely to produce paradoxical statements, but to produce paradoxical statements which seem to threaten the very foundations of logic. In itself, ‘mentior ’ might seem an idle curiosity: Cicero’s sentences indicate — in a less than pellucid form — how the malaise of ‘mentior ’ infects modus ponens reasoning and the most elementary of logical truths. It is clear, too, that Cicero is right to reject the feeble claim that the ¼ æÆ form ‘exceptions’ to the general rules of logic: the rules of logic, unlike the laws of physics, hold everywhere if they hold anywhere. There is, nonetheless, a weakness — and, I think, an evident weakness — in the case which Cicero makes. The whole argument presupposes that in uttering the sentence ‘mentior ’ I make a assertion, and indeed make the assertion that I am thereby lying. Without that presupposition, the argument collapses. But the presupposition is anything but evidently true. Cicero does not attempt to support it. He does not even observe that his argument requires it.52 52 I am very grateful for the comments which were sent to me by Jaap Mansfeld and by Mario Mignucci (who, inter alia, pointed out a grotesque logical error in the first draft).

3 Logical form and logical matter* I

A proof in Euclid The first theorem of the first Book of Euclid’s Elements is this: On a given finite straight line, there can be constructed an equilateral triangle. For the proof of the theorem, Euclid takes a finite straight line AB and constructs two circles: the first with centre A and radius AB, the second with centre B and radius BA. Let C be one of the points at which these circles intersect. Join A to C and B to C by straight lines; and consider the triangle ABC thus formed: C E

D A

B

Euclid argues as follows: Since the point A is the centre of the circle CDB, AC is equal to AB. Again, since the point B is the centre of the circle CAE, BC is [8] equal to AB. But it was proved that CA is equal to AB. Therefore each of CA, CB is equal to AB. But things equal to the same thing are also equal to one another. Therefore CA is equal to CB. (elem I i)1

* First published in A. Alberti (ed), Logica Mente e Persona (Florence, 1990), pp.7–119. 1 Kd B  ŁÅ PŁÆ æÆ
Å æªø

N ºıæ
ıÆŁÆØ. ... ŒÆd Kd e ` ÅE
Œ
æ
Kd  F ˆ˜´ ŒŒº ı, YÅ Kd
`ˆ fiB `´
ºØ
Kd e ´ ÅE
Œ
æ
Kd  F ˆ`¯ ŒŒº ı, YÅ Kd
´ˆ fiB ´`. KåŁÅ b ŒÆd ˆ` fiB `´ YÅ
ŒÆæÆ ¼æÆ H
ˆ`, ˆ´ fiB `´ Kd
YÅ
a b fiH ÆPfiH YÆ ŒÆd Iººº Ø Kd
YÆ
ŒÆd ˆ` ¼æÆ fiB ˆ´ Kd
YÅ. — I cheat slightly by writing ‘there can be constructed’; for Euclid himself uses an imperatival infinitive. But the difference between constructions and theorems proper is of no importance in the present context.

44

Logical Matters

And hence we may infer that the triangle ABC is equilateral. Q.E.D. At the heart of the proof 2 lies an argument which I shall call the Euclidean Argument. It can be set out as follows: (1) Things equal to the same thing are equal to one another. (2) CA is equal to AB. (3) CB is equal to AB. Therefore: (4) CA is equal to CB. The argument is utterly clear and utterly simple. It might stand as a paradigm of deductive inference. The first premiss of the Euclidean Argument is the first of Euclid’s ‘common notions’; that is to say, it is one of the axioms of Euclid’s geometry. If we omit the axiom, we are left with the following argument: (1) CA is equal to AB. (2) CB is equal to AB. Therefore: (3) CA is equal to CB. This argument, which I shall call the Truncated Argument, is also utterly simple and utterly clear. It too might be regarded as a paradigm of deductive inference. It is plain that both the Euclidean Argument and the Truncated Argument are deductively valid. Their conclusions follow from their premisses. It is plain, moreover, that the Euclidean Argument is, so to speak, one member of a large family of arguments, each of which is valid. In his commentary on Euclid, Proclus observes that even if you make the line double the one set out in the [9] exposition, or treble, or of any other length greater or less than it, the same constructions and proofs will fit. (in Eucl 210.2–5)*

The proof, in other words, does not depend for its validity on the particular line, AB, which Euclid invites us to consider.3 What is more, the Argument I have extracted from the proof does not depend on the fact that AB, CA, and

2 For a logical analysis of the proof, see I. Mueller, ‘Greek mathematics and Greek logic’, in J. Corcoran (ed), Ancient Logic and its Modern Interpretations (Dordrecht, 1974), pp.35–70, on pp.37–43. Mueller concludes that ‘Euclid’s tacit logic is at least the first order predicate calculus, nothing less’ (p.43). (See also I. Mueller, Philosophy of Mathematics and Deductive Structure in Euclid’s Elements (Cambridge MA, 1981), pp.11–15.) Note that here I am concerned not with the whole proof but only with the embedded argument. * Œi
ªaæ c
غÆÆ
B
F
KŒŁÅ  Øfi Å  
Å
ƃ ÆPÆd ŒÆÆŒıÆd ŒÆd I Ø ±æ  ıØ
, Œi
æغÆÆ
Œi
¼ººÅ
›ø F
Ç
Æ ÆÅ j Kº
Æ ºfi Å. 3 This is not an accidental feature of the Argument; for Euclid’s proof purportedly holds for any finite straight line. The general theorem will not have been proved unless the particular argument

Logical form and logical matter

45

CB are lines rather than magnitudes of some other sort. It is a thoroughly general, abstract, formal argument. Something similar holds for the Truncated Argument. Its validity is evidently not dependent on the particular lines for which it is formulated; nor, equally evidently, is it dependent on the fact that its terms refer to lines. It too is thoroughly general, abstract, formal.

The utility of logic The Euclidean Argument and the Truncated Argument were familiar enough to the later Greek logicians — to Alexander of Aphrodisias, to his contemporaries, to his successors.4 The Arguments were paraded as perfectly normal inferences. They were not held to be idiosyncratic in their form or structure. Thus we should expect ancient logic to have taken the Arguments under its wing;5 for the science of logic has as its business the analysis and explanation of valid arguments. Moreover, ancient logicians stressed the utility of their subject.6 The thesis that logic must be ‘useful’, or that the [10] arguments which the discipline of logic analyses must match the proofs which the other sciences construct, is a commonplace among the later Peripatetic logicians. Indeed, they regarded logic as purely instrumental: it is an instrument or ZæªÆ

of the sciences; it is not a part or æ  of philosophy — that is to say, it is not an object of study in its own right.7 Alexander’s commentary on the Prior Analytics is peppered with references, explicit or implicit, to the instrumental status of the subject. For example: which Euclid produces in some sense holds for every line (see [Ammonius], in APr 70.20–22: below, pp.[79–80]). How and why Euclid is entitled to this generalization — which he himself makes without explanation — are questions which do not concern me here. See Proclus, in Eucl 270.3–25; Mueller, ‘Greek mathematics’, pp.37–43; id, Philosophy of Mathematics, pp.11–15; J. Barnes, Truth, etc. (Oxford, 2007), pp.347–354. 4 The main texts will be mentioned or discussed in the course of the paper. Note also that Euclid’s proof of his first theorem served as a stock example of a proof or I ØØ: e.g. Philoponus, in APst 8.21–30. 5 Note that Alexander will sometimes expound a Euclidean proof in some detail (e.g. in APr 260.9–261.24; 268.6–269.15; 359.2–14): he states or implies that these proofs proceed by way of categorical or Aristotelian syllogisms — but his presentations are never explicitly syllogistic in form, nor does he give any indication of how the arguments might be ‘analysed’ syllogistically. 6 See further J. Barnes, ‘Galen and the utility of logic’, in J. Kollesch and D. Nickel (eds), Galen und das hellenistische Erbe (Stuttgart, 1993), pp.33–52 [reprinted in volume III]. 7 The ancient debate over the status of logic was not the sterile word-chopping it is sometimes taken to be. Rather, the issue defines and determines a particular attitude to logical study. For an excellent discussion, see Tae-Soo Lee, Die griechische Tradition der aristotelischen Syllogistik in der

46

Logical Matters

Aristotle here [i.e. at APr ` 32b18–22] indicates to us that in this study we should only take up and work out what is useful for proofs — what is useless we should ignore, even if it contains some valid arguments. Now certain things which are useless for proofs he did not discuss, although the moderns8 do discuss them (e.g. duplicated arguments, arguments which conclude indifferently, what is called indefinite matter, and in general what the moderns call the second thema) — but he omitted these items because they are useless and not because he was ignorant of them. For every instrument has its limits set by the utility of what is produced or proved by it. What is no longer useful is not even an instrument. A plane which is no use to a carpenter is no longer a plane (except homonymously). (in APr 164.25–165.2)*

Alexander’s utilitarianism is uncompromising — and he duly ascribes it to Aristotle himself. Alexander’s contemporary, Galen, had a comprehensive knowledge of logic and a profound and permanent interest in it.9 He too took a thoroughly utilitarian view of logical studies: references to the utility of logic are as common in his writings as they are in Alexander’s; and he, like Alexander, will reject one or another putative element in logical study on the grounds that it is [11] useless.10 Galen’s attitude is vigorously expressed in a celebrated text which offers an account of his early studies in logic: When I observed that all men, when they disputed over anything, claimed to prove their own views and essayed to refute their neighbours, there was nothing I was so eager to study — and to study above all else — as the theory of proof. I asked the Spa¨tantike, Hypomnemata 79 (Go¨ttingen, 1984), pp. 44–54; cf Barnes, ‘Utility’, pp.33–34 (with references to the pertinent texts, and some bibliography). 8 For the moderns, ƒ
æ Ø, see below pp.[71–73]. * ... K
،

 E
‹Ø E e håæÅ
K
fiB fiB æƪÆfi Æ æe a ØåŁÅ 
Æ 

ºÆ
Ø
 ŒÆd KæªÇŁÆØ, e  ¼åæÅ
, N ŒÆd å Ø Ø
a ıº Œ
, ÆæÆØEŁÆØ. ‹Ł
Bº
‹Ø ŒÆd ÆFÆ æd z
ÆPe b
PŒ YæÅŒ ºª ıØ b ƒ
æ Ø Iåæø
Z
ø
æe I ØØ
, Ø IåæÅÆ
P Ø ¼ª
ØÆ
ÆæºØ
, x  NØ
Øç æ 
Ø ƒ º ª Ø j IØÆç æø æÆ

 j ¼Øæ  oºÅ ºª 
Å ŒÆd ŒÆŁ º ı e ŁÆ e æ
ŒÆº 

Ææa  E
øæ Ø. Æ
e ªaæ Oæª
ı æ
åæÆ æe e  ÆP F ØŒ


 ŒÆd ªØ



e b ÅŒØ åæØ
P i
ZæªÆ

YÅ
e ªaæ ¼åæÅ
ŒÆæ

fiH Œ
Ø PŒØ ŒÆæ

Iºº j ›ø
ø. 9 On Galen’s logic, see J. Barnes, ‘Galen on logic and therapy’, in F. Kudlien and R.J. Durling (eds), Galen’s Method of Healing (Leiden, 1991), pp.50–102 [reprinted in volume III] — with bibliography on p.55 n.21. 10 See e.g. PHP V 224–226, 781–782; and the testimonium to the æd I ø in al-Farabi (see F. Zimmermann, Al-Farabi’s Commentary and Short Treatise on Aristotle’s de Interpretatione (Oxford, 1981), p.186). Note, too, Galen’s essays æd åæÆ ıºº ªØH
(lib prop XIX 43), and æd B åæÆ H
N  f ıºº ªØ f ŁøæÅø
(lib prop XIX 47). See I. von Muller, ¨ ber Galens Werk vom wissenschaftlichen Beweis, Abhandlungen der Bayerischen Akademie 1895.2 U (Munich, 1897), pp. 417–426; Barnes, ‘Utility’.

Logical form and logical matter

47

philosophers (for I had heard that they practised it) to keep until later anything else they taught in the logical part of philosophy and to ease the pains of my desire for proofs by teaching me this method by learning which you can both recognize accurately whether an argument offered by somone else is really demonstrative ... and also yourself, in any inquiry you undertake, proceed methodically to a discovery. (lib prop XIX 39)*

For Galen, the purpose of studying logic was the acquisition of the theory of proof: other pieces of logic you may keep until later — or rather, keep for ever. Logic is estimable to the extent, and only to the extent, that it provides a method and a structure for scientific proof. On this ideological point, Galen and Alexander were at one. The Stoics, it might be thought, disagreed. For, and notoriously, they did not take logic to be purely instrumental: for them, logic was a genuine part of philosophy; and they were prepared to investigate arguments which lacked — and which evidently lacked — any possible scientific application. Nonetheless, the Stoics too stressed the utility of the subject. Indeed, they actually defined ØƺŒØŒ, or logic in general, as the art of discriminating the true and the false;11 and ‘they say that the study of syllogisms is of the greatest utility [PåæÅ Å
]’ (Diogenes Laertius, VII 45). If the Stoics — unlike Alexander and Galen — encouraged the study of argument forms which have no scientific application, they were perfectly sure — like Alexander and Galen — that logic was essentially an applied discipline: it fails in its duties, and ceases to be ‘most useful’, if it does not address itself to actual scientific argumentation. For any ancient logician, a satisfactory logical theory must be [12] capable of analysing the arguments and proofs which are used in the sciences. It would have been a scandal had the simplest and most familiar arguments of Euclid been blandly ignored by the discipline of logic. Then how did the later Greek logicians deal with the Euclidean Argument and the Truncated Argument? * –Æ
Æ I
Łæ ı ›æH
K
x  IçØÅ FØ
Æı   I ØŒ
Ø
Kƪªºº 
ı KºªåØ
  f ºÆ KØåØæ F
Æ, Pb
oø K ÆÆ ÆŁE
±
ø
æH
‰ c
I ،،c
ŁøæÆ
Mø  Ææa H
çغ  çø
— KŒ
ı ªaæ XŒ ı
ÆPc
ØŒØ
— N 
Ø ŒÆd ¼ºº ŒÆa e º ªØŒe
æ  B çغ  çÆ ØŒÆØ çıºØ
NÆFŁØ, c
 TE
Æ B æd a I Ø KØŁıÆ ÆFÆØ ØÆ
Æ lØ ¼æÆ Ł   KØ
m
› ÆŁg
æ ı  ºª
  º ª
I ،،e
IŒæØH ª
øæØE  æ
Z
ø Kd  Ø F  ... ÆP   ı
ÆØ ŒÆŁ ŒÆ
H
ÇÅ ı
ø
›fiH Ø
Ø åæ
 Kd c
oæØ
ÆP F Ææƪ
ŁÆØ: 11 See e.g. Sextus, PH II 94; M XI 187; Diogenes Laertius, VII 62; and K. Hu¨lser, Die Fragmente zur Dialektik der Stoiker (Stuttgart/Bad Canstatt, 1987/8), items 55–66.

48

Logical Matters

Two syllogistic theories They were familiar with two distinct logical theories:12 with the theory of predicative or ‘categorical’ inference, which was associated with Aristotle and the Peripatetics; and with the theory of ‘hypothetical’ inference, which belonged rather to Chrysippus and the Stoic school. There were disputes about whether, or in what sense, the inferences codified by one theory could be ‘reduced’ to those codified by the other, and about whether, and in what sense, one theory was ‘prior’ to the other. Yet it seemed clear to most ancient thinkers that, however they stood in relation to one another, Peripatetic and Stoic logic together exhausted the theory of inference. Thus Alcinous, in his introduction to Platonic philosophy, could state, as though it were a commonplace, that ‘of syllogisms some are categorical, some hypothetical, and some mixed from the two’ (didasc vi [158]).13 And in order to exhibit Plato’s competence in logic, he showed how examples of each sort of syllogism are to be found in the dialogues. Alcinous was not a logician himself, and he was not defending an idiosyncratic or a controversial thesis. His view is significant precisely because it was commonplace: there are two types of syllogism, two theories of inference. Then if the Euclidean Argument and the Truncated Argument are valid, their validity should be explicable either within categorical syllogistic or within hypothetical syllogistic — or else (in case the Arguments are, in Alcinous’ phrase, ‘mixed’) within the [13] ‘mixed’ theory which comes from conjoining categorical and hypothetical syllogistic. Now it must seem evident that hypothetical syllogistic cannot cope either with the Euclidean Argument or with the Truncated Argument. Hypothetical syllogistic is essentially concerned with compound propositions, and the formal features to which it attends are propositional connectives. (In the standard Stoic theory, attention is limited to conditional, disjunctive and conjunctive connectives.) A paradigm hypothetical inference is this: (1) If it is day, then it is light. (2) It is day. Therefore: (3) it is light. 12

With the next paragraphs, compare J. Barnes, ‘Terms and sentences’, Proceedings of the British Academy 69, 1983, 279–326, on pp.279–283 [reprinted below, pp.433–478.] 13 H
b ıºº ªØH
ƒ 
NØ ŒÆŪ æØŒ , ƒ b  ŁØŒ , ƒ b ØŒ d KŒ  ø
. — A typical ‘mixed’ argument will be a reductio ad impossibile : see e.g. [Ammonius], in APr 69.11–28, for the analysis of reductio arguments into categorical and hypothetical components. (Other ancient texts use the term ‘mixed syllogism’ in other senses.)

Logical form and logical matter

49

The argument is valid, and the crucial logical feature — in a sense the only logical feature — of the argument is the presence in it of the propositional connective ‘if ... , then — ’. Neither of our Arguments contains — at least on the surface — any propositional connective. And that in itself is enough to suggest that they are not hypothetical syllogisms: their validity is not to be analysed and explained by reference to any propositional or hypothetical form. Again, neither of the Arguments seems to be a categorical syllogism. Categorical syllogistic attends to the internal structure of propositions. The structure is that of subjects and predicates — that is to say, the propositions in question are treated by categorical syllogistic insofar as they ascribe a predicate to a subject (to all or some of it, positively or negatively). A paradigm categorical syllogism is this: (1) Every animal is a substance. (2) Every man is an animal. Therefore: (3) every man is a substance. The argument is valid, and the crucial logical features — in a sense the only logical features — of the argument are the presence in it of the quantifying particle ‘every’ and the subject–predicate structure of its component propositions.14 [14] The Truncated Argument contains no quantifying particles, and its component propositions are not — at least on the surface — in subject–predicate form. The Euclidean Argument does not explicitly contain any quantifying particles; and even if we allow that there is an implicit ‘every’ in its first premiss, the other two premisses and the conclusion lack quantification. Further, the component propositions of the Euclidean Argument do not — at least on the surface — exhibit any pertinent subject–predicate form. This suggests that neither Argument can be brought under the umbrella of categorical syllogistic: the validity of neither is explicable by reference to any predicative or ‘categorical’ syllogism.

14

In what follows I shall regularly use the standard abbreviations for the forms of categorical propositions and syllogisms. The four term connectives are written as ‘a’, ‘e’, ‘i’, and ‘o’. The predicate term is written before the subject term (see G. Patzig, Aristotle’s Theory of the Syllogism (Dordrecht, 1968), pp.8–12). Hence the four logical forms of orthodox categorical syllogistic can be represented as: ‘AaB’, ‘AeB’, ‘AeB’, ‘AoB’. Note that in the formula ‘AaB’, ‘A’ and ‘B’ are dummy letters whereas ‘a’ is a constant (with the fixed sense of ‘ ... holds of every — ’). Modal operators are prefixed to their sentences: ‘L’ marks ‘necessarily’; and a prefixed ‘X’ is a sign that the sentence is non-modal (or, as Alexander prefers, has the modality of ‘actuality’).

50

Logical Matters

A third kind of syllogism? If the Euclidean Argument and the Truncated Argument are valid, and yet are neither hypothetical nor categorical syllogisms, then it will be tempting to infer that there must be a third kind of syllogism in addition to the two kinds commonly recognized by the ancient logicians. At least one ancient logician drew exactly that inference. My phrase ‘a third kind of syllogism’ is taken from Galen.15 In his Institutio Logica Galen presents elementary and unoriginal expositions both of categorical and of hypothetical syllogistic; and then he turns to the novelty — to his third kind of syllogism (xvi 1). He thought that the third kind was important. For our Arguments are among his examples of syllogisms of the third kind, and he rightly supposed that these Arguments are typical of innumerable inferences produced by geometers and arithmeticians (xvi 1, 5). Moreover, the third kind also contains innumerable [15] non-mathematical arguments which are valid and yet are neither categorical nor hypothetical syllogisms (xvi 10). It is no accident that the very first argument produced in inst log — an argument intended to illustrate what a syllogism is (i 2–3) — is a close congener of our two Arguments and belongs to Galen’s third kind. Galen named the third kind of inference ‘relational syllogisms [ŒÆa e æ  Ø ª
ŁÆØ]’ (xvi 1). Behind the nomenclature lay the thought that the Truncated Argument, say, owes its validity to some features of the relation of equality (the relation which its constituent propositions invoke); and Galen must have imagined that the third kind of argument was somehow to be characterized by reference to the logical properties of relational propositions. The Truncated Argument, then, is a relational syllogism: it is valid, let us say, in virtue of its relational form. Galen does not explain why the Argument is neither a categorical nor a hypothetical syllogism. But we may plausibly assume that he was moved by something like the train of reasoning which I rehearsed in the previous section. 15 The so-called documentum Ammonianum (i.e. the Ammonian scholia printed by Wallies in the preface to his edition of Ammonius, in APr) also refers to a third kind of syllogism; for its author takes syllogisms ŒÆa æ ºÅłØ
to constitute such a kind (IX 23–24; XII 3). But these syllogisms (on which see W.C. Kneale, ‘Prosleptic propositions and arguments’, in S.M. Stern, A. Hourani, and V. Brown (eds), Islamic Philosophy and the Classical Tradition: essays presented to Richard Walzer (Oxford, 1972), pp.189–207, have nothing to do with our two Arguments. (See further, below, p.[77].)

Logical form and logical matter

51

That train of reasoning is suggestive, not probative. It establishes a prima facie case against the adequacy of the two ancient logical theories. Further investigation might upset the case. It might emerge — for example — that the components of the Arguments do, despite their surface appearance, possess a pertinent underlying subject–predicate structure, and that they can after all be analysed within categorical syllogistic. But whether or not that (or something like it) should eventually turn out to be true, it is undeniable that the Arguments offer a challenge to ancient logic. The challenge was recognized by Galen, who found its force decisive. It was also recognized by Alexander of Aphrodisias, who tried to meet it. The main purpose of this chapter is to examine the way in which Alexander responded to the challenge.16 But first I shall attempt to articulate the terms of the challenge — which will [16] involve an extended discussion of the notion of formal validity. This will lead, in Part III, to some reflexions on the old Peripatetic conception of the form or r   of propositions and arguments, which in turn will provoke — in Part IV — some thoughts about Stoic logic and the arguments which the Stoics called ‘unmethodically concludent’. Finally, Part V will examine Alexander’s attempt to meet the challenge thrown down by the Euclidean and the Truncated Arguments.

II

A mediaeval distinction Any argument can be represented by a sequence of sentences: P1, P2, ... , Pn: therefore Q. where the Pis are, collectively, the premisses of the argument and Q is the conclusion. For any argument, there is a ‘corresponding conditional’, viz the conditional proposition in which the antecedent is the conjunction of the Pis and the consequent is Q, thus: If (P1 and P2 and ... and Pn), then Q. 16 My original intention had been to discuss Galen’s view of the matter, and this chapter was to have been a preliminary study for the edition of the institutio which Michael Frede and I were preparing. But in order to deal with Galen, I found that I needed to look at the comparable texts in Alexander — and hence also at the Stoic º ª Ø IŁ ø æÆ

. The propaedeutics then ousted the study proper. For some thoughts on the Galenic text, see below, Part V; Truth, pp.419–447; ‘Proofs and syllogisms in Galen’, in J. Barnes and J. Jouanna (eds), Galien et la Philosophie, Entretiens Hardt 49 (Vandœuvres, 2003), pp.1–24 [reprinted in volume III].

52

Logical Matters

Some arguments are valid and others are invalid. A rough account of validity will say that an argument is valid provided that its conclusion follows from its premisses, or provided that its premisses entail its conclusion, or provided that its conclusion must be true if its premisses are true, or provided that its corresponding conditional is necessarily true.17 A distinction among valid arguments was commonly drawn by the mediaeval logicians.18 John Buridan’s account is perhaps the clearest and best. In chapter 4 of Book I of his Tractatus de [17] Consequentiis,19 he distinguishes between consequentiae formales and consequentiae materiales.20 A consequence is called formal if it is valid for all terms, the form remaining the same. Or, if you wish to remark explicitly about the force of the word, a consequence is formal if every proposition similar in form which might be formed would be a good consequence — for example: A is B. Therefore: B is A. A consequence is material if not every inference similar in form which might be formed would be a good consequence, or (as it is usually put) if it does not hold for all terms, the form remaining the same — for example: A man runs. Therefore: an animal runs. For that is not valid for the following terms: A horse walks. Therefore: a log walks. It seems to me that no material consequence has an evident validity except by reduction to a formal consequence. It is reduced to a formal consequence by the addition of some necessary proposition (or of some necessary propositions), whose annexation to the assumed antecedent makes the consequence formal. Thus if I say: A man runs. 17 These formulas are not precise; and they run together two different notions — semantic and syntactic validity — which modern logicians are careful to distinguish. Here I take for granted the general notion of validity: my concern is not with the genus but with its species. 18 See e.g. E.A. Moody, Truth and Consequence in Mediaeval Logic (Amsterdam, 1953), pp.70–80; J. Pinborg, Logica e Semantica nel Medioevo (Turin, 1984), pp.173–182; N.J. GreenPedersen, The Tradition of the Topics in the Middle Ages (Munich, 1984), pp.287–291; A. Broadie, Introduction to Mediaeval Logic (Oxford, 1987), pp.58–62. 19 See H. Hubien (ed), Iohannis Buridani Tractatus de Consequentiis, Philosophes Medievaux 16 (Louvain/Paris, 1976). 20 A consequentia is defined at I 3 in such a way that it is — in effect — either a sound conditional of the form ‘If (P1 and P2 and ... and Pn), then Q’ or a valid argument of the form ‘P1, P2, ... , Pn: therefore Q’. I shall ignore the apparent confusion (or conflation) of arguments and conditionals which inheres in the notion of a consequentia. (And which also inhered in its Greek original, IŒ º ıŁÆ.)

Logical form and logical matter

53

Therefore: an animal runs. I shall prove the consequence by the fact that every man is an animal. For if every man is an animal and a man runs, it follows by a formal consequence that an animal runs.21

Later, Buridan explains that no material consequence is a syllogism; and that although all syllogisms are formal [18] consequences, not all formal consequences are syllogisms. (He restricts the term ‘syllogism’, with confessed artificiality, to categorical syllogisms.22) The distinction between formal and material consequences was, as I have said, a commonplace in mediaeval logic.23 It remained a standard element in traditional, or pre-Fregean, logic;24 and it is still found, in a somewhat different guise, in some modern texts.25 The whole weight of the distinction falls on the notion of the ‘form’ of a consequence. The form of a consequence is fixed by the form of its constituent propositions, and in I 7 Buridan duly explains what he understands by the matter and the form of a proposition: the matter of a proposition consists solely of its component terms; any other items in the proposition (the copula, signs of quantity, negations, modal operators, sentential connectives) — and also any other aspects of the proposition (the number and the order of the terms, and so on) — collectively constitute the form of the proposition. Thus in the proposition that every man is an animal, the terms man and animal furnish the matter — and everything else belongs to the form.26 Buridan’s account of logical form — deriving ultimately from classical antiquity — will serve as an  ªæÆç or delineation: that is to say, it is a useful preliminary sketch of the business. But for various reasons it will not suffice as an ›æØ  or definitive account. And before I turn back to antiquity, I shall try to develop, in a pretty elementary fashion, such an ›æØ . [19] 21 Consequ I 4 [22–23] (the consequentia formalis constructed at the end of the passage is a categorical syllogism in Disamis, i.e. of the form ‘AiB, CaB: therefore AiC’). 22 Consequ III i 1 [79–81]. 23 See e.g. Ockham, Summa logicae, III iii 1 (in P. Boehner, G. Gal, and S. Brown, Guillelmi de Ockham Opera philosophica et theologica: opera philosophica I (St Bonaventure NY, 1974), p.589). But Ockham’s account of the matter is not exactly the same as Buridan’s. See also the texts cited by S. Read, Relevant Logic (Oxford, 1988), pp.119–123. 24 See e.g. § 59 of Kant’s Logik. 25 e.g. A. Church, Introduction to Mathematical Logic (Princeton, NJ, 1956), pp.1–3 (and compare the passage from Tarski quoted below, p.[29]). Note also the related distinction between ‘material’ and ‘formal’ implication (for which, see A.N. Whitehead and B. Russell, Principia Mathematica (Cambridge, 19272), pp.7, 20–21). 26 See e.g. Moody, Truth and Consequence, pp.16–18.

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Sentence forms I shall use the word ‘form’ in a liberal sense; and I shall talk of (declarative) sentences rather than of propositions.27 I assume that questions of form are essentially questions of syntax — that formal features are either determined by or identical with syntactical features. And I take for granted the availability of a finished syntax in terms of which questions of form may be discussed.28 But the notion of form is not tied to any one particular type of syntax. (Indeed I see no reason to think that, for any language, there is a unique syntactical theory, or that for any sentence, there is a unique syntactical description.) All I require is that the favoured syntax be capable of distinguishing different components in a sentence and of ascribing them to appropriate syntactical categories. Thus a decent syntax for English will recognize the sequence Alexander read Aristotle’s Analytics as a sentence (as belonging to the category S). It will discern, as components of the sentence, the name ‘Alexander’, the verbal phrase ‘ ... read Aristotle’s Analytics’, the name-forming operator ‘Aristotle’s ... ’ (i.e. ‘ ... of Aristotle’), and so on. It will not recognize, say, ‘ ... read Aristotle — ’ as a component of the sentence. The notion of form is best introduced by way of the notion of sharing a form or of being conformal. Thus two sentences, S and S*, are conformal when S is just like S* except that where S has one or more components c1, c2, ... , cn, S* has different components of the same category, c*1, c*2, ... , c*n. Consider the sentences: (1) Alexander read the Analytics and [20] (2) Alexander read the Metaphysics. Clearly, (1) is just like (2) except that, where (1) has the component ‘the Analytics’, (2) has the component ‘the Metaphysics’. Each of those two components is a name (or belongs to the category N). Hence (1) and (2) are conformal. 27

Later on I shall oscillate between ‘sentence’ and ‘proposition’: the familiar philosophical issues which those words raise are not relevant to my present concerns. 28 See e.g. P.T. Geach, ‘A program for syntax’, in D. Davidson and G. Harman (eds), Semantics of Natural Language (Dordrecht, 1972), pp.483–497; D. Lewis, ‘General semantics’, ibid, pp.169–218 [= his Philosophical Papers I (Oxford, 1983), pp.189–232]; and Chapter 7 of D. R. Dowty, R.E. Wall, and S. Peters, Introduction to Montague Semantics (Dordrecht, 1981).

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If two sentences are conformal, then there is — trivially — a form which they share. And the shared form may be expressed or represented by means of a familiar device: we may replace the similar components in (1) and (2) by a letter, thus: (Fi) Alexander read y. Here the letter ‘y’ is a dummy letter, to which different meanings may be assigned on different occasions — assign ‘y’ the sense of ‘the Analytics’ and you get (1); assign it the sense of ‘the Metaphysics’ and you get (2).29 Take a third sentence: (3) Galen read the Categories. Clearly, (3) is just like (1) except that where (1) has ‘Alexander’, (3) has ‘Galen’, and where (1) has ‘the Analytics’, (3) has ‘the Categories’. Thus (1) and (3) are conformal, and they share the form: (Fii) x read y. Of course, sentence (2) also has the form (Fii). Now add a fourth sentence: (4) Alexander commented upon the Analytics. This plainly shares a form with (1), viz: (Fiii) Alexander R the Analytics — where ‘R’ is ‘ ... read — ’ in (1) and ‘ ... commented upon — ’ in (4). (Different sorts of dummy letters are used for components of [21] different syntactical categories: ‘x’, ‘y’, ‘z’ are assigned to the syntactical category of names; ‘R’ is assigned to the category of polyadic verbs; ‘F’ will be used for monadic verbs.) Sentence (4) also shares a form with (2), viz: (Fiv) Alexander R y. And, lastly, it shares a form with (3), viz: (Fv) x R y. Finally, take a fifth sentence: (5) Aristotle did not take snuff. Does (5) share a form with any of (1)–(4)? Yes; it shares with all those sentences the form: (Fvi) Fx — in (5) ‘F’ is ‘ ... did not take snuff’, in (1) it is ‘ ... read the Analytics’, and so on.

29 For the notion of a dummy letter — and the distinction among dummy letters, schematic letters, and variables — see C.A. Kirwan, Logic and Argument (London, 1978), pp.5–8.

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It is convenient to regard any sentence as a component of itself (as the ‘limiting case’ of a component). Hence we may also say that (1) and (2) share the form: (Fvii) p30 — in (1) ‘p’ is ‘Alexander read the Analytics’, in (2) it is ‘Alexander read the Metaphysics’. Evidently, (1)–(5) all share the form (Fvii). Evidently, every sentence is — trivially — conformal with every other sentence; for every sentence exhibits the form (Fvii). Given that account of form, we may, if we wish, introduce the notion of the ‘matter’ of a sentence: we can say that the matter of a sentence is — to put it loosely — whatever replaces the dummy letters of a sentence’s form. It is evident, then, that the concept of matter is a relative one, and relative to form. Sentence (1) has the form (Fi): relative to (Fi), the matter — the material component — of (1) is ‘the Analytics’. Sentence (1) also has the form (Fiii): [22] relative to (Fiii), the matter of (1) is ‘ ... read — ’. And so on. In general, the matter of a sentence S relative to a form (Fj) consists of just those components of S which are replaced in (Fj) by dummy letters. Any sentence is likely to exhibit numerous forms and matters;31 and it is a mistake — at best an infelicity — to speak of ‘the’ form of a sentence. In the Physics Aristotle expressly recognizes that the notion of matter or oºÅ is a relative one; and one might perhaps have expected that those logicians who adapted Aristotelian oºÅ to their own ends would have acknowledged the relative status of logical matter. Some ‘traditional’ logicians did do so. Thus according to Augustus de Morgan: The form may again be separable into form of form and matter of form; and even the matter into form of matter and matter of matter; and so on.32

But as far as I know no ancient or mediaeval logician made the point: they all speak — misleadingly — of ‘the’ form and ‘the’ matter of propositions and arguments. 30

I use lower case ‘p’, ‘q’, ... , as dummy letters for sentences: upper case ‘P’, ‘Q’, ... , are schematic letters. 31 I say ‘is likely to’: it might be thought that some sentences — e.g. ‘It’s raining’ — have only one form, viz (Fvii). 32 A. de Morgan, ‘On the syllogism III’, in his On the Syllogism and other logical writings, ed P. Heath (London, 1966), pp.74–146, on p.75. — There is something similar in Kant: he holds that, whereas the matter of a categorical judgement ‘AxB’ consists of the terms ‘A’ and ‘B’, the matter of a hypothetical judgement ‘If AxB, then CyD’ consists of its two component categorical propositions. See § 24 of Kant’s Logik; cf §§ 18, 25, 28.

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Among the several forms of a sentence, some will be — in an obvious sense — more abstract than others. Now when logicians speak of ‘logical’ forms they usually have in mind highly abstract forms. Wholly abstract forms are those forms whose expressions contain nothing but dummy letters; and every wholly abstract form might well be counted as a logical form.33 But it is not only wholly abstract forms which are normally understood as logical forms — for with wholly abstract forms alone, a logician will be able to analyse few inferences. Call ‘constants’ those parts of the expressions of a form which are not dummy letters. (Thus the expressions ‘Alexander’ and ‘ ... read — ’ are constants in (Fi).) Some constants are logical constants. And then [23] a logical form may be defined as a form whose expression contains nothing but dummy letters and logical constants. (Hence all wholly abstract forms are logical forms. For they contain nothing but dummy letters — and therefore nothing but dummy letters and logical constants.) That definition will be clear and precise to the extent that the technical term ‘logical constant’ is clearly and precisely defined. One mode of definition is by catalogue; that is to say, we might follow Buridan and offer a list of logical constants. Thus, for ancient purposes, the primary logical constants are, first, the four term connectors of categorical syllogistic ‘a’, ‘e’, ‘i’, ‘o’) and, secondly, certain sentential operators (in the first place, ‘It is not the case that ... ’, ‘If ... , then — ’, ‘Either ... or — ’ and ‘Both ... and — ’34). For modal logic we shall need to add operators such as ‘It is necessary that ... ’ and ‘It is possible that ... ’.35 And further developments of logic will require their own characteristic logical constants.36

Argument forms Definitions by catalogue are not very satisfactory — particularly if the catalogue ends with an etcetera. And we shall want to ask whether there is some 33 Hence it is already clear that any sentence is likely to have several logical forms. Sentence (1) has each of the forms (Fi)–(Fvii). Of these, (Fv)–(Fvii) are wholly abstract and therefore — on the present assumption — logical forms; so that sentence (2) will have at least three logical forms. 34 Strictly, the last two connectors should be treated as multi-placed rather than two-placed; i.e. ‘or’ and ‘and’ may disjoin or conjoin any number of sentences. 35 Compare Alexander’s remarks about the modal æ  Ø cited below, p.[50]. 36 e.g. ‘ ... knows that — ’, ‘ ... believes that — ’, etc., in epistemic logic; ‘It is obligatory that ... ’, ‘It is permissible that ... ’, etc. in deontic logic; and so on. (But we may not simply assume that these things are logical constants: see below, pp.[28–32])

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general principle or rule by which we may distinguish logical from non-logical constants. But a catalogue, a` la Buridan, will at least give us a preliminary idea of what we are after; and we may for the moment rest content with it. For there is a little more work to be done: thus far I have spoken of forms of sentences — we also need the notion of the form of an argument. Since arguments may be represented by sequences of sentences, a form of an argument may be represented by a [24] sequence of sentence forms. The pertinent sentence forms will, of course, be forms of the constituent sentences of the argument.37 Each of the constituent sentences of an argument will typically exhibit several forms. Hence every argument will typically exhibit several forms. Plainly, an argument form will be a logical form just in case each of its constituent sentence forms is a logical form. Next, we may say that an argument A is valid in virtue of the form (FÆ) provided that (i) A exhibits the form (FÆ) and (ii) every argument which exhibits (FÆ) is valid. An argument A is formally valid provided that there is at least one logical form (FÆ) such that A is valid in virtue of (FÆ). An argument A is materially valid provided that (i) A is valid and (ii) there is no logical form in virtue of which A is valid. If an argument is formally valid, it follows that it is valid. If an argument is valid, it does not follow that it is formally valid. Compare the following two arguments: (A1) (1) If it is day, then it is light. (2) It is day. Therefore: (3) it is light. 2 (A ) (1) A man is running. Therefore: (2) An animal is running. Plainly, both arguments are valid. Plainly, Al is formally valid. One of its forms is this: (FÆ) If p, then q. p. Therefore: q.

37

i.e. if ‘FP’ expresses a form of the sentence ‘P’, then a form of the argument P1, P2, ... , Pn: therefore Q will be FP1, FP2, ... , FPn: therefore FQ

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Every expression in each of the three sentential constituents of (FÆ) is either a dummy letter or a logical constant.38 Hence the [25] form (FÆ) is a logical form. Evidently, every argument of the form (FÆ) is valid. Hence argument A1 is formally valid. Argument A2, on the other hand, is not formally valid. For there is no logical form exhibited by A2 such that every argument of that form is valid. (How do I know? Well, it seems quite clear — though I cannot prove — that none of the logical forms of A2 is a form in virtue of which A2 is valid.) What can we now say about the Euclidean Argument and the Truncated Argument? The Euclidean Argument was this: (1) Things equal to the same thing are equal to one another. (2) CA is equal to AB. (3) CB is equal to AB. Therefore: (4) CA is equal to CB. One of the forms of the Argument is this: Whatever x, y, z may be: if xRz and yRz, then xRy.39 xRz. yRz. Therefore: xRy. Let us grant that this form is a logical form. (In the Argument, ‘R’ takes the sense of ‘ ... is equal to — ’.) It is plain that every argument of the form is valid. Hence the Euclidean Argument is a formally valid argument. What of the Truncated Argument? It ran: (1) CA is equal to AB. (2) CB is equal to AB. Therefore: (3) CA is equal to CB. One of its forms is: xRz. yRz. Therefore: xRy [26] 38

What about the ‘Therefore’? You might think that if anything is a logical constant, then ‘therefore’ is one. Or you might (better) argue that ‘therefore’ is not really a constituent of argument Al at all: the conclusion of the argument is not ‘Therefore: it is day’, but rather ‘It is day’; and the ‘Therefore’ is not a component of the conclusion but rather an adjoined indication that ‘It is day’ is the conclusion of the argument. Ancient logicians were pretty casual about that sort of thing. But see Barnes, Truth, pp.259–263. 39 This formula presents a standard modern way of ‘formalizing’ premiss (1) of the Euclidean Argument. It is not obvious that it is a form of (1); but the issues involved here are difficult — and since they do not bear upon the course of my current argument, I shall not pursue them.

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— and plainly not all arguments of that form are valid. (Suppose that ‘ ... R — ’ is given the sense ‘ ... lived some centuries later than — ’ and that ‘x’, ‘y’, and ‘z’ are given the senses ‘Alexander’, ‘Galen’, and ‘Aristotle’.) But it would, of course, be rash to infer that the Truncated Argument is not formally valid — for it may have another logical form in virtue of which it is valid. And there is in fact a line of thought which yields the conclusion that the Truncated Argument is formally valid — and which, at the same time, will lead us back to the problem of defining the notion of a logical constant. A starting-place is provided by a contention of the geometer Apollonius of Perga which is reported by Proclus. I am far from praising the geometer Apollonius, who has constructed, as he thinks, proofs of the axioms ... The proof which Apollonius was persuaded he had discovered for the first of the axioms : Let A be equal to B and this to C. I say that A is equal to C. Since A, being equal to B, occupies the same space as it, and since B, being equal to C, occupies the same space as it, A therefore occupies the same space as C. Therefore they are equal. (Proclus, in Eucl 194.9–11, 194.20–195.5)*

Apollonius purported to offer a proof of the first of Euclid’s common notions — of premiss (1) of the Euclidean Argument.40 His argument was dismissed by Proclus — and it had earlier been dismissed by Geminus (see Proclus, in Eucl 183.13–23). Modern scholars have imagined that Apollonius did not really intend to prove the Euclidean axiom — rather, his argument was designed to establish the transitivity of congruence among lines.41 For my

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[27] part, I see no reason to doubt Proclus’ report or to deny that Apollonius sought to prove Euclid’s axioms; nor is Apollonius’ argument without value. But here I am interested in the Apollonian contention only insofar as it bears upon the Truncated Argument. Apollonius supposes that equality is a matter of occupying the same space: A is equal to B just in case A occupies the same space as B. He does not, of course, mean the same area of space — for equal objects generally occupy different areas of space. He means the same amount of space. In other words, Apollonius is implicitly offering us something like the following definition of equality: (EA) x is equal to y if and only if the magnitude of the space Sx occupied by x is identical with the magnitude of the space Sy occupied by y. If we accept (EA) — equality according to Apollonius — , then we may indeed produce a proof of Euclid’s first axiom. More to the present point, we may rewrite the Truncated Argument.42 For by (EA) premiss (1) turns out to be equivalent to: (1*) The magnitude of Sca is identical with the magnitude of Sab. And similarly for (2) and (3). Now one form of premiss (1*) is: x is identical with z — where ‘x’ and ‘z’ in (1*) take the senses of ‘the magnitude of Sca’ and ‘the magnitude of Sab’. Hence one form of the rewritten argument is this: x is identical with z. y is identical with z. Therefore: x is identical with y. In modern predicate logic ‘ ... is identical with — ’, or ‘ ... ¼ — ’, is generally taken as a logical constant. In that case, the form I have just given is a logical form. Hence the rewritten version of the Truncated Argument is formally valid. For it is plain that every argument of the form is valid. [28] Should we conclude that the Truncated Argument actually is formally valid? Two reasons might be offered against that conclusion. First, it might be urged that the rewritten version of the Argument should not be identified with the original version: when (1) is replaced by (1*), we get a new argument — and from the fact that the new argument is formally valid we cannot decently infer pp.335–429, on pp.389–390]. According to von Fritz, it is clear from the text that Apollonius’ argument is meant to apply only to lines and not to all magnitudes. To me, the text hints at no such restriction. 42 And, of course, the Euclidean Argument too.

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that the original argument is formally valid. That contention raises some curious questions. (If two sentences are synonymous, may they nonetheless exhibit different forms?) But I shall pass them by. Secondly, it might be wondered if the relational predicate ‘ ... is identical with — ’ really is a logical constant. Is there any good reason for adding ‘ ... is identical with — ’ but not, say, ‘ ... is equal to — ’ to the list of logical constants?

Logical constants Modern philosophers have attempted to discover or invent a principle by which logical constants can be separated off from non-logical constants. Some have favoured a semantic characterization. Roughly speaking, logical constants are abstract or ‘topic neutral’ words, items which may appear in discourse about any topic whatever and which in themselves give no indication of what the sentences they appear in are about.43 Now ‘ ... is identical with — ’ is surely a highly abstract and topic neutral predicate: it may sensibly be flanked by names for any sort of object whatsoever. Contrast ‘ ... is equal to — ’, which is restricted in its application to magnitudes. Hence ‘ ... is identical with — ’, but not ‘ ... is equal to — ’, may properly be classified as a logical constant. Other philosophers have preferred a syntactic characterization. Thus the style of logical analysis which derives from the work of Gottlob Frege is said to reveal two distinct types of expression. One of these types consists of ‘sentence-forming operators, such as sentential operators and quantifiers, which induce the reiterable transformations which lead from atomic to complex sentences’: it [29] is precisely these expressions which are the logical constants of a language.44 Philosophers who take this line ought, in principle, to deny that ‘ ... is identical with — ’ is a logical constant; for it is a predicate and not a sentenceforming operator.45 43

See e.g. G. Ryle, ‘Formal and informal logic’, in his Dilemmas (Cambridge, 1954), pp.111–129, on pp.115–118. (Ryle describes but does not espouse this characterization.) 44 So M. Dummett, Frege (London, 1973), pp. 21–22. Dummett adds that the logical constants should also include ‘any term-forming operators, such as the description operator, which form singular terms from incomplete expressions such as predicates’. 45 In fact Dummett holds that ‘ ... is identical with — ’ is a logical constant and he devises a supplementary condition which will let him have his way: p.22 n.*.

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Now it is not clear that there is much to be said for either of the suggestions.46 The former is pretty vague (what is to count as a ‘topic neutral’ term?); and the latter seems ad hoc and arbitrary. Moreover, a little reflexion may induce a deeper perplexity: we may come to wonder whether either suggestion is satisfactory because we may come to wonder what the criterion of satisfactoriness might be. What, after all, is the point or importance of trying to distinguish sharply between logical and non-logical constants? And this perplexity may lead to a certain sceptical relativism. In his classic paper ‘On the concept of logical consequence’, Alfred Tarski came to the following conclusions: Underlying our whole construction is the division of all terms of the language discussed into logical and extra-logical. This division is certainly not quite arbitrary. If, for example, we were to include among the extra-logical signs the implication sign, or the universal quantifier, then our definition of the concept of consequence would lead to results which obviously contradict ordinary usage. On the other hand, no objective grounds are known to me which permit us to draw a sharp boundary between the two groups of terms. It seems to be possible to include among logical terms some which are usually regarded by logicians as extra-logical without running into consequences which stand in sharp contrast to ordinary usage. In the extreme case we could regard all terms of the language as logical. The concept of formal consequence would then co-incide with that of material consequence.47 [30]

Ordinary usage — by which Tarski must mean the use commonly made by logicians of the phrase ‘logical constant’ — may impose certain constraints on what we may call a logical constant; but, in the end, the decision to classify something as a logical constant is a pragmatic decision. The category of logical constants is inherently indeterminate. Tarski himself suggested that ‘future research will doubtless greatly clarify the problem which interests us. . . .But I regard it as quite possible that investigations will bring no positive results in this direction ... ’.48 Tarski’s 46 See further e.g. G. Evans, ‘Semantic structure and logical form’, in G. Evans and J.H. McDowell (eds), Truth and Meaning (Oxford, 1976), pp.199–222 [¼ his Collected Papers (Oxford, 1985), pp.49–75]. Note that the issue was debated, in a slightly different form, in the nineteenth century: see de Morgan, ‘On the syllogism’, pp.75–83. 47 See A. Tarski, ‘On the concept of logical consequence’, in his Logic, Semantics, Metamathematics (Oxford, 19832), pp.409–420, on pp.418–419. The paper was first published, in Polish, in 1936. 48 Tarski, ‘Logical consequence’, p. 420. There is a splendid example of ‘future research’ in J. Etchemendy, The Concept of Logical Consequence (Cambridge MA, 1990).

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paper was first published in 1936. ‘Future research’ has, I think, pursued the course he anticipated. But that does not mean that the ‘problem’ is still unsolved. Rather, if Tarski is right, then there is no problem — the attempt to find or construct a sharp boundary between the logical and the extralogical is simply misguided. Within modern logic, ‘ ... is identical with — ’ is generally treated as a logical constant. Similarly, within preference logic ‘ ... prefers — to ***’ is treated as a logical constant.49 Now — or so the thought runs — it would be quite wrong to suppose that preference logic takes ‘ ... prefers — to ***’ as a logical constant because it actually is a logical constant: rather, it is a logical constant (within preference logic) precisely because preference logic construes it as a logical constant. Similarly with identity: ‘ ... is identical with — ’ is a logical constant (relative to most modern systems) precisely and solely because it is taken as a logical constant (in those systems). In general, instead of wondering whether c is a logical constant simpliciter, we should wonder whether c is a logical constant in system S. Words come to be logical constants by being taken as logical constants in some logical system. Hence words are logical constants relative to logical systems. And that is all there is to being a logical constant. [31] Why, then, it might be asked, should we not accept Tarski’s ‘extreme case’ and construe any predicate (or indeed any expression at all) as a logical constant? Let us take ‘ ... is brother of — ’ as a logical constant and invent fraternal logic. Well, perhaps fraternal logic could be invented. Perhaps it is only a sort of logical puritanism which inclines us to reject it. But what would be the point of the invention? Or rather, what would have been invented? Modern predicate logic — like ancient categorical and hypothetical syllogistic — is a rich system, capable both of complex internal development and of fruitful application to actual arguments. Preference logic — like deontic logic and epistemic logic — is also a (reasonably) rich system. And the ultimate justification for treating ‘ ... prefers — to ***’ as a logical constant consists — on the present view — simply in the fact that it is possible to develop a system of preference logic. Fraternal logic, were it invented, would be poor and 49

For my part I prefer to construe the constant as ‘ ... would rather that — than that ***’ — in which case preference will be construed as a sort of sentential operator rather than as a (three-place) predicate. Note that if we construe preference in this way, then it will satisfy Dummett’s syntactical test for logical constancy — though Dummett himself wants to exclude it (p.22). I do not suppose that it is false to parse preference by way of a triadic relation — merely that it is open to us to take the other syntax. As I said earlier, I am happy to allow the possibility of different syntaxes for one and the same sentence.

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trifling. And thus it is pointless to treat ‘ ... is brother of — ’ as a logical constant.50 On the other hand, it is clear that the ‘logic of identity’ is interesting and fruitful. Hence we may reasonably construe ‘ ... is identical with — ’ as a logical constant. That pragmatic view has much to be said for it.51 For in point of fact, nothing of substance seems to hang on the question whether ‘ ... is identical with — ’ is or is not a logical constant. The answer to the question determines nothing beyond the nomenclature of things. Similarly with preference. Some arguments which essentially involve the notion of preference are valid — that point is not in dispute. If you wish to study those arguments, you will treat ‘prefer’ (in some form) as a constant — that point, too, is not in dispute. Some philosophers assert, and some deny, that ‘prefer’ functions as a logical constant, and that there is such a thing as the ‘logic of preference’. Nothing whatever turns on those assertions and denials. Nothing, that is, [32] apart from the fact that some will include under the general rubric of ‘logic’ an area of study which others will exclude. When the issues are insubstantial in that fashion, pragmatism is the wise man’s attitude.

Logic and universality The pragmatic view affords a perfectly clear way of talking about logical form and matter. Relative to any system S, there will be a determinate set of logical constants. If a form (FÆ) of an argument A exhibits nothing but dummy letters and constants from this set, then (FÆ) is a logical form of A relative to S. And there is no more to be said about the logical form of A than that. And yet there must surely be a little more to the business. For if the pragmatic view, as I have sketched it, is correct, then we might just as well accept the Truncated Argument in its original formulation (with the predicate ‘ ... is equal to — ’) as formally valid: the Apollonian definition of

50 Or is it? I once heard an anthropologist speaking about the logic of kinship relations. Perhaps, from the point of view of some sciences, it would be fruitful and illuminating to treat kinshippredicates as logical constants? But what might the theorems of kinship logic be? Well, one theorem would be this: If anyone has two siblings, then at least three people have two siblings. (See G.J. Warnock, J.L. Austin (London, 1989), p.59.) 51 See further esp A.N. Prior, ‘What is logic?’, in his Papers in Logic and Ethics (London, 1976), pp.122–129.

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equality, and the consequent reformulation of the Argument in terms of identity, are idle manoeuvres. Here I may again quote de Morgan. He expressly considers the suggestion that of the two versions of the Truncated Argument — the original version and the rewritten or Apollonian version — the former is materially valid and the latter formally valid. What is the difference of the two syllogisms above? In the first case the mind acts through its sense of the transitiveness of ‘equals’: in the second, through its sense of the transitiveness of ‘is’. Transitiveness is the common form: the difference between equality and identity is the difference of matter. But the logician who hugs identity for its transitiveness, cannot hug transitiveness: let him learn abstraction.52

Thus de Morgan suggests that the two syllogisms are on a level: both are equally formal and both are equally material. And he also suggests that each of the two exhibits a more abstract form, viz: [33] xTy yTz Therefore: xTz — where ‘T’ may take the sense of any two-place verb which expresses a transitive relation, Those suggestions are intriguing — but they are to be rejected. First — as the Apollonian definition shows — , equality and identity are not on a level. Rather, equality can be defined as a determinate case of identity, viz. as identity of quantity or magnitude. (Thus equality specifies identity in the way in which, say, ‘codurability’ specifies equality: two events are ‘codurable’ if they last for an equal length of time.) Secondly, in introducing ‘T’ de Morgan abuses the notion of form. The form of a sentence is given by its structure, by its syntax. But de Morgan’s ‘T’ must be given a semantic characterization; for verbs expressing a transitive relation do not form a syntactical category — and hence they cannot mark a formal feature of a sentence, unless the notion of form is greatly modified.53 Yet de Morgan’s injunction, ‘let him learn abstraction’, is to the point. Consider the matter thus. Call a form (Fn) more general than a form (Fm) if everything of form (Fm) is also of form (Fn) but not vice versa. Now call (Fø) a highest form of an argument A provided that (i) A is valid in virtue of (Fø), 52

de Morgan, ‘On the syllogism’, p.79 n.2. Transitive verbs form a syntactic category; but transitive verbs do not all express transitive relations. 53

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67

and (ii) A exhibits no form which is more general than (Fø) and in virtue of which A is valid. Let us now stipulate that logical forms are highest forms: (FÆ) is a logical form of A if and only if it is a highest form of A. And let us further stipulate that logical constants are those constants which appear in logical forms. Or better: c is a logical constant relative to argument A if and only if c appears in some highest form of A. (Thus on this understanding of logical constancy, a word will be a logical constant relative not to a system S but to an argument A.) The Truncated Argument exhibits the form: (F) x is equal to z. y is equal to z. Therefore: x is equal to y. [34] But it is not formally valid in virtue of (F); and (F) is not a logical form of the Argument. For the Argument also — let us allow — exhibits the Apollonian form: (FØ) x is identical with z. y is identical with z. Therefore: x is identical with y. Now (FØ) is more general that (F) — and that is why (F) is not a logical form of the Argument. (FØ) is in fact — or so it seems — a highest form of the Argument. Hence ‘ ... is identical with — ’ is a logical constant — relative to the Argument. That way of understanding logical form and logical constants has certain disadvantages; for it surely does not correspond exactly to the traditional way. Thus — and trivially — every valid argument will have a highest form.54 Hence every valid argument is formally valid.55 And so we shall have to regard, say, the argument: Socrates runs. Therefore: Socrates moves as formally valid in virtue of the form: x runs. Therefore: x moves. 54

i.e. at least one highest form. And also at most one? That may sound plausible. But I know no way of proving that it is true; and in fact I cannot see why A should not exhibit two forms, (Fø) and (Fø*), each of which is a highest form. This will be so if, for example, extended Aristotelian syllogistic and extended Fregean predicate logic each offer distinct and satisfactory formalizations of the same arguments. 55 ‘Is there any consequence without form?’ (de Morgan, ‘On the syllogism’, p.79 n.2).

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And we shall take the predicate ‘ ... runs’ as a logical constant (relative to this argument).56 Yet the idea also has certain advantages, which may do something to commend it as a stipulative definition. Thus it ensures that logic is concerned with the most general and the most [35] abstract. Since there is no more general form to an argument than its logical form, logic is thereby determined to work at the highest level of generality. There will be valid argument-forms which do not fall within the province of logic; but for every such form there will be a more general form which logic will study. A second point may be more controversial. Logic is traditionally concerned not simply to display valid patterns of inference but also to explain such validities. Logic is a science, and — like any other science — it has an explanatory goal. That is why I have talked of an argument’s being valid in virtue of a form: the form somehow explains the validity of the argument. Consider again the Truncated Argument: (1) CA is equal to AB. (2) CB is equal to AB. Therefore: (3) CA is equal to CB. Why is the Argument valid? What explains or accounts for its validity? Evidently, nothing about the particular lines we happen to be talking about — for their names may be replaced or reconstrued without affecting the validity of the Argument. And by the same token, the Argument cannot be valid in virtue of referring to the relation of equality — for the designation of that relation may be replaced or reconstrued and the Argument remain valid. It seems plain that, if we follow out this line of thought, we shall reach a highest form of the Argument. Any valid argument, then, will be valid in virtue of a highest form, i.e. in virtue of a logical form. Hence, in studying logical forms, logic will study or expose the explanatory ground of an argument’s validity. On this view, the Truncated Argument is valid in virtue of, say, the form: (FØ) x is identical with z. y is identical with z. Therefore: x is identical with y. 56 May we not treat ‘ ... runs’ as a complex predicate, roughly equivalent to ‘ ... moves quickly on its feet’? Then there will be a more abstract form of the argument, viz: !Fx Therefore: Fx — where ‘!’ takes the sense of some adverbial phrase. But see below, p.[54].

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It is not merely that every argument of the form (FØ) is valid. Rather, (FØ) accounts for the validity of every argument which exhibits it57 — for the validity is explained precisely by reference [36] to the semantic features of the constants in (FØ). The Argument is valid because the relation of identity is symmetrical and transitive; it is valid because the sole constant in (FØ) has certain semantic features. But there is a possible objection to all that; for the notion of explanatoriness might be sceptically questioned.58 I said that in the Truncated Argument, the names of the particular lines ‘may be replaced or reconstrued without affecting the validity of the Argument’. And the implicit idea was this: the validity of the Argument cannot be explained by its possession of some feature ç if even without ç the Argument would be valid. (In general, the fact that Fx cannot explain why Gx if Gx would hold even if not Fx.) But this implicit idea — a sceptic may suggest — is incoherent. For it implies that the Argument might not have contained, say, the relation of equality. Yet that is absurd: the Argument could not lack the relation of equality — nor could it lack the referential expressions it actually contains. The argument: FD is equal to DE. FE is equal to DE. Therefore: FD is equal to FE is not the Truncated Argument equipped with a fresh set of referential names. It is a completely different argument (which, of course, shares many of its forms — and all its interesting forms — with the Truncated Argument). If that were right, then we should have undermined the thought which grounded the idea that logical form explains validity; and we should be inclined to doubt the coherence of any such idea. On this view of things, we may say that an argument A is valid — and we may add that A exhibits a form (FÆ) such that every argument of form (FÆ) is valid. Yet we may not add — it makes no sense to add — that A is valid in virtue of (FÆ). There can be no further fact, beyond the fact that all arguments of this form are valid, which is the fact that (FÆ) explains the validity of A. I shall not pursue those thoughts any further: I mention them because they will recur, in a slightly different guise, in Part V. [37]

57

And which exhibits no higher form. Note that some of the ancients similarly doubted the coherence of the (Aristotelian) notion of explanation in geometrical arguments: see Proclus, in Eucl 202.9–14. 58

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Systems of logic There is one clear notion of logical form whereby ‘FP’ is a logical form of the sentence ‘P’ relative to a system S provided that ‘FP’ contains only dummy letters and words which S takes as logical constants. There is a second clear notion of logical form whereby ‘FP’ is a logical form of ‘P’ relative to an argument A provided that ‘FP’ is a highest form of ‘P’ relative to A. Neither of those clear notions answers exactly to what most logicians, ancient and modern, have had in mind — or have taken themselves to have had in mind — when they have spoken of logical form and logical constants. Is there a third clear notion which will better capture their ideas? Suppose a logician were told that the argument: Socrates runs. Therefore: Socrates moves is formally valid in virtue of the logical form: (F) x runs. Therefore: x moves. Suppose, further, that he were therefore urged to make room for this argument, and its associated logical form, in his logical studies. He would surely be unimpressed. He would perhaps allow that the argument is valid, and formally valid, in virtue of the form (F). He would perhaps allow that, in a perfectly intelligible sense, ‘ ... runs’ is a logical constant relative to the argument. He would no doubt also recognize that there are very many arguments which exhibit forms similar to (F) — for example: Socrates breathes. Therefore: Socrates lives or: Socrates thinks. Therefore: Socrates exists. But none of those admissions amounts to a confession that (F) is of any concern to a logician. [38] Why not? Because (F) lacks any systematic interest. Logic is not simply the business of analysing valid arguments, nor even of tabulating the highest forms of valid arguments. It is also a systematic discipline. It builds theories and it derives theorems. Now compare ‘ ... runs’ with, say, ‘ ... is identical with — ’. If you take ‘ ... is identical with — ’ and add it to predicate logic as a

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new logical constant, then you will be able to express a vast new range of thoughts and to prove a vast new range of theorems. Any logical tiro is familiar with the fact. But add ‘ ... runs’ as a new constant, and what do you get? Nothing — or nothing worth thinking about.59 That suggests a third, and hybrid, notion of logical form. Let us say that, in this third sense, (FÆ) is a logical form of an argument A provided that (i) (FÆ) is a highest form of A (in the sense explained earlier), and (ii) every symbol in (FÆ) is either a dummy letter or else a logical constant relative to some suitably elaborate system S. On that account of logical form, not all valid arguments will be formally valid. For some arguments will surely have no form which satisfies the two conditions. Or rather (since every argument trivially has a highest form) there will be some arguments whose highest forms contain non-logical constants, words which are not taken as constants in any suitably elaborate system of logic. A plausible candidate for this status is: Socrates runs. Therefore: Socrates moves. This third account of logical form seems likely to capture more or less all and more or less only those features of arguments which most logicians are more or less happy to count as formal features. And here is the rub. ‘More or less’ is vague, and ineliminably so. For the characterization of logical form essentially invokes the idea of a ‘suitably elaborate’ system, and that idea is irremediably vague. Thus is: x would rather that p than that q. Therefore: it is not the case that x would rather that q than that p. [39] a logical form? The answer depends on whether ‘ ... would rather that — than that ***’ is taken as a logical constant in a suitably elaborate system of logic. In other words, the answer depends on whether or not preference logic is a suitably elaborate system. Is it? I cannot think that there is an answer to the question. Pragmatism, of a Tarskian variety, is the appropriate response. Some may find that perfectly palatable. Vague predicates are, after all, an ineradicable feature of natural language; and why should it be disturbing to find that the predicate ‘ ... is a logical constant’ is vague? Others will wince. I leave the issue open. 59

See above, p.[31], on ‘fraternal’ logic. — You will, of course, get infinitely many ‘new’ theorems; but these will simply be instantiations, for the predicate ‘ ... runs’, of theorems already proved quite generally for any predicate.

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This Part of my chapter began with a mediaeval text; and it has ended a long way from anything we can find in Buridan. It is time to return to antiquity.

III

Form and matter — the terminology The mediaeval distinction between material and formal consequence derives ultimately, both in name and in substance, from ancient texts.60 Form and matter, r   and oºÅ, are Peripatetic twins, and the mediaeval distinction — and hence the modern notion of ‘formal’ logic — comes in the end from Aristotle. Those claims are indisputable — but they are vague. If we inquire more closely into the business, dispute and controversy appear. For some historians of logic have claimed that the later Peripatetics, at least, had a clear understanding of the notion of [40] logical form and hence of the essential nature of formal logic;61 whereas others have maintained, to the contrary, that the modern ideas of formal validity and of the logical form of an argument have no genuine counterparts in the ancient texts.62 In fact — and predictably — , the truth lies dully between the two exciting extremes; and if we are to see just 60 For the links between the ancient and the mediaeval accounts, see esp S. Ebbesen, Commentators and Commentaries on Aristotle’s Sophistici Elenchi, Corpus Latinum commentariorum in Aristotelem Graecorum VII (Leiden, 1981), vol. I, pp.95–101; cf Pinborg, Logica e Semantica, pp.74–80. For the importance of the distinction in Arabic texts, see Zimmermann, Al-Farabi’s Commentary, pp.XXXVIII–XLI. (But Zimmermann claims too much for Farabi. ‘Striking an individual note in the very first sentence of his Commentary al-Farabi says that the De Int. is about the ‘composition’ [ta’lif ], not the ‘matter’ [madda]), of propositions. I do not find this opposition of terms, which recurs as a kind of leitmotiv throughout the work, in the Greek commentaries; and the fact that it is usually in criticizing his predecessors that he invokes it confirms that here we have a new departure in the exegesis of the De Interpretatione’ (pp.XXXVIII–XXXIX), Not entirely new, I think — and in any case, the opposition of terms which al-Farabi deploys was thoroughly familiar to the Greek commentators on the Analytics.) 61 Thus the Peripatetic commentators ‘show us that they had an excellent conceptual grasp of the essence of what is today called ‘‘formal’’ logic’ (Lee, Die griechische Tradition, p.38); and Alexander had ‘a clear insight into the essence of formal logical laws’ (I.M. Bochen´ski, Formale Logik, Orbis Academicus III 2 (Freiburg/Munich, 1956), p.157). 62 Thus ‘it seems that neither the Stoics nor the Peripatetics ever say that an argument is valid because of its logical form, which would be strange if they actually had thought that the validity had to be explained as being due to the form. And even when it is said that a certain form of argument is valid for every matter (i.e. for every suitable substitution of the letters), this does not seem to be the same as saying that the validity is due to the form’ (M. Frede, ‘Stoic vs. Aristotelian syllogistic’, AGP 56, 1974, 1–32 [¼ his Essays in Ancient Philosophy (Oxford, 1987), pp.99–124 and 368], on p.4 [p.103]). (In a note, Frede allows that there are apparent counter-examples to his thesis — he cites

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73

how and where it lies, we must proceed by a plodding examination of the relevant texts. Aristotle himself only once applies the concepts of matter and form to the syllogism: at Phys ´ 195a18–19 he observes laconically that ‘the hypotheses for the conclusion’.* (He uses the word ‘hypotheses’ here to designate the premisses of the syllogism.) The later commentators pick up the point. Alexander, it is true, was not happy with it,63 and he does not make use of it in his own logical writings. But Philoponus had no qualms: he repeats the idea that the premisses of a syllogism are, as it were, the stuff out of which the conclusion is made.64 Yet whatever we make of Phys 195a18–19, the text has nothing to do with the distinction between formal and material validity. [41] Several other logical applications of the twin concepts are found in the later commentators: thus the modal status of a proposition is called its ‘matter’;65 or the subject of a proposition stands to the predicate as matter to form;66 or an unquantified proposition is matter, the quantifier form;67 and so on.68 None of those applications of the Aristotelian distinction is illuminating; and none is relevant here. Alexander preferred to invoke matter and form in a different logical context; and it is his preferred distinction between logical matter and logical Boethius, hyp syll II ii 4–5, iii 6, iv 2 [see below, p.[42]] — , and says that these passages ‘would have to be dealt with individually’ (p.368 n.3).) I am not sure exactly what Frede concedes and what he denies. But the main point appears to be this: the ancient logicians do not ever say of an argument that it is valid because of its form. Now, taken absolutely literally, that may well be true; at least, I have not come across a text in which a conclusion is said ı
ªŁÆØ Øa e r   vel sim. But there are, as Frede allows, a few passages which say something very close to that (e.g. that a conclusion is drawn Øa c
º Œ
); and there are numerous passages which imply something like it (e.g. passages which contrast syllogisms with arguments which conclude Øa c
oºÅ
). My own reasons for qualifying the enthusiastic view exemplified in the last footnote are not Frede’s. Rather, first, I hold that the use of the matter/form distinction by Alexander (and the later commentators) is not always coherent [see below, pp.[58–65]]. And secondly, I doubt if the ancients had any clear or coherent notion of form. They had (contra Frede) a rough and ready notion of formal validity; but (contra Lee) they had no precise and rigorous notion. (Of course, if the reflections in the previous Part of this paper are correct, then the ancients were in this respect no worse off than most moderns.) * ... ŒÆd ƃ  ŁØ  F ıæÆ  ‰ e K y ÆYØ KØ
. 63 See the passage quoted by Simplicius, in Phys 320.1–10. 64 See e.g. in APr 6.10–14; 32.31–33.2. The idea survived to become a commonplace of traditional logic: see e.g. § 59 of Kant’s Logik. 65 See below, pp.[44 and 48]. 66 e.g. Philoponus, in APr 65.11–13; [Ammonius], in APr 71.14–16. 67 e.g. Ammonius, in Int 111.19–23. 68 For yet other uses of matter and form, see e.g. [Ammonius], in APr 68.33–69.11; Philoponus, in APr 6.2–3 (cf 10.18); 44.24–26; 66.7–26.

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form which is to the present point.69 The idea first appears early in Alexander’s commentary on the Prior Analytics: The figures are like a sort of common mould. You may pour matter into them and shape the same form for different matters. Just as, in the case of moulds, the matters fitted into them differ not in respect of form or figure but in respect of matter, so too is it with the syllogistic figures. (in APr 6.16–21)*

Alexander says no more than that to explain what distinguishes the form from the matter of an argument. Similarly, the distinction enters his commentary on the Topics in its first pages (in Top 2.1–3.4) — and again, there is no serious explanation. After their introduction, the concepts are used with frequency and without apology throughout the commentaries. The twins reappear in the later Peripatetic commentators. Ammonius presents them in a cautious manner near the beginning of his commentary on the Prior Analytics: In every syllogism there is something analogous to matter and something analogous to form. Analogous to matter are the objects themselves by way of which the syllogism is combined, and analogous to form are the figures. (in APr 4.9–11)**

As this passage suggests, Ammonius does not greatly like the term [42] ‘oºÅ’; and to convey the Alexandrian distinction he will in fact more often employ the word ‘æAªÆ’.70 But his pupil Philoponus was content with ‘oºÅ’, and he uses ‘oºÅ’ and ‘æAªÆ’ as equivalents (in APr 9.6). In Ammonius, the æªÆÆ contrast not only with the form or r   but also with what he calls ‘bare rules without objects’.71 Again, the ‘nature of the objects’ contrasts with the ‘force of the expressions’ (e.g. in Int 113.13–15); and matter contrasts with the ‘force of the propositions’ (in Int 272.24–25). Philoponus contrasts the matter of a syllogism with its ıº Œ (in APr 69 On Alexander’s use of matter and form in logic, see esp Lee, Die griechische Tradition, pp.38–44. * fiø ªæ Ø
Ø Œ Ø
fiH a åÆÆ  ØŒ
K
x  Ø
K
Ææ Æ
Æ oºÅ
r   Ø I
ÆÆŁÆØ ÆPe
Kd ÆE ØÆç æ Ø oºÆØ
‰ ªaæ Kd H
ø
H
ÆPH
ØÆç æa P ŒÆa e r   ª
ÆØ ŒÆd e åBÆ  E K
Ææ Ç 
Ø Iººa ŒÆa c
oºÅ
, oø c ŒÆd Kd H
åÅø
H
ıºº ªØØŒH
. ** K
Æ
d ıºº ªØfiH e 
 KØ
I
º ª
oºfi Å e b YØ
oºfi Å b
s
I
ƺ ªE a æªÆÆ ÆPa Ø z
› ıºº ªØe ºŒÆØ, YØ b a åÆÆ. 70 Alexander too occasionally uses ‘æAªÆ’ (e.g. in APr 295.1; 301.12–13); and he takes this usage from Aristotle (APr ` 43b3–4). 71 See in APr 11.3; cf e.g. Philoponus, in APr 46.29. The phrase ‘łØº d ŒÆ

’ comes from Plotinus: enn I iii 5. Perhaps Ammonius’ caution in using the word ‘oºÅ’ also finds an explanation in Platonic thought.

Logical form and logical matter

75

321.3; 349.30), or with its Iªøª (321.9), or with the proposition ‘itself’ (51.2–4; 83.23–24), or with ‘the necessity of the propositions’ (75.17–20); and, equivalently, he contrasts the terms or ‹æ Ø with the propositions (75.25) or with their ıº Œ (75.28). The Ammonian scholia contrast matter and º Œ.72 Boethius provides Latin parallels. In his de hypotheticis syllogismis he invokes the Peripatetic distinction in a variety of ways: propositionis ipsius conditio contrasts with rerum natura (II ii 4); propositionum complexio with rerum natura (II ii 5); complexionis natura or figura with termini (II iii 6; iv 2); complexionis natura with terminorum proprietas (II iv 3; x 7; III vi 5); complexio with termini (II xi 1).73 Boethius is dependent on Greek sources,74 and his terminology largely translates their terminology. Thus the later authors used a variety of linguistic turns. But it would be rash to look for any substantial difference behind the linguistic fac¸ade. Boethius and the later Greeks adopted and deployed an established and apparently uncontroversial distinction. How the distinction was referred to and by what names it was called were questions of taste and style. Alexander too had taken the thing for granted; and we must [43] infer from his commentaries that earlier Peripatetics had applied the concepts of matter and form to logic. On independent grounds we may believe that Alexander’s teacher, Herminus,75 had probably spoken of the form and matter of arguments.76 So far as I know, there is no other evidence for the use of matter and form in logical theory before Alexander: it is not found in Aristotle’s own works; nor is there any text ascribing it to Theophrastus or Eudemus, or to Boethus or Aristo. But the silence proves little, and Alexander’s attitude shows that by his time it was already thoroughly familiar.77

72

See e.g. [Ammonius], in APr 70.12, cited below, p.[80]. Note also the interesting passage at in Cic Top 360.25–28 Orelli, where ‘res ’ contrasts with ‘tractatus ’. At in Cic Top 327.11–19, forma and materia are distinguished in the account of definitio. 74 See e.g. J. Barnes, ‘Boethius and the study of logic’, in M. Gibson (ed), Boethius (Oxford, 1981), pp.73–89 [reprinted below, pp.666–682]. 75 On whom, see P. Moraux, Der Aristotelismus bei den Griechen II, Peripatoi 6 (Berlin, 1984), pp.361–363. 76 See [Ammonius], in APr 39.32: I say ‘probably’ because [Ammonius] is paraphrasing rather than quoting, and because we cannot be sure of the reliability or the accuracy of his paraphrases. (See below, p.[80].) 77 Bochen´ski is therefore wrong when he says (Formale Logik, p.157) that ‘Alexander seems to have been the first to give an explicit account of the difference between form and matter ’. 73

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If we ask why some Peripatetic scholars thought to apply matter and form to logic, we can give no worthwhile answer. Was the idea part of a general attempt to systematize Aristotle, so that his customary analytical concepts should be applied in every part of his philosophy? Was it rather reflexion on the Analytics themselves (perhaps on the sense and function of Aristotle’s dummy letters78) which encouraged the invocation of matter and form? Was it the influence of the Stoics, whose own distinction between an argument or º ª  and a mode or æ   might have put a Peripatetic in mind of matter and form?79 There is no evidence from which to answer such questions.

Form and matter defined No doubt the first philosopher to speak of logical matter and logical form explained what he had in mind. Alexander, as I have said, does not. Ammonius might be thought to do so. The distinction appears in his commentary on the de Interpretatione, in a passage where he is discussing the different relations or åØ [44] which may hold between the subject and the predicate of a sentence. Those who are interested in the technical study of these things80 call the relations the matters of the sentences, and they say that they are either necessary or impossible or possible. The explanation of the latter names is evident; and they determined to call the relations in general matters because they appear together with the objects which underlie the sentences and they are taken not from our thinking or predicating them but from the very nature of the objects. ... Now since the objects underlie the sentences, and since we say in general that what underlies something either is the matter or has the status of matter for that which it underlies, for that reason they determined to call these things matters. (in Int 88.17–23, 26–28; cf 215.9–16)* 78

See below, p.[51]. See below, pp.[65–66]. 80 It is not clear to whom Ammonius is referring; but the anonymous mode of reference should not be read as derogatory: cf the similar reference to the technical canons developed by Proclus at in Int 181.31 (cf 223.18). * ÆÆ b a åØ ŒÆº FØ
x  KºÅ B  ø
å
º ªÆ H
æ ø
oºÆ, ŒÆd r
ÆØ ÆPH
çÆØ c
b
I
ƪŒÆÆ
c
b I
Æ
c
b K
å 
Å
. ŒÆd  ø
b
H
O
ø
ÆNÆ æ çÆ
, ‹ºø b ŒÆºÆØ a åØ ÆÆ oºÆ MøÆ
ܯ  E  ί
Ø ÆE æ Ø æªÆØ ı
Æ
ÆçÆ

ÆØ ŒÆd PŒ Ie B æÆ Nø j ŒÆŪ æÆ Iºº I ÆPB B H
æƪø
ºÆ

ÆØ çø
... Kd s
a æªÆÆ ÆE æ Ø
 ί
ÆØ, e b  Œ

Æ
Æå F j oºÅ
r
Æ çÆ
j oºÅ º ª
åØ
æe KŒE
fiz  ŒØÆØ, Øa  F oºÆ ÆPa æ ƪ æØ
MøÆ
. 79

Logical form and logical matter

77

Here Ammonius may seem to hint at a general characterization of the matter — and hence of the form — of a sentence. For he appears to suggest that some parts or aspects of sentences ‘are taken ... from our thinking or predicating’, whereas other parts or aspects are identical with, or depend on, the objects which underlie the sentences; and the idea is that the former parts or aspects are formal, the latter material. Now there is a coherent distinction behind those curious words.81 But it is not the distinction we want. For Ammonius’ distinction is a distinction between what is explicitly said in a sentence and what is in fact true of the items mentioned in the sentence. The ‘matters’ he has in mind are not items in a sentence, nor even items named or expressed by items in a sentence. Thus the åØ holding between Socrates and movement, if Socrates is moving, is the åØ of contingency. Hence the matter of: Socrates moves. is contingent. But the contingency is not expressed in the sentence itself. Hence Ammonius is not making a distinction between parts or aspects of a sentence, and his distinction does [45] not allow us to divide sentences into formal and material components. No other passage in Ammonius appears to offer any general elucidation of logical matter and logical form. But his penchant for the word ‘æAªÆ’ may offer indirect help. He prefers ‘æAªÆ’ to ‘oºÅ’, and he indicates that the æªÆÆ underlying a sentence are the correlates of its significant expressions or ÅÆ
ØŒÆd çø
Æ (in APr 1.3–9). Hence — or so one might optimistically surmise — there is a clear definition of ‘oºÅ’, and hence of ‘r  ’ to hand: the matter of a sentence consists of, or is determined by, all and only its significant expressions; the remainder of the sentence constitutes its form.82 That is helpful to the extent that the concept of a significant expression is determinate.83 In Ammonius the notion is sometimes given content by the contrast with insignificant expressions or çø
ÆØ ¼Å Ø, examples of which are nonsense words such as ‘ºıæØ’ and ‘ŒØ
Æł ’ (in APr 1.6–7). But 81

See below, p.[48]. ‘The use of æAªÆ shows in the present context that the reference or meaning of the words is irrelevant to the existence of the syllogism ... The positive conceptual determination of the nonformal, material, elements in a concrete syllogism runs like this: The meaningful words are the matter of the syllogism’ (Lee, Die griechische Tradition, p.41: I have translated Lee’s ‘Bedeutung’ as ‘meaning’). 83 As Lee recognizes: Die griechische Tradition, p.42 n.33. 82

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Logical Matters

then the whole of every sentence will be material — there will be no formal or logical constants at all, since no component of an intelligible sentence is a nonsense word: all the component expressions of a sentence will be significant expressions and hence material. Elsewhere, Ammonius draws a different distinction. He distinguishes between the parts of a sentence which are parts of the ºØ and the parts which are parts of the º ª  (in Int 12.30–13.18). Now the items which are parts of the º ª  are those expressions which signify æªÆÆ — that is to say, they are items which signify certain natures, or simply persons, or activities or affections, or some combination of those things, as do names and pronouns and verbs and participles. (in Int 11.9–11)84

Other expressions — connectors, for example, or adverbs — do, of course, have a meaning: they are [46] not nonsense expressions. But they do not signify objects: either they signify relations among objects (in Int 11.14–16) or else they do not signify anything ‘in themselves [ŒÆŁ’ ÆÆ]’ (12.13–15) but only in combination with other items. Thus we may develop an Ammonian specification, and an Ammonian explanation, of the material and formal elements in a sentence. An element in a sentence is material provided that it is either a noun or a verb (better: either a subject or a predicate). All other elements are formal. And material elements are material insofar as they signify or refer to the objects which underlie or make up the stuff of the sentence. Ammonius’ account of logical matter and logical form is Platonic in inspiration;86 but it can, of course, be expressed in impeccably Peripatetic terms. The logical syntax of the Peripatetics takes as central the generic form: AxB — where ‘A’ and ‘B’ are dummy letters which take the sense of general terms, and ‘x’ is a dummy letter which takes the sense of a term-connective. Since there are four term-connectives, there are exactly four specific Peripatetic forms, viz: AaB, AeB, AiB, AoB. 84 a 
KØ ÅÆ
ØŒa ç
Ø
ø
j ±ºH æ ø
j K
æªØH
j ÆŁH
X Ø
  ø
ıº ŒB, ŒÆŁæ Z
  ήd I
ø
ıÆ ŒÆd ÞBÆ ŒÆd  å. — Names (proper names, common nouns, and adjectives) signify natures; pronouns signify mere persons (where ‘person’ has its grammatical sense); verbs and participles signify actions and affections. 86 See in Int 13.9–18; cf Plutarch, Plat quaest 10, 1009B–1011F.

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79

Relative to this syntax we may give a perfectly clear account of Ammonius’ conception of logical form and logical matter. If a sentence S exhibits the form ‘AxB’, then those elements in S which correspond to ‘A’ and ‘B’ are the material elements of S, and those elements which correspond to ‘x’ are formal. Or again, the item in S which corresponds to ‘x’ is a logical constant: all other items in S are non-logical. Take the sentence ‘All men are mortal’: ‘man’ and ‘mortal’ are the material components, and it is a material fact about the sentence that it deals with men and mortality; ‘AaB’ is a form of the sentence, and it is a formal fact [47] about it that it is universal and affirmative (and also, say, that it contains exactly two terms).87

Adsentences Evidently, that will be satisfactory as a general account of matter and form only to the extent that two conditions are met: first, that the sentences with which logic is concerned exhibit the generic form ‘AxB’; and secondly, that the valid arguments with which logic is concerned depend for their validity on the fact that their component sentences exhibit that generic form. The second of the two conditions — or rather, one aspect of the second condition — will in effect be the subject of Part V of this chapter. Here the first condition requires a few more words. For, as I have formulated it, it does not correspond exactly to the Peripatetic view. At in APr 27.27–28.30 Alexander argues that certain ‘modifiers’ or æ  Ø are formal features of syllogisms; for the modal modifiers or modal operators — ‘necessarily’, ‘possibly’, and so on — belong to the form and not to the matter of the sentences in which they appear.88 Alexander does not explain what he means by ‘æ  ’.89 Ammonius, however, devotes some pages to 87 When the account is extended to cover arguments as well as single sentences, then the formal features will include the mode of the syllogism (see e.g. Alexander, in APr 190.7–9) and its figure. (Compare the Latin use of ‘forma ’ for ‘åBÆ’: e.g. Martianus Capella, IV 408–409 (Apuleius, in his int, always uses ‘formula ’ for ‘åBÆ’: e.g. ix [203.11]). Note that Capella elsewhere uses ‘forma’ for the Stoic ‘æ  ’: see IV 420 — where he confusingly remarks that when you use a forma, as opposed to a metalogical description of a argument-schema, you can grasp the inference ipsis rebus. 88 Further on Peripatetic æ  Ø, see J. Barnes, ‘Ammonius and adverbs’, in H.J. Blumenthal and H.M. Robinson (eds), Aristotle and his Successors, Oxford Studies in Ancient Philosophy suppt (Oxford, 1991), pp.145–164 [reprinted below, pp.621–638]. 89 Evidently, the theory of æ  Ø was already familiar to Alexander; and I suppose that it was developed in the renascent Peripatos of the first century bc. (For it is not found in Aristotle, nor in the early Peripatetics; and I do not find this use of ‘æ  ’ any non-Peripatetic texts — it is not,

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Logical Matters

æ  Ø in his commentary on the de Interpretatione, and he begins with a definition: [48] A æ   is a word signifying how the predicate holds of the subject — e.g. ‘quickly’ when we say ‘The moon completes her revolution quickly’. (in Int 214.25–27)*

As examples of æ  Ø Ammonius offers ‘quickly’, ‘finely’, ‘completely’, ‘always’. It is easy to conclude that æ  Ø are adverbs. Yet adverbs standardly modify verbs,90 whereas Ammonius asserts that æ  Ø say ‘how the predicate holds of the subject’. So it is better to parse æ  Ø as ‘adsentences’ rather than as adverbs in the strict sense. That is to say, æ  Ø may be construed as sentence-forming operators on sentences. That construe does not do full justice to Ammonius’ text; for he takes ‘ŒÆºH’ in: øŒæÅ ØƺªÆØ ŒÆºH as a paradigm æ  ; yet it can hardly be construed as modifying the sentence øŒæÅ ØƺªÆØ rather than the verb ‘ØƺªÆØ’. But I am not concerned to elucidate Ammonius; and I shall ignore those difficulties. Alexander’s view that modal æ  Ø are formal rather than material elements in sentences raises two questions. One of these will take us briefly back to the passage of Ammonius which I cited in the previous section.91 It arises from a position which Alexander had taken earlier in his commentary on the Analytics. He had remarked that the various species of syllogism — demonstrative, dialectical, sophistical — are distinguished from one another in virtue of their matter: the matter of a demonstrative syllogism must be necessary, that of a dialectical syllogism reputable, and so on.92 Thus we might construct a pair of arguments, one demonstrative and the other

e.g., in the grammarians.) The thing reappears in later logical texts (e.g. Blemmydes, epit log xxvii ¨ bersetzung von Boethius’ ‘De hypotheticis syllogismis’, 12–13 (cf D.Z. Nikitas, Eine byzantinische U Hypomnemata 69 (Go¨ttingen, 1982), pp.92–94); but that adds nothing to our knowledge of the earlier history of these æ  Ø. * æ   b
s
KØ çø
c ÅÆ
ıÆ ‹ø æåØ e ŒÆŪ æ 

fiH  ί
fiø, x
e Æåø ‹Æ
ºªø
º
Å Æåø I ŒÆŁÆÆØ: 90 That is how the Greek grammarians explain KØææÆÆ: see e.g. Apollonius Dyscolus, adv 120.6–122.34. 91 See above, p.[44]. 92 See in APr 12.23–24; 13.12–20; cf e.g. in Top 2.15–3.4; 15.20–25; Ammonius, in Int 88.12–28; in APr 19.15–17; anon Heiberg, 64 [47.25–48.12].

Logical form and logical matter

81

dialectical, which ‘do not differ at all in their form’ (both are standard syllogisms in Camestres) but which do differ in respect of their matter (in Top 2.26–3.4). And that material difference consists, in part at least, in [49] the different modal status of the component sentences of the two arguments. Now at in APr 27.27, Alexander observes that Aristotle himself treats the modal status of sentences as an intrinsic part of syllogistic theory — and hence, by implication, as something formal rather than material. Is Aristotle not wrong in discussing material aspects of sentences in the purportedly formal discipline of logic? To answer the question, Alexander distinguishes the modal status of a state of affairs from the æ   or modal operator which may be affixed to a sentence, whatever the status of the state of affairs to which it adverts. Consider the three sentences: (1) Socrates moves. (2) The sun moves. (3) Necessarily, Socrates moves. Here (1) and (2) are alike in form and differ in matter; in particular, the matter of (1) is contingent whereas the matter of (2) is necessary. Sentence (3) differs from (2) both in form and in matter. It differs from (1) in form alone; for the æ   ‘necessarily’ is a formal feature present in (3) and absent in (1).93 The second of Alexander’s questions is more interesting. The modal operators, as I said, qualify as formal elements of sentences. But there are many other æ  Ø — innumerably many, according to Ammonius (in Int 214.29–31) — and most of them are of no logical interest and constitute material rather than formal elements of the sentences which they grace. Why is that so? What makes the modal æ  Ø formal and such æ  Ø as ‘finely’ and ‘clearly’ material?94 Why, in other words, is ‘necessarily’, but not (say) ‘plausibly’, a logical constant? 93

The examples come from Ammonius (Alexander offers none), and they are specifically designed to show how the addition of a æ   may affect the truth-value of a sentence — for (1) is (suppose) true, but (3) is false. Ammonius (in Int 215.7–28) raises Alexander’s question, and he answers it in the same way (see above, p.[44]). 94 No text explicitly says that ‘ŒÆºH’ and the rest are material rather than formal; and it is, I suppose, just possible that Alexander and Ammonius might have regarded all æ  Ø as formal. But in that case the connexion between form and logic would be severed; and in any event, the real question would remain, in a different guise — for now we should simply ask ‘Why is ‘‘ÆçH’’, though a formal element of its sentences, nonetheless not a logical constant?’

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Logical Matters

But before turning to that question, let me draw an immediate moral. For the Peripatetic view on æ  Ø shows that there can be [50] no purely syntactical account of the difference between matter and form. All æ  Ø belong to the same syntactic category: they are all adsentences. Yet not all æ  Ø constitute formal elements of their sentences.95 Ammonius’ simple syntactical test for form and matter is inadequate to a language which includes adsentences; and the test cannot be revised to accommodate adsentences. (Nor will Ammonius’ semantical test help. For some adsentences are not formal; yet no adsentences signify objects.)

Form and universality Then why are only modal æ  Ø formal? According to Alexander, it is because they mark or induce a certain generality or universality: Regardless of the matter in question, Aristotle adds the æ  Ø themselves to the sentences and constructs universal proofs about them, thereby proving that the difference among the syllogisms depends not on this or that matter but on the added æ  . (in APr 28.13–16)*

Modal æ  Ø somehow allow for ‘universal proofs’. Ammonius seems to make the same point. He asserts that Aristotle deals only with the modal æ  Ø because they are ‘both most universal and most appropriate to the objects’.96 And in general, there is a close connexion between formal features and universality. Thus, having shown that o-propositions do not convert,97 Alexander makes the following observation:

95 ‘Perhaps all genuine adsentences are formal, or logical constants? ‘‘ŒÆºH’’, of course, is not formal — but then it is not, pace Ammonius, a genuine æ  ’. That will not do. There are numerous genuine adsentences which no ancient logician would have counted as a formal element (e.g. ‘Hopefully ... ’ (in the American sense), ‘God knows if ...’, ... ). * åøæd ª F
B oºÅ ÆP f  f æ  ı æ ØŁd ÆE æ Ø ŒÆŁ ºØŒa K ÆPH
a Ø  ØEÆØ, P Ææa e 
 c
oºÅ
j 
 r
ÆØ ØŒ
f c
ØÆç æa
ªØ

Å
H
ıºº ªØH
Iººa Ææa e
æ Œ

æ 
. 96 See in Int 214.31–215.3. — Stephanus, in Int 53.15–27, has a different answer: he holds that all æ  Ø are ‘summed up [I
ÆŒçƺÆØ 
Ø: 53.15]’ under the modal æ  Ø, so that in effect all æ  Ø are formal and encompassed in Aristotle’s modal logic. That leads Stephanus to such egregious claims as that in ‘Socrates likes it a lot [
ı]’ the æ   ‘a lot’ signifies possibility (53.22). 97 i.e. from AoB you may not infer BoA.

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83

If certain propositions can sometimes be taken and found to hold true in their conversions, what I have said is not thereby overturned. For in all cases of this sort it is enough to refute a universal [51] claim if you prove that it does not hold in some cases. For what is not true in all cases converts not because of its proper nature but because of the peculiarity of a particular matter. (in APr 30.21–26)*

In some cases in which AoB holds, BoA also holds; but in some cases it does not — and that is enough to show that AoB does not convert. For what holds in some cases only, holds ‘because of the peculiarity of a particular matter’. It does not hold because of the ‘proper nature’ of the propositions, i.e. because of their form or formal structure. Universality is determined by formal considerations — and the science of logic is and must be concerned only with universal features. Hence the crucial connexion between the form of an argument and its status as a syllogism: Conversions, and in general inferences in the figures, hold not because of the peculiarity of the matter, as I have already said (for this is different in different cases), but because of the very nature of the figures. That is why the proofs in these cases are universal. (in APr 35.6–9)**

Or again: Syllogistic are those pairs of premisses which conclude to something from necessity; and they are the pairings in which the same holds in the case of every matter. (in APr 208.16–18)98

Or again, in his presentation of syllogistic, Aristotle regularly uses dummy letters rather than concrete terms. Alexander explains the practice: He conducts his exposition by way of letters in order to indicate to us that the conclusions hold not because of the matter but because of the figure and the combination of the propositions and the mood. For such-and-such is concluded syllogistically not because the matter is thus-and-so but because the premiss-pairing is

* PŒ Y Ø
    K
ÆPÆE ı
ÆºÅŁı 
ÆØ ºÅçŁE
K
ÆE I
Øæ çÆE, Øa  F e NæÅ

ç H
ØƺºÆØ
ƒŒÆ
e
ªaæ Kd 
ø
H
 Ø ø
æe I
ÆæØ
 F ŒÆŁ º ı ŒÆd e Kd Ø
e EÆØ c oø å

a ªaæ c Kd 
ø
ı
ÆºÅŁı 
Æ P Ææa B NŒÆ çø e I
ØæçØ
åØ Iººa Ææa c
Ø
e oºÅ NØ ÅÆ. ** ƃ ªaæ I
Øæ çÆd ŒÆd ‹ºø ƃ ŒÆa a åÆÆ ı
ƪøªÆd P Ææa c
B oºÅ NØ ÅÆ ª

ÆØ, ‰ r 
XÅ (ÆoÅ b
ªaæ ¼ºº  Iºº Æ), Iººa Ææ ÆPc
c
H
åÅø
çØ
. Ø ŒÆŁ ºØŒÆd ƃ Ø K ÆPH
. 98 ıºº ªØØŒÆd b ƃ ıÇıªÆØ ÆyÆØ Æƒ K I
ªŒÅ Ø ı
ª ıÆØ
 ØÆFÆØ b K
Æx  Kd Å oºÅ ª
ÆØ e ÆP . cf e.g. in APr 52.19–25; 55.21–23; 56.16–27; 227.7–9.

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Logical Matters

of a certain sort. Thus the letters indicate that this will be the conclusion universally and always and in the case of every assumption. (in APr 53.28–54.2)99 [52]

Logic is a science, and sciences are concerned with the universal. Logic deals with inferences which hold universally. Hence logic deals with inferences whose validity is determined not by the matter of their propositions but by their form and figure. Alexander speaks as though it is form which guarantees universality. And so it is. But we may prefer to look at the business from the other end: if we want to determine which features of a sentence are formal, let us look and see which are universal. The case of the æ  Ø is clear: why is ‘necessarily’, but not ‘finely’, a formal feature of the sentences in which it appears? Simply because the former and not the latter induces universality. But what does that mean? In what sense may a æ   ‘induce universality’? Alexander implies that the crucial fact is that there are ‘universal proofs’ about — or perhaps involving — modal æ  Ø.100 But it seems plain that there are universal rules bearing upon, say, the æ   ‘finely’ or ‘ŒÆºH’. Thus from: øŒæÅ ØƺªÆØ ŒÆºH we may infer: øŒæÅ ØƺªÆØ And we may do so in virtue of the general rule that from ‘(ŒÆºH-F)x’ we may infer ‘Fx’. Similarly for many other æ  Ø. Perhaps, then, the modal æ  Ø induce universality in a different way. When Ammonius appeals to the universality of the modal æ  Ø he almost certainly has something different in mind. For he is almost certainly alluding to the fact, remarked upon by the grammarians, that some adverbs or KØææÆÆ are ‘particular’ rather than ‘universal’. The grammarians mean that some adverbs are restricted in their range of application. Take the adverb ‘yesterday’: you may intelligibly say ‘It rained yesterday’, but you may not say ‘It will rain yesterday’.101 Then to say that the modal æ  Ø are universal, or 99 Kd  Øåø
c
ØƌƺÆ
 ØEÆØ bæ  F K
ÆŁÆØ E
‹Ø P Ææa c
oºÅ
ª
ÆØ a ıæÆÆ Iººa Ææa e åBÆ ŒÆd c
 ØÆÅ
H
æ ø
ıº Œc
ήd e
æ 

P ªaæ ‹Ø l oºÅ, ı
ªÆØ ıºº ªØØŒH  , Iºº , ‹Ø ıÇıªÆ  ØÆÅ. a s
 ØåEÆ  F ŒÆŁ º ı ŒÆd Id ŒÆd Kd Æ
e  F ºÅçŁ
   Ø F
ŁÆØ e ıæÆÆ ØŒØŒ KØ
. cf in APr 125.26–28; 379.14–380.27; 414.9–10; 415.10–12; and e.g. Philoponus, in APr 46.24–47.11. 100 See in APr 28.13–16, quoted above, p.[50]. 101 See e.g. Apollonius, adv 123.1–125.5.

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85

induce universality, is to say this: if ‘’ is a modal æ  , then for any sentence ‘p’, the modal ‘:p’ is semantically well formed. [53] That suggestion is in effect the suggestion that the modal æ  Ø are ‘topic neutral’ — they may intelligibly appear in discourse about no matter what topic.102 And thus it may become tempting to ascribe to the Peripatetics the following view. Logical constants are topic neutral terms. A sentence form is a logical form provided that it contains nothing but dummy letters and topic neutral constants.

Form and argument But there is at any rate a further strand to the Peripatetic idea of logical form. Alexander, at in APr 28.13–16, speaks not only of ‘universal proofs’ but also of ‘differences among the syllogisms’. Not all æ  Ø have the same status and power as modal æ  Ø. According to Alexander, Aristotle mentions these æ  Ø because they are useful for syllogistic method. This is clear from the fact that there are differences among sentences in virtue of other æ  Ø. Thus an added ‘well’ or ‘badly’ or ‘for a long time’ or ‘for a short time’ or ‘quickly’ or ‘slowly’ is a sentential æ   and makes a difference among sentences — e.g. ‘Socrates talks well’ (or ‘at length’, or ‘concisely’). But Aristotle does not refer to any of these æ  Ø when he makes his distinctions among sentences; for none of them contributes to the generation or the differentiation of syllogisms. (in APr 28.17–24)*

Thus ‘well’ and ‘badly’, unlike ‘necessarily’ and ‘possibly’, do not make any syllogistic difference. Every argument of the form Barbara LXL103 is valid; not every argument of the form Barbara XLL is valid.104 Arguments of the form Barbara LXL are 102 See above, p.[28]. * ‹Ø ªaæ ‰ æe c
ıºº ªØØŒc
Ł 
H
æ ø
 ø
åæÅø
Z
ø

Å
Ø Bº
KΠ F r
ÆØ b
æ ø
ŒÆd ŒÆ ¼ºº ı Ø
a æ  ı ØÆç æ
ŒÆd ªaæ e ŒÆºH æ Œ

ŒÆd e ŒÆŒH ŒÆd e ÆŒæH ŒÆd e æÆåø ŒÆd e Æåø ŒÆd e æÆø æ  Ø æ 
NØ ŒÆd ØÆç æÆ, x
øŒæÅ ŒÆºH ØƺªÆØ j ÆŒæH j ı
 ø. Iºº P
e  Ø  ı 
Å
Ø  Ø 
 c
H
æ ø
ØÆæØ
, ‹Ø Åb
æe ª
Ø
j ØÆç æa
ıºº ªØH
ı
º FØ. 103 i.e. a syllogism of the form: ‘Necessarily AaB; BaC: therefore necessarily AaC.’ 104 Or so Aristotle notoriously contends: APr ` 30a15–32. The validity of Barbara LXL was denied by Theophrastus; and Aristotle’s distinction between Barbara LXL and XLL in point of validity has long been a crux for interpreters of his modal logic. The crux is part of a larger issue concerning the validity of ‘mixed’ modal syllogisms, on which Alexander wrote a special monograph (see e.g. in APr 125.30; 127.16; 249.38). The monograph does not survive, but we can learn

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formally valid, and the specification of their modal structure (the fact that they are LXL rather than XLL) is essential to the form in virtue of which they are valid. [54] Hence ‘necessarily’ does ‘contribute to the generation and differentiation of syllogisms’ — and for that reason it is a formal feature of the sentences in which it suitably appears. Other æ  Ø do not share that logically endearing feature. Is that true? Well, as I said, from ‘(ŒÆºH-F)x’ we can infer ‘Fx’ — and is not that a decent inference? But it will be said, first, and uncontentiously, that such simple adverbial inference-rules will not generate any ‘interesting’ logical structures — there cannot be a ‘logic of beauty’ as there is a logic of modality;105 and secondly, that there will not be any generalizations of such adverbial rules. For the only possible general rule would be one allowing us to infer from ‘(çly-F)x’ to ‘Fx’. And such a rule would permit invalid inferences.106 But even if Alexander is right about ‘ŒÆºH’ and its congeners, it is far from clear that he is right tout court. Consider, say, ‘probably’, ‘certainly’, ‘It is known that’, ‘It is permitted that’. There are some æ  Ø which have been taken by some modern logicians to mark logical constants. These æ  Ø do seem — or have seemed — to generate interesting logical structures. Alexander says nothing at all to show that they, like ‘ŒÆºH’, are material rather than formal constituents of propositions. It might be said that, though no doubt Alexander ought to have considered those modern items, it surely never entered his mind to do so — and it is silly to criticize him for failing to anticipate the subtle developments of twentiethcentury logic. Well, Alexander observes that the matter of demonstrative propositions, being necessary, differs from the matter of dialectical propositions, which is reputable or 
 
.107 He recognizes that, corresponding to the modality of demonstrative propositions, there is a æ   ‘necessarily’ — which sustains a branch of formal logic. He knows too that Aristotle himself had at least mooted the possibility of examining the logical relations among propositions marked as 
 Æ.108 And so he should surely have been alive to Alexander’s views, and some of the history of the dispute, from in APr 123.28–128.16 (cf 238.22–38; 249.15–250.2). 105 See above, p.[31], on ‘fraternal’ logic. 106 Evidently not all adverbs can be ‘dropped’ (e.g. ‘allegedly’). But perhaps all ‘genuine’ adverbs — as opposed to adsentences — can be? That is a contentious area. I cannot enter it here. 107 See the texts cited above, n.92. 108 See esp Top ¨ 162a19–23; cf Alexander, in Top 571.20–572.3; in APr 270.17–25.

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the possibility of an ‘endoxic’ æ  , with its own syllogistical rules. Even if we should not expect him to have [55] anticipated modern epistemic logic, we may reasonably wonder why he did not even raise the question of treating the æ   ‘
 
’ as a formal feature of sentences. But we get no enlightenment from the texts — unless it is enlightening to learn that Alexander was not a particularly adventurous logician. Yet those last reflexions will show, at most, that Alexander misidentifies certain items as being material when they are in fact, according to his own ideas, formal. They do not show any flaw in his general ideas — and I introduced the æ  Ø in order to illuminate Alexander’s general conception of logical matter and logical form. And if we put together the stuff of this section and the stuff of its predecessor, we may tentatively reach the following conclusion. According to Alexander, an element in a sentence is a logical constant provided that (i) it is universal or topic neutral, and (ii) it grounds, or appears ineliminably in, some (‘interesting’) rule of inference. The first condition will rule out, say, ‘yesterday’ as a logical constant (and hence will outlaw one variety of chronological logic). The second condition will rule out, say ‘It is true that’ as a logical constant (inasmuch as ‘It is true that P’ is equivalent to ‘P’). The first condition remains vague — and is in any event contentious. The second condition is also vague — but it should recall the remarks at the end of Part II, to which I shall return in the next section.

Necessity and syllogism Alexander holds that there are valid arguments which are not formally valid. Typically — and often — Alexander makes the point in terms of a distinction between the necessary and the syllogism, between e I
ƪŒÆE
and › ıºº ªØ . The distinction goes back to Aristotle.109 At APr A 47a22–23, Aristotle distinguishes between what follows from certain assumptions by necessity and what follows from certain assumptions syllogistically: [56] some people miss this, and think that there is a syllogism because something necessary follows from the assumptions.* 109

And so it is, as one would expect, a commonplace in the commentators: see e.g. Alexander, in APr 17.25–18.1; 21.28–30; 22.1; 265.16–18; 347.18–20; Philoponus, in APr 322.33–323.10. * 
Ø Ø b ºÆ
Ł
ıØ ŒÆd  Œ FØ ıºº ªÇŁÆØ Øa e I
ƪŒÆE
Ø ıÆ
Ø
KΠH
ί
ø
.

88

Logical Matters

Alexander comments: In these words he clearly tells us that one should not simply look at the conclusion and think that there is a syllogism if something necessarily follows from the assumptions. For it is not the case that, because syllogisms prove something of necessity, we therefore have a syllogism when something is proved by necessity in virtue of following from the premisses. For the necessary has a broader scope than the syllogism. (in APr 344.9–13)*

Thus Alexander distinguishes two sorts of case in which the conclusion of an argument follows from its premisses. In general, the premisses of a valid argument necessitate the conclusion: if the premisses are true, then by that token the conclusion too must be true. But not all valid arguments are syllogisms; for there are cases of logical necessitation which are not cases of syllogistic necessitation.110 And Alexander explains the distinction in terms of matter and form: Things are often proved to conclude something because of their matter, although they are not syllogistic. (in APr 379.20–21)**

Or again: Often enough, something follows necessarily from certain premisses because of the particular character of their matter, even though the items on which the necessity depends are not assumed syllogistically — e.g. in the case of definitions and properties in the second figure when two affirmative propositions are assumed. (in APr 344.27–31)***

The general point is clear enough: necessitation is wider than [57] syllogistic necessitation because validity is a wider notion than formal validity. All formally valid arguments are valid (in other words, all syllogisms necessitate); but not all valid arguments are formally valid (in other words, not all necessitation is syllogistic). Alexander shows that this is the point he is making by referring to cases in which the validity of an argument depends * Greek text in the Appendix. 110 Lee, Die griechische Tradition, p.98, remarks (in connexion with the single-premissed argument discussed by Alexander at in APr 17.20–29) that ‘the necessary relation here is not logical in nature but rests essentially on two observable phenomena in the world’; and he suggests that all cases of non-syllogistic necessitation involve some non-logical species of necessity. That is surely wrong; or rather, it is plain that Alexander is operating with a single — and perhaps naive — notion of necessity, such that A necessitates B just in case B must hold if A holds. See also H. Maconi, ‘Late Greek syllogistic’, Phronesis 30, 1985, 92–98, on p.95 [reprinted below, pp.659–665]. **  ººŒØ Œ
ıÆ Ø
Æ Ææa c
oºÅ
ı
ª
 Ø PŒ Z
Æ ıºº ªØØŒ. *** Greek text in the Appendix.

Logical form and logical matter

89

on its matter: there are cases in which the necessitation depends not on the form of the inference but on its matter. There are cases of material validity.111 But what exactly is Alexander doing when he distinguishes material from formal inference? Some of my remarks in Part II suggest an initial dilemma. First, Alexander may construe the terms ‘form’ and ‘matter’ as relative — and relative to a system, namely the system of categorical syllogistic. In that case, his thesis will be this: there are some valid arguments none of whose forms is the form of any categorical syllogism. Not all necessitation is syllogistic: not all valid inference is formal: not all deductions are categorical. Now that is no doubt true. But it is also uncontroversially true: if we choose to call materially valid any valid argument which is not a categorical syllogism, then the Stoics — and any other logicians — will be perfectly content to profess that they study a class of ‘materially valid’ argument. For arguments which are materially valid relative to categorical syllogistic may, of course, be formally valid relative to another logical system. Now it is evident that Alexander wishes to assert more than that. Secondly, then, he may insist on construing ‘form’ and ‘matter’ in an absolute sense. Must he not then suppose that a logical form of an argument is a highest form? But in that case every valid argument will be formally valid. And so Alexander’s [58] contention that there are materially valid arguments will be false — and triflingly so. I suppose it is clear that Alexander wants to be impaled on neither horn of this dilemma. And, as I have already hinted, the final section of Part II indicates what he needs to say. ‘There are some valid arguments which do not exhibit categorical syllogistic form. Those arguments do, of course, exhibit some form — they must, trivially, have a highest form and hence a logical form. But (and this is the crucial thing) their highest forms will all contain non-logical constants. That is to say, they will all contain words which no suitably elaborate logical system takes as constants.’ 111 Furthermore, just as valid arguments may possess either a formal or a material validity, so sophistical arguments may be either formally or materially at fault. And thus the distinction between matter and form was regularly used in the later Peripatetic classification of fallacies. (See Alexander, in Top 21.5–15; Philoponus, in APst 150.29–151.26; [Alexander], in Soph El 4.9–28; and the later commentaries and scholia printed by Ebbesen, Commentators (e.g. Comm I proem [volume II, pp. 242–243]; Comm III on Soph El 164a20–24 [II, 201–202], 176b29 [I, 215–216]; Leo Magentinus, on Soph El 164a20 [II, 282] — and see volume I, pp.95–101). Yet matter and form did not and could not serve the logicians well in this case and the distinction between ‘formal’ and ‘material’ fallacies amounts in effect to the distinction between invalid arguments and valid arguments with false premisses.

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Logical Matters

Alexander should say that, or something like it. He does not actually say it, and he was not conceptually equipped to say it. But the position which such thoughts generously put at Alexander’s disposal is at least a coherent position — and a position which, I suspect, would be taken by many logicians.

Invalidity and incompatibility However that may be, Alexander is not altogether felicitous in his deployment of matter and form, even on his own terms. I shall end this Part by discussing two of his infelicities. The first concerns Alexander’s conception of material validity. As a schematic illustration of arguments which are valid but are not syllogisms, he refers — in a text I have already quoted — to the case of definitions and properties in the second figure when two affirmative propositions are assumed. (in APr 344.29–31)

It is clear that he has in mind an argument such as the following: (1) All men are capable of laughter. (2) All Greeks are capable of laughter. Therefore: (3) all Greeks are men.112 [59] The premisses of this argument mark it for the second figure (the middle term is predicate in both of them).113 But each premiss is a universal affirmative proposition. Hence the argument is not a valid second figure syllogism.114 Yet the argument is — Alexander supposes — valid. It is valid in virtue of its matter. Thus the argument is a case of material validity, of non-syllogistic necessitation. There are two objections to Alexander’s suggestion. First, he does not show that the argument is not formally valid. In general, an argument is formally 112 See in APr 125.17–23; 380.4–9 (cf 35.3–4); in Top 192.4–10. See too Philoponus, in APst 158.28–159.17, who thinks that Aristotle anticipates the Alexandrian point at APst ` 77b40–78a6. Since Philoponus depends heavily on Alexander’s lost commentary on APst (for which see P. Moraux, Le commentaire d’Alexandre d’Aphrodise aux ‘Seconds Analytiques’ d’Aristote, Peripatoi 13 (Berlin, 1979)), we may reasonably assume that Alexander, too, thought he had Aristotelian authority for his view. Indeed, Alexander may have found it at APr ` 45b21–27: see in APr 328.10–30 (but see below, n.115). 113 The figure of a syllogism is determined by the structure of its premiss-pairing or ıÇıªÆ: a ıÇıªÆ of the form ‘BxA, BxC’ determines the second figure (see APr ` 26b34–36; Alexander, in APr 46.32–47.4). 114 The premiss-pairing is ‘BaA, BaC’. For proof of its inconcludency, see APr ` 27a18–20; Alexander, in APr 81.3–82.1.

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91

valid if it exhibits some logical form (Fj) such that every argument of form (Fj) is valid. Hence an argument is not formally valid if it exhibits no logical form (Fj) such that every argument of form (Fj) is valid. Alexander sees that his argument exhibits one logical form — the form: (FÆ) BaA. CaA. Therefore: BaC. — such that not every argument of that form is valid. He does not show that all its logical forms lack universal validity. Of course, if we ask what categorical form Alexander’s specimen argument may take, then it seems that there is indeed only one answer. If the argument is to be assigned a categorical form, then that form can only be (FÆ). Since not all arguments of the form (FÆ) are valid, Alexander may conclude that the argument is not formally valid within categorical syllogistic. Yet the conclusion he desires and needs is, as I urged in the preceding section, far stronger than that; and it is a conclusion which he cannot reach. For from the fact that an argument is not valid in virtue of any categorical form, he cannot infer that it is not valid in virtue of any logical form whatever. Secondly, Alexander does not show that the specimen argument is valid at all. The peculiarity of the ‘matter’ of the argument consists in the fact that the middle term is a ‘property’ [60] or YØ
of the major, or in other words that necessarily all and only men are capable of laughter. I imagine that Alexander is reasoning tacitly as follows: ‘Since the middle term is a property of the major, we can infer from (1) that (1*) all things capable of laughter are men. And then, from (1 *) and (2), we can infer to (3). For (1*) and (2) yield (3) by a categorical syllogism in Barbara. Hence the argument from (1) and (2) to (3) is valid. But we can infer (3) only because of the special features of the terms used in the example, i.e. only because of the peculiarity of the matter.’ If that is not Alexander’s train of thought, then I do not know how he was thinking. But it is a bad train of thought. The argument works only if (1*) follows from (1). And (1*) clearly does not follow from (1): were baboons capable of laughter, then (1) would be true and (1*) false.115

115 Alexander perhaps sees the point at in APr 328.10–30: there he discusses what is in effect the same argument, claiming that (3) will follow under special conditions — but he makes the crucial remark that (3) follows ‘if we assume that follows alone’ (328.21–22), i.e. if we assume (1*) rather than (1). (But the ‘ºÆH
’ comes from Aristotle, APr ` 45b24, and I fear that Alexander may not have seen its importance.)

92

Logical Matters

Sophisticated readers may excogitate a sophisticated defence for Alexander.116 But sophistication would be misplaced. For the infelicity which I detect at in APr 344 is by no means singular in Alexander’s commentary. On the contrary, it is parallelled by a pervasive error in his discussion of Aristotle’s method of disproving the validity of a putative syllogistic form. Thus when he tackles the question of whether the first-figure pairing ‘AaB’, ‘BeC’ will yield a syllogistic conclusion, he claims: That nothing necessary is concluded — which is the characteristic feature of syllogisms — when the propositions are of this sort, Aristotle proves by setting down the matter. For he will show that, for certain matter, a universal affirmative can be concluded and that for other matter a universal negative — and that is the clearest sign that [61] this pairing has no syllogistic force, given that contraries and opposites, which destroy one another, are proved in it. (in APr 55.21–26)*

Thus Alexander supposes that in some cases — for some matter — ‘AaB’ and ‘BeC’ together entail ‘AaC’ and that in other cases — for other matter — they together entail ‘AeC’. Now in order to show that ‘AaB’ and ‘BeC’ together yield no categorical conclusion of the form ‘AxC’, it is sufficient to show that ‘AaB’ and ‘BeC’ are jointly compatible both with ‘AaC’ and with ‘AeC’. In order to show that ‘AaB’ and ‘BeC’ are jointly compatible with ‘AaC’, it is sufficient to produce concrete terms for which sentences in all three forms are true. And that is precisely the function of the ‘matter’ — the specific terms — which Aristotle supplies when he proves the impotence of the ıÇıªÆ in question (see APr ` 26a8–9). His terms are: animal, man, horse. Animal holds of every man. Man holds of no horse. Animal holds of every horse. Hence in at least one case, sentences of the forms ‘AaB’, ‘BeC’, and ‘AaC’ are all true together. Hence the form:

116

And we can, of course, find valid arguments which exhibit the form (FÆ), e.g. All men are mortal. All men are mortal. Therefore: all men are mortal. (Not that Alexander would have thought much of that example.) * ‹Ø ªaæ oø Kå ıH
H
æ ø
Pb
I
ƪŒÆE
ı
ªÆØ, ‹ KØ
YØ
ıºº ªØ F, ÆPe b
Œ
ıØ fiB B oºÅ ÆæÆŁØ
ŒÆd ªaæ ŒÆŁ º ı ŒÆÆçÆØŒe
K Ø
 oºÅ Ø ı


ı
ªŁÆØ ŒÆd ºØ
K ¼ººÅ ŒÆŁ º ı I çÆØŒ
, n K
ÆæªÆ
ÅE
 F ÅÆ
åØ
c
ıÇıªÆ
ÆÅ
Nåf
ıºº ªØØŒ
, Y ª   K
Æ
Æ ŒÆd a I
،
Æ K
ÆPfiB Œ
ıÆØ, Z
Æ Iºººø
I
ÆØæØŒ.

Logical form and logical matter

93

AaB. BeC. Therefore: AoC. is not valid. A different trio of terms invalidates the form: AaB. BeC. Therefore: AiC. Since ‘AeC’ entails ‘AoC’ and ‘AaC’ entails ‘AiC’, no conclusion of the form ‘AxC’ follows from the ıÇıªÆ. Q.E.D. Alexander gets that all wrong. He supposes that the terms which Aristotle offers us are meant to be collected into two arguments, one of which is: (1) Animal holds of every man. (2) Man holds of no horse. Therefore: (3) Animal holds of every horse. Alexander holds that this argument is valid — but materially rather [62] than formally valid. And similarly for the second ‘argument’. An elementary mistake.117

Conversion I turn to the second infelicity. I have thus far written as though there were an exact match in Alexander between formal validity and syllogistic validity. That is not quite right. I am not here thinking of Alexander’s treatment of ‘ecthetic’ proofs. Rather, I am thinking of his attitudes to ‘wholly hypothetical’ arguments and to the rules of conversion and of subalternation. An argument is ‘wholly hypothetical’ if each of its component sentences is a hypothetical sentence. One form of hypothetical sentence is the conditional: If p, then q. And a paradigm wholly hypothetical argument will have the form: If p, then q. If q, then r. Therefore: if p, then r.118

117 See Patzig, Theory of the Syllogism, pp.168–183. The error was not confined to Alexander: see e.g. Apuleius, int viii [203.3–6]; xiv [215.4–8]; Philoponus, in APr 34.7–10; 75.3–7; 75.23–30 — and in many other places. 118 I simplify: for a detailed discusion of the Peripatetic accounts of such arguments, see Barnes, ‘Terms and sentences’.

94

Logical Matters

Alexander holds that there are valid arguments of that form; and he nowhere suggests that such arguments are materially valid, that they conclude Øa c
oºÅ
. Yet he is emphatic that they are not syllogisms: The wholly hypothetical kind of syllogism is useless for proof and positing; for by them nothing is proved to hold or not hold, whether universally or particularly — and that, Aristotle said, is the mark of the syllogism. (in APr 265.13–16)119

The conclusion of a wholly hypothetical argument is not of the [63] form ‘AxB’. Therefore wholly hypothetical arguments are not syllogisms. Alexander has more to say on the topic, but I shall not analyse his views here. It is clear, I suppose, that his decision to outlaw wholly hypothetical arguments is capricious. More interesting are the conversion-rules. For they, unlike wholly hypothetical arguments, certainly do involve categorical propositions; and they are indispensable parts of the Peripatetic theory of categorical syllogistic. Now surely the rule of e-conversion (from ‘AeB’ infer ‘BeA’) is — or can readily be formulated as — a formally valid argument? A form exhibited by any econversion is this: AeB. Therefore: BeA. Every argument of the form is valid. The form is categorical — its elements are all standard elements of categorical grammar. Hence it is formally valid relative to categorical grammar. Yet Alexander does not treat it as a syllogism. He cannot treat it as a syllogism for the simple reason that every syllogism must, in his view, have more than one premiss (e.g. in APr 17.10–18.2). Then what is Alexander to say about conversions? Some scholars have supposed that, in Alexander’s view, conversions are not inferences at all, and hence are neither materially nor formally valid.120 At first blush, the suggestion may seem merely silly: how could a conversion be anything other than an inference? Yet Alexander does sometimes seem to regard conversion less as the inferring of one proposition from another than as a relation between propositions.

119

cf in APr 326.12–19; 330.28–30; 348.9–19; 350.16–18. See Barnes, ‘Terms and sentences’, pp.307–308. 120 So e.g. Frede, ‘Stoic vs. Aristotelian’, p.22 [p.114]; Lee, Die griechische Tradition, pp.90–91, 98–99.

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95

Thus ‘propositional conversion is a sharing by propositions of two terms, conversely posited, together with being true at the same time’ (in APr 46.5–6).* Conversion is a ‘sharing’, and sharing is a relation between propositions rather than an operation upon them. Consider, too, the fact that Alexander sets conversions on a level with oppositions or I
ØŁØ: just as ‘AeB’ is the contrary of ‘AaB’, so ‘AeB’ is the converse of ‘BeA’ (see in APr 45.14–46.16). Again, consider the way in which he speaks of what he calls the [64] conversion of terms, whereby ‘AaB’ converts with ‘BaA’ (in APr 29.25–27). From ‘AaB’ we may not infer ‘BaA’; but we may so to speak ‘move’ from ‘AaB’ to ‘BaA’ by a conversion of the terms. Alexander treats conversion of terms and conversion of propositions not as two utterly different types of thing — a non-inferential relation and an inferential operation — but rather as examples of exactly the same type of thing. Thus his idea may be that when you convert the proposition ‘AeB’ to the proposition ‘BeA’, you do not really make an inference — you simply ‘move’ from the one proposition to the other. Yet that view is incoherent. The point and purpose of e-conversion, and the reason why it figures in categorical syllogistic, is that it is truth-preserving. The ‘move’ from ‘AaB’ to ‘BaA’ is simply an interchange of terms; it is not a logical operation. The ‘move’ from ‘AeB’ to ‘BeA’ has its rationale in the logical fact that if ‘AeB’ is true, then so too is ‘BeA’. Nor does it help to regard propositional conversion as a form of substitution rather than a form of inference.121 It is true that ‘AeB’ and ‘BeA’ are intersubstitutable; for each follows from the other — the two propositions are logically equivalent. But the idea of intersubstitutability cannot lie behind, say, the ai-conversion rule.122 For this rule is one-way: ‘AaB’ and ‘BiA’ are not intersubstitutable.123 * Ø ªaæ æ ø I
Øæ çc Œ Ø
ø
Æ æ ø
ŒÆa  f  ‹æ ı I
ƺØ
ØŁ
ı a  F ı
ÆºÅŁØ
. 121 As a text in Philoponus might suggest: see in APr 40.2–8, where he says that I
Øæ ç is the same as N æ ç (cf Alexander, in Top 3.27–28). 122 i.e. from ‘AaB’ infer ‘BiA’. 123 Frede, ‘Stoic vs. Aristotelian’, p.22 [p.114], ignores this rule; Lee, Die griechische Tradition, p.90, argues that Alexander did not regard it as a genuine case of I
Øæ ç, and he appeals to in APr 392.19–26. At in APr 392.23 Alexander does indeed say that ÆyÆØ ... Œıæø I
ØæçØ
ºª
ÆØ Æƒ ÆÆE I
Øæç ıÆØ: But that is a piece of special pleading to account for an imaginary difficulty at APr ` 50b31–32; and I find no parallel to it elsewhere in Alexander. Of course, even if Lee is right, the ai rule remains: it must be treated as an argument — and as a formally valid argument — whether or not it is counted as a conversion. Note that Philoponus holds ai-conversions to be the simplest I
Øæ çÆ (in APr 42.13–19).

96

Logical Matters

If Alexander thought that conversion-rules were not a sort of inferencerule, then he was wrong. But in fact — and of course — he usually treats them as inference-rules. And sometimes, at least, he shows himself explicitly aware of their inferential status: for example, he expressly denies that the rules are valid on account of their matter.124 Consequently, he must have regarded the rules as formally valid — and yet not as genuine syllogisms. [65] There is nothing in principle wrong with such a view. But we shall be obliged to conclude that here, too, Alexander showed a less than perfect understanding of what he meant by formal validity. For the mass of his text (where conversion is not at issue) gives the plain impression that all valid arguments are either materially valid or else syllogisms. Yet his insistence that syllogisms must depend on more premisses than one, obliges him to make a pointless distinction among formally valid arguments, only some of which will count as syllogisms in the proper sense. IV

k¸coi peqamtijoß Stoic texts do not discuss arguments or propositions in terms of their formal and material components.125 But the Stoic logicians126 did make distinctions which are evidently related the Peripatetic distinction between form and matter. I mention first the Stoic distinction between a º ª  and a æ  .127 A º ª  is an argument, for example: (1) If it is light, it is day. (2) It is light. Therefore: (3) it is day. 124

See in APr 35.6–9, quoted above, p.[51]. But reports of their views may of course be expressed in Peripatetic terminology — e.g. Origen, c Cels VII 15: çæ ıØ b ŒÆd Kd oºÅ e
æ 
 F
ƒ Ie B  A ... (See also below, p.[80], on [Ammonius], in APr 70.10–13.) 126 ‘The Stoic logicians’: which logicians? I am writing primarily about ancient logic in the time of Alexander and Galen; and by Stoic logic I mean, essentially, the logic which they and their contemporaries recognized as Stoic in origin and content. All Stoic ideas which I shall discuss were, I think, certainly current during the period in which I am interested. They all had a history and a pedigree — and no doubt many of them derive, directly or indirectly, from Chrysippus, the father of Stoic logic. But in large part the histories and pedigrees are obscure to us — and seem likely to remain obscure. Some interesting conjectures have been made (see e.g. Mueller, ‘Greek mathematics’, pp.58–59, 63 — but see below, n.147, on Mueller’s understanding of the term ‘
æ ’). 127 See e.g. Diogenes Laertius, VII 76; Sextus, M VIII 227; Galen, inst log vi 6. 125

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A æ   (in this Stoic sense), is, so to speak, the shape or form of an argument. The æ   corresponding to the argument I have just given is this: If the first, the second. [66] The first. Therefore: the second. Evidently, a æ   can be understood as a form of an argument; and we might be tempted say — on the Stoics’ behalf — that an argument is formally valid provided that it is an instance of a æ   all the instances of which are valid. How close the Stoic idea of a æ   is to the Peripatetic idea of an r  , and whether there was any historical connexion between the two notions, are questions which I shall leave aside. More interesting, from my present point of view, is a distinction which the Stoics made within the class of arguments. An argument or º ª  they defined as a structure of assumptions and conclusion (e.g. Diogenes Laertius, VII 45; Sextus, PH II 135; M VIII 302);128 and of arguments, some were ‘concludent’ (æÆ
ØŒ  or ı
ƌ، ) and others ‘inconcludent’ (IæÆ
 Ø; I
ÆŒ Ø).129 The Stoics held that an argument was concludent provided that its corresponding conditional was sound (see Sextus, PH II 137; M VIII 417); and that an argument was inconcludent provided that the negation of its conclusion did not conflict with its premisses (Diogenes Laertius, VII 77). No doubt the two characterizations were taken to be equivalent. And they show that the Stoic notion of concludency was, at least roughly, the same as our general notion of validity.130 Concludent arguments were divided into two subclasses: the members of one subclass they called ıºº ªØØŒ , while to the members of the other they gave the same name as the genus, calling such arguments æÆ
ØŒ  in the special sense (Diogenes Laertius, VII 78).131 Our sources do not tell us the basis for the distinction. We learn that arguments are æÆ
ØŒ  in the special sense if they conclude but do not conclude syllogistically [67] (ibid); we learn, unhelpfully, that syllogisms are arguments which are ıºº ªØØŒ  128

See M. Frede, Die stoische Logik (Go¨ttingen, 1974), pp.118–119. See e.g. Diogenes Laertius, VII 77; Sextus, PH II 137; M VIII 303. — I assume that ‘æÆ
ØŒ ’ and ‘ı
ƌ، ’ are synonyms; and I imagine that the latter term was used because of the systematic ambiguity of the former. 130 See Frede, Stoische Logik, pp.119–121. 131 Clement urges us to get our logic right and not worry about the nomenclature. For example, ‘you should take great care to determine what follows from what premisses, but you should not care at all whether someone wants to call it a º ª  æÆ
ø
or æÆ
ØŒ  or ıºº ªØØŒ ’ (strom VIII iii 8.2). Clement has failed to see that, unlike the words ‘æ ÆØ’ and ‘ºBÆ’ (his other example), the terms ‘æÆ
ØŒ ’ and ‘ıºº ªØØŒ ’ are significantly different in sense. 129

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Logical Matters

(id, VII 45). We are also told that an argument is syllogistic provided that it is either I
Æ ØŒ  — unproved or indemonstrable — or else reducible, by way of the themata, to arguments which are themselves unproved or indemonstrable (id, VII 78). This last remark might be construed as a definition of what a syllogism is;132 but it is rather more plausible to construe it as a theorem about syllogisms. (The Stoics held that all syllogisms — defined in some way unknown to us133 — could be reduced to certain unproved or indemonstrable argument forms.) And then we are still in the dark about the sense which the Stoics gave to the term ‘ıºº ªØ ’. A few texts tell us something about the arguments which the Stoics classified as æÆ
ØŒ  in the special sense — as concludent but nonsyllogistic arguments. The most important of the texts is a passage in Galen’s institutio logica which is desperately corrupt.134 The other texts offer examples but contain little in the way of theory or general explanation. Among the non-syllogistic arguments were some called ‘subsyllogistic’ or ‘ ıºº ªØØŒ ’.135 These appear to have been arguments which were linguistic variants on syllogisms, i.e. arguments whose component sentences were equivalent in meaning to the component sentences of a syllogism.136 In one passage, Alexander mentions the following argument form: q follows p. p. Therefore: q. [68] This, he says, was taken by ƒ
æ Ø to be a linguistic variant on the form: If p, then q. p. Therefore: q. And he adds that ƒ
æ Ø regarded the latter form as syllogistic but the former as merely æÆ
ØŒ  and not ıºº ªØØŒ  (in APr 373.29–35). 132 So Frede, ‘Stoic vs. Aristotelian’, p.2 [p.101] (‘the definition of the syllogism quoted above undoubtedly is the Stoic definition’); cf id, Stoische Logik, pp.124–127. But note that in the paper Frede allows that the ‘definition’ presupposes a pretechnical notion of syllogism, and that this notion is the crucial one. 133 For an attemped elucidation, see Frede, ‘Stoic vs. Aristotelian’, pp.2–4 [pp.101–103]. I am doubtful about that, for reasons which do not matter here. 134 See Barnes, ‘Utility’. 135 The word occurs only at Galen, inst log xix 6, and Alexander, in APr 84.12. Alexander ascribes it to ƒ
æ Ø and applies it to a deviant categorical syllogism: see below, n.153. 136 See the texts cited in the last note; but the passage in Galen (if I understand it aright) suggests that º ª d  ıºº ªØØŒ  were actually a subclass of the class of arguments which are linguistic variants on proper syllogisms. (See Barnes, ‘Utility’. — contra, T. Ebert, Dialektiker und fru¨he Stoiker bei Sextus Empiricus, Hypomnemata 95 (Go¨ttingen, 1991), p.169 n.35.)

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Alexander does not expressly say that arguments of this form were called subsyllogistic; but it is a reasonable conjecture that they were. However that may be, subsyllogistic arguments are not my present concern. At any rate, no ancient text suggests that either the Euclidean Argument or the Truncated Argument is subsyllogistic. Another group of arguments is of more immediate interest. For the Stoics referred to ‘arguments which conclude unmethodically’, IŁ ø æÆ

. The Truncated Argument fell — as we shall shortly see — into this category.

Some unmethodical arguments A number of ancient texts refer to unmethodical arguments and offer illustrative examples. In the most extensive of the texts, a passage in Alexander’s commentary on the Prior Analytics (344.9–346.6),137 the examples fall into three classes. First — class (A) — comes a pair of mathematical arguments, the first of which is a generalized form of the Truncated Argument:138 A is equal to B. C is equal to B. Therefore: A is equal to B. (344.14–15).139 Class (B) concerns family relations: [69] A has the same parents as B. B has the same parents as C. Therefore: A has the same parents as C. (344.31–34). And class (C) concerns truth-telling, for example: Dio says that it is day. Dio speaks truly. Therefore: it is day. (345.28–29). Alexander explicitly introduces class (C) to illustrate ‘the arguments which ƒ
æ Ø call unmethodically concluding’ (345.15). And the run of the text distinctly suggests — though it does not expressly state — that 137

Quoted below, pp.[83–85]. The Truncated Argument is limited to lines: Alexander’s specimen argument applies to magnitudes in general. 139 The letters here are ‘dummy’, in the sense described above, p.[20]. The name ‘Dio’ in the class (C) example is also, of course, a dummy name. Lee, Die griechische Tradition, p.109, comments that ‘Alexander certainly understands the letters A, B, and C not as variables but rather as abbreviated examples [sic : i.e. as abbreviated names]’. The letters are not variables; but neither are they shortened versions of actual names (otherwise we could sensibly ask, of the sentences in the example, ‘To which putatively equal objects are you here referring?’). But see Barnes, Truth, pp.337–359. 138

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(A) and (B) are not cases of what ƒ
æ Ø regarded as unmethodical arguments. An earlier passage, in APr 21.28–22.25, also assembles examples of three types. Here too we find class (A) (21.31–22.7) and class (C) (22.17–23). Between them, forming class (D), comes an example allegedly taken from Plato’s Republic (22.7–17).140 Again, Alexander explicitly introduces (C) as the sort of thing which ƒ
æ Ø called unmethodical (22.18). But at 21.31, just before he introduces (A), he alludes to ‘the unmethodically concluding arguments of the Stoics’; and that strongly suggests that he took class (A) to contain examples of Stoic unmethodicals.141 A final Alexandrian passage confirms this suggestion. At in Top 14.20– 15.14, Alexander again offers examples from class (A) (14.21–27) and class (C) (14.27–15.3). He then adds a new sort of example, which I shall put in class (E): Law is contrary to anarchy. Law is not bad. [70] Anarchy is bad. Therefore: law is good. (15.5–14). At 14.20, Alexander introduces (A) in illustration of ‘the arguments which are called unmethodically concluding by those from the Stoa’. And the run of the text implies that (C) and (E) are also illustrations of what the Stoics called unmethodical arguments.142 140

Alexander is referring to Rep 408C; but Plato is certainly not presenting the (rather silly) argument which Alexander reads into his text. Later commentators and scholars frequently ‘cite’ arguments from Plato. It is rare that the arguments occur explicitly in Plato — and often enough what they present is scarcely a plausible reconstruction or formalization of Plato’s thought. 141 There is, of course, no suggestion that (D) is Stoic in origin; and the fact that Alexander refers to ƒ
æ Ø at 22.18 is surely to be explained by the fact that he has followed the Stoic class (A) with the non-Stoic class (D). 142 For the sake of completeness, I mention five other texts. (1) [Ammonius], in APr 70.11–13, gives an instance of (A) and asserts that it is an argument which the Stoics called unmethodical. I discuss this text below, p.[80]. (2) Philoponus, in APr 321.7–322.18, gives (A), (B), (C); he refers explicitly neither to the Stoics nor to unmethodical arguments. But he expressly claims (321.8) to be paraphrasing Alexander (i.e. Alexander, in APr 344.9–346.6), so that his text has in any case no independent value. (3) Philoponus, in APr 36.5–13: examples of type (A), explicitly said to be the sort of thing the Stoics call unmethodical. (4) [Themistius], in APr 121.20–123.8: (A), (B), (C), with (C) offered as examples of what ƒ
æ Ø call unmethodical (122.18). Again, the text has no independent value; for it is copied directly from Alexander, in APr 344.9–346.6. (5) Galen, inst log xvi–xix discusses examples of some six different types, including (A), (B), and (C). He does not mention the Stoics in this context, nor does he say that the arguments were, or were taken by anyone to be, unmethodical. Despite its close similarity in content to the other texts, this Galenic passage has no immediate bearing on my present question.

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If we assume — as scholars generally do — that Alexander means the Stoics whenever he writes ‘ ƒ
æ Ø’, then these texts present a little puzzle. For in APr 344–346 will then suggest that only class (C) was taken by the Stoics to exemplify unmethodical arguments. (The other classes will presumably have been juxtaposed by other logicians who thought they saw some relevant similarity in them.) But in Top 14–15 and in APr 21–22 have it that (A) and (B) and (E), as well as (C), had been invoked by the Stoic logicians as providing illustrations of unmethodical arguments. If we cleave to in APr 344–346, what shall we say of in Top 14–15? Perhaps Alexander simply blundered? But he wrote in Top after he had written in APr.143 So we should have to assume that when he came to write in Top 14–15, he had forgotten what he knew when he wrote in APr 344– 346. A better hypothesis: at in Top 14.20, he does not mean to say of class (A) that ‘these are arguments which the Stoics called unmethodical’; rather, he means to say that ‘these are arguments of the same sort as those arguments which the Stoics called [71] unmethodical’. Then the Stoics will have produced class (C) to exemplify their unmethodical arguments; and other logicians produced other arguments which they supposed to belong to the same group as class (C). — The hypothesis is possible. But I find it highly implausible: no ingenuous reader of Alexander’s text would discover such subtlety in it. Suppose, then, that we cleave to in Top, interpreting it in the easy and ingenuous way: what are we to say of in APr 344–346? Well, we could, of course, simply charge Alexander with a minor infelicity. It is true, we might say, that the text implies that (A) and (B) were not offered by ƒ
æ Ø as unmethodical arguments; but the implication was not intended — Alexander knew that (A) and (B), as well as (C), were Stoic unmethodicals, but he did not signal his knowledge until he reached (C). Infelicitous, no doubt, but venial. Another possibility is worth airing. The puzzle arises only if we assume that when Alexander used the term ‘ ƒ
æ Ø’ at 345.15 he intended to refer to the Stoics. Must we so assume? The question is worth a moment’s reflexion.

143 Or so we may probably infer from in Top 7.10–12. But it should be said that cross-references in the commentaries may determine a pedagogical ordering of the texts rather than betray the chronology of composition.

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oi“ meþteqoi* The first point is obvious enough: the word ‘
æ ’ does not mean ‘Stoic’. Literally, it means ‘younger’ or ‘more recent’ or — better — ‘modern’. (Morphologically, the word is a comparative adjective; but the force of the comparative termination is often slight or non-existent.) And although the term was often used to refer to the Stoics, the reference was neither so constant nor so conventional that it affected the sense of the word. Thus Galen, for example, frequently cites — usually to their disadvantage — the views of ƒ
æ Ø: he has different groups of people in mind on different occasions, and the groups in question are usually indicated by the context and by the contrast which the context invokes. We cannot always tell whom Galen had in mind, and sometimes perhaps Galen’s reference was vague. But in principle, occurrences of the term ‘ ƒ
æ Ø’ will get their reference from their context. It would be absurd — and in any case demonstrably [72] false — to suppose that whenever Galen uses the term ‘ ƒ
æ Ø’ he always has in mind some single and determinate group of people. It would be utterly absurd — and in any case demonstrably false — to suppose that he always refers to the Stoics. Later Greek scholars and commentators use the term ‘ ƒ
æ Ø’ in a similar fashion.144 The word is standardly used to pick out, anonymously, a group — often vaguely conceived — of ‘modern’ thinkers, who contrast, according to the context, with one or another group of ‘old’ thinkers. The ‘modern’ thinkers may, of course, be Stoic; but if they are Stoics, their identity is determined not by the term ‘ ƒ
æ Ø’ but by the contextual fact that, here or there, the later men in whom the scholar is interested are in fact Stoics.145 So, too, with Alexander. ˇƒ
æ Ø are ‘the moderns’, to be identified (if we can identify them at all) from the context. We may not assume that Alexander always has the same group of moderns in mind; we may not * With this section, cf J. Barnes, Porphyry: Introduction (Oxford, 2002), pp.317–319. 144 A search through Ammonius and Philoponus and Simplicius will throw up a hundred examples. The term is also often used by the grammarians. There is a celebrated occurrence in Cicero, ad Att VII ii 1, where ‘ ƒ
æ Ø’ designates a group or school of fashionable poets. There is an early occurrence in Philodemus, poet V [PHerc 403 frag 4]: see A. Angeli (ed.), Filodemo: Agli Amici della scuola (Naples, 1988), pp.92–97. And note the occurrence of ‘ ƒ IæåÆE Ø’ in two Chrysippean titles: ºØ ŒÆa  f IæåÆ ı æe ˜Ø Œ ıæÅ
Æ
(Diogenes Laertius VII 197); æd  F KªŒæ
Ø
 f IæåÆ ı c
ØƺŒØŒc
f
ÆE I Ø æe ˘
ø
Æ 
(ibid, 201). 145 Of course, ƒ
æ Ø may, in certain contexts, be contrasted with the Stoics — see e.g. Iamblichus, in Nic xii [11.5–9].

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assume that he always has the Stoics in mind. Sometimes, indeed, it is clear that ƒ
æ Ø are not Stoics.146 Sometimes it is plain that the ‘moderns’ are not terribly modern — that is to say, that they are not particularly close in time to Alexander himself.147 Nonetheless, it may still be claimed that Alexander — at least [73] in in APr — does in fact normally have the Stoics in his sights when he talks of the ‘moderns’. And I think that that claim is true. Most often, when Alexander invokes ƒ
æ Ø he is concerned to contrast a ‘modern’ terminology with the older terminology of Aristotle; and almost always — perhaps always — it is right to identify the ‘modern’ terminology with Stoic terminology.148 But that fact does not tell against the simple and straightforward point that for each use of ‘ ƒ
æ Ø’ in Alexander we must ask ‘Who does he mean to refer to here?’.

Some critics of Aristotle’s syllogistic Then who does Alexander mean to refer to at in APr 345.15? One straightforward argument leads us back to the Stoics. For at 22.18 ‘ ƒ
æ Ø’ surely designates the Stoics, who are explicitly mentioned at 21.31. And ƒ
æ Ø at 22.18 are surely the same men as ƒ
æ Ø at 345.15. Hence ƒ
æ Ø at 345.15 are the Stoics. The argument is plausible. But it is not irrefragible. For it is not absolutely clear that we must identify 146 See e.g. [Alexander], in Met 645.36, where Aristotle’s terminology for geometry is contrasted with that of ƒ
æ Ø — the ‘modern’ geometers. 147 Note that the ‘moderns’ need not be contemporaries of, or even very close in time to, the author who invokes them: Iamblichus can call Aristotle a ‘modern’, in contrast to Pythagoras (see Simplicius, in Cat 351.4–7). Mueller, ‘Greek mathematics’, pp.57–59, argues that Alexander normally uses the phrase ‘ ƒ
æ Ø’ to refer to post-Chrysippean Stoics. After all, Alexander ‘never ascribes to the neoteroi terminology or doctrine elsewhere attributed explicitly to Chrysippus’ (p.58). But Mueller’s purportedly best illustration of his claim is false. He says that ‘the most certain case is the idea of the argument with one premiss ... which Sextus Empiricus explicitly dissociates from Chrysippus and attributes to Antipater’ (p.58). At in APr 17.12 Alexander refers to ƒ ºª 
Ø e H

øæø

ºÆ Ø. According to Sextus, Antipater held that such arguments could be valid syllogisms whereas Chrysippus had denied it (M VIII 443; cf Alexander, in Top 8.17; Apuleius, int vii [200.16–19] — see Frede, ‘Stoic vs. Aristotelian’, pp.27–28 [pp.118–119]). Clearly, then, Sextus does not dissociate the idea of single-premissed arguments from Chrysippus: on the contrary, he strongly implies that Chrysippus entertained — and rejected — the idea. Hence Alexander’s
æ Ø, who use the term ‘º ª  
ºÆ ’, need not be later than Chrysippus. 148 See in APr 17.12; 18.16; 19.5; 22.18; 164.28; 164.31; 262.9; 263.31; 278.7; 324.17; 345.13. This list of terminological observations accounts for two thirds of the references to ƒ
æ Ø in in APr.

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ƒ
æ Ø at 22.18 with the Stoics of 21.31, and it is not absolutely clear that we must identify them with ƒ
æ Ø of 345.15. However that may be, we can say a little more about the men of 345. Here is the immediate context in which they are introduced: Such too are the arguments which the moderns say conclude unmethodically. When they say that these arguments do not deduce syllogistically, they are quite right (for many of them are of this sort); but when they think that the arguments, formulated in the way in which they formulate them, are like the categorical syllogisms with which the present study is concerned, they are wholly mistaken. (in APr 345.13–17)*

Thus Alexander’s ‘moderns’ held two theses about unmethodical arguments of class (C): they held that they were not syllogisms; and they held that they were ‘like’ Aristotelian categorical syllogisms. Now their two theses were surely connected. How connected? [74] The simplest hypothesis seems to me to be this: the ‘moderns’ argued that Aristotelian categorical syllogisms were not genuinely syllogistic on the grounds that they were in certain crucial respects similar to arguments which were admittedly not syllogistic. These ‘moderns’, then, were critics of Aristotelian logic. A further text may be adduced. At the end of his discussion of hypothetical syllogisms Alexander observes that Aristotle’s view is the converse of what the moderns claim: hypothetical arguments are concludent but are not syllogisms (as we have already said), and categorical arguments are syllogisms. (in APr 390.16–18)**

The moderns here therefore held that hypothetical arguments were genuine syllogisms, whereas categorical arguments, though valid, were not syllogistically valid. It is plausible to identify the moderns of this passage with the moderns of in APr 345.149 One thing is undeniable: the moderns to whom Alexander is adverting in these passages are people who make certain claims about categorical syllogistic;150 in particular, they are people who call on the arguments which the * Greek text in the Appendix. ** u I
ƺØ
ŒÆ ÆPe
j ‰ ƒ
æ Ø IØ FØ
, ƒ  ŁØŒ d º ª Ø æÆ
، d b
P ıºº ªØ d , uæ çŁ

NæÅŒ , ıºº ªØ d  ƒ ŒÆŪ æØŒ . 149 And they are also no doubt to be identified with the
æ Ø of in APr 262.28, who ‘want to say that the only syllogisms are’ the standard hypothetical syllogisms of Stoic logic (see 262.28–36). 150 Well, even that is not strictly undeniable; but if you do deny it, then you must take Alexander to be misrepresenting the views he reports — and we have no particular reason to lay such a charge against Alexander.

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Stoics dubbed ‘IŁ ø æÆ

’ in order to make a point about the nature of categorical arguments. Who were they? Not early Stoics; for it would be unhistorical to claim that Chrysippus and his immediate followers had interested themselves in the details of Aristotelian syllogistic.151 Then were they a later group of Stoic logicians, who knew about the renascence of Aristotelian logic towards the end of the first century bc and who were concerned to contrast and compare their own Stoic heritage with the Aristotelian legacy? (After all, [75] we know that some Stoics — Athenodorus and Cornutus — had discussed certain aspects of Aristotle’s logic (in a broad sense of the term) in considerable detail.152) Or should we entertain the thought that the moderns were heterodox Peripatetics, who used some of the terminology and content of Stoic logic in order to raise penetrating questions about Aristotle’s syllogistic?153 (Certainly there were commentators on the Analytics before Alexander, and some of them offered heterodox interpretations of Aristotle and heterodox views of categorical syllogistic.) And of course we might simply decline to classify the moderns as either Stoic or Peripatetic: they were logicians who swore allegiance to no school. (After all, we need not suppose that Galen was the only ancient thinker who declined to belong to a school.) In the end, the answers to those historical questions escape our knowledge. And they are perhaps less interesting than the theoretical question which lies behind them. For whoever the moderns of 345 may have been, we shall properly wonder why they maintained their curious view that there is an affinity between unmethodical arguments and categorical syllogisms. I return to this question in Part V.

More critics of Aristotle Unmethodical arguments are connected with categorical syllogisms in another Alexandrian text. Alexander endorses the Aristotelian theorem that 151

See F.H. Sandbach, Aristotle and the Stoics, Proceedings of the Cambridge Philological Society suppt 10 (Cambridge, 1985), pp.18–23. Sandbach’s arguments require supplementation and correction; but his general negative conclusion is fundamentally right. (See J. Barnes, ‘Aristotle and Stoic logic’, in K. Ierodiakonou (ed), Topics in Stoic Philosophy (Oxford, 1999), pp.23–53 [reprinted below, pp.382–412].) 152 See e.g. Simplicius, in Cat 62.24–30. 153 Compare perhaps in APr 84.12–19, where Alexander might appear to imply that ƒ
æ Ø had claimed that a particular version of Baroco was  ıºº ªØØŒ  and therefore not a syllogism. If that were so, then these
æ Ø would be either Stoic commentators on APr or else — and perhaps more probably — unorthodox Peripatetics who made use of Stoic notions. But against such an interpretation of in APr 84.12–19, see Barnes, ‘Utility’.

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no categorical syllogism can have two particular premisses. Some logicians had disputed this;154 and Alexander refers briefly to those who think that something can be inferred syllogistically from two particulars — for example, those who offer in proof of this what the Stoics call unmethodically concluding arguments and who assemble various other examples. (in APr 68.21– 24)* [76]

Like the moderns of 345, these people draw a parallel between categorical syllogisms and unmethodical arguments; like them, they draw a moral from the parallel. Yet — if we take Alexander at his word — we shall not identify the men of 68 with the moderns of 345; for the former hold that from two particulars something may be inferred syllogistically, whereas the latter were concerned to show that categorical arguments were not syllogisms at all. Hence we have the following scheme of beliefs: Alexander holds (A) that there is no relevant similarity between categorical syllogisms and unmethodical arguments. His various opponents hold (B) that there is a relevant similarity. But the opponents of 345 allege (B1) that, since unmethodical arguments are not syllogisms, neither are categorical arguments. And the opponents of 68 allege (B2) that, since unmethodical arguments are syllogisms, so too are categorical arguments with two particular premisses. Who were the men of 68, the upholders of (B2)? They can hardly have been Stoics. For consider the way in which Alexander refers to them: those who offer in proof of this what the Stoics call unmethodically concluding arguments ...

It would be very odd to use such a phrase were these people in fact identical with the Stoics The sentence strongly implies that the men of 68 were not Stoics at all. A more engaging suggestion will name Galen. Galen says, it is true, that unmethodical arguments are ‘superfluous’.155 But he also ranks among his third kind of syllogism most, if not all, the arguments which were standardly

154

I return to this point, below p.[77]. * ‹ Ø b ª F
ÆØ KŒ  Kd æ ı ıºº ªØØŒH Ø ı
ªŁÆØ, ‰ ƒ  f Ææa  E øœŒ E ºª 
ı IŁ ø æÆ

Æ Ææå 
Ø N EØ
  ı ŒÆd ¼ººÆ Ø
a ÆæƪÆÆ IŁæ Ç
 ... 155 See inst log xix 6, with Barnes, ‘Utility’, for text and interpretation.

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called unmethodical;156 and his view could be — loosely — characterized by the proposition that unmethodical arguments are in fact syllogistically valid. Yet the men of 68 did not merely affirm the syllogistical status of arguments commonly held to be unmethodical: they adduced these arguments to demonstrate something about categorical syllogistic, namely that there are valid syllogisms the premisses of which are each particular (i.e. of the form ‘AiB’ or ‘AoB’). Galen [77] may conceivably have done that — or have seemed to do it — in one of his lost works. But there is no evidence at all, and no likelihood, that he did do it; and it would be foolish to find Galen behind the men of 68. Some centuries after Alexander another unorthodox claim on syllogisms with two particular premisses was made in the school of Ammonius. In the scholium known as the documentum Ammonianum we find the following remark: ‘But, they say, arguments in virtue of a proslepsis157 are not syllogisms at all since they transgress the rules of syllogisms. For they conclude from two negatives and from two particulars and from propositions of the same form in the second figure — and all these are against the rules.’ — But so far as that goes, hypothetical syllogisms will no longer be syllogisms since they conclude from two particulars and negatives. E.g. ‘My dear Phaedrus, if I don’t know Phaedrus, then I don’t know myself either.’ The two propositions here are particular negative. So there is a common solution. (XII 10–16)*

It is tempting to associate the view of the scholiast with the view of the men of 68: hypothetical syllogisms and arguments in virtue of a proslepsis will then have been among the ‘various other examples’ which the men of 68 adduced in support of their view (Alexander, in APr 68.23–24). And we might hazard the further conjecture that the men of 68 were heterodox Peripatetics, whose ideas were later revived under Ammonius. But what exactly is the view of the scholiast? He does not give us his ‘common solution’ to the problematical cases he mentions. It is plain that he thinks there may be syllogisms with two particular premisses. And it is 156

See inst log xvi–xvii; below, pp.[98–99]. For these arguments, see above, n.15. * Iºº’ PŒ Nd
‹ºø ıºº ªØ , çÆ
, ƒ ŒÆa æ ºÅłØ
KØc ÆæÆÆ
ıØ a YØÆ H
ıºº ªØH

ŒÆd KŒ  ªaæ I çÆØŒH
ı
ª ıØ ŒÆd KŒ  æØŒH
ŒÆd K › åÅ
ø
K
ıæfiø åÆØ. Iºº’ ‹
Kd  fiø P ƒ  ŁØŒ d ıºº ªØ d Ø ıºº ªØ  NØ
‰ KŒ  æØŒH
ŒÆd I çÆØŒH
ı
ª
 x
t çº !ÆEæ, N Kªg !ÆEæ
Iª
H, ŒÆd KÆıe
Iª
H [Plato, Phdr 228A]. ƃ  ªaæ ÆyÆØ æ Ø ŒÆd æØŒÆd ŒÆd I çÆØŒÆ. Œ Ø
c s
ºØ. See also Boethius, in Int2 316.12–317.8 — doctissimi viri have recognized valid syllogisms with two negative premisses. 157

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equally plain that these will not be categorical syllogisms. For, first, he has already explicitly said that syllogisms in virtue of a proslepsis form a third class of syllogism (IX 23; XII 3), and hence are not categorical. Nor, secondly, is it easy to think that he took the hypothetical argument from the Phaedrus to be in reality a categorical syllogism with two particular premisses. (At any rate, if he did interpret the argument as having two [78] premisses of the form ‘AoB’, then he was risibly wrong.158) And of course if he did not interpret the argument in that way, then his contention has nothing to do with categorical syllogistic. Thus the documentum Ammonianum does not help us to identify the men of 68. I abandon the hunt for the men of 68. And I postpone to Part V the more interesting question of why they maintained their unorthodox view.

The Stoics on unmethodical arguments We can identify certain illustrative inferences as examples of what the Stoics called unmethodical arguments. What more can we say about the things? In particular, how are they related to the classification of Stoic º ª Ø? How are they to be characterized as a group or class of arguments? What did the Stoics actually say about them? ¸ ª Ø IŁ ø æÆ

 were of course valid arguments — they were º ª Ø æÆ
ØŒ  in the broad sense of the word ‘æÆ
ØŒ ’. How were they related to other º ª Ø æÆ
ØŒ ? It is, I think, nowhere explicitly said that unmethodical arguments were not taken by the Stoics to be a species of syllogism.159 But there is no real doubt about the business. All our sources clearly imply that the Stoics took them to be distinct from syllogisms; and when Galen makes them a subclass of º ª Ø æÆ
ØŒ  (in the narrow sense), we may reasonbly take him to be reflecting a Stoic — indeed, a 158 But how did he interpret the argument? He gives us a single conditional sentence of the form ‘If not-p, then not-q’. The context in the Phaedrus itself does not offer any decisive help. Perhaps the scholiast took the argument to have the form: If not-p, then not-q. Not-not-q. Therefore: not-not-p. But it is then unclear why we should agree that both the premisses are negative; and it is clear that we should not agree that both premisses are particular if that means that they both have the form ‘AoB’. 159 The
æ Ø of in APr 345.13 certainly held that unmethodical arguments were not syllogistic; but — as I have just argued — we cannot confidently identify those people with (any) Stoic logicians.

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Chrysippean — classification.160 Moreover, their very [79] name shows that they were not syllogisms — for syllogisms surely do conclude methodically. What was the general characteristic of an unmethodical argument? If we consider the examples, we shall get nowhere: from a formal or structural point of view, the examples are a farrago. Nor is that surprising; for the class is characterized by a lack of something — its members are unmethodical, and we should not suppose that they all have something positive in common. What, then, do they all lack? Or rather, what is it for an argument to lack a method or to conclude unmethodically? The terminology is explained, after a fashion, by Galen: Last, consider the arguments they call unmethodical, by which we are to syllogize even though there is no methodical argument of any kind. (inst log xix 6)161

Unmethodical arguments, then, are arguments where one makes an inference even though there is no methodical argument at all. The phrase ‘methodical argument’ may perhaps have been a technical term; but if it was, we do not know its technical sense. Hence Galen’s explanation helps us little. Yet here conjecture is neither difficult nor dangerous. An argument — I conjecture — concludes methodically provided that there is some formal rule which validates it. And there will be such a formal rule just in case the argument is valid in virtue of a logical form. (For any logical form will determine a formal rule and any formal rule will conversely determine a logical form.162) Hence methodically concluding arguments are, in effect, formally valid arguments; and unmethodically concluding arguments are materially valid arguments. The conclusion might seem to be confirmed by a passage in the Ammonian notes on the Prior Analytics. The scholiast considers an argument of class (A) and observes: [80] Thus let not the geometers say: Since A is equal to B and B is equal to C, therefore A is equal to C.

160

See inst log xix 6, with Barnes, ‘Utility’. For the text and interpretation see Barnes, ‘Utility’. 162 I mean: to any logical form (Fj) P1, P2, ... , Pn: therefore Q there corresponds the rule: (Rj) From ‘P1’, ‘P2’, ... , and ‘Pn’ infer ‘Q’ and vice versa. There is a ‘method’ for getting from ‘P1, P2, ... , Pn’ to ‘Q’ just in so far as the form (Fj) is underwritten by the rule (Rj). 161

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For they deduce truths not because of the combination but because of the matter. That is why the Stoics call them unmethodically concluding. ([Ammonius], in APr 70.10–13)*

The false Ammonius thus explains the Stoic notion of unmethodical arguments by reference to non-formal or material validity. But the Ammonian text provides flimsy evidence. Its author is late, and he makes mistakes.163 And in any case, the text does not say that the Stoics had actually claimed that unmethodical arguments were arguments whose validity depended on their matter. The proper paraphrase of the pertinent sentence in the text is not this: ‘The Stoics say: ‘‘These arguments are unmethodical because they are materially valid’’.’ Rather, it is this: ‘Because these arguments are materially valid, the Stoics say: ‘‘They are unmethodical’’.’ And that tells us nothing about the Stoics’ own reason for calling arguments unmethodical. It remains to ask what attitude the Stoics themselves took to their unmethodical arguments. In particular, did they attempt to produce any theory for such arguments? We know virtually nothing of what any Stoic thought or said about the things. Not absolutely nothing; for a passage in Galen’s institutio seems to imply something about the attitude of Posidonius to the unmethodicals.164 But virtually nothing — too little to sustain any fruitful conjecture. Yet there is no need for conjecture. For one piece of evidence lies before us, viz the evidence provided by the nomenclature. The Stoics called these arguments unmethodical, and they called them unmethodical because (or so I have supposed) they thought [81] there was no general method in terms of which their validity could be established or explained. It is reasonable to infer that they regarded such arguments as outside the scope of ØƺŒØŒ, as untreatable by the science of logic.165 There is no counterindication, no * c s
ºªøÆ
ƒ ªøæÆØ KØc e ` fiH ´ Y
, e b ´ fiH ˆ Y
, ŒÆd e ` ¼æÆ fiH ˆ Y

IºÅŁB ªaæ ıºº ªÇ
ÆØ P Øa c
º Œc
Iººa Øa c
oºÅ

Øe ŒÆd ƒ øœŒ d IŁ ø æÆ

 çÆØ
ÆP . 163 Moreover, the text itself is not beyond suspicion: in 70.13 ‘ÆP ’ lacks an antecedent (it cannot, of course, refer to ƒ ªøæÆØ in 70.11), and the plural is surprising. We are dealing with a text which is preserved in (or, at least, which was edited from) a single, corrupt manuscript and which, moreover, gives the impression of having been carelessly excerpted from a fuller commentary. 164 See inst log xviii 8: but the text here is corrupt, and the passage is usually misinterpreted (see J. Barnes, review of Hu¨lser, Fragmente, CR 39, 1989, 263–264). 165 See e.g. Mueller, ‘Greek mathematics’, p.63: the arguments ‘were regarded as simply unsystematic — i.e. incapable of analysis’. Frede says that ƒ IŁ ø æÆ

 are ‘arguments ... in which one or possibly more assumptions on which the inference is based have been taken for granted

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evidence that the Stoics attempted to reduce unmethodical arguments to proper syllogisms or to transmute them into formally valid arguments.166

The Truncated Argument again Now since the Truncated Argument is unmethodical — it is a member of class (A) — , we may properly conclude that the Stoic attitude to it was precisely this: the Argument is valid, æÆ
ØŒ , but it is not a syllogism. It is — in the rival Peripatetic jargon — materially valid, but not formally valid. It cannot be analysed or formalized or accounted for within the science of logic. The conclusion will perhaps seem dispiriting. In effect, it denies that logic can answer the challenge thrown down by the Truncated Argument: there are, after all, valid arguments, of great importance to the sciences, which the discipline of logic cannot analyse. Exactly how dispiriting is the conclusion? And why were the Stoics content with it? Neither question can be answered on the basis of any ancient text. But each merits a brief paragraph of speculation. As to the first question, we should need to know what attitude the Stoics took to the Euclidean Argument. Suppose that they held (1) that the Euclidean Argument is a syllogism (or perhaps a subsyllogistic argument), and also (2) that, just as to the Truncated Argument there corresponds the Euclidean Argument, [82] so to any scientifically interesting unmethodical argument there corresponds a syllogistic argument. Then they might maintain that science could work with the Euclidean Argument and had no need for the Truncated Argument.167 And they might reasonably conclude that their attitude to unmethodical arguments was not dispiriting from a scientific point of view. And why did the Stoics hold that the Truncated Argument was unmethodical? Why — to put the same point in a different way — should they have denied that a ‘method’ was adequately determined by the following rule? and not been made explicit’ (‘Stoic vs. Aristotelian’, p.3 [p.102]; cf Stoische Logik, pp.122–233); and he means that this was the Stoic account of unmethodical arguments. (Earlier Mueller had anticipated Frede’s view: ‘we are justified by the evidence from Alexander in assuming that the Stoics turned unsystematically conclusive arguments into syllogisms by adding a premiss’: ‘Stoic logic and Peripatetic logic’, AGP 51, 1969, 173–187 — on p.179.) But the texts which Frede adduces do not support this view; for they all report Peripatetic (or Galenian) responses to the arguments which the Stoics took to be unmethodical. The Stoics — or so our meagre evidence implies — took these arguments be complete as they stood: they did not speak of ‘omitted premisses’. 166 167

Again, Posidonius may be an exception: above, n.163. Note that Euclid himself uses the Euclidean and not the Truncated Argument.

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From ‘x is equal to z’ and ‘y is equal to z’, infer ‘x is equal to y’. Why should they not have accepted ‘ ... is equal to — ’ as a logical constant? The old question of logical form and logical constants returns. And the Stoics initially face the dilemma which confronted Alexander near the end of Part III. First, they might appeal to relativized notions of logical form and logical constant. If we suppose that, crudely speaking, the logical constants of Stoic grammar are all of them sentential connectives, then evidently ‘ ... is equal to — ’ will not be a logical constant, and the Truncated Argument will not be formally valid, relative to the Stoic system.168 But that conclusion is uninteresting. It merely invites the retort: So much the worse for Stoic logic. Secondly, then, the Stoics might invoke the absolute notions of logical form and logical constant. But then, and trivially, the Truncated Argument is formally valid. And it is a simple error to label it — or any other argument — unmethodical. Plainly the Stoics, like Alexander, would have hoped to evade both horns of the dilemma. They, like Alexander, would surely have said something like this. ‘The Truncated Argument is not a formally valid syllogism within Stoic logic. Of course, it is valid in virtue of a logical form, i.e. in virtue of a highest form. But its highest forms are at a very low level of generality: they all contain [83] non-logical constants, i.e. they all contain elements which no suitably elaborate system recognizes as constants.’

V

Alexander and unmethodical arguments The arguments which the Stoics called unmethodically concludent were, as I have already indicated, discussed and examined by Alexander. He has his own view and theory about such arguments. He holds, first and negatively, that they are not syllogisms, i.e. that they are not formally valid; and he holds, secondly and positively, that every valid argument which concludes unmethodically may be associated or paired with an argument which itself is a

168 Nor, of course, will the rewritten or Apollonian version of the Argument be formally valid relative to Stoic logic.

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syllogism. I shall say something about each of these ideas in turn.169 But first I shall cite at some length a text which has already been called upon in earlier Parts of this paper. The text is in APr 344.9–346.6, where Alexander is commenting on Aristotle’s remark, at APr ` 47a22–23, that ‘the necessary’ is more extensive than the syllogism.170 For that reason, it is not the case that, if A’s being equal to C follows by necessity from the assumption that A is equal to B and C to B, then that is thereby a syllogism. It will be syllogistically deduced if, first, we assume in addition the universal proposition which says ‘Things equal to the same thing are equal to one another’ and secondly, we contract what we assumed as two propositions into a single proposition which has the same force as the two, namely ‘A and C are equal to the same thing (for they are equal to B)’; for in that way we may deduce by a syllogism that A and C are equal to one another. Similar to that is the belief that if you assume that A is greater than B and B than C, then — since the conclusion follows necessarily — you show syllogistically that A is greater than C. But that is not yet a [84] syllogism — unless you assume in addition a universal proposition which states ‘Everything which is greater than something greater is also greater than what is smaller than it’, and unless also the two assumptions become one, namely the minor premiss which says ‘A is greater than B, which is greater than C’. For in that way you will deduce by a syllogism that A is greater than C. ... The following argument too is similar to the ones just set out. One man has the same parents as another — say, A as B. But B has the same parents as C. Therefore A has the same parents as C. In order for there to be a syllogism we need a universal proposition which says that anyone who has the same parents as someone is his sibling. If to that proposition there is added the divided proposition, rendered single and saying ‘A and C have the same parents as B’ — in that way it is deduced that A and C are siblings.171 ... The following arguments are of this sort: Dio says that it is day. 169

For discussion of this text, see e.g. Mueller, ‘Stoic logic’, pp.175–178; Lee, Die griechische Tradition, pp.108–111; J. Barnes, ‘ ‘‘A third sort of syllogism’’: Galen and the logic of relations’, in R.W. Sharples (ed), Modern Thinkers and Ancient Thinkers (London, 1993), pp.172–194. 170 The texts bearing on unmethodical arguments occur in three contexts: (1) the Aristotelian distinction between ‘the necessary’ and the syllogism; (2) the Aristotelian thesis that every syllogism must contain at least one universal premiss; and (3) the ‘fiH ÆFÆ r
ÆØ’ clause in Aristotle’s definition of the syllogism. It must be emphasized that Alexander is primarily concerned to interpret and explain Aristotle’s text: he is not primarily engaged with the history of logic — or even with logic itself. 171 The syntax of this sentence is odd — but the exact parallel at in APr 22.21–22 defends the received text.

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But Dio speaks truly. Therefore: it is day. And again: Dio says that it is day. But it is day. Therefore: Dio speaks truly. For if it is assumed that what someone says is the case, it follows that he is speaking truly; and if it is assumed that he is speaking truly, it follows that what he says is the case. In each of the arguments a true universal proposition has been omitted. In the one it is ‘Everything someone says when speaking truly is the case’. 172 ‘Dio, saying that it is day, speaks truly’ — which has been divided into ‘Dio says that it is day’ and ‘But Dio speaks truly’. And in this case a conclusion — ‘Therefore: it is day, as Dio says’ — follows by a syllogism. In the other case, the omitted proposition, which is universal, is to the effect that someone who says of what is the case that it is the case speaks truly. And ‘Dio says, while it is day, that it is day’ has been divided — it has been divided into ‘Dio [85] says that it is day’ and ‘And it is day’. The conclusion, ‘Dio speaks truly’, follows syllogistically and no longer unmethodically when the propositions are taken in this way. (in APr 344.13–27; 344.31–345.3; 345.28–346.4)173

For ease of reference, I shall repeat three of Alexander’s illustrative arguments and give them identifying names. As his first example of a materially valid argument, or of something which is necessary but not a syllogism, Alexander takes Argument A: (1) A is equal to B. (2) C is equal to B. Therefore: (3) A is equal to C. As Argument B I take Alexander’s third example: (1) A has the same parents as B. (2) B has the same parents as C. Therefore: (3) A has the same parents as C. And as Argument C, the first of the two arguments involving Dio: (1) Dio says that it is day. (2) Dio speaks truly. Therefore: (3) it is day. 172 The text at this point is either corrupt or else exceedingly compressed. In either case, my insertion corresponds to what Alexander meant to say. 173 The omitted passages contain general reflections and comments: they are mostly quoted and discussed elsewhere in this chapter. For the Greek, see the Appendix.

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Thus — and as their names are intended to suggest — we have one example from each of the classes of argument which I earlier called (A), (B), and (C).174

ufucßai of two particular propositions Alexander holds that the illustrative arguments are none of them syllogisms. He also holds that they are valid or ‘necessary’ — [86] materially but not formally valid.175 Why does he hold that they are not formally valid? One fairly simple line of thought might present itself. It did present itself to Philoponus. Commenting on a variant of Argument A, he writes thus: That the conclusion does not follow syllogistically is clear from the fact that both propositions are particular and are affirmative in the second figure. (in APr 321.12–14)*

In other words, the argument has the form of a second-figure syllogism in that its premisses make up a second-figure ıÇıªÆ of the form: BiA, BiC. And the unreliability of that ıÇıªÆ176 is doubly determined: every valid categorical syllogism must contain at least one universal premiss; and every valid second-figure syllogism must contain one negative premiss. The same line of thought can be found in the Ammonian notes. The false Ammonius asserts of the same variant of Argument A that its premisses are particular. Moreover, he explains why they are so.

174

The other examples in the present passage (and the examples found elsewhere in Alexander and in the other commentators: references above, n.142) add nothing of interest — except that the three-premissed argument from class (E), cited at in Top 15.3–14, shows that the arguments in which Alexander is interested are not restricted to two-premissed inferences. 175 One or two passages give the impression that Alexander does not regard the arguments, as they are formulated, as being valid at all (in APr 345.25; 347.25: the same point appears in the corresponding passage in Philoponus’ commentary, in APr 321.1–6, in which he is explicitly following Alexander). But it is quite plain that Alexander’s real view is that the arguments are valid. When he says something which seems to imply that they are not valid, we should understand a suppressed ‘syllogistically’ with the word ‘valid’. (Similarly, but in a different context, Alexander says that we should understand a suppressed ‘ıºº ªØØŒH’ in Aristotle’s text: in APr 185.2–3.) * ‹Ø ªaæ P ıºº ªØØŒH, Bº
K z
Iç æÆ  ƃ æ Ø Nd æØŒÆd ŒÆd K
ıæfiø åÆØ ŒÆÆçÆØŒÆ
oø b Kå ıH
H
æ ø
ıºº ªØe PŒ Kª
 . 176 See APr ` 27b36–38; Alexander, in APr 92.25–93.11 (cf 266.16–267.27); Philoponus, in APr 100.1–10. Later on, it is the standard example of a fallacy Ææa e åBÆ: e.g. [Alexander], in Soph El 89.4–6, 20–24; Comm II on Soph El 171b8–12 [volume II 81–83]; Comm III on Soph El 176b29 [volume II 215–216].

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That this is equal to that is particular not because of the deictic element (for the geometers always conduct their arguments on universals) but because the indeterminate has the same force as the particular. (in APr 70.20–22)*

(A little later, he considers another example, drawn from APr [87] ` 41b15–20, and urges that in it too ‘both premisses are particular, since they are indeterminate’: 71.3–4.**) Aristotle explains that a proposition is indeterminate or IØ æØ  if it says that something holds or does not hold, without being either universal or particular — ‘e.g. that of opposites the science is the same, or that pleasure is not good’ (APr ` 24a19–22). And he maintains that indeterminate propositions are equivalent to particular propositions. Let ‘AuB’ represent the indeterminate form ‘A holds of B’. Then ‘AuB’ will be true just in case either ‘AaB’ is true or ‘AiB’ is true. Hence ‘AuB’ is logically equivalent to the disjunction of ‘AaB’ and ‘AiB’. But since ‘AaB’ entails ‘AiB’, it follows that ‘AuB’ is equivalent to ‘AiB’.177 (And similarly for ‘AyB’ or ‘A does not hold of B’.) That view of the logical status of indeterminates was accepted by almost all the later commentators,178 and it underlies the diagnosis which Philoponus and the Ammonian scholiast make of Argument A. The same diagnosis was doubtless made for Arguments B and C. It was also made for ‘wholly hypothetical’ syllogisms.179 According to Philoponus, such inferences are necessary but not syllogistic — they necessitate ‘because of their matter’. And they are not syllogisms precisely because their two premisses are Iæ Ø æØ Ø or indeterminate in quantity, and therefore equivalent to particulars.180 The idea underlying this general diagnosis — the idea that both (or all) of the premisses in an unmethodical argument are particular — was known to Alexander. For he reports, as I have already remarked, that some people had argued that there were valid syllogisms with two particular premisses and that * æØŒe
b e   fiH Y
P Øa e ،،
ðKd ªaæ H
ŒÆŁ º ı  Ø F
ÆØ e
º ª
Æ
Æå F ƒ ªøæÆØÞ, Iºº ‹Ø e Iæ Ø æØ
N ı
ÆE fiH æØŒfiH. ** ŒÆd ªaæ ¼çø æØŒÆd KØc Iæ Ø æØ Ø. 177 From ‘p if and only if (either q or r)’ and ‘If q, then r’, we may infer ‘p if and only if r’. 178 But note the essay in Ammonius, in Int 111.10–120.12, which argues at length against some unnamed philosophers who had denied the equivalences. 179 On which, see above, p.[62], and Barnes, ‘Terms and sentences’. 180 See in APr 322.32–323.14 (cf Boethius, hyp syll I ix 2–3). This view of wholly hypothetical syllogisms was familiar to Alexander (in APr 347.18–348.23: he says that you might construe the premisses as IØ æØ Ø). But for his own view on the matter, see above, pp.[62–63].

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the unmethodicals were examples of such arguments (in APr 68.21–24). Did Alexander himself share the view? At in APr 345.18–20 he says that [88] as a matter of fact, many of such arguments [i.e. of the arguments which conclude unmethodically] consist wholly of particular propositions; and we have shown that no categorical syllogism comes about without a universal proposition.*

The word ‘many’ suggests that not all unmethodical arguments are constructed solely from particular propositions.181 But, and more significantly, the passage also strongly suggests that in the examples before us Alexander was prepared to discover particular propositions.182

Singular terms Then are the premisses of Argument A indeterminate and hence equivalent to particular propositions? There is no clear answer to the question. For the propositions are singular propositions. The false Ammonius notices this fact, but tries to explain it away. He urges us to disregard ‘the deictic element’ in the premisses;183 for he claims that ‘the geometers always conduct their arguments on universals’ (in APr 70.20–22). I take the point to be this: ‘Do not be misled by the fact that the premisses of the argument contain deictic elements and thus appear to be singular propositions. In reality, as the geometers’ own practice shows, they must be construed as general propositions — and hence as indeterminates.’ But it is quite unclear why we should not insist, against the scholiast, on the singularity of the propositions. The geometers aim, of course, at universal conclusions; but they conduct their arguments on singular instances.184 Now you might say that singular propositions are, trivially, indeterminate; for they are neither universal nor particular, and [89] indeterminate propositions are precisely those propositions which are neither universal nor * Greek text in the Appendix. What of those unmethodicals which do not contain exclusively particular premisses? I assume that they are the unmethodicals which Alexander regards as syllogisms: at in APr 345.14–15, he says that ƒ  ºº  of the unmethodicals are not syllogisms, and this ‘ ƒ  ºº ’ is probably picked up by the ‘ ƒ  ºº ’ of 345.18. Then what arguments were accepted as ıºº ªØ  by Alexander and yet classified as unmethodical by ƒ
æ Ø? Certainly, none of the illustrative unmethodicals paraded in our extant sources. 182 cf in APr 68.31–69.1; and see below, p.[98]. 183 See in APr 70.21: he has reformulated the argument with demonstratives in place of proper names. 184 See above, n.3. 181

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particular. Or you might say that singular propositions are not indeterminate; for Aristotle defines the term ‘indeterminate’ with general propositions in mind. — Of course, it does not matter a hang which of the two things you choose to say. The serious question is this: are the premisses of Argument A to be construed as, or to be taken as equivalent to, particular propositions? Now singular propositions are a standing puzzle for categorical syllogistic. And since singular relational propositions, like the constituent propositions of Arguments A and B, are doubly puzzling, let us start with Argument C. Any solution to the puzzle must dissolve the singularity of singular terms, replacing them by or reconstruing them as general terms. That is in itself neither difficult nor unfamiliar to modern logic: the name ‘Dio’ in Argument C can be replaced by the general term ‘thing identical with Dio’ or ‘Dionizer’.185 Given that transfiguration, you have a choice over the reconstrual of, say, proposition (2) of Argument C: Dio speaks truly. You may reconstrue singular propositions as universals. Dio speaks truly. is then construed as: Every Dionizer speaks truly. — and in general, ‘Fx’ becomes ‘FaX*’ (where ‘X*’ is the term corresponding to the name ‘x’). Or you may treat singular propositions as particular, so that: Dio speaks truly. emerges as: [90] Some Dionizer speaks truly. — and, in general, ‘Fx’ becomes ‘FiX*’. Or else you may treat singular propositions as ‘wild’, that is to say, as being interpretable, according to the demands of the context, either as universals or as particulars: Dio speaks truly. will be read now as: Every Dionizer speaks truly. now as: Some Dionizer speaks truly.

185 Students of Quine are familiar with such ways of ‘eliminating’ singular terms, and ‘pegasize’ has almost become an English verb. In general, Quine shows how we may replace singular terms by one-place predicates; and to any one-place predicate there corresponds a general term of the sort needed by Peripatetic logic.

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— and in general, ‘Fx’ will be read now as ‘FaX*’, now as ‘FiX*’.186 Which option should we take? In a way, it does not matter. For, given the sense of the term ‘Dionizer’, ‘Some Dionizer is F’ is true if and only if ‘Every Dionizer is F’ is true. (Each sentence is true if and only if Dio, the unique Dionizer, is F.) The premisses of Arguments A and B require more work. In the proposition: (1) A is equal to B. we have two names, ‘A’ and ‘B’. Either name may be turned into a general term. But we may not turn both names into general terms at the same time; for then the proposition will contain three terms (equality providing the third), whereas every categorical proposition has exactly two terms. The solution to this problem consists in amalgamating the relational predicate ‘ ... is equal to — ’ with one or other of the names ‘A’ and ‘B’, thereby forming a monadic predicate, from which we can then construct a general term. The remaining name will be reconstrued as a general term. [91] Again, there is nothing shoddy or unfamiliar about those manoeuvres. Sentence (1) exhibits all three of the forms: (Fi) x is equal to B. (Fii) A is equal to y. and: (Fiii) x is equal to y. The current suggestion, in effect, invites us to opt for (Fi) or (Fii). Each is an instance of the general form: (iv) Fx. — and ‘Fx’ has already been reconstrued as ‘FaX*’ or ‘FiX*’. Thus there are several ways of discovering a decent categorical form for sentence (1) and its fellows. One way will reconstrue the premisses of Argument A as: (1*) Being equal to B holds of some A. (2*) Being equal to B holds of some C. Both sentences are particular. Together they make a ıÇıªÆ of the form ‘BiA, BiC’. And so, as Alexander and the later commentators say, the

186

Note that taking singular terms as ‘wild’ in this way is not equivalent to construing singular propositions as indeterminate. The ‘wild’ interpretation does not equate singular propositions with disjunctions: it equates them now with one disjunct, now with another. On wild terms, see e.g. F. Sommers, The Logic of Natural Language (Oxford, 1982), pp.15–21.

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premisses of an unmethodical argument are — or can be construed as — particular propositions.187 Here I may return briefly to the anonymous logicians whom Alexander mentions at in APr 68.188 According to Alexander, they too held that the premisses of (at least some) unmethodical arguments were particular in form — each had the categorical form ‘AiB’. But they also held, or so Alexander implies, that these arguments are syllogisms, or formally valid, as they stand. How can they have held such a view? There seem to be two possibilities. [92] First, we may suppose that the men of 68 simply maintained that some arguments which exhibit the categorical form: (FÆ) BiA. BiC. Therefore: CiA.189 were formally valid — and valid in virtue of this categorical form. If that was their view, then they were straightforwardly mistaken. We could try to explain how they came to err, but we could not hope to put a decent face on the error. Secondly, perhaps they maintained a subtler thesis. There are some arguments which exhibit the categorical form (FÆ) and which are also formally valid. But they are valid not in virtue of this form but rather in virtue of some other logical form which they also exhibit. That is an intelligible view. The difficulty is that we can expound it no further: we have no evidence at all to suggest what other logical forms the men of 68 might have descried in these arguments. (I could guess. So can you.)

‘The conclusion must depend upon the premisses’ What is gained by construing the premisses of Argument A as particular sentences? It is true that if the premisses are so construed, then no conclusion may be validly drawn within categorical syllogistic. But that hardly establishes that Argument A is not formally valid.190 We may simply object that even if 187 I do not claim that my construction of (1*) and (2*) is historically correct: I leave for another time the problem of singular terms and singular sentences in the commentators. (Alexander in fact says nothing about singular terms in his commentary on APr; but he is perfectly content to use them — with quantifiers — in syllogisms: e.g. in APr 350.30–351.7.) But one thing is clear: whatever the commentators say about singular sentences, their analysis of Argument A requires either sentences (1*) and (2*) themselves or else a pair of equivalent sentences. 188 See above, p.[76]. 189 Or the form ‘AiB, BiC: therefore AiC’, or ... 190 Note that there is no advantage from this point of view in construing the premisses as universal propositions. For if Argument A is construed as a categorical syllogism, then it must be a

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(1*) and (2*) are permissible formulations of the premisses of Argument A, they are not the only way of looking at the logical syntax of those propositions. The propositions exhibit several other forms — non-categorical forms. For all that the train of [93] reasoning thus far shows, the Arguments may be formally valid in virtue of one or another of those non-categorical forms. Thus reflexion on the categorical status of the premisses of unmethodical arguments is inadequate; and if Alexander intended to argue — as Philoponus and the false Ammonius surely did — that unmethodical arguments were non-syllogistic simply because their component propositions were particular in form, then his argument was feeble. But although Alexander held that the premisses of unmethodical arguments were particular, he need not have taken that fact as the sole mark and proof of their lack of formal validity. He may have taken this view about the status of the premisses without sharing the Philoponan diagnosis of the nature and cause of the unmethodical status of the arguments. And in point of fact, Alexander had a different — or perhaps an additional — reason for denying that Arguments A–C are syllogisms. The reason can be elicited from a passage dealing with Argument B. That the syllogism depends on the added universal proposition is clear from the fact that if the universal is not true, the conclusion drawn from what is thus assumed is not true either. For if we assume ‘A is sibling of B, B is sibling of C’, it is no longer true that A is necessarily sibling of C — since the universal proposition that siblings of the same person are also siblings of one another is not true. For if someone has a son, marries another woman who herself has a son, and has a son by her, then this boy will be sibling of each of the two earlier children, but the earlier children will not for this reason be siblings of one another. (in APr 345.3–12)*

Alexander thus implicitly invites us to consider a further argument, viz Argument B*: (1) A is sibling of C. (2) B is sibling of C. Therefore: (3) A is sibling of C.

second-figure syllogism. But every valid second-figure syllogism has one negative premiss. Hence Argument A cannot be construed as a valid categorical syllogism. (See above, p.[86].) Second-figure syllogisms with two affirmative premisses are stock examples of formal fallacy (see above, n.175): see e.g. Alexander, in Top 21.16–19; Philoponus, in APst 158.28–159.6; [Alexander], in Soph El 89.4–10; 136.6–8; Comm II on Soph El 171b8–12 [volume II 81–83]. * Greek text in the Appendix.

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He proves that this argument is invalid, i.e. not even materially valid, and he implicitly suggests that its invalidity shows that Argument B is only materially valid.191 The structure of Alexander’s reasoning is this. ‘Argument B* [94] has the same logical form as Argument B. But Argument B* is not valid. Therefore Argument B is not formally valid’. And that line of reasoning is — almost — good. In order to make it good, only a slight modification is needed, thus: ‘Every logical form exhibited by Argument B is also exhibited by Argument B*. But Argument B* is not valid. Hence Argument B is not formally valid.’ That is, in principle, a perfect argument. Does it establish Alexander’s contention? The answer to the question turns, once more, on the question of what parts of the arguments we are prepared to regard as logical constants. One of the forms of Argument B is this: x has the same parents as y. y has the same parents as z. Therefore: x has the same parents as z. Every argument of this form is valid. Therefore, if we allow that ‘ ... has the same parents as — ’ is a logical constant, Argument B will be formally valid. No doubt it would be idiosyncratic to take ‘ ... has the same parents as — ’ for a logical constant. But another option is open. Recall the Apollonian account of equality: equality is identity of magnitude. In the same way — and, if anything, more obviously — having the same parents is identity of parents. Now let ‘f( )’ be a name-forming operator on names, such that ‘f(x)’ names the parents of whatever ‘x’ names.192 We may say: (PA) ‘x has the same parents as y’ means ‘f(x) is identical with f(y)’. — where (PA) is the ‘Apollonian’ account of parenthood, analogous to (EA), the Apollonian account of equality. One form of Argument (B) will thus be: f(x) is identical with f(y). f(y) is identical with f(z). Therefore: f(x) is identical with f(z).

191

See the close parallel at in APr 347.33–348.9. Items of the form ‘f(x)’ are thus plural names: on which, see P. Simons, Parts (Oxford, 1987), pp.141–144. Plural names are neither odd nor frightening: we read Russell and Whitehead, we go to law with Sue, Grabbitt, and Runne. 192

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Every argument of this form is valid. Therefore, if we allow that [95] ‘ ... is identical with — ’ is a logical constant, Argument B is formally valid.193 (I assume that the Apollonian transformation leaves us with the same argument and does not replace Argument B by some new argument.194) Yet the last paragraphs have missed the point — or one of the points — which Alexander is trying to make. His invention of Argument B* is designed to show that Argument B depends on a universal proposition which is not contained among its premisses. The nature of this universal proposition will concern us in the next section. Here it is the notion of dependence which matters. Aristotle’s definition of a syllogism requires that the conclusion must not only follow from the premisses — it must also come about because of the premisses, fiH ÆFÆ r
ÆØ (APr ` 24b20). Alexander insists upon the requirement: the premisses must be the ÆNÆ — the cause or explanation — of the conclusion (in APr 21.10–23.2). He is aware that the notion is obscure and open to misunderstanding;195 but it is, for him, constitutive of the notion of a syllogism.196 Now in unmethodical arguments, he claims, the explanatory condition is not met: in them, the conclusions depend on something not explicit in the premisses. In Argument B, the conclusion depends not only on the premisses but also on a universal proposition; and the parallel with the invalid Argument B* is invoked to establish precisely that fact. And that, at bottom, is the reason why Argument B cannot be a genuine syllogism.197 [96]

193 (PA) will not please everyone; but several other analyses are possible, each of which will make Argument B formally valid. Perhaps the simplest is this: ‘x has the same parents as y’ is explained as ‘For any z, z is a parent of x if and only if z is a parent of y’. A form of Argument B will then be this (I use obvious abbreviations): (8z)(zPx iff zPy) (8z)(xPy iff zPu) Therefore: (8z)(zPx iff zPu). Every argument of that form is valid; and if any form at all is a logical form, then surely that form is a logical form. 194 See above, p.[36]. 195 See in APr 21.12–21; cf Philoponus, in APr 35.17–35. 196 I have argued elsewhere that this is not an idea peculiar to the Peripatetics (see J. Barnes, ‘Proof destroyed’, in M. Schofield, M.F. Burnyeat, and J. Barnes (eds), Doubt and Dogmatism (Oxford, 1980), pp.161–181, on pp.168–173 [reprinted in volume III]); and I believe that it was in fact taken for granted by all ancient logicians. 197 The point is not that it is an enthymeme. An enthymeme is invalid as it stands: to get a valid argument you must add a premiss or two — but the additions are so obvious that they are not normally made explicit. An unmethodical argument is valid as it stands: nothing, in a sense, needs to be added to it; but something needs to be made explicit.

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This contention of Alexander’s is obscure. I shall for the moment leave it on the table: it will be better discussed after we have looked at the positive part of Alexander’s thesis about unmethodical arguments.

The added universal premiss And so I turn now to Alexander’s positive thesis, and to what I have called the ‘associated’ syllogisms. For each valid unmethodical argument, there is an associated valid syllogism. How is the associated syllogism to be discovered or constructed? And what is the nature and the significance of the relation of ‘association’? I deal with the former question first. The abstract answer emerges without difficulty from several Alexandrian texts. In order to construct the associated syllogism, you must do two things: first, you must add an appropriate universal proposition to the premisses of the original argument; secondly, you must fuse or amalgamate the plural premisses of the original argument into a single proposition.198 Suppose, then, that there is an unmethodical argument: [Æ] P1, P2, ... , Pn: therefore, Q. Then the associated syllogism will be: [] U, P*: therefore, Q. — where [] is a valid categorical syllogism, and ‘U’ is an appropriate universal proposition, and ‘P*’ is a fusion or amalgamation of ‘P1, P2, ... , Pn’. ‘U’ first. And first, where does it come from? What is it for something to be an ‘appropriate’ universal proposition? Alexander does not tell us. But his examples illustrate the technique of producing appropriate universals, and we may conjecture a recipe. Since [] is a categorical syllogism, ‘U’ must be in categorical form: it must be of the form ‘AaB’.199 Further, since ‘U’ is to [97] serve as a premiss for the conclusion ‘Q’, one (and only one) of its terms must be the same as one of the terms in ‘Q’. Again, since ‘U’ must form a ıÇıªÆ with the amalgamated premiss, its other term must somehow pick up a term which is found among ‘P1, P2, ... , Pn’. (This term will be the middle term in the associated syllogism.) The recipe is vague insofar as the phrase ‘pick up a term which is found among’ is vague; but the vagueness is deliberate and, I think, unavoidable. 198 For the two operations, see in APr 344.15–18, 23–26; 344.34–345.1; 345.23–28, 32–35; 345.37–346.2 (cf 346.35–347.2); in Top 14.23–26; 15.1–3, 4–5, 7–10; cf [Ammonius], in APr 70.13–14 (cf 71.4–5). For apparent exceptions to the twofold operation see below, p.[100]. 199 Or ‘AeB’? Although Alexander only gives affirmative examples, he does not say that ‘U’ must be affirmative. Yet is is clear that only affirmatives will do.

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There is no mechanical way of producing an appropriate universal proposition. The recipe should, however, at least give a rough and preliminary idea of what is needed. (I shall not yet offer an illustrative construction: the constructions are in actual fact fairly convoluted — and the reason for their convolutions will not emerge until we have considered the second part of Alexander’s positive thesis.) Alexander says that ‘U’ must be a true universal proposition; and in fact it is plain enough that if [Æ] is materially valid and ‘U’ is appropriate to [Æ], then ‘U’ must be not merely true but also necessary — the necessity of ‘U’ mirrors, as it were, the validity of [Æ]. Must ‘U’ therefore be an axiom? Not all necessary truths are axioms; for an axiom, in the Peripatetic view, must be a primary and self-warranting necessary truth. According to the false Ammonius, the added universal proposition ‘has the power in syllogisms and holds the rank of an axiom’.200 But I do not find this in Alexander;201 and I suspect that it came into the Peripatetic tradition later and from a different source.202 Thus we may see, at least in rough outline, how to find an appropriate universal proposition. But what is the point of adding one? That question, at least, is readily answered. Every valid categorical syllogism contains at least one universal proposition. That is an established metatheorem of Aristotelian syllogistic, and Alexander explicitly alludes to it in the present context.203 In [98] other words, Alexander’s associated syllogism is to be a categorical syllogism, and for that reason it must be given a universal premiss. (If Alexander’s reason for adding ‘U’ is to ensure that [] contains at least one universal premiss, then he must be assuming that [Æ] does not itself contain any universal premiss. It is true that he could have maintained the need to add ‘U’ even if [Æ] already contained a universal premiss; but he could not have done so on the same grounds — he could not have said that ‘U’ was needed because a syllogism must contain at least one universal premiss. Hence Alexander’s addition of ‘U’ — not the fact that he adds ‘U’, but his reasons for adding ‘U’ — confirms the supposition that he regarded the

200 See in APr 71.4–5. Strictly speaking, [Ammonius] is not referring here to the syllogisms associated with unmethodical arguments; but there is no doubt that his comment should be extended to them. 201 At in APr 269.5–8, Alexander observes of a particular argument that an IøÆ must be added if is to be a ıºº ªØ . But this is a special (Euclidean) case, and we may not draw any general moral. 202 See below, n.210, on Galen. 203 See in APr 345.18–24; 347.20–23; in Top 14.17.

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premisses of unmethodical arguments as being, or as being equivalent to, particular propositions.204)

Galen’s metatheorem So take the Truncated Argument and add an appropriate universal premiss to it. You will get the Euclidean Argument.205 Now according to Galen, the Euclidean Argument is a perfectly reputable syllogism. The details of Galen’s views about these matters are highly obscure, in part for textual reasons;206 but I think there need be no doubt about the general thrust of his argument. For Galen in effect upholds the following ‘metatheorem’: For any materially valid argument: [Æ] P1, P2, ... , Pn: therefore, Q. there is a proposition ‘Pa’ such that (i) ‘Pa’ is an axiom, and (ii) [Æ] depends for its validity upon the truth of ‘Pa’, and (iii) the argument: [ª] Pa, P1, P2, ... , Pn: therefore, Q. is a formally valid syllogism (in fact, a ‘relational’ syllogism). I shall not comment here on the precise sense or value of this [99] metatheorem; nor shall I discuss its origins207 or its influence.208 Rather, I want to stress the similarity — and the difference — between Galen’s metatheorem and Alexander’s theory of the ‘associated’ syllogisms. First, the similarity — which is evident. Galen’s addition of ‘Pa’ closely parallels Alexander’s addition of ‘U’.209 As I have said, Alexander’s ‘U’

204

See above, p.[88]. I anticipate: shortly we shall see that, on one account, the appropriate universal for the Truncated Argument is in fact Euclid’s first common notion. 206 See Barnes, ‘Proofs and syllogisms’. 207 Some scholars have jumped on the reference to Posidonius at inst log xviii 8 and have seen him as the author of Galen’s metatheorem: see esp I.G. Kidd, ‘Posidonius and logic’, in J. Brunschwig (ed), Les stoı¨ciens et leur logique (Paris, 1978 [20062]), pp.273–282 [29–40]; also Ebbesen, Commentators I pp.113–116. That involves imputing an extreme disingenuousness to Galen, who plainly claims the metatheorem as his own; and it is in any case based upon an untenable text at xviii 8. (See above, n.164.) 208 For some interesting suggestions, see Ebbesen, Commentators I pp.117–120. (Compare Buridan’s remark, quoted above, p.[17], on the need to add a necessary truth to materially valid consequences if their validity is to be seen.) 209 Perhaps they used the same term for the ‘omitted’ universal proposition. For Galen wrote an essay æd H
ÆæƺØ 
ø
æ ø
K
fiB ºØ H
I ø
(lib prop XIX 43), and it is tempting — though scarcely mandatory — to associate the æ Ø ÆæƺØ 
ÆØ with the Pa of the metatheorem. 205

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probably need not be an axiom, whereas Galen insists on the axiomatic status of ‘Pa’. But ‘Pa’, like ‘U’, must certainly be universal.210 Secondly, the dissimilarity. The argument [ª] is not, and is intended not to be, a categorical syllogism. Galen expressly states that ‘relational’ syllogisms, of which [ª] is one, form a third class of syllogism; and he explicitly condemns the Peripatetics for forcing relational syllogisms into a categorical figure (inst log xvi 1).211 The crucial difference, of course, is that Galen has no wish to perform Alexander’s second operation on unmethodical arguments and to amalgamate ‘P1 P2, ... , Pn’. It is this second stage in Alexander’s procedure for [100] constructing associated syllogisms which marks him off from Galen and his metatheorem.212 Now it might be said that Alexander’s first account of unmethodical arguments in his commentary on the Analytics actually suggests that the addition of ‘U’ is all that is needed to produce a syllogism; at any rate, he says that ‘U’ must be added in order to make a syllogism and he does not mention any second condition.213 But the later and fuller account plainly shows that ‘U’, by itself, is insufficient; and we must regard the earlier passage as a preliminary and partial sketch rather than as a different — and Galenian — theory about unmethodical arguments. Moreover, in the earlier passage there is at least a hint of the second condition.214 [101] 210 Perhaps, then, Galen influenced the view of the later commentators that ‘U’ must be an axiom? 211 See below, p.[108]. There is a difficulty. At xvi 5 the unique MS of inst log has Galen say that ‘we shall be able to reduce such syllogisms to categorical arguments’. The context of the sentence is undeniably corrupt; but the word ‘ŒÆŪ æØŒ ’ is plainly in the MS, and scholars have not thought to change it. Yet changed it must be — for Galen cannot coherently say both that the Peripatetics are wrong in reducing relational arguments to categorical syllogisms and also that he himself can make such a reduction. It is far from clear what the correct emendation might be (‘I ،، ’ for ‘ŒÆŪ æØŒ ’? — but a prudent editor will print the whole of xvi 5 between obeli). 212 I.G. Kidd, Posidonius II, Cambridge Classical Texts and Commentaries 14 (Cambridge, 1988), p. 694, misses this point — perhaps because the only text from Alexander which he cites is in APr 21.28–22.25 (see below) — , and so in order to ensure that Galen’s view does not collapse into Alexander’s he thinks he must construe Galen as holding that ‘Pa’ is not a premiss in an argument but an implicit axiom validating [Æ]. The suggestion is obscure; and it will not fit Galen’s text (although it is admittedly suggested by some passages in inst log ). In any case, it is not needed as a way of distinguishing between Alexander and Galen. (A similar criticism applies to the notion advanced by Barnes, ‘Third sort of syllogism’.) 213 See in APr 22.2–3, 5–6, 9–12, 20–21. 214 Thus at in APr 22.10–15, in connexion with the Platonic example of class (D), Alexander says that we should take a universal proposition, add X to it, and then draw the desired conclusion; and it is fairly clear that X is intended to represent ‘P*’, the amalgamation of the original premisses of [Æ]. — There is a further difficulty with Alexander’s treatment of class (C) in this passage. To the argument:

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A casual reading of Philoponus’ account of unmethodical arguments might suggest that he followed Galen rather than Alexander and the Peripatetic tradition. For he records the need to add a universal proposition to [Æ], but he does not mention the second and crucial Alexandrian operation of amalgamating the original premisses.215 Moreover, one of the examples he offers of a syllogism — of an associated syllogism — explicitly retains the two original premisses, just as Galen’s metatheorem requires.216 Perhaps, then, Philoponus, like Galen, believed in a ‘third kind of syllogism’? Alas, that is a fantasy. For, first, Philoponus does sometimes amalgamate the two original premisses, even if he does not expressly remark upon the fact.217 And secondly, he purports simply to be rehearsing the views of Alexander — his commentary here is explicitly marked (at in APr 321.8) as a paraphrase of the text which we can read for ourselves in Alexander’s surviving pages. If Philoponus seems to differ from Alexander and to follow Galen, that is not by any conscious desire: it is simply testimony to Philoponus’ carelessness and incompetence in logical matters. (1) It is day. (2) You say that it is day. Therefore: (3) you speak truly. we must, he says, add the universal proposition: (4) Anyone who says of what is the case that it is the case speaks truly. Further, to this proposition we must append: (5) Anyone who, when it is day, says that it is day, says of what is the case that it is the case. And then we can reach the conclusion: (6) Anyone who, when it is day, says that it is day, speaks truly. (See in APr 22.18–23.) Plainly, proposition (4) represents ‘U’. But what of (5)? As a matter of fact, (5) is not an amalgamation of (1) and (2) — and evidently not. Hence we might infer that Alexander did not intend it as such an amalgamation. In that case, the syllogism (4)–(6) will not be similar to the associated syllogisms which Alexander later constructs; and we must either give a more generous account of those associated syllogisms or else suppose that the argument (4)–(6) fulfils some other function in connexion with (1)–(3). (For example, we might think that (6) rather than (4) is the appropriate universal proposition for (1)–(3), and that (4)–(6) presents in effect a prosyllogism, designed to establish the universal premiss of the associated syllogism.) But if that was Alexander’s intention, why did he not make it plain? It is hard to avoid the suspicion that Alexander is muddled: he sees that (4)–(6) is relevant to (1)–(3); but he fails to see that its relevance cannot be that of an associated syllogism. 215 216 217

See in APr 36.9–10; 321.16, 20; 322.15 (cf 323.11). See in APr 321.18–20. See in APr 322.1–3, 17–18; cf 323.11–14.

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The amalgamated premiss According to Alexander, then, the Euclidean Argument, which we get by adding ‘U’ to the Truncated Argument, is not a syllogism — or at least, it is not the syllogism ‘associated’ with the Truncated Argument. For to reach the associated syllogism, [], a second operation is necessary. In addition to annexing a universal proposition, we must somehow amalgamate or fuse the original premisses of [Æ] into a single proposition. How are we to perform the amalgamation? And what is the point of it? Alexander states the amalgamated premiss for each of our three arguments. For Argument A the proposition is this: A and C are equal to the same thing (for they are equal to B). (in APr 344.19) [102]

For Argument B the amalgamated proposition is: A and C have the same parents as B. (345.1–2)

And for Argument C: Dio, speaking truly, says that it is day. (345.34–35)

Look, first, at the first example. The parenthesis it contains is odd. For Alexander seems in effect to have given us two propositions, not one — viz: (a) A and C are each equal to B. and: (b) A and C are each equal to the same thing. Which is the proposition he actually means to offer us? He says explicitly that the new proposition must ‘have the same force as’ the two old premisses (344.18). The phrase probably means ‘have the same sense as’ (see 372.31–2);218 and at very least, it must imply that the combined proposition is logically equivalent to the original pair. Now the old premisses were: (1) A is equal to B. (2) C is equal to B. They are jointly equivalent to a single conjunctive proposition, viz: A is equal to B and C is equal to B.

218

But ‘Y

ÆŁÆØ’ and its cognates are used with a wide spread of meaning: if they sometimes mark strict synonymy, they sometimes mark a far looser relation. See Barnes, ‘Utility’.

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And that conjunctive proposition might easily be abbreviated to proposition (a). Hence (a), rather than (b), is what Alexander ought to intend as his new, amalgamated premiss. Furthermore, the combined proposition for Argument B is plainly parallel to (a) rather than to (b); and that supports the view [103] that Alexander intends us to construe the new premiss for Argument A as (a) rather than as (b). Yet this view faces a severe obstacle. As the appropriate universal proposition for Argument A, Alexander produces the Euclidean axiom: Things equal to the same thing are equal to one another. Now the axiom and ‘P*’ must together form a ıÇıªÆ; that is to say, they must share one (and only one) term. But it seems plain that the Euclidean axiom does not share any term with sentence (a). Hence the axiom and (a) will not generate a syllogistic conclusion.219 (The same is clearly true if we take the universal proposition which Alexander suggests for Argument B and set it alongside his (a)-like amalgamated premiss.) On the other hand, the axiom does share a term with sentence (b), viz the term ‘thing equal to the same thing’. Hence, and despite the reasons I have just given, we should perhaps opt for (b) rather than (a) as the amalgamated premiss for Argument A. Here, then, is a quandary. Alexander evidently intends (i) that ‘U’ and ‘P*’ form the ıÇıªÆ of a categorical syllogism. It is undeniable (ii) that the version of ‘U’ which his text presents requires a (b)-style amalgamated premiss. It is further plain (iii) that Alexander prefers — and indeed requires — an (a)-style proposition for ‘P*’. He cannot have it all ways. There is no doubt that Alexander is in a wretched muddle. If we want to extricate him — if we want to say on his behalf what he might best have said — , there are, evidently, three possibilities. First, (i*), we might drop the condition that ‘U’ and ‘P*’ together ground a categorical syllogism. From an abstract point of view, this may well be the best option. Yet from a historical and from an exegetical point of view it is silly. The whole point of Alexander’s operation on ‘P1, P2, ... , Pn’ lies in his determination to produce a standard categorical syllogism. Abandon the attempt, and the whole business with ‘P*’ is pointless — we might as well follow Galen.

219

So Lee, Die griechische Tradition, p.109.

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Secondly, (ii*), we might ignore the universal propositions which Alexander himself offers in the text and replace them with [104] other universal propositions better suited to pair with (a)-style amalgamations. Thirdly, (iii*), we might — conversely — ignore the (a)-style amalgamations in the text and plump for (b)-style fusions. Option (iii*) may have been taken by some later logicians. At any rate, the false Ammonius clearly prefers a (b)-style amalgamation (see in APr 70.14); and unless his preference is purely fortuitous (as it may well be), we should credit the Ammonian school with the realization that something must be done to get Alexander out of the mess he is in. In what follows, I shall take option (ii*). There is no textual or historical warrant for doing so. But it seems to me, in the end, to give Alexander a better — or at least a less bad — theory.

Associated syllogisms Then the syllogism associated with Argument A — Syllogism A, as I shall unoriginally call it — has, as its amalgamated premiss, ‘P*’, the proposition: (2*) A and C are each equal to B. Since the conclusion of Syllogism A is to be: (3*) A and C are equal to each other. it is plain that the universal premiss, ‘U’, must be: (1*) Things equal to B are equal to each other. How can we get a categorical syllogism from these three propositions? Well, the middle term — the term shared by (1*) and (2*) — must surely be the complex term ‘thing equal to B’. Hence the second term in (2*) must somehow be extracted from ‘A and C’. Thus we must construe ‘A and C’ as a single term — as a plural name for the pair consisting of A and C.220 That explains why the original premisses of Argument A must be fused or amalgamated: the fusion in not, as one might have supposed, a simple operation [105] of conjunction; rather it is an operation which creates a new term for Syllogism A. For from the plural name ‘A and C’ we shall, of course, form the general term ‘A-and-C-izer’.221 In sentence (2*), the term ‘things equal to B’ — or better: ‘things co-equal with B’ — is ascribed to the pair A and C. (It is easy enough to define the complex term: the predicate ‘ ... is co-equal with B’ will be true of an object y 220

See above, n.192.

221

See above, p.[89].

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just in case y is a plurality and each element of y is equal to x.) Thus we shall produce for the second premiss of Syllogism A a choice between: (2  ) Being co-equal to B holds of every A-and-C-izer. and: (2 þ ) Being co-equal to B holds of some A-and-C-izer. Which of (2  ) and (2 þ ) should we choose? The false Ammonius plainly prefers (2 þ ); for he explicitly says that the amalgamated premiss is particular in quantity: Let the geometers not say: Since A is equal to B and B is equal to C, therefore A is equal to C. ... Let them make one particular proposition from the two particulars, and let them add the universal, thus: A and B are equal to the same thing. All things equal to the same thing are also equal to one another. Therefore: A and B are equal to one another. (in APr 70.11–15)*

The first premiss of the new argument is the amalgamated premiss; and the commentator expressly says that it is — that it is to be construed as — a particular proposition. Alexander is not explicit on the point. But in his case, too, it is clearly better to take (2 þ ): ‘P*’ is a fusion of sentences each of which Alexander takes to be particular; and it is difficult to see how the operation of fusion could introduce universality.222 So much for (2*) or ‘P*’. [106] What of (1*) or ‘U’? There is no need for further pedantry. We need the term ‘being self-co-equal’, which is true of an object x just in case x is a plurality and every element in x is equal to every other element in x. Then (1*) becomes: (1 þ ) Being self-co-equal hold of everything co-equal with B. Now from (1 þ ) and (2 þ ) we can conclude, by a syllogism in Darii, to: (3 þ ) Being self-co-equal holds of some A-and-C-izer. (3 þ ) is equivalent to (3*). Q.E.D.223 * c s
ºªøÆ
ƒ ªøæÆØ KØc e ` fiH ´ Y
, e b ´ fiH ˆ Y
, ŒÆd e ` ¼æÆ fiH ˆY
... Iººa a  æØŒa Æ
æØŒc
 ØøÆ
ŒÆd æ ØŁøÆ
c
ŒÆŁ º ı
x
a `´ fiH ÆPfiH YÆ

Æ a fiH ÆPfiH YÆ ŒÆd Iººº Ø YÆ
a `´ ¼æÆ YÆ Iººº Ø. 222 Lee, Die griechische Tradition, p.109, and Barnes, ‘Third sort of syllogism’ opt for (2  ) without argument and without mentioning (2 þ ). 223 If you opt, with Lee and Barnes (above, n.222) for premiss (2  ), you will produce (3  ) rather than (3 þ ) by a syllogism in Barbara.

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Argument B offers nothing novel. Syllogism B will be precisely analogous to Syllogism A: replace ‘co-equal’ by ‘co-parental’ (with the obvious definition), and you get the appropriate syllogism. Argument C is, on the face of it, quite different.224 Alexander’s own reformulations are not inspiring. He offers, as the associated syllogism, the following argument: (1) Everything someone says when speaking truly is the case. (2) Dio, saying that it is day, speaks truly. Therefore: (3) it is day, as Dio says. What are the three terms of this supposed syllogism, and how are the three propositions to be put into categorical form? Various answers might be essayed — but the essays are not worth making. For it is plain that, once again, Alexander is [107] careless or confused.225 His proposition (3) is not the conclusion of Argument C. The conclusion of C is simply ‘It is day’ — and that is evidently not equivalent to ‘As Dio says, it is day’.226 Some radical revision is required. Here is one suggestion. We need, first, the predicate ‘ ... is the case’, and its associated term, ‘being the case’. The predicate is true of an object x just in case there is some P such that x is the proposition that P, and P. (Thus ‘ ... is the case’ is true of Pythagoras’ theorem; for Pythagoras’ theorem is the proposition that the square on the hypotenuse is equal to the sum of the squares on the other two sides, and the square on the hypotenuse is equal to the sum of the squares on the other two sides.) We need, secondly, a way of 224 There is a trivial indeterminacy inasmuch as ‘IºÅŁØ › ˜ø
’ might be taken either generally (‘Dio is a truth-teller’) or singularly (‘Dio is speaking truly here and now’). The general interpretation might well seem a more plausible way of taking the Greek; and in some variants on Argument C the general interpretation is certainly right. But if the amalgamated premiss is to have the same force as the two original premisses of Argument C, then the singular interpretation must be taken. ‘Dio, speaking truly, says that it is day’ may be equivalent to ‘Dio says that it is day, and Dio is there speaking truly’; it is certainly not equivalent to ‘Dio says that it is day, and Dio is a truth-teller’. 225 Note Mueller’s harsh judgement: ‘Alexander’s attempt to deal with is, I think, a complete failure’ (‘Stoic logic’, p.176); ‘anyone willing to regard such arguments as categorical syllogisms obviously lacks a clear sense of the limitations of Peripatetic logic’ (ibid, p.177). Mueller is right — but unsympathetically right. In the text I try to show, not how Alexander actually proceeded, but how he might better have proceeded in order to reach his clearly defined goal. 226 It might be suggested that Alexander modified the conclusion of C because, in its original form, it seems not to have a categorical structure. (What is the subject and what the predicate of the sentence ‘It is day’?) But the suggestion is idle. Even if (3) were replaced by a standard categorical proposition — even if Dio had taken it into his head to say ‘All men are mortal’ — , Alexander would be no better off. For it must seem that no conclusion of the form ‘p, as Dio says’ contains two terms, one of which figures in each of the premisses of Syllogism C.

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producing names for propositions. Let us opt for a standard nominalization: ‘Its being day’ is a nominalization of the sentence ‘It is day’, and so it will be taken to name the proposition which that sentence expresses. Thus — in full syllogistic fig — Syllogism C might be presented as follows: (1 þ ) Being the case holds of everything truly said by Dio. (2 þ ) Being truly said by Dio holds of some of its being day. Therefore: (3 þ ) being the case holds of some of its being day. And that is a syllogism in Darii.

Alexander’s metatheorem So Syllogisms A, B, and C may be constructed. But their construction is uncommonly contrived.227 And what is the point [108] and purpose of it all? More generally, what is the point of producing associated syllogisms? How do the syllogisms stand to their parent arguments? What is the relation of association? I have represented the construction of the associated syllogism as the production of a new universal premiss and the amalgamation of the two original premisses. Alexander tends to view the matter from the other end. He sees the unmethodical argument as having been produced from the associated syllogism. For example: In all such arguments the universal, which is true, has been omitted, and the other proposition has been divided into two (or even more). (in Top 15.3–5)*

It seems as though Alexander takes the associated syllogism somehow to be the ‘real’ argument; for he says that the proponents of unmethodical arguments ‘omit’ the universal premiss, and that they ‘divide’ the other premiss into two. And that ought to mean that the unmethodicals give an elliptical and inaccurate presentation of a syllogism which Alexander himself is able to construct completely and accurately. Thus we might infer that the associated syllogism is actually to be identified with the original argument: it is the very same argument — the very same argument properly dressed. And we might further think that that was 227 But no more contrived than other syllogisms which Alexander is content with: see e.g. in APr 357.20–358.25 for the use of complex terms in syllogistic æ Ø; cf Barnes, ‘Terms and sentences’, pp.314–315. * K
AØ ªaæ  E  Ø  Ø º ª Ø e b
ŒÆŁ º ı IºÅŁb k
ÆæƺºØÆØ, b æÆ æ ÆØ N  ØÆØæEÆØ j ŒÆd ºø.

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Galen’s interpretation of the Peripatetic procedure. At the beginning of his own discussion of some of the unmethodical arguments, he reports that ‘Aristotle’s followers force things and count them among categorical syllogisms’ (inst log xvi 1).228 If Galen thinks that the Peripatetics wrongly assimilate unmethodical arguments to categorical syllogisms, then he may seem to be supposing [109] that the associated syllogisms were regarded by them as the very same arguments as the unmethodicals with which they are associated. But that is certainly wrong. No doubt different identity criteria for arguments may be devised.229 But no possible criteria will allow us to identify, say, Syllogism A, which contains a universal premiss, with Argument A, which contains nothing universal at all. Moreover, Alexander himself cannot have identified the Syllogisms with the Arguments; for he holds that the Arguments are not syllogisms — they are materially but not formally valid. Hence they cannot be identical with their associated syllogisms. Then what is the relation of association? Alexander gives us a hint or two; but the hints are hard to interpret. They concern the notion of dependence, to which I have already alluded.230 Thus: That the syllogism [i.e. Syllogism B] comes about because of the added universal proposition is clear from the fact that if the universal is not true the conclusion, given the assumptions, is no longer true. (in APr 345.3–5)*

Alexander suggests here that the conclusion of Argument B somehow depends on the universal proposition made explicit in Syllogism B. The same thought emerges with perhaps greater clarity from a text in Philoponus. According to Philoponus, in non-methodical arguments, the conclusion follows

228

ØÇ
ÆØ  ÆP f ƒ æd e
`æØ ºÅ
 E ŒÆŪ æØŒ E ı
ÆæØŁE
. — There are obscurities of detail. Is ‘ØÇ
ÆØ’ passive (cf e.g. Sextus, M VIII 371) or rather middle (cf e.g. Plato, soph 246B8; Galen, PHP V 385; and — with an active infinitive — Alexander, in APr 69.4)? Again, scholarly orthodoxy now insists that ‘ ƒ æd ’ always means either ‘X and his followers’ or, more simply, ‘X’: it does not mean ‘X’s followers’ (see S.L. Radt, ‘Noch einmal Aischylos, Niobe Fr 162 N2 (278 M)’, ZPE 38, 1980, 47–58). But Aristotle did not discuss the arguments in question — and Galen can hardly have thought that he did. 229 Alexander holds that if the æ Ø of syllogism  differ from the æ Ø of syllogism *, then  differs from * (in APr 272.33–35); and he holds that if two sentences differ in meaning, then they are (or express) two different æ Ø (in APr 410.30–32). 230 See above, p.[95]. * Greek text in the Appendix.

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Logical Matters

because the matter which is assumed contains the necessity — I mean, because the universal proposition is true ... In such arguments, the necessity follows because of a certain universal proposition which has been omitted. (in APr 321.3–5, 7–8)231

Argument B is valid, and its validity depends on — is grounded in and explained by — the truth of a universal proposition. This universal proposition is precisely the universal proposition which [110] figures explicitly in the associated syllogism, Syllogism B. Philoponus is here avowedly paraphrasing Alexander.232 We may then say that the associated syllogism grounds or explains the validity of the unmethodical argument. Syllogism B is not identical with Argument B. But it underlies Argument B insofar as it makes explicit what was only implicit in — and yet essential to the validity of — Argument B. Thus we could say that Alexander implicitly subscribes to the truth of a certain metatheorem. The metatheorem can be put like this. For any materially valid argument [Æ] P1, P2, ... , Pn: therefore Q there is a formally valid argument: [] U, P*: therefore Q. where [] is a categorical syllogism, ‘U’ is the universal proposition which grounds the validity of [Æ], and ‘P*’ is an amalgamation of ‘P1, P2, ... , Pn’. This metatheorem affirms that, in a reasonably perspicuous sense, all materially valid arguments can be ‘reduced’ to categorical syllogisms. The metatheorem finds its place in what I have elsewhere called the Peripatetic programme.233 There was a conviction, derived from Aristotle, 231 ... Øa e c
oºÅ
c
ÆæƺÅçŁEÆ
e I
ƪŒÆE
åØ
, ºªø c Øa e c
ŒÆŁ º ı æ ÆØ
IºÅŁB r
ÆØ ... ‹Ø ªaæ Ø Ø
Æ ŒÆŁ º ı æ ÆØ
ÆæƺºØ
Å
ÆØ e I
ƪŒÆE
K
 E  Ø  Ø, ‰ ŒÆd fiH `º
æfiø  ŒE, ... See also in APr 321.15–16, 26–27; 322.15–16. 232 The exact parallel in Alexander is at in APr 345.24–27:

ªaæ ÆNÆ  F  f ºª 
ı IŁ ø æÆ
Ø
åØ
K I
ªŒÅ  E ŒØ
Ø  

e  ΠF
ı
ªŁÆØ Ææa e ŒÆd K
  Ø IºÅŁB r
ÆØ c
ŒÆŁ º ı æ ÆØ
Z
ø
 Ø ø
H
ºÆÆ

ø
m
Ææƺ ıØ
.

The syntax is horrid. But if we follow the paraphrase in Philoponus (and note the rough parallel in Alexander himself, at in APr 347.23–25), we shall take the word ‘Ææ’ to mark the main break in the sentence, and we shall gloss it thus: In an unmethodical argument, the conclusion follows from the premisses only because the relevant universal proposition is true — so that in this sense the argument depends upon the universal proposition which is omitted. 233 See Barnes, ‘Terms and sentences’.

Logical form and logical matter

137

that categorical syllogistic was in some fashion the very foundation of all logical inference; and the programme was the project of justifying and explaining that conviction — more precisely, of showing how, despite superficial appearances, recalcitrant inferences could be ‘reduced’ to categorical form. The conviction, we all now suppose, was false; and the [111] programme misconceived. And it is easy to conclude that Alexander’s labours on unmethodical arguments were a waste of effort. He was in the thrall of a dogma, and his convoluted subtleties are the sign of a stubborn mind, determined to defend the dogma at whatever cost. He heard his master’s voice, and he yelped like a Pavlovian puppy.234 Yet such a dismissive conclusion would, I think, be unjust. At any rate, the metatheorem is not merely a mechanically dogmatic production. Its stipulation that [] be a categorical syllogism, and the consequent insistence on the fused proposition ‘P*’, are no doubt determined by Peripatetic prejudices. But the crucial feature of the metatheorem is the requirement that [Æ] be backed by a syllogism containing a universal and explanatory premiss. This requirement, as we have seen, is shared by Galen, and in Galen’s version it is not derived from any desire to magnify categorical syllogistic.

A regress Let us then concentrate on the universal element in []; for, whether or not we can always construct an associated syllogism, [], for a material argument, [Æ],235 we can surely always construct an associated Galenian argument, [ª] — where [ª] is simply [Æ] with the addition of an appropriate universal premiss. (The Euclidean Argument, as I remarked earlier, is the [ª] for the [Æ] of the Truncated Argument.) The question is this: is [ª] somehow preferable to [Æ]? Will the associated argument always be logically ‘better’ than the original argument? Alexander offers, in effect, the following general reason for preferring [ª] to [Æ]. On the one hand, [ª] is built from the same materials as [Æ]; for the See e.g. Mueller, ‘Greek mathematics’, p.62: ‘The transformations make no sense. Alexander makes them only because he is bent on defending Aristotle’s general claims about the universality of the categorical syllogism’. 235 Can we? I do not know how to establish that we can; but it seems to me plausible to hold that — with enough ingenuity and patience, and given a generous tolerance for outlandish terms — a [] will always be discoverable. 234

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only novelty in [ª] is a premiss, ‘U’, which is already presupposed by [Æ], so that in recommending [ª] over [Æ] we are not requiring any extra research or knowledge of a non-logical variety (the recommendation is epistemically [112] conservative). On the other hand, [ª] makes explicit what is only implicit in [Æ]: it states what [Æ] shows; it makes the logical dependency of ‘Q’ on its premisses completely open and transparent. Now if [ª] is better than [Æ] because [ª] states what [Æ] merely shows, then we might guess that — in Alexander’s eyes — [] is better than [Æ] because in [] everything is plain. Syllogisms contain in their premisses everything upon which their conclusions depend: that is part of the point of the ‘fiH ÆFÆ r
ÆØ’ condition in the definition of the syllogism.236 And thus syllogisms are logically perfect arguments. In preferring [] to [Æ] Alexander is not merely preferring the formal to the material: he is also preferring the explicit to the implicit. Moreover, he is preferring the explanatory to the non-explanatory. And here I may recall some remarks I made at the end of Part II to the effect that the logical form of an argument is sometimes thought to explain its validity. Alexander maintains, I take it, that the syllogistic form of [] is explanatory; and perhaps Galen maintains the same for [ª]. If a logician wants not only to exhibit the structure of an argument but also to explain its validity, then — or so the idea runs — he must ascend from [Æ] to [ª] or to []. Now there is something fishy about all that. For we might well wonder if everything is really explicit in []; and, generally, we might wonder if any argument could make explicit everything on which it depends. For a regress threatens.237 Take any argument you like: (1) P1, P2, ... , Pn: therefore, Q. If the argument is valid, then it is valid in virtue of a rule, R1, which allows us to infer ‘Q’ from ‘P1, P2, ... , Pn’. Corresponding to the rule R1 there is a conditional sentence C1. Argument (1) depends on R1, and hence on C1. Thus if we are to make explicit everything on which the conclusion of (1) depends, we must replace (1) itself by: [113] (2) C1, P1, P2, ... , Pn: therefore, Q.

236

See Alexander, in APr 343.21–344.6; 350.11–16. What follows is a version of an argument classically developed by Lewis Carroll, ‘What the Tortoise said to Achilles’, Mind 4, 1895, 278–280. 237

Logical form and logical matter

139

And now the same reasoning applies once more: if (2) is valid, then it is valid in virtue of a rule, R2. So (2) depends on R2, and hence on C2. Thus instead of (2) we must — if we are to make everything explicit — resort to: (3) C1, C2, P1, P2, ... , Pn: therefore, Q. And so ad infinitum. That is absurd. Every valid argument, however formal its validity may be, is valid in so far as some rule of inference, R, licenses the move from its premisses to its conclusion. Every pertinent rule R, however abstract and general, can be associated with a true conditional proposition, C. Any valid argument depends on R, and hence on C. Yet it is patently absurd to demand that C be added as a premiss to the argument, and to aspire to a syllogism in which all rules are made explicit as premisses. For that is an incoherent idea. Suppose  is such a syllogism. Then  depends on Rs, and hence on Cs. But Cs is not a premiss of . Hence  is not, after all, a syllogism.

Stopping the regress? Evidently, Alexander does not intend to subscribe to the incoherent thesis that a genuine syllogism must embrace in its premisses all the rules on which it depends. But he does think that some arguments are not syllogisms because their premisses do not present the items upon which they depend. If he is to make out his case and block the regression, then he must do one of two things. Either he must deny that an argument depends on the rule which validates it, so that  is validated by Rs but does not depend on Rs and hence need not be afforced by the addition of Cs to its premisses. Or else he must hold that some arguments need not make explicit everything on which their conclusions depend, so that although  does depend on Cs, there is no need to afforce  by the adjunction of Cs. How might Alexander find a way of justifying either of those options? Let us approach the question crabwise. [114] Consider the wholly hypothetical argument.238 (1) If he is a man, he is an animal. If he is an animal, he is a substance. Therefore: if he is a man, he is a substance. One form of the argument is:

238

See above, pp.[62] and [87].

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Logical Matters

(Fi) If p, then q. If q, then r. Therefore: if p, then r. And one might well think that (Fi) is a logical form if anything is. Alexander demurs. According to him, Argument (1) is not a syllogism (and hence (Fi) is not a logical form). Why not? Here no universal has been assumed. But inasmuch as the universal which has been omitted (and the positing of which will yield a syllogism) is true, what seems to follow the suppositions seems to be true. The universal proposition is ‘Everything which follows something also follows whatever that thing follows’. In ‘If he is a man, he is an animal, and if an animal, a substance’ substance follows animal and animal follows man. Therefore substance follows man. (in APr 347.23–29)*

Thus Alexander invites us to replace Argument (1) by something like: (2) Whenever one thing follows another and the other follows a third, then the one thing follows the third. His being a substance follows his being an animal. His being an animal follows his being a man. Therefore: his being a substance follows his being a man. And one of the forms of Argument (2) is, let us allow: (Fii) For any p, q, r: if both (if p, then q) and (if q, then r), then if p, then r. If p, then q. If q, then r. Therefore: if p, then r. (That is not yet a syllogism in Alexander’s eyes: to produce a [115] syllogism we need further to amalgamate the original premisses of (1). But our present interest is in the status of ‘U’ rather than of ‘P*’, and so that further complication may be left aside.) It is clear what is happening here. Alexander notices that (1) depends or R1 and hence on C1. And he therefore adds C1 to the premisses of (1), thereby producing (2).

* K
ÆFŁÆ b PÆ YºÅÆØ ŒÆŁ º ı. fiH 
 Ø c
ŒÆŁ º ı IºÅŁB r
ÆØ c
ÆæØÆ
Å
w ŁÅ ıºº ªØe ÆØ IºÅŁb  ŒE e  E ŒØ
Ø ŁÆØ  Œ F
. Ø b ŒÆŁ º ı æ ÆØ A
e  

Ø
Ø ÆØ ŒÆd fiz KŒE
ÆØ. K
b fiH N I
Łæ ı Z
  ÇfiH
KØ ŒÆd Çfi ı Z
  PÆ fiH b
Çfifiø ÆØ PÆ, fiH  I
Łæfiø ÆØ e ÇfiH

ήd fiH I
Łæfiø ¼æÆ ÆØ PÆ.

Logical form and logical matter

141

But now take any ordinary syllogism in Barbara. It will exhibit the form: (Fiii) AaB. BaC. Therefore: AaC. Just as Alexander generates (2) from (1) by adding C1 to (1), so from Barbara, by adding the appropriate universal proposition, we may produce a new argument of the form: (Fiv) For any X, Y, Z: if XaY and YaZ, then XaZ. AaB. BaC. Therefore: AaC. If we must move from (Fi) to (Fii) in order to get a genuine syllogism, must we not also move from (Fiii) to (Fiv)? The question becomes more pressing once we notice the close parallel between the Euclidean Argument and the extended version of Barbara. One of the forms of the Truncated Argument was: (Fv) x is equal to z. y is equal to z. Therefore: x is equal to y. One of the forms of the Euclidean Argument was: (Fvi) For any x, y, z: if x is equal to z and y is equal to z, then x is equal to y. x is equal to z. y is equal to z. Therefore: z is equal to y. It seems that (Fvi) stands to (Fv) in exactly the same relation as (Fiv) to (Fiii). [116] Consider the three universal propositions added one to each of (Fi), (Fiii), and (Fv): (U2) For any p, q, r: if both (if p, then q) and (if q, then r), then if p, then r. (U4) For any X, Y, Z: if XaY and YaZ, then XaZ. (U6) For any x, y, z: if x is equal to z and y is equal to z, then x is equal to y. According to Alexander, the wholly hypothetical syllogism depends on (U2), so that (Fi) must give way to (Fii); and similarly, the Truncated Argument depends on (U6), so that (Fv) should be replaced by (Fvi). But Alexander

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Logical Matters

does not hold that Barbara depends in the same way on (U4), or that (Fiii) ought to be replaced by (Fiv). Why not?239 Return for a moment to the ‘moderns’ who, according to Alexander, maintained that categorical inferences were in the same boat as unmethodical arguments, members of neither class being genuine syllogisms.240 We can now make a good guess as to why they held their odd view. Just as Alexander holds that (U2) is like (U4) and (U6) unlike (U4), and that (Fi) must therefore give way to (Fii) whereas (Fv) should not give way to (Fvi), so — and conversely — the moderns must have held that (U6) is like (U4) and (U2) unlike (U4), and that (Fv) must therefore give way to (Fvi), whereas (Fi) need not give way to (Fii). The views of Alexander and the moderns are mirror images of each other, and we shall understand the one to the extent that we can understand the other.241 Can Alexander defend his view? I end by sketching two possible lines of defence, neither of which, I fear, will ultimately prove satisfactory. First, Alexander might have argued along the following lines. If we add (U4) to an argument in Barbara, then what we end up with is — an argument in Barbara. If we take a categorical syllogism and apply the Alexandrian operations to it, purportedly [117] converting an [Æ]-type argument to a []-type argument, we shall necessarily achieve nothing; for the ‘new’ argument will have exactly the same form as the old. That is to say, the old argument — the syllogism in Barbara — already, in a sense, explicitly contained its own rule of inference. The moral might be this. Any argument A depends on a rule of inference, RA. Usually, if you add CA to the premisses of A, the new argument, A*, which you thereby produce will be validated by a different rule, RA*. And in that case, if you are after a syllogism, then you must add CA to your existing premisses. But sometimes it will turn out that the new syllogism depends on the very same rule, RA, as argument A does. And in that case there is evidently no need to add CA. For everything is already explicit. I am not sure how far that line of thought can sensibly be traced out. But I cannot think that it will serve Alexander well. For it is simply not true that the

239

The matter was discussed by the mediaeval logicians: see Pinborg, Logica e semantica, p.181. Above, pp.[73–75]. That is not quite exact; for the
æ Ø were probably not referring to wholly hypothetical syllogisms. But the logical point is not thereby affected; and it seemed permissible to cut an exegetical corner in order to arrive more swiftly at the philosophical goal. 240 241

Logical form and logical matter

143

addition of (U4) to Barbara produces a new argument in Barbara — it is not true because the new argument has three premisses. In general, given the condition that a categorical syllogism must have exactly two premisses, no categorical syllogism can be self-generating in the way the present argument supposes. There is a second, simpler and more familiar, line of thought. First consider (U6). Alexander will surely say that (U6) is a truth of geometry, whereas (U4) is a truth of logic. And he might then add that a syllogism must include in its premisses all the truths on which it depends — save the truths of logic. Euclid himself prefers the Euclidean to the Truncated Argument; for he wants his arguments to make explicit all the geometrical truths on which they depend. Hence he makes (U6) explicit in his reasoning. But no one wants — or coherently could want — his arguments to make explicit all the logical truths on which they depend. Thus far, so good. But what of (U2)? Surely (U2) is a logical truth, and hence — by our present argument — does not need to be made explicit as a premiss of argument (1)? And here we are back at a familiar position in the maze. Sentence (U2) will be a logical truth (in the relevant sense) provided that it (is true and) contains no elements which are not either dummy letters or logical constants. Are the constants of (U2) logical constants? Evidently, they are not logical constants relative to categorical syllogistic; hence if you want to get the conclusion of Argument (1) by a [118] categorical syllogism, you must add (U2) — and perform a few more operations. But that, of course, is trifling. The claim Alexander means to be making is stronger. In effect he is saying something like this: the constants in (U2) are not taken as constants by any suitably elaborate logical system. However unsatisfactory the notion of a ‘suitably elaborate system’ may be, however subjective and elastic judgements on the issue may appear, it seems perfectly plain that Alexander is mistaken.242

242

This chapter was conceived by accident; it swelled with uncomfortable rapidity; and it was prematurely delivered. Parts of it formed the basis of two lectures which I gave in Florence, under the auspices of Erasmus, in April 1989. I am grateful to my Florentine audiences for their patience and their criticism; I am indebted to Erasmus for making the lectures possible; and I especially thank Antonina Alberti for ensuring that my stay in Florence was an unbroken pleasure. Many of the ideas in the chapter emerged during seminars on ancient logic which I held in Oxford in 1987, 1988, and 1989. I thank the participants in the seminar, who helped me on more points than I can hope to remember. I am grateful to Kevin Flannery for a set of nice criticisms. And I owe an especial debt to

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Logical Matters

APPENDIX: Alexander, in APr 344.7–346.4 ’mioi dº kamh›mousi jad dojoFsi sukkocßfeshai dia te ImacjaE¸m ti sulbaßmeim Kj tHm jeile†mym. [APr ` 47a22-24] ‹Ø c ±ºH åæc ºØ
æe e ıæÆÆ ŒÆd N  E ŒØ
Ø [10] I
ƪŒÆø Ø ÆØ ªEŁÆØ ıºº ªØe
r
ÆØ, ÆçH A Øa  ø
KçÅØ
. P ªaæ N › ıºº ªØe K I
ªŒÅ Œ
ı Ø; XÅ ŒÆd 
ŁÆ i
fi q K I
ªŒÅ Ø ØŒ


fiH  E ί
Ø ŁÆØ;  F ıºº ªØ  KØ

Kd º
ªaæ e I
ƪŒÆE
 F ıºº ªØ F. Øe Påd N ÆØ K I
ªŒÅ ºÅçŁ
Ø fiH e ` fiH ´ Y
r
ÆØ ŒÆd e ˆ [15] fiH ´ e ŒÆd e ` fiH ˆ Y
r
ÆØ; XÅ ŒÆd ıºº ªØe  F . ÆØ b ıºº ªØØŒH ı
ƪ 

i
æ ºÆ
 ŒÆŁ º ı æ ÆØ
c
ºª ıÆ
a fiH ÆPfiH YÆ ŒÆd Iººº Ø Kd
YÆ; a NºÅ
Æ ‰  æ Ø N Æ
ıºø
æ ÆØ
m Y
ÆE  
ÆÆØ. Ø b ÆoÅ e b ` ŒÆd ˆ fiH ÆPfiH (fiH ªaæ ´) Y
. ı
ªÆØ ªaæ [20] ŒÆa ıºº ªØe
oø e ` ŒÆd e ˆ Iººº Ø r
ÆØ YÆ. ‹ Ø
 fiø ŒÆd e ºÆ
Æ e ` EÇ
r
ÆØ  F ´ ŒÆd e ´  F ˆ

ªEŁÆØ ıºº ªØØŒH Œ
ıŁÆØ e ŒÆd e `  F ˆ EÇ
r
ÆØ Kd I
ƪŒÆø  F ÆØ. Iºº hø ıºº ªØe  F i
c æ ºÅçŁfiB ŒÆŁ º ı æ ÆØ ºª ıÆ A
e  F Ç
 Ø
 EÇ
ŒÆd  F Kº
 KŒ
ı EÇ
[25] KØ; a b Œ
Æ  æ ÆØ ª
ÅÆØ Æ

Kºø
K
fiH ıºº ªØfiH ºª ıÆ e b `  F ´ Ç
 Z
   F ˆ EÇ
KØ
. ı
ÆåŁÆØ ªaæ oø e ŒÆd e `  F ˆ EÇ
r
ÆØ ŒÆa ıºº ªØ
. Kd I
ƪŒÆø ª  ººŒØ ºÅçŁE  ØØ
IŒ º ıŁE ŒÆd Ææa c
B oºÅ NØ ÅÆ ŒÆ Ø Iıºº ªø ŒØ
ø
H
Kç x  e I
ƪŒÆE
; ‰ [30] Kd H
›æØH
ήd H
Nø
K
ıæfiø åÆØ  ŒÆÆçÆØŒH
ºÅçŁØH
æ ø
. ‹ Ø   E æ ØæÅ
Ø ŒÆd y  › º ª . ‹ Ø fiH KØ
KΠH
ÆPH
ª
ø
; x
› ` fiH ´.Iººa ŒÆd › ´ fiH ˆ KŒ H
ÆPH
KØ ª
ø

› ` ¼æÆ fiH ˆ KŒ H
ÆPH
ª
ø
K
. ºØ ªaæ æe e ıºº ªØe
ª
ŁÆØ ŒÆŁ º ı æ ÆØ ºª ıÆ [35] 
Æ  f fiH ÆPfiH KŒ H
ÆPH
ª
ø
Z
Æ Iºç f r
ÆØ
[345] fi w æ Ø i
æ ŁfiB Øfi ÅæÅ
Å Æ ª

Å ºª ıÆ ƒ b ` ŒÆd ˆ KŒ H
ÆPH
ª
ø


Katerina Ierodiakonou and to my Balliol colleagues, Susanne Bobzien and Ian Rumfitt, each of whom gave me invaluable aid and saved me from serious errors.

Logical form and logical matter

145

Nd fiH ´
oø ªaæ ı
ªÆØ e  f ` ˆ Iºç f r
ÆØ. ‹Ø ªaæ Øa c
ŒÆŁ º ı æ ÆØ
c
æ ŁØ
Å
› ıºº ªØ ; Bº
KΠ F i
c e ŒÆŁ º ı IºÅŁbfi q; ÅŒ IºÅŁb [5] ª
ŁÆØ e Kd  E oø ºÅçŁEØ ıæÆÆ
P ªaæ Ø IºÅŁb ª
ÆØ; i
ºø
› `  F ´ Iºç  KØ
; › ´  F ˆ Iºç ; e ŒÆd e
`  F ˆ K I
ªŒÅ Iºçe
r
ÆØ fiH c r
ÆØ c
ŒÆŁ º ı æ ÆØ
IºÅŁB c
‹Ø ƒ fiH ÆPfiH Iºç d ŒÆd Iººº Ø Nd
Iºç . › ªaæ ÆEÆ åø
ŒÆd IªÆª 
 ¼ººÅ
ªı
ÆEŒÆ ÆEÆ ŒÆd ÆPc
å ıÆ
i
[10] åfiB K ÆPB ÆEÆ; ŒÆæ ı b
H
æ ßÆæå
ø
ÆP E ÆØø
Iºçe ÆØ  F ; P c
Øa  F ŒÆd Iºººø
Iºç d ƒ æ ßæå
.  Ø F  NØ ŒÆd R ºª ıØ
ƒ
æ Ø IŁ ø æÆ

Æ. R ‹Ø b
c ºª ıØ ıºº ªØØŒH ı
ªØ
; ªØH ºª ıØ.  ºº d ªaæ [15] ÆPH
NØ  Ø F Ø. ‹Ø b ª F
ÆØ ›  ı ÆP f r
ÆØ  E ŒÆŪ æØŒ E ıºº ªØ E æd z
Ææ FÆ æƪÆÆ; oø ºÆÆ

ı ‰ ØŁÆØ
ÆP ;  F Æ
e ØÆÆæ
ıØ
. N ªaæ qÆ
  Ø ‹ Ø Ø r å
i
ήd e r
ÆØ ıºº ªØ .
F
b ƒ b
 ºº d H
 Ø ø
º ªø
KΠ
ø
Kd æ ı N
. E b KÆ
Å
Æ H
ŒÆŪ æØŒH
[20] ıºº ªØH
ªØ


åøæd ŒÆŁ º ı æ ø. N ªaæ Kª
 Ø ŒÆa ıºº ªØe
ıæÆÆ Kd  æ Ø
K
æØ; Ø Kd Å oºÅ e ‹ Ø
ª
ŁÆØ ıæÆÆ· Øe ŒÆd y Ø PŒ Z
 ŒÆŁ Æ f ıºº ªØØŒ d æ ŁÅ ÆP E B ŒÆŁ º ı æ ø; ‰ NæŒÆ
; ª

ÆØ ıºº ªØ . ªaæ ÆNÆ  F  f ºª 
ı IŁ ø [25] æÆ
Ø
åØ
K I
ªŒÅ  E ŒØ
Ø  

e  ΠF
ı
ªŁÆØ Ææa e ŒÆd K
  Ø IºÅŁB r
ÆØ c
ŒÆŁ º ı æ ÆØ
Z
ø
 Ø ø
H
ºÆÆ

ø
m
Ææƺ ıØ

ØÆØæ FØ b c
Kº
Æ N  æ Ø.  Ø F Ø ªæ NØ
ƒ  Ø 
ºªØ ˜ø
‹Ø æÆ K

Iººa ŒÆd IºÅŁØ ˜ø

æÆ ¼æÆ K
. ºØ
ºªØ ˜ø

‹Ø [30]

æÆ K

Iººa ŒÆd æÆ K
· IºÅŁØ ¼æÆ ˜ø
. æ ºÅçŁ
Ø b
ªaæ fiH r
ÆØ  F n ºªØ Ø; ÆØ e IºÅŁØ
ÆP
; N b IºÅŁØ
æ ºÅçŁÅ; ÆØ e r
ÆØ  F n ºªØ r
ÆØ. K
ŒÆæfiø ªaæ H
º ªø
ÆæØŁÅÆ
ŒÆŁ º ı æ Ø IºÅŁE sÆØ; K
fiH b
e A
n ºªø
Ø IºÅŁØ; KŒE
Ø

IºÅŁØ b ˜ø
ºªø
‹Ø [35] æÆ K
; n ØfiæÅÆØ Y  e ºªØ ˜ø
‹Ø æÆ K
ŒÆd e Iººa ŒÆd IºÅŁØ ˜ø

Kç x  ıæÆ ŒÆa ıºº ªØe
e æÆ ¼æÆ Kd
n ºªØ ˜ø
. K
b fiH æfiø b
ÆæØ
Å æ ÆØ sÆ ŒÆŁ º ı Kd
‹Ø › e k
ºªø
‹Ø K
; IºÅŁØ
ØfiæÅÆØ b ˜ø
[346] b æÆ hÅ ºªØ ‹Ø æÆ K

ÆoÅ ªaæ ØfiæÅÆØ Y  c
ºªØ ˜ø
‹Ø

146

Logical Matters

æÆ K ŒÆd c
ŒÆd æÆ K
. ıæÆÆ ªaæ ıºº ªØØŒH PŒ IŁ ø oø ºÅçŁØH
H
æ ø
e ˜ø
IºÅŁØ. ‹
c ƒ oø ºÆÆ

Ø H
KŒ
ø ØÆçæ ıØ;[5]   F
ŒÆd ƒ ŒÆŪ æØŒ d ıºº ªØ d H
ºª 
ø
IŁ ø æÆ
Ø
.

4 Grammar on Aristotle’s terms* I According to Frege, ‘the fundamental logical relation is that of an object falling under a concept’.1 The fundamental relation finds its canonical expression in singular sentences of the form ‘F(a)’. Such sentences consist of two parts: there is a designating expression, which Frege calls an Eigenname;2 and there is a descriptive expression, which Frege calls a Begriffswort. Grammatically speaking, the simplest sentences of this sort contain two words and show the structure ‘E þ B’. More generally, and a little more rigorously: in Fregean grammar, (1F) primary sentences3 have two significant parts; (2F) the two parts belong to different and mutually exclusive grammatical categories: no Eigenname may hold the place of a Begriffswort and no Begriffswort may hold the place of an Eigenname; and (3F) in virtue of their heterogeneity, the two elements in a primary sentence bind together into a syntactic unity — [176] the Eigenname ‘completes’ or ‘saturates’ the Begriffswort, which is itself essentially incomplete or unsaturated.4 * First published in M. Frede and G. Striker (eds), Rationality in Greek Thought (Oxford, 1996), pp. 175–202. 1 G. Frege, ‘Ausfu¨hrungen u¨ber Sinn und Bedeutung’, in his Nachgelassene Schriften, ed H. Hermes, F. Kambartel, and F. Kaulbach (Hamburg, 1983), pp.128–136 [English translation in Posthumous Writings, ed P. Long and R. White (Oxford, 1979), pp.118–125], on p.128 [¼ p.118]. ¨ ber Scho¨nflies, Die 2 For Frege’s explanation of his use of the word ‘Eigenname’, see e.g. ‘U logischen Paradoxien der Mengenlehre’, in Nachlass, pp.191–199 [¼ 176–183], on p.192 [¼ p.178]. The English ‘proper name’ is a misleading translation (‘The man who broke the bank at Monte Carlo’ is an Eigenname, but it is not a proper name); ‘singular term’ is better — but note that an Eigenname may designate a plurality of items (‘Graf and Becker won the mixed doubles’). 3 I take the phrase ‘primary sentence’ from Plato: see below, p.[180]. A simple sentence is a sentence none of whose subcomponents is itself a sentence; a primary sentence is, as it were, the simplest sort of simple sentence. The notion of a primary sentence is not exact; but exactitude is unnecessary in this context. 4 ‘The unsaturatedness of the concept brings it about that the object, insofar as it brings about the saturation, sticks directly to the concept, without needing any special cement. Object and concept are originally dependent on one another, and in subsumption we have their original union’ ¨ ber Scho¨nflies’, p.193 [¼ p.178]). Just as (in this text) the object saturates or completes the (‘U concept, so the object-word saturates or completes the concept-word: e.g. ‘Ausfu¨hrungen’, p.129 [¼ p.119]; ‘Logik in der Mathematik’, in Nachlass pp.219–270 [¼ 203–250], on pp.246–247, 253 [¼ pp.228, 234]. These passages, among many others, insist that the unsaturatedness of the conceptword constitutes its predicativity.

148

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Thus the sentence: Theaetetus flies consists of two parts, the name ‘Theaetetus’ and the concept-word ‘ ... flies’; the parts belong to different grammatical categories; and in the sentence they bind together into a unity. For Frege, primary sentences are essentially heterogeneous: ‘objects and concepts are fundamentally different and cannot stand in for one another; and the same goes for the corresponding words or signs’.5 Frege himself took the heterogeneity to be crucial. Standard modern logic is based on Fregean grammar.6

II Traditional logic, which was the final form of Aristotle’s syllogistic, has a grammar of its own; and this grammar — or so the story goes — is foreshadowed in and presupposed by the Analytics. According to the traditionalists, the fundamental logical relation is the relation of predication. This relation finds canonical expression in sentences of the form ‘TxT*’, in which two terms or ‹æ Ø, a subject and a predicate, are attached to one another by a copula or  . In the simplest case, each term is a ‘name’ or Z
Æ, and the [177] sentences show the structure ‘O þ D þ O’. More rigorously: in traditional grammar, (1A) every primary sentence contains two significant parts; (2A) the two parts must belong to the same grammatical category, namely the category of O
ÆÆ, so that any subject may stand in predicate position and any predicate may stand in subject position; and (3A) in virtue of their homogeneity, subjects and predicates will not unite by themselves but must be glued or bound together by a third item.7 5 ‘Ausfu¨hrungen’, p.130 [¼ p.120]. cf e.g. ‘Logik in der Mathematik’, p.258 [¼ p.239] (‘Here we must again insist on the fundamental difference between object and function. No function-name can stand in a place where an object-name (an Eigenname) stands; and conversely no Eigenname can stand ¨ ber die Grundlagen der Geometrie II’, in G. Frege, Kleine Schriften, where a function name stands’); ‘U ed I. Angelelli (Darmstadt, 1967), pp.267–272 [English translation in Collected Papers on Mathematics, Logic, and Philosophy, ed B. McGuinness (Oxford, 1984), pp.273–284] on p.269 [¼ pp.280–281]. 6 ‘Frege’s definitive elucidation of the logical connexions in elementary predication’ is one of three ‘significant advances in logic and philosophy’ which he made: G. Patzig, Sprache und Logik (Go¨ttingen, 1970), p.86. 7 ‘Since the predicate in such sentences [sc sentences such as ‘Man is just’] is a name [Z
Æ], e.g. ‘‘just’’, and cannot in itself produce a complete sentence when coupled [ı
ıÆŁ] with the subject, they needed as it were a sort of chain [ ] which would link them to one another

Grammar on Aristotle’s terms

149

Thus the sentence: Pleasure is good contains two significant parts, ‘pleasure’ and ‘good’. These two parts belong to the same category, being both O
ÆÆ; and they are united by the copula, ‘is’, which signifies nothing in itself. Traditional primary sentences are crucially different from Fregean primary sentences. Instead of the heterogeneity which lies at the heart of Frege’s logic, we find a homogeneity: subjects and predicates are essentially interchangeable. I say ‘essentially’ because this homogeneity underlies traditional syllogistic: it is presupposed by the conversion rules and it is presupposed by every categorical syllogism. Thus the rule of E-conversion licenses the inference from ‘No As are Bs’ to ‘No Bs are As’, and so presupposes the homogeneity of simple sentences. Were these sentences not homogeneous, the conversion rule would license nonsense. Or again, take the first syllogistic form, Barbara: Every B is A Every C is B ———— Every C is A Here the term-marker ‘B’8 appears once in subject and once in predicate position. And in every syllogistic form there is one term-marker which plays such a dual role. The role could not be played but for the homogeneity of subjects and predicates. [178] I II Frege’s grammar of Eigenname and Begriffswort was self-consciously innovative. In the Begriffsschrift he wrote that ‘when I first sketched a formal language, I allowed myself to be misled by the example of language and to compound judgements out of subject and predicate. But I soon became convinced that this was an obstacle to my particular goal and was leading only to useless complications’. Hence at the beginning of the work he insisted that ‘a distinction between subject and predicate is not found in my representation of judgements’; and in the preface he expressed his belief that ‘the replacement of the concepts subject and predicate by those of argument and function will in the end prove justified’.9 In fact, and despite himself, and make a complete sentence — and that is what ‘‘is’’ does’ (Ammonius, in Int 160.10–14; cf e.g. Philoponus, in APr 26.22–8). Ammonius may be thinking of Plato, Tim 30C. 8 ‘B’ is not a term — just as ‘Every B is A’ is not a sentence, and the form Barbara is not a syllogism. 9 G. Frege, Begriffsschrift (Halle, 1879) [English translation by T.W. Bynum, under the title Conceptual Notation (Oxford, 1972)], pp.4, 2, VII [¼ pp.113, 112, 107].

150

Logical Matters

Frege continued to speak of subjects and predicates;10 but he never wavered from his conviction that ‘it would be best to place a complete ban on the words ‘‘subject’’ and ‘‘predicate’’ in logic’;11 for ‘the grammatical categories of subject and predicate cannot be of any importance for logic’.12 In rejecting the categories of subject and predicate Frege rejected traditional grammar and hence traditional logic. What exactly is wrong with traditional grammar? Inadequacies have been alleged on three levels. On the metaphysical level, the thing is a monster. In particular, the theory of the copula insinuates an absurdity. The copula is introduced because the two terms of a categorical sentence must be stuck together by some sort of cement. But the copula is not an adhesive. On the contrary, it must itself be stuck to each of the terms: first we had two items to glue together — and now we have three. So we must find two more connectors — and then we shall have five items to glue ... At the semantic level, traditional grammar leads to logical disaster. Fregean logic is superior — infinitely superior — to traditional syllogistic. For any argument which can be analysed within syllogistic can also be analysed within Fregean logic;13 but there are [179] many — infinitely many — arguments which can be analysed within Fregean logic and not within traditional syllogistic. A celebrated example is this. From: All horses are animals it follows, and follows formally, that: All heads of horses are heads of animals. Traditional logic cannot analyse the inference. For every syllogism has two premisses and three terms; but this argument has one premiss and four terms.14 In Fregean logic the analysis is child’s play. And that, ultimately, is a consequence of Fregean grammar. ¨ ber Sinn und Bedeutung’, in Kleine Schriften, pp.143–162 [ ¼ pp. 157–177], on 10 See e.g. ‘U p.150 [¼ p.164]. 11 ‘Ausfu¨hrungen’, p.130 [¼ p.120]. 12 ‘Logik’, in Nachlass, pp.137–163 [¼ pp.126–151], on p.153 [¼ p.141]; cf pp.154, 155 ¨ ber Begriff und Gegenstand’, in Nachlass, pp.96–127 [¼ pp.87–117], on p.117 [¼ pp.142, 143]; ‘U [¼ p.107]. 13 See e.g. the early remarks in Begriffsschrift, pp.9–10 [¼ pp.119–120]; and cf e.g. p.53 [¼ p.165] for Frege’s version of the traditional Barbara. Note also Frege’s claim that his own formal language is superior to Boole’s inasmuch as he has ‘departed further from Aristotelian logic’: ‘Booles rechnende Logik und die Begriffsschrift’, in Nachlass, pp.9–52 [¼ pp.9–46], on p.16 [¼ p.15]. 14 Hence the argument cannot be exhibited as a single syllogism. Evidently, it cannot be reformulated as a sequence of traditional syllogisms.

Grammar on Aristotle’s terms

151

At the syntactical level, traditional grammar is linguistically wrongheaded.15 The syntactical structure of the sentence ‘Pleasure is good’ is not given by Tree A: S

O

D

O

Pleasure

is

good

Rather, we must prefer Tree B: S

N

Pleasure

VP

J

Adj

is

good

[180] (A VP is a verbal phrase, i.e. an item which takes a noun and makes a sentence; a J is a ‘junctor’, i.e. an item which takes an adjective and makes a verbal phrase. And the underlying structure indicated in the tree, namely ‘N þ VP’, is roughly the same as Frege’s ‘E þ B’.) Traditional logicians wrongly take sentences such as ‘Pleasure is good’ to be the simplest sort of simple sentence; and then they misparse the sentences. 15 Frege sometimes writes as though traditional grammar is good grammar but bad logic. Thus: ‘We shall completely abjure the expressions ‘‘subject’’ and ‘‘predicate’’ which are so dear to the logicians — the more so in that they not only make similar items more difficult to recognize but also conceal genuine distinctions. Instead of blindly following grammar, the logician should rather see his task as one of freeing us from the shackles of language’ (‘Logik’, p.155 [¼ p.143]). But in truth, if Frege is right, then the traditional logicians were misled not by language but by a false grammar imposed upon language — and imposed on it by logicians rather than by grammarians (see J. Barnes, Truth, etc. (Oxford, 2007), pp.93–99).

152

Logical Matters

The syntactical level is the basic level, and errors at the syntactical level are basic errors. Hinc illae lacrimae.

IV Thus Aristotle started logic down the wrong grammatical road. Or rather, Aristotle diverted logic down the wrong grammatical road. For Fregean grammar may be found in Plato. In the Sophist, at 261D–262E, Plato takes a few first steps in logical grammar. Although his remarks purport to be about º ª Ø or sentences in general, in point of fact he only discusses what he calls æH Ø º ª Ø, ‘first’ or ‘primary’ sentences.16 According to Platonic grammar, primary sentences contain two parts, one a name or Z
Æ and the other a verb or ÞBÆ; so that their structure may be represented by the formula ‘O þ R’. More rigorously: in Platonic grammar, (1P) every primary sentence is a compound of two significant parts; (2P) these parts are of different types:17 no name is a verb and no verb is a name; and (3P) in virtue of their heterogeneity, the two parts will — in Plato’s metaphor — ‘interweave’ into a sentential unity.18 Thus in the sentence ¨ÆÅ  ÆØ there are two significant parts, ‘¨ÆÅ ’ and ‘ÆØ’; the two parts belong to different categories, ‘¨ÆÅ ’ being an Z
Æ [181] and ‘ÆØ’ a ÞBÆ; and the two heterogeneous items weave together into a sentential unity. All that is at least superficially clear19 — and it must seem reasonably Fregean, to the extent that Plato’s O and R can be assimilated to Frege’s E and B. Now Plato’s grammar was familiar to Aristotle. In the de Interpretatione 16 He refers to a º ª  which is æH  ŒÆd ØŒæ Æ  (262C–D7) or æH  ŒÆd KºåØ  (262C10). 17 As Plato puts it, there is a Øe
ª
 of words, Z
Æ and ÞBÆ (261E6–262A1). 18 The succession of words ‘lion stag horse’ names [O
ÇØ] three items, but it is not a º ª  and it does not say [ºªØ
] anything (262B9–C2); for a succession of names, or of verbs, is a mere succession (ı
åH ºªŁÆØ etc.: 261E1; 262B2–3, 6, C1). The succession of words ‘lions roar’ not only names two items, an agent and an action, but also says something; for the two words ‘fit together’ [±æ Ø
: 262C5, E1; cf 261D5, E1], ‘mix’ [Œæ

ı
ÆØ: 262C5], or ‘interweave’ [ıºŒØ
: 262D4; cf 262C6; 262D6]. 19 For a full and critical account, see N. Denyer, Language, Thought and Falsehood in Ancient Greek Philosophy (London, 1991), pp.146–182. — See also W. Cavini, ‘L’ordito e la trama: il Sofista Platonico e la tessitura del º ª ’, Dianoia 14, 2009, 9–25 (with a large bibliography).

Grammar on Aristotle’s terms

153

he first expounds something very like Platonic grammar and then widens its range by considering the structure of simple quantified sentences and of modally qualified sentences. The de Interpretatione is a short essay and in it Aristotle travels only a short distance; but the direction of his progress we may fairly call Fregean. And yet in the Analytics all that is forgotten: Aristotle executes a sharp left turn and marches confidently off in the wrong direction. Thus — to complete the charge for the prosecution — Aristotle made an egregious error at the start of his Analytics: it was a disaster, according to one critic, ‘comparable only to the Fall of Adam’.20 By abandoning Platonic grammar, Aristotle fell into a metaphysical muddle, he imposed suffocating limitations on his logic, and he committed himself to an inept syntactical analysis. However much we may admire the Analytics for its rigour and its elegance, we must recognize that it was built on grammatical sand. Logic did not find a secure foundation until 1879.

V Such is the charge. Can anything be said in Aristotle’s defence?21 I begin with a swipe at Plato. ‘¨ÆÅ  ÆØ’ is one of the examples of a primary sentence which Plato himself offers (263A8). But it is not the only example. The first example of a primary sentence is ‘¼
Łæø  Æ
Ł
Ø’ (262C9). It is plain that the sentence does not contain anything which Frege would have called an Eigenname: the Z
Æ [182] ‘¼
Łæø ’ is a common noun. Nor, in the immediate context of the Sophist, is this surprising; for when Plato gave examples to illustrate what he meant by an ‘Z
Æ’ he chose the Greek words for ‘lion’, ‘stag’, and ‘horse’ — all of them common nouns.* Thus Plato’s O is not at all the same as Frege’s E; and although that fact does not discredit the three-part characterization of Platonic grammar which I gave earlier, it does mean that Plato missed the particular heterogeneity which is fundamental to Fregean logic.22 Hence Plato did not offer Aristotle a good 20 P.T. Geach, ‘History of the corruptions of logic’, in his Logic Matters (Oxford, 1972), pp.44–61, on p.47. 21 For an extended defence of traditional logic, see F. Sommers, The Logic of Natural Language (Oxford, 1982). Here I am only concerned with a few ancient issues. * So what does the sentence ‘¼
Łæø  Æ
Ł
Ø’ mean? ‘Man learns’ — i.e. ‘Men can learn things (whereas worms can’t)’? ‘A man is learning’ — i.e. ‘A man over there seems to be getting something out of your lecture’? 22 Then what is Plato’s heterogeneity? In the Sophist he gives a semantical criterion for distinguishing O
ÆÆ from ÞÆÆ: the former signify agents (262A6–7), the latter actions (262A3–4). Aristotle, in the de Interpretatione, also makes the distinction in semantical terms: ÞÆÆ are

154

Logical Matters

Fregean grammar; and if Aristotle erred in the Analytics, it is false to claim that the truth lay naked at his erring feet. Those considerations seem to argue for a mitigated sentence.23 Closer examination leads to the contrary judgement. It is true that neither Plato nor Aristotle distinguishes proper names from common nouns; and in the de Interpretatione, as in the Sophist, we find proper names and common nouns offered indifferently as examples of Z
ÆÆ.24 But in Chapter 7 Aristotle announces that ‘of objects some are universal and others individual — ... e.g. man is universal, Callias individual’ (17a38–b1); and the chapter proceeds to distinguish singular propositions of the Fregean form ‘Fa’ from general propositions. Aristotle plainly supposes that the distinction had some logical importance. Thus Plato sketched a grammar which has a Fregean tang but which misses the crucial Fregean heterogeneity. In the de Interpretatione, Aristotle started out from Platonic grammar and managed to overcome one of its disadvantages, thereby sidling up to the Fregean heterogeneity. And yet, in the Analytics, all that was lost. [183]

VI The plea of mitigation having failed, can we answer the charges directly? Against the metaphysical objection, at least, a full defence is possible. It is wrong to deny that there is any heterogeneity in traditional grammar. Although the two terms in a traditional primary sentence belong to the same category as one another, they must belong to a different category from the copula. That is obvious enough in itself — and it was plain to the ancient commentators, who insisted that the copula is not a third term marked off from O
ÆÆ insofar as they ‘co-signify time’ (16b6). The ancient grammarians combine the two ideas: see e.g. Dionysius Thrax, 12 [24.3] (an Z
Æ is something which signifies HÆ j æAªÆ); 13 [46.4–5] (a ÞBÆ is a ºØ KØ،،c åæ
ø
 ŒÆd æ ø
ŒÆd IæØŁH
K
æªØÆ
j Ł  ÆæØAÆ); for variants on those accounts, see e.g. Apollonius Dyscolus, frag X [GG II iii, pp.38–39], frag XI [pp.70–71]; scholia to Dionysius Thrax, GG I iii [215.26–30]. Modern grammar books continue the tradition. 23 But not if Geach is the judge: he recognizes that in Plato and in the de Interpretatione both proper and common nouns count as names; but he thinks that that is the right way to think about naming — Aristotle, on Geach’s view, actually had a better grammar than Frege’s in front of him when he fell. See Geach, ‘History’, p.61. 24 For proper names, see e.g. 16a21 (‘Callippus’), 32 (‘Philo’).

Grammar on Aristotle’s terms

155

alongside subject and predicate.25 If the copula were simply a third item of the same type as the two items it links, then to be sure it would be a useless addition and the metaphysical monster would shamble in. But the whole point of the copula, in traditional grammar, lies in the fact that it is not a term. Just as the two items in a Fregean primary sentence must belong to different categories, thereby generating the Fregean heterogeneity, so in traditional primary sentences it is essential that ‘x’ has a different semantic function from ‘T’ and ‘T*’. Hence a heterogeneity, roughly analogous to the Fregean heterogeneity, is present in traditional grammar. Again, Fregean concept-words are essentially incomplete, so that it is apt to represent them by the schema ‘F( )’, where the parenthetical gap is a visible mark of the incompleteness. In the same way, a traditional copula is essentially incomplete. If ‘TxT*’ is the schema for a Peripatetic sentence, then we should represent the copula as ‘( )x( )’, where the gaps have a similar function. The copula contained in ‘Pleasure is good’ is best written as ‘ ... is — ’. I shall return later to the function of the traditional copula. What I have thus far said should be enough to explode the first charge against Aristotle and the traditionalists.

VII Even if the copula is metaphysically innocent, it is surely sinful at the syntactical level if it encourages us to taste the fruit of Tree A. [184] And yet why think that Aristotle favoured Tree A? Two sets of considerations are relevant here, the first bearing on certain turns of phrase which Aristotle habitually uses in the Prior Analytics and the second bearing on some of his scattered remarks about the verb ‘r
ÆØ’. My schema ‘TxT*’ is an invention. Traditional logicians often use the formula ‘S is P’, where ‘S’ represents the subject term and ‘P’ the predicate term, ‘is’ being the copula. Aristotle himself frequently uses the following formulas: e ` æåØ fiH ´; e ` ŒÆŪ æEÆØ ŒÆa  F ´; e ` ºªÆØ ŒÆa  F ´.26 The formulas are artificial in the sense that no Greek who

25 See e.g. Alexander, in APr 15.4–22; Ammonius, in APr 23.25–28. Later logicians make the same point when they say that the copula gives the ‘form’ of the judgement. (This notion is found in early Frege: see ‘Dialog mit Pu¨njer u¨ber Existenz’, in Nachlass, pp.60–75 [¼ pp.53–67], on p.71 [¼ pp.63–64]; cf ‘Begriff und Gegenstand’, pp.99–100 [¼ pp.90–91].) 26 There are also trifling variants upon, and elliptical versions of, these formulas; and Aristotle sometimes uses the verbs ‘ ŁÆØ’ and ‘IŒ º ıŁE
’.

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Logical Matters

wanted to say that pleasure was good would normally have expressed himself by way of any of them.27 Later Greek logicians found the formulas strange — or at any rate in need of some explanation.28 Then why does Aristotle use them?29 Modern logicians invite us to say things like ‘For any x, if x is a man, then x is mortal’. Such formulas are barbarisms (and potentially misleading into the bargain). Logicians propose them in the name of ‘regimentation’. Ordinary language may mask the logical structure of sentences and hence make it hard to see their logical properties, hard to determine what follows from them and what [185] they follow from. Regimentation is intended to overcome the disadvantage: it rephrases ordinary sentences by way of sentences which, though shaggy in external form, are sleek in internal structure. Just so, we may easily suppose, Aristotle’s formulas are regimental in purpose. ‘e ` æåØ fiH ´ ’ patently shows the categorical structure ‘TxT*’: ‘e `’ corresponds to ‘T’, ‘e ´ ’ to ‘T*’, and ‘æåØ’ to ‘x’. The same goes for Aristotle’s other two formulas. Regimental sentences may be taken to reveal the ‘deep’ or ‘underlying’ structure of ordinary sentences. Perhaps, then, Aristotle ‘was induced to deviate from ordinary language because he wanted his linguistic expression to reveal with all possible clarity the logical structure of the propositions which enter the syllogisms as premisses or conclusion’.30 Thus natural sentences are to be replaced by sentences which employ one or other of the artificial formulas. The formulas reveal the true structure of categorical sentences. 27 But the formulas are not barbarisms, nor indeed are they entirely unknown in ordinary Greek. More particularly: (i) there is a common use of ‘æåØ
’ in fourth-century prose which often amounts to an exemplification of Aristotle’s formula: e.g. Demosthenes, vii 31 (  Ø ... æåØ
øÅæÆ
); cf xviii 3; xix 84; xxiv 99; Xenophon, anab VII vii 32 ( ıºÆ æåØ ÆP E); cf Mem IV v 1; Plato, Charm 155A3 (E
e ŒÆºe
æåØ); Rep 535B6 (æØÅÆ ... E ÆP Ø ... æåØ
); cf Crat 396B2; Parm 143E1, 160D4. (ii) For ‘ºªØ
ŒÆ’, see e.g. Plato, Pho 81A8; Crat 395C7; Men 76A5; Rep 362A4, 391A3. (iii) The verb ‘ŒÆŪ æE
’ þ genitive in the sense of ‘accuse’ is common enough; but in this sense it seems not to be followed by ‘ŒÆ’ þ genitive, and before Aristotle it does not bear the sense ‘say of ’ or ‘predicate of ’. See Barnes, Truth, pp.93–99. 28 See esp Alexander, in APr 54.21–29, on which, see G. Patzig, Aristotle’s Theory of the Syllogism (Dordrecht, 1968), pp.10–12, 15 nn.22–24. Note that Alexander does not say that the Aristotelian formulas are unnatural or barbarous — he merely distinguishes between the formulas which Aristotle uses in his ØÆŒÆºÆ (i.e. in the main exposition of syllogistic in APr ` 1–23) and the expressions which are normal in ıºº ªØØŒc åæBØ. See also Apuleius, int xiii [212.4–10] (the text, which is preceded by a lacuna, is corrupt and difficult to understand; but it is plain that Apuleius regards the ‘Peripatetic’ style of expressing syllogisms as odd). 29 See esp Patzig, Aristotle’s Theory, pp.8–12; T. Ebert, ‘Zur Formulierung pra¨dikativer Aussagen in den logischen Schriften des Aristoteles’, Phronesis 22, 1977, 123–145, on pp.132–137. 30 Patzig, Aristotle’s Theory, p.11.

Grammar on Aristotle’s terms

157

Their syntax is plainly given by trees of the same form as Tree A. Hence, in using his formulas, Aristotle is implicitly subscribing to the view that Tree A manifests the syntax of primary sentences. That argument is frail and its conclusion hasty. First, it is not plain that a sentence couched in one of the formulas must be parsed in a manner analogous to Tree A. It is at least possible to provide a different parsing and to imagine a tree more like Tree B in structure. Secondly, regimentation need not be construed as an attempt to reveal the underlying structure of ordinary sentences. Regimental sentences may equally well be viewed as ‘paraphrases’; that is to say, a sentence S regiments S* provided that S conveys the same semantic content as S* and conveys it in a logically perspicuous fashion. The syntax of S, on this view, may differ utterly from the syntax of S*.31 [186] Thirdly, did Aristotle intend his formulas to serve as regimental expressions? He does not say so. And he does not normally use the formulas in that way — indeed, he rarely shows any interest in regimentation.32 He uses the artificial formulas when he is producing sentential schemata.33 When he presents illustrative syllogisms, he usually produces ordinary Greek sentences. Thus at APr ` 47b20–36 illustrative arguments in ordinary Greek are interlaced with schemata in the artificial formulas:34 there is no hint that the ordinary sentences might better be rewritten in the artificial style. Again, at APr ` 48a40–49a5, Aristotle considers some of the different ways in which categorical sentences may be formulated in ordinary Greek, and he mentions some difficulties which face a logician who needs to determine what are the

31 In ‘Logische Allgemeinheit’, Nachlass, pp.278–282 [¼ pp.258–262], on pp.279–280 [¼ pp.259–260], Frege remarks that the following three sentences (1) Alle Menschen sind sterblich (2) Jeder Mensch ist sterblich (3) Wenn etwas ein Mensch ist, ist es sterblich differ in expression and yet convey the same thought. He clearly takes the difference in ‘expression’ to be — or at least to include — a difference in syntax. He prefers, for familiar reasons, to use sentences which share a structure with (3). Hence, in Frege’s view, (3) is a paraphrase of (1) and (2) which differs from them in syntactical structure. 32 In APr ` 32–45 he is concerned with ‘reducing’ syllogisms to the figures, i.e. with formalizing ordinary arguments within categorical syllogistic (see 46b40–47a2; 51b3–5). It is there, if anywhere, that we should expect to find regimentations using the artificial formulas. And in fact there are such things (see e.g. 48a6–18). But they are few and they are casual — there is no general recommendation to regiment. 33 The only exceptions are found at APr ` 46b3–11. 34 See Patzig, Aristotle’s Theory, pp.9–10.

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subject and what the predicate terms in these sentences.35 He does not suggest that the sentences should be rewritten. Later logicians deal with syllogisms in the same way: when Alexander wants to ‘reduce’ an ordinary argument — say, one of Euclid’s arguments36 — to syllogistic form, he does not make use of ‘ŒÆŪ æEŁÆØ’ or ‘æåØ
’. He uses more or less normal Greek. Then what is the function of the Aristotelian formulas? It is striking that at least two of the three37 are metalinguistic.38 I suggest [187] that the formulas are intended in part as semantic descriptions of categorical sentences. Thus when Aristotle says ‘If A is predicated of every B, ... ’ he is not offering a schema in accordance with which categorical sentences may be regimented. Rather, the schema indicates the semantic structure which an appropriate categorical sentence must display — ‘If you have a premise which predicates A of every B, ... ’.39 If, in the spirit of Frege, we say that the sentence ‘Theaetetus flies’ shows that an object falls under a concept, we do not take this to imply that the syntactical structure of the sentence is the same as the structure of ‘An object, a, falls under a concept, F’. On the contrary, it would be an egregious error to make the inference. In the same way, if, in the spirit of Aristotle, we say that the sentence ‘Horses sleep’ shows that one thing is predicated of another, this should not be taken to imply that the syntactical structure of the sentence is the same as the structure of ‘One item, A, is predicated of another item, B’. To do so would be to make an egregious error. The sentence ‘Horses sleep’ is a perfectly good categorical sentence: it predicates one term of another; in it, sleep is said of horses, A is predicated of 35 The first example is: H
K
Æ
ø
KØ Æ KØÅ. Aristotle affirms that the predicate term is ‘there being one science’ and the subject term ‘contraries of one another’. His formulation is not perfect; but what he means is plain: the sentence says of items which are contrary to one another that they are items which belong to the same science as one another. If we wished to regiment, we might say, e.g.: Being co-scientific holds of every contrariety — where the artificial terms ‘co-scientific’ and ‘contrariety’ are readily defined. But Aristotle makes no attempt at regimentation. 36 See e.g. in APr 260.18–261.28; 268.7–269.15. 37 And we could construe ‘e ` æåØ fiH ´’ in a metalinguistic way, as Michael Frede reminded me. 38 I do not mean to say that Aristotle himself was at all clear about this, or about the interpretation I am about to put upon it. 39 Compare the following passage from pseudo-Frege: ‘If an object, a, falls under a concept, F, and if F is subsumed under G, then a falls under G’.

Grammar on Aristotle’s terms

159

B. What are the terms in the sentence? ‘Horses’ and ‘sleep’. What is left? Nothing. Where, then, is the copula? There is no copula; nor need there be.40

VIII What, next, of Aristotle’s sundry remarks about the verb ‘r
ÆØ’? The Analytics provides what ought to be the decisive text — but it is a notorious crux. The received text is this: ‹æ
b ŒÆºH N n
ØƺÆØ æ ÆØ x
  ŒÆŪ æ 

ŒÆd e ŒÆŁ y ŒÆŪ æEÆØ; æ ØŁ
ı j ØÆØæ ı
ı  F r
ÆØ j c r
ÆØ. I call a term that into which a sentence resolves, i.e. the predicate and that of which it is predicated, to be or not to be being added or subtracted. (APr ` 24b16–18) [188]

The last clause is a standing puzzle: the ancient commentators offer elaborate and unconvincing elucidations;41 and the modern editors have done no better.42 We must turn to the de Interpretatione. As I have said, Aristotle first introduces a Platonic grammar for primary sentences. The subsequent development of the argument is perplexing;43 but we get a new start in Chapter 10. Here Aristotle clearly marks off (1) primary sentences, of which ‘Ø
¼
Łæø ’ is his first example; (2) quantified sentences, exemplified by ‘Ø A ¼
Łæø ’; and then (3) sentences in which ‘KØ
’ ‘is co-predicated as a third item’. Aristotle indicates that the ‘KØ
’ in his examples of (1) and (2) stands in for any ordinary verb (19b13). Thus in effect (1) consists of primary Platonic sentences with the structure ‘O þ R’, and (2) consists of 40 ‘Aristotle neither had nor needed any theory of the copula; a proposition just consisted of a subject and a predicate’ (Geach, ‘History’, p.55). But I cannot entirely agree with Geach’s earlier remark, in the same vein: ‘The verb ‘‘applies to’’ [i.e. ‘‘æåØ’’] in the schema ‘‘A applies to B’’ was meant only to give a sentence a lecturer can pronounce, not to supply a link between ‘‘A’’ and ‘‘B’’ ’ (p.53). — On the copula, see also J. Barnes, ‘Some remarks on the copula’, Dianoia 14, 2009, 27–62. 41 See Alexander, in APr 15.4–16.17; Ammonius, in APr 22.34–24.24; Philoponus, in APr 25.30–30.21. 42 See e.g. W.D. Ross, Aristotle’s Prior and Posterior Analytics (Oxford, 1949), pp.290–291; R. Smith, Aristotle: Prior Analytics (Indianapolis IN, 1989), pp.108–109; G. Striker, Aristotle: Prior Analytics Book I (Oxford, 2009), p.247. — Ross excises ‘j ØÆØæ ı
ı’, comparing Int 21b27; and Striker supports the excision. If the received text is retained, then the least implausible interpretation is this: ‘When ‘‘is’’ or ‘‘is not’’ is either present or absent’; i.e. the resolution of a sentence into its two terms may or may not leave a residue, which will be ‘is’ or ‘is not’. 43 Thus in Chapter 7 he calls in the quantifiers. But his illustrative sentences are surprising. He invites us to consider ‘A ¼
Łæø  ºıŒ ’, ‘ Pd ¼
Łæø  ºıŒ ’, and the like (17b6). And yet these items should not count as sentences at all, since they lack verbs. (Perhaps ‘ºıŒ ’ is treated as a verb (cf 16a15)? No; for verbs essentially signify time, and the word ‘ºıŒ ’ does not do so.)

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quantified sentences with the structure ‘Q þ O þ R’ (where ‘Q’ is a quantifier). It is with (3) that the copula apparently enters the de Interpretatione. What is the grammar of these new sentences? Aristotle’s introductory remarks are not very clear:44 When ‘is’ is co-predicated as a third item, ... I mean e.g. ‘Man is just’: I say that the ‘is’ is compounded as a third item, noun or verb, in the affirmation. (19b19–22)45

At first sight, that looks like the traditional doctrine of the copula: ‘Man is just’ contains three items; two of them are names; and the third, ‘is’, is the copula, and a verb. (When Aristotle says ‘noun or verb’ he must presumably mean ‘noun, or rather [189] verb’.46) That construal appears to be confirmed by a later passage: in the sentences ‘A man is white’ and ‘A man is not white’ to be and not to be are additions, whereas the underlying objects are white and man. (21b27–28)*

Thus ‘is’ and ‘is not’ are superadded, as third items, to the two main elements of the sentences. And all that seems merely to confirm something which Aristotle had said near the beginning of the essay: To be and not to be are not signs of the object, not even if you say being by itself. For in itself it is nothing — but it co-signifies a certain composition which cannot be thought without the items compounded. (16b22–25)47

The semantic function of ‘is’, in other words, is to indicate that the subject and the predicate are conjoined; and its syntactical role is to take a pair of names into a sentence. Aristotle, it is true, knows no word for ‘copula’;48 but the copula is surely present in the de Interpretatione. 44 Boethius, in Int 2 264.14, calls the passage perobscurum and proceeds to a lengthy commentary. 45 ‹Æ
b e KØ æ
æ ŒÆŪ æÅŁfiB; ØåH ºª
ÆØ Æƒ I
ØŁØ. ºªø b x
Ø ŒÆØ  ¼
Łæø . e Ø æ
çÅd ıªŒEŁÆØ Z
Æ j ÞBÆ K
fiB ŒÆÆçØ. — For ‘ıªŒEŁÆØ’ Boethius gives ‘adiacere’ (in Int 2 263.22), which suggests that he read ‘æ ŒEŁÆØ’. 46 See e.g. Ammonius, in Int 166.2–5. * e r
ÆØ ŒÆd c r
ÆØ æ ŁØ; a ’  Œ
Æ æªÆÆ e b
ºıŒe
e b ¼
Łæø . 47 P ªaæ e r
ÆØ j c r
ÆØ ÅE
KØ  F æªÆ  P’ Ka
e k
YfiÅ łØº
. ÆPe b
ªaæ P
KØ
; æ ÅÆ
Ø b 
Ł
Ø
Æ m
¼
ı H
ıªŒØ
ø
PŒ Ø
BÆØ. — cf e.g. Alexander, in APr 15.8–9. 48 Nor do the later Greek sources: the word ‘ ’ first appears in this connexion in Ammonius — but for him it is still a live metaphor (see in Int 160.13, quoted above, p.[177] n.7); and it is not restricted to the copula. The word ‘
 ’ is also used, but always in a vague and generic sense: thus Ammonius, in APr 24.6–10, counts the modal æ  Ø as 
 Ø, and Philoponus, in APr 25.3–4, holds that every item in a sentence apart from the two terms is a 
 . So too in earlier texts: see e.g. Plutarch, quaest Plat 1001B, in his discussion of Plato’s grammatical remarks in the Sophist. Again, the Latin word ‘copula ’ never means ‘copula’ in classical

Grammar on Aristotle’s terms

161

And yet the texts I have cited are less than probative. At 16b22–25, Aristotle ought to be talking of existential ‘r
ÆØ’ and not of the predicative ‘is’ which we find in ‘Pleasure is good’.49 At 21b27–28 he is primarily concerned to draw a parallel between predicative ‘r
ÆØ’ and the modal æ  Ø.50 And in any case, neither of those passages is concerned explicitly with syntactical issues. As for [190] 19b19–22, it is worth attending closely to Aristotle’s terminology. Here he uses the verb ‘æ ŒÆŪ æEŁÆØ’, which I have Englished as ‘co-predicate’: what is its force? A few lines later, at 19b24–25, Aristotle remarks that ‘the ‘‘is’’ will be adjoined either to ‘‘just’’ or to ‘‘not just’’’.51 The verb ‘adjoin’ or ‘æ ŒEŁÆØ’ will indicate a syntactical connexion.52 In other words, Aristotle means to say that in the sentence ‘A man is just’ the word ‘is’ should be construed together with the word ‘just’: the sentence consists of two main parts, ‘man’ and ‘is just’, the second of which is composite. That suggests an interpretation of ‘æ ŒÆŪ æEŁÆØ’. The prefix ‘æ -’ should indicate that ‘KØ
’ is adjoined to the predicate term; and that seems to be implied by a second occurrence of the verb, at Prior Analytics ` 25b22–24.53 The verb stem ‘-ŒÆŪ æEŁÆØ’ should indicate that ‘KØ
’ has a predicative function; and that seems to be implied by a third occurrence of the verb, at Met  1054a16–17.54 The verb is common in the later texts. It is sometimes used in the general sense of ‘
 ’ or (very roughly) ‘particle’ (e.g. Varro, ling Lat VIII iii 10). Similarly, Boethius uses the word ‘colligamentum ’ generically for ‘
 ’ (e.g. syll cat 796D) — and earlier Apuleius had used various metaphors (pegs and pitch and glue) in the same generic fashion: int iv [192.1–7] (on which see Barnes, Truth, pp.231–235). 49 For the interpretation of this passage, see Ammonius, in Int 57.1–33. 50 The parallel, which Aristotle more than once draws, might be illuminating were we clear about the grammar of the æ  Ø in Aristotle. 51 ºªø b ‹Ø e Ø
j fiH ØŒÆfiø æ ŒÆØ j fiH P ØŒÆfiø. — Ammonius, in Int 171.1–6, and Boethius, in Int 2 264.8–14, signal a variant reading (‘man’ and ‘not man’ for ‘just’ and ‘not just’), which was defended by Herminus and by Porphyry (Boethius, in Int 2 272.28– 273.2) but rejected by Alexander (ibid 272.14–17). T. Waitz, Aristotelis Organon (Leipzig, 1844), I pp.345–346, argued strongly in favour of the variant. If he is right, then we should suppose (with Boethius) that Aristotle has tacitly switched his examples from ‘A man is just’ and ‘A man is not just’ to ‘Socrates is a man’ and ‘Socrates is not a man’. 52 See e.g. Rhet ˆ 1407b12–18, on the celebrated syntactical ambiguity in the first sentence of Heraclitus’ book. 53 ‘‘‘KØ
’’ always and in all cases makes what it is co-predicated with into an affirmation, e.g. ‘‘is not good’’, ‘‘is not white’’ ... ’. I take it (i) that ‘Kd
PŒ IªÆŁ
’ represents the verbal phrase, ‘ ... is not good’, rather than the sentence ‘It is not good’; and (ii) that ‘ x  i
æ ŒÆŪ æBÆØ ... ’ stands for ‘ÆFÆ x  i
æ ŒÆŪ æBÆØ ... ’. 54 ‘‘‘one man’’ is not co-predicated as anything different from ‘‘man’’ ’: for the point, see Met ˆ 1003b26–29. — It is true that the form of the verb ‘æ ŒÆŪ æEŁÆØ’ does not oblige us to infer that ‘KØ
’ is itself predicated. Michael Frede has pointed out to me that when Aristotle says that a verb ‘æ ÅÆ
Ø’ time, we should not think that it signifies time — or at least, not that it signifies time in the same sense in which it signifies a æAªÆ. (See Int 16b6, 8, 9, 12, 18; 19b14; Poet

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commentators, and they adopt the interpretation which I have just sketched. Thus Alexander, who assimilates ‘æ ŒÆŪ æEŁÆØ’ to ‘KØŒÆŪ æEŁÆØ’,55 holds that [191] ‘KØ
’ is to be construed with the predicate and that it is predicated of the subject.56 And Ammonius, who makes the same assimilation, holds that ‘KØ
’ completes the predicate and is said of the subject.57 In sum, the Aristotelian syntax for ‘A man is just’ — or ‘Pleasure is good’ — is not the traditional syntax of Tree A but rather the quasi-Fregean syntax expressed by Tree B; and the structure of primary sentences should be given not as ‘O þ D þ O’ but rather as ‘O þ [D þ O]’, where the brackets are significant.58 That is the construal implicit in the commentators. It is also implicit in those many texts which loosely equate subjects with names and predicates with verbs.59 For the equation clearly presupposes that primary categorical sentences have the Platonic syntax ‘O þ R’. [192] 1457a17. For other uses of ‘æ ÅÆ
Ø
’ see Int 16b24, 20a13; Top Z 140a19, 155a33; Soph El 169b11; Rhet ` 1374a12: in none of those passages does ‘x æ ÅÆ
Ø y’ mean ‘x signifies y in addition to signifying something else’.) But for ‘æ ŒÆŪ æEŁÆØ’ the evidence suggests that the verbal stem does carry its full sense. 55 See in APr 369.12–24; 369.34–370.6. For ‘KØŒÆŪ æEŁÆØ’, see APr ` 49a25. 56 e.g.: ‘To be and not to be are not parts of the sentences, i.e. are not terms; rather, they are external to the terms, being added externally to the predicate terms in the analysis of the sentences into terms’ (in APr 16.7–10); cf e.g. 44.27–28 (‘The predicate term is that to which ‘‘is’’ (or something equivalent to ‘‘is’’ and containing ‘‘is’’ potentially within itself ) is added’); 406.32–34 (‘Aristotle takes ‘‘is white’’ and ‘‘is not white’’ [at APr A 52a2–3] not as sentences [i.e. ‘KØ ºıŒ
’ is not here to be construed as the sentence ‘It is white’] but as predicates in the sentences’). — Alexander is not consistent, however: at in APr 15.12 he insists that ‘is’ is not a part of the predicate. This parallels Frege’s inconsistency in identifying concept words: below n.61. 57 See e.g. in APr 23.27–28: ‘KØ
’ ‘is an adjunct, and it is adjoined to the predicated term; hence it makes a unity, and Aristotle says ‘æ ŒÆŪ æBÆØ’; in Int 165.8–16: ‘when we say ‘‘A man is just’’, we primarily predicate just of the subject, man, since that is what we intend to affirm about man. But because just is not in itself sufficient, when interwoven with the subject, to make an affirmation, ‘‘KØ
’’ is adjoined to them, binding them together (as I said earlier) and being additionally predicated of the subject — thus we say this whole thing about man, that he is just’; in Int 208.3–8: ‘KØ
’ ‘alone of verbs naturally combines with the predicate, being itself said to be co-predicated, and it makes the predicate — and hence the whole sentence — a unity’. — See also Boethius, in Int2 264.24–265.28, who remarks that in the sentence ‘Socrates in Lycio leget ’, ‘in Lycio ’ is ‘co-predicated as a third item’: i.e. ‘in Lycio ’ is adjoined to ‘leget ’ to form the complex verbal phrase ‘in Lycio leget ’. 58 So too Waitz, Organon, I p.345. — I might also refer to APr ` 51b22–52a14 where Aristotle argues that there is a difference between not being T and being not-T, between c r
ÆØ IªÆŁ
(say) and r
ÆØ c IªÆŁ
. It is quite clear that he regards expressions of the form ‘ ... is T’ as unities. Indeed, too much so; for at 51b36–38 he takes ‘not being good’ and ‘being not good’ as replacements for term-markers. That is a confusion — but an understandable confusion, given the view I uphold in the text. 59 e.g. Apuleius, int iv [191.16–192.14]; Galen, inst log ii 2; Alexander, in APr 14.28–29; Ammonius, in Int 177.5; Philoponus, in APr 11.19–25. There is an interesting qualification to the view in Martianus Capella: having affirmed, traditionally enough, that ‘a sentence has two parts: one, consisting of a name, is called subject, and the other, consisting of a verb, predicate’ (IV 393),

Grammar on Aristotle’s terms

163

To avoid any misunderstanding, let me observe that the word ‘is’ does of course form a genuine syntactical component of the sentence ‘Pleasure is good’. Indeed, any decent grammar must recognize that such verbal phrases as ‘ ... is good’, ‘ ... is just’, and ‘ ... is green’ have a common constituent; and hence must recognize the element ‘ ... is —’. But that does not imply a recognition of the copula. A copula, syntactically speaking, is a word which takes two names and makes a sentence: it is an item in the syntactical category S:O,O.60 But in the sentence ‘Pleasure is good’, ‘is’ does not have this syntax and is not a copula. Rather, ‘is’ is a verb-forming operator on names: it takes a term and makes a verb (or a verbal phrase); it belongs to the syntactical category R:O. IX A further Aristotelian remark about ‘r
ÆØ’ should be considered. I shall approach it crabwise. What would Frege say about a Peripatetic primary sentence such as ‘Pleasure is good’? The notion of predicativity and the metaphor of unsaturatedness suggest that if we are to find a Begriffswort in the sentence, then it must be the ‘word’ ‘ ... is good’. And in point of fact Frege more than once considers sentences of this sort and expressly says that the ‘is’ is part of the conceptword.61 He also remarks that the word ‘ist ’ ‘may sometimes be replaced by the mere verbal ending, e.g. ‘dieses Blatt ist gru¨n ’, ‘dieses Blatt gru¨nt ’.62 Roughly speaking, then, we may ascribe to Frege the equation: [193] D þ O ¼ B, so that any Peripatetic primary sentence with the structure ‘O þ [D þ O]’ will also show the typically Fregean structure ‘E þ B’ — provided that the first O is also an E.

he notes that ‘it may come about that a verb is in subject position and a noun in predicate position’ (IV 394). His example is ‘qui disputat Cicero est ’. 60 It may be objected that this is a mere stipulation on my part; and certainly many authors use the word ‘copula’ in such a way that any predicative ‘is’ is, trivially, a copula. But the crucial question is this: did Aristotle accept the traditional grammar for primary sentences? And one good way of phrasing this question is by asking whether Aristotle accepted the copula. If that formulation takes the word ‘copula’ in a tougher sense than usual, I do not greatly mind. 61 See e.g. ‘Logik in der Mathematik’, pp.256, 258–259 [¼ pp.237, 240]. Often, it is true, Frege will write as though ‘good’, by itself, were the concept-word. I assume that this is a mere laxity of expression. (Note ‘Begriff und Gegenstand’, p.106, n.* [¼ p.96, n.*]: the draft version says that ‘red’ is the predicate in ‘This rose is red’; the published version emends to ‘is red’.) But see D. Wiggins, ‘The sense and reference of predicates: a running repair to Frege’s doctrine and a plea for the copula’, Philosophical Quarterly 34, 1984, 311–328, who argues that Frege would have done better to separate the ‘is’ from the concept-word proper. 62 ‘Begriff und Gegenstand’, pp.99–100 [¼ p.91].

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We might jib at calling ‘ ... is good’ a concept-word (just as we might jib at calling it a verb) — it is not a word but a couple of words (not a verb but a verbal phrase). Perhaps it should rather be called a concept-expression.63 Then we might say that the syntactical structure of sentences of the form ‘F (a)’ was ‘E þ BA’ (where ‘BA’ stands for ‘Begriffsausdruck ’). ‘E þ B’ is the special case of ‘E þ BA’ which marks off primary sentences. At de Interpretatione 20a3, Aristotle briefly reverts to simple quantified sentences, remarking that in cases where ‘is’ does not fit — e.g. ‘to flourish’, ‘to walk’ — in these cases they have the same effect as if ‘is’ were annexed. e.g. ‘Every man flourishes’, ... (20a3–6)*

If we ignore the quantifiers, we may put the point like this: there are some sentences with the structure ‘O þ R’ which do not show the special structure ‘O þ [D þ O]’; and Aristotle claims that, logically speaking, those sentences work in just the same way as sentences with the special structure. A few pages further on he remarks that it makes no difference whether we say ‘¼
Łæø  ÆÇØ’ or ‘¼
Łæø  KØ
ÆÇø
’. (21b9–10).64

Thus any sentence with the structure ‘O þ R’ may be associated with a sentence which has the same semantic content and shows the structure ‘O þ [D þ O]’.65 Just as Frege may use the equation ‘D þ O ¼ B’ in order to accommodate traditional primary sentences, so Aristotle may [194] invoke the equation ‘R ¼ D þ O’ in order to accommodate Fregean primary sentences.

X The formula ‘O þ [D þ O]’ allows Aristotle to have things both ways. On the one hand, there is a heterogeneity; for ‘O’ and ‘D þ O’ belong to different categories. On the other hand, there is a homogeneity; for the formula contains 63 Frege himself shows little interest in syntactical matters. He writes as though any replacement for ‘F( )’ in ‘F(a)’ will count as a concept-word (just as any replacement for ‘a’ will be an Eigenname). * Kç’ ‹ø
b e Ø c ±æ Ø x
Kd  F ªØÆ
Ø
ŒÆd ÆÇØ
; Kd  ø
e ÆPe  ØE oø ØŁ
Æ ‰ i
N e Ø æ  . x
ªØÆ
Ø A ¼
Łæø  ... 64 cf Met ˜ 1017a27–30. The remark refers to Greek usage and does not translate into English: the periphrastic ‘KØ
ÆÇø
’ is not a progressive form of the verb, so that ‘is walking’ suggests the wrong idea. For the periphrasis, common enough in ordinary Greek, see KG II i, pp.38–39. 65 This became standard doctrine: see e.g. Boethius, in Int 2 314.7–315.18; 317.8–16 (ascribing the view to Alexander and ceteri complures).

Grammar on Aristotle’s terms

165

‘O’ twice. The homogeneity is required by Aristotle’s syllogistic. The heterogeneity is demanded by the decencies of syntax. So far, so good — or so I hope. But I must briefly address one wholesale objection to Aristotelian grammar. It has been urged that ‘it is logically impossible for a term to shift about between subject and predicate position without undergoing a change of sense as well as a change of role. Only a name can be a logical subject; and a name cannot retain the role of a name if it becomes a logical predicate’.66 If that is right, then my defence of Aristotle is quixotic. For even if the structure ‘O þ [D þ O]’ gives Aristotle a syntactical homogeneity, it will not underpin the semantic homogeneity which his syllogistic requires. If a pair of sentences of the form (1) No A is B and (2) No B is A are both well formed, then the words which replace ‘A’ and ‘B’ must have different senses in (1) and (2). In that case the rule of E-conversion would simply be inapplicable and every syllogism an equivocation. It is hard to believe that that is correct. Of course, a term in predicate [195] position plays a different role from a term in subject position: in the one case, its role is to be subject of the sentence and in the other to be predicate. But why should the change of role carry with it a change of sense so that genuine interchange of one and the same term is impossible? Why, that is to say, should we hold that the sense of ‘horses’ and the sense of ‘animals’ is different in the following two sentences: Horses are animals and Animals are horses? There are, admittedly, difficulties of various kinds with the interchange of terms in various ordinary sentences. But I cannot see that there is any universal difficulty; and the objection I have just canvassed, which would be annihilating were it sound, is surely a false objection. However that may be, numerous problems remain. Thus categorical sentences may contain complex terms, while only the simplest sentences show the structure ‘O þ [D þ O]’. We need to expand the syntax, and to expand it considerably, while at the same time preserving something 66 Geach, ‘History’, p.48. Geach then (p.49) praises Aristotle for his willingness to consider apparently intractable sentences such as ‘Knowledge of contraries is the same’ (above, n.35); but he urges that Aristotle’s procedure with them ‘makes nonsense of interchangeability thesis’: interchanging the terms in such sentences leads to something which ‘is simply gibberish’.

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analogous to the primary structure ‘O þ [D þ O]’.67 More pressingly, we are owed a reasonably clear and coherent description of the category of O
ÆÆ. Presumably the category must contain proper names, common nouns (both singular and plural), and adjectives; and it is not clear whether the items in such a category show any syntactical uniformity. The difficulty is apparent in the sentence which I have been using as a paradigm primary sentence: ‘Pleasure is good’. For ‘pleasure’ and ‘good’ surely belong to different syntactical categories, one being a noun and the other an adjective; and if we try, naively, to interchange the terms in the sentence, we get ‘Good is pleasure’ which is either ill formed or else a line of an Epicurean hymn. I shall not try to solve those problems; but one aspect of the second requires comment. [196] XI ‘¨ÆÅ ’ and ‘¼
Łæø ’ — a proper name and a common noun — are both of them O
ÆÆ, and the category of O
ÆÆ has no significant subdivisions. Many scholars would agree that ‘in his survey of the possible propositional forms ... , Aristotle fails to mention singular propositions, and he is obviously inclined to exclude them from his systematic discussions of syllogistic form’.68 It is true that singular propositions appear only rarely in the Analytics; but when they do appear, no warning sign is posted, nor are they given any peculiar attention. Later Peripatetic logicians betray no anxieties about them either: their logical gaze rarely falls on proper names; but when it does, they act as Aristotle had acted — and nonchalantly treat proper names as though they were uncontroversial members of the category of O
ÆÆ. Now the distinction between an Eigenname and a concept-word is fundamental to Fregean logic, and we might therefore infer that the crucially disabling feature of Peripatetic grammar was precisely its failure to distinguish between ‘Theaetetus’ and ‘ ... flies’, between ‘pleasure’ and ‘ ... is good’ or ‘good’. That, I assume, was Frege’s view; for he held that the traditional notions of subject and predicate ‘ever and again mislead us into confusing two fundamentally different relations: that of an object falling under a concept and that 67 The general lines along which the expansion must go are clear: every categorical sentence must show the structure ‘OP þ [D þ OP]’, where an OP is a name-phrase which may itself have a complex structure. 68 Patzig, Aristotle’s Theory, p.5.

Grammar on Aristotle’s terms

167

of one concept being subordinated to another’.69 If you fail to distinguish between Eigenname and Begriffswort, then you will treat ‘Theaetetus is flying’ and ‘Pigs are flying’ as having the same logical form — and your logic will go to pot. If we attempt to defend Aristotle by stressing his ‘obvious inclination’ to exclude singular propositions from his syllogistic, we do him small favour: in eliminating the confusion we thereby emasculate the logic. In short, the fundamental error lies in Aristotle’s grammar — and in that part of it which he took over from Plato. The category of O
ÆÆ includes items of at least two logically distinct types. If we leave the category alone, Aristotle’s syllogistic is fundamentally confused. If we exclude proper names from the category, the syllogistic loses its potency. Yet that is not an entirely satisfactory diagnosis of Aristotle’s [197] infirmities. After all, there are unfamiliar modern logics in which the distinction between singular term and general term is systematically ignored; and there are familiar techniques for ‘eliminating’ singular terms from an otherwise Fregean logic. In either way, terms such as ‘Theaetetus’ and ‘pleasure’ are taken to be, or to behave as though they were, general terms or common nouns — and logic marches happily onward. In short, no bar is set to logical progress by the failure to distinguish proper names from common nouns. It is worth noting, in passing, that if singular terms are eliminated or assimilated to general terms, then certain consequences follow for Aristotelian grammar. Thus the primary sentence Theaetetus is flying must be regarded as an ‘indeterminate’ or unquantified sentence, like the paradigm Pleasure is good. Hence it is properly taken as elliptical, either for Every Theaetetus is flying or for Some Theaetetus is flying.70 It follows that all primary sentences are quantified. The simple Platonic structure for primary sentences turns out to be a sham. For no sentence has the structure ‘O þ R’. At best, we may say that ‘O þ R’ stands at the heart of primary sentences. The primary sentences themselves are syntactically more complicated.

69 ‘Ausfu¨hrungen’, p.130 [¼ p.120]. 70 It does not matter which: if there is only one F, then ‘Every F is G’ is equivalent to ‘Some F is G’.

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None of that would have been particularly palatable to Peripatetic logicians; but none of it requires any substantial alterations to the fabric of Aristotelian logic.

XII In point of fact, Frege’s grand logical advance did not depend only, or even primarily, on his grasp of the distinction between [198] Eigenname and Begriffswort. In addition, and rather, it depended on his connected grasp of the notion of multiple quantification, and hence on the concept of a many-placed predicate. The inference about horses’ heads, which the traditionalists cannot cope with, involves the two-placed predicate ‘ ... is a head of —’; and its conclusion is a multiply quantified proposition.71 It is trite to observe that most deductive arguments of any complexity — and in particular, most arguments in the mathematical sciences — depend on multiple quantification. Aristotle’s syllogistic was intended as a logic for the sciences; and he expressly claims that ‘the mathematical sciences — arithmetic, geometry, optics — and pretty well all the sciences which inquire into the reason why, produce their proofs by way of the first figure’ (APst ` 79a18–21).* Aristotle’s claim is false; and it is false because his syllogistic cannot deal with multiply quantified propositions.72 In order to grasp the notion of multiple quantification it is necessary to have the idea of a many-placed verb or verbal phrase. Platonic verbs are all one-placed: an R takes a single O to make a sentence. So too, of course, with complex verbal phrases of the structure ‘D þ O’. It is this fact about Aristotelian grammar — a fact which has nothing to do with the copula — which explains the debility of Aristotelian syllogistic. How might many-placed verbs be superadded to Aristotelian grammar? Well, why not treat the verb in a primary sentence — the ‘is’ in ‘Every horse is an animal’ — as itself a two-placed predicate? You might then treat terms as Eigennamen of, say, classes; and the schema for a categorical sentence will 71 In more or less standard notation, the inference moves from: (8x)(if horse(x), then animal(x)) to: (8y)(if (9x)(horse(x) & head(y,x), then (9x)(animal(x) & head(y,x)). * Æ¥  ªaæ ÆŁÅÆØŒÆd H
KØÅH
Øa   ı çæ ıØ a I Ø; x
IæØŁÅØŒc ŒÆd ªøæÆ ŒÆd OØŒ; ŒÆd åe
‰ NE
‹ÆØ  F Ø Ø  Ø F
ÆØ c
ŒłØ
. 72 On these issues, see e.g. I. Mueller, ‘Greek mathematics and Greek logic’, in J. Corcoran (ed), Ancient Logic and its Modern Interpretations (Dordrecht, 1974), pp.35–70.

Grammar on Aristotle’s terms

169

become ‘tXt*’,73 which is a special case of the post-Fregean schema for twoplaced relational sentences: ‘(a1)R(a2)’. Categorical syllogistic turns out to be the logic of a particular relation or set of relations on classes.74 [199] And once we have attended to the two-placed verb ‘( )X( )’, we may hit upon the idea that there are also many other two-placed verbs — and some threeplaced verbs, and so on.75 But that line of thought is muddled — there are familiar objections to treating ‘is’ in ‘Every horse is an animal’ as a two-placed predicate. Nor would it have been welcomed by the ancient logicians, who rightly maintained — in effect — that there can only be one copula.76 In any case, there is another way to introduce relations. For it must surely seem easy and natural to extend the Platonic structure, ‘O þ R’, so that it will embrace two-placed verbs. Once ‘Lions growl’ is seen to have the structure ‘O þ R’, then surely ‘Lions eat antelope’ can be seen to have the structure ‘O þ R* þ O’, where ‘R*’ is a twoplaced (or transitive) verb? And after that you may, if you wish, move on to the general notion of an n-placed verb, as an item which takes n O
ÆÆ and makes a sentence. Two-placed verbs express dyadic relations. Ancient philosophers, from Plato onwards, were well aware of relational items, of a æ  Ø. They puzzled over them at length and with ingenuity. But they were all fearfully muddled — as Sextus Empiricus proved with devastating accuracy.77 Despite all their reflexion on relational items, Plato and Aristotle never hit upon the 73 I interchange lower and upper cases to accord with the post-Fregean conventions. 74 Compare the remarks in Patzig, Aristotle’s Theory, pp.52–57. But note Geach, ‘History’, p.53: ‘By this slide the rake’s progress of logic ... reaches its last and most degraded phase: the two-class theory of categoricals. The subject and predicate terms are now said to denote two classes’. 75 Compare Augustus de Morgan’s pioneering attempt to generalize categorical syllogistic into a logic of (certain) two-placed relations. He first followed the heterodox line of ‘quantifying the predicate’, so that e.g. ‘Every horse is an animal’ was construed as ‘Every horse is some animal’. He then read the copula — the ‘is’ — in categorical sentences as signifying identity, thus arriving at ‘Every horse is identical with some animal’. And finally he reflected that if the copula could be interpreted to mean ‘is the same as’, there was no reason why it should not also be read as ‘joins’ or ‘is tied to’ or ‘gives’ or any of numerous other two-placed relations. (I summarize the story told by D.D. Merrill, Augustus de Morgan and the Logic of Relations (Dordrecht, 1990), pp.60–78.) 76 See Ammonius, in Int 176.17–177.18; 207.28–208.8. (Ammonius notes that some scholars had taken a contrary view.) — The function of a   is simply that of taking an Z
Æ into a verbal phrase: if ‘’ is any  , then you know what ‘’ means if you know that it take a name and makes a verbal phrase — there is nothing more to know. It follows that there cannot be a plurality of  . (Ancient logicians said that ‘is’ in ‘is good’ does not ‘signify’ anything. They did not, of course, mean that it was a meaningless noise; rather, they meant that there was nothing to its semantic role beyond the fact that, syntactically, it takes a name into a verb.) 77 See J. Barnes, ‘Scepticism and relativity’, Philosophical Studies 32, 1988/90, 1–31 [reprinted in volume III].

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notion of a relational predicate; and their one-placed verbs never spawned many-placed verbal phrases. The Stoics said a few things which point towards the [200] notion of a two-placed verb; but multiple quantification does not appear in Stoic logic. In Galen’s Introduction to Logic there is an attempt — unique in ancient philosophy — to analyse a ‘third sort of syllogism’, which Galen called relational syllogisms and which he realized were of the first importance, especially in the mathematical sciences. But Galen himself did not get far; and the later Peripatetics, who developed Aristotle’s syllogistic in various minor ways and who were alive to the importance of the arguments which Galen tried to analyse, trudged doggedly backwards: in effect, they attempted to reduce two-placed predicates to one-placed predicates.78 The notion of a many-placed predicate is now so familiar that we may find it hard to sympathize with the ancient muddles. So it is perhaps worth noting that the matter was not wholly plain even to Frege. In the Begriffsschrift, it is true, he introduces what he calls ‘functions of two and more arguments’ without any special explanation.79 Much later, in the Grundgesetze, we find a similar nonchalance: ‘hitherto I have spoken only of functions of a single argument; but we can easily pass on to functions of two arguments ’.80 But other texts appear to exhibit a weaker grasp. Thus in the Grundlagen he writes of two-placed relations as follows: The individual pairs of correlated objects stand to the relation-concept in the same way — as subject, we might say — as the individual object stands to the concept under which it falls. Here the subject is composite.81

A sentence such as ‘Plato taught Aristotle’ is here implicitly construed as containing a one-placed predicate, ‘ ... taught’, and a plural subject, ‘Plato and Aristotle’. Moreover, Frege never coined a general term to pick out the notion of an nplaced predicate. A one-placed predicate he will call a concept-word. A twoplaced predicate is not a concept-word but a relation-word. And on those rare occasions when he adverts to three-placed predicates he speaks, clumsily, of relations-with-three-fundaments.82 I do not suggest that Frege was confused. But he was not altogether pellucid. 78 See J. Barnes, ‘Logical form and logical matter’, in A. Alberti (ed), Logica Mente e Persona (Florence, 1990), pp.7–109 [reprinted above, pp.43–146]. 79 See Frege, Begriffsschrift, pp.17–18 [¼ p.128]. 80 G. Frege, Grundgesetze der Arithmetik I (Jena, 1893) [partial English translation by M. Furth (Berkeley CA, 1967)], p.8 [¼ p.36]. 81 G. Frege, Die Grundlagen der Arithmetik (Breslau, 1884) [English translation by J.L. Austin (Oxford, 1953)], p.78 [¼ p.82]. 82 See ‘Logik in der Mathematik’, p.269 [¼ p.249].

Grammar on Aristotle’s terms

171

However that may be, Aristotelian syllogistic concerned itself [201] exclusively with monadic predicates. Hence it could not begin to investigate multiple quantification. And that is why it never got very far. Nonetheless, the underlying grammar of Aristotle’s logic did not in itself block the path to polyadicity. The later Peripatetics were conservative creatures and they lacked logical imagination. Moreover, Aristotle himself had assured them that his syllogistic was adequate for all serious scientific needs. As for Aristotle, his service to logic is nonpareil, and it would be grotesque to chide him for lack of inventiveness. It is true that, in logical grammar, he did not climb above the level which he attained in the de Interpretatione. But the Analytics does not represent a fatal, or even a new, grammatical excursion. And the story of Aristotle’s fall, like the story of the fall of Adam, is a myth.83 83 An early draft of this chapter was read to an Oxford seminar, where David Charles gave it a drubbing. The second version, which I read at Berlin at Gu¨nther Patzig’s birthday party, was severely mauled — especially by Michael Frede, Mario Mignucci, and Gisela Striker. I have gained enormously from those friendly thrashings — but I fear that a few more touches of the lash would have made me still fitter.

5 Peripatetic negations* But with an affirmation and negation one will always be false and the other true whether he exists or not. For take ‘Socrates is ill’ and ‘Socrates is not ill’: if he exists it is clear that one or the other of them will be true or false, and equally if he does not; for if he does not exist ‘He is ill’ is false but ‘He is not ill’ is true. (Cat 13b27–33)

I Ancient logicians did not question the Aristotelian view that ‘for every affirmation there is an opposite negation, and for every negation an opposite affirmation’ (int 17a32–33); nor did they doubt that ‘a single affirmation has a single negation’ (17b37): every affirmation, P, has one and only one negation neg:P. Moreover, it was taken to be constitutive of the notion of negation that P and neg:P cannot both be true and cannot both be false.1 And it was supposed that a negation, neg:P, will normally be constructed from its affirmative twin, P, together with a negative operator.2 Those common notions form the background to a short essay on negation which Alexander of Aphrodisias inserted into his commentary on Aristotle’s Prior Analytics. Alexander defends an Aristotelian account of negation and argues against a rival account.3 The rival account is generally supposed to be

* First published in the Festschrift for John Ackrill — Oxford Studies in Ancient Philosophy 4, 1986, 201–214. 1 It does not follow, nor was it universally accepted, that the Law of Bivalence has unrestricted validity. 2 See e.g. Galen, inst log vi 2 (where exceptions to the normal rule are noted). 3 in APr 402.1–405.16. Scholarly attention was drawn to the passage by A.C. Lloyd, ‘Definite propositions and the concept of reference’, in J. Brunschwig (ed), Les Stoicı¨ens et leur logique (Paris, 1978 [2006]2), pp.286–294 [pp.223–233]. I have had the advantage of reading an unpublished paper by Paul Moraux on the passage. Only after finishing this piece did I see a copy of Walter Cavini’s long paper on ‘La negazione di frase nella logica greca’, in AA.VV., Studi su Papiri Greci di Logica e Medicina, Studi dell’Accademia Toscana di scienze e lettere ‘la Colombaria’, LXXIV (Florence, 1985), pp.6–126. Cavini discusses the passage from Alexander on pp.67–80; on pp.122–126 there is a large bibliography on negation in Greek.

Peripatetic negations

173

Stoic or even Chrysippean; and it [202] contains indisputably Stoic elements. But Alexander does not name his opponents, nor does he offer any information about the history of the dispute.4 The dispute concerns singular affirmations (‘Callias walks’, ‘This man walks’, ‘Socrates walked’) and their negations. Alexander expresses the Peripatetic view thus: In the negations of singular propositions the negation operator should be construed with the predicate. (405.15–16)*

The contrary view, which he argues against, holds that in such cases the negation operator should be taken to govern the whole proposition. The disagreement is syntactical.5 The Peripatetics hold, in effect, that (for singular propositions) negation is a predicate-forming operation on predicates; their opponents maintain that negation is a proposition-forming operation on propositions. If we represent singular propositions in the standard modern fashion by the schema ‘Fa’, then the Peripatetic view is that the negation of ‘Fa’ is ‘[not-F]a’, whereas their opponents hold that the negation of ‘Fa’ is ‘not-[Fa]’.6 [203] 4 Alexander is not normally reluctant to name his opponents. He frequently speaks of ƒ øœŒ  or ƒ Ie B  A, he frequently uses the expression ‘ ƒ
æ Ø’ to refer to the Stoics, and he more than once cites Chrysippus by name. In the essay on negation, however, the opponents remain anonymous (they are introduced impersonally at 402.3 — NØ ... x   ŒE — and never later identified); and that is perhaps an indication that the men in question were not simply identifiable as Stoics or Chrysippeans. — See further J. Barnes, ‘Aristotle and Stoic logic’, in K. Ierodiakonou (ed), Topics in Stoic Philosophy (Oxford, 1999), pp.23–53 [reprinted below, pp.382–412], on pp.41–45. * På ªØE c ƃ K
Ø ƃ æe e E
e I çÆØŒe
K
ÆE H
ŒÆŁ’ ŒÆÆ I çØ fiH ŒÆŪ æ ı
fiø ı
ŁÆØ ªØ

ÆØ. 5 Alexander talks of the negation operator being ‘construed with [ı
ŁÆØ]’ (404.7; 405.16) or ‘attached to [æ ŁŁÆØ]’ (402.9; 404.9) the predicate or the whole sentence. (Compare Sextus’ use of ‘govern [ŒıæØØ
]’ at M VIII 90, in connection with the Stoic view of negation.) He also talks of the negative particle being ‘placed before [æe ... ŁŁÆØ]’ (402.5, 27; 403.10) the predicate expression or the whole sentence. (Compare the Stoic view that the negation sign should be ‘prefixed [æ Ø
]’ to the whole sentence: e.g. Sextus, M VIII 90; Apuleius, int iii [191.10–11].) There are two distinct issues there, though Alexander does not trouble to distinguish them. The Peripatetics and their opponents, while agreeing on the semantic properties of negation, disagreed both about the syntactic structure of negations and about the most appropriate linguistic devices for expressing negations in Greek. The former disagreement is fundamental, the latter consequential — and relatively trivial. (For discussion of some of these issues, see e.g. D. Wiggins, ‘The de re ‘‘must’’: a note on the logical form of essentialist claims’, in G. Evans and J. McDowell (eds), Truth and Meaning (Oxford, 1976), pp.285–324; G. Englebretsen, Logical Negation (Assen, 1981).) 6 Alexander’s essay is occasioned by Aristotle’s remark that the sentence øŒæÅ Kd
P ºıŒ 

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Logical Matters II

Alexander’s essay is clearly articulated.7 He first explains what view his opponents advance; then he rehearses three arguments by which the opponents seek to refute the rival Peripatetic view; and the major part of the essay is an attempt to rebut the three arguments and hence to preserve the Peripatetic view. The first of the opponents’ arguments is the most challenging, and Alexander’s reply to it occupies by far the longest section of his rebuttal. The section divides into six subsections which contain six more or less independent arguments.8 The second of these subsections is the most intricate and the most interesting; for it includes a positive passage in which Alexander tries to give a deeper account of the Peripatetic view.

expresses an affirmation and not a negation (APr ` 51b32). Here the negation operator occurs within the predicate. There are thus three syntactically possible ways of introducing negation into the affirmative sentence (1) øŒæÅ Kd ºıŒ  Alexander represents the ways by the following sentences: (2a) øŒæÅ Kd
P ºıŒ  (2b) øŒæÅ PŒ Kd ºıŒ  (2c) Påd øŒæÅ Kd ºıŒ  The form introduced by (2a) plays no part in Alexander’s essay. 7 (A) The opponents’ view: 402.1–12 (B) The opponents’ arguments: 402.12–36 (1) 402.12–19 (2) 402.20–33 (3) 402.33–36 (C) Alexander’s rebuttal: 402.36–405.15 (1) of argument (B1): 402.36–404.31 (i) 402.36–403.11 (ii) 403.11–404.11 (a) the objection: 403.11–14 (b) the opponents’ reply: 403.14–18 (c) rebuttal of (b): 403.18–26 (d) Alexander’s positive suggestions: 403.27–404.11 (iii) 404.11–18 (iv) 404.18–24 (v) 404.25–27 (vi) 404.27–31 (2) of argument (B2): 404.31–405.10 (3) of argument (B3): 405.10–15 8 But the division is not fully determinate: the lines classified as (C)(1)(iv) in note 7 contain a bundle of similar counterexamples — it is not clear whether they should be counted for one or several objections.

Peripatetic negations

175

I II The first argument against the Peripatetic view runs as follows. Alexander says of his opponents that [204] they support their view by the claim that ‘Callias walks’ and ‘Callias does not walk’ can sometimes be false together, whereas contradictory opposites9 are never false together. For they say that if Callias does not exist, then ‘Callias does not walk’ is no less false than ‘Callias walks’. For in both of them what is meant is: There exists some Callias and to him belongs either walking or not walking. But ‘It is not the case that Callias walks’ can never itself be false when the affirmation, ‘Callias walks’, is false. (402.12–19)*

‘Fa’ and ‘[not-F]a’ are both false if a does not exist; hence ‘[not-F]a’ is not the negation of ‘Fa’.10 They are both false because ‘Fa’ means the same as ‘There exists some a and it is F’ and ‘[not-F]a’ means ‘There exists some a and it is not-F’; and both those longer versions are evidently false if no a exists. Alexander ascribes to his opponents a general thesis about the proper analysis of singular propositions.11 His text hints at several slightly different formulations of the thesis, and the thesis itself contains an apparently

9 a I
،
Æ I
ØçÆØŒH: ‘I
ØçÆØŒH’ is Wallies’ correction of the received ‘I çÆØŒH’. * Ø F
ÆØ b  F fiH –Æ b

ÆŁÆØ łıB   r
ÆØ   ˚ƺºÆ æØÆE ŒÆd e ˚ƺºÆ P æØÆE, Å  b a I
،
Æ I
ØçÆØŒH –Æ ª
ŁÆØ łıB. c ªaæ Z
  ˚ƺº ı Pb
w
çÆØ B ˚ƺºÆ æØÆE łıB r
ÆØ c
˚ƺºÆ P æØÆE· K
Iç æÆØ ªaæ ÆPÆE r
ÆØ e ÅÆØ


Ø Ø ˚ƺºÆ,  fiø b æåØ j e æØÆE
j e c æØÆE
. e 
 Ø P ˚ƺºÆ æØÆE P  
ÆÆØ łı F hÅ B ŒÆÆçø B ˚ƺºÆ æØÆE łF  r
ÆØ ŒÆd ÆP . 10 Note that the opponents have no quarrel with the structure ‘[not-F]a’: it is not the negation of ‘Fa’, but it is well formed and intelligible — see 402.8–12. (For the Stoic categorization of ‘[not-F] a’, see e.g. Apuleius, int iii [101.6–15].) What was the Peripatetic attitude to ‘not-[Fa]’? If it is not the negation of ‘Fa’, then what is it? Perhaps the Peripatetics denied that negation could operate on the whole of a singular affirmation, and held that there was no such syntax as ‘not-[Fa]’. Compare 403.18–26, where Alexander rejects ‘V[Fa]’ (below, p.177). 11 The general thesis is expressed only at 404.14–15 (and even there not with complete generality); but there are numerous illustrative applications of it. ‘Fa’ is analysed as: (i) Ø Ø a  fiø b æåØ e ! (ii) Ø Ø a n ! (iii) Ø Ø a ‹Ø ! For (i), see 402.17; 404.28, 29 (with ‘ŒIŒE
’ instead of ‘ fiø ’); for (ii), see 402.30, 33; 403.12, 14 (read ‘Ø Ø’ for ‘Ø’?); 404.12 (where for ‘k
ŒÆa  F K’ read ‘Ø
e k
n KØ
’), 14, 15; for (iii), see 403.5, 6, 34 (read ‘Ø Ø’ for ‘Ø’?).

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illegitimate feature.12 But the main thrust of the thesis and its relevance to the dispute over negation are both plain. Alexander sums the matter up by saying that according to his opponents ‘the name in the propositions signifies ... the existence of the thing named’ (402.37–403.2).* We might put it thus: the sense of [205] ‘Fa’ includes an existential component, in that part of the meaning of ‘Fa’ is conveyed by ‘a exists’.

IV Alexander thinks to rebut his opponents’ first argument by discrediting the general thesis on which it rests; and his several objections to the first argument are in fact objections to that general thesis. The second objection is this: If ‘Socrates is not alive’, which we [sc Peripatetics] call a negation [i.e. the negation of ‘Socrates is alive’], is false because it means ‘There exists some Socrates who is not alive’, then ‘Socrates died’ will be false for the same reason; for it will mean ‘There exists some Socrates who died’. (403.11–14)**

Alexander tacitly assumes that ‘Socrates died’ has the form ‘Fa’ — that it is a singular affirmation. He also tacitly assumes that ‘a died’ implies ‘a does not exist’. Given the first assumption, the opponents must apply their thesis and analyse ‘Socrates died’ as ‘There exists some Socrates and he died’. But by the second assumption that proposition must be false. Hence the opponents’ thesis implies that every proposition of the form ‘a died’ is false — and that is a reductio ad absurdum of the thesis. 12 ‘Ø Ø a’ (see n.11) is ill formed, since ‘a’ is a proper name. The historical explanation for this oddity is surely to be found in the old Stoic view of proper names (see J. Brunschwig, ‘Remarques sur la the´orie stoı¨cienne du nom propre’, Histoire, Episte´mologie, Langage 6, 1984, 3–19 [¼ E´tudes sur les philosophies helle´nistiques (Paris, 1995), pp.115–139; English translation in Papers in Hellenistic Philosophy (Cambridge, 1994), pp.39–56]; J. Barnes, Porphyry: Introduction (Oxford, 2003), pp.152–154, 314–316). One way of making the phrase grammatical is to replace the name ‘a’ by a one-place predicate ‘A’ — ‘Aristotle’ by ‘ ... is the same man as Aristotle’, for example; so that ‘There is some Aristotle and he is intelligent’ becomes ‘Someone is identical with Aristotle and is intelligent’ — in general: Fa ¼ df( 9 x)(Ax & Fx) — where ‘A’ is a predicate corresponding to ‘a’ (‘pegasize’ or what you will). * Iºº’ ‹Ø ª e ºª 

’ ÆPH
łF  KØ ŒÆd P ÅÆ
Ø e Z
Æ K
ÆE æ Ø
... e r
ÆØ e O
ÆÇ 

... ** Ø N Øa  F łı KØ
m
ºª 
I çÆØ
ºª ıÆ øŒæÅ P ÇB ‹Ø ÅÆ
Ø e Ø Ø øŒæÅ n P ÇfiB, Øa e ÆPe  F łıc ÆØ ŒÆd ºª ıÆ øŒæÅ IŁÆ

· ÆØ ªaæ ŒIŒ
Å ÅÆ
ıÆ e Ø øŒæÅ n IŁÆ
.

Peripatetic negations

177

V The opponents are given an ingenious reply to the objection. In effect, they reject the first of Alexander’s two tacit assumptions. For they say that ‘Socrates died’ has two constructions: in one, it consists of the name ‘Socrates’ and the verb ‘died’, and that is indeed false; in the other, it is derived as a whole from ‘Socrates dies’ — and then it is true. (403.14–18)*

Past-tensed propositions, the opponents assert, can be construed in either of two ways: we can take the tense as a predicate-forming operator on predicates (when the verb gathers the transformation), and we can take it as a propositionforming operator on propositions (when the proposition is transformed as a whole). An artifice will be helpful. Let ‘V’ be a past-tensed operator, so that ‘VFa’ represents singular propositions in the past tense. ‘VFa’ is syntactically ambiguous: it can be parsed either as ‘[VF]a’ or as ‘V[Fa]’. If ‘Socrates died’ is parsed in the former way, the general thesis of the opponents will give it the analysis: ‘There exists some Socrates and [206] [V dies] holds of him’. Then ‘Socrates died’ entails ‘Socrates exists’ and is false. The latter parsing yields, after analysis: ‘V[there exists some Socrates and he dies]’. And that does not entail ‘Socrates exists’.13 It can be no accident that this treatment of the past tense is structurally similar to the opponents’ treatment of the negation operator. Just as ‘not-Fa’ is ambiguous, syntactically, between ‘[not-F]a’ and ‘not-[Fa]’, so ‘VFa’ is ambiguous between ‘[VF]a’ and ‘V[Fa]’. Both cases exhibit the same syntactic structure.

VI Alexander proceeds to claim that ‘Socrates died’ cannot be construed as ‘V[Socrates dies]’. He produces two arguments for his claim, neither of * e b ºªØ
‹Ø e øŒæÅ IŁÆ
 Ø
KØ
, £
b
n ªŒØÆØ K O
Æ  b
 F øŒæÅ ÞÆ  b  F IŁÆ

, n ŒÆd łF  KØ
, ¼ºº b n KªŒŒºØÆØ ‹º
Ie  F øŒæÅ I Ł
ŒØ, n ŒÆd IºÅŁ KØ
... 13 The opponents no doubt hold a similar view about future-tensed propositions: ‘ZFa’ is ambiguous between ‘[ZF]a’ and ‘Z[Fa]’: cf 403.34. The same can be done for the present tense: ‘GFa’ is either ‘ [GF]a’ or ‘G[Fa]’ — but here the two constructions will always carry the same truth-value.

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which is convincing and one of which is obscure. But he follows the arguments with a positive passage which is designed to show how on the Peripatetic view propositions like ‘Socrates died’ pose no problems. The passage is difficult: the train of thought is far from plain; Alexander’s expressions are, I suspect, sometimes misleading; and there is certainly some textual corruption.14 For the moment I translate Wallies’ text. [i] ‘Socrates’ does not mean the same thing in ‘ ... dies’ and in ‘ ... died’; for in ‘Socrates dies’ it is indicative of the existing Socrates, but in ‘Socrates died’ it is used by anaphora — for then ‘Socrates’ means the man who was, not who is, Socrates. And for that reason the proposition ‘Socrates died’ is true — for the man whom the name ‘Socrates’ meant died. [ii] Similarly with ‘A son will be born to me’ (not who is a son but who will be) and ‘I will have a house’; for we are not saying that there exists a house which I will have, nor yet is it derived from something. [iii] When the subject term is taken in this way, each of the previously mentioned propositions is true. Yet it is not the case that someone who utters the proposition determines in addition, by uttering the name, that when the subject term in the proposition holds in a different way, the proposition [207] which is taken to hold in this way is true. Or rather, if the predicate should fail to hold of some of the subjects, in this way; if it is clear that it does not exist, in that way. [iv] For a name, when uttered in its own right, does not itself mean either that it exists or that it does not exist; for what is meant by it neither means in addition that it does not exist nor is in itself indicative of what exists rather than of what existed or what will exist. The name itself is only a sign of the object, and whether the object exists or will exist is indicated by what is construed with the name. Thus ‘Socrates lived’ or ‘ ... died’ or ‘ ... philosophized’ are all uttered anaphorically, in that what is attached to the name indicates that what is signified by the name existed before. Hence, since each of these is true, their contradictories — ‘ ... did not die’ or ‘ ... did not live’ or ‘ ... did not philosophize’ — are false. (403.26–404.11)* 14 The crux at 404.2 is discussed below. At 404.5 Wallies’ ‘æ ÅÆ
Ø’ (for ‘æ ÅÆ
Ø’) is correct (cf ‘æ Ø æÇØ’: 403.36), and at 404.6 Wallies’ ‘N (for ‘q
’) restores syntax and sense. For other textual points in Alexander’s essay, see n.11. Something is awry also at 404.34 and at 405.13– 14. At 404.34 it is perhaps easiest to excise ‘Øa  F y  Kd
› ØŒ

 ‹’. At 405.13–14 I tentatively suggest ‘w
’ for ‘Aºº
’ and ‘ P øŒæÅ’ for ‘øŒæÅ P’. * P ÆPe
b
s
ÅÆ
Ø e øŒæÅ 
 fiH I Ł
ί ήd K
fiH IŁÆ

· Kd b
ªaæ  F øŒæÅ I Ł
ί  F Z
  øŒæ ı Kd źøØŒ
, Kd b  F øŒæÅ IŁÆ

ŒÆ’ I
Æç æa
ºªÆØ·ÅÆ
Ø ªaæ   e øŒæÅ  F
n q
øŒæÅ, På n Ø
. ŒÆd Øa  F IºÅŁc æ ÆØ øŒæÅ IŁÆ

· n
ªaæ KÆØ
 e øŒæÅ Z
Æ, y  IŁÆ

.  Ø F
 KØ ŒÆd e åŁÆ  Ø ıƒ  ð P ªaæ n Ø
ıƒ , Iºº’ n ÆØÞ ŒÆd e ÆØ  Ø NŒÆ· P ªaæ  F ºª 
‹Ø Kd
NŒÆ lØ ÆØ· Iºº’ P’ I Ø
 KªŒŒºØÆØ. oø b
ºÆÆ

ı  F  ŒØ
ı IºÅŁÆØ ŒÅ H
æ ØæÅ
ø


Peripatetic negations

179

VII The content of paragraph [i] is at first sight startling; for Alexander seems to be asserting that the subject terms in ‘Socrates dies’ and ‘Socrates died’ refer to two different things, and he seems to be suggesting that the two propositions are synonymous with ‘The man who is Socrates dies’ and ‘The man who was Socrates died’. The apparent suggestion is surprising — even though it is not formally incompatible with Alexander’s rejection of his opponents’ thesis. And the apparent assertion is insane: it entails that when Phaedo says on Monday ‘Socrates is dying’ and then on Tuesday ‘Socrates died yesterday’, he is talking about two different people. Alexander cannot mean to suggest what he appears to be suggesting or to assert what he appears to be asserting: the function of paragraph [i] is preparatory, and it avers only that the name ‘Socrates’ is used differently in ‘Socrates dies’ and ‘Socrates died’ — in the former it has deictic reference to Socrates, in the latter anaphoric reference. For in paragraph [iv] Alexander states plainly that a name is ‘only a sign of the object’: the name ‘Socrates’ is a sign for Socrates — and that fact exhausts its meaning.15

VIII Paragraph [ii] makes the same point about two future-tensed propositions. (Alexander had earlier claimed that propositions similar to [208] them posed problems for his opponents: see 403.2–9.) The examples are

æ ø
. P c
› ºªø
c
æ ÆØ
K
fiH e Z
Æ ºªØ
æ Ø æÇØ  F ‹Ø ¼ººø å
   F  ί
ı ‹æ ı K
fiB æ Ø IºÅŁc æ ÆØ ª
ÆØ m oø åØ
ºÆ
ÆØ. N b
s
Ø
Ø H
 ί
ø
c æå Ø e ŒÆŪ æ 

, oø· N b Bº
‹Ø c Ø
, KŒ
ø. e ªaæ Z
Æ ÆPe ŒÆŁ’ Æe ºª 

h e r
ÆØ ÅÆ
Ø h e c r
ÆØ· e ªaæ ÅÆØ


’ ÆP F h e c r
ÆØ æ ÅÆ
Ø h  F Z
  Aºº
j ªª
  j K 
ı źøØŒ
KØ ŒÆŁ’ Æ , Iºº’ ÆPe  F 

ÅE
KØ æªÆ , n N j Ø
j q
j ÆØ e ı
Æ 

ÆPfiH ź E. oø  
ı
ŒÆd e ÇÅ øŒæÅ j IŁÆ

j Kçغ  çÅ 
Æ æe I
Æç æa
ºªÆØ fiH a æ ØŁ
Æ fiH O
ÆØ ź F
‹Ø e ÅÆØ


e  F O
Æ  æ æ
q
. Øe Kd ŒÆ
 ø
IºÅŁ, łF  e I
،

e PŒ IŁÆ

j PŒ ÇÅ
j PŒ Kçغ  çÅ
. 15 On Alexander’s view, you know what ‘Socrates’ means if you know that ‘Socrates’ denotes Socrates. Alexander does not discuss the problem of ‘empty’ names. I suppose he would hold that if ‘a’ is empty, then the sentences ‘Fa’ and ‘not-Fa’ do not express any thought — they do not have any meaning.

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in certain respects anomalous, and I shall not discuss them here.16 But Alexander’s conclusion is easily transposed into the past tense: ‘(1) we are not saying ... nor yet (2) ... ’. (1) In saying that Socrates died we are not saying that there exists a Socrates who died; nor yet (2) is ‘Socrates died’, the past-tensed proposition, ‘derived from something’ — that is, it is not derived from ‘Socrates dies’ by a past-tense transformation on the whole present-tensed proposition. Thus Alexander reiterates his rejection of the two possible analyses of ‘Socrates died’ which his opponents were supposed to advance.

IX Alexander denies that the use of a name in singular affirmations carries any existential implications: when you utter the name ‘Socrates’ you mean or refer to Socrates — and you do nothing more. But he does not assert that singular affirmations are themselves wholly neutral with regard to the existence of the objects denoted by their subject terms. His own view of the matter is explained in paragraphs [iii] and [iv]. It is easier to begin with [iv]. The general purport of paragraph [iv] is plain. Alexander looks not to the name but to the predicate (what is ‘construed with’ or ‘attached to’ the name) in order to elucidate the existential import of singular propositions. Take ‘Socrates philosophized’: here the predicate ‘ ... philosophized’ indicates that Socrates ‘existed before’. (If you utter the proposition ‘Socrates philosophized’, then the predicate you use indicates that Socrates existed at some time before your utterance.) Alexander does not mean that ‘Socrates philosophized’ is synonymous with ‘Socrates, who existed earlier, philosophized’; rather, he means that the predicate determines the existence of the subject to a past period of time. (And hence it indicates that the mode of reference of ‘Socrates’ is here anaphoric rather than deictic.) It is tempting to construe Alexander’s thesis as stating that the tense of the verb which expresses the predicate determines the existential import of the proposition: if ‘F’ in ‘Fa’ is present-tensed it indicates that a exists, if pasttensed that a existed, if future-tensed that a will exist. But there are simple 16 The problem is that ‘A son will be born’ is not a singular affirmation of the form ‘Fa’. It is not clear why — or that — the Peripatetics (or their opponents) must treat such propositions as though they were singular affirmations.

Peripatetic negations

181

counterexamples to this thesis — consider, [209] say, ‘Socrates is widely admired’ or (one of Alexander’s own favourites) ‘Socrates is not alive’. And in fact Alexander does not explicitly say that the tense alone determines existential import: he says that what is construed with the name does so, and he can quite plausibly hold that in cases like ‘Socrates is admired’ or ‘Socrates is not alive’ the predicates indicate that Socrates existed in the past. What existential indications a predicate ‘F’ carries depends on the whole semantic nature of ‘F’: the tense of the predicate is only one of its relevant semantic features.

X Paragraph [iii] is far harder to understand. The following interpretation is tentative and tortuous. [1] When the subject term is taken in this way, each of the previously mentioned propositions is true. Take again ‘Socrates died’. The name ‘Socrates’ refers to Socrates and does no further semantic work. The predicate ‘died’ indicates past existence and shows that ‘Socrates’ here refers anaphorically. Hence the proposition is true provided that ‘died’ is true of what ‘Socrates’ refers to, and that what ‘Socrates’ refers to existed in the past. The conditions are in fact met so that the proposition is in fact true. [2] Yet it is not the case that someone who utters the proposition determines in addition, by uttering the name, ... We expect Alexander to say that by using the name ‘Socrates’ in the proposition ‘Socrates died’ you do not determine or imply that Socrates now exists (or, come to that, that he will exist). Alexander’s words are contorted, but they can perhaps be interpreted in that way. For he says that you are not committed to the truth of the proposition which results from taking the subject term ‘in a different way’. In ‘Socrates died’ the subject term is taken anaphorically: perhaps the ‘different way’ is the way of deictic reference. Then Alexander’s point is this: the fact that you use the name ‘Socrates’ in ‘Socrates died’ does not commit you to the truth of the proposition ‘Socrates (here) died’ — where ‘Socrates (here)’ is intended to indicate that ‘Socrates’ refers deictically and hence purports to refer to an existing Socrates. And since

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you are not committed to this (false) [210] proposition, you do not ‘determine in addition’ (and falsely) that Socrates exists. [3] Or rather, [a] if the predicate should fail to hold of some of the subjects, in this way; [b] if it is clear that it does not exist, in that way.17 The first problems here concern ‘ ... in this way’ and ‘ ... in that way’. How are the elliptical apodoses to be understood? No verbal phrase in the immediate vicinity provides a suitable filling. I guess we are to understand a neutral ‘ºŒ
’. Next, to what do ‘this way’ and ‘that way’ refer? It is natural to imagine that one of them refers to the account of existential indication which Alexander has just endorsed, the other to the opponents’ view which he has earlier rejected. In that case [3] modifies [2]: things are sometimes as [2] says they are, sometimes as the opponents assert. But it is hard to believe that that was Alexander’s meaning. For his next sentence (‘a name ... does not itself mean ... ’) immediately expresses the conviction that names do not determine existential indication, a conviction which he takes his opponents to deny. If sentence [3] contains a concession to the opponents, then it is paradoxically followed by an unqualified rejection of their view. We must find some other reference for ‘this way’ and ‘that way’. As far as I can see, we must find it inside sentence [2] itself. Sentence [2] has the form ‘It is not the case that so-and-so’. Sentence [3], I suggest, qualifies that remark: sometimes it is not the case that so-and-so, sometimes it is the case that soand-so. According to [b], ‘if it is clear that it does not exist, in that way’: by ‘it does not exist’ Alexander can only mean ‘the subject of the proposition in question does not now exist’. Given the following sentence, about the determinative function of the predicate, we may suppose it to be ‘clear’ that the subject does not exist just in case the predicate indicates as much. Cases of this sort are not far to seek; for it is plain that the predicate ‘died’ in ‘Socrates died’ indicates that Socrates does not exist. But these are just the propositions with which Alexander’s account in sentence [2] was supposed to deal. Hence by ‘that way’ in [3b] Alexander must be referring to the content of sentence [2]. The general [211] structure of [2] and [3] is now a little plainer. Alexander means this: ‘When you utter ‘Fa’ you do not commit 17 ‘Bº
’ — ‘it is clear’ — is Wallies’ emendation for ‘E’ (which a second hand corrected to ‘’ in the manuscript B). I suppose that this gives the intended sense; but I wonder if ‘ź E’ (sc ‘e ŒÆŪ æ 

’) is not better (cf 404.7).

Peripatetic negations

183

yourself to any existential propositions about a, over and above those determined by ‘F’. Or rather, [a] in some cases you do, but [b] in the cases which interest me here you do not’. What, next, are the cases in which you do commit yourself to additional determinations? We might expect Alexander’s division, signalled by ‘
’ and ‘’, to be exhaustive, so that the cases in question would be all those in which it is not made clear that the subject does not exist. But that cannot be right: first, Alexander’s descriptions of the two sets of cases are evidently not conjunctively exhaustive; secondly, Alexander implies in 404.8–10 that ‘Socrates philosophized’ determines nothing but the past existence of Socrates, even though ‘philosophized’ does not make it clear that Socrates does not exist. We must conclude that the two sets of cases were not meant to be exhaustive. However that may be, the case we are now concerned with occurs, according to the manuscript text, ‘if the predicate should fail to hold of some of the subjects’. That might mean: ‘if the proposition in question is false’. But what a proposition implies does not depend on whether it is true or false, and I cannot believe that, in Alexander’s view, ‘Socrates was a bachelor’ (which is false) implies that Socrates exists or will exist (or does not exist or will not exist). We might secondly think to construe Alexander’s words as meaning: ‘if the proposition is negative’. But again it is hard to believe that, in Alexander’s view, ‘Socrates was not married’ implies anything at all about the present or future existence (or non-existence) of Socrates; and in any case, Alexander certainly thinks that some negative propositions fall under his second heading. Perhaps, then, the text of [a], like the text of [b], is corrupt. I suggest that we excise the ‘’.19 Then we are left with: ‘if the predicate should hold of some of the subjects’, which we might paraphrase as: ‘if the predicate is one which applies to presently existing subjects’. And it is possible to make some sense of the paraphrase, namely: ‘if in a proposition of the form ‘‘Fa’’ the predicate indicates that a now exists, then it does, after all, determine certain further existential committments’.20 [212]

19 Perhaps change ‘’ to ‘
F
’ rather than excise it? 20 That is desperately contrived. But it enables us to see why Alexander wrote ‘Ø
Ø H
 ί
ø
’ (rather than ‘fiH  ŒØ
fiø’) and ‘æå Ø’ (rather than ‘æåØ’): he does not want to say ‘if the predicate does hold of its subject’, but rather ‘if the predicate is of the sort which holds of some subject’, i.e. ‘if the use of the predicate indicates a presently existing subject’.

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Could Alexander have held such a view? I think he could, though on metaphysical rather than strictly logical grounds. Suppose, plausibly, that there are no instantaneous subjects — that nothing exists just at a moment. Or, more weakly, that it is not possible to refer to anything unless it has some temporal duration, however brief. In that case, a reference to something which now exists will indicate in addition past or future existence, since nothing — or, more weakly, nothing which can be referred to — can exist just at the present instant. The present tense thus carries in addition an indication of the past or future. The reason for this is the metaphysical singularity of the present — similar considerations do not apply to other tenses.21

XI A very loose paraphrase of 403.36–404.10 might run as follows: When we say ‘Fa’ we do not, in uttering ‘a’, imply anything about the existence or non-existence of a, over and above whatever existential indications ‘F’ may carry. (Or rather, we do so only in cases where ‘F’ indicates the present existence of a.) For it is not the name ‘a’, but the attached predicate, ‘F’, which carries the existential indications of ‘Fa’. The paraphrase does not sit close to the text, and my interpretation of the passage is untidy and far from compelling. But it has the small advantage of extracting a moderately coherent view from the text. The view can be expressed in the following way. (1) Singular propositions of the form ‘Fa’ do not, as such, carry any general information about the existence or non-existence, past, present, or future, of their subjects. The fact that such propositions contain singular terms does not in itself determine the answers to any questions about existential import. (2) Such answers are determined, however, by the predicate: different predicates will determine the answers in different ways, but in general existential import is a function of the semantic content of the predicate and not of the referential force of the subject. (3) Given that a predicate determines a [213] particular existential answer, nothing further can be inferred, in general, about the

21 All that is at any rate consistent with, and perhaps even supported by, the essay edited by R.W. Sharples, ‘Alexander of Aphrodisias, On Time’, Phronesis 27 1982, 58–81.

Peripatetic negations

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existence of the subject. For example, if ‘F’ in ‘Fa’ determines that a will exist, nothing follows about the past or present existence or non-existence of a. (4) But in some cases, namely those in which ‘F’ determines the present existence of a, further existential information is implied.

XII The discussion of existential import falls within the dispute over negation. In the last sentence of [iv] Alexander returns briefly to the main topic: Hence, since each of these is true, their contradictories — ‘ ... did not die’ or ‘ ... did not live’ or ‘ ... did not philosophize’ — are false.

Alexander’s ‘hence’ is hardly justified in the present context, and the examples he cites are not quite as straightforward as he here pretends. But let us allow that he is right in what he says: in that case, the Peripatetic analysis of existential import can deal with the cases where the opponents’ analysis allegedly fails. But what of the cases in which the opponents allege that the Peripatetic account of negation breaks down? Can Alexander’s analysis save the day there? Suppose that Callias does not (any longer) exist; and consider the propositions that Callias walks and that Callias does not walk, Fa and [not-F]a. Can Alexander show that it is not the case, as his opponents argue, that both of these are false? It is clear that, in Alexander’s view, a proposition whose existential indications are false is itself false. If ‘Fa’ carries the indication that a exists, then if a does not exist, ‘Fa’ is false. It is clear, too, that in Alexander’s view ‘Callias walks’ indicates that Callias exists; so that under the present hypothesis ‘Callias walks’ is false. (And that, in any event, is the familiar Aristotelian view.) Now it is easy to suppose that the predicate ‘ ... does not walk’ also indicates the present existence of its subject. The verb is in the present tense, and nothing about the predicate appears to point to any other time period. But if that is right, Alexander is scuppered. For ‘Callias does not walk’ will turn out, after all, to be false: it indicates the present existence of Callias, and Callias, ex hypothesi, does not now exist. Alexander has only one possible answer to the objection. He must deny that [214] ‘ ... does not walk’ indicates the present existence of its subject. He

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does not explicitly give that answer, but we must surely credit him with it. Moreover, it is an intelligible answer: when the predicate is negated, the negation operator (sometimes at least) also has the effect of cancelling or negating the existential implications of the positive predicate. Thus when the predicates in ‘[VF]a’ and ‘[ZF]a’ imply that a existed or that a will exist, the predicates in ‘[V[not-F]]a’ and ‘[Z[not-F]]a’ need not carry those implications. Then what existential indications does the predicate ‘ ... does not walk’ carry? Perhaps merely the sometime existence (past, present, or future) of its subject. Since Callias did once exist, the existential indication in ‘Callias does not walk’ is successful; for it is true that Callias sometime exists. Both ‘Callias walks’ and ‘Callias does not walk’ refer to Callias: the former says falsely of him that he now walks; the latter says truly of him that he does not now walk. In addition, the former carries a false existential indication — that Callias now exists. The latter carries the indication that Callias sometime exists, and that indication is true.

XIII The interpretation which I have tentatively advanced in the last few pages goes beyond Alexander’s text in several particulars. In addition, it is fundamentally — indeed necessarily — incomplete; for it envisages an essentially piecemeal approach to the problems raised in the dispute over negation. If I am right, Alexander does not and perhaps cannot offer any universal rules for determining existential indications. On behalf of the interpretation, I offer only a Pyrrhonian avowal: it seems to me at the moment to be the least bad way of eliciting an intelligible set of ideas from an unusually difficult text. As to the piecemeal nature of the analysis which the interpretation ascribes to Alexander, it seems to me that here, as elsewhere in the philosophy of language, a Heath-Robinson contraption, though less chic than a Harley-Davidson, is more likely to putter along to the truth.22 22 This chapter was written while I was a Fellow of the Wissenschaftskolleg zu Berlin: it gained much from discussion with my Berlin colleagues, Jacques Brunschwig, Michael Frede, and Gu¨nther Patzig. Jim Hankinson was kind enough to scrutinize a later draft, and to save me from further errors.

6 Aristotle’s Categories and Aristotle’s ‘categories’* Aristotle The theory of categories is one of Aristotle’s better known doctrines; and the pamphlet which we call ‘Categories’ is one of his better known works. But what is it all about? What is a category? Come to that, what does the word ‘category’ mean? The Oxford English Dictionary divides its entry on ‘category’ into two parts, and subdivides the second part. So it distinguishes three senses, or three uses, of the word, thus: (1) ‘a term (meaning literally ‘predication’ or ‘assertion’) given to certain classes of terms, things, or notions’; (2a) ‘a predicament; a class to which a certain predication or assertion applies’; (2b) ‘a class, or division, in any general scheme of classification’. It is a rum entry — not only is the allegedly literal meaning of ‘category’ — namely ‘predication’ or ‘assertion’ — not a meaning of that English word at all, but in addition it is hard to see any essential difference in sense among the three allegedly different definitions. Still, the normal sense of the English word is not obscure: ‘category’ means the same, or much the same, as ‘class’, ‘kind’, group’, ... Aristotle’s theory or doctrine of categories certainly deals with ‘certain classes of terms, things, or notions’; and the Categories presents — among other things — a classification of some sort or another. So aren’t Aristotle’s categories groups or kinds or classes of things? The OED presumably thinks so; for it lists Aristotle’s ‘ten categories’ in illustration of its sense (1). But the OED is at best half right; for when Aristotelians speak of ‘Aristotle’s categories’, they do not mean ‘Aristotle’s classes’. * This chapter is a version of ‘Les cate´gories et les Cate´gories’, in O. Bruun and L. Corti (eds), Les Cate´gories et leur histoire (Paris, 2005), pp.11–80. The last section, ‘Twenty centuries on’, has been remodelled, and the last few pages have been amputated. The Appendix is an expanded version of something which first appeared in CR 53, 2003, 59–62, as a review of R. Bode´u¨s (ed), Aristote: [Cate´gories] (Paris, 2001).

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In French, the word ‘cate´gorie’ has two senses — at any rate, it has two senses according to M. Robert. The first sense is that of ‘class’ — the same as the unique sense of the English word ‘category’. The second, according to Robert, is this: ‘Quality which can be ascribed to an object — cf ‘pre´dicat’. This sense is described as ‘philosophical’, and it is illustrated by a list of the ten cate´gories of Aristotle. Moreover, it is said to derive from the first sense ‘by analogy’. So perhaps Aristotle’s categories are actually qualities, and so somehow derivatively categories? Well, ‘quality’ is no doubt better than ‘class’ (though it is hard to see by what species of analogy the sense ‘quality’ might be derived from the sense ‘class’); but it is not much better — as Robert himself should have seen. For according to Robert (and also according to the OED), one of Aristotle’s ten categories is precisely quality. [12] If ‘cate´gorie’ means ‘quality’ when it is used of Aristotle’s theory, then quality is one of ten qualities. The dictionaries are mildly perplexing. A little etymology may clear the cobwebs. The words ‘category’ and ‘cate´gorie’ derive from the Latin ‘categoria’, which in turn derives from the Greek ‘ŒÆŪ æÆ’. In truth, the word ‘derive’ is scarcely apposite: the word ‘categoria’, which is found only in late Latin, is simply the Greek word written in Roman letters; and as for ‘category’ and ‘cate´gorie’, they are the Latin word with an English or a French pronunciation. In any case, what counts is the meaning of the Greek ‘ŒÆŪ æÆ’. In ordinary Greek, both before and after Aristotle, the noun ‘ŒÆŪ æÆ’ means ‘accusation’ — it twins with ‘I º ªÆ’, which means ‘defence’. The noun comes from the verb ‘ŒÆŪ æE
’, which means ‘accuse’. You accuse someone of something: in Greek ‘ŒÆŪ æE
’ þ genitive þ accusative. For example, Demosthenes complains that ‘Aeschines accuses me of philippism [K F çغØØ
ŒÆŪ æE]’ (xviii 294). Aristotle found the verb, pulled it from its natural environment, and planted it in his philosophical hothouse. In doing so, he extended both the sense and the range of application of the verb: what was a hostile accusation became a neutral imputation or attribution; and the object of the imputation need not be a person but might be anything whatever. ‘Accuse someone of something’ became ‘attribute something to something’; ‘accuse X of Y’ became ‘say Y of X’. That little history is told by the ancient commentators on the Categories (see e.g. Porphyry, in Cat 55.3–56.13). Aristotle’s use of the verb, and of the associated noun, was technical — that was why the commentators explained what it meant. And although the words were used by other philosophical

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schools, and were also adapted to other scientific contexts, they remained firmly tied to Aristotelian philosophy. Latin authors who wanted to translate ‘ŒÆŪ æE
’, in its philosophical use, paid no attention to the origins of the Greek word: they used ‘declarare ’ or ‘praedicare ’, neutral verbs which mean ‘declare’ or ‘call’. It was ‘praedicare ’, together with ‘praedicatio ’, ‘praedicativus ’, and the other members of its family, which prevailed — in English ‘praedicare ’ became ‘to predicate’ (and in French it became ‘pre´diquer’). So: ŒÆŪ æÐ Ø
Y of X, praedicare Y of X, predicate Y of X — say Y of X. If the verb ‘ŒÆŪ æE
’ is translated by ‘predicate’, then the noun ‘ŒÆŪ æÆ’ must become ‘predicate’ or ‘predication’ or something similar. (And Robert is right when he gives ‘pre´dicat’ as a synonym of ‘cate´gorie’ in the philosophical sense of the word.) In Greek, Aristotle’s opuscule was generally titled ‘˚ÆŪ æÆØ’.* The Latin authors translated that as ‘Praedicamenta ’. The English title ought therefore to be something like ‘Predications ’. But scholars will not change their spots, [13] and I shall continue to use ‘Categories ’ as the title of the work. It may serve as an English title, though not as an English translation of a Greek title. However that may be, if a ‘category’ is a predicate, or a predication, then a theory or doctrine of categories ought to be a theory or doctrine of predication or of predicates. Now one of the theories which underlies Aristotle’s Topics and which was later elaborated in Porphyry’s Isagoge is indeed a theory of ‘categories’. The theory, which is sometimes referred to as the doctrine of the predicables, is based on a classification according to which, if Y is predicated of X — or rather, if Y is true of X —, then Y is either a definition of X or a genus of X or a property of X or an accident of X. But when Aristotelians speak of Aristotle’s theory or doctrine of categories, it is not the theory of predicables which they have in mind: it is a different theory — but a theory which also involves a classification. What classification? Here is a passage from the Topics. Aristotle has just expounded his doctrine of predicables, to which the phrase ‘the four predications we have described’ refers: Now we must determine the kinds of predication in which are found the four predications we have described. They are ten in number: what is it?, of a certain quantity, of a certain quality, relative to something, somewhere, at some time, to be positioned, to have, to do, to undergo. For accidents, genera, properties and * See below, pp.[14–15].

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definitions will always be in one or another of those predications. For all propositions made by way of the four signify either what it is or of a certain quantity or of a certain quality or one of the other predications. From this it is clear that someone who signifies what something is sometimes signifies a substance, sometimes something of a certain quantity, sometimes something of a certain quality, and sometimes one of the other predications. For example, if the item in question is a man, and he says that the item in question is a man, or an animal, then he says what it is and he signifies a substance; and if the item in question is the colour white and he says that the item in question is white, or a colour, then he says what it is and he signifies something of a certain quality. (Top ` 103b20–33)1

[14] Read the text rapidly, and you will discover a theory of ten sorts of predications, or ten categories, which might be set out like this. Every time you take some subject, X, and predicate something, Y, of it, the predication does one of ten things: (1) it gives an answer to the question ‘What is X?’; (2) it says that X is of a certain quantity; (3) it says that X is of a certain quality; ... ; (10) it says that X undergoes something or other. If, speaking of Lorenzo, I say that he is a llama, I give an answer to the question ‘What is he?’; if I say that he is white, I indicate that he is of a certain colour and hence of a certain quality; if I say that he is in his house, then I say that he is somewhere. (Suppose I say that he is a white llama? Then I say both what he is and of what quality he is — I give not one predication but two. The ancient commentators on the Categories consequently explain that Aristotle’s doctrine of ten predicates or categories concerns only ‘simple’ predications, predications which predicate just one thing of a subject.) Every predication — every simple predication — belongs to one of the ten classes, and apparently to one only. The ten classes are highest genera, or genera which are not themselves species. For example, there is no higher class or genus of which somewhere and somewhen are two species. That theory — that rough and partial outline of a theory — is based upon the passage from the Topics, which offers the merest sketch. The theory is sometimes used — or at any rate, mentioned — in other parts of the corpus 1 a  
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Aristotle’s Categories

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aristotelicum — for example, in the Posterior Analytics, in the Physics, in the Nicomachean Ethics, and especially in the Metaphysics. But if you are looking for a detailed account of Aristotle’s theory or doctrine of categories, then you will turn first to the essay which bears the title ‘Categories ’. In Greek, ‘˚ÆŪ æÆØ’ was the normal title of the essay from the end of the second century ad if not from much earlier. The ancient commentators discussed the question of the correct title (see e.g. Porphyry, in Cat 56.14– 57.12). They plainly had no direct evidence for what was the authentic or original title; and since Aristotle himself never refers to the work, we do not know his own name for it — if indeed he ever gave it a name. The question of the title has a certain interest.* But it is no doubt less interesting than the question of the authenticity of the essay [15] itself. The ancient commentators all discussed that question too; but the rules of the commentatorial game obliged them to discuss the authenticity of the work they were commenting upon, and their discussions of the authenticity of the Categories are perfunctory formalities: Simplicius deals with the matter in ten lines (in Cat 18.7–17); Ammonius says that ‘everyone is agreed that the book is a genuine work of Aristotle’s’ (in Cat 13.25).2 True, the discussion in Olympiodorus appears to contradict his master. Olympiodorus begins thus: Is the book a genuine work of the old man or not? Some people mark it as spurious, for four reasons ... (in Cat 22.38–40)3

But we are not obliged to suppose that when Olympiodorus says ‘some people’ he has any real critics in his sights. During a certain period, modern scholarship declared itself at odds with ancient scholarship on the matter; and various reasons were discovered for thinking that the Categories did not come from Aristotle’s pen: first, the book neither mentions nor is mentioned in any other Aristotelian work; secondly, the style of the work is ‘scholastic’, and in this way the Categories is closer to * See Appendix. 2 ‹Ø b ª
Ø
 F çغ  ç ı e ªªæÆÆ 
 › º ª FØ. After all, he explains, in all his books he is seen to mention the theorems which are set out here, so that if the Categories is spurious, so are all the other works, and if they are genuine, so is the Categories. [çÆ
ÆØ ªaæ K
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Øa ÆæÆ ÆNÆ ...

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such unAristotelian essays as the de mundo than it is to the genuine works of the corpus; and finally, there are differences of doctrine — striking differences of doctrine — between the Categories and the Metaphysics. Nevertheless, current orthodoxy ascribes the essay to Aristotle. The latest editor of the Greek text of the Categories gives the question a lengthy discussion; and in the end votes — with some qualification — in favour of authenticity.4 In any event, it is certain that the Categories was written, at the latest, before the middle of the first century BC; and for most of its career the book has been accepted as authentic Aristotle. In fact the question of authenticity is rather more complicated that at first it seems. The complications arise from the work’s structure. The Categories take up no more than fifteen pages in Immanuel Bekker’s edition of the corpus aristotelicum. True, they are large pages [16] in double column. Still, the text would take up fewer than forty ordinary pages. The essay begins abruptly, without preface or explanation: Aristotle introduces and defines the notions of homonymy, synonymy, and paronymy; he distinguishes between things said ‘according to a connection’ and things said ‘without connection’; and he distinguishes between being said of a subject and being in a subject. That last distinction is then used to sort all beings into four groups: things neither said of any subject nor in any subject (that is to say — in the jargon of the commentators — individual substances), things said of a subject but not in any subject (universal substances), things in a subject but not said of any subject (individual accidents), things both in a subject and said of a subject (universal accidents). The fourfold classification, despite its obscurities, was to prove one of the most influential parts of the Categories. After the classification there are two short sections, one on the relation between subjects and their predicates and the other on genera and their differences. And so ends the first part of the work — the part which is sometimes called the Antepraedicamenta. It is only two pages long, and the pages seem to say nothing at all about categories or predications — indeed, they seem to be a set of miscellaneous notes. To be sure, every commentator has attempted to find some theme to unify these opening paragraphs, and also some bridge to link them to the rest of the Categories; but no commentator has convinced his colleagues. If the first part has a structure, it is remarkably well hidden. As for

4 See Bode´u¨s, [Cate´gories], pp.XC–CX.

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the bridge to the rest of the work, it may justly be said that, had the first two pages of the work been lost, no one would ever have missed them. The second and central part of the Categories fills ten Bekker pages, from 1b25 to 11b14. It begins like this: Of things said according to no connection, each signifies either a substance or something of a certain quantity or of a certain quality or relative to something or somewhere or at some time or to be positioned or to have or to do or to undergo. (1b25–27)1

There are ten things — no doubt the ten categories. Aristotle then gives illustrative examples. He states that the ten things — like anything else [17] ‘without connection’ — are never true or false, but that they combine with one another to make connected items which are true or false. Then, at 2a11, he sets off on a detailed discussion of the first of the ten things: substance. After substance, at 4b20, Aristotle turns to quantity; then, at 6a36 and against the order of the introductory list, to relative items; then to quality, at 8b25. The discussion of each of those four items is thorough; and if the style is indeed on occasion rather scholastic, the material is presented in a manner more aporetic than didactic. The account of quality stops at 11a38. We expect the fifth item, ‘somewhere’ — and then the remaining five. The expectation is frustrated. It is true that the manuscripts continue, at 11b1–7, with a few sentences about doing and undergoing; but — despite the subtitle which some of the manuscripts insert — it is plain that the sentences do not amount to a discussion of the ninth and tenth of the ten items. It has been plausibly suggested that the lines are out of place, and that they should be printed between 11a14 and 11a15 as part of the account of quality. Next, at 11b8 (or immediately after 11a38, once 11b1–7 has been shunted back to its proper place), comes the following passage: As for those matters, that is what is said. As for being positioned, it has been said in the account of relatives that being positioned is said paronymously on the basis of position. As for the other items — somewhere, at some time, to have —, since they are clear nothing more is said about them than what was said at the beginning, namely that being shod and being armed signify having, that in the Lyceum (for example) signifies somewhere — and whatever else was said about them. So as for the 1 H
ŒÆa ÅÆ
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genera before us, what has been said is enough. Next we must discuss opposites, and how many sorts of opposites there are. (11b8–17)1

And then begins the third part of the Categories, or the Postpraedicamenta: a detailed discussion of the four sorts of opposites; a short essay — offered without explanation or introduction — on priority and simultaneity; and to end with, a paragraph on moving and a paragraph on having. There is no evident connection between the Postpraedicamenta and the central part of the Categories; and there is no unity to the Postpraedicamenta themselves. [18] If the Antepraedicamenta are odd, the Postpraedicamenta are bizarre. The ancient commentators noted as much. Simplicius, for example, introduces his discussion of the Postpraedicamenta as follows: First, we must ask why on earth this passage is added at the end of the Categories and what is its function. For some scholars, among them Andronicus, say that it was added on at the end, against the plan of the book, by someone who had titled the Categories ‘Before the Topoi’. (in Cat 379.7–10)1

A little later, Simplicius remarks that it is plain that Aristotle took his remarks about opposites from Archytas’ book On Opposites — which Archytas did not attach to his account of the genera but regarded as a separate treatise. (382.7–10; cf 407.15–20)2

Aristotle, of course, took nothing from Archytas — or rather, from pseudoArchytas (to whom I shall return). But Simplicius’ remark shows that when pseudo-Archytas came to write his pastiche of the Categories, he had the wit to turn the Postpraedicamenta into a separate essay. Of course, as for the Antepraedicamenta, so for the Postpraedicamenta — and with the same degree of success — scholars have sought out theoretical explanations or justifications for the attachment to the central part of the Categories. 1 bæ b
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Aristotle’s Categories

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The bridge passage between the Categories and the Postpraedicamenta is in a poor state, textually speaking; and the editors have recognized that it cannot have been written exactly as it stands by Aristotle himself. But it is not just a matter of ordinary textual corruption, or of the sort of thing which happens to every ancient text. Rather, both content and style prove that at any rate the major part of the passage was written not by the author of the Categories but by an ancient editor, or reader, who noticed that there was a gap between the end of the discussion of quality and the beginning of the discussion of opposites. But if 11b8–17 were added in order to fill a gap, why was there a gap to be filled? Was the gap left by the author, who never completed his work and left an evidently lacunose autograph? Was it rather the result of some accident in the textual history of the Categories, a scribe failing to copy a few columns [19] of the text in front of him and his failure infecting the whole of the later tradition? In the former case, we shall ask ourselves what the author would have written: in the second, what he actually wrote. It is hard to believe that Aristotle did not write, or would not have written, something about each of the last six items on his introductory list. (It is hard so to believe — but some scholars have believed it.) In how many pages? The last six items are sometimes called ‘the little categories’ — or rather, in French they are sometimes called ‘les petites cate´gories’ — as though they had little importance in Aristotle’s scheme of things; and in that case he wouldn’t have spent much papyrus on them. But as a matter of fact the ‘categories’ of somewhere and at some time, and also of doing and undergoing, are items of capital importance to Aristotle’s philosophy; and it would be easy to imagine their being discussed at considerable length. After the missing discussion of the last six of the ten items, what came next? Did Aristotle actually write, or would he have attempted to write, a passage to attach the Postpraedicamenta to the account of the ten items? Or — if the gap is the result of an accidental loss of a few columns of text — , did he write: ‘Here ends the Categories. Now for the Postpraedicamenta ’?1 However that may be, it is the central part of the Categories which concerns me here, since it is in the central part that Aristotle sets out his doctrine of the categories. 1 On the unity of the Categories, see M. Frede, ‘Titel, Einheit und Echtheit der aristotelischen Kategorienschrift’, in P. Moraux and J. Wiesner (eds), Zweifelhaftes im Corpus Aristotelicum, Peripatoi 14 (Berlin, 1983), pp.1–20 [¼ Essays in Ancient Philosophy (Oxford, 1987), pp.11–28].

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At least, that is how a long tradition has understood things. But in truth it is not evident, at first blush, that the long tradition is right. In the Categories Aristotle never says that he is going to examine and classify predicates or predications. Indeed he only uses the word ‘ŒÆŪ æÆ’ twice — and that in relatively unimportant contexts. What he announces is something rather different: a discussion of ‘things said according to no connexion’ — that is to say, a discussion of simple expressions. A classification of predicates, or of predications, will explain that when you say that X is Y, then you predicate Y of X in a certain mode or manner or style. A classification of simple expressions will explain that the term T belongs to, or perhaps rather signifies something which belongs to, a certain class or sort or group of items. A classification of predicates or predications will explain, for example, that, when I say Socrates is pink, [20] I say that Socrates is qualified in a certain way, I predicate a quality or a qualification of him. A classification of simple expressions will explain that the term ‘pink’ — in that sentence and in most others — is a qualitative expression or signifies something which is a quality or a qualification. The two classifications are quite different from one another; and it is the second which appears to be what Aristotle is concerned with in the Categories. That classification says nothing at all about predicates or predication. And so the Categories has no interest in the classification of predicates, or in the categorization of ‘categories’. Can such a paradoxical conclusion be correct? And if it is, then how did such a long and learned tradition come to think that the Categories was about predication? There are at least two reasons which might explain how predication came to be read into the Categories. The first reason is textual. For the Categories gives us a list of ten items, and the Topics offers us a list of ten predications. The two lists are identical, the only difference being that where the Categories has as its first item ‘substance [ PÆ]’, the first of the ten items in Topics is ‘what is it? [ KØ;]’. And even that difference may appear trivial, or nonexistent; for when the list appears elsewhere in the Topics, the expression ‘what is it?’ is replaced by the word ‘substance’ (see ˜ 120b36–121a9). It would be perverse to hold that the two lists are, so to speak, accidentally identical. So the items listed in the Categories must be types of predicate, or types of predication, even if Aristotle does not say that they are. The second reason to account for the presence of predication in the Categories is theoretical in character. A classification of predicates of the sort

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found in the Topics is in fact equivalent to a classification of simple expressions of the sort found in the Categories. For if when I say Socrates is pink, I make a predication in the style of quality, then the term ‘pink’ must signify a certain sort of quality or qualification. And conversely, if the expression ‘in the Lyceum’ signifies a certain way of being somewhere, then when I say Aristotle’s in the Lyceum I make a predication in the style of ‘somewhere’. To be sure, it is one thing to classify predications and another to classify simple expressions. But the two things, though different, are equivalent. There are the two reasons. They are not good. First, the difference between ‘what is it?’ and ‘substance’ is anything but trifling — as the Topics itself shows. For there Aristotle asserts that [21] someone who signifies what something is sometimes signifies a substance, sometimes something of a certain quantity, sometimes something of a certain quality, and sometimes one of the other predications. (Top ` 103b27–29)

That is to say, if in saying X is Y I make a predication in the style of ‘what is it?’, it does not follow that ‘Y’ signifies a substance. In that passage it is clear that ‘what is it?’ and ‘substance’ are not two different names for the same thing. There are undeniably relations of great intimacy between the classification of ten sorts of predication in the Topics and the classification of ten sorts of simple expression in the Categories. But there are two classifications, not one, and the two are not equivalent. What’s to be done? Any serious examination of what Aristotle himself thought about the classification of types of predication or of categories — any serious examination of Aristotle’s doctrine of categories — must take its start from the Topics and go on to consider various other passages in the corpus where Aristotle invokes, or seems to invoke, a classification of predicates. But as far as the fortune, or the later history, of the doctrine of categories is concerned, any serious examination must begin with a piece of fudge. The Peripatetic tradition, when it came to concern itself with the theory of predication, did not worry about the distinction between ‘what is it?’ and ‘substance’. In the list of ten predications, ‘substance’ simply replaced ‘what is it?’. The list of ten types of predication could then be observed, slightly

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disguised, in the list of ten simple expressions which the Categories discusses. For just as Socrates is pale predicates something qualitatively of Socrates if and only if ‘pink’ is a qualitative expression, so Lorenzo is a llama predicates something substantially of Lorenzo if and only if ‘llama’ is a substance expression. In general, then, X is Y is a predication of style S if and only if ‘Y’ is a predicate of the sort S*. So we can forget about predications, or styles of predication, and speak instead about predicates, or sorts of predicate. And the ten items in the Categories turn into ten kinds of predicate.2

The Hellenistic Period The history of Aristotle’s theory of categories is the history of a doctrine and the history of a text — or rather, [22] of a small corpus of texts. For the text which Aristotle himself wrote — the Categories — was abridged and paraphrased and attacked and defended and commented upon and translated, so that its fifteen pages are accompanied by a vast library of secondary literature. The Categories had an extraordinary success, in late antiquity and after, and the doctrine of the categories had an immense influence on the history of philosophy — ancient, medieval, and modern. But if the theory was familiar in all parts of the republic of letters, knowledge of the Aristotelian doctrine did not always carry with it an acquaintance with Aristotle’s text. Sometimes it is plain that an author who ‘cites’ the Categories has read no more than an epitome or a doxographer’s report. Often enough, Aristotle’s theory is exploited on the basis of a paraphrase or a commentary. And in any event — what ought to depress but not to astonish — an understanding of the doctrine was always filtered through the secondary literature, and the doctrine took some flavour from the particular filter it passed through.

2 The secondary literature on Aristotle’s account of predication and predicates is vast. What I have said in the last few paragraphs is largely inspired by M. Frede, ‘Categories in Aristotle’, in D.J. O’Meara (ed), Studies in Aristotle, Studies in Philosophy and the History of Philosophy 9 (Washington DC, 1981), pp.1–24 [¼ Essays, pp.29–48].

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With hindsight, the triumph of the doctrine may seem inevitable — after all, a glorious future presupposes a distinguished past, and if the past is distinguished, then the future is likely to be rosy. But in reality things were otherwise. The birth of the doctrine (as I have just recalled) was difficult. Its adolescence was neither robust nor promising. Aristotle’s successors often worked on the same subjects and wrote under the same titles as he had done: they attempted to fill the gaps which he had left (and sometimes indicated), they tried to state more clearly what he had set out obscurely or approximatively, and they sometimes sought to mend his errors. Thus Philoponus assures us that the pupils of Aristotle — Eudemus, Phanias, Theophrastus — each wrote in imitation of their master a Categories and a de Interpretatione and an Analytics. (in Cat 7.20–22)1

There was the start of the post-Aristotelian career of the Categories. The evidence on these matters is thin, and its reliability is questionable.* The thickest text comes from Olympiodorus: It was not only Aristotle who wrote a Categories: so too did his pupils, Theophrastus and Eudemus. So it often happened that someone reading the Categories of (say) Theophrastus thought that they were Aristotle’s ... Often, too, someone wrote a commentary on a work [23] which carried a shared title, and it was believed to be a commentary on the other work — for example, Theophrastus wrote a commentary on his own Categories which people often wrongly think to be a commentary on Aristotle’s. Again, people have often read Alexander’s commentary on the Categories with the conviction that it was certainly concerned with Aristotle’s work and unaware that Alexander had written not only on Aristotle’s Categories but also on the work of Theophrastus. (in Cat 13.24–35)1

If we are to believe Olympiodorus, Theophrastus had not only written a Categories — he had also written a commentary on his own work. Not only

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ƺıØŒ. * The pertinent texts are in W.W. Fortenbaugh, P.M. Huby, R.W. Sharples, and D. Gutas (eds), Theophrastus of Eresus: sources for his life, writings, thought and influence, Philosophia Antiqua 54 (Leiden, 1992), pp.124–131; there is a commentary in P.M. Huby, Theophrastus of Eresus: commentary 2 – Logic, Philosophia Antiqua 103 (Leiden, 2007), pp.14–24. 1 ... c 
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that — the work was exciting enough to persuade Alexander of Aphrodisias to write a commentary on it. Should we believe Olympiodorus? He wrote more than eight centuries after Theophrastus, and you need only leaf through one or two of the commentaries which survive from that period to realize that they were written in a fog of ignorance: some of the historical information which they put on show is a product of the imagination, and most of the information which derived from a pure source or was originally based on a reasonable conjecture has been contaminated or deformed in the course of its derivation. In short, Olympiodorus and his mates are not to be relied upon. What is more, the list of Theophrastus’ works which Diogenes Laertius has preserved does not mention a Categories (let alone a commentary upon it); and to the best of my knowledge no ancient author ever cites or paraphrases such a work. I have heard it replied that the evidence which we have, late and suspect though it is, is nevertheless circumstantial; and that if a Byzantine scholar might perhaps have dreamed up a Categories for Eudemus and Theophrastus, he would scarcely have done so for the obscure Phanias — nor would he have invented a self-commentary by the hand of Theophrastus or thought to attribute a fictional commentary to Alexander. Well, I confess to a boundless admiration for the imaginative fecundity of such men as Philoponus and Olympiodorus — and for their uncanny capacity to grasp any stick by its wrong end. Perhaps there are grains of truth in the reports I have cited; but we cannot separate them from the chaff of invention. Perhaps there was a fashion for writing Categories just [24] after Aristotle’s death; but I am not bold enough to believe it. Of course, if Theophrastus never wrote and commented upon his own Categories, he surely read Aristotle’s work; and — despite both the paucity of evidence and the romantic stories about the decline of the Peripatetic school during the Hellenistic period — it is reasonable to believe that every student in the Lyceum will have learned something about the categories. But did anyone else? Was the theory of categories known outside the walls of the Lyceum? In answer to that question, four groups of witnesses have been ¼ººÅ r
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summoned: novelists, librarians, orators, and philosophers. I start with the philosophers. By chance, and thanks to a papyrus fragment, we know that Epicurus had seen Aristotle’s Analytics and also his Physics. Chance has provided no reference to the Categories on the part of Epicurus — nor on the part of any Stoic or any Academic. But if there are no explicit references to the Categories, perhaps there are subtler indications that Aristotle’s theory of categories had some influence on the course of Hellenistic philosophy? If there are such indications, then there is one place in which they might especially be looked for: in the texts which report the Stoic theory of categories. For did not the Stoics elaborate a theory of four categories? Must not their theory have been modelled upon Aristotle’s theory? Must it not have been presented as a rival? That is what Simplicius, for one, seems to suggest: The Stoics think that the number of primary genera should be reduced, and they change some of those in their reduced number. They make a four-fold division into subjects, things qualified, things disposed, and things disposed in relation to something. It is plain that they have left a lot out — not only things quantified but also things in time and in place. For if they think that these latter items are included among things disposed — on the grounds that what is last year or in the Lyceum or sitting or shod is disposed in a certain way in virtue of those very facts —, then we shall reply, first, that there are very great differences among these cases so that it lacks specificity to say that being disposed in a certain way is common to them all; secondly, that this common feature of being disposed in a certain way holds also of subjects and especially of things qualified (for such things too are disposed in a certain fashion). (in Cat 66.32–67.8)1

[25] If the passage is read as a piece of history, then it tells us that the Stoics reflected upon Aristotle’s theory of ten ‘primary genera’ or categories; that they found his list too generous; that they excluded six of the ten items; that they modified two, or perhaps three, of the four items which remained; 1 ƒ  ª øœŒ d N Kº
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and that they then defended their new theory of four categories against Peripatetic objections. But the passage should not be read in that way. Simplicius is not recounting the historical origins of the Stoic theory: he is making a philosophical comparison between a Stoic theory and an Aristotelian theory. As for the Stoic theory, it is mentioned for the first time by Plotinus.* Having discussed at length the ten Aristotelian categories, which he construes as ten highest genera of beings, Plotinus devotes a few paragraphs to another theory. He introduces them like this: Against those who postulate four genera, dividing things into four — subjects, things qualified, things disposed, things disposed in relation to something —, and who postulate something common to them all, including everything in a single genus — against these people, given that they claim that all things have something in common and a single genus, there is much that might be said. (enn VI i 25)1

Plotinus does not mention the Stoics; but it is certain that the fourfold theory which he here briefly describes and which he goes on to criticize is Stoic in origin. Plotinus does not call it a theory of categories; but he treats the Stoic theory of four genera as an alternative to the Peripatetic theory of ten categories. Plotinus does not suggest that the Stoics invented their theory as a result of reflecting upon Aristotle’s categories — but then he says nothing at all about the origins of the theory. In truth, the Stoic theory is something of a puzzle. First, its very existence is not immune to doubt. No Stoic text ever alludes to any such theory. To be sure, the Stoics spoke of subjects and of things qualified — indeed, of things qualified in various ways; and they also spoke of dispositions and of relations. But did they construct a theory out of those items? The bricks are Stoic. It is not evident that the building too was Stoic. Secondly, [26] if the theory did indeed exist, its origins are covered in darkness. In particular, there is no reason to believe that it was modelled upon or produced as a rival to an Aristotelian theory. The comparison between the four items of the theory and the ten Aristotelian categories was surely an invention of the Aristotelian commentators. We happen to know that certain Stoics of the imperial period criticized, in some detail, Aristotle’s doctrine of categories: not a single text * But there is presumably a glancing allusion in Plutarch, comm not 1083E. 1 æe b  f ÆæÆ ØŁ
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Aristotle’s Categories

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suggests that their criticism was based upon, or somehow reflected, a Stoic theory of categories. Again, even if the theory was modelled upon Aristotle’s theory of categories and conceived of as a rival to it, its date remains to be determined — and nothing in the pertinent texts requires us to suppose a Hellenistic origin. Finally, although modern scholars frequently speak of ‘the Stoic categories’, no ancient text ever uses the word ‘ŒÆŪ æÆ’ in connexion with the theory. In short, the Stoic theory of categories is a myth.* The philosophers who refer to the Stoic fourfold classification form the first of the four groups of witnesses who might be summoned to testify to the influence of Aristotle’s theory on Hellenistic thought. The second group is composed of orators — or rather, of teachers of rhetoric. In his Institutions Quintilian says that Aristotle was the first to establish the ten elements around which every question is seen to be organized. (III vi 23)1

And he gives his readers an account — a brief and inexact account — of Aristotle’s theory of categories. Long before Quintilian’s time, rhetoricians had taught a theory of ‘commonplaces’ — loci communes or   Ø. Their principal source was Aristotle’s Rhetoric, but they no doubt owed something also to the Topics, at the beginning of which (as we have seen) there is a sketch of the theory of categories. So a rhetorical education came to include some sort of instruction in the theory of categories, perhaps because the Topics had associated the theory with the loci communes or commonplaces. Cicero thought that he owned a copy of Aristotle’s Topics and he recommended the book to his friend Trebatius. But — so he reports — Trebatius couldn’t understand the text, and when he sought help from a professor of rhetoric, that eminent rhetorician answered by saying: ‘That’s by Aristotle — I think — and I don’t know it’. In truth, I am not at all surprised [27] to find that that philosopher

* For a more balanced account of the matter, see e.g. S. Menn, ‘The Stoic theory of categories’, OSAP 17, 1999, 215–247. Menn, like several other scholars, thinks that there was a Stoic theory, that it was probably put together by Chrysippus, and that it concerned four basic and most general kinds of beings. However that may be, there is no reason to associate that Stoic theory with the Aristotelian doctrine of categories. 1 ac primum Aristoteles elementa decem constituit circa quae versari videatur omnis quaestio. — See below, pp.[63–64].

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is unknown to the rhetoricians, for he is unknown to the philosophers themselves, with a few rare exceptions. (Top i 3)1

Cicero suggests that Aristotle’s Topics was unknown to the rhetoricians, a suggestion which is, in a curious way, confirmed by the fact that the text which Cicero himself possessed and which he translated into Latin was not a copy of Aristotle’s Topics. In any event, no one imagined that a student of rhetoric was going to read the Topics — nor even the Rhetoric. But if a student could master an Aristotelian theory of commonplaces without ever reading a word of Aristotle, then he might in the same way get some small knowledge about the theory of categories. If the theory of categories was taught by the rhetoricians, it is not strange that among the criticisms of the theory one at least was advanced in a rhetorical context: at any rate, according to Porphyry, Lucius Annaeus Cornutus — Stoic philosopher and friend of poets — criticized the Categories in his Arts of Rhetoric (Porphyry, in Cat 86.22–24).2 Nor is it odd that, much later, Marius Victorinus refers to the theory in his commentary on Cicero’s de inventione: Aristotle asserts that all things — everything said, everything done, everything in the world — are ten in number. Let us set down their names: the first is substance, ... (in Cic rhet I 9 [183.32–33])3

Victorinus’ account is similar to, but does not derive from, the account in Quintilian.* The Categories are found in the same context in Augustine, who was introduced to them by his teachers of rhetoric; a Byzantine commentator on Aristotle’s Rhetoric advises us to consider a certain question ‘according to all ten categories’ (anon, in Rhet 109.31–32);4 and whoever wrote the brief description which prefaces one of Michael Psellus’ essays on logic claims that this ‘concise and extremely clear exposition of the ten categories, and of

1 rhetor autem ille magnus haec ut opinor Aristotelica se ignorare respondit. quod quidem minime sum admiratus eum philosophum rhetori non esse cognitum qui ab ipsis philosophis praeter admodum paucos ignoretur. 2 See below, p.[36]. 3 Aristoteles ait res omnes quae in dictis et factis et in omni mundo aguntur decem esse. quarum rerum nomina ponemus: prima substantia est ... * On Victorinus and the Categories, see also below, pp.[64–66]. 4 ŒÆd æd ±Æ a ŒÆ ŒÆŪ æÆ Œ
N e ª


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.

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propositions, and of syllogisms’ will help its readers to make progress ‘in every other science and art — and especially in rhetoric’ (philosophica minora lii 1–5).* [28] In short, the categories were always a part of the rhetorical tradition, or at any rate they were always on the margins of the tradition. So we may believe that during the Hellenistic period too, and whether or not the philosophers were particularly interested in them, they would have been half familiar to any well educated young gentleman. That is an agreeable construction — but it is a house of cards. The Psellan text allows us to infer nothing about the Hellenistic period, nor does an allusion — isolated and unexpected — in a Byzantine commentary. As for Augustine, this is how he brags about his acquaintance with the Categories: When I was almost twenty something of Aristotle’s called the Ten Categories came into my hands. When a certain rhetorician from Carthage — he was my teacher — mentioned them, his cheeks puffed with pride and others who had a name for learning did the same thing, it quite took my breath away and I seemed to be in touch with something wonderful and divine. But I read them and understood them without any help. (conf IV xvi 28)1

The passage doesn’t imply that the theory of categories was taught in the rhetorical schools: quite the opposite. The teachers didn’t discuss the categories — they mentioned them, doubtless in the style of schoolmasters throughout the ages: ‘The Categories, boys, the Categories ... what a work, what a theory — and how very difficult, how very very difficult ... ’. Then Augustine found a text and read it with ease. Whatever you make of the story — and no doubt it is as close to the truth as anything else in Augustine’s Confessions — it tells you nothing about knowledge of the theory of categories in the schools of rhetoric. As for Victorinus and Quintilian, in each case the categories occupy a couple of sentences in a vast treatise, and they are mentioned in an aside. Indeed, so far as I am aware, there is no ancient rhetorical text, Greek or Latin, in which the categories are discussed. In Martianus Capella, for example, the ten categories are treated in Book IV, which is given to dialectic, * ØÆŒÆºÆ 
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and not in Book V, which is the book on rhetoric. It is the same in the Etymologies of Isidore and in the Institutions of Cassiodorus. The theory of categories never formed a part of rhetorical education. There is no reason to think that it was studied by rhetoricians and their pupils during the Hellenistic period. Let it be added that no ancient grammarians ever showed any interest in the theory. (And why should they have done? The theory of predication belongs [29] to logic, not to grammar; and so the grammarians had no reason — I mean, no professional reason — to be interested in a theory which classified predicates or predications.) The third group of witnesses comes from the libraries. We possess three catalogues of Aristotle’s writings, all of which mention the Categories.1 One of them is preserved only in an Arabic translation. It is the work of an otherwise unknown Ptolemy. It derives, ultimately if not immediately, from the —
ÆŒ of Andronicus of Rhodes, a catalogue raisonne´ of Aristotle’s works prepared by the scholarch of the Lyceum towards the end of the first century bc. And so Ptolemy does not tell us anything about the history of the Categories in the Hellenistic period.2 The two other catalogues survive in Greek, one in Diogenes Laertius and the other in an anonymous biography of Aristotle known as the Vita Menagiana. The two lists have a common source, the identity of which is controversial: some scholars have argued that it was a catalogue of Aristotle’s works made in the Hellenistic Lyceum; others have urged that it was part of the catalogue of one of the great Hellenistic libraries — perhaps of the Alexandrian library. The question is delicate; but one capital point is undisputed: the source of the two catalogues shows no trace of Andronicus’ work on the corpus aristotelicum. In that case, it is in all probability earlier than Andronicus — and therefore Hellenistic. Since the Categories is found in both catalogues — and therefore was found in their common source — we may infer that the work was read, or at any rate could have been read, in the Hellenistic period. That conclusion may seem modest (it is hardly audacious to suppose that you could have read a copy of the Categories either in one of the large libraries or else in the Lyceum); but in fact it is too bold. For in the two Greek 1 The fundamental study is P. Moraux, Les listes anciennes des ouvrages d’Aristote (Louvain, 1951). Moraux prints the pertinent texts, which may also be found in I. Du¨ring, Aristotle in the Biographical Tradition, Go¨teborgs Universitets A˚rsskrift 63 (Go¨teborg, 1957), pp.41–50, 83–89; 221–231; and in O. Gigon, Aristotelis Opera III: librorum deperditorum fragmenta (Berlin, 1987), pp.22–28, 39–45. But for the text of Ptolemy, see C. Hein, Definition und Einteilung der Philosophie: von der spa¨tantiken Einleitungsliteratur zur arabischen Enzyklopa¨die (Frankfurt, 1985), pp.415–439. 2 On Ptolemy’s catalogue, see further below, pp.[53–54].

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catalogues the Categories keep strange company: though it is followed by the de Interpretatione (which, in the Vita Menagiana, is followed in its turn by the Analytics), it is not [30] placed among the logical works, nor even among the philosophical works — rather, it is at the end of the list in a miscellaneous group of items. Why? The best explanation suggests that the Categories, along with the de Interpretatione — and also, in the case of the Vita Menagiana, the Analytics — were late additions to the list, and that they were not present in the common source. In that case, the catalogues tell us nothing about the Categories in the Hellenistic period.1 The fourth and final group of witnesses consists of writers of fiction. There is a story told by some of the ancient commentators on the Categories when they come to explain why we should accept the text as a genuine work of Aristotle’s. Here is the story in Ammonius’ version: You should know that in the old libraries there were found forty books of the Analytics and two of the Categories. One of the two books of the Categories began like this: ‘Of the things which exist, some are called homonyms and some synonyms.’ The second is the text now before us. It was preferred because it is superior both in organization and in contents, and also because on every page it cries out that Aristotle is its father. (in Cat 13.20–25)2

Ammonius speaks drably of the contents of old libraries. His pupil, Philoponus, adds some local colour: They say that Ptolemy Philadelphus had a passion for the works of Aristotle (as indeed he had for books in general), and that he offered money to anyone who brought him any books by the philosopher. So various people, hoping to make a profit, brought him works on which they had written the philosopher’s name — and so it is that they say that the [31] great library contained forty books of Analytics and two of Categories. (in Cat 7.22–28)3

1 The Categories has sometimes been discovered in the body of the catalogues, hidden under a nickname. Both catalogues include among the logical works a text called ‘a æe H
 ø
’. Certain late authorities tell us that the Categories had gone under several titles, one of them being ‘a æe H
 ø
’. (See Frede, ‘The title’, pp.17–21; Bode´u¨s, [Cate´gories], pp.XXXIV–XLI — despite the title on its cover, Bode´u¨s’ edition calls itself ‘Avant les lieux ’.) See Appendix. 2 N
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A royal bibliophile deceived, counterfeiters laughing on their way to the bank, the Alexandrian library containing two Categories and forty Analytics — an intoxicating tale. More sober is the corresponding passage in Simplicius’ commentary: Adrastus, in his book On the Order of Aristotle’s Works, says that another book of Categories is in circulation under Aristotle’s name. This book too is short and concise. In a few places it differs from the other in expression, and at the beginning it has ‘Of the things which exist, some are ... ’. But Adrastus records the same number of lines for each book. (in Cat 18.16–20)2

Adrastus doesn’t mention the Alexandrian library. What he means is that, in his own time, there were (at least) two versions of the Categories in circulation. He does not speak of counterfeiters (although his manner of expression has suggested to some scholars that he had counterfeiting in mind). And the little which Simplicius reports suggests that it was not a matter of two different works each called Categories and each ascribed to Aristotle, but rather of two different editions, or perhaps simply of two different copies, of one and the same work — namely, of the Categories. After all, we know that at Adrastus’ time there were many differences, and sometimes striking differences, between one copy of an Aristotelian work and another. In any event, what Adrastus says has nothing to do with the Hellenistic fortune of the Categories. Adrastus’ remarks about the two Categories were, I suppose, taken up by later commentators, each adding a little more spice to the story which, in the end, became the romance which Philoponus tells. Many scholars, it is true, have accepted the story as Philoponus tells it; but Philoponus is telling a story. That account of the Aristotelian categories during the Hellenistic period may perhaps seem a touch too sceptical. But even the most unsceptical of scholars must allow that we hear precious little about the categories between the time of Theophrastus and the time of Andronicus. It is true that we hear [32] very little about anything Aristotelian during that period. Nonetheless, the silence about the categories is striking. Ø
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209

In his Life of Aristotle, Diogenes Laertius includes a short account of the Peripatetic philosophy. The two paragraphs given to logic do not allude to the Categories, and nothing in the account hints that Aristotle had a theory of categories. Diogenes does not name his source; but in all probability he was using a Hellenistic manual.2 Cicero boasts that he knew his Aristotle, and he certainly had, for his time, a fair knowledge of Aristotelian philosophy. He never refers to the Categories or to the categories.3 In all the pages of Sextus Empiricus there is no allusion to Aristotle’s theory of categories. True, for Sextus the Peripatetic philosophy is far less important than the Stoic philosophy. But Sextus was interested in logic, he discusses Aristotelian syllogisms, and he had every opportunity to criticize the categories. He was writing at the end of the second century ad; but he composed his works by copying out earlier texts, so that what he writes represents the philosophical situation of the past.4 The Categories made no splash in the Hellenistic period.

From Andronicus to Porphyry Every Aristotelian knows and blesses the name of Andronicus of Rhodes. After all, it is Andronicus who was responsible for the text of Aristotle which we read today. During the Hellenistic period there were few copies of Aristotle’s works, and those few copies were in a bad state. Towards the end of the first century bc, Andronicus, who was head of the Lyceum in Athens, made public a new edition of the text. His edition, which carried as preface a biography of Aristotle and a list of his writings, was backed up by a number of commentaries and paraphrases. The edition itself was soundly based; [33] for Andronicus was able to use a celebrated collection of manuscripts which, after various adventures, had ended up in Rome — the collection consisted of the papers of Theophrastus, and of Aristotle himself.

2 On Diogenes’ Life of Aristotle, see P. Moraux, ‘Dioge`ne Lae¨rce et le Peripatos ’, Elenchos 7, 1986, 254–294. 3 On Cicero and Aristotle, see J. Barnes, ‘Roman Aristotle’, in J. Barnes and M. Griffin (eds), Philosophia Togata II (Oxford, 1996), pp.1–60 [reprinted in volume IV], on pp.44–59. 4 On Sextus and Aristotle, see L. Repici Cambiano, ‘Sesto Empirico e i Peripatetici’, in G. Giannantoni (ed), Lo Scetticismo Antico, Collana Elenchos 6 (Naples, 1981), pp.689–711.

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Andronicus’ edition was epoch-making. And it caused a resurgence of interest in Aristotle’s philosophy. That, in summary, is the usual story about Andronicus. It is disputable — indeed, I believe that it is largely false.1 But the resurgence of interest in Aristotle’s philosophy is a fact. From the end of the first century bc up to the last years of antiquity volumes of stuff were written on Aristotle’s thought — commentaries and paraphrases, monographs both elucidatory and critical, manuals and epitomes and doxographies. Not every morsel of his thought was devoured with the same appetite, and not every part of the corpus was perused with the same assiduity. But the doctrine of the categories was never neglected: indeed, no Aristotelian text was more commented upon than the Categories, no Aristotelian doctrine more discussed than his theory of the Ten Things. It was in the age of Andronicus — whether or not it was also because of Andronicus — that the Categories gained a reputation which they would retain for more than fifteen centuries. At the beginning of his commentary on the Categories, Simplicius, not unreasonably, thinks that he needs to defend himself. After all, he is offering his readers some 400 exegetical pages on a short and familiar essay — and already ‘many people have set out many thoughts on Aristotle’s Categories ’ (in Cat 1.3–4).2 Simplicius explains that different authors have written their dissertations on this book for different reasons. (1.8–9)3

So there are paraphrases, the only aim of which is to make Aristotle’s expressions easier to understand; there are elementary expositions of the thought of the work; there are detailed discussions of particular issues; and so on. For each sort of work Simplicius refers to a couple of authors, and he mentions all told a dozen or so of his predecessors. Those remarks do not constitute a history of scholarship on the Categories, and Simplicius does not claim to have given a complete list [34] of earlier scholars — indeed, in the course of his commentary, which frequently alludes to the earlier literature, he names another dozen scholars who were not noticed in his prefatory remarks. To the two dozen names we find in Simplicius we can ourselves add a few more — that of Galen, for example; 1 See Barnes, ‘Roman Aristotle’. 2  ºº d  ººa ŒÆº
 çæ
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 F æØ º ı غ
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and it is certain that there are other pertinent authors whom Simplicius does not mention and we do not know. Simplicius’ own commentary did not bring scholarship to an end. He had contemporaries and he had successors: scribble, scribble, scribble. Why all that scholarly scurry? Simplicius offers no answer to the question — which he does not raise. Yet he might have raised it. For he states more than once that the Categories is an introduction to philosophy, an Nƪøª, something which was written for tiros and avoids the deep questions (see e.g. in Cat 110.24–25; 264.2–4). His view of the matter was anything but idiosyncratic.* It had been advanced, for example, by Alexander’s teacher, Herminus — for, according to Porphyry, Herminus says that the Categories does not propose to deal with what is primary in nature or with the most general genera, since an exposition of that sort is not suitable for the young ... (in Cat 59.20–22)2

But if the Categories is an introductory manual written for students at the start of their philosophical initiation, then why all those thousands of pages of commentary? There are two answers to the question, answers which correspond roughly to two phases in the history of the commentaries. Simplicius himself once refers to ‘the more recent interpreters [ ƒ
æ Ø KŪÅÆ]’ (in Cat 152.13), and the context shows that Iamblichus is one of the more recent men, whereas Alexander is not. Simplicius does not state, or even imply, that there was a particular turning-point in the commentatorial tradition sometime between Alexander and Iamblichus; but in fact there was one: it was made by Porphyry. Before Porphyry, the Categories and its doctrines were controversial — they were attacked, they were defended. After Porphyry, the Aristotelian doctrine became an accepted truth — and the Categories was reclassified as a work for tiros. First controversy, then pedagogy, each of which encourages commentaries — and commentaries of different sorts. To be sure, the distinction between what I have called the two phases is not [35] a sharp one: the Categories had been taught before Porphyry’s day, and Aristotle’s theory was contested, at least in some of its details, long after Porphyry was dead. Nonetheless, the distinction is not a fiction. If you taught the theory of * See further below, pp.[49–50]. 2 ºªØ  
ı
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212

Logical Matters

categories before Porphyry, you were teaching Aristotelianism — after Porphyry, you were teaching philosophy. If you discussed the problems raised by Aristotle’s theory before Porphyry, you were taking part in a living debate — after Porphyry, you were playing a part (the part of exegete). Dexippus wrote after Porphyry; but the first question in his Questions and Answers about the Categories looks toward the past: What caused the old philosophers to dispute with one another in so many and such varied ways about this work of Aristotle’s which we call the Categories? For I have observed that no other subject has given rise to more disputes or produced warmer controversies — not only on the part of the Stoics and the Platonists, who do their best to shake these categories of Aristotle, but also among the Peripatetics themselves, some claiming to have come closer to the intentions of the master, others believing that they can readily resolve the puzzles which others have proposed. (in Cat 5.16–25)1

For the phase which ends with Porphyry — the phase of disputes and controversies — Simplicius’ commentary supplies us with the names of seventeen scholars, eleven of them Peripatetics. First, the Peripatetics, in roughly chronological order: towards the end of the first century bc Andronicus of Rhodes, Boethus of Sidon, Aristo of Alexandria; in the following century Alexander of Aegae and Apollonius of Alexandria, each as obscure as the other; then Achaicus, Adrastus, Herminus, and — at the end of the second century — Alexander of Aphrodisias. A passage in Galen allows us to add Aspasius to the list (lib prop XIX 42).2 Some of Alexander’s commentaries still exist — but not his commentary on the Categories. Aspasius’ commentary on the Ethics survives — but not his work on the Categories. For the other scholars on the list we have a handful of [36] fragments and a few allusions. The pickings are slim; but they tend to confirm Dexippus’ statement that there were disagreements among the Peripatetics over at least some parts or aspects of the Categories. 1  s
  q
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Æ. 2 The text is cited below, p.[55]. — On the commentators, see e.g. the pertinent pages in P. Moraux, Der Aristotelismus bei den Griechen (Berlin, 1973/1984/2003), and the pertinent articles in DPhA.

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The eight non-Peripatetic scholars whom Simplicius names are Eudorus, Athenodorus, Cornutus, Lucius, Nicostratus, Atticus, Plotinus, and Porphyry. (We may add Galen: see lib prop XIX 42.) Six are Platonists, two Stoics. As for the Stoics, Porphyry says that Athenodorus the Stoic who wrote books against the Categories of Aristotle rejected this view, and so did Cornutus, in his Arts of Rhetoric and in his reply to Athenodorus, and so did many others. (in Cat 86.22–24)1

Several Stoics carried the name ‘Athenodorus’, and there is no telling to which one Porphyry refers. Cornutus is Lucius Annaeus. His ‘reply to Athenodorus’ is no doubt the work ‘which Cornutus entitled Against Athenodorus and Aristotle ’ (Simplicius, in Cat 62.28)2 — and unless Simplicius is mistaken (or his text corrupt), a Stoic wrote an essay which attacked, at the same time, both Aristotle’s categories and an earlier Stoic attack on them. We know little enough about the criticisms advanced by Athenodorus and Cornutus. I have already said that nothing suggests that they compared Aristotle’s theory of categories with a rival Stoic theory. Of the Platonists, Eudorus is the oldest. The references in Simplicius’ commentary indicate that he had put together a number of detailed objections to the Categories, perhaps in a commentary on the work. We also know that he had something to say about at least some parts of Aristotle’s Metaphysics.3 Lucius is only the shadow of a name. As for Nicostratus, an inscription shows him at Athens in the 160s. According to Simplicius, other scholars decided to write nothing but puzzles for what Aristotle says. That is what Lucius did, and after him Nicostratus — who took over what Lucius had written. They tried to bring objections against pretty well everything in the work — and they did so not respectfully but with an angry vehemence. Nonetheless, we should be grateful to them too — after all, most of their puzzles are serious, and in addition they gave their successors [37] some hints in the direction both of a solution to the puzzles and also of many other excellent ideas. (in Cat 1.18–2.2)1 1 ŁÅ
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Atticus probably wrote shortly after Nicostratus. He was no lover of Aristotle nor, in particular, of his categories. What use is it to learn that some things are good simpliciter, others not good for everybody? Or that there are goods of the soul and goods of the body and external goods? Or again, that some goods are capacities, some dispositions and habits, some actions, some ends, some matter, some instruments? And if someone learns to divide the good into ten parts according to the ten categories, what have such teachings to do with Plato’s thought? (Atticus, apud Eusebius, PE XV iv 19)2

If Atticus showed a general disdain for Aristotle and all his works, he also — like Lucius and Nicostratus — elaborated various detailed objections. Thus, for example, Simplicius remarks that Nicostratus raised puzzles on the subject of homonyms — but Atticus set the puzzles out even more illuminatingly. (in Cat 30.16–17)3

We do not know how thoroughly Atticus had mauled the Categories; but as for Lucius and Nicostratus, Simplicius’ description of their work suggests that they read every sentence of the work and that they discovered a puzzle in every paragraph. But they raised not only questions of detail but also more general problems. For example, how many categories are there? In the Categories and in the Topics Aristotle lists ten. But he never explicitly states that there are exactly ten categories; and more often than not he lists two of three and then adds an ‘et cetera ’. Once or twice he seems to give the impression that there are really only eight categories. Once or twice he perhaps intimates [38] that their number is indeterminate.1 Ancient scholars and commentators all considered the question of number. Galen, for example, explains that if you are trying to find out how someone wove a dress or knotted a net or a basket or a hammock, then you are looking for the manner of composition. That is something غ
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Aristotle’s Categories

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which Aristotle omitted in his work on the ten categories, as I showed in my commentaries on the book — for the kind of category which he usually calls position is different. (inst log xiii 11–12)2

More generally, how could you determine the number of categories? What principle underlies the classification? Aristotle never indicates how he arrived at his own list. Later scholars tried to fill the gap by suggesting a priori ways of deducing the classification. Again, what is the order of the ten items? Aristotle’s various lists, and partial lists, show some variety; and we might imagine that the question, like many questions of order, is trifling — that it is a matter of convention, or a matter for stipulation. But scholars of late antiquity took a different view on such matters, and they came up with an answer which seems to have been found largely satisfactory. According to Simplicius, Aristotle nowhere offered any explanation for the order of the genera; but Archytas, who gives a reasoned exposition of the order of the categories, retains the same order in the majority of cases (except that he too sometimes changes the order). (in Cat 340.26–29)3

Archytas had explained the order of the categories. Since Aristotle copied Archytas, the order of his categories is explained by reference to the order of Archytas’ categories — and no doubt it was precisely because Archytas had already explained the order that Aristotle felt no need to do so. (That is what Simplicius suggests. Of course, Archytas is pseudo-Archytas, and his explanations of order of the categories are implicitly attempts to explain Aristotle’s order.) There was another general question of rather more importance: what sort of things does the doctrine of categories classify? The answer is, trivially, that is classifies categories or predications or predicates. But what, then, is a predicate? In particular, if Y is predicated of X, then is Y a word or is it a thought or is it a thing? It seems that it’s not a word; [39] for in that case the theory of categories would belong to grammar and not to logic. Nor is it a 2 › b KØÇÅH
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216

Logical Matters

concept; for in that case the theory would be a piece of psychology. Nor is it a real thing; for in that case, again, the theory of categories would not be a part of logic. But if a predicate is neither a word nor a thought nor a thing, then what on earth can it be? Porphyry proposed an answer to the question, and his answer prevailed. This is what he says: Every simple meaningful expression, when it is affirmed or said of what it signifies, is called a predication. For example, this stone which is being pointed to, and which we can touch or see, is an object, and when we say of it that this thing is a stone, the expression ‘stone’ is a predicate; for it signifies an object of that sort and it is affirmed of the object which is being pointed to. (in Cat 56.8–15)1

A predicate or ŒÆŪ æÆ, then, is indeed an expression — but it is not an expression tout court. Rather, a predicate is an expression which signifies a certain sort of object and which is affirmed of objects of that sort. Later, the Porphyrean answer will be formulated thus: a predicate is an expression which signifies an object by the mediation of a concept. The value of Porphyry’s answer — both its exegetical value and its philosophical value — might be discussed. But it closed, at least temporarily, a long chapter in the history of the interpretation of Aristotle’s categories.2 The questions I have mentioned so far were primarily exegetical in nature: they asked what Aristotle meant. But they were also, and at the same time, philosophical questions: the critics and commentators asked them, at least in part, because they wanted to know whether Aristotle’s theory, properly understood, was true or false. A critic or commentator of a Platonist bent would hold that Aristotle’s theory was true only if, or to the extent that, it is compatible with Platonism; and the question of whether Aristotle’s theory of categories is compatible with Platonism was a question of considerable importance for Platonists. Platonism presented itself, as a matter of course, as a complete philosophy. Philosophy divided, according to a commonplace of the time, into three 1 u AÆ ±ºB ºØ ÅÆ
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parts: logic, [40] physics, ethics. So Platonism must have its logical part. But Plato’s works — or so it surely appears — contain nothing which might correspond to the logical works of Aristotle. Indeed, Aristotle claims, with great plausibility, that he was himself the first philosopher to elaborate an art of logic (Soph El 183b37–184a8). What, then, was a Platonist to do? He must either invent a new logic or borrow an old; and borrowing was the easier option. So the Platonists annexed Aristotle’s logic. And they then persuaded themselves that although Plato hadn’t actually invented the art of logic, he had at any rate anticipated all of its chief parts in one or another of his writings. Adding the Analytics or the Topics to Plato’s philosophy caused no embarrassment. For the logic which those two works present is philosophically neutral — or at least, it can be expressed in a philosophically neutral fashion. The same is true of the de Interpretatione. But what of the Categories? On the one hand, the doctrine of categories was, or came to be seen as, an essential part — the first part — of Aristotle’s logic. On the other hand, the doctrine is not, or not evidently, neutral from a philosophical point of view. After all, Aristotle calls upon the doctrine in his Metaphysics, which is certainly not a neutral work; and he uses it in his Ethics in order to construct an argument against one of Plato’s pet theories (EN ` 1096a23–34). There were Platonists who wanted to have nothing to do with the Categories — Atticus has already been cited to that effect. But a majority of Platonists took a different line. So Alcinous, in his handbook of Platonism, colonized the categories — and claimed that they were prefigured by Plato: ‘as far as the ten categories go, Plato has hinted at them in the Parmenides and elsewhere’ (didask vi [159.43–44]).2 And when Hippolytus, writing in the first decades of the third century, reports that, according to Pythagoras, the first of all things is substance, to which nine accidents are attached, so that the sum of things is equal to the perfect number ten, he ascribes the Aristotelian theory to the Pythagoreans — and by implication to Plato.3 [41] 2 ŒÆd c
a ŒÆ ŒÆŪ æÆ 
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ÅH
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The ascription is absurd, but the absurdity is not simply a misunderstanding on the part of Hippolytus. Pseudo-Archytas has already been alluded to en passant: it is time to say a little more about him. Simplicius states that even before Aristotle, the Pythagorean Archytas, in the book he entitled On the Universe, had divided the primary kinds into ten. (in Cat 2.15–16)1

Simplicius is thinking of a work which is perhaps better known under the title ‘On the Universal Formulas [—æd H
ŒÆŁ º ı º ªø
]’. There, after a short introduction, Archytas gives an account of the ten Aristotelian categories. The account is closely based on the Categories — it is a pastiche. It purports to be written by Archytas of Tarentum, the eminent Pythagorean who was a contemporary of Plato; but its author was a counterfeiter, and the work — like almost all Pythagorean writings — is a pious fraud.2 Nonetheless, the late Platonists took the work to be genuine. According to them, Aristotle copied his Categories from it, so that we must interpret Aristotle by reference to Archytas. And in addition, we can see why there appear to be prefigurations of the Categories in Plato: they are not prefigurations but traces, and not of Aristotle but of Archytas. Any Platonist who believed that Plato owed many or even most of his best thoughts to Pythagoras — and that curious belief was a commonplace among the imperial Platonists — could annex the Categories without a qualm. The date of pseudo-Archytas’ pseudo-Categories is uncertain. Iamblichus knew it and held it to be authentic. Porphyry does not mention it, and so far as I know there is no clear reference to it in any author earlier than Iamblichus. But it is tempting to imagine that the remark in Hippolytus which I have just quoted derives, perhaps indirectly, from pseudo-Archytas; and in point of fact, scholars tend to date the pseudo-Categories to somewhere between the second century bc and the second century ad, a period during which Pythagorean texts sprouted like mushrooms in a dark cellar. Indeed, it has been suggested that the pseudo-Categories is a by-product of the revival of Aristotelian studies which took place [42] in the first century bc, and that the earliest commentaries on the Categories suggested to pseudo-Archytas the idea 1 æå ı ªaæ  F —ıŁÆª æØŒ F ŒÆd æe æØ º ı c
N ή H
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 KªæÆł ... 2 The works of pseudo-Archytas are printed in H. Thesleff, The Pythagorean Texts of the Hellenistic Period, Acta Academiae Aboensis, A 30.1 (A˚bo, 1985), pp.2–48. — As well as Universal Formulas, there is a second text called ‘Ten Universal Formulas [˚ÆŁ ºØŒ d º ª Ø ŒÆ]’; but it is a very late piece, perhaps even later than Simplicius.

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of writing a Pythagorean Categories. However that may be, there is no evidence that the work had any serious effect on Platonism before Iamblichus. So much — or rather, so little — for four of the six Platonists who commented upon the Categories in the first phase of its imperial history. The other two men are well known: they are Plotinus and Porphyry. Porphyry arrived in Rome in 263, and he soon became — according to his own account — Plotinus’ favourite pupil. In 268 he was obliged by his health to leave Rome for Sicily, and he never again saw his master, who died in 270. During Porphyry’s short Roman period Plotinus had written three essays on the ‘genera of beings’ — essays which appear as Enneads VI i–iii, in the edition of Plotinus’ works which Porphyry prepared. Most of Ennead VI i is given over to the ideas presented in the Categories — although Plotinus never names either the work or its author. The end of VI i looks at the four Stoic ‘categories’, which Plotinus puts on the same level as Aristotle’s ten items. The second essay, VI ii, turns to Plato and the five ‘greatest kinds’ or highest genera of the Sophist. And then VI iii is entirely given to Aristotle. Plotinus’ discussion of the Aristotelian categories is long and detailed. It is not all new — Simplicius tells us, for example, that so far as substance is concerned, Plotinus and Nicostratus both puzzle about how substance can be a single genus. (in Cat 76.13–14)1

That passage, and several others like it, suggest that Plotinus collected rather than invented puzzles about, or objections to, what Aristotle says in the Categories. But given how little we know about Plotinus’ predecessors, the suggestion cannot be assessed; and in any event, although it is certain that several, at least, of the issues raised by Plotinus had been raised by others before him, it need not be supposed that Plotinus presented and developed them in the same way as his predecessors had done. In constructing his criticisms of Aristotle, Plotinus builds on Platonic foundations — something which is scarcely remarkable. Sometimes his judgement is hasty, and sometimes he misunderstands the position he is criticizing — that, too, is unsurprising. But pretty well every page of Enneads VI i and iii displays a dazzling intelligence, and taken together the pages offer 1 I æ FØ b ŒÆd æe e
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the most subtle and the most profound examination which Aristotle’s doctrine of categories has ever received. [43] It is a hard and unrelenting examination. Plotinus never says of this or that part of the doctrine that it is not too bad, or that a little tinkering might make it more or less watertight. He hammers, and he hammers again; and Aristotle’s doctrine is crushed. But if the doctrine is reduced to fragments, the fragments are not swept up and put in the dustbin: I mean, Plotinus takes the doctrine seriously; if he sometimes seems impatient, he never suggests that he is wasting his time; nor does he ever say or imply that the Categories is something which young philosophers should leave to one side. As I have said, Plotinus’ criticism is detailed — and it is in the details that is to be discovered its chief philosophical value. But the details are in the service of two general theses. According to the first thesis, which is laid out in Ennead VI i, Aristotle’s theory cannot be applied to the real world. For Plotinus, like Plato, holds that there are two worlds: there is the real world, the world which is
Å  or an object of thought; and there is the world ‘here below’, the world in which we now find ourselves, and which is often (and inaccurately) characterized as ÆNŁÅ  or an object of perception. Real beings, things which exist in the strict sense, are in the real world. Man, or the Form of man, inhabits the real world, and is a being. Men inhabit this world of ours — they have no being and do not exist save in some derivative or secondary manner. Aristotle’s doctrine of categories, according to Plotinus, doesn’t apply to the real world, it doesn’t provide a division of the genera of beings. For the real world, we must (of course) turn to Plato, as Plotinus does in VI ii, where, on the basis of the Sophist, he develops a theory of genera applicable to the real world. Plotinus’ second main thesis is elaborated in VI iii. If Aristotle’s theory does not apply to the real world, neither does it apply — save very approximately and partially — to the world of perception. Even if it is construed as a theory of the genera of perceptible objects, the theory is as full of holes as a Swiss cheese. By the end of VI iii Plotinus has argued that, so far as this world of ours is concerned, ten categories are excessive — we need only five. Not that we should retain five of Aristotle’s ten (nor, come to that, invent shadows of the five Platonic genera of VI ii): rather, Plotinus sketches a new theory of categories for the perceptible world. Plotinus’ criticism of the Categories sparked off a vigorous debate. In particular, it provoked Porphyry: Next, Plotinus, that great man, subjected the book of the Categories to a very substantial examination in three books entitled On the genera of beings. After him,

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Porphyry, to whom we owe all things good, wrote with great industry [44] a full commentary on the book in which he answered all the objections. It is in seven books, addressed to Gedalius. (Simplicius, in Cat 2.3–8)1

The large commentary addressed to Gedalius is lost, and the short commentary which Porphyry also wrote and most of which has survived, does not contain detailed answers to Plotinus’ objections. But we can recover a few passages from the large commentary;* we know that Dexippus, in his Questions and Answers (of which we possess perhaps two thirds), depended largely on Porphyry; and Simplicius’ own commentary includes numerous arguments taken from Porphyry. Porphyry defended Aristotle against Plotinus. His defence ran, in its general lines, like this. As far as the second of Plotinus’ two theses — the thesis which underlies Ennead VI iii — is concerned, pretty well all the detailed criticisms can be countered; and in point of fact Aristotle’s theory of ten categories is adequate as an account of beings in our perceptible world — for which Plotinus’ theory of five genera is not satisfactory. As for the first thesis, which underlies Ennead VI i, it is at bottom correct: Aristotle’s theory does not apply to the real world. But on that point we can and should agree with Plotinus without disagreeing with Aristotle; for the Categories is an elementary treatise, and in it Aristotle deliberately restricts himself to the perceptible world — higher things are reserved for the Metaphysics. In order to establish his position, Porphyry had to overcome several obstacles, the most daunting of which was perhaps this: according to the Categories, perceptible substances are the primary substances: A substance — what is called substance most strictly and primarily and especially — is one which neither is said of a subject nor is in a subject: for example, a given man, a given horse. (Cat 2a11–14)2

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Aristotle could hardly have been more clear: it is Napoleon and Marengo, Wellington and Copenhagen, which are the true substances, the primary substances. Man and horse are, it is true, also substances; but they are second or secondary substances. For a Platonist, that is upside-down; and a Platonist could scarcely welcome a work which proposed such topsy-turvy notions. Worse, Aristotle himself came to reject the notions; [45] for if you read the Metaphysics, and in particular Book Lambda, you will see that Aristotle, just like the Platonists, ascribed primacy to divine and imperceptible beings. Porphyry’s way around that large obstacle depended on a distinction between two senses of primacy or priority: in one sense, perceptible substances are primary, and in another non-perceptible substances are primary. Porphyry’s position will not, or should not, persuade, either exegetically or philosophically; but it had a powerful influence on the history of metaphysics.1 However that may be, Porphyry was not the first philosopher to restrict Aristotle’s doctrine of categories to our perceptible world. Pseudo-Archytas, for example, states that man himself [i.e. the Form of Man] ... has neither quality nor quantity, he is not related to anything else, he does not do or undergo anything, he has no position and no possession, he is not in a place or at a time. For all those things are accidents of natural and corporeal substances, not substances which are thinkable and motionless and also partless. (ŒÆŁ º ª 30.18–31.5)2

The Form of Man is not subject to Aristotle’s categories, which apply not to Platonic entities but to the quasi-entities of the perceptible world. The same view was ascribed to Eudorus, who was perhaps the first Platonist to discuss the Categories: Eudorus says that the discussion of quantity, and the following discussion of quality, are linked to the discussion of substance (for substances exist together with the qualified and the quantified), and after them the categories of time and space are

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Aristotle’s Categories

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dealt with (for every substance is in some place and at some time — every perceptible substance, I mean). (Simplicius, in Cat 206.10–15)3

The last phrase — ‘every perceptible substance, I mean’ — has been taken to show that Eudorus took the substances discussed in the Categories to be perceptible substances. Most probably, that is indeed the sense; but to me the phrase [46] looks like a gloss appended by Simplicius’ report of Eudorus’ view rather than a part of that report. In any event, the notion that Aristotle’s doctrine of categories concerns only the perceptible world was certainly known to Platonists long before the time of Porphyry; but it was not a specifically Platonic interpretation: the Peripatetic Boethus had taken the same view. According to Simplicius, ‘Boethus will have it that these inquiries are superfluous here because Aristotle is not there talking about thinkable substances’ (in Cat 78.4–5):1 certain deep questions about substances are not pertinent to the Categories, which deals with only one sort of substance. The interpretation of Boethus and pseudo-Archytas and Porphyry became an orthodoxy, and it was rehearsed and endorsed in all the later commentaries and monographs. Thanks to it, Aristotle’s categories could be appropriated by the Platonists as a part of their own philosophical system. And yet the interpretation raises a number of curious questions for the Platonists, one of which is this: if, as a Platonist, you decide that the theory of the ten categories applies only to the perceptible world, then what are you going to say about the real world? The ten categories, after all, are ten sorts of predicates; so if you say that Aristotle’s theory applies only to the real world, then it seems to follow that the predicates which the theory concerns apply only to the perceptible world. But those predicates — together, of course, with any complex predicates compounded from them — are the only predicates we’ve got. That difficulty was to have a certain influence on mediaeval theology.* In antiquity, philosophers imagined at least three solutions to it. First, there is a solution implicit in the Enneads. According to Plotinus, the entities of the real world fall into different genera; but they are genera elaborated by Plato 3 ŒÆd ¯høæ  b fiH æd B PÆ º ªfiø e
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and they have little to do with any of Aristotle’s categories. So you might think that we could describe the real world by using an exclusively Platonic vocabulary and avoiding the predicates which the Aristotelian theory classifies. That solution to the difficulty thus supposes that the Aristotelian predicates — the predicates classified by the theory of categories — are not, after all, the only predicates which we’ve got. A second solution is proposed in Dexippus’ Questions and Answers: There is another solution which invokes the doctrine which Aristotle set out in the Metaphysics. The genera being ten in all, he claims that all of them are found in composite items ... so that in [47] perceptible things there are ten categories (so that you could point to them in the case of Socrates), whereas in thinkable things not all the genera are found — only those which are appropriate to things which are wholly simple and wholly perfect. (in Cat 42.18–26)1

You can’t find all the ten categories in the real world: some of them — for example, the categories of somewhere and sometime — do not apply to thinkable entities. But other categories do: thinkable items have qualities and quantities, they are related to other thinkable items (and also, perhaps, to perceptible items), and so on. That solution implies that we don’t need any non-Aristotelian predicates in order to describe the real world: a selection of Aristotelian predicates will serve us. And although we might continue to say that the theory of ten categories applies only to the perceptible world, we shall have to add a gloss: a part of the theory applies also to the real world. The most elaborate solution to the difficulty, and doubtless the most widely accepted, is set out by Simplicius. He speaks of an ‘analogical transference’: It is clear that the analogical transference which goes from perceptible to thinkable things is well adapted to Aristotle’s ideas. He sets up form and matter as principles both for perceptible things and also for thinkable things, and then he says that they are the same by analogy but different in their mode of subsistence. In that case, what prevents our finding in the case of the ten genera too both an analogical sameness and also a difference between perceptible things and thinkable things? Now if there are 1 ª
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ten genera here in the perceptible world and ten among the thinkables, will the relation between them be one of synonymy or homonymy or rather neither simple synonymy nor simple homonymy but that of deriving from a single item and being referred to a single item? (in Cat 74.22–31)2

There are substances and quantified items and the rest in the perceptible world: the substantial predicate ‘horse’, for example, was true of Copenhagen, and so too was the quantitative predicate ‘14 hands’. There are also substances and quantified items and the rest in the real world. The substantial predicate ‘triangle’, for example, applies to the Form of Triangle, and so too does the quantitative predicate ‘having three sides’. Such terms are used both of perceptible things and of thinkable things, and they are not so used homonymously — the predicates which apply in both worlds are not on that account straightforwardly ambiguous. Nor, however, are they straightforwardly unambiguous. Rather they are a case of what contemporary scholars tend to call ‘focal meaning’. Galen’s De methodo medendi is a medical book, a scalpel is a medical instrument, what Hippocrates invented is the medical art. In those three sentences the word ‘medical’ is used thrice: it is not used ambiguously, nor yet is it used three times in the same sense — rather, there is a focal meaning. The book and the instrument can be truly called ‘medical’ thanks to [48] a relation between each of them and the medical art, which is called ‘medical’ in the primary way. So too, Copenhagen and the Form of Horse are each truly called ‘horse’: Copenhagen is so called because he stands in a certain relation to the Form of Horse, which is called ‘horse’ in the primary way. None of those three solutions to the problem can be called satisfactory. And a fourth solution came to have a certain success. Aristotle’s categories, and in consequence all the predicates we’ve got, do in fact apply only to the perceptible world. It follows that we can talk only about the perceptible world: the real world and its inhabitants cannot be spoken of; they are ineffable in the strict sense of that word. (Curiously, those Platonists

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who held the real world to be ineffable nevertheless found a great deal to say about it.) If the first three solutions are unsatisfactory, and the fourth solution is merely silly, then is there a fifth solution? No — there is no solution at all. For there is no problem to solve.

After Porphyry Porphyry colonized the Categories and made them part of the Platonist empire. The questions which the work raised had in principle been answered, the problems in principle resolved. Nonetheless, the work continued to provoke commentaries. For the post-Porphyrean phase of the history, Simplicius mentions Iamblichus, Maximus, Themistius, Dexippus, and Syrianus, and he speaks of the opinions of ‘our masters [ ƒ æ Ø ØŒÆº Ø]’ (in Cat 13.17) — that is to say, of Ammonius and of Damascius. There is also, of course, the commentary of Simplicius himself — and commentaries by Philoponus, by Olympiodorus, by Elias or David. Pedagogy no less than controversy encourages the composition of commentaries. But why such vast and prolonged labours on such a small book? First, the labours were in fact somewhat less vast than they appear. Commentaries are rarely works of great originality, and in antiquity one commentator would normally paraphrase, or even copy down, large chunks of what his predecessors had written — which, in its turn, was in large part taken from earlier scholars. Simplicius is typical: he affirms that his own commentary owes a great deal to his predecessors; he gives particular praise to Porphyry; he frequently cites Iamblichus; and very often he cites or paraphrases without saying that that is what he is doing. That is how ancient commentaries were made — as Porphyry describes with disarming candour.* That is how modern commentaries are made. And after all, crambe repetita is sometimes a nutritious dish. [49] Nonetheless, there is a lot of the cabbage. The commentaries are numerous, and they are long. Simplicius’ commentary uses up more than 400 large pages. To explain how, after so many splendid exegetical works, he dare write something himself, Simplicius says this: * See the passage from in Ptol harm cited and discussed in J. Barnes, ‘‘‘There was an old person from Tyre’’’, Rhizai 5, 2008, 127–151 [reprinted in volume I, pp.100–124], on pp.128–131.

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If I too have managed to add something, for that too I thank, first of all, the Gods and, after them, those great men who have enabled me to add here a not wholly trifling problem and there an elucidation of the text which is worth pondering. But I urge my readers never to look down on the works of Porphyry and of Iamblichus or to prefer my notes to their commentaries: rather, they should treat these notes as an introduction and a training for the more exact comprehension of what those men have said. (in Cat 4.4–11)1

Simplicius’ 400 pages are merely an introduction to a reading of the great commentaries. So why the labour? For at least two distinct reasons — and reasons which tend to pull in opposite directions. First, although the Categories was no longer a contested work which had to be defended against punishing frontal attack, it was nonetheless found to be, in parts at least, a difficult work and a deep work. It was difficult — or perhaps rather, it had become difficult — thanks partly to the commentators themselves. If you read the Categories you would read them in the shadow of Plotinus’ criticisms and of Porphyry’s defence and of Iamblichus’ theoretical reflections — and that is a dark and heavy shadow. Perhaps the Categories is elementary, perhaps it only touches on metaphysical matters: nonetheless, anyone who read the work together with its secondary literature was likely to drown in a metaphysical ocean. Secondly, the Categories had become a school handbook, an introductory text for students, the second book — after Porphyry’s Isagoge — which philosophy students were required to read. Teaching, then as now, produced writing: you lectured on the Categories; you wrote up your notes — or your students wrote them up for you; they were copied and circulated; and lo, there was another commentary on Aristotle’s Categories in the bookshops. Students cut their philosophical teeth on the Categories. According to Porphyry, ‘this book is quite elementary and [50] serves as an introduction to all the parts of philosophy’ (in Cat 56.28–29).1 According to Dexippus, Aristotle ‘is writing for young men who are capable of following simpler

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matters’ (in Cat 40.20–22).2 It was a commonplace to describe the Categories as an elementary text. But that commonplace is supported by nothing in the text itself — Aristotle himself never suggests that he was writing for tiros. Moreover, if the late Platonists repeated the commonplace, they cannot have believed it. That is shown not only by the number and nature of the commentaries they wrote but also by the fact that no student started at once on the Categories: before the Categories he had to read Porphyry’s Isagoge — and before the Isagoge he would read, or at least hear, various Prolegomena to Philosophy. Of course, the Categories is simpler than, say, the Metaphysics; of course, the Categories does not descend into the profundities of philosophy: nonetheless, it is not the very first thing a student of philosophy should be set to study.3 It is worth remembering that even in the Isagoge students would come across the categories. At one point in his discussion Porphyry remarks that what I am saying will be clear as follows: in each category there are some things which are most general, others which are most special, and yet others between the most general and the most special. (isag 4.14–16)4

And a little later: What I am saying may become clear in the case of a single category: substance is, itself, a genus ... (4.21–22)5

And again: Let it be supposed, as in the Categories, that the primary genera are ten — ten first starting-points, as it were. (6.6–7)6

In the Isagoge Porphyry doesn’t explain what a category is, and his student readers ought to be perplexed. Has Porphyry for a moment forgotten his readership? Or is he teasing them with a glimpse of the future? In any event, the Isagoge, which was written as ‘a short account ... in the form of an introduction ... which does not go into [51] deep questions but considers 2  åÇÆØ ªaæ H

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simple things in a simple manner’ (1.7–9),1 became a school text, a text which was taught — and so a text which was itself commented upon. The Isagoge is addressed to Chrysaorius. According to the ancient commentators, Chrysaorius decided one morning to read the Categories. He found it difficult. His teacher, Porphyry, was not in Rome. He wrote to Porphyry, asking him either to return at once or else to write him an explanation of the text. And so Porphyry dashed off the Isagoge and posted it to Chrysaorius. (See e.g. Ammonius, in Isag 22.12–22.) Nothing in that pretty little story need be believed — but it serves to show that the difficulty which the Categories could present to tiro readers was recognized. It is not that the Categories was used as a school text because it is elementary: rather, it is elementary because it was used as a school text. You might then wonder how and why it became a school text. An answer to the question comes in two parts. The first part considers the role which logic played in philosophical studies. Philosophy, as most of the ancients allowed, has three parts: logic, physics, ethics. The correct order of the parts had been an object of discussion since the Hellenistic period — and there are, of course, different sorts of order or of orderings. One sort is pedagogical: what is the right order, or the best order, in which to teach the three parts of philosophy? That question received different answers; but the standard answer decreed that you must start with logic. After all, logic is the science which distinguishes the true from the false, and the valid from the invalid. And according to Epictetus, that is why, I suppose, they start with logic — just as before measuring the wheat we start by looking at the measure. After all, if we don’t first know what a bushel is or first know what a pair of scales is, then how shall we be able to measure or weigh anything? Here too, if we haven’t gained a thorough and precise knowledge of the yardstick of things — the yardstick by means of which everything else is learned — then how shall we be able to gain a thorough and precise knowledge of anything else? We shan’t. (diss I xvii 6–9)3 [52] 1 
 
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Logic provides the tools of philosophy. Before engaging in any trade you must first learn to use its tools. Before engaging in philosophy you must first master logic. If you must start with logic, how are you to tackle it? The tools or instruments which logic produces are proofs or probative arguments — more precisely, they are general inferential forms or structures which may be used to construct proofs: they are forms or types of syllogism. A syllogism is a combination of propositions — of premisses and conclusion. Propositions are combinations of terms. In the normal case — in the case of which Aristotle’s syllogistic takes note — a proposition has two terms, a subject and a predicate. Now in order to understand a complex item, you must first become au fait with its elementary parts. So when you set out to study logic, you must begin with the elementary parts of syllogisms — that is to say, you must begin with a study of terms. That argument is found in one form or another in all the ancient commentaries on the Categories. The most extended version occurs, unsurprisingly, in Simplicius. Even in its most refined form, the argument is at best of doubtful worth.1 And in any event, if it is to justify the position of the Categories in the philosophical syllabus, the argument needs reinforcement — the reinforcement constitutes the second part of the answer to the question ‘Why did the Categories become a school-text?’. According to the Peripatetics of the imperial age, logic is not, strictly speaking, a part of philosophy. Rather, insofar as logic produces instruments or tools for the use of philosophy and the other sciences, logic is itself an instrument or tool of philosophy. It is an ZæªÆ

. And so the word ‘Organon ’ came to be used as a title for a collection of Aristotle’s logical works. Who introduced the title we do not know, nor when; but everything suggests that the Organon — the collection, not its name — was put together by Andronicus of Rhodes. First, we know that, according to Andronicus, you must start philosophy by studying logic. Boethus thought that you should start with physics; but his teacher, Andronicus of Rhodes, examined the matter with more care and said that you should start with logic, which occupies itself with proofs. (Philoponus, in Cat 5.18–20)2 1 See B. Morison, ‘Les Cate´gories d’Aristote comme introduction a` la logique’, in Bruun and Corti, Cate´gories, pp.103–119. 2 › b   ı ،ƺ  
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[53] Secondly, we know that in his edition of Peripatetic writings, Andronicus divided the works of Aristotle and of Theophrastus into treatises, collecting related subjects in the same place. (Porphyry, v Plot xxiv 9–11)1

So it must seem likely that Andronicus collected together those of Aristotle’s works which, in his eyes, dealt with the subject of logic — in other words, that he assembled an Organon. And he will have set his Organon at the head of his edition of Aristotle’s works, insofar as it was the first part of Aristotle’s philosophy to be studied. But what was the contents of the Andronican Organon? The catalogue of Aristotle’s writings written up by the unknown Ptolemy derives, as I have said, from a catalogue raisonne´ which Andronicus had made. It is reasonable to imagine that Andronicus’ catalogue will have indicated, explicitly or implicitly, the number and the order of the works which made up the Organon. And so it is reasonable to look to the Ptolemaic catalogue for information about the Andronican Organon.* The published version of the catalogue contains the following sequence of items: 28 his book which he called On Love, three volumes 29 his book known as Qatiguriyas, which is the first book of logic 30 his book known as Barirminiyas, which is the second of the books on logic, one volume 31 his book known as Analutiqa, which is in two volumes 32 his book known as Tubiqa, which is in eight volumes 33 his book known as Afudiqtiqa, which is in two volumes 34 his book on al-sufista’i, one volume.2 The first book of logic is the Categories, the second the de Interpretatione (‘Barirminiyas’ being as it were a transliteration of the Greek ‘æd æÅ
Æ’). Although the text does not expressly say so, it is difficult to avoid the notion that the next four titles, which indicate the Prior Analytics, the Topics, the Posterior Analytics (or I ،،), and the Sophistici Elenchi, 1 › b a æØ º ı ŒÆd ¨ çæ ı N æƪÆÆ ØEº a NŒÆ  ŁØ N ÆPe
ı
ƪƪ
. * On the Ptolemaic catalogue, see esp Hein, Definition, pp.388–439; cf Barnes, ‘Roman Aristotle’, pp.32–37. 2 I am greatly indebted to Marwan Rashed, who translated the Arabic for me and saved me from several horrid errors.

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are the third, fourth, fifth, and sixth books of logic. Ptolemy regarded the six works as a sequence and a sort of unity — he regarded them as an Organon (whether or not he used that term as a collective title). It seems, then, that Ptolemy’s Organon — if I may be allowed the term — was made up, in order, of these works: Cat, Int, APr, Top, APst, Soph El. Our Organon is made of the same texts, but in a different order: Cat, Int, APr, APst, Top, Soph El. (That is how things stand in the mediaeval manuscripts, and hence in Immanuel Bekker’s edition. The late ancient commentators knew of something which has been called the ‘long’ Organon and which [54] adds the Rhetoric, and sometimes also the Poetics, to the six works which constitute Ptolemy’s Organon and our own.1) So the sole difference between Ptolemy’s Organon and ours lies in the fact that he places the Topics before rather than after the Posterior Analytics. Or does he? The order in the received text is not merely unorthodox — it is absurd. First, the end of the Sophistici Elenchi shows it to be an appendix to the Topics — or rather, to be the last book of the Topics. Secondly, it is plain that the Prior and the Posterior Analytics belong together. The order APr–Top–APst–Soph El conflicts with those two evident facts. It is hard to see why any scholar or cataloguer should have chosen to go against the facts. The received text of the catalogue is surely corrupt: Ptolemy’s order was no doubt the same as ours. So it seems that Ptolemy’s Organon was exactly the same as our Organon. Or was it? The published version of the catalogue depends on three Arabic witnesses: a manuscript, an edited version in a work by Ibn al-Qifti, an edited version in a work by Ibn Abi Usaybi‘a. None of the three witnesses has the text of the published version. The manuscript has: Cat, APr, Top, APst, Soph El — Int is missing. al-Qifti has Int, APr, APst, Soph El. Usaybi’a has Cat, Int, Top, APr, APst, Soph El. There are large differences there, which need to be explained in one way or another but which do not matter in the present context. One difference does matter: the manuscript omits the de Interpretatione, which is present both in al-Qifti and in Usaybi’a. Did Ptolemy list the de Interpretatione or did he omit it? (Did the title drop from his text by scribal oversight, or was it added 1 See e.g. Philoponus, in Cat 5.8–14; and below, pp.[67–68].

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to his text by al-Qifti and Usaybi’a, who thought that an Organon ought to contain it?) Andronicus thought that the de Interpretatione was not a genuine work of Aristotle’s (see e.g. Ammonius, in Int 5.24–6.4). In that case it must seem unlikely that he would have included it in his catalogue raisonne´ as the second book of logic or the second book of the Organon. (If he listed it at all in the catalogue, he will presumably have marked it as spurious.) So surely the fact that Int is missing from the manuscript of the Ptolemaic catalogue is not due to chance, or mischance — Int is not in Ptolemy’s list because it was not in Andronicus’ list. That is an engaging conclusion. But it is false. The items in the manuscript of the catalogue are numbered. The Categories is numbered 29 and the Analytics, which in the manuscript is the immediately following item, is numbered 31. Plainly, item 30 was omitted by a careless copyist. Certainly, item 30 was de Interpretatione. So Int was a part of Ptolemy’s list until a careless copyist lost it. The Ptolemaic Organon contained Int. The Andronican Organon in all probability did not. So whatever the exact relation between Ptolemy and Andronicus may have been, the Andronican Organon was not Ptolemy’s (nor, by the same token, was it ours). In that case, we do not know what was the form and what the content of Andronicus’ Organon. Nonetheless — to return at length to our sheep — , we can be pretty sure that the first element of Andronicus’ Organon was the Categories: after all, in later antiquity the Categories was invariably taken to be the first part of the Organon; no commentator hints that the work had ever held any other position, nor even that its position had been seriously discussed. Had Andronicus placed the Categories in some other position, his heterodoxy would have been mentioned somewhere in the surviving literature.3 Why begin an Organon with the Categories? There is, of course, nothing in the text itself which imposes or even insinuates such a position; nor does any ancient commentator ever speculate either that Aristotle had written the Categories before the other books of the Organon or that he had ordained that it be read before the other works of the Organon. The Categories was put first for theoretical reasons, nor for historical or exegetical reasons; and if we 3 On the history of the Organon, see J. Brunschwig, ‘L’Organon: tradition grecque’, DPhA I, pp.482–502; on Andronicus, see Barnes, ‘Roman Aristotle’.

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ask what those theoretical reasons might have been, then only one plausible suggestion shows up: you should begin with the Categories because they discuss terms, then read the de Interpretatione because it deals with propositions, ... In short, you start with the Categories not because the book is an easy introduction to logic, nor because Aristotle had written it for beginners, but because a certain theory decrees that you must begin logic by a study of terms and the Categories deals with terms. [55] That was the way in which, for centuries, the Organon and its component parts were understood. But what a strange way it is. It is not just that Aristotle himself never suggests that his several works be put together in that way and read according to that understanding. It is not just that the works do not read easily according to that understanding — that the contents of one work do not always either exploit the contents of its supposed predecessor or prefigure the contents of its supposed successor. Nor is it just that there are apparent inconsistencies within the Organon. (For example, whereas the Analytics requires — and rapidly sketches — a theory according to which every proposition contains two homogeneous terms, or in which the subject and the predicate term may be exchanged without any loss of grammaticality, the de Interpretatione suggests a ‘theory of the proposition’ (as it has been called) in which subject and predicate are essentially heterogeneous.) Rather, there is something more perplexing about the construction — and something which particularly affects the place within it of the Categories and of the doctrine of ten categories. For that doctrine has nothing whatever to do with the theory of the proposition which is set out in the de Interpretatione: the theory of the proposition never alludes to any sorting or classification of terms, nor is it evident how such an allusion could have been dragged into the discussion. Again, the doctrine of categories has nothing whatever to do with the theory of the syllogism which is elaborated in the Prior Analytics: the theory of the syllogism never makes use of any doctrine of categories. Nor is that, so to speak, a curious accident: Aristotle’s syllogistic is entirely neutral with regard to the type or sort of terms which may enter into a syllogism. A predicate may be a term for a substance, for a quality, for a relative — that makes not the slightest difference from the point of view of Aristotle’s syllogistic. Again, a predicate in a syllogism may possess absolutely any degree of complexity: nothing whatever intimates that syllogisms ought, in principle at least, to limit themselves to the simple terms which the doctrine of categories classifies. The Latin de Interpretatione which the manuscripts ascribe to

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Apuleius is an introductory handbook to Aristotelian syllogistic. In it the categories are never mentioned. No reader notices a gap in the exposition. To be sure, there are pages in the Categories which have something to do with Aristotelian logic — you might think especially of the Postpraedicamenta. It is also true that the theory of categories is once exploited in the Analytics — in a passage in the Posterior Analytics in which Aristotle wants to establish that the number of predicates, and hence the number of possible propositions, is finite (see APst ` 83a21–23). But although the ten classes of predicates are invoked, all that matters to the argument is the distinction between predicates which are essential to their subject and predicates which are accidental — and that distinction has in fact nothing to do with the classification made in the Categories. The point emerges clearly from a consideration of what Galen has to say about categories. Galen was not an Aristotelian — nor a Platonist, nor a Stoic ... He detested isms, and he had no school loyalties or local patriotisms which might have led him to revere the Aristotelian doctrine of categories. Nonetheless, he did revere the doctrine. Relatively late in his life, and at the urging of friends, Galen put together a long and scholarly commentary on the Categories: Earlier I had not made a commentary, neither for my own use nor to give to others. So when, later on, one of my friends asked me if he could have some commentaries containing what he had heard about the book with reference to the solutions to the problems which are found in it, I made one; and I urged him to share the commentaries only with people who had read the book with a teacher or had at any rate already been introduced to it by other exegetical works such as those of Adrastus or of Aspasius. (lib prop XIX 42)*

The commentary was not written for beginners; and it occupied four books (ibid, 47). In his own Introduction to Logic Galen had spoken of categories twice over: near the beginning of the book he presents a classification of predicative propositions which corresponds, grosso modo, to an exposition of *  F b H
ŒÆ ŒÆŪ æØH
PŒ K ØÅÅ
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j 
ø ª æ ØŪ
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› EÆ   æ ı ŒÆd Æ ı K
. — The received text is corrupt. I follow, with little confidence, the Bude´ edition of V. Boudon-Millot, Galien I (Paris, 2007) — save that I adopt Mu¨ller’s addition of ‘æØå
Æ’ after ‘åØ
’. The general sense of the passage is not in doubt.

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Aristotle’s doctrine of categories (inst log ii); and somewhat later, when he comes to speak of scientific proofs, he returns to the categories and sets out the theory again (xiii). Galen frequently, and sharply, criticizes his medical colleagues for their ignorance of logic. A doctor must, after all, know what a proof is — but anyone who wants to follow these things accurately must first have been trained in the categories. ... Just as there is an order which must be followed when you are preparing wool, so too is it with learning the sciences. ... In all the arts there is a first and a second and a third. That is why in logic too you can’t follow a proof unless you have first trained yourself in the first things and in, as it were, the elements. (diff puls VIII 624)*

The theory of categories is the first thing in logic. Without mastering it, you will never master the theory of proof. Without mastering the theory of proof, you will never be a competent doctor — or a competent scientist of any sort. And yet the doctrine of categories is scarcely present in Galen’s works. The Introduction to Logic may sketch the doctrine twice — but in its exposition of syllogistic the categories are never alluded to. In his other works — which are voluminous and include several hundred pages of philosophy — you will never meet any discussion of a theory of categories. To be sure, here and there Galen talks about categorial distinctions. For example, he says that difference in bigness and smallness isn’t a quality — unless you say that ‘three feet long’ is a qualification. For my part, I thought it was a quantification. But I know that on the subject of big and small there has been a long debate: do they signify something quantified or something relative? Or rather — what is in fact true — something relative in the category of the quantified? (diff puls VIII 580)**

No doubt distinctions between quality and quantity and between quantity and relation are sometimes hard to make out, and perhaps they are of some * ‹Ø b IŒæØH   Ø ŁÆØ  ºÆØ ªªı
ŁÆØ æ æ
ÆPe
åæc æd a ŒÆŪ æÆ. ... Ø ªæ KØ
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e b
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ŒÆa ªŁ  ŒÆd ØŒæ ÅÆ ØÆç æa  Ø Å PŒ Ø
N c ŒÆd e æÅåı  Øe
KæE. Kªg b
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. Iººa ŒÆd æd  F ªº ı ŒÆd ØŒæ F PŒ Oºª
r Æ ªª
Æ º ª
 æ
 
Ø ź FØ
j æ  Ø j ‹æ ŒÆd IºÅŁb æ  Ø b
K
b fiB  F   F ŒÆŪ æfi Æ. — cf diff puls VIII 594; PHP V 661–662; morb diff VI 867–868; dign puls VIII 839–840.

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consequence. But nothing in Galen’s works suggests that the doctrine of categories had any particular importance, either logical or philosophical. In theory, the doctrine of categories is the alpha of logic, and hence the alpha of philosophy. In practice, the doctrine of categories has no importance at all for syllogistic and a very limited application in the rest of philosophy. [56]

The Christians The Organon is jerry-built. Why did some Peripatetic philosopher botch it up? The doctrine of categories is of no pertinence to logic. How did it come to be the first step in logic taken by any student? There is a popular answer to those questions which runs roughly like this. Once upon a time, decades after Aristotle’s death, the Stoics developed a logic which rivalled — or which was thought to rival — the theory which Aristotle had left behind. It was a logic which promised to do what Aristotle’s logic had been supposed to do — and to do it better. After all, Stoic logic was younger than Aristotelian logic, and so more lithe. Now in the Stoa, you started logic by looking at the elementary parts of propositions — at what they called cases and predicates and so on; then you moved on to propositions, and to the differences between simple and compound propositions, and to the sorts of compound proposition; and in the end you came to the theory of inference, and to the theory of syllogism. Such being the Stoic system, the Peripatetics determined to create an Aristotelian counterpart. So they had to find, inter alia, an Aristotelian theory of the elements of propositions, and they had to find it somewhere in Aristotle’s writings. The only text which seemed to offer them what they were looking for was the Categories. So the Categories must present a theory of terms, and the Categories must become the first part of the Aristotelian summa logica. Perhaps it wasn’t exactly a counterpart to the Stoic stuff — but the Peripatetics had to do something. That is a story, and it may be true. But there is no evidence in its favour, and no reason to believe it. Better confess that, for us, the origins of the Aristotelian Organon are hidden in the mists of the past. Yet if the origins of the monster are obscure, its career was spent in the sunlight. It is extraordinary that a beast so ill favoured should have survived for so many centuries. [57]

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The doctrine of categories came to stand at the gateway to philosophy. Some centuries after Aristotle’s death his Peripatetic successors constructed their Organon and based it on the Categories. The absence of any Platonic logic encouraged the Platonists to colonize Aristotle. Porphyry’s arguments trumped the arguments of Plotinus so that the theory of categories became a part of the Platonic philosophy. From the end of the third century Platonism was practically the only pagan school of philosophy: Aristotelianism had been absorbed, Stoicism and Epicureanism had largely disappeared. Any young man who learned a little philosophy — any young man of breeding — would read Aristotle’s Categories or at any rate learn about Aristotle’s categories. But in the late imperial period there was a second school of philosophy which came to rival, and eventually to triumph over, Platonism. I mean the Christian philosophy. So in order for the dominion of Aristotle’s categories to be complete, it had to include the Christians. The expression ‘Christian philosophy’ uses the word ‘philosophy’ in its ordinary sense, and not a a mere fac¸on de parler. In his Dialogue with Trypho Justin narrates his spiritual autobiography. (A fictional autobiography, no doubt — but that does not matter here.) When he was young, in the 130s, Justin decided to devote himself to philosophy. Like every other young man, he found himself faced with a choice: he wanted to be a philosopher — but what sort of philosopher, a philosopher of what school? Like any prudent shopper, he looked around a bit before he bought. The local supermarkets offered him, on prominent display, Aristotelianism and Stoicism and Platonism. The first two displeased him, for different reasons. Plato was better — but even Platonism left him dissatisfied. Then he found that there was another philosophy still to try: he tested the Christian philosophy and found — what a surprise — just what he had been looking for. For Justin, Christianity is a philosophy. It is one philosophical school or persuasion among others. To be sure, it towers above the others as an elephant towers above the little mice. But it is nonetheless a philosophical school like Platonism, like Aristotelianism, like Stoicism. In taking that view, Justin was not idiosyncratic. On the contrary, despite the profound differences which divided the early Christian intellectuals, they all — with a few rare exceptions — supposed that their religion was, or at any rate included, a philosophy. The pagans [58] did not deny it. The Platonist Alexander of Lycopolis, for example, begins his essay against the Manicheans like this:

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The philosophy of the Christians is called simple. It is especially concerned with moral education, making veiled allusions to the more exact theories about God. (adv Man i)1

‘The philosophy of the Christians’: Alexander does not think to wonder if the votaries of Christ had a right to the noble title of philosopher. The Christian philosophy is simple, according to Alexander. He doesn’t mean that it is elementary or childish: he means that it does not deal with all three of the parts of philosophy. It had an ethical part, and it gestured in a covert fashion toward theology (and hence toward the highest part of physics). But that was all: in order to become a full-grown philosophy, Christianity needed to develop a physics and to devise a logic. It did just that — with results which Alexander found repugnant. A Christian physics was not inherently difficult to discover. For example, there was the cosmogony of the Book of Genesis — which Galen judged inferior to the cosmogony of the Timaeus but superior to the cosmogony of the Epicureans (see us part III 904–906). But a Christian logic? Perhaps it wasn’t absolutely indispensable for a philosophy to have its logic? After all, were not some pagan philosophers said to have rejected logic? The Cynics, for example, and the Cyrenaics, the Epicureans (according to some), even a few Stoics.3 Why not elaborate a Christian philosophy along the same lines, a philosophy which modestly — or perhaps proudly — held aloof from logic? Were there not in fact reasons which might lead a Christian in the direction of a philosophy which neglected the sophisticated and sophistical refinements of dialectic and cleaved instead to faith and the words of Holy Writ? Several of the Fathers declared themselves, in Greek or in Latin, enemies of logic — which they sometimes denounced with an energy and a violence which seem out of all proportion to their object. Here are a couple of illustrative examples. In the West, Jerome thundered against dialectic, urging his fellow Christians to do their utmost to avoid the traps of the logicians ‘of whom Aristotle is the chief [dialectici quorum Aristoteles princeps est]’ (in Tit iii [PL XXVI 596AB]). In the East, Gregory of Nazianzus, condemning the logical displays of his enemy [59] Eunomius, asserted that logic does nothing 1 æØØÆ
H
çغ  çÆ ±ºB ŒÆºEÆØ. ÆoÅ b Kd c
 F XŁ ı ŒÆÆŒıc
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æd Ł F. 3 On this, see e.g. J. Barnes, Logic and the Imperial Stoa, Philosophia Antiqua 75 (Leiden, 1997), pp.6–9.

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but ‘tie the feeble in spiders’ webs — as though there were anything noteworthy about that’ (orat xxvii 9).1 ‘Your bishop is Aristotle [Aristotelis episcopi vestri]’, said Faustinus to the heretical Arians (trin xii [PL XIII 60B]). And there is a chief part of the problem: logic was an instrument of the heretics, it was an instrument of the Adversary. According to Tertullian, for example, all heresies derive from Greek philosophy, and Greek logic in particular is an ever-running source of error, the logic of Aristotle being the most dangerous thing on earth (see praescr vii 3–8). According to Hippolytus, all heresies call upon pagan philosophy: the errors of Basilides, for example, derive from Aristotle — and Hippolytus refers in particular to the Categories (ref haer VII xxi). The apostle himself had warned: ‘Beware lest any man spoil you through philosophy and vain deceit’ (Col ii 8). It is worth citing a passage from the Church History of Socrates. He is speaking of the heretic Ae¨tius: From the start, he disconcerted the people he met. He did so because he believed in Aristotle’s Categories (there is a book by Aristotle with that title). He based his arguments on that book and he constructed sophisms for himself — and yet he neither knew nor was prepared to learn from the experts what Aristotle’s aim there was. For it was on account of the sophists who in his time ridiculed philosophy that Aristotle wrote the book — it was an exercise for young men which pitted dialectic and all its sophisms against the sophists. In point of fact, the sceptical philosophers, when they explain the doctrines of Plato and Plotinus, reject Aristotle’s technicalities. But Ae¨tius, who found no sceptic among his masters, never got himself free from the sophisms of the Categories. (HE II 35)6 [60]

Ae¨tius relies on Aristotle, and in particular on the Categories: his whole heresy depends on the doctrine of that work. But he thereby displays his own

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philosophical ignorance: he does not realize that the ‘sceptical’ philosophers — Socrates plainly means the Platonists — have rejected the Categories, realizing that it was merely a collection of sophisms and that Aristotle had put it together so that his young pupils could learn to shoot down the sophists with their own feathers. That extraordinary paragraph merits a detailed discussion. Here I cite it to illustrate an attitude which some Christians took to the doctrine of categories. In any event, there certainly were Church Fathers who howled logic down. But such howling is not always to be taken too seriously. After all, the Epicureans were commonly said to have rejected logic. It is true there was never an Epicurean logic, as there was a Stoic logic and an Aristotelian logic; nor did the Epicureans, like the Platonists, take a logic from another school. Nonetheless — witness for example Philodemus’ On Signs — there were Epicureans who interested themselves in logical questions. At least some Epicureans had studied logic, even though the Epicureans were in general held to have rejected logic. The case of the Christians is similar, though more intricate.1 First, whereas the Epicureans never formally conceded that logic was a part of their philosophy, the Christians finally recognized the subject as a part of theirs: from the sixth century onward few Christian voices descanted against logic. Secondly, for every Christian Father who condemned logic there were two of his contemporaries who praised it. Thirdly, most of those Christians who howled at logic also hymned it. A couple of paragraphs ago I cited Jerome and Gregory against logic. Here are some sentences from Gregory’s panegyric on Basil: Who was as strong in philosophy as he was? I mean in that philosophy which is truly sublime and which climbs ever higher — practical philosophy and theoretical philosophy and also the philosophy which occupies itself with logical proofs and antitheses and conundrums and which is called dialectic. In truth, it was easier to escape from a maze than to extricate yourself from the snares of his arguments if ever he needed to ensnare you. (orat xliii 23)2 1 For the Christians and their attitude to logic, see M. Frede, ‘Les Cate´gories d’Aristote et les Pe`res de l’E´glise grecs’, in Bruun and Corti, Cate´gories, pp.127–167. 2  b çغ  çÆ
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[61] And here are some sentences taken from one of Jerome’s letters. Jerome was vexed because a young deacon had criticized him in front of his own lady admirers for his ignorance of logic: This logician ... has not even read Aristotle’s Categories, nor the de Interpretatione, nor the Analytics, nor even Cicero’s Topics, ... And was it in vain that I turned the pages of Alexander’s commentaries, or that my learned master introduced me to logic by way of Porphyry’s Isagoge? (ep 50 1)1

Jerome barked furiously to warn his flock against the dangers of logic: he had studied logic himself, he was proud of his dialectical education, he was incensed when someone suggested that he was ignorant of the subject. Gregory asserted that logic was an instrument of heresy and the Devil: he also believed that it was a part of the most sublime Christian philosophy and he lauded the sainted Basil for excelling in it. The Fathers often inveighed against rhetoric. They were also, almost all of them, masters of rhetoric. They had studied it, they practised it. It is the same with logic. The Fathers sometimes rail against it. They sometimes laud it. They often practise it. The Bible could be cited in either of two senses — it always can be. Paul warned against philosophy and logic? Perhaps. But on the other hand, we know that the our Lord Jesus Christ, who is the Second Person of the Trinity and the divine ¸ ª  or Reason, was himself a logician. It is Augustine who says so, invoking the Gospel of Matthew xxii 21 (see c Crescon I xvii 21). According to Eusebius, the prophets too were versed in logic: If you are willing to take their books in your hands and read with diligence, you will find that throughout the prophetic writings the discipline of logic is treated in a manner appropriate to their wisdom and to their mode of expression. (PE XI v 5)3

The apostate emperor Julian was outraged: Eusebius, a wicked man, ... claims that the discipline of logic was known among the Hebrews — although the very name of logic is something which he has learned from the Greeks. (c Gal 222A)1 [62] 1 hunc dialecticum ... non legisse quidem ŒÆŪ æÆ Aristotelis, non æd æÅ
Æ, non I
ƺıØŒ, non saltim Ciceronis   ı. ... frustra ergo Alexandri verti commentarios; nequiquam me doctus magister per Nƪøª
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But Julian’s was a voice crying in the wilderness. In truth, whether they spoke for or against logic, the Church Fathers were inclined to exaggerate. Their rhetoric was effervescent: the truth — as so often — was flat. Clement of Alexandria had said all that needed to be said. First, you must distinguish between rhetoric and dialectic: He who judges everything by reference to the moral life, taking his exempla both from the Greeks and from the barbarians, is an experienced skilled seeker for truth ... He will be able to distinguish sophistry from philosophy, cosmetics from gymnastics, the art of the pastry-cook from the art of the physician, rhetoric from logic. (strom I viii 44.2)2

Philosophy, gymnastics, medicine, logic — there are four arts which an intelligent Christian will exploit. But a certain caveat must be noticed; for now we have a good supply both of arguments and of deeds, each supporting the other — but we must utterly reject the art of eristics and sophistry. (I x 47.2)3

Eristics and sophistry: that is logic, but a logic perverted to bad ends, a logic to be avoided. It is one thing to accept Aristotelian logic, the theory of categories included, and another to use it. For those Platonists who taught Aristotelian logic, it was essentially a propaedeutic to the study of Plato: in order to follow the arguments which Plato sets before his readers, in order to unmask the sophisms which Plato’s adversaries have invented against him, in order to construct the syllogisms which will turn philosophy into a genuine science — to do all that, it was necessary first to master and then to apply logic. The Christians of the Byzantine period studied logic for the same sort of reasons: Aristotle’s logic was to serve as a propaedeutic to the study of the Holy Scriptures.4 According to John of Damascus, the theory of categories had such a function [63] — it was both propaedeutic and prophylactic.1 Five centuries earlier, Origen had expressed similar notions. The description 2 › b æe e

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which Gregory the Thaumaturge gives of Origen’s teaching includes this passage: He educated in a logical fashion that part of our soul which judges expressions and arguments — not by way of the judgements of the great orators as to whether something is Greek or barbarous as far as its style is concerned (that is a trifling and dispensable piece of learning). What he taught is absolutely indispensable for Greeks and barbarians, for the learned and the laymen, and quite generally ... for all men in whatever way of life they may be, given that for anyone who is discussing any subject whatsoever it is a matter of importance not to be misled. And logic alone can ensure success in that area. (ad Orig vii 106–109)2

It is absolutely indispensable for everyone — and hence for Origen’s pupils who were going to study Scripture and devote themselves to theology — to master logic. Gregory does not mention the Categories in particular. But it is a safe bet that Origen had read them — and that his students learned about the doctrine of categories. Logic was indispensable to students of the Bible and to theology. It might be wondered exactly how logic could help the amateurs of divinity; and in particular, it might be wondered exactly what the doctrine of categories had to say to Christian savants. But first I shall turn briefly to another and more concrete issue.*

Translation Eunomius had — perhaps — read Aristotle’s Categories; and if he had read them, then he read them in Greek. Jerome read the Categories, and several other logical writings: did he read them in Greek? Perhaps — but the answer, so far as I know, is unsure. Augustine read the Categories, according to the story he tells in his Confessions (IV xvi 28–29); and although there is no obligation to believe everything which that saint confesses, no doubt

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Å YºÅå. * See below, p.[71].

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Augustine had read the Categories — and no doubt he read them in a Latin version.3 And in that case there was a Latin version of the Categories for Augustine to read. In the passage in his Institutions in which he mentions [64] Aristotle’s categories, Quintilian refers to PÆ which Plautus calls essentia (and there is certainly no other Latin word for it). (III vi 23)*

Plautus — Lucius Sergius Plautus — is also mentioned by Pliny and by Apuleius, each time for his translations of Greek technical terms. According to Quintilian, Plautus proposed ‘essentia ’ as a translation of ‘ PÆ’: he did so in the context of Aristotle’s theory of categories — and so, perhaps, in the course of translating the Categories into Latin? Plautus’ ‘essentia ’ translates the Greek name of the first of the ten sorts of predicate. As far as the other nine are concerned, Quintilian lists them under Latin names without reporting the Greek term or referring to any translator. It has been inferred that the other nine categories did not get their Latin names from Plautus; and in that case, of two things one: either Plautus translated only the name of the first category, letting his successors worry about the other nine; or else a Latin version of the names of the ten categories existed before Plautus, and he proposed a new translation for the name of the first category. In either case, it is clear that the Aristotelian categories had been given Latin names well before Quintilian’s day. But was there a Latin translation of the Categories? To the best of my knowledge there is no surviving trace of such a thing — unless this passage from Quintilian is a trace. Another text, much later than Quintilian, refers explicitly to a Latin translation of Aristotle’s work. The standard edition of Cassiodorus’ Institutions contains the following passage: The rhetorician Victorinus translated the Isagoge, and the noble Boethius published a commentary on the text in five books. The same Victorinus translated the Categories, on which he himself made a commentary in eight books. (inst II iii 18 [128.14–17])2 3 See A.J.P. Kenny, ‘Les Cate´gories chez les Pe`res de l’E´glise latins’, in Bruun and Corti, Cate´gories, pp.121–133, on pp.124–128 (cf above, p.[28]). * ... PÆ
quam Plautus essentiam vocat (neque sane aliud est eius nomen latinum). 2 Isagogen transtulit Victorinus orator; commentum eius quinque libris vir magnificus Boethius edidit. Categorias idem transtulit Victorinus; cuius commentum octo libris ipse quoque formavit. — R.A.B. Mynors (ed), Cassiodori Senatoris Institutiones (Oxford, 1937).

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The text is clear and unambiguous: Marius Victorinus, rhetor urbis Romae, who converted to Christianity in about 355, [65] translated the Categories. And in the next few lines it is reported, again with neither ambiguity nor obscurity, that Victorinus translated the de Interpretatione, that he wrote on hypothetical syllogisms and on definitions, and that he composed a commentary in four books on Cicero’s Topics.1 The text is clear — but did Cassiodorus write it? The textual history of the Institutions is peculiarly intricate; and the intricacies affect our present concerns. The manuscripts fall into three clearly defined groups. I have cited II iii 18 according to group (. In the other two groups, ! and ˜, the passage looks rather like this: The patrician Boethius translated the Isagoge on which he left two commentaries. The same patrician Boethius translated the Categories on which he himself wrote a commentary in three books.2

Victorinus’ Categories has disappeared; and the Latin Categories was done by Boethius, a century and a half later. Moreover, in ! and ˜ the name of Victorinus is entirely absent from II iii 18. The situation is puzzling. Two sets of questions may be distinguished, one set concerning the textual history of the Institutions and the other set turning about the historical reliability of the text in (. The two sets of questions are not, of course, entirely independent; but it is only the second which concerns me here. The text according to ( tells us three things about Victorinus: he translated Porphyry’s Isagoge; he translated Aristotle’s Categories; he wrote a commentary on the Categories in eight books. The first claim is correct: we know that Victorinus translated the Isagoge — or at the very least, translated some parts of it; for Boethius used Victorinus’ translation for the first of his two commentaries on Porphyry’s work. Moreover, there is independent and unimpeachable evidence that Victorinus wrote a commentary on Cicero’s Topics, a treatise on definitions, and something on hypothetical syllogisms. So why not conclude that — however the text of ! and ˜ is to be explained — the text of ( is historically reliable? Now we possess an early Latin Categories to which the manuscripts give the title ‘Treatise on Aristotle’s categories’. It isn’t a treatise on Aristotle’s 1 On Victorinus, see P. Hadot, Marius Victorinus: recherches sur sa vie et ses œuvres (Paris, 1971) — for the passage in Cassiodorus, see pp.105–113. 2 Isagogen transtulit patricius Boethius, commentaque eius gemina derelinquens. Categorias idem transtulit patricius Boethius, cuius commenta tribus libris ipse quoque formavit.

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categories — nor on Aristotle’s Categories. It used to go under the nickname of ‘Paraphrasis Themistiana ’ [66] — for it was held to be a translation of a Greek paraphrase of the Categories made by Themistius. But it isn’t a translation of anything by Themistius. In fact, the author of the Ten Categories — for that is what the work is usually called now —explains that his aim is not to translate everything Aristotle has said but rather to set out more clearly those parts which seemed obscure to beginners. (lxx [149.1–2])1

Up to the end of the tenth century Aristotle’s doctrine of categories was known in the West by way of this text. Alcuin, who copied it into his Dialectica, attributed it to Augustine. The attribution is mistaken; but the date which attribution implies is roughly correct — for the author mentions Themistius as ‘the learned philosopher of our age [erudito nostrae aetatis Themistio philosopho]’ (xx [137.20–21]; cf clxxvi [175.18–19]). Some scholars have ascribed the work to Vettius Agorius Praetextatus; others have suggested that it was written by Albinus, a man otherwise unknown; yet others have supposed that the Ten Categories is none other than the translation of the Categories which the ( manuscripts of Cassiodorus’ Institutions ascribe to Marius Victorinus.3 Marius Victorinus is not an obscure figure. The group ( apart, nothing is heard of his translation of the Categories, and nothing of any commentary from his hand. That loud silence tells rather against the view that he is the author of the Ten Categories — and, more generally, against the notion that he translated and commented upon Aristotle’s work. But however that may be, we have in the Ten Categories a Latin version, if not a Latin translation, of Aristotle’s work which dates from the second half of the fourth century. The other groups of manuscripts of the Institutions mention a translation of the Categories and a commentary on the work by Boethius. The translation and the commentary still exist. The translation was a part of the summa logica which Boethius had proposed to translate from Greek into Latin; and the parts of the summa were to have Latin commentaries attached to them. The commentary on the Categories is dated by Boethius to the year of his 1 ... non transferre omnia quae a philosopho sunt scripta ... , sed ea planius enarrare quae rudibus videbantur obscura. — For the text, see L. Minio-Paluello, Aristoteles Latinus: I 1–5 — Categoriae (Bruges, 1961). 3 See Kenny, ‘Les Cate´gories ’, pp.130–133; and cf Minio-Paluello, Aristoteles Latinus, pp. LXXVII–LXXX.

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consulate — and thus to 510 (see in Cat 201B). On the first and third parts of the summa — that is to say on Porphyry’s Isagoge and on Aristotle’s de Interpretatione — Boethius made two commentaries, a short and a long. It is possible that he did the same, or intended to do the same, on the second part of the summa. It is even possible that we possess a fragment of his second commentary on the Categories.5 Boethius’ originality and his modus operandi have excited a lively discussion. Two things seems to be beyond doubt: first, Boethius did not use the commentaries of his Greek contemporary Ammonius; and secondly, that he took a vast amount from Porphyry — indeed, thanks to Boethius we can recover the general lines of the lost final part of Porphyry’s shorter commentary on the Categories. [67] At the end of the tenth century Boethius’ translation of the Categories supplanted the Ten Categories and became the chief source of mediaeval knowledge about the theory of categories. But there were other Latin translations of Aristotle’s work, the most celebrated being the one done by William of Moerbeke in the thirteenth century.1 Moerbeke, one of nature’s stakhanovites, also translated into Latin Simplicius’ commentary on the Categories. The Categories was translated not only into Latin: we have an Armenian version — ascribed, like all such things, to David the Invincible, and dating from the fifth century.2 We have three Syriac translations, the earliest of which was done in the sixth century. And there is a more celebrated Syriac translation which is now lost: it was made in the ninth century by Hunayn ibn Ishaq, whose son, Ishaq ibn Hunayn (he died in 910), translated it into Arabic. The Arabic version has survived.4

5 Boethius’ translation has been edited by Minio-Paluello, Aristoteles Latinus. On the commentaries, see M. Asztalos, ‘Boethius as a transmitter of Greek logic to the Latin west: the Categories ’, Harvard Studies in Classical Philology 95, 1993, 367–407. For the supposed fragment of the second of Boethius’ commentaries, see P. Hadot, ‘Un fragment du commentaire perdu de Boe`ce sur les Cate´gories d’Aristote dans le codex bernensis 363’, Archives d’histoire doctrinale et litte´raire du Moyen Aˆge 26, 1959, 11–27 [¼ Plotin, Porphyre: ´etudes ne´oplatoniciennes (Paris, 1999), pp.383–410]. 1 Edited by Minio-Paluello, Aristoteles Latinus, pp.81–117; cf Bode´u¨s, [Cate´gories], pp.CLXXI– CLXXII. 2 See Bode´u¨s, [Cate´gories], pp.CLVII–CLXI; and on the Armenian tradition more generally, see V. Calzolari, ‘David et la tradition arme´nienne’, in V. Calzolari and J. Barnes (eds), L’Œuvre de David l’Invincible et la transmission de la pense´e grecque dans la tradition arme´nienne et syriaque, Philosophia Antiqua 116 (Leiden, 2009), pp.15–36. 4 On the Syriac and Arabic translations, see H. Hugonnard-Roche and A. Elamrani-Jamal, ‘L’Organon: tradition syriaque et arabe’, DPhA I, pp.502–528.

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Those translations encouraged, and were perhaps accompanied by, commentaries and other sorts of secondary literature. For example, at the beginning of the sixth century Sergius of Res’aina wrote a logical treatise in Syriac: its second book is a paraphrase of the Categories. Again, there was a sequence of Arabic commentaries on the Categories; and if Avicenna insisted — despite the long tradition which the Arabs had inherited from the Greeks — that the Categories has nothing to do with logic,3 nevertheless he wrote, rather unwillingly, a commentary on the work; and his view of the Categories, true though it is, was rejected by all his successors. For the Arabic philosophers, as for the Greek, the Categories constituted the first part of the Organon. But there was a difference: the Arabic Organon was usually a long Organon — our Organon with the Rhetoric and the Poetics added. The long Organon was not an Arabic innovation — it was known to the later Greek commentators; but to the best of my knowledge no Greek text ever took it seriously.* You might think that it made little difference to the Categories whether it introduced a short or a long Organon, [68] or rather that the difference it made was pedagogical rather than philosophical. But that is not so. The short Organon is, in principle, a summa logica. Its final cause is the elaboration of a theory of inference — of a syllogistic — which may be useful both in scientific and philosophical contexts (the Posterior Analytics) and also in other affairs (the Topics). Our Organon interests itself exclusively in propositions which have a truth-value, which are either true or false. Aristotle says as much: Not every saying is declarative; for declarative sayings are those in which truth and falsity are found, and they are not found everywhere. For example, a prayer is a saying but it is neither true nor false. Let us therefore set aside the other sorts of saying (they belong rather to rhetoric or to poetics): here we are studying declarative sayings. (int 17a2–7)1

By ‘here’ Aristotle meant — or rather, was later taken to mean — ‘in the Organon ’; and what he asserts is this: logic, the discipline to which the Organon is devoted, is concerned with only a limited number of sorts of expression. (That, at least, is how a long tradition took this text.) 3 I take this from Bode´u¨s, [Cate´gories], p.XX n.1. * See above, pp.[53–54]. 1 I çÆ
ØŒe b P A Iºº K
fiz e IºÅŁØ
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Påc º ª  
, Iºº h IºÅŁc h łı. ƒ b
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¼ºº Ø IçŁøÆ
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A long Organon does not limit its concerns to declarative sayings. If the subject of a short Organon might be crudely defined as º ª  in the sense of ‘reason’ or ‘argument’, a long Organon might be defined by the same word taken in its sense of ‘speech’ or ‘saying’. A long Organon thus suits a Stoic conception of the nature of logic: As for the logical part of philosophy, some say that it divides into two sciences — dialectic and rhetoric — , and others add a species concerned with definitions, and also one concerning canons and criteria. (Diogenes Laertius, VII 41)2

There were different Stoic conceptions of logic, and different ways of dividing or articulating that part of philosophy. One thing they all have in common is this: they all include rhetoric, and also poetics. And that is one of the chief ways in which the Stoic notion of logic is distinguished from the Peripatetic notion. [69] Al-Farabi’s commentaries on the Categories show that the difference between a short and a long Organon could have heavy consequences.1 Enchanted by translations and by their implications for the transmission and the understanding of the Categories, scholars easily forget that Greek was never a dead language — that the Categories continued to be read in Greek and to be commented upon in Greek up to the end of the Byzantine Empire. Indeed, when we use the phrase ‘mediaeval philosophy’ we tend — or perhaps I should say: I tend — to think of a philosophy the language of which was Latin. If the Byzantine philosophers of the mediaeval period are referred to, such reference is rare and it is a gesture of politeness: the Byzantine philosophy which flourished between, say, 800 and 1450 has been virtually eclipsed by its Latin contemporary. There are surely more reasons than one for that state of affairs. But one reason for the eclipse is a lack of stars: ask a colleague in your Philosophy Department to name two Byzantine philosophers and he will probably change the subject. Not only were there no stars: there were no innovations, no novelties. And yet the Byzantine philosophers were something rather more substantial than glittering stars and something rather more enduring than glib innovators: they were preservers. What God abandoned, these defended: 2 e b º ªØŒe
æ  çÆd

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. Ø
b b ŒÆd N e ›æØŒe
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ø
ŒÆd ŒæØÅæø
. — The ‘’ is Usener’s supplement. 1 See S. Dibler, ‘Cate´gories, conversation et philosophie chez al-Farabi’, in Bruun and Corti, Cate´gories, pp.275–305.

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they gathered up and stored away those fragments of learning which had come down to them; they zealously collected and conscientiously copied ancient texts. The oldest surviving manuscript of the Categories is now in the library of St Mark’s in Venice, where it is known as Urbinus graecus 35. It contains all the pieces of our Organon, preceded, of course, by Porphyry’s Isagoge. It owes its existence to Arethas. Arethas was born in about 865. He had a brilliant career in the Church. He was also a considerable scholar — and, above all, a great patron of scholarship. He wanted a copy of the Organon. In about 900 he put his hands on a text which he was able to get copied. He then began to read his copy, and to annotate it. In the margin of the Isagoge and of the first pages of the Categories there are notes written — or so it is thought — by Arethas himself. [70] The notes do not make a continuous commentary, nor do they represent Arethas’ own thoughts as he read his text. In most cases their source can be identified — they are extracts from the earlier commentaries of Ammonius and Olympiodorus and David. No doubt all the notes were thus copied from earlier work for Arethas did not aspire to write a new commentary on the Categories: he aspired to keep the old commentaries alive.2 What was true of Arethas was true of his colleagues: their ambition was to conserve rather than to create. But it should not be inferred that they were antiquarians or directors of the museum of antique thought. They preserved texts not because of their venerable antiquity but because of their admirable content. If they copied the Categories and commented upon the text, that was because the Categories conveyed important philosophical truths. They were also, some of them at least, modest scholars: whereas it is unamazing that Byzantine commentaries were translated into Latin (omne graecum pro magnifico), it is perhaps a surprise to learn that towards the end of the Byzantine period Greek scholars were prepared to consult and to learn from their Western colleagues. The Urbinus graecus 35 is not the only Greek manuscript to preserve the Categories, and even without the work of Arethas the Categories would have survived. But without the collective efforts of Byzantine scholarship, we would not be reading the Greek Categories today. Indeed, at bottom it is

2 On Arethas, see Ierodiakonou, ‘Re´ception byzantine’; N.G. Wilson, Scholars of Byzantium (London, 1983), pp.120–135. Arethas’ notes are published in M. Share (ed), Arethas of Caesarea’s Scholia on Porphyry’s Isagoge and Aristotle’s Categories, Commentaria in Aristotelem Byzantina 1 (Athens, 1994).

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thanks to Byzantium that Aristotle still exists in Greek. It is agreeable to learn that the last of the Greek commentators on the Categories dedicated his work to the last emperor of Byzantium.

The Categories in the Latin Middle Ages In the West as in the East, mediaeval thinkers were persuaded that the study of theology required a preliminary training in logic — and hence some knowledge of Aristotle’s theory of categories. The mediaeval philosophers of the Latin West lavished time and effort on the interpretation of the Categories: if late antiquity produced a considerable number of commentaries on the work, the Middle Ages produced ten times as many. [71] Logic is the handmaid of theology. But how exactly does she serve her mistress?* Part of the reply to the question is obvious and flat: logic is an instrument of the arts and sciences; theology is a science or an art; therefore logic will aid theology in exactly the same way as it aids the other sciences and arts. There is also another part of the reply, which is specific to theology and which also refers explicitly to the doctrine of categories. For according to mediaeval theologians, there were particular links between logic and theology, and especially between the theory of categories and theology. Logic, that is to say, has a special relationship with theology: it is far closer to theology than it is to geometry, say, or to physics. Alcuin assured Charlemagne that he could refute those people who saw little utility in your most noble intention to learn the lessons of the science of dialectic, lessons which the blessed Augustine in his books on the Holy Trinity judged absolutely indispensable when he proved that the deepest questions about the Holy Trinity cannot be answered without the subtle doctrine of the categories. (de fide Sanctae Trinitatis 415.9–14)1

What are those deepest questions, and how do the subtleties of the categories aid us to answer them?

* I here return to the question mooted above, p.[63]. 1 ... eos qui minus utile aestimabant vestram nobilissimam intentionem dialecticae disciplinae discere velle rationes quas beatus Augustinus in libris de sancta Trinitate adprime necessarias esse putavit dum profundissimas de sancta Trinitate quaestiones non nisi categoriarum subtilitate explanari posse probavit. — I take the passage from J. Marenbom, ‘Les Cate´gories au de´but du Moyen Aˆge’, in Bruun and Corti, Cate´gories, pp.223–243, on p.227.

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The Aristotelian Categories develops a conception of substance, it distinguishes between substantial predicates and non-substantial predicates, it marks the difference between essence and accident. Most of the deepest questions raised by the doctrine of the Trinity, and most of the deepest problems of Christology, turn about issues of substance and of essence. In that way, it must have seemed evident that, in principle at least, the doctrine of categories was pertinent to Trinitarian concerns. And yet those concerns needed both less and more than Aristotle offered them. They needed less: they needed a notion of substance and a notion of essence, and they therefore needed a notion of accident — but the distinctions among nine sorts of accident, which after all occupy a good half of the Categories, was of no direct concern to them. They needed more: in addition to the Aristotelian twins of substance and accident, of PÆ and ıÅŒ , they were obliged to invoke the notions of hypostasis and person, of  ÆØ and æ ø
— and those two notions were unknown to Aristotle and are not hinted at in the the Categories. [72] Another issue which pushed the theologians in the direction of the Categories was the matter of ‘theological predication’.1 Theology is the science of things divine. In order to express the truths of the science, we must therefore be able to speak about things divine — we must be able to make divine predications, to apply predicates to divine subjects. But how can we do that? How can we apply to divine beings predicates which have been conceived in relation to the inhabitants of this mundane world and which are understood essentially by way of such reference? I may say, for example, that God is wise; but how can the predicate ‘wise’, understood by way of its application to withered human sages, be truly — or even intelligibly — applied to a divine Person? The question of theological predication is similar to a question which Plotinus put to the Aristotelians: how can you possibly find in the higher world, in the real world, the ten kinds of being which the Categories distinguishes with reference to this world below?* The two questions are, to be sure, distinct. The theological question is limited to divine subjects, whereas Plotinus’ question concerns all intelligible beings. The theological

1 On which, see A. de Libera, ‘L’onto-the´o-logique de Boe`ce: doctrine des cate´gories et the´orie de la pre´dication dans le de Trinitate ’, in Bruun and Corti, Cate´gories, pp.175–222; S. Ebbesen, ‘Les Cate´gories au Moyen Aˆge et au de´but de la modernite´’, in Bruun and Corti, Cate´gories, pp.245–274. * See above, pp.[43–48].

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question concerns predicates, whereas Plotinus is concerned with kinds of being. Nonetheless, it is plain that there is a similarity between the two questions. If the questions are similar, perhaps their answers are also alike? And in point of fact the answers to Plotinus’ questions have their counterparts in the answers to the question of theological predication. For example, Boethius’ answer to the question of theological predication adapts one of Porphyry’s replies to a question raised by Plotinus. In that way too, then, the Categories had an indirect influence on some of the most urgent questions of mediaeval theology. To be sure, rude shepherds will wonder whether there is any problem to be solved. After all, if I sing ‘Immortal, invisible, God only wise’, why not think that I mean the predicate ‘wise’ in its ordinary everyday sense? Indeed, how could I mean it in any other sense? But theology avoids the roads which rude shepherds and homeward ploughmen plod and prefers to trip delicately along the primrose path to everlasting incoherence. A little later, another theological question, no less pressing, had brought the Categories to mind. During the Eucharist, the bread and the wine change their substance, becoming flesh and blood. But if the substance is different, the attributes are apparently the same — the flesh tastes of bread, not of meat; the blood is not salty but slightly alcoholic. Ever since antiquity theologically minded thinkers had racked their brains over the knotted problems [73] — theological, metaphysical, logical — which the Eucharist raised. One of the problems was this: the particular taste of a piece of bread is an accident, and an accident depends for its existence on the existence of the substance of which it is an accident. As Porphyry put it, an accident is something which can hold or not hold of the same thing, or something which is neither genus nor difference nor species nor property but which always subsists in a subject. (isag 13.3–5)1

But then an accident can’t move from one substance to another — and the Eucharist is an impossibility. The question of the transference of accidents, or of sensible qualities, was not noticed by Aristotle; but it was raised, and minutely discussed, by the commentators on the Categories. Once again, the Categories indirectly came to the aid of theology. 1 ıÅŒ  KØ
n K
åÆØ fiH ÆPfiH æåØ
j c æåØ
, j n h ª
 Kd
h ØÆç æa h r   h YØ
, Id  KØ
K
 ί
fiø çØ

.

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In one way or another, Aristotle’s categories were part of mediaeval theological thought. And yet it might justly be said that, in each of the cases I have just mentioned — and no doubt in any other similar cases there may be — , it is not the doctrine of categories itself which is in play: certain passages in the Categories were indirectly important in theological controversies; certain questions which had been discussed in the margins of the Categories had a connection with certain theological questions. But as to Aristotle’s doctrine of categories — his theory according to which every simple predicate falls into exactly one of ten general classes or kinds of predicate — , that doctrine might have been forgotten or abandoned without any harm to the mediaeval theologians. Yet such is the force of blind tradition that when Lorenzo Valla dared to doubt the doctrine of categories, he was accused — or so it is said — of heresy.2

Twenty centuries on What had been heresy on Valla’s part became orthodoxy for his inheritors. The new philosophers, who rejected Aristotelianism, and with it Aristotle’s logic, would have nothing to do [74] with his doctrine of categories. Not that they rejected the very idea of a theory of categories. On the contrary, many of the enlightened philosophers thought that their philosophy would scarcely be complete without some theory of categories: they replaced Aristotle’s oldfangled theory with something more snazzy. And numerous snazzy new versions were produced: in the nineteenth century German philosophers manufactured refined versions for the learned; and in the degenerate twentieth century Lenin constructed a theory of categories for the proletariat.1 I may rapidly notice two of the more celebrated such things. In Kant’s Critique of Pure Reason there is a section entitled ‘On the pure concepts of reason, or on categories’. Kant sketches his own ‘table of categories’. He assures us that it is systematic and that it is grounded on a rational principle of division. He explains that 2 I learn this from B.P. Copenhaver, ‘Translation, terminology and style in philosophical discourse’, in C.B. Schmitt and Q. Skinner, The Cambridge History of Renaissance Philosophy (Cambridge, 1988), pp.77–110, on p.105: Copenhaver doesn’t give his source. 1 For details, see H.M. Baumgartner, G. Gerhardt, K. Kohnhardt, and G. Scho¨nrich, ‘Kategorie, Kategorienlehre’, in J. Ritter and K. Gru¨nder (eds), Historisches Wo¨rterbuch der Philosophie 4 (Darmstadt, 1976), pp.714–776.

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these concepts we shall, with Aristotle, call ‘categories’; for our design is, in its origins, the same as his, though diverging widely from it in the manner of its development.

Kant adds, graciously, that we shouldn’t blame Aristotle for his errors. To be sure, the division he presented was empirical, it had no foundation in reason, it was completely mistaken — in short, it should be tossed into the wastepaper basket. Nonetheless, Aristotle had, in a very approximate way, anticipated Immanuel Kant; and that was no mean achievement. (See Critique, A 80–82 ¼ B 105–107.) John Stuart Mill was less generous than Kant. Before outlining his own theory of categories, or of classes of ‘things denoted by names’, Mill adverts to Aristotle’s categories. He lists them. He dismisses them: The imperfections of this classification are too obvious to require, and its merits are not sufficient to reward, a minute examination. It is a mere catalogue of the distinctions rudely marked out by the language of familiar life, with little or no attempt to penetrate, by philosophic analysis, to the rationale even of common distinctions. (System of Logic I iii 1)

Like Kant, Mill holds that Aristotle’s theory is somehow ‘empirical’. Unlike Kant, Mill has nothing against empiricism. In Mill’s view, Aristotle’s theory goes wrong because it is a shoddy piece of empirical work. Aristotle took his material from the man in the street — more precisely, his empirical data consisted of [75] certain contingent features of the Greek language as it existed in his day. The animadversions of Kant and of Mill are severe. They are also unpersuasive. Moreover, the theories they offer as superior replacements for Aristotle’s doctrine are themselves of dubious value. What is more, they are not, except in the loosest of senses, replacements: they are classifications; but they do not classify what Aristotle tried to classify — or at any rate, they do not classify what the traditional Porphyrean version of Aristotle’s doctrine purported to classify. Quite generally, a modern philosopher who talks about categories does not mean by the word ‘category’ what Aristotle meant by the word ‘ŒÆŪ æÆ’. Modern categories are not predicates: they are categories in the normal English sense of the word — classes or kinds of things, whether of expressions or of concepts or of things. And when such modern philosophers nod, as they usually do, to Aristotle, it is a nod of politeness, a piece of lip-service.

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Modern philosophy did not destroy Aristotelianism; and in particular, traditional logic, of which the Aristotelian categories formed an integral part, continued to be taught in the schools and universities — taught as a piece of ¨ berphilosophy, not as a piece of ancient history. In Germany, Friedrich U weg’s System der Logik contained an account of the Aristotelian doctrine of ¨ berweg treats categories, and also a history of modern theories of categories. U Kant — of course — with the respect which any German philosopher requires. But he is naughty with the English Mill. And in any event, he does not hide his own view — that, whatever Kant and Mill may have thought, modern logic cannot afford to ignore Aristotle and his categories.1 In England at about the same time, H.L. Mansel, Fellow and Tutor of St John’s College, Oxford, put together a new edition of the Artis logicae rudimenta of John Aldrich, which had first appeared in the sixteenth century and had remained ever since a textbook for Oxford undergraduates. The Rudimenta are of course based on Aristotle. But they do not contain a theory of categories. Mansel added ten appendices to his new edition. The second is called ‘On the Categories’: Mansel there explains Aristotle’s theory and defends it against the objections of Kant and of Mill.2 ¨ berweg and despite a hundred other tradiDespite Mansel and despite U tionalists, the theory of categories has disappeared from modern treatments of logic: it is no longer an essential chapter in any Introduction to Logic, it is no longer drummed into the reluctant heads of tiros. It has no part to play in Frege’s logic, and Frege’s logic is the starting-point for contemporary logic. To be sure, the Categories has never lost its importance for historians of philosophy — how could it do so? — and Aristotle’s doctrine of ten categories is [76] still a lively subject of interest and debate among scholars who are interested in Aristotle’s philosophy and in the Aristotelian tradition. But the doctrine is no longer a part of philosophy. The history of the Categories and of Aristotle’s doctrine of categories is a history of triumph and disaster: more than two millennia of triumph — and then nemesis. Is the history a tragedy? Is nemesis the final scene? I imagine that it is — but it is no doubt foolish to speculate about where philosophy may turn in the next hundred years, or in the next ten. And it may also be observed that the millennia of triumph were, to some degree at least, a sham ¨ berweg, System der Logik (Bonn, 18825). 1 F. U 2 H.L. Mansel, Artis logicae rudimenta from the text of Aldrich, with notes and marginal references (Oxford, 18522) — I have not seen the first edition.

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and a fiction. The categories were, in Galen’s phrase, the first elements of logic — and yet they were never of any real significance for the Aristotelian logic which did indeed have a triumphant career. The categories were invoked by philosophers and theologians in a variety of contexts, and to serve a variety of supposedly profound lucubrations — and yet what was invoked was never in fact the doctrine of categories itself. Beneath the triumphal vestments, the doctrine of categories was half-dead. It is now, I suppose, as dead as the dodo. I like dodos.

Appendix The Bude´ Categories has a vast introduction, a bibliography, a text with double apparatus and facing translation, miscellaneous notes (divided between foot and end), three appendixes, and a thematic index. In his Introduction, the editor, Richard Bode´u¨s, urges that Cat is not a lacunose treatment of the ten ‘categories’; ‘for nothing authorizes us to believe that the original text of our treatise contained accounts of any category whatever after the study of quality’ (p.141 n.1). Rather, it is an introduction to certain dialectical issues; as such it exhibits a ‘perfect unity’ (p.XLII n.2); and its rightful title is ‘—æe H
 ø
’, or ‘Before the Commonplaces ’. Those are bold assertions. I take them up in turn. The text is not lacunose. Bode´u¨s contends that the passage at 11b8–17 is a misguided attempt to turn Cat into a treatment of the ten categories, not an attempt to fill a lacuna in some ancient MS of the work. It is, in any event, an interpolation. But does not the paragraph at 11b1–8 indicate that Cat originally said something about at least one of the ‘missing’ categories, namely the category of doing and undergoing? Minio-Paluello wanted the lines transposed to follow 11a14, and that is where Bode´u¨s prints them. (If POxy 2403 shows that the MS order goes back to the third century ad, that merely proves that the displacement is ancient: p.284 n.117; cf pp.CXL, 140 n.1.) But unlike Minio-Paluello, Bode´u¨s does not suppose that there are lacunas after 11a38 and b8. Moreover, he holds that 11a15–16 — ‘Well, as for the genera which were set down earlier, what has been said is sufficient’ — do not form part of the interpolated passage; and they refer not to the ten items set down at 1b25–27 but rather to the four items (substance, quantity, relatives, quality) which have just been discussed. So that the text as it stands — as it stood before the interpolator got to work — is unimpeachable.

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I cannot believe that Bode´u¨s is right: 11a15–16 is clearly the penultimate sentence of the interpolation, and it patently refers to the list at 1b25–27. (Nor — though this is another and a larger matter — do I find persuasive Bode´u¨s’ arguments in favour of the ‘perfect unity’ of Cat. But had he contended, more modestly, that Cat has as much unity as many other Aristotelian works, it would be difficult to gainsay him.) Cat is a preface to certain dialectical matters. In section 3 of his Introduction, Bode´u¨s finds some striking similarities between Cat and Met ˜ — and also enough dissimilarities to suggest that the two essays belong to different fields of endeavour, Cat being a work of dialectic (pp.LIX, LXI, LXIV; cf CLXXXVII). Hence section 4 turns to Top, between which and Cat it records numerous links. So perhaps Cat was written as an introduction to Top? Or, better, to a work similar to Top — say, to the lost ) ØŒH
æe  f ‹æ ı? On the other hand, the preliminary pages of Cat ‘were, it seems, composed almost entirely from elements literally drawn from the Topics ’ (p.LXXIII; cf LXXV). So it is Top which prepares for Cat, not the other way about: ‘the teaching of the Topics provided the author of Cat with a starting-point for the development of an original essay on substance’ (p.LXXIX). Or did it? Some pages later Bode´u¨s repeats the thesis that Cat was written as an introduction to a topical work (p.LXXXVI; cf LXXXIX), and that appears to be his final conclusion. No doubt Cat is dialectical — in a sufficiently stretched sense of that most elastic of terms. But, as Porphyry said (in Cat 56.24), it is no more a —æe H
 ØŒH
than it is a —æe H
I
ƺıØŒH
; and in point of fact it is neither. The rightful title of Cat is ‘—æe H
 ø
’. Bode´us claims that the modern title, ‘˚ÆŪ æÆØ’, or ‘Predications ’, was given to the work by Andronicus. Andronicus certainly called the work ‘˚ÆŪ æÆØ’; but no text, so far as I know, states — or even suggests — that he invented the name (pace e.g. pp.XXV, XXVI, XXXIII). Porphyry, who discusses the question of the title, does not notice ‘—æe H
 ø
’. But he does report that some had called the work ‘—æe H
 ØŒH
’ or ‘Before the Topics ’ (in Cat 56.18–31); and a passage in Boethius’ commentary — which no doubt derives from Porphyry — shows that this title was known to, and disliked by, Andronicus. (See in Cat 263BC: the text is difficult, and Boethius cannot have written what is printed in Migne’s edition; but its general drift is clear.) But nothing, so far as I can see, suggests that ‘—æe H


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 ØŒH
’ was the standard title before Andronicus. (Simplicius, in Cat 15.36–16.13, says that Adrastus, in his essay On the Order of Aristotle’s Writings, placed Cat immediately before Top. That perhaps suggests — but Simplicius does not say — that, despite Andronicus, Adrastus favoured the title ‘—æe H
 ØŒH
’.) As for ‘—æe H
 ø
’, it first appears in a passage in Simplicius’ commentary in which he says that ‘some scholars, among them Andronicus, say that were added on at the end, against the plan of the book, by someone who had entitled the Categories ‘Before the Topoi ’ (in Cat 379.8–10). It is difficult not to associate that passage with the report in Boethius that Andronicus disliked the title ‘Before the Topics ’. In that case we should correct the text of Simplicius: read ‘—æe H
 ØŒH
’ for ‘—æe H
 ø
’. And in any event, that correction should be made; for in his discussion of the different titles of Cat Simplicius has ‘—æe H
 ØŒH
’ three times — in Cat 15.28, 30, and 16.14 — and never ‘—æe H
 ø
’. Later, Ammonius, in Cat 14.20, Olympiodorus, in Cat 22.34, 134.2, 7, Elias, in Cat 132.26, 133.3, 241.30, and Arethas, in Cat 136.12–13 all allude to ‘—æe H
 ø
’ (Arethas saying that it was used by Adrastus). But all those texts, which are not, of course, independent of one another, are patently confused in one way or another (as Bode´u¨s observes: p.XXXIV n.4); and it would be rash to suppose that they have preserved a rare fragment of truth which escaped the eye of Porphyry. Bode´u¨s also notes that the title ‘—æe H
 ø
’ appears in two of the catalogues of Aristotle’s works (Diogenes Laertius, V 24; [Hesychius], vit Arist [item 57]). It also appears in a list of Theophrastus’ works (Diogenes Lartius, V 49): Bode´u¨s urges that there was a single work ‘attributed now to Aristotle and now to Theophrastus because its author was not exactly known’ (pp.CIV–CV). However that may be, Bode´u¨s finds here evidence — indeed, ‘the earliest evidence’ — that Cat was called ‘—æe H
 ø
’ (pp.XXXIII–XXXIV); and he refers to ‘the ancient lists of Aristotle’s works according to which ‘a æe H
 ø
served as an introduction to ) ØŒH
æe  f ‹æ ı’ (p.LXXII). Diogenes Laertius has the one title immediately before the other; but he does not present the one as an introduction to the other. Nor is there any reason to identify the —æe H
 ø
of the catalogues with Cat. Quite the contrary: Alexander knew ‘—æe H
 ø
’ as a name for Top ` for which it is, of course, a highly appropriate name (in Top 5.27–28, cf Moraux, Listes, pp.57–65).

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Bode´u¨s’ argument is never less than ingenious, and the texts are slippery. But there is no case for holding that ‘—æe H
 ø
’ was an early title for Cat, let alone the author’s title. In section 7 of the Introduction, Bode´u¨s turns to the text. There are over 160 MSS of Cat, some 50 of them being earlier than the fourteenth century. For his Oxford Classical Text, Minio-Paluello used two of these: Bode´u¨s, who has collated all 50, uses eleven. He divides the 50 into five families, it being impossible to establish a stemma (p.CLXXIII); and he refers to his chosen eleven as ‘the principal witnesses’ (p.CXII). It is irritating that his full account of all this is published elsewhere (p.CXII n.1). In addition to the mediaeval MSS, there are three scraps of papyrus, discovered after Minio-Paluello’s edition.* And there is the indirect tradition — the evidence of the Greek commentaries and of the early translations. Bode´u¨s is more generous than Minio-Paluello in his references to the indirect tradition, but he has a lower estimate of its value. (See pp.CLI–CLII; cf CLXXV, CLXXXII.) He is right to insist that it is often difficult to ascertain exactly what text the tradition supposes. But he is wrong when he asserts that, given five independent families of MSS, then, ‘rich though it is, the indirect tradition is only useful for the establishment of the text in very rare cases — and even then its utility consists, without exception, in supporting a known reading which looks authentic in its own right’ (p.CLXXVI). Minio-Paluello thought the indirect tradition to be independent of a, the archetype of the mediaeval MSS. If that is so, then a reading offered by Porphyry or Boethius is equal in weight, ceteris paribus, to all the readings in all the MSS, however many families they divide into. Bode´u¨s agrees that the indirect tradition is independent of a (see pp.CLIII, 254, 277; cf p.CLXVI.) He ought therefore to share Minio-Paluello’s evaluation of it. And in practice he does: his Cat differs from Minio-Paluello’s in more than 170 places. He claims that this is ‘the effect of the attention which we have given to a far richer MS tradition’ (p.CLXXXIV). But, on my count, there are only four places where Bode´u¨s prefers a MS reading and Minio-Paluello the indirect tradition, and on more

* POxy 2403 — a new edition in Corpus dei Papiri Filosofici greci e latini I 1* (Florence, 1989), pp.256–261. Bode´u¨s follows the papyrus twice. At 11a35 he prints ‘ŒÆŁ’ –æ’, where the rest of the tradition divides between ‘ŒÆŁ –’ and ‘ŒÆŁ –  ’. He says that ‘the reading of the papyrus is very certainly the right one’ (p. 285 n.121): why? At 11a36–37 he prints ‘ ’’ rather than ‘ ’, ‘NØ
’ rather than ‘NØ’, and ‘ÆPe ŒÆ’ rather than ‘e ÆP ’. He does so ‘simply on principle’ (p.285 nn.122–123 — what principle?). The additional ‘ŒÆ’ is significant, and might be correct. For the other two (wholly trivial) items neither papyri nor MSS have any weight, contrary to what Bode´u¨s implies both here and elsewhere.

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than a dozen occasions Bode´u¨s gives more weight to the indirect tradition than does Minio-Paluello. A striking example of that last phenomenon occurs in the second line of the text. At 1a2 (and again at a4, a7, and a10), where Minio-Paluello, with all the MSS, reads ‘› º ª  B PÆ’, Bode´u¨s follows Waitz and reads simply ‘› º ª ’. He does so because he thinks that was the reading of Andronicus and of Boethus, and hence the oldest known form of the text. Why does he think that it was the reading of Andronicus and Boethus? Minio-Paluello writes in his apparatus to 1a2: ‘B PÆ ? om. Andronicus et Boethus testibus Porph. et Dexippo’; Bode´u¨s refers to Porphyry, but not to Dexippus, and he writes ‘om.’ rather than ‘? om.’. Dexippus says this: First, the expression ‘› b º ª  B PÆ’ is not added in all the manuscripts, as Boethus and also Andronicus report. (in Cat 21.18–19)*

Minio-Paluello’s reference to Dexippus is thus true — but it might reasonably be regarded as misleading. In any event, Dexippus is drawing on Porphyry’s longer, and lost, commentary on Cat; and he misread his text. For Simplicius says that Porphyry says that first, this [sc ‘B PÆ’] was not written in all the manuscripts; for, he says, Boethus does not know it ... and, though he explains the text word by word, Boethus leaves out ‘B PÆ’ as though it were not written; and Andronicus paraphrases as follows ... (in Cat 29.29–30.5)**

Andronicus and Boethus did not say that the phrase was missing from their MSS; rather, Porphyry infers that it was missing inasmuch as Boethus, who is a punctilious commentator, does not explain the phrase, and Andronicus does not have anything answering to it in his paraphrase. Porphyry’s inference is evidently frail insofar as it concerns Andronicus — the more so in that Porphyry himself insists that it makes no odds whether you say ‘› ŒÆa  h
Æ º ª ’ or simply ‘› º ª ’ (in Cat 68.15–18). The inference concerning Boethus is stronger — but of course we have no means of controlling it. Plainly, Minio-Paluello’s cautious ‘? om.’ is better than Bode´u¨s’ categorical ‘om.’. Myself, I doubt if the expression ‘B PÆ’ was * æH
b
s
PΠK
–ÆØ  E I
تæç Ø e › b º ª  B PÆ æ ŒØÆØ, ‰ ŒÆd ´ ÅŁ  
Å
Ø ŒÆd 
æ
ØŒ . ** › — æçæØ  æH

çÅØ
Åb K
AØ  F ªªæçŁÆØ  E I
تæç Ø·  ªaæ ´ ÅŁ
N
ÆØ ... ŒÆd KŪ 
 b › ´ ÅŁ  ŒÆŁ ŒÅ
ºØ
e B PÆ Ææƺº Ø
‰ Pb ªªæÆ

· ŒÆd › 
æ
ØŒ  b ÆæÆçæÇø
e غ
...

Aristotle’s Categories

263

missing from any ancient MSS. In any event, we should, with Porphyry, retain it at 1a2 (though I should be tempted to omit it at 1a7 and 1a10). Here are a few more examples of the same phenomenon. At 1b23 Bode´u¨s omits ‘NØ’ with Boethus, Alexander, and Porphyry (p.254 n.5). Alexander, in Top 319.22–23, cites 1b23–24 without ‘NØ’; and Simplicius, reporting Boethus ŒÆa ºØ
(no doubt by way of Porphyry), does not have the verb (in Cat 58.27–29). (And Simplicius himself once gives the sentence without the verb: in Cat 58.24–25.) What should we make of that? Boethus, even if Simplicius reports him word for word, was paraphrasing Aristotle — the lack of the verb in his text shows nothing. Alexander is citing a familiar tag while commenting on another of Aristotle’s works: he was probably citing from memory, and he will scarcely have strained for pedantic precision. Perhaps the ‘NØ’ should go — but there is really little reason for thinking that the earliest texts omitted it. Again, at 2a10 Bode´u¨s follows Boethius’ translation, against allcomers, in omitting ‘
ØŒfi A’ (p.255 n.8). Again, Bode´u¨s transposes 2b5–6 to follow 2a35, claiming the authority of Porphyry (pp.256–257 n.15). Minio-Paluello follows the MSS: earlier editors followed Simplicius, who said that the lines should be deleted (in Cat 88.24–29). The lines are redundant, or worse: I cannot see that Bode´u¨s’ transposition helps much — nor that it is suggested or supported by Porphyry, in Cat 89.16–17. Again, at 2b37 Bode´u¨s adds ‘æÆØ’, claiming to follow Porphyry (pp.257–258 n.19); but although the word does indeed appear at in Cat 92.15–16, Porphyry is there paraphrasing and not citing. Where Bode´u¨s — against his own principles — is more favourable than Minio-Paluello to the indirect tradition, he is, I think, almost always wrong. And indeed, in the vast majority of the 170 differences between the Bude´ and the OCT, I vote for the OCT. Most of the differences are individually trifling in that they do not make any difference to the sense (cf p.CLXXXIII); but the trifles are collectively significant. For Bode´u¨s believes that Cat is a ‘scholastic’ text (cf p.CLXXXV); and in general he will prefer, other things being more or less equal, a reading which gives a simpler text — a text which tolerates a certain amount of repetition and redundancy, which has a ‘natural’ wordorder, and so on. (So, for example, at 12a2–4 there is a sentence which is repeated a few lines later at a9–11: Minio-Paluello excises, Bode´u¨s retains it — ‘given the redundant character of Cat ’ (p.288 n.128).) The result of that general preference — which accounts for three-quarters of the differences between the two editions — is a Cat distinctly unAristotelian in style. But then Bode´u¨s suspects that Cat was not written by Aristotle.

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In section 6 of the Introduction he mentions and scouts various arguments which have been advanced against authenticity; but he is impressed by the fact that Cat neither mentions nor is mentioned by any Aristotelian work, a feature which it shares only with incontestably spurious texts (pp.XX–XXI; CIII); and he also assembles some lexical data which distinguish Cat from other works in the Aristotelian corpus and which therefore shed some doubt on authenticity (pp.CVII–CX). The principle which favours repetition and redundancy adds a further body of evidence against authenticity. Then should we follow Bode´u¨s in his general preference? Should we, that is to say, suppose that copyists are more likely to drop redundancies and repetitions and to complicate word-order than to simplify word-order and to introduce redundancies and repetitions? Surely not. It is violently improbable that a copyist — or a group of copyists — should, either accidentally or deliberately, make a large number of minor changes to a text and thereby produce something which not only makes sense, and makes the right sense, but is also stylistically more Aristotelian than it was before. On the other hand, it is a familiar phenomenon that successive copyings will sometimes produce successively easier texts — and it is quite unremarkable that the phenomenon should show itself in connexion with a school text like Cat. Thus as far as the numerous minor differences are concerned, I think that Minio-Paluello is almost invariably right and Bode´u¨s wrong. Bode´ u¨s’ translation is accurate and close — it aspires to the sort of fidelity characteristic of the Clarendon Aristotle series. True, Bode´u¨s says that he ‘has not hesitated to make explicit things which are elliptically expressed in the Greek’ (p.CLXXXV); but apart from 2a19–21 and 6a30–32, I could find nothing dangerously paraphrastic. On the other hand, Bode´u¨s has decided to translate most of Aristotle’s particles, which makes for heavy reading. Technical and semi-technical terms are usually given their orthodox translations; but ‘imputer’ etc for ‘ŒÆŪ æE
’ etc strikes me as being pointlessly eccentric; nor is ‘quelque chose de pre´cis’ a felicitous version of ‘  Ø’. Again, ‘ 
’ and ‘ Ø
’ are usually given by ‘quantite´’ and ‘qualite´’ (though ‘qualifie´’ is the official version of the latter — but see p.48 n.1). That is, I think, never correct; and it is particularly misleading at 3b10 and b20: ‘man’ does not signify a quality but a qualified so-and-so, i.e. an animal of such and such a sort. Under the text there are two apparatuses. The upper, the function of which is unclear, lists ‘testimonies’. With a single exception, all the passages noted come from Plotinus or from the CIAG; but the richest source for such

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things — the CIAG commentaries on Cat — are not mentioned here: they are listed separately in an appendix (and then by author, not by passage). The single exception is a passage from Quintilian. Antiquity throws up dozens more references to Cat: why is Quintilian singled out for favour? Why not, say, the citations in Didymus (CPF I 1*, pp.289–292)? Or the familiar allusions in Hippolytus, or in Galen? The lower apparatus is an app crit. Bode´u¨s says that it contains ‘only the variants which are most important for the understanding of the text itself’ (p. CLXXXI); but he has a comprehensive idea of what is important. Moreover, the apparatus is positive (although the need for perspicuity obliges Bode´u¨s to admit a few negative entries: p.CLXXX), and it does not make use of the family names of the MSS. The result is thick, forbidding, and difficult to consult. Since all the material — and a little more — is repeated in Appendix II, the reader would have gained much and lost nothing had a more stream-lined apparatus been placed beneath the text. (Bode´u¨s might then have found room for a few conjectures — for example, the palmary correction of 1b23–24, made in antiquity (see Simplicius, in Cat 58.24–60.10) and supported by Ackrill (see p.85 n.3); or, at 14a26, ‘ ººÆåH’ for ‘æÆåH’.*) As for the numerous notes — several of which I have invoked —, most of them are useful and several of them are excellent. If their corporate function is unclear, and if their division between footnotes and endnotes (a division based on no exegetical principle and answering to no typographical exigency) is inexcusably exasperating, Bode´u¨s is not responsible for the general foibles of the Bude´ people. Bode´u¨s’ edition of the Categories represents a vast labour and presents a vast number of facts. It does not replace Minio-Paluello’s OCT; but it complements it. * At 15a16–17, where the transmitted text makes no sense and Minio-Paluello obelizes, Bode´us prints his own conjecture, ‘[ Pb ] øØ’, which he describes as ‘palmary’ (p.300 n.171).

7 Syllogistic and the classification of predicates* I According to Galen, logic is at the bottom of every scientific undertaking, and the theory of predication is at the bottom of logic: First you must have trained yourself in the matter of predications. For according to the bon mot of Arcesilaus, no-one takes a fleece to the fuller’s. There is an order in the teaching of disciplines just as there is in the working of wool: no-one is taught to read before he has learned all his syllables, nor his syllables before he has learned all his letters ... It is the same with logic: before he has trained himself in the first things — in the letters, as it were — no-one can follow the proofs which come next. (diff puls VIII 624).1

The theory of predication is concerned with the elements of logic, which it must try to classify: that is why Galen can say that ‘classifying the predications is the beginning of logical theory’ (meth med X 148).2 So it is unremarkable that in his own Introduction to Logic Galen offers, twice over, a classification of predicates. Galen was a free spirit, proud that he belonged to no philosophical school. But the classification of predicates which he offers is a version, mildly modified, of a celebrated theory of Aristotle’s, according to which there are ten basic sorts of predicate.3 What is more, when he set this classification at * This is a version of a French piece written for a volume which has not yet appeared. 1 ... ªªı
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a ŒÆŪ æÆ Iæåc B º ªØŒB KØ ŁøæÆ. 3 I refer, of course, to what is commonly called Aristotle’s ‘doctrine of categories’. Those who speak of Aristotle’s categories use the word ‘category’ either in its ordinary English sense or else as a transliteration of the Greek ‘ŒÆŪ æÆ’: in the former case, why not say rather ‘class’ or ‘type’ or ‘sort’? In the latter case, why not translate the Greek and say ‘predicate’ or ‘predication’? Either way, it is better to avoid the word ‘category’.

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the bottom of logical theory, Galen adopted an idea which was characteristic if not of Aristotle himself then certainly of Aristotle’s successors, for whom the study of logic should properly begin with predicates, then turn to the propositions which are constituted by predicates, and finally rise to the syllogisms which are constituted by propositions. That Peripatetic idea is realized in the structure of the Peripatetic Organon: first, the Categories,4 which deals with predicates; next, the de Interpretatione, the subject of which is propositions; and then the Analytics, and the theory of the syllogism. That Peripatetic idea became a commonplace of western philosophy, so that for pretty well two thousand years every student of philosophy began his study by conning some version of the Aristotelian theory of ten sorts of predicate.5 So it is not unreasonable to ask what in fact is the relation between syllogistic and the classification of predicates. Before I address that question, two or three preliminary remarks. First, when I speak of a classification of predicates I mean to speak of a theory which organizes into a relatively small number of groups the members of a certain class of expressions.6 A rough characterization of the class might run like this: a Greek expression is a predicate provided that it may replace the word ‘ºıŒ ’ in the sentence ‘øŒæÅ Kd
ºıŒ ’; and an English expression is a predicate provided that it can replace ‘pale’ in ‘Socrates is pale’ or ‘man’ in ‘Socrates is a man’. (One expression ‘may replace’ another in a sentence if the result of the substitution is a grammatically well-formed sentence.) Predicates are represented by the Greek letters ‘A’, ‘B’, ‘ˆ’, ... as Aristotle uses them in the formal account of his syllogistic in the Prior Analytics. Secondly, the question I am concerned with refers to classifications of a fundamentally Aristotelian kind — to classifications based on the sense or meaning of the items classified (and not, say, on any grammatical or syntactical features they may have). They are, you might say, strictly semantic classifications. 4 Or should I say ‘the Predications ’? Perhaps; but I suppose that ‘Categories ’ is the standard English title of the work and not an English translation of the standard Greek title. 5 On the Peripatetic idea, and its shortcomings, see B. Morison, ‘Les Cate´gories d’Aristote comme introduction a` la logique’, in O. Bruun and L. Corti (eds), Les Cate´gories et leur histoire (Paris, 2005), pp.103–119; on the construction of the Organon, see J. Brunschwig, ‘L’Organon: tradition grecque’, DPhA I, pp.482–502. 6 I agree with Porphyry in thinking that the classification discussed in the Categories is best taken to deal with expressions and not with concepts or with ‘beings’; but that view plays no essential part in the argument which I shall develop here. (cf J. Barnes, Truth, etc. (Oxford, 2007), pp.114–123.)

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Thirdly, the question addresses, on the one hand, a classification of that sort and, on the other, the theory of inference: I shall have nothing to say about the importance which a classification of predicates might have for metaphysics, for ontology, for logic taken in a broad sense, ... Nor shall I have anything to say about those parts of the Categories which are not concerned with the classification of predicates — with the antepraedicamenta and the postpraedicamenta. Fourthly, the question is primarily theoretical or philosophical and not historical: I shall have little to say, save per accidens, about Aristotle or about the part which his classification of predicates plays in his thought — or in the thought of his ancient and mediaeval successors. Finally, it is worth giving the question a more precise, or pedantic, formulation. That might be done in several ways. Here is one of them. Take a valid inference which contains, once or more, a predicate ‘P’, which belongs to a given class C.7 Suppose that if ‘P’ is replaced at each of its occurrences by another predicate of class C, then the result is always a valid inference. Then ask — this is the precise version of the question — whether it is possible that there be a predicate ‘P*’ belonging to a different class C* such that if ‘P’ is replaced at each of its occurrences by ‘P*’ then the result is not a valid inference. For example, take the following inference: If Socrates is pale, then Socrates is afraid Socrates is pale Therefore Socrates is afraid The argument is valid. It contains, twice, the predicate ‘pale’. The predicate belongs to Aristotle’s class of ‘qualifieds’ or  Ø. It is evident that if ‘pale’ is replaced at each of its occurrences by another predicate from the same class (by ‘red’, say, or by ‘wise’), then the result will always be a valid argument.8 What happens — this is the question in its precise formulation — if ‘pale’ is replaced by a predicate belonging to some other class? By ‘short’, for example, which belongs to the class of ‘quantifieds’, or by ‘shod’, which belongs to the class of havings?

7 A pedantic reader will rightly object that syllogisms don’t contain predicates inasmuch as predicates are expressions and syllogisms aren’t composed of expressions. Let such readers understand ‘syllogism which contains the predicate ‘‘P’’ ’ to be short for ‘syllogism which contains an element which might be expressed by means of the predicate ‘‘P’’ ’. 8 The replacements may, of course, change the truth-value of the premisses; but that is quite another matter, and one which is of no account here.

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That example is what some ancient logicians liked to call a hypothetical syllogism. Ancient logic generally recognized two sorts of syllogism: there are hypothetical syllogisms and there are predicative or ‘categorical’ syllogisms. Hypothetical syllogistic turned about certain sorts of compound proposition — conditionals, disjunctions, and (sometimes) conjunctions. It was not concerned with the internal structure of simple propositions, nor therefore with the predicates which may be parts of simple propositions. For that reason, if for no other, a classification of predicates can have nothing to do with hypothetical syllogisms. (Replacing ‘pale’ by ‘short’ or ‘shod’ in the example cannot produce anything but a valid inference.) Predicative syllogistic — the syllogistic elaborated in the first part of the Prior Analytics — turned about the predicative structure of propositions. That is why ancient logicians, and their mediaeval and modern successors, thought that an account of predicative syllogistic ought to be introduced by some analysis and classification of predicates: if you have not thought about the nature of predication, and about the different sorts of predicates there are, how can you hope to grasp a theory of inference in which predicates play the star role? At any rate, if the classification of predicates is pertinent to any sort of syllogism, it must surely be pertinent to predicative syllogisms.

II So let us ask this question: is there a predicative syllogism which contains, once or more, a predicate ‘P’ belonging to a class C such that the replacement of ‘P’ at each of its occurrences by another predicate belonging to C always results in a valid argument whereas the replacement of ‘P’ by ‘P*’, which belongs to a different class C*, does not always produce a valid argument? It may seem perfectly evident that the answer is No. In the standard modern predicate calculus, no semantic classification of predicates has any part to play: the letters ‘F’, ‘G’, ... or ‘ç’, ‘ł’, ... , which habitually represent predicative expressions are not differentiated according to any semantic criterion. The same is true of Aristotelian syllogistic: the letters ‘`’, ‘´’, ‘ˆ’, ... , which habitually represent predicates are not differentiated according to any semantic criterion. When Aristotle presents a valid syllogistic form, he never once intimates — let alone states — that its validity might be restricted to a certain range of predicates. Take Barbara:

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When three terms are related to one another in such a way that the last is in the middle as in a whole and the middle is in the first as a whole ... , necessarily there is a perfect syllogism of the extremes.... For if ` is of every ´ and ´ is of every ˆ, it is necessary that ` is predicated of every ˆ. (APr ` 25b32–39)9

No reference there to any particular class of predicates. Of course not. For suppose that Barbara isn’t valid for every class of predicate. Then there will be at least one triad of predicates for which the form is invalid — that is to say, there will be at least one triad of predicates ‘P’, ‘Q’, and ‘R’ such that (1) every P is Q (2) every Q is R whereas (3) there is at least one P which isn’t R. Suppose that the P — or one of the Ps — which isn’t R is the object x. Since, according to (1), every P is Q, the object x is Q. Since, according to (2), every Q is R, x is R. So x is R and x isn’t R. So the supposition that there is a triad of predicates for which Barbara isn’t valid is false. That argument about Barbara is not taken from Aristotle — but it is modelled on an Aristotelian type of reasoning. There are syllogistic forms which Aristotle rejects; or rather, there are certain syzygies — combinations, or couples of propositions — from which, according to Aristotle, no syllogistic conclusion can be inferred. The first example which the Analytics considers is this: If the first term follows all the middle and the middle holds of none of the last, then there will be no syllogism of the extremes. For nothing necessary follows from the supposition that things are so; for it is possible that the first hold of all the last and that it hold of none of the last ... Terms for holding of all: animal, man, horse. For holding of none: animal, man, stone. (APr ` 26a2–9)10

Consider a syzygy of the form: ` holds of every ´, ´ holds of no ˆ. There is at least one triad of terms which satisfies those conditions and which is such that ` holds of every ˆ (every horse is an animal). Hence the syzygy does not imply a proposition of the form 9 ‹Æ
s
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` does not hold of some ˆ, nor, a fortiori, a proposition of the form ` holds of no ˆ. There is also at least one appropriate triad such that A holds of no ˆ (no stone is an animal). Hence the syzygy does not imply a proposition of the form ` holds of some ˆ, nor, a fortiori, a proposition of the form ` holds of every ˆ. That is to say, the syzygy does not imply any of the propositions which, in the context of the Prior Analytics, are possible conclusions to a syllogism. This method of Aristotle’s raises several questions;11 but one thing is plain: the choice of terms does not depend on, or in any way advert to, the class into which Aristotle shoves them. As a matter of fact, the terms invoked in the example I have just given all belong to the class of substantial predicates. But that is, so to speak, an accident — any triads whatsoever will do the trick, provided only that they satisfy the appropriate formal conditions. One of the triads must make true the three propositions of the form ` holds of every ´, ´ holds of no ˆ, ` holds of every ˆ and the other must make true ` holds of every ´, ´ holds of no ˆ, ` holds of no ˆ Given that those conditions are satisfied, nothing else matters — and in particular, the class to which the predicates in the triads may belong has nothing to do with the case. In short, the validity of an Aristotelian syllogism is uniquely determined by the force of certain types of proposition: universal or particular, affirmative or negative. Nothing else is relevant. (Nothing else, I mean, in the case of assertoric syllogisms: in the case of modal syllogisms, there is also the question of the force of certain modal operators, ‘necessarily’ and ‘possibly’. But there too the semantic classification of the predicates plays no role.) The Prior Analytics does not look back to the Categories. Nor, let it be added, does the Categories look forward to the Prior Analytics. For Aristotle’s classification is concerned with a particular sub-class of predicates: it is concerned, uniquely, with simple predicates. It will tell you that the predicate 11 For example, Aristotle’s method does not consider — and hence does not exclude — ‘reversed’ conclusions (‘CxA’ rather than ‘AxC’). Or again, once Aristotle has established that a given syzygy yields a given conclusion, he does not consider whether it may not give other conclusions too. Hence there are gaps in his syllogistic, as it is presented in APr ` 4–6: for example, he fails to notice Fapesmo (a ‘CxA’ case), and Barbari (a case in which a syzygy yields more than one conclusion).

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‘parrot’, say, belongs to the class of substantial predicates and that the predicate ‘blue’ belongs to the class of qualitative predicates. But it will have nothing to say about the compound predicate ‘blue parrot’. That predicate is, so to speak, an amalgam of a substantial predicate and a qualitative predicate — itself it belongs to no Aristotelian class. Predicative syllogistic, of course, is happy to admit predicates such as ‘blue parrot’ — the proposition Every blue parrot is Norwegian has exactly the same status, so far as the syllogistic goes, as the proposition Every parrot is blue. Each is a universal affirmative proposition — and that is the only relevant fact about the things so far as syllogistic is concerned. The letters `, ´, ˆ, ... of the Prior Analytics may represent predicates of any degree of complexity: ‘llama’, ‘white llama’, ‘white llama born in Chile and now living in France’, and so on, and on, and on. Of course, predicative syllogistic applies to simple predicates — but it does not apply to them qua simple. The question of the simplicity of a predicate is not of the slightest pertinence to predicative syllogistic.12 Galen said that the classification of predicates is the foundation of logic, and he was thinking in particular of Aristotelian syllogistic. When he comes to his own presentation of predicative syllogistic, he never once mentions the classification of predicates. Every handbook of traditional logic begins with the ‘theory of categories’ or with the classification of predicates. No handbook of traditional logic mentions the classification once it gets on to the theory of the syllogism. Those are striking facts — which might properly induce a certain melancholy. But they are not mysterious facts: the classification of predicates is not mentioned in the exposition of predicative syllogistic because the classification of predicates has nothing to do with predicative syllogistic.

III Or is that conclusion not too swiftly drawn? Several different sorts of consideration have suggested, or might suggest, that there is a little more to be said about the matter. I shall briefly rehearse four such considerations. 12 Ancient scholars wondered what the criterion of simplicity might be, and they found no satisfactory answer. But their embarrassment is of no account here: however simplicity is to be determined, syllogistic has no interest in it.

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The first of the four introduces a problem familiar to amateurs of Aristotle’s syllogistic, and it bears upon the claim that the syllogistic forms recognized by the Prior Analytics are valid for any predicates whatsoever or that the letters ‘`’, ‘´’, ‘ˆ’, ... represent terms of any grammatical form and any semantic character. Consider, then, the third figure syllogism Darapti: ` holds of every ´ ` holds of every ˆ Therefore ´ holds of some ˆ Take the triad of terms ‘animal’, ‘bird’, ‘bird and not a bird’, and construct a concrete syllogism of that form. The two premisses turn out true; for every bird is an animal, and everything which is a bird and not a bird is an animal. (For everything which is a bird and not a bird is, a fortiori, a bird, and every bird is an animal.) But the conclusion is false. The conclusion says that some things which are birds and not birds are animals — but no things which are birds and not birds are animals, since no things are birds and not birds. If you don’t like the predicate ‘bird and not a bird’, then take the triad ‘animal’, ‘bird’, ‘phoenix’: again, the premisses are true (every bird is an animal and every phoenix is an animal) and the conclusion is false (it is not the case that some phoenixes are animals — for there are no phoenixes at all). Aristotle thinks to prove the validity of Darapti by reducing it to the first figure Darii. The reduction relies on the rule of conversion according to which from ‘` holds of every ´’ it may be inferred that ‘´ holds of some `’. But take ‘bird’ for ‘`’ and ‘bird and not a bird’ (or ‘phoenix’) for ‘´’. Everything which is a bird and not a bird is a bird (every phoenix is a bird); but it is not the case that some birds are birds and not birds (nor that some birds are phoenixes). So is Darapti invalid, the conversion rule improper, and Aristotle’s syllogistic in ruins? One suggestion has received some favour: the problem concerns ‘empty’ terms — terms which are not true of anything at all (like the term ‘phoenix’) and which in some cases cannot be true of anything at all (like the term ‘bird and not a bird’). So — the suggestion runs — why not say that predicative syllogistic — or at any rate, that Aristotelian predicative syllogistic — applies only to non-empty terms, to terms which are in fact true of at least one item? If that suggestion is accepted, then the claim that that the letters ‘`’, ‘´’, ‘ˆ’, ... represent terms of any grammatical form and any semantic character is abandoned — and a classification of predicates is after all highly pertinent to predicative syllogistic.

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There are delicate issues here; but so far as I can see they do not really bear upon the question which I am addressing. To be sure, the suggestion I have just canvassed implies that not every sort of predicate comes within the scope of the syllogistic; but it is according to their denotation or extension, and not according to their sense or meaning, that predicates are excluded from or included within the scope of syllogistic. Even if the suggestion is accepted, that gives no reason to imagine that a classification of predicates, of the sort which is here in play, is pertinent to predicative syllogistic. The second of my four considerations bears upon the rejection of syzygies as non-concludent. Aristotle hopes to show that ` holds of every ´, ´ holds of no ˆ is non-concludent by appealing to two triads of terms; and his argument does in fact show that the syzygy yields no conclusion with ‘`’ as predicate and ‘ˆ’ as subject.13 But perhaps the syzygy is concludent for a restricted range of predicates? Perhaps, say, the inference ` holds of every ´ ´ holds of no ˆ Therefore ` holds of no ˆ is valid for a limited range of predicates? (Thus an invalid form will have a valid subform. But there is nothing in the least untoward about that — after all, every valid form of inference is a subform of at least one invalid form.) Take, then, the inference All animals are animals No stones are animals Therefore no stones are animals To be sure, that is not an Aristotelian syllogism — it does not fit the definition according to which the conclusion of a syllogism must be distinct from each of its premisses. Nonetheless, it is a valid inference. Moreover, every inference of the form ` holds of every ` ` holds of no ˆ Therefore ` holds of no ˆ is valid; and that form is a special case — a subform — of the form ` holds of every ´ ´ holds of no ˆ Therefore ` holds of no ˆ 13 But — see n.11 — it does yield ‘CoA’.

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So after all, and in spite of Aristotle’s argument, the syzygy ` holds of every ´, ´ holds of no ˆ is not, as it were, wholly non-concludent. And if it is semi-concludent in the way I have just described, may it not be semi-concludent in other ways too? May it not be concludent for certain classes or sorts of predicate? Aristotle’s argument for non-concludency uses two triads which together assemble four distinct terms: ‘animal’, ‘man’, ‘horse’, ‘stone’. Those terms are all substantial predicates. I said earlier that that is an accident, and that any triads whatsoever will do the trick, provided only that they satisfy the appropriate formal conditions. That is, of course, true. But it is also true that Aristotle’s argument, insofar as it invokes substantial predicates, leaves open the possibility that the syzygy in question is concludent for other classes of predicate — for relational predicates, say, or for predicates of having. Once again, there are delicate issues here — and this time they are pertinent to the question. To be sure, it would not be difficult — though it would be horribly tedious — to go through each of Aristotle’s ten classes of predicate and to discover pertinent pairs of triads in each case. But that would not satisfy a fervid partisan of the classification of predicates. After all, perhaps the syzygy is concludent for mixed triads? or for triads which belong to non-Aristotelian classes? And the number of possible non-Aristotelian classes of predicate is indeterminately vast. Aristotle’s method could not show that there is no class of predicate for which the syzygy ` holds of every ´, ´ holds of no ˆ is concludent. But that, of course, does not imply, or even suggest, that in fact there is, or at least might be, some class for which the syzygy yields a conclusion. It is not audacious to claim that there is no such class. The third of the four observations wonders if the class to which a predicate belongs might not bear upon the validity of a syllogism in some indirect or surreptitious fashion. Acording to Aristotle, a subject and a predicate are linked by a copula, and the copula may always be represented by the verb ‘r
ÆØ’ or ‘to be’. Now — still according to Aristotle — the copulative ‘r
ÆØ’ is multivalent, its value on any given occasion being determined by the nature of the predicate which it attaches to the subject. This is the chief text: Everything signified by the figures of predication is said to be in its own right. For ‘to be’ signifies in as many ways as they are said. So since of predicates some signify what it is, some a qualified item, some a quantified item, some a relational item, some

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doing or undergoing, some where, some when, ‘to be’ signifies the same as each of these things. (Met ˜ 1017a22–27)14

It will be allowed that the text is anything but limpid. Alexander’s commentary gives what is, I suppose, the traditional interpretation: He says that things are called beings in their own right in ten ways, and he explains why this is so. When the word ‘to be’ is attached to something which is, it signifies the same thing as the item to which it is attached — ‘being’ is homonymous and it signifies the way of holding which is appropriate to each thing. Thus if the most general classes of things are ten, then ‘being’ and ‘to be’ will be said in ten senses: when ‘to be’ attaches to a substance, it signifies a substantial holding, when it is attached to a quantity, a quantitative holding, ... (in Met 371.20–26)15

Suppose you say Socrates is a man. Then the copula ‘is’ is attached to a substantial predicate, ‘man’, and signifies that humanity holds substantially of Socrates. On the other hand, if you say Socrates is pale, the ‘is’ is attached to a qualitative predicate, and signifies that pallor holds qualititatively of Socrates. In the light of that, consider this syllogism: Every man is capable of laughter No stone is capable of laughter Therefore no man is a stone The word ‘is’ signifies qualitative holding in each of the two premisses (for ‘capable of laughter’ is a qualitative predicate), but in the conclusion it signifies substantial holding (for ‘stone’ is a substantial predicate). So the syllogism slides from one sense of ‘is’ to another. Such slides — such equivocations — are surely to be avoided; and if we are to avoid them, then we must ensure that all the predicates in a given syllogism belong to the

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Syllogistic and the classification of predicates

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same class. And in this way the classification of predicates is vital to the proper construction of syllogisms.16 The argument is hopeless — for two chief reasons. First, and most obviously, it is false to say that the word ‘is’, when it is used copulatively, has ten different senses: ‘is’ does not sometimes mean ‘is, substantially speaking’, sometimes ‘is, quantitatively speaking’, and so on. And what holds of the English verb ‘to be’ holds equally of the Greek verb ‘r
ÆØ’. How Aristotle came to suggest such a strange view I do not know — and it may be noted that he never hints at it in the Analytics or in any context in which syllogistic is in the air. Secondly, even if the strange view were true and the copulative ‘r
ÆØ’ did have ten distinct senses, that would have no bearing on predicative syllogistic. After all, the syllogism I just adduced — about men and stones and risibility — in which (according to Aristotle) the verb ‘is’ has one sense in the premisses and another in the conclusion, is a valid syllogism. If there is an equivocation, it is a benign equivocation — it introduces no fallacy into the argument. The fourth of the four considerations invites a longer discussion. Ancient logic, as I have said, standardly recognized two sorts of syllogism, the predicative and the hypothetical. But according to Galen, there is also another, third, species of syllogism which is useful for proofs, and I myself say that they come about in virtue of a relativity. (inst log xvi 1)17

There are not only predicative and hypothetical syllogisms — there are also relational syllogisms. Is not the species of relational syllogism defined by reference to the Aristotelian class of relational predicates? And in that way does not Aristotle’s classification of predicates have some pertinence to the theory of inference? True, no one apart from Galen ever showed any interest in this third species of syllogism. True, at most one out of Aristotle’s ten classes of predicate is pertinent to it — or rather, what is pertinent is not a general classification of predicates but a distinction between relational and non-relational predicates. Nonetheless, does not Galen’s relational syllogistic tie the classification of predicates to the theory of inference? The answer is No. And for three chief reasons. First, despite what he claims, Galen did not discover a third species of syllogism. He realized that 16 I am indebted to Francis Wolff for bringing this argument to my attention. 17 Ø ŒÆd ¼ºº æ
r   ıºº ªØH
N I Ø åæØ
, R Kªg ... O
Çø ŒÆa e æ  Ø ª
ŁÆØ ...

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there are some inferences which cannot be formulated — or at any rate, which cannot be formulated without extreme artificiality — in terms of the two species of syllogistic with which his contemporaries were acquainted. There is an argument which is part of the proof of the first theorem in Euclid’s Elements and the pertinent form or schema of which is this: x is equal to z y is equal to z Therefore x is equal to y Plainly, that argument cannot be formulated as a hypothetical syllogism — there are no propositional connectives for it to turn around. And Galen rightly regarded as forced the efforts made by the Peripatetic logicians to turn it into a predicative syllogism. Galen noticed that the argument depends not on connectives nor yet on subject–predicate structure but rather on the characteristics of a relation — of the relation of equality; and he noticed that many other arguments likewise depended on relations of one sort or another. Hence his claim: these arguments are all members of a third species of syllogism. But Galen offers no rules of inference for his third species: he proposes nothing comparable to Barbara (in predicative syllogistic) or to modus ponens (in hypothetical syllogistic). He does not offer such rules because there are no such rules to offer. For Galen had collected not several members of a species of formal argument but rather a miscellany of particular arguments which have nothing in common bar the fact that they all — well, almost all — depend on the features of some relation or other.18 Secondly, the validity of the Euclidean argument does not depend on the fact that it contains a relational predicate. To be sure, the argument is valid, and it contains the predicate ‘equal’ which belongs (let us allow) to the class of relational predicates. Moreover, if ‘equal’ is replaced in each of its occurrences by a predicate of another stripe — say by the qualitative predicate ‘pink’ —, the result will not always be a valid argument: indeed, the result is never a valid argument — rather, it is a piece of nonsense, a sequence of three ill-formed pseudo-sentences. But — and this is the crucial point — if ‘equal’ is replaced consistently by another relational predicate, the result is not always a valid argument. The point was noticed in antiquity. Alexander, for example, says that if — in an argument very similar to the Euclidean 18 See J. Barnes, ‘Proofs and syllogisms in Galen’, Entretiens Hardt 49, 2003, 1–29 [reprinted in volume III].

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argument — you replace ‘equal’ by ‘brother’, the result is an argument which is not valid: It is not true that if we assume ‘A is brother of B, B is brother of C’, then A is by necessity brother of C. For the universal proposition according to which brothers of one and the same person are also brothers of one another is not true. (in APr 345.5–8)19

Suppose — it is Alexander who makes the supposition — that the widower Mr X, who has a son by the first Mrs X, marries en deuxie`mes noces the widowed Mrs Y, who also has a son by her first marriage; and suppose that the new couple has a son ... That is to say, the validity of the Euclidean inference does not depend on the fact that the predicate ‘equal’ belongs to the class of relational terms. What counts, of course, is the fact that the relation of equality is transitive. There is a third consideration. Even if there were a third species of syllogism, as Galen claimed, that species would have nothing directly to do with the Aristotelian classification of predicates. It is perhaps worth explaining why that is so. Let us say that a predicative expression is a sequence of expressions and of gaps such that if each gap is filled by a proper name the result is a sentence; or equivalently, that a predicative expression is what results when you take a sentence containing one or more proper names and remove from it one or more of the said proper names. Thus the sequence ‘ ... is walking’ is a predicative expression: fill the gap with a proper name — say, with ‘Socrates’ — and you get a sentence: ‘Socrates is walking’. Similarly, ‘ ... eats well’ is a predicative expression: it’s what you get when you take the sentence ‘John eats well’ and remove from it the proper name ‘John’.20 The expressions ‘ ... is walking’ and ‘ ... eats well’ are called ‘one-place’ predicative expressions: they have a single gap the filling of which by a proper name produces a sentence; they take one proper name to make a sentence. The predicative expression ‘ ... is fond of ... ’ is two-place: there are two gaps to fill in order to arrive at a complete sentence, the expression takes two proper names to make a sentence. There are three-place predicative expressions (for 19 P ... IºÅŁb ª
ÆØ i
ºø
› `  F ´ Iºç  KØ
, › ´  F ˆ Iºç , e ŒÆd e
`  F ˆ K I
ªŒÅ Iºçe
r
ÆØ fiH c r
ÆØ c
ŒÆŁ º ı æ ÆØ
IºÅŁB c
‹Ø ƒ fiH ÆPfiH Iºç d ŒÆd Iººº Ø Nd
Iºç . 20 What I here call predicative expressions are normally called predicates in the context of contemporary logic. Since I here use ‘predicate’ with an Aristotelian reference, it is better to adopt a different name for the contemporary items.

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example ‘ ... gives ... to ... ’, or ‘ ... times ... is equal to ... ’); and in principle there may be predicative expressions of any number of places. When a contemporary logician talks of relations, he usually has in mind two-place predicative expressions. And it is with that sense of the term ‘relation’ in mind that we may properly speak of Galen’s ‘relational syllogisms’. For, as I have said, what the members of the supposed species have in common is the fact that all of them — well, nearly all of them — essentially contain some relational expression such as ‘ ... is equal to ... ’. It is sometimes said that Aristotelian logic is limited to one-place predicative expressions — and that that explains the poverty of Aristotelian syllogistic compared to contemporary logic. If that is so, then the members of Aristotle’s class of relational predicates will all be one-place predicative expressions — just like the members of his other nine classes. And so they cannot be identified with the relational expressions around which Galen’s relational syllogisms are constructed. On the contrary, there will be no overlap at all between Aristotle’s relational predicates, which are all oneplace, and Galen’s relational expressions, which are all two-place. The conclusion of that argument is true, but the argument itself limps. For the predicates with which Aristotelian logic is concerned are not one-place predicative expressions — they are not predicative expressions at all (in the sense which I have given to the phrase). The words ‘man’, ‘pale’, and ‘slave’, for example, are all Aristotelian predicates: none is a predicative expression — none contains a gap, none is an expression which takes one or more proper names to make a sentence. Again, if you take the sentence ‘Socrates is pale’ and remove the proper name ‘Socrates’, the result is not ‘pale’, which is the pertinent Aristotelian predicate, but rather ‘ ... is pale’. Things stand like this: an Aristotelian predicate is an expression which takes a copula to make a oneplace predicative expression. Or equivalently, if you take a one-place predicative expression of the form ‘ ... is P’ and remove the gap and the copulative ‘is’, then the result is an Aristotelian predicate. Those expressions which belong to the Aristotelian class of relational items are not relations in the modern sense — not because they have only one gap to them, but because they are not predicative expressions of any sort. There is, to be sure, a close connection between, say, the Aristotelian predicate ‘slave’ and the two-place predicative expression ‘ ... is a slave of ... ’: an item is a slave if and only if it is a slave of someone. You might think to define the Aristotelian predicate by saying that ‘slave’ is true of an item if and only if that item is a slave of someone. It would be pleasing to suppose that, in

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general, if ‘R’ is an Aristotelian predicate of the relational class, then ‘R’ is true of an item if and only if that item is R of something. But that is not so. For example, ‘greater’ is an Aristotelian relational predicate, but it is not the case that ‘greater’ is true of an object if and only if that object is greater than something; and ‘equal’ is an Aristotelian relational predicate, but it is not the case that ‘equal’ is true of an item if and only if that item is equal to something. (You might rather think that ‘greater’ is true of an item if and only if that item is greater than some specific item or sort of item, the context serving to identify the item; and that ‘equal’ is true of a group of items if and only if each item in the group is equal to every other item in the group. But that is by way of digression.) In any event, the Aristotelian classification of predicates has nothing to do which Galen’s imaginary third species of syllogism. It is possible that Galen hit upon the notion of a third species by reflecting on Aristotelian relational predicates. But there is nothing to be said in favour of such a hypothesis, which is (of course) without any theoretical interest.

IV And that is the end of the matter. Or almost. For consider this inference: Socrates is running Therefore, Socrates is doing something The inference is not, of course, an Aristotelian syllogism; nor is it a hypothetical syllogism, nor a relational syllogism, nor an inference recognized in the modern predicate calculus. Nonetheless, it is a valid inference; its conclusion follows from its premiss. The inference contains a predicate, ‘running’, which belongs to the class of action predicates. If you replace ‘running’ by any other predicate of that class, the result is a valid argument. If you replace it by a predicate from another class — say by ‘pale’, from the class of qualitative predicates — the result is not (always) a valid argument. For Socrates is pale Therefore, Socrates is doing something is not a valid inference.

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It is evident that you could produce examples of a similar sort for every class of predicate. For any predicate ‘P’ which belongs to a class C, there are valid arguments of the form x is P Therefore x is F such that if you replace ‘P’ by another member of C, the result is always a valid argument, and if you replace ‘P’ by a member of C*, the result is not (always) a valid argument. Or again, take the inference Socrates is a man Therefore Socrates is an animal. That inference is surely valid. Every inference of the form x is an A Therefore x is an animal is valid for a restricted number of predicates — for example, for those predicates which designate sorts or species of animal. And there are (of course) classes of predicate for which the inference is not valid. And that is enough to show that the answer to the question I am considering is after all not No but Yes. For although the classification of predicates has nothing to contribute to any logical system, ancient or modern, there are nevertheless cases in which the fact that a predicate belongs to this class rather than to that makes the difference between a valid and an invalid argument. The mediaeval logicians distinguished between consequentia formalis and consequentia materialis, between formal consequence and material consequence. The distinction, which has ancient antecedents,21 is explained thus by Jean Buridan: A consequence is called formal if it holds good for every term, the form remaining constant. Or ... a consequence is formal if every proposition which can be formed in the same form is a good consequence — as, for example: What is A is B, so what is B is A. A consequence is material if it is not the case that every proposition of the same form is a good consequence; or — as it is more usually put — if it does not hold good for every term, the form remaining the same — for example: A man is running, so an animal is running. (Tractatus de Consequentiis I iv)

21 See J. Barnes, ‘Logical form and logical matter’, in A. Alberti (ed), Logica Mente e Persona (Florence, 1990), pp.7–109, on pp.39–58 [reprinted above, pp.43–146].

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Plainly, the inferences I have just mentioned — among them Socrates is running Therefore, Socrates is doing something — are material consequences in Buridan’s jargon. Now Buridan himself thinks that material consequences are never evident, but that they can always be transformed into formal consequences by the addition of a premiss, for example: Everyone who is running is doing something Socrates is running Therefore, Socrates is doing something Hence, according to Buridan, certain consequences hold good in virtue of their matter, so that they are not formal consequences ... And no consequence of that sort can properly be called a syllogism. (ibid III i 1)

Material consequences are inferences, and they are valid inferences. But they do not form part of the subject-matter of logic. For by their very nature, material consequences are not amenable to a systematic treatment — they are inferences which reach their conclusions unmethodically (as the Stoics put it), they are IŁ ø æÆ

. There is, to be sure, very much more to be said on the distinction between formal and material inferences; and there is more to be said about the notion that a systematic or scientific logic cannot study material inferences. But at any rate this much seems to be uncontroversial: material inferences are, so to speak, on the margins of logic. If the classification of predicates is pertinent to the theory of inference only in the case of certain material inferences, then it is on the margins of the margins of logic.

8 Speusippus and Aristotle on homonymy* The Hambruch thesis ‘There are important differences between Aristotle’s notions of homonymy and synonymy on the one hand, and Speusippus’ notions on the other. In particular, Aristotle treats homonymy and synonymy as properties of things, whereas Speusippus treats them as properties of words. But in certain significant passages Aristotle fell under the influence of Speusippus and used the words ‘‘homonymous’’ and ‘‘synonymous’’ in the Speusippan way.’ That is a rough expression of what I shall call the Hambruch thesis. The thesis was advanced by Ernst Hambruch in 1904 in his monograph on the relation between Academic and early Aristotelian logic.1 Hambruch first argued for the fundamental difference between Speusippus and Aristotle; and then he singled out Topics ` 15 as a peculiarly Speusippan passage, conjecturing that it was based on some written work of Speusippus. The Hambruch thesis was supported by Lang in his edition of the fragments of Speusippus;2 and again by Stenzel in his Pauly-Wissowa article.3 It was accepted, and slightly embellished, by Cherniss.4 It was accepted, and * A revised version of ‘Homonymy in Aristotle and Speusippus’, CQ 21, 1971, 65–80. When the article first appeared, W.F.R. Hardie sent me a long and detailed letter about it, and some years later Leonardo Tara´n argued vigorously against its principal contentions in his ‘Speusippus and Aristotle on homonymy and synonymy’, Hermes 106, 1978, 73–99 — the arguments were taken over in his Speusippus of Athens, Philosophia Antiqua 39 (Leiden, 1981), pp.406–414 (cf pp.72–77); see also C. Luna, Simplicius: Commentaire sur les Cate´gories III, Philosophia Antiqua 51 (Leiden, 1990), pp.159–164). Many of the criticisms made by Hardie and Tara´n are just; and I have revised the article in their light. But the revision does not take up all the points they made; nor does it take up any of them in the detail they merit. 1 E. Hambruch, Logische Regeln der platonischen Schule in der aristotelischen Topik (Berlin, 1904), pp.28–29. 2 P. Lang, de Speusippi Academici scriptis (Bonn, 1911), pp.25–26. — There are two later collections: M. Isnardi Parente, Speusippo: frammenti (Naples, 1980); Tara´n, Speusippus. 3 J. Stenzel, ‘Speusippos’, RE IIIA (1929), cols 1636–1669, in col 1654. 4 H.F. Cherniss, Aristotle’s Criticism of Plato and the Academy (Baltimore, MD, 1944), pp.56–58; cf id, The Riddle of the Early Academy (Berkeley CA, 1945), p.40.

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differently embellished, by Anton.5 There have been, to my knowledge, few signs of dissent.6 There are two preliminary matters to be cleared up. First, the Hambruch thesis turns on an antithesis between words and things — Speusippan homonyms and synonyms are words, Aristotelian synonyms and homonyms are things. How is that fundamental antithesis best expressed? Start with Aristotle’s familiar account of homonymy at the beginning of the Categories: (A1) Items are called homonymous if their name alone is common, the account of their essence in respect of the name being different. (Cat 1a1–2)*

By-passing the several stock problems raised by that sentence,7 I offer the following as a slightly more formal definition: [66] (D1) The members of a group of items are homonymous with respect to a term T if and only if T is true in a different sense of each member of the group. For example, the animal which William has just deposited on the carpet, the blotch on my right cheek, and the construction which Pepys had to blow up at Tangier form a little group of three items. They are homonymous in respect of the term ‘mole’: the term ‘mole’ is true of each of them, but in each case in a different sense.** 5 J.P. Anton, ‘The Aristotelian doctrine of homonyma in the Categories and its Platonic antecedents’, Journal of the History of Philosophy 6, 1968, 315–326, on p.323. Anton’s other pertinent articles are: ‘The meaning of › º ª  B PÆ in Aristotle’s Categories 1a’, Monist 52, 1968, 252–267; ‘Ancient interpretations of Aristotle’s doctrine of homonyma ’, Journal of the History of Philosophy 7, 1969, 1–18. 6 But see e.g. G.E.L. Owen, ‘A Proof in the —æd ’H
’, Journal of Hellenic Studies 57, 1957, 103–111, on p.104 n.1 [¼ Logic, Science and Dialectic (London, 1986), pp.165–179]; W. Leszl, Logic and Metaphysics in Aristotle, Studia Aristotelica 5 (Padua, 1970), p.92 n.14. — P. Merlan, ‘Beitra¨ge zur Geschichte des antiken Platonismus: I, Zur Erkla¨rung der dem Aristoteles zugeschriebenen Kategorienschrift’, Philologus 39, 1934, 35–53, criticizes the Hambruch thesis not on the grounds that it is false but on the grounds that it is trivially true (pp.47–53): see below, p.[70] n.2. * ›
ıÆ ºªÆØ z
Z
Æ 

Œ Ø

, › b ŒÆa  h
Æ º ª  B PÆ æ . 7 See e.g. Porphyry, in Cat 59.34–67.32. (This is Porphyry’s shorter commentary on the Categories; his larger work, inscribed to Gedalius — and which I refer to as ad Ged —, is lost: see Simplicius, in Cat 2.5–9; R. Beutler, ‘Porphyrios’, RE XXII (1953), cols 275–313, in col 283.) Porphyry’s is the earliest of the seven commentaries on the Categories published in CIAG. The later commentators are heavily dependent on their predecessors, and especially on Porphyry — a dependence well illustrated by their comments on Aristotle’s definitions of homonymy and synonymy (cf K. Praechter, review of CIAG, Byzantinische Zeitschrift 18, 1909, 516–538, on pp.526–531 [¼ Kleine Schriften (Hildesheim, 1973), pp.282–304]; L.G. Westerink, Anonymous Prolegomena to Platonic Philosophy (Amsterdam, 1962), pp.xxvi–xxvii). ** That defines the relation ‘ ... is homonymous with respect to ... ’: homonymy simpliciter is then quickly defined: (D1*) The members of a group of items are homonymous if and only if there is at least one term with respect to which they are homonymous.

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Aristotle explains synonymy by the sentence: (A2) Items are called synonymous if their name is common and in addition the account of their essence in respect of the name is the same. (Cat 1a6–7)*

So: (D2) The members of a group of items are synonymous with respect to a term T if and only if T is true in the same sense of each member of the group.** According to the commentators, Aristotelian homonymy and synonymy are properties of ‘things’ rather than of words;1 but that is false — or at any rate, it is misleading. What is true is this: if the members of a group of items are homonymous or synonymous in the sense of (D1) and (D2), it does not follow from that fact that they are all words (nor, more generally, that they are all linguistic items of some sort or other). But neither does it follow that none of them is a word or a linguistic item of some sort. For example, the words ‘beetroot’, ‘rhubarb’, and ‘parsnip’ are synonymous with respect to the term ‘English’; and my cat William and the Latin word ‘sublatum’ are homonymous with respect to the term ‘supine’. Is it possible to give an account of homonymy and synonymy which makes them properties of linguistic items exclusively? Yes — and in more ways than one, of which this is the simplest: (D10) An item is homonymous if and only if it has more than one sense. (D20) An item is synonymous if and only if it has exactly one sense. If an item is synonymous or homonymous according to those definitions, then it follows that the item is a linguistic item of some sort; for only linguistic items can be said to have sense (in the sense of ‘sense’ supposed by the definitions).3 * ı

ıÆ b ºªÆØ z
  Z
Æ Œ Ø
e
ŒÆd › ŒÆa  h
Æ º ª  B PÆ › ÆP . ** Hence: (D2*) The members of a group of items are synonymous if and only if there is at least one term with respect to which they are synonymous. 1 See e.g. Porphyry, in Cat 61.14; 68.12; Ammonius, in Cat 18.16; cf e.g. H.W.B. Joseph, An Introduction to Logic (Oxford, 19162), p.47; K.J.J. Hintikka, ‘Aristotle and the ambiguity of ambiguity’, Inquiry 2, 1959, 135–151, on p.140 [revised version in his Time and Necessity (Oxford, 1973), pp.1–26]; J.L. Ackrill, Aristotle’s Categories and De Interpretatione (Oxford, 1962), p.71. But note the opposite sentiment in Simplicius, in Cat 25.7–9 (cf 28.1); and see below, p.[73]. In practice, the commentators occasionally speak of homonymous words — e.g. Ammonius, in Isag 81.23; 83.21; 84.21. 3 In English, the term ‘synonymous’ is generally predicated of two or more items, and it means something like ‘having the same sense’. The sense determined by (D20) is related to, but different

Speusippus and Aristotle on homonymy

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So there is at least this difference between the two pairs of definitions: (D10) and (D20) imply that homonymous and synonymous items are linguistic, (D1) and (D2) do not. [67] What more can be said about the relations between the two pairs? Well, first, if certain items are homonymous, in sense (D1), with respect to a term T, then the term T is homonymous in sense (D10). Secondly, if an expression E is homonymous in sense (D10), it does not follow that any items are homonymous, in sense (D1), with respect to E. (For, first, E may not be a term at all — it may not be the sort of expression which can be true of an item. Some philosophers have thought that the word ‘if ’ is homonymous; but it is not a term, and no items could be homonymous with respect to it. Again, E may be a term — but a term which is true of no items at all. Again, E may be a term which is true of some items — but always in the same sense.) Thirdly, if certain items are synonymous in sense (D2) with respect to a term T, it does not follow that T is synonymous in sense (D20). (The animal deposited by William and the animal deposited by Arthur are synonymous with respect to the term ‘mole’: the expression ‘mole’ is not synonymous in sense (D20).) Fourthly, if an expression E is synonymous, then if it is a term and if it is true of a plurality of items, then the members of that plurality are synonymous with respect to E. In what follows I shall distinguish between Aristotelian homonymy and synonymy, where — as in (D1) and (D2) — being homonymous or synonymous does not entail being a linguistic item, and ‘Speusippan’ homonymy and synonymy, where — as in (D10) and (D20) — being homonymous or synonymous does entail being a linguistic item. There are inverted commas for the ‘Speusippan’ onymies but not for the Aristotelian. (D10) and (D20) supply only one out of several fashions of defining ‘Speusippan’ onymies. Here is another pair of Speusippan definitions, which are in an obvious way closer to the Aristotelian pair (D1) and (D2).* (D11) A term T is homonymous over a group of items if and only if T is true in a different sense of each member of the group. (D12) A term T is synonymous over a group of items if and only if T is true in the same sense of each member of the group.

from, that normal sense. (Of course, (D20) is not meant to give the normal sense — or even a sense — of the English word.) * I owe these definitions to Hardie.

288

Logical Matters

Those two definitions are ‘Speusippan’: being homonymous or synonymous entails — trivially— being a term, and hence being a linguistic item. So they are different from (D1) and (D2). But they are nearly related to (D1) and (D2): a group of items is homonymous or synonymous with respect to a term T (according to the Aristotelian definitions) if and only if T is homonymous or synonymous over the group (according to the ‘Speusippan’ definitions). According to the Hambruch thesis, Speusippus’ onymies are ‘Speusippan’, and in certain passages Aristotle tacitly abandons Aristotelian onymies and tacitly adopts ‘Speusippan’ onymies. The force and the interest of those contentions will depend in part on what particular variety of ‘Speusippan’ onymies Speusippus may have embraced. The second preliminary matter may be more briskly dispatched. It concerns the relative dating of Speusippus and Aristotle. Hambruch must suppose that Speusippus thought — and perhaps wrote — about homonymy and synonymy before Aristotle wrote Topics `. The evidence for Speusippus’ life has been sifted by Merlan:2 his death can be placed in 339, and his birth in about 410; but his writings, with a few uninteresting exceptions, cannot be dated. Aristotle’s Topics is generally taken to be an early work — though most scholars suppose that it was compiled over a longish period of time rather than written in one feverish weekend; and many scholars suppose that Book `, in particular, was written towards the end of that longish period.3 Attempts to give a more precise date to the Topics, or to this or that part of the Topics, are mere fantasies. So as far as the chronology is concerned, our evidence — such as it is — is compatible with Hambruch’s supposition, and compatible with the contrary supposition according to which Speusippus’ supposed work on the onymies was written after Aristotle’s Topics.

Speusippus on homonymy One of the types of fallacy discussed in the Sophistici Elenchi is fallacy ‘on account of homonymy [Ææa c
›ø
ıÆ
]’. Aristotle makes it clear that he was not the first to discuss the thing, and at one point he says that ‘it is plain that not all refutations are on account of equivocation [Ææa e Ø
], 2 P. Merlan, ‘Zur Biographie des Speusippos’, Philologus 103, 1959, 198–214. 3 See e.g. J. Brunschwig, Aristote: Topiques livres I–IV (Paris, 1967), pp.LXXII–LXXVI, LXXXIII–CIV.

Speusippus and Aristotle on homonymy

289

as some people suppose’ (Soph El 177b7–9). Poste identified these people with the equally anonymous people who are earlier said to divide arguments falsely into those bearing on the words [æe  h
Æ] and those bearing on thoughts [æe c
Ø
ØÆ
].4 Cherniss accepted the identification, and gave Poste’s people the name of Speusippus; and Tara´n argued in favour of Cherniss’ position.* And those arguments are comforted by a further passage in the Sophistici Elenchi, at 174b23–27: although Aristotle does not mention Speusippus, the Mandrobulus which he does mention is surely Speusippus’ essay of that title (Diogenes Laertius, IV 4), and the passage proves that Speusippus had some interest in fallacies of homonymy.7 Poste’s identification of the two groups of anonymous people is a guess.5 Cherniss offers an argument of sorts in favour of Speusippus.6 Tara´n has produced additional reasons in support of Poste and of Cherniss.** I am persuaded that Speusippus might perhaps lie behind the two anonymous groups — but not that he does lie behind them nor even that it is probable that he does. So I prefer to leave the people under the cloak of anonymity with which Aristotle has decently covered them. [68] In any event, far more interesting than the uncertain intimations of the Sophistici Elenchi are three passages in Simplicius’ commentary on the Categories.*** The longest of them is this: Boethus records that Speusippus adopted a division of the following sort which includes all names. Of names, he says, some are tautonymous and others heteronymous; of the 4 E. Poste, Aristotle on Fallacies, or the Sophistici Elenchi (London, 1866), p.151. * Cherniss, Aristotle’s Criticism, p.57 n.47; Tara´n, Speusippus, pp.414–418 (the two texts are his frag 69a and 69b); cf Anton, ‘The Aristotelian doctrine’, p.320. 7 The passage was discussed and the attribution to Speusippus suggested by I. Bywater, ‘The Cleophons in Aristotle’, Journal of Philology 12, 1883, 17–30. The attribution was accepted by Lang, Speusippi, pp.39–40 (the passage appears as his frag 3a — and then as frag 120 in Isnardi Parente and frag 5a in Tara´n). 5 The two views which Aristotle rejects are no doubt compatible; but they are logically independent of one another. There is perhaps some reason to connect the people of 177b7–9 with those criticized (again anonymously) at 179b38–180a7 and 182b22–27. 6 He refers to ‘the importance which Speusippus attached to the division of words and the relation of word to concept as the basis of this division’. But there is no evidence that Speusippus attached any importance of the required sort to that sort of division; and if there were, that would be curious ground for ascribing to him the view that all fallacies are due to homonymy. ** See Speusippus, pp.414–418, which argues, first, that Poste was right (for Aristotle’s objections in 170b12–171b2 show that the people who divide arguments into two kinds in fact also held that all fallacies are fallacies of ambiguity), and secondly, that several considerations make it probable that Speusippus held the views which Aristotle criticizes. *** They are collected as frags 32a, 32b, and 32c in Lang, frags 45–47 in Isnardi Parente, and frags 68a, 68b, and 68c in Tara´n.

290

Logical Matters

tautonymous, some are homonymous and others synonymous (where we understand ‘synonymous’ according to the usage of the old philosophers); of the heteronymous, some are heteronymous in the proper sense, some polyonymous, and others paronymous. The others have been explained: polyonyms are a plurality of different names for the same thing, where their account is one and the same ... ; heteronyms are items different both in name and in account and in thing ... (in Cat 38.19–39.2)2

Boethus, whom Simplicius is quoting, was a contemporary of Strabo who succeeded Andronicus of Rhodes as head of the Lyceum.3 He wrote, among other scholarly works, a commentary on the Categories (see e.g. Porphyry, in Cat 59.17), and it is doubtless from this that Simplicius quotes. Simplicius had a high opinion of Boethus (in Cat 1.17; 159.14); and he often refers to

2 Ø
 
ı
ƒ æE ´ ÅŁ   ØÆÅ
ØÆæØ
ÆæƺÆ
Ø
a O
ÆÆ 
Æ æغÆ
ıÆ
: H
ªaæ O
ø
, çÅ, a b
ÆP
ı KØ
, a b æ
ıÆ: ŒÆd H
ÆPø
ø
a b
›
ı KØ
, a b ı

ıÆ, ŒÆa c
H
ƺÆØH
ı
ŁØÆ
IŒ ı
ø


H
a ı

ıÆ: H
b æø
ø
a b
r
ÆØ Nø æ
ıÆ, a b  ºı
ıÆ, a b Ææ
ıÆ. Iººa æd b
H
¼ººø
I  ÆØ,  ºı
ıÆ  KØ
a Øç æÆ ŒÆd  ººa O
ÆÆ ŒÆŁ 
e æªÆ  ‹Æ
x  ŒÆd › ÆPe ÆPH
fi q º ª , uæ ¼ æ ç  åÆØæÆ çªÆ

· æ
ıÆ  KØ
a ήd  E O
ÆØ
ŒÆd  E æªÆØ
ŒÆd  E º ª Ø æÆ, x
ªæÆÆØŒc ¼
Łæø  º
. — This is frag 32a Lang, 45 Isnardi Parente, 68a Tara´n. There are no significant variant readings. (Perhaps we should add ‘ŁÅ’ at 38.26 to complete the iambic pentameter: cf e.g. Scholia to Dionysius Thrax, Grammatici Graeci I iii [236.14].) At 38.19 I translate ‘ÆæƺÆ
Ø
’ by ‘adopt’. In contexts of this sort the verb usually means ‘take over [sc from someone else]’. It seems improbable that Boethus means that the ØÆæØ was inherited rather than invented by Speusippus; and in the original version of this chapter I suggested that the verb might be corrupt. Tara´n, ‘Speusipus and Aristotle’, p.81 n.28, says that it means ‘take upon oneself’ or ‘undertake’, and he refers to LSJ. I doubt if the word can mean that here; but I now suppose that you may adopt something without adopting it from someone else. — Peter Lambeck found a part of the text in one of the MSS he catalogued (Petrus Lambecius, Commentaria de augustissima Bibliotheca Caesarea Vindobonensi VII (Vienna, 1675), p.135 — Lang’s ‘185’ is a misprint). L.G. Westerink and B. Laourdas, ‘Scholia by Arethas in Vindob. Phil. Gr. 314’, Hellenika 17, 1962, 105–131, have discussed the matter. The title ‘ ı ı ØÆæØ’ heads a miscellaneous appendix to the MS (published on pp.127–131), only the first entry of which has anything to do with Speusippus. That entry reads: H
O
ø
a b
ÆP
ıÆ a b æ
ıÆ· H
b ÆPø
ø
a 
KØ
›
ıÆ, a b ı

ıÆ· H
b æø
ø
a 
KØ
Ææ
ıÆ a b  ºı
ıÆ. That presumably comes from Simplicius. The MS dates from 924 or 925 and was copied from a codex belonging to Arethas, who is known to have read and excerpted from Simplicius’ commentary on the Categories (see Kalbfleisch’s preface to his edition of Simplicius, in Cat, p.XIV). See also J.H.C. Schubart, ‘Einige Bemerkungen u¨ber das griechische Scholienwesen’, Zeitschrift fu¨r die Altertumswissenschaft 1, 1834, 1137–1144. The passage is not found in Arethas’ notes on Cat: M. Share, Arethas of Caesarea’s Scholia on Porphyry’s Isagoge and Aristotle’s Categories (Athens, 1994). 3 See P. Moraux, Der Aristotelismus bei den Griechen I, Peripatoi 5 (Berlin, 1973), pp.143–179; J. Barnes, ‘Roman Aristotle’, in J. Barnes and M. Griffin (eds), Philosophia Togata II (Oxford, 1997), pp.1–60, on pp.21–24 [reprinted in volume IV].

Speusippus and Aristotle on homonymy

291

him. Whether or not he knew Boethus’ commentary at first hand is disputed, most scholars inclining to the view that he relied for his knowledge on the citations made by Porphyry in the longer of his two commentaries on the Categories.4 How much of the passage is Speusippus? The answer turns on the identification of the referents of three expressions. (i) In the phrase ‘where we understand [IŒ ı
ø
H
]’, to whom does the ‘we’ refer? Two pages earlier Simplicius quotes [69] verbatim a passage from Porphyry’s ad Ged which contains the sentence: ‘Boethus is wrong when he says that Aristotle omitted what the moderns call homonymy’ (36.28–29 — see below [p.70]). Here it is certainly Boethus who refers to the use of the term ‘›
ı ’ by ‘the moderns’: it is a reasonable conjecture that the person who refers in our passage to the use of ‘ı

ıÆ’ by ‘the old philosophers’ is again Boethus. I conclude that Boethus and his contemporaries (and not Speusippus nor yet Simplicius) are referred to by ‘we’. (ii) Who is subject of ‘he says [çÅ]’? ‘Speusippus’ and ‘Boethus’ are the possible answers. I think that ‘Boethus’ is right: if you write ‘X reports that Y holds that such-and-such. He says that ... ’, you will take ‘he’ to refer to X rather than to Y. Tara´n thinks that the right answer is ‘Speusippus’: the ‘çÅ’ is part of Simplicius’ verbatim quotation of Boethus.* I find it difficult to read the text like that; but the point is of little importance (as Tara´n allows) — for on any account the ØÆæØ is reported by Boethus and ascribed to Speusippus. (iii) ‘The others have been explained’: by whom? Does the phrase continue Simplicius’ quotation of Boethus? In that case it must mean that the other items have been explained by Speusippus or by Boethus himself. Or has Simplicius stopped quoting and started speaking again in propria persona? In that case the phrase must mean that the other items have been explained by Simplicius himself or (perhaps) by Aristotle. I cannot think that the answer to question (iii) is ‘Speusippus’; for it is hard to think of any context, in his 4 So e.g. Lang, Speusippi, p.66; Tara´n, ‘Speusippus and Aristotle’, pp.76–77 and n.16. It is certain that Simplicius sometimes relies on Porphyry for his references to Boethus (see in Cat 11.23; 29.30; 78.20); and he expresses a general debt to Porphyry, whom he claims to follow closely (2.5–9). But that does not show that he did not know Boethus’ work at first hand (modern scholars may know their texts at first hand and yet also, for convenience, refer to them at second hand — by reference to Diels-Kranz, or to von Arnim, say); and I find no passage which proves that all Simplicius’ knowledge of Boethus came to him from Porphyry. On the other hand, the phrase ‘u çÆØ
’ at in Cat 29.5 strongly suggests that Simplicius did not have first-hand knowledge of Speusippus’ works. * ‘Speusippus and Aristotle’, pp.80–81.

Logical Matters

292

˜ØÆØæØ or elsewhere, in which Speusippus would first explain homonymy, synonymy, and paronymy; then give his ‘division’; and finally explain polyonymy and heteronymy. On the other hand, that order of exposition is readily intelligible in a commentary on the first chapter of the Categories (though in fact none of the extant commentators adopts it).1 So the answer to the question might be ‘Boethus’. But Tara´n has argued persuasively that the quotation from Boethus ends with the words ‘ ... and others paronymous’ (certainly, there is no later point at which it might more plausibly end); and he answers question (iii) by ‘Simplicius’. Simplicius has indeed already explained homonymy, synonymy, and paronymy — but then he has also already described polyonymy and heteronymy (22.14–23.3), and the present text rather implies that polyonymy and heteronymy have not yet been explained. Perhaps that is not a serious objection; or perhaps — as I now incline to think — Simplicius means that ‘the others have been explained’ by Aristotle. In any event, the crucial question is not ‘Who has explained the others?’ but rather ‘Who is offering us the definitions of polyonymy and heteronymy which Simplicius proceeds to give?’. And whatever the answer to question (iii) may be, the answer to this question must be either ‘Boethus’ or ‘Simplicius’ — it cannot be ‘Speusippus’. Of course, Boethus (directly) or Simplicius (indirectly) might be paraphrasing Speusippus and thereby giving us information about Speusippus’ definitions. But those are, so far as the present text goes, mere possibilities: if we want evidence about Speusippus’ definitions of the things, we must turn to the other two passages in Simplicius’ commentary. Still, the passage under consideration shows something: it shows that Boethus ascribed to Speusippus a certain ØÆæØ or division, that it was a division of O
ÆÆ — of names, or of words; and that it looked like this: names

tautonyms

homonyms

synonyms heteronyms

heteronyms

polyonyms

paronyms

1 But see Porphyry, in Cat 68.28–69.13 — which might, I suppose, here reflect Boethus’ commentary.

Speusippus and Aristotle on homonymy

293

There are some odd features about the diagram: although Boethus calls it a ØÆæØ and sets it out in the style of one (a b
... a b ... ), it is not a division — or at any rate, it is not a division in the strict sense of the word. In addition, the presence of paronyms in the bottom line is at best awkward and at worst incoherent.* Nonetheless, the text shows that Boethus represented Speusippus’ onymies as ‘Speusippan’. The second Simplician passage is brief: Speusippus, they say, was content to say ‘the account is different’. (in Cat 29.5)2

Simplicius is engaged with the question: Why did Aristotle include the phrase ‘ŒÆa  h
Æ’ in his definition of homonymy? The question was standard from Porphyry onwards (see his in Cat 62.34–64.22). It is allied to, but distinct from, another standard question asked by Porphyry (in Cat 64.23– 65.11), and then by all the commentators, including Simplicius (in Cat 29.13–29). This is the question: Why did Aristotle include the phrase ‘B PÆ’ in his definition of homonymy? Simplicius suggests (in Cat 29.25) that the latter question arose as a result of an objection by Nicostratus.3 Speusippus is nowhere mentioned in connection with it. The second clause of Aristotle’s definition of homonymy is this: › b ŒÆa  h
Æ º ª  B PÆ æ . Speusippus’ definition of homonymy did not include the phrase ‘ŒÆa  h
Æ’. Did it include or exclude the phrase ‘B PÆ’? The sentence from Simplicius might seem to prove that it excluded it — for was not Speusippus ‘content to say ‘‘the account is different’’’? But in its context the sentence should not be so read: the context, and the sentence within it, is concerned solely with the phrase ‘ŒÆa  h
Æ’. And the silence of Simplicius and [70] all the other commentators when they discuss the phrase ‘B PÆ’ is, I think, some evidence that on this particular point Speusippus did not differ from Aristotle.1

* See below, pp.[74–75]. 2 Ø  , u çÆØ
, MæŒE ºªØ
› b º ª  æ . Frag 32b Lang, 46 Isnardi Parente, 69b Tara´n. — Comparable cases of contentment (‘MæŒE’) are found in Porphyry, in Cat 63.1–2n, 64.25, and in Dexippus, in Cat 20.21–23: that might be taken as a flimsy indication that in 29.5 Simplicius is drawing on Porphyry’s ad Ged. 3 Platonist, teacher of Marcus Aurelius, and author of a minute and critical examination of the Categories: see K. Praechter, ‘Nicostratos der Platoniker’, Hermes 57, 1922, 481–517 [¼ Kleine Schriften, pp.101–137]. 1 That tells against the conjecture (noted in T. Waitz, Aristotelis Organon I (Leipzig, 1844), p.270, and supported by Anton, ‘Meaning’, pp.258–259) that Speusippus’ influence accounts for

294

Logical Matters

Can we reconstitute Speusippus’ definition of homonymy on the basis of the Simplician sentence? The sentence implies that Speusippus’ definition was largely similar to Aristotle’s — otherwise it would be fatuous to remark that Speusippus omitted ‘ŒÆa  h
Æ’. But if Speusippus’ definition differed in that particular respect, neither Simplicius nor anyone else mentions any other respect in which it differed. That suggests that Speusippus defined homonymy by means of a sentence at most trivially different from: (S1) Items are called homonymous if their name alone is common, the account of their essence being different. ›
ıÆ ºªÆØ z
Z
Æ 

Œ Ø

, › b º ª  B PÆ æ .2 That suggestion has certain implications — before remarking on them I must introduce the third and last of the passages from Simplicius. The third passage is part of a quotation from Porphyry’s ad Ged. It goes like this: Where it is a matter of a plurality of words and the multiple nomenclature of things — as in the Poetics and the third book of the Rhetoric — we need the other sort of synonyms, which Speusippus called polyonyms. And Boethus is wrong when he says that Aristotle omitted what the moderns call synonyms and Speusippus called polyonyms: he did not omit them but rather dealt with them in other works where such a discussion was pertinent. (in Cat 36.25–31)*

Speusippus used the term ‘ ºı
ıÆ’ for what the moderns call ‘ı

ıÆ’. Who were Boethus’ moderns, and how did they define ı

ıÆ? Simplicius is discussing the rival merits of the Aristotelian and the Stoic uses of ‘ı

ı ’ (36.8–31). He draws heavily on Porphyry’s discussion;3 the omission of ‘B PÆ’ in some copies of the Categories at 1a2 and 1a7. (Bode´u¨s is the latest editor to follow Waitz and expunge ‘B PÆ’: see my notice in CR 53, 2003, 59–62 [reprinted above, pp.258–265]. Tara´n, ‘Speusippus and Aristotle’, pp.83–85, believes that ‘B PÆ’ was in Aristotle’s text and argues that it was not in Speusippus.) 2 Merlan, ‘Beitra¨ge’, p.50, offers the same reconstruction; but he supposes that it is only trivially different from a ‘Speusippan’ account of homonymy. — Tara´n, ‘Speusippus and Aristotle’, p.85, offers a couple of versions of a ‘Speusippan’ definition of homonyms, which he ascribes to Speusippus. (Neither version is Greek — nor are the ‘Speusippan’ definitions of synonyms and polyonyms which he gives on p.88. But it is not just that which makes them implausible.) * 
ŁÆ b æd a º ı çø
a  ıc ŒÆd c
 ºıØB Œ ı O
ÆÆ
, uæ K
fiH —æd  ØÅØŒB ŒÆd fiH æfiø —æd ÞÅ æØŒB,  F æ ı ı
ø
 ı  ŁÆ ‹æ  ºı
ı
› Ø  KŒºØ. ŒÆd P ŒÆºH › ´ ÅŁ  ÆæƺºEçŁÆØ fiH `æØ ºØ çÅd a Ææa  E
øæ Ø ŒÆº 
Æ ı

ıÆ –æ Ø  KŒºØ  ºı
ıÆ· P ªaæ ÆæƺºØÆØ Iºº’ K
¼ººÆØ æƪÆÆØ K
Æx  q
NŒE  › º ª  ÆæºÅÆØ. 3 Though the question was discussed by Porphyry it was apparently raised again only by Simplicius and by Olympiodorus (in Cat 38.6–12).

Speusippus and Aristotle on homonymy

295

and he identifies Porphyry’s ‘other sort of synonyms’ with Stoic synonymy, so that the phrase ‘the moderns’ refers to the Stoics.4 Simplicius explains Stoic synonymy like this: The Stoics called synonyms items which have several names at the same time — as Paris and Alexander are the same — and, generally, what are called polyonyms. (in Cat 36.8–11)*

So it is clear that Stoic synonyms, which are the same as Speusippus’ polyonyms, are Aristotelian and not ‘Speusippan’.** The example of Paris5 might suggest that the items in question are a strictly limited class of thing — that Stoic synonyms are objects which have more than one proper name. But Simplicius’ reference to polyonymy corrects that impression; and he himself gives as [71] examples of polyonyms: ¼
Łæø  æ ł æ   ‘and anything of that sort’ (in Cat 22.26). And that makes clear two things (which in any event are perhaps obvious): the ‘many names’ need not be proper names — ‘name’, here, embraces also common nouns (and no doubt adjectives, and perhaps also verbs), and all the ‘many names’ have the same meaning. If Speusippus gave a definition of polyonymy, then this passage makes it probable that he expressed it in a sentence at most trivially different from: (S3) An item is called polyonymous if it has several names each with the same account.  ºı
ıÆ ºªÆØ z
 ººa O
ÆÆ › b º ª  › ÆP . Porphyry says that ‘items are polyonymous if they have many different names of which the account is one and the same’ (in Cat 69.1–2).*** That differs from his own earlier definition of polyonymy in terms of four possible sorts

4 As indeed it very frequently does in the commentators: see J. Barnes, Porphyry: Introduction (Oxford, 2003), pp.317–319. — Who are ‘the Stoics’ here? von Arnim gives the sentence to Chrysippus (it is text 150 in volume II of SVF); and Chrysippus is known to have written at length about ambiguity. But it is equally possible that Simplicius’ remark derives ultimately from one of the many Stoic critics of the Categories (on whom see Praechter, ‘Nicostratos’). In general: C. Atherton, The Stoics on Ambiguity (Cambridge, 1993). * ƒ ø€ØŒ d [sc ŒŒºŒÆØ ı

ıÆ] a  ººa –Æ å
Æ O
ÆÆ, ‰ —æØ ŒÆd ºÆ
æ  › ÆP , ŒÆd ±ºH a  ºı
ıÆ ºª 
Æ. ** Tara´n, p.86 n.39, claims that Stoic synonyms are ‘Speusippan’, and that Simplicius has misinterpreted the Stoic view because he was ‘simply unable to conceive’ of the possibility of ‘Speusippan’ onymies. 5 Perhaps a standard Stoic example: cf Sextus, PH II 227. ***  ºı
ı KØ
z
Øç æÆ b
ŒÆd ºEÆ O
ÆÆ, › b º ª  x  ŒÆd › ÆP , ‰ ¼ æ, ç , çªÆ

...

296

Logical Matters

of Œ Ø
ø
Æ (60.22–34: see below, p.[74] n.3): it is a sporting guess that he took or adapted it from Boethus, and ultimately from Speusippus.2 How did Speusippus explain tautonymy, heteronymy, synonymy, heteronymy in the special sense, and paronymy? There is no direct evidence; but synonyms and heteronyms in the special sense are readily defined by analogy with (S1) and (S3): (S2) Items are called synonymous if they have a name in common and the name has the same account in each case. ›
ıÆ ºªÆØ z
Z
Æ Œ Ø
e
ŒÆd › º ª  › ÆP . (S4) An item is called heteronymous (in the special sense) if it has several names, each with a different account.  ºı
ıÆ ºªÆØ z
 ººa O
ÆÆ › b º ª  æ .3 Then tautonyms will be groups of items which have a name in common, the two sorts of tautonyms being those in which the common name has the same sense and those in which it has different senses for each item. A heteronym in the general sense will be an item which has several names, the two sorts of heteronyms being those in which the names have the same sense and those in which they have different senses. As for paronyms (which, as I have said, fit uneasily into the ‘division’), they were perhaps explained as Aristotle explained them. All that is, of course, guess-work; and the guess-work supposes that Speusippus defined all the pertinent terms, that he defined them according to a single pattern, and that the definitions had a systematic unity. There is no textual evidence for those suppositions; but in the absence of counter-evidence they are perhaps reasonable. How are (S1) and (S2) related to Aristotle’s account of homonymy and synonymy in the Categories? First, it is plain that if X and Y are homonyms or synonyms in the senses given by (S1) and (S2), then it does not follow that X and Y are words, or, in general, that they are linguistic items. (The same goes for (S3) and (S4).) In that case, Speusippus’ homonymy is not ‘Speusippan’ and Speusippus’ synonymy is not ‘Speusippan’ (in general Speusippan onymies are not ‘Speusippan’). 2 See also Alexander, in Met 247.27–29: ... ‰ r
ÆØ H
 ºıø
ø
e  Œ

ÆP E z
ºø b
O
ÆÆ, ŒÆŁ ŒÆ
b H
O
ø
› ÆPe º ª , ‰ çƪ
ı ŒÆd ÆåÆæÆ, ŒÆd ºø ı ŒÆd ƒÆ ı. cf 281.24. 3 See Porphyry, in Cat 69.12: æ
ıÆ  KØ
z
  Z
Æ ŒÆd › º ª  æ .

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That conclusion fits with what Speusippus’ terminology would lead you to suppose. If his onymies were ‘Speusippan’, then ‘ÆP
ı ’ would have to mean ‘being the same name as’, and, in general, ‘ç-
ı ’ would have to mean (roughly) ‘being a ç name’. And that would be untoward: compounds in ‘-
ı ’ are frequent in Greek, and in all cases ‘ç-
ı ’ usually means (roughly) ‘having [72] a ç name’ and not ‘being a ç name’.4 From a linguistic point of view, Speusippus’ onymies are naturally taken in an Aristotelian and not in a ‘Speusippan’ manner. So at least one part of the Hambruch thesis is false: if Speusippus’ and Aristotle’s onymies do differ, it is not because the former are and the latter are not ‘Speusippan’. The Speusippan definitions (S1) and (S2) do indeed differ from the Aristotelian (A1) and (A2). But the two pairs of definitions are equivalent to one another — indeed, they express exactly the same ideas. They express the ideas which I have formulated as (D1) and (D2). For the only difference between the two pairs is the presence of ‘ŒÆa  h
Æ’ in (A1) and (A2); and that phrase does no more than make explicit a proviso which we must assume to be implicit in (S1) and (S2).1 Thus the evidence so far considered yields the conclusion that, contrary to the Hambruch thesis, there are no differences at all between Aristotle’s and Speusippus’ accounts of homonymy and synonymy. The conclusion receives some support from the fact that the Greek commentators, whose ears were attuned to ‘word’/‘thing’ disputes in connection with the Categories (see below, p.[73] n.1), report no differences between Speusippus and Aristotle save the presence or absence of ‘ŒÆa  h
Æ’.

4 C.D. Buck and W. Petersen, A Reverse Index of Greek Nouns and Adjectives (Chicago IL, 1948), pp.210–211, list 91 such compounds, 22 being found earlier than Speusippus. — The correct ‘Speusippan’ words would be compounded from ‘ÅÆ
ø’, like the late ‘æ Æ
 ’ and ‘ÆP Æ
 ’ (or ‘ÆP Å ’ — cf ‘ ºÅ ’, already in Democritus, apud Proclus, in Crat xvi [7.3–6]). 1 Why does Aristotle include ‘ŒÆa  h
Æ’ in (A1) and (A2)? (See Porphyry, in Cat 62.34– 64.22: confused, but influential.) Both Plato and Socrates have a name in common, viz ‘man’; and they have different definitions, inasmuch as what it is for Plato to be flat-footed (e.g.) is different from what it is for Socrates to be snub-nosed (e.g.). A sophist would take (S1) to imply that Plato and Socrates are in that way homonyms. The qualification in (A1) and (A2) is implicit in (S1) and (S2) in that anyone who uttered (S1) and was faced by the sophistical argument would reasonably retort that what he meant was of course (A1). — At Cat 3b7, Aristotle says: (A2*) ı

ıÆ  ª q
z
ήd  h
Æ Œ Ø
e
ŒÆd › º ª  › ÆP  Aristotle means by that exactly what he meant by (A2).

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Is there evidence against that conclusion and in favour of the Hambruch thesis? There is. I shall now consider three arguments which support the Hambruch thesis. The first is the most obvious of the three and the most powerful. According to Simplicius (in Cat 38.19–20), Boethus referred to Speusippus’ account of the onymies as a ‘division which includes all names’; and Simplicius continues thus: ‘Of names, he says, some are ... ’. Boethus explicitly ascribes ‘Speusippan’ onymies to Speusippus. Were my conclusion correct, then Speusippus’ ‘division’ ought rather to have begun: ‘Of things [H
ªaæ Z
ø
], some are ... ’.2 In order to maintain my conclusion, then, I must suppose that Boethus found a text which read in that way, decided that it offered a division which included all names, and therefore changed ‘Z
ø
’ into ‘O
Æø
’. Such a supposition is implausible and indecent. Or is it? There was a prolonged controversy among the early commentators about the aim or purpose — the Œ   or æ ŁØ — of [73] the Categories, and the controversy turned about the question of what sort of items Aristotle was there bent on classifying.1 Was he classifying things? or concepts? or words? An answer to the question was likely to influence, or even to determine, an answer to the different question: What is it that is homonymous or synonymous?2 More precisely, you might plausibly suppose that the sorts of items which may be homonymous or synonymous are the very same sorts of items which Aristotle is bent on classifying. Now Boethus held that the Categories classified neither things nor concepts but rather words (Porphyry, in Cat 59.17–34; Simplicius, in Cat 11.23–29). So he is likely to have thought that the onymies are, or ought to be construed as, properties of words rather than of concepts or of things in general; and that may have led him to interpret the onymies as linguistic properties. In fact, it seems that he did so interpret them. Simplicius preserves a passage from Boethus (25.18–26.2) in which he addresses the question of why Aristotle refers to names or O
ÆÆ at Cat 1a1 ‘although homonymy is found also among verbs [ŒÆd K
ÞÆØ
]’ (25.11). In his reply Boethus says that

2 As in the opening of the ‘alternative’ Categories (e.g. Philoponus, in Cat 7.25–31), and in the anonymous paraphrase of Cat [CIAG XXIII 2], 1.2–5). 1 There is a history of the controversy in Simplicius, in Cat 9.4–13.26; see e.g. J. Barnes, Truth, etc. (Oxford, 2007), pp.113–123. 2 Note the difficulties which Porphyry avows at in Cat 61.13–27, and the odd statement by Simplicius at in Cat 25.7–9.

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we call two different sorts of thing names: items which take a prefixed article (they are names in the special sense) and items which belong to any part of speech. Now when we inquire, in the case of any sort of expression whatever, whether or not it is homonymous we prefix an article, whether it is a name in the strict sense or any other expression — we say, for example, ‘e Œø
›
ı
KØ
’ and ‘e M
æÆ ØÆØ ›
ı
KØ
’. (in Cat 25.18–23)*

The details need not detain us: what counts is the fact that Boethus clearly and explicitly supposes that words — and words of any grammatical type — are the things which are homonymous. He has an overtly ‘Speusippan’ conception of the onymies.3 If Boethus himself construed the onymies as linguistic properties, then it is not surprising that he read Speusippus’ ‘division’ as a classification of words — after all, he read Aristotle’s onymies as linguistic properties: in Boethus’ view, the fundamental difference between Aristotle and Speusippus is not that Aristotle was talking about things and Speusippus about words — it was that Aristotle omitted two of Speusippus’ onymies. Could Boethus have got Speusippus — and Aristotle — so horribly wrong? There are two answers to the question. First, Aristotle does not present his account of his three onymies in the form ‘Of the so-and-so’s, some ... , some ... ’ — ‘H
 a 
... a  ... ’. If you wonder what sorts of things are being called homonymous and synonymous and paronymous, then you must work the answer out for yourself — Aristotle doesn’t tell you. Perhaps Speusippus was equally unforthcoming, his text beginning with no helpful ‘H
X’. It was up to the reader to determine what he was talking about. Boethus supposed that he was talking about words — that he must have been talking about words; and so in paraphrasing Speusippus he began with ‘H
O
ø
’. (That suggestion is more plausible if the subject of ‘çÅ’ at in Cat 38.20 is Boethus than if it is Speusippus.) Secondly, even if Speusippus explicitly said that he was talking about a Z
Æ, we need not suppose that Boethus misunderstood the text nor even that he wilfully ignored its true sense. Here, as in other parts of his work, Boethus * ´ ÅŁ  b ØåH çÅØ
e Z
Æ ºªŁÆØ,   æ ÆØ
¼æŁæ ı ºÆ

n ŒÆd Nø Z
Æ ºªÆØ ŒÆd e Kç –Æ
Æ a  F º ª ı  ØåEÆ ØÆE

· KØc s
K
fiH ÇÅE
Kç’ › ØÆ F
ºø N ›
ı  KØ
, æ  
e ¼æŁæ
› ø K  H
Œıæø O
ø
ήd H
¼ººø
ºø
, ºª
 e ο
›
ı
KØ
ήd e M
æÆ ØÆØ ›
ı
KØ
, ... 3 The question which Boethus is engaged in became a stock one, and the substance of Boethus’ answer was taken over by the later commentators (e.g. Porphyry, in Cat 62.1; Ammonius, in Cat 18.21) — who, however, overlook or choose to ignore the ‘Speusippan’ implications of what Boethus said.

300

Logical Matters

(I believe) was concerned not so much to interpret the great texts of the past as to present the truths which they, sometimes darkly, held out to us. Boethus thought that a true account of the onymies must construe them as linguistic properties, and so he generously read Aristotle and Speusippus in that sense. The second argument in favour of the Hambruch thesis remarks that the account of polyonymy which Simplicius gives or reports at in Cat 38.24–26 explicitly says that polyonyms are words: ‘Polyonyms are a plurality of different names for the same thing, where their account is one and the same’. If Speusippus’ polyonyms are ‘Speusippan’, as that definition implies, then surely all his onymies are ‘Speusippan’. Or perhaps not — after all, this is the definition of heteronyms: ‘Heteronyms are items different both in name and in account and in thing’ (in Cat 38.26–39.2).5 The reference to both names and things is puzzling: you can say that two things differ in name, and I suppose you can say that two names differ in thing (or hold of different things); but how can items differ both in name and in thing? The idea is presumably this: there is a case of heteronomy when you have a number of different items (Arthur and Lorenzo, say) and a number of different words (‘cat’ and ‘llama’, say) which have different senses and one of which is true of each of the different items. [74] Is that an Aristotelian or a ‘Speusippan’ onymy? As it stands, it is neither Aristotelian nor ‘Speusippan’ but indeterminate; and if you want to determine it, you may do so either in an Aristotelian or in a ‘Speusippan’ sense. Still, the definition of polyonymy is certainly ‘Speusippan’: doesn’t that tell in Hambruch’s favour, whatever we care to make of the definition of heteronymy?* Well, it does so only if the definitions come from Speusippus. I have already argued that the answer to the question ‘Who is offering us the definitions at in Cat 38.24–39.2?’ must be either ‘Boethus’ or ‘Simplicius’ and cannot be ‘Speusippus’. True, the definitions may derive ultimately from Speusippus. But we have no particular reason to think that they do, and some particular reason to think that they don’t — namely the evidence which supports the ascription of (S1)–(S4) to Speusippus. 5 Compare the definition of ‘ æ ’ where it is opposed to ‘æ
ı ’: Ammonius, in Cat 16.24–17.3; Simplicius, in Cat 22.31–33. That distinction lies behind the remarks of Alexander, in Met 247.9–24 (cf 366.31; 377.25–27: note the examples, which probably go back to Phys ˆ 202bl4 and GA A 724b19–21). * Tara´n, ‘Speusippus and Aristotle’, p.83 n.33, says that these definitions of heteronymy and polyonymy ‘express Aristotelian, not Speusippean relations’. The definition of polyonymy is explicitly ‘Speusippan’ — indeed, it is the only explicitly ‘Speusippan’ definition in the surviving texts.

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The third argument for the view that Speusippus’ onymies are ‘Speusippan’ is this. Speusippus is explicitly said to have produced a ØÆæØ or formal division.* Aristotelian onymies are not mutually exclusive and jointly exhaustive, and hence do not fall into a division.1 ‘Speusippan’ onymies are, and do. First, Aristotelian onymies are not kinds of things or of beings, of æªÆÆ or of Z
Æ: no single thing is either synonymous or homonymous. Rather, it is groups of things which are onymous in one way or the other. Secondly, the Aristotelian onymies do not divide groups of things into mutually exhaustive sets. The ancient commentators, parrying a shaft from Nicostratus (Simplicius, in Cat 30.16), regularly note that two things can be both homonymous and synonymous (e.g. Dexippus, in Cat 21.5–7; Simplicius, in Cat 30.16–31.21).2 So, for example, a fish and a mammal are synonymous with respect to the term ‘ÇfiH
’ and homonymous with respect to the word ‘Œø
’. That is possible because things in general have more than one predicate true of them — they have more than one name. If it were supposed that each thing had only one name, then Aristotelian synonymy and Aristotelian homonymy would be mutually exclusive. It is hard to avoid the impression that the commentators at times come near to adopting that supposition;3 but it is an absurd supposition. So Aristotelian onymies do not in fact make up a division, neither a division of things nor a division of sorts of things. (Aristotle, of course, does not say that they do.) What about ‘Speusippan’ onymies? Do they form a division — a division of words, or of expressions? * This section has been largely rewritten: if it is better than its predecessor, then the improvement is entirely due to Hardie, who showed me that neither Aristotelian nor ‘Speusippan’ onymies can be construed in terms of a ØÆæØ. 1 The argument does not allude to Boethus’ complaint that the onymies which Aristotle gives in Cat omit two sorts of item (Simplicius, in Cat 36.28–30 — later commentators offered explanations and excuses: see e.g. Porphyry, in Cat 60.34–61.4). Rather, it is claimed that even if the onymies of Cat are afforced by the addition of polyonymy and heteronymy, the result will not be a proper division of things. 2 The contrary seems to be asserted by Dexippus at in Cat 20.24–27 and by Simplicius at in Cat 29.5–12 (cf Olympiodorus, in Cat 31.19–26); but their point is presumably the one made more clearly by Ammonius, in Cat 19.18. 3 See e.g. the standard way of introducing the four onymies as the four possible åØ K
 E æªÆØ H
º ªø
æe a O
ÆÆ (Porphyry, in Cat 60.22–34 — note the definite articles; cf Ammonius, in Cat 15.16–16.6). — In his definition of homonymy Aristotle speaks of a name (‘Z
Æ’ without an article: Cat 1a1), in his definition of synonymy he speaks of the name (e Z
Æ: la6; cf 3b7). I cannot think that there is any significance in those facts.

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Logical Matters

(i) The presence of paronyms in Speusippus’ theory is, as I have already indicated, uneasy. If heteronymy (in the special sense) is a matter of sameness of meaning and polyonymy a matter of difference of meaning, then there is no room alongside those two onymies for paronymy. As some of the ancient commentators half realized, Aristotelian paronymy has no place alongside the homonymy and the synonymy of the Categories;* and certainly Aristotelian paronyms cannot appear in a division which also includes homonyms and synonyms (nor, as I have already remarked, does Aristotle pretend to be offering a division). The same is true of ‘Speusippan’ paronymy — assuming that ‘Speusippan’ paronymy is understood as, so to speak, a linguistic version of Aristotelian paronymy. I cannot help speculating that there were no paronyms in Speusippus’ theory. He had a neat tetrad of onymies. A commentator on the Categories — Boethus, of course, — tacked on the paronyms in order to improve and complete the theory in the light of Aristotle’s elaborations. Of course, there is not a jot of evidence in favour of such a speculation. (ii) ‘Speusippan’ homonymy and synonymy are easily — and naturally — taken as predicates of names or words (they are so taken in (D10) and (D20)). ‘Speusippan’ heteronymy is not: no word is heteronymous — and polyonymy is a relation among words or a property of groups of words. So the ‘Speusippan’ onymies cannot form a division of anything — neither of words nor of groups of words. Unless, of course, homonymy and synonymy can be somehow be construed as properties of groups of words or as relations among words. Leonardo Tara´n has so construed them. He supposes that Speusippus’ ØÆæØ starts by postulating that ‘either two or more words are identical ... or they are different’: in the first case the words are tautonyms, in the latter they are polyonyms. Next, the members of a group of words either have the same sense or they have different senses: if they are tautonyms, then the former case gives synonyms and the latter homonyms.** That reconstruction presupposes that Speusippus is ‘dividing’ occurrences of words, or ‘wordtokens’. (How many words are there in the phrase ‘To be or not to be’? There are six word-tokens and four word-types.) And Tara´n’s somewhat curious clause ‘two or more words are identical’ means ‘two or more word-tokens * See e.g. Ammonius, in Cat 23.25–24.12; Olympiodorus, in Cat 39.23–40.13; cf Ackrill, Categories, p.72. ** Tara´n, ‘Speusippus and Aristotle’, p.91.

Speusippus and Aristotle on homonymy

303

are examples of the same word-type’. I cannot show that that is a false interpretation of Speusippus; but I do not know of any other ancient text on the onymies which deals with word-tokens. Even if Tara´n is right, his interpretation does not give Speusippus a division of groups of words. It is indeed true that any two token words are either of the same type or of different types. But if a group has three or more members, then there are more possibilities — in a group of three tokens, say, either all or two or none may be of the same type. Take the Shakespearean sextet ‘to be or not to be’: its members are neither ‘Speusippan’ polyonyms (since they don’t all have the same sense) nor ‘Speusippan’ heteronyms (since they don’t all have different senses). (That is not an objection against the theory which Tara´n ascribes to Speusippus: it shows no more — and no less — than that the theory is not a ØÆæØ.) [75] (iii) The definition of heteronymy (in the special sense) which Simplicius gives at in Cat 38.26–39.2 suggests something which, though it is not a ØÆæØ in the strict sense of the term, does possess the features of exclusivity and exhaustivity which a division requires. It concerns possible permutations of groups of items, names, and meanings, thus: (1) Several items, one name, one meaning (2) Several items, one name, several meanings (3) One item, several names, one meaning (4) One item, several names, several meanings Cases (1) and (2) you might call tautonymies, case (1) being synonymy and case (2) homonymy. Cases (3) and (4) you might call heteronymies, case (3) being heteronymy in the special sense and case (4) polyonymy. Perhaps something like that underlies Speusippus’ ‘division’? In that case, were his onymies Aristotelian or ‘Speusippan’? The answer, as I indicated earlier, is undetermined. You might choose to define synonymy, say, by decreeing that a name is synonymous with respect to a given group of several items if and only if it is true, in the same sense, of each of the items. Then synonymy is ‘Speusippan’. You might choose to define synonymy by decreeing that the members of a group of items are synonymous with respect to a given name if and only if the name is true of each item in a different sense. Then synonymy is Aristotelian. The choice between a ‘Speusippan’ definition and an Aristotelian definition is purely terminological and has no substantive implications. I suspect that Speusippus, Aristotle, and the later commentators all agree on the substance of the matter; and that few if any of them were exercised

304

Logical Matters

by — or had even reflected upon — the terminological choice. Any disagreements among the various accounts of the onymies which I have mentioned are superficial, and testify to no substantive discord. The arguments for the first part of the Hambruch thesis which the preceding three sections have run through are not strong; and I incline to reassert an earlier conclusion, and to claim that Speusippus’ onymies were Aristotelian. But if Hambruch is right and Speusippus presented ‘Speusippan’ onymies, it will still be true that the Aristotle’s and Speusippus’ onymies were in substance identical, the difference between them being superficial and terminological.

Aristotle’s use of ‘˙lþmulor’ What, then, of the second part of the Hambruch thesis and the claim that sometimes Aristotle appeals to ‘Speusippan’ onymies and thereby shows the influence of Speusippus? Well, if Speusippus’ onymies were ‘Speusippan’ and if Aristotle sometimes invokes ‘Speusippan’ onymies, then it might perhaps be true that those Aristotelian passages show the influence of Speusippus. But the influence can only have been terminological, and of no doctrinal importance. But if Aristotle’s onymies are essentially the same as Speusippus’ onymies, as I have argued, then a more interesting question of influence arises. We shall scarcely suppose that Aristotle and Speusippus hit upon their onymies independently and in ignorance of one another. So either Speusippus was first in the field, and Aristotle later adopted, for his own ends, two members of Speusippus’ tetrad, improved their definitions by adding ‘ŒÆa  h
Æ’, and subjoined paronymy. Or else Aristotle was first in the field, and Speusippus later took over two of Aristotle’s triad of onymies and added heteronymy and polyonymy to them. I don’t think there is any demonstrative reason for preferring one of those options to the other; but if I had to bet, I should put my money on the first of them. And in that case, Speusippus had a strong influence on Aristotle’s notion of the onymies — a far stronger influence than the one which Hambruch discovered. However that may be, it is perhaps worth looking briefly at the claim that in certain places Aristotle makes use of ‘Speusippan’ notions. I shall first make some general remarks about Aristotle’s use of the word ‘›
ı ’; and then

Speusippus and Aristotle on homonymy

305

consider a few passages which have been mentioned in connection with the Hambruch thesis.* I distinguish four chief Aristotelian uses of the word ‘›
ı ’.1 (i) Aristotle often uses phrases of the sort ‘X, Y, Z, ... are called T homonymously’. (For clear examples, see Met Z 1035b1; EN E 1129a30.) Such phrases are explained directly by way of (D1) The members of a group of items are homonymous with respect to a term T if and only if T is true in a different sense of each member of the group. Or rather, when the members of the group are individuals, the application of (D1) is perfectly straightforward: it is slightly less so when the members are pluralities. You might, for example, say that ‘rational’ is true of men in one sense and of numbers in another: what does ‘‘‘rational’’ is true of men’ mean? Surely it means ‘‘‘rational’’ is true of every man’? But that won’t do for numbers. So presumably we should understand ‘T is true in different senses of X and of Y’, where ‘X’ is replaced by a common noun vel sim, like this: ‘T is true in one sense of those Xs of which it is true and in another sense of those Ys of which it is true’. That, I suppose, is the first or fundamental use of the word ‘›
ı ’. Aristotle will also write sentences of the sort (ii) ‘X is homonymous with Y’, or ‘X and Y are homonymous’ (e.g. Cat 1a2–6; Phys H 248b7–9) and (iii) ‘X is called T homonymously’ or ‘X is T homonymously’. (A common case of use (iii) concerns the status of dead organs: e.g. GA B 734b25; Meteor ˜ 389b31.) Each of those uses is, as it were, a truncated version of use (i). Use (ii) is explicated by reference to (D1*) The members of a group of items are homonymous if and only if there is at least one term with respect to which they are homonymous — and hence by reference to (D1). Use (iii) may be codified by (D1**) An item is homonymous with respect to a term T if and only if it is a member of a group of items which are homonymous with respect to T.

* Compare Tara´n, ‘Speusippus and Aristotle’, pp.92–99, who finds many more ‘Speusippan’ uses in Aristotle than I do. 1 The following pages are based on a consideration of (a) all occurrences of ‘›
ı ’ etc. listed in Bonitz’ Index, and (b) all occurrences in the Topics. It is often difficult to decide how to classify a given occurrence; and there are some occurrences which fit none of the classes.

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Logical Matters

Use (ii) expresses a homonymy relation without specifying in respect of which [76] term the items in question are homonymous. But it is precisely that term which is the philosophically interesting feature of homonymy: that, say, Socrates and courage are homonymous is in itself of no consequence; what excites Aristotle is the claim that they are homonymous with respect to the term ‘being’.1 But where use (ii) is found, there is usually some contextual indication of the pertinent term. Use (iii) generally has a certain nuance to it: when Aristotle says, for example, that corpses are called ‘men’ homonymously, he intimates that a corpse is a man only in a secondary or derivative or off-colour sense of the word ‘man’.2 (Not that ‘homonymously’ means ‘derivatively’.) Instead of saying ‘Corpses are men homonymously’, Aristotle will sometimes say ‘Some men are homonymous’ vel sim: e.g. Met Z 1035b25; Int 23a7. ‘Some men are homonymous’ means the same as ‘Some items are homonymously men’. That is a special case — one among several — of use (iv). In use (iv), the term in respect of which items are said to be homonymous becomes the subject-term and is used to designate the items which are said to be homonymous. So instead of saying, for example, ‘Some items — a certain species of fish and a certain type of quadruped — are homonymous with respect to the term ‘‘dog’’’, you may say ‘Dogs are homonymous’, or ‘Dogs are (so-)called homonymously’, or ‘The dog is homonymous’, and so on. It is not easy to give a precise definition of the underlying idea — something like this must do: (D***) Xs are homonymous if and only if the items of which the term ‘X’ is true are homonymous with respect to the term ‘X’. Use (iv) is by far the most frequent of the four which I have distinguished: for examples see Top A 106a21; Z 139b21; Met ˆ 1003a34; EE ˙ 1236a17, b25. There is a close connection between (iv) and another standard Aristotelian formula: ‘Xs are (so-)called in several ways [ ººÆåH (º
ÆåH) ºªÆØ e `]’.3 1 Hardie wrote: ‘such a use, without specification of the term T, would surely be a senseless mystification, or a move in a guessing-game, or a clue in a puzzle, not just philosophically uninteresting’. 2 So in his commentary on Meteor ˜ 389b31 Alexander contrasts ‘›ø
ø’ with ‘Œıæø’: in Meteor 223.27 (cf Rhet ˆ 1405a1, quoted below, p.[79]). 3 In the Topics at least this phrase is interchangeable with (iv): elsewhere, Aristotle sometimes distinguishes between homonymy and ‘being said in many ways’ (see Hintikka, ‘Ambiguity of ambiguity’).

Speusippus and Aristotle on homonymy

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Those four cases account, I think, for Aristotle’s central uses of ‘›
ı ’.4 [77] Is it plausible to suppose, with regard to any of uses (i)–(iv), that homonymy ought to be construed in a ‘Speusippan’ manner? Of course not — all the uses are explicable by reference to (D1), and (D1) is Aristotelian rather than ‘Speusippan’. Yet it might be thought that use (iv) lends itself to a ‘Speusippan’ interpretation. When Aristotle writes ‘ ººÆåH ºªÆØ e `’, doesn’t the expression ‘e `’ designate the word ‘A ’? And isn’t the same true — often if not always — in phrases of the sort ‘›
ı
KØ
e `’? It is a familiar fact that the Greek definite article, in the neuter singular, may function in the way in which modern inverted commas sometimes function: put inverted commas round the expression ‘honorificabilitudinitatibus’ and you get a name for that sesquipedalian word; put ‘ ’ in front of ‘’ and you get a name for that insignificant particle. Thus expressions of the form ‘e `’ may mean ‘(the word) ‘‘A’’’ as well as ‘the A ’ — so ‘e æÆ 
’ may mean ‘(the word) camp’ as well as ‘the camp’.1 Hence it is possible to translate ‘›
ı
KØ
e `’ as ‘The expression ‘‘A’’ is homonymous’ where ‘homonymous’ is overtly predicated, in ‘Speusippan’ vein, of a linguistic item. Grammar undoubtedly permits such a translation, some cases of use (iv) appear to require it,2 and anyone who tries to English Aristotle will 4 Quite distinct are the cases in which Aristotle uses ‘›
ı ’ in its non-technical sense of ‘having the same name as’: references in Bonitz, Index, 514b13–18; see also Alexander, in Met 51.15; 77.12 (Alexander says that Aristotle took this use over from Plato: cf Anton, ‘Aristotelian Doctrine’, p.318, with references). 1 See e.g. KG I, pp.586–597; and for Aristotle e.g. Soph El 182a18, 21, 30; Met ˆ 1006a31, b2, 14, 17, 23, 26 (cf Boethus, apud Simplicius, in Cat 25.18–26; Porphyry, in Cat 61.31–62.6). — The situation is complicated by several factors. For example, (a) sometimes the definite article takes the gender of the term it governs, even when the term is masculine or feminine and the article has its inverted comma use: see e.g. Cat 3b17; Top E 130b3; Z 141a13; 142b5; Poet 1457a28. (b) Aristotle subscribes to the view that every term can be used autonymously — that ‘A’ means both ‘A’ and ‘(the word) ‘‘A’’ ’: Soph El 174a8–9 (presumably this is the source of the medieval distinction between formal and material supposition: cf E.A. Moody, Truth and Consequence in Mediaeval Logic (Amsterdam, 1953), pp.23–25). (c) In practice, Aristotle — like most people and even most philosophers — is often very casual about the difference between use and mention. In practice, of course, it often doesn’t matter; but it sometimes introduces irritating ambiguities and occasionally produces horrors (for a peculiarly unpleasant example see APst A 71a15–16). — See further Barnes, Porphyry, pp.319–322. 2 I am thinking of cases in which the ‘A ’ of ‘e `’ isn’t a name — e.g. ‘e ŒÆŁ ‹’ (e.g. Met ˜ 1022a14) or ‘e Œ Ø
 r
ÆØ’ (1023a26). But Aristotle uses nominalizations of that sort in contexts where the inverted comma reading of the definite article is out of the question — for example, the expressions ‘e  q
r
ÆØ’ and ‘e Øa ’ never mean ‘the expression ‘ q
r
ÆØ’’ or ‘the expression ‘Øa ’’.

308

Logical Matters

frequently — and justifiably — resort to it.* But even if there are cases in which a ‘Speusippan’ construal is correct, it is certainly not generally correct and I do not think that it is often correct. In sum: Aristotle’s standard uses of ‘›
ı ’ are, all of them, Aristotelian and not ‘Speusippan’. That conclusion leaves open the possibility that the word sometimes occurs in a ‘Speusippan’ fashion — either because it is not used in accordance with any of the standard uses I have distinguished or else because special contextual features make a ‘Speusippan’ interpretation of a standard occurrence obligatory or preferable. In the next few paragraphs I shall look at a few Aristotelian passages in which ‘›
ı ’ and the like have been or might be taken to be ‘Speusippan’. The most significant passage is Topics A 15, which is concerned expressly with the dialectical issues raised by ‘items said in several ways’. The chapter contains ten occurrences of ‘›
ı ’, each in use (iv), and two of ‘ı

ı ’. Hambruch asserted that ‘ı

ı ’ here designates ‘Speusippan’ [78] synonymy.1 One of the two occurrences of ‘ı

ı ’ is at 107b16–17: So e ºıŒ
and e O are homonymous; for everything which is synonymous is comparable — either they will be said to be similarly so-and-so or one of them will be said to be more so-and-so.**

The explanatory sentence, ‘For everything ... ’ means that if X and Y are synonymously A, then they are comparable with respect to A (i.e. either they are equally A or one is more A than the other). (On comparability see e.g. Phys H 248a10–249a29; Pol ˆ 1283a1–10. The rule applies only to terms * When Hambruch finds ‘Speusippan’ onymies in Top A 15 all the translators appear to side with him — so e.g. Pickard-Cambridge’s Oxford Translation, Forster’s Loeb, and Brunschwig’s Bude´. — Hardie writes: ‘Might not a translator, while taking the expressions to be non-‘‘Speusippan’’, think that a liberty was justified by a gain in brevity and neatness?’ A translator might indeed take such a liberty (perhaps without thinking that it was a liberty at all) — and he would usually be right to do so. 1 In this, as he says, he follows Waitz, Organon II, p.452. — Hambruch does not explicitly assert that the occurrences of ‘›
ı ’ in A 15 are ‘Speusippan’, but I assume he thought they were: (a) he identifies ‘Speusippan’ ›
ıÆ with  ººÆåH ºª 
Æ (p.28 n.1), and ‘›
ı ’ is used synonymously with ‘ ººÆåH ºª 
’ in A 15; and (b) Waitz’s argument that the ı

ıÆ of A 15 are ‘Speusippan’ depends on his construing the ›
ıÆ in the same context as ‘Speusippan’. Waitz, however, thought that all Aristotle’s onymies were ‘Speusippan’ — at any rate, in his notes on the Categories he says that ‘definit [sc. Aristoteles] vocum et homonymiam et synonymiam, non rerum ’ (I, p.272). ** uŁ ›
ı
e ºıŒe
ŒÆd e O. e ªaæ ı

ı
A
ıºÅ
· j ªaæ › ø ÞÅŁÆØ j Aºº
Łæ
.

Speusippus and Aristotle on homonymy

309

which admit comparatives.) The synonymy referred to in the explanatory sentence is — pace Hambruch — certainly Aristotelian. So the homonymy in the previous sentence ought also to be Aristotelian. Another occurrence of ‘›
ı ’, at 107a39, is shown by its context to be non-‘Speusippan’. The other nine occurrences — one of ‘ı

ı ’ and eight of ‘›
ı ’ — are, in their contexts, indeterminate. But the fact that all twelve occurrences are of parallel grammatical form strongly suggests that if any of the onymies in A 15 is ‘Speusippan’, then all are. Hence none are.2 Cherniss finds a ‘Speusippan’ usage at PA A 643b4–7, part of a long argument which he thinks is directed against Speusippus:* Pretty well all tame animals are also found wild — men, horses, cows, dogs, pigs, goats, sheep. In each case, if they are homonymous, they are not divided separately ... **

If wild pigs and tame pigs are homonymous with respect to the term ‘pig’, then wild pigs and tame pigs aren’t subspecies of the species pig. What you might (wrongly) so divide into subspecies is not the term ‘pig’ but the species of pigs. It is pigs, not the term ‘pig’, which is supposed (counterfactually) to be homonymous; and that is Aristotelian and not ‘Speusippan’ homonymy. Owen offers two passages in support of his contention that ‘Aristotle’s usage [sc. of ‘›
ı ’] is far from being as rigid as Hambruch supposes’.*** I take it that he thinks the two passages exhibit ‘Speusippan’ usage. The first passage is this: If the extremes are homonymous, then the middle is homonymous; and if they are of a kind, the middle will have the same character ... For in these cases e ‹ Ø
is homonymous. (APst B 99a7–13)**** 2 Hambruch (Logische Regeln, p.29 n.1 — L. Robin, La The´orie platonicienne des ide´es et des nombres d’apre`s Aristote (Paris, 1908), p.138) also suggests that the account of numerical identity in Top A 7 is influenced by Speusippus: the first definition of ‘one in number’ (103a9–10, 25–27) is, he claims, at once inconsistent with what Aristotle says elsewhere about numerical identity and identical with what Speusippus says about polyonymy. (Alexander, in Top 58. 8–11 takes things numerically one to be polyonymous; cf in Met 281.24.) But Aristotle’s numerical identity is not a relation which holds only among linguistic items. * See Aristotle’s Criticism, p.57 n.47. — 642b5–644a11 is printed as frag 67 in Tara´n’s Speusippus. ** 
Æ ªaæ ‰ NE
‹Æ læÆ ŒÆd ¼ªæØÆ ıªå
Ø Z
Æ, x
¼
Łæø Ø ¥  Ø   Œ
 o Ær ª æ ÆÆ· z
ή
, N b
›
ı
, P ØfiæÅÆØ åøæ ... — D.M. Balme, Aristotle’s de Partibus Animalium I and de Generatione Animalium I (Oxford, 1972), pp.116–117, argues that ‘
’ should be changed to ‘’: contra Tara´n, ‘Speusippus and Aristotle’, p.97 n.77. *** See Owen, ‘A proof ’, p.104 n.1. **** N b
›
ıÆ [a ¼ŒæÆ], ›
ı
e 
, N  ‰ K
ª
Ø, › ø Ø. ... ›
ı
ªaæ e ‹ Ø
Kd  ø
[sc åæÆ  ŒÆd åÆ ].

310

Logical Matters

In the first sentence Aristotle is talking of the terms of a syllogism, and you may readily suppose him to be designating linguistic items. Nonetheless, the items which are ‘of a kind’ are not the words (‘substance’, ‘animal’, ‘man’, and so on) but the [79] things to which the words allude. So what is homonymous is not the word ‘‹ Ø
’ but rather the similar items to which the word applies.1 The second passage is Phys H 248b12–21: in H 4 as a whole the word ‘›
ı ’ occurs seven times (‘›ø
ıÆ’ appears twice; ‘ı

ı ’, probably, once). Three of the occurrences are shown by their context to be non-‘Speusippan’: at 248b12–13, for example, Aristotle asks: First, perhaps it isn’t true that if things are not homonymous they are comparable?*

(cf Top A 107b16–17.) Those three non-‘Speusippan’ examples are all of type (iv). Three more of the seven are also of type (iv), and I infer that they too are non-‘Speusippan’. The remaining occurrence is at 248b7: Of some of the items the definitions too are ›
ı Ø.**

Surely definitions are linguistic items, so that the homonymy, here at least, must be ‘Speusippan’? Perhaps. Whatever may be thought of that last example, there are certainly a few ‘Speusippan’ onymies dotted about in the corpus Aristotelicum. Thus at Soph El 175a37 there is the phrase ‘a non-homonymous contradiction’ (cf Int 17a35). At Rhet ˆ 1404b37–1405a2 Aristotle remarks that of names, homonymies are useful to sophists ... and synonymies to poets. By proper and synonymous I mean ... ***

That is to say, ‘by proper and synonymous ’ I mean ... ’. Phys ˆ 207b9 mentions paronymous words; Soph El 167a24 uses the phrase ‘nonsynonymous name’; Top E 129b30 (cf GC A 322b30) talks of names being said in many ways. 1 W.D. Ross (Aristotle’s Prior and Posterior Analytics (Oxford, 1949), p.668) paraphrases thus: ‘If the major is ambiguous, so is the middle. If the major is a generic property ... , so is the middle term’. The reference of ‘the major’ and of ‘the middle’ shifts from the first to the second of those sentences. I don’t think we need charge Aristotle with such a shift. * j æH
b
 F PŒ IºÅŁb ‰ N c ›
ıÆ ıºÅ; ** K
ø
ŒÆd ƒ º ª Ø ›
ı Ø. cf Top A 107b6; E 129b31. *** H
b O
ø
fiH  çØfiB ›ø
ıÆØ åæØ Ø ... fiH  ØÅfiB b ı
ø
ıÆØ· ºªø b ŒæØ  ŒÆd ı

ıÆ ...

Speusippus and Aristotle on homonymy

311

Porphyry, in Cat 61.14, says that although homonyms are things, homonymies are words; and in several passages, in addition to Rhet ˆ 1404b37, it is natural to construe homonymies as words (e.g. Rhet ˆ 1412b11; APst A 85b16; B 97b36), and perhaps ‘›ø
ıÆ’ is so used in the phrases ‘ºªŁÆØ r
ÆØ ŒÆŁ’ ‘›ø
ıÆ
’ and ‘Ææa c
›ø
ıÆ
’.* That list does not pretend to be exhaustive; but I do not believe that ‘Speusippan’ uses of ‘›
ı ’ and the like are anything other than rare in Aristotle.

Conclusion The Hambruch thesis states (a) that Speusippus’ notion of homonymy and synonymy differs from Aristotle’s, and in particular (b) that Speusippus’ onymies, unlike Aristotle’s, are properties specific to linguistic items; the thesis maintains further, (c), that in certain passages, notably in the first book of the Topics, Aristotle fell under Speusippus’ influence and temporarily forsook his own notion of the onymies. [80] Against that, I have argued (b*) that on the whole our evidence suggests that Speusippus did not define his four onymies as specifically linguistic properties, and in general, (a*), that in all probability Speusippus’ accounts of homonymy and synonymy differed only trivially from Aristotle’s definitions at the beginning of the Categories. Further, I have indicated that in the corpus Aristotelicum the words ‘›
ı ’ and ‘ı

ı ’ occur in a number of different but connected ways, almost all of them explicable in terms of the definitions set out at the beginning of the Categories. But I agree (c*) that in a few places homonymy and synonymy appear as specifically linguistic properties. That concedes something to part (c) of the Hambruch thesis; but it differs from (c) inasmuch as those uncharacteristic passages cannot be taken to betray the backstage influence of Speusippus. * But Hardie, rightly I think, regards such expressions as neutral or indeterminate.

9 Property in Aristotle’s Topics * Introduction Property, or YØ
, is one of the four so-called predicables which Aristotle introduces and explains in Book A of the Topics. The schema of the predicables gives the Topics its structure: after the introductory remarks in A, Books B and ˆ deal with accident; ˜ with genus; E with property; Z and H with definition. Although in one place Aristotle remarks that interesting claims of the form ‘X is property of Y’ are sparse (˜ 120b12–15), he nevertheless devotes a whole book to them where he more than once asserts that ‘we establish a property for the sake of knowledge’ (E 129b7; 130a5; 131al). Elsewhere in the corpus of Aristotle’s writings properties often assume an important role.i In this paper I discuss (1) the definition of ‘YØ
’ given in Book A of the Topics; (2) and (3) some ways in which Aristotle later departs from this definition; and (4) a confusion that permeates his discussion of properties. Finally, (5) I shall comment on a controversial    in Book E. I think that Book E is the work of Aristotle. In some respects E is strikingly different, in matter and in style, from the other Books of the Topics; and it has been supposed that the whole book is spurious,ii or at least that Aristotle never meant it to be placed between ˜ and Z.iii However, although the central books of the Topics may well have been written — perhaps ‘compiled’ is a better word — more or less independently of one another,iv they were certainly assembled in their present order by Aristotle himself: the programme indicated in Book A and summarized in Book I — that is to say,

* The first five sections of this chapter were originally published in AGP 52, 1970, 136–155. The article carried no foot-notes: the new notes are given in Roman numerals rather than asterisks. i See G. Verbeke, ‘La notion de proprie´te´ dans les Topiques’, in G.E.L. Owen (ed), Aristotle on Dialectic (Oxford, 1968), pp.257–276. ii See especially J. Pflug, De Aristotelis Topicorum libro quinto (Leipzig, 1908). iii See J. Brunschwig, Aristote: Topiques livres I–IV (Paris, 1967), pp.LXXIII–LXXIV; cf p.LXXIX. iv An independence which is probably reflected in Diogenes Laertius’ catalogue of Aristotle’s writings: see Brunschwig, Topiques, p.LXXIII n.2.

Property in Aristotle’s Topics

313

in the Sophistici Elenchi — (183a37–b15) gives the general proof of the claim; in the particular case of E, there is no reason to reject the references at ˜ 120b11 and Z 139b4–5, which imply that a discussion of property intervenes between the accounts of genus and of definition. Scholars who reject Book E are obliged to conclude that Aristotle wrote a book on property to stand between ˜ and Z, [137] that the book was lost, and that its place filled by some pious Aristotelian who wrote our Book E. The oddities of E do not seem to me sufficient to justify so extravagant an hypothesis.i Following tradition, I translate ‘X is YØ
of Y’ by ‘X is proper to Y’ or ‘X is a property of Y’; and to save paper I abbreviate the formula to ‘I(X,Y)’. ‘F is a property’ means ‘For some Y, I(X,Y)’. ‘E(X,Y)’ abbreviates ‘X reveals the essence of Y’ — an Aristotelian expression which I shall not attempt to interpret. The rest of the abbreviations and symbols are self-evident or standard, except that the arrow, ‘!’, marks strict implication or entailment (‘P ! Q’ is true if and only if it is not possible that it be true that P and not true that Q).

The definition of ‘proper’ Property is the second of the four predicables which Aristotle defines and discusses in A 5 of the Topics. The definition goes: A property is that which, while not showing the essence of its subject, holds of it alone and is counter-predicated of the thing. (102a18–19)ii

The two clauses conjoined by the word ‘and’ do not indicate two distinct conditions: rather, ‘counter-predicated of’ and ‘holds of alone’ are equivalent — and ‘holds of alone’ is dropped when the definition is picked up at 103b11–12 (cf E 132a4–9; 133a5–11 — contrast H 155a26). ‘A is counter-predicated of B [e ` I
ØŒÆŪ æEÆØ  F ´]’ is one of the means by which Aristotle expresses the two-way implication which modern logic symbolizes as ‘(8x)(Ax $ Bx)’.iii He also uses the highly ambiguous i

A less extravagant hypothesis has been advanced, forcefully and convincingly, by T. Reinhardt, Das Buch E der Aristotelischen Topik: Untersuchungen zur Echtheitsfrage (Go¨ttingen, 2000): according to Reinhardt, although Book E is at bottom Aristotelian, it contains a large number of fairly substantial passages which were added by a later author. ii YØ
 Kd
n c ź E b
e  q
r
ÆØ, 
fiø  æåØ ŒÆd I
ØŒÆŪ æEÆØ  F æªÆ . iii See Bonitz, Index, 64a8–14.

314

Logical Matters

formula ‘A converts with B’,i and the clearer phrase ‘A and B follow one another’, ‘ ÆØ Iººº Ø’, formulas which are used of properties elsewhere (e.g. APst A 73a7; B 91a15–16). It will prove convenient to write instead of ‘(8x)(Ax $ Bx)’ the equivalent expression ‘(8x)(Ax ! Bx) & (8x)(Bx ! Ax)’. Aristotle’s definition can then be symbolized as: (D1) I1(A,B) ¼ df ¬E(A,B) & (8x)(Ax ! Bx) & (8x)(Bx ! Ax) Essentially the same account is given by Jacques Brunschwig.ii I disagree with him on a point of detail: he holds that it is the variable ‘x’ in (D1) which answers to Aristotle’s word ‘the thing’, ‘ F æªÆ ’, at 102a19; I prefer the traditional view that the thing is the predicate B (cf A 103b19; E 129b14; 132b33; 133a7, 10; Z 140b21–26). (I do not understand Brunschwig when he says that ‘the predicables do not stand for real relations which can hold between a subject and the properties it [138] possesses, but intentional relations which can hold between a subject and the properties a proposition attributes to it’.iii (D1) makes no reference to the ascription of properties by, or in, propositions.) (D1) is immediately exemplified: e.g. being capable of literacy is proper to men; for if he is a man he is capable of literacy, and if he is capable of literacy he is a man. (102a19–22)iv

Presumably it is taken for granted that being capable of literacy does not ‘reveal the essence’ of men. In his illustration Aristotle uses the connective ‘If ... , then ... ’, which perhaps encourages a weaker interpretation than the arrow of entailment which I have used in (D1). The fact that Aristotle uses ‘A and B follow one another’ as a synonym for ‘A is counter-predicated of B’ is, I think, enough to justify the arrow in (D1). But there is stronger evidence than that in the next sentence of the text: For no-one calls proper what can hold of something else — e.g. being asleep of men — even if for a while it actually holds of its alone. (102a22–23)v

i I
ØæçØ
: see W.D. Ross, Aristotle’s Prior and Posterior Analytics (Oxford, 1949), p.93; Brunschwig, Topiques, p.LXXXVII n.5. ii Topiques, p.122 n.1. iii Topiques, p.L. iv x
YØ
I
Łæ ı e ªæÆÆØŒB r
ÆØ ŒØŒ
· N ªaæ ¼
Łæø  KØ, ªæÆÆØŒB ŒØŒ  KØ, ŒÆd N ªæÆÆØŒB ŒØŒ  KØ
, ¼
Łæø  KØ
. v PŁd ªaæ YØ
ºªØ e K
å 

¼ººfiø æåØ
, x
e ŒÆŁØ
I
Łæfiø, P i
åfi Å ŒÆ Ø
Æ åæ


fiø æå
.

Property in Aristotle’s Topics

315

The particle ‘for’ shows that this is meant in support or explanation of (D1). The position it supports is this: if A is proper to B, then it is not possible for anything to be A and not B. The same thing is stated more clearly a little later on: It is plain that none of the things which can hold of something else is counterpredicated; for it is not necessary that if something is asleep then it is a man. (102a28–30)i

Those two passages prove only that the first implication in (D1) — the implication from A to B — is entailment; they say nothing about the second implication. That deficiency is made up in Book E where Aristotle once or twice states that if I(A,B), then A holds necessarily of B or that whatever is B must be A (131a31–32; 133a12–23; cf 129a3–4). Why did Aristotle require a necessary tie between properties and propertyowners? He gives two reasons. The first we have already seen: no one calls A proper to B if it can hold of something non-B. Ordinary Greek usage dictates that if I(A,B), then [139] any A must be B. The other half of the requirement, that if I(A,B), then any B must be A, seems to be based on epistemological grounds; this at least is suggested by a    in Book E: Then, in attack, see if he has given a property the holding of which is not evident except by perception. For the property will not be correctly laid down. For everything perceptible becomes unclear when it gets out of the range of perception; for it is uncertain if it still holds since it is recognized by perception alone. This attack will be good in the case of things which do not always follow from necessity. (131b19–25; cf 131a32–35; APr B 67b1)ii

The argument is this: the purpose of property-claims is to increase our knowledge; but a property-claim of the form I(A,B) cannot give knowledge about B unless it is certain that A holds of B; and it cannot be certain that A holds of B unless A necessarily holds of B. The argument is mistaken; but I think it explains why Aristotle required a necessary bond between a property and its owner — and at the same time it illustrates the connexion between the

i ‹Ø b H
K
å 
ø
¼ººfiø æåØ
PŁb
I
ØŒÆŪ æEÆØ, Bº
· P ªaæ I
ƪŒÆE
Y Ø ŒÆŁØ, ¼
Łæø
r
ÆØ. ii Ø I
ÆŒıÇ
Æ b
N  Ø F I øŒ e YØ
n çÆ
æe
c Ø
¼ººø æå
j ÆNŁØ· P ªaæ ÆØ ŒÆºH Œ

e YØ
. –Æ
ªaæ e ÆNŁÅe
ø ªØ


B ÆNŁø ¼ź
ª
ÆØ· IçÆ
b ªæ KØ
N Ø æåØ Øa e fiB ÆNŁØ 

ª
øæÇŁÆØ. ÆØ  IºÅŁb  F Kd H
c K I
ªŒÅ Id ÆæÆŒ º ıŁ 
ø
.

Logical Matters

316

work Aristotle hoped properties could do and the conditions he laid down to define them. There are passages in E where Aristotle appears to require more than a necessary connexion between a property and its owner: he demands that A hold of B ‘qua ’ B (132a27–b3; 134a18–25 — but cf 134a32–33 and b10–13; 137b3–13; cf 133a24–34; 133a35–b14; for the sense of ‘qua ’ see APst A 73b25–74a3). However, it seems that if A and B are counterpredicated, then A must hold of B ‘qua ’ B; and if that is so, then these passages do not introduce anything new. It has often been thought that properties include the so-called ‘per se accidents’, a ŒÆŁ Æa ıÅŒ Æ — those predicates which, according to the Posterior Analytics, occur in the conclusions of demonstrative deductions;i and the fact that Aristotle uses the singular phrase ‘accidental properties’ at an A 402a15 to refer to per se accidents seems to be evidence for the view. But the view is false. Aristotle expressly states that demonstrations are very rarely concerned with counter-predications (APst A 73al6–18; 78a10–13). The Metaphysics defines per se accidents as ‘those things which hold of each thing in itself without being in its essence’ (˜ 1025a31–32); since the Posterior Analytics states that holding ‘in itself’ and [140] holding necessarily are equivalent (A 74b5–12), the definition yields: () (A,B) $ ¬E(A,B) & (8x)(Bx ! Ax) It is plain from (D1) and () that ‘(A,B)’ is entailed by but does not entail ‘I1(A,B)’. Hence per se accidents are not properties. The phrase in the de Anima must be explained by reference to such passages as APst A 76b3–11. In truth, per se accidents do not fit at all neatly into the fourfold classification of the predicables. They are neither definitions nor genera nor properties. Therefore, by Aristotle’s first definition of ‘accident’ (A 102b4–5), they are accidents. But they hold necessarily of their subjects; therefore, by the second definition of ‘accident’ (A 102b6–7), they are not accidents. This shows that the two definitions are not equivalent, and hence that the predicables are not well defined.

i

So e.g. Verbeke, ‘Notion de proprie´te´’, p.263 n.1.

Property in Aristotle’s Topics

317

Strong and weak senses of ‘property’ In A 4 Aristotle first offers a list of three predicables: Every proposition and every problem reveals either a property or a genus or an accident. (101b17–18)i

The canonical four are achieved by splitting property in two: Since property sometimes signifies the essence and sometimes does not signify it, let property be divided into the two aforesaid parts, and let the part which signifies the essence be called definition and let the other part be called by the name given in common to both of them, viz property. It is clear then from what has been said that by the present division there come to be four things in all: either definition or property or genus or accident. (101b19–25)ii

The word ‘property’ thus has two senses, the one given in (D1) and a wider sense. Aristotle does not explain the wider sense in A 4 or A 5, but clearly it is given by: (D2) I2(A,B) ¼ df (8x)(Ax ! Bx) & (8x)(Bx ! Ax) All (D1) properties are (D2) properties, but not all (D2) properties are (D1) properties. Thus (D2) gives a weaker sense to the term ‘proper’ than (D1). Brunschwig marks the distinction by talking of ‘exclusive’ and ‘inclusive’ interpretations of the predicables. He argues that the inclusive interpretation — in which ‘proper’ is read in the sense of (D2) — is the earlier.iii [141] (D1) is set down formally in A 5, and it is reasonable to expect that it will determine the sense of ‘property’ for the rest of the Topics. The major part of Book E is compatible alike with (D1) and (D2): 27 out of 36   Ø are so framed that it cannot be said whether ‘proper’ occurs in them in its strong or its weak sense. Of the remaining   Ø, three demand the strong sense of (D1), namely: 132b35–133a11, 133a12–23, and 135a9–19. On the other hand, at least four, and possibly five,   Ø require the weak sense of (D2):

i

AÆ b æ ÆØ ŒÆd A
æ ºÅÆ j YØ
j ª
 j ıÅŒe ź E. Kd b  F N ı e b
e  q
r
ÆØ ÅÆ
Ø, e  P ÅÆ
Ø, Øfi ÅæŁø e YØ
N ¼çø a æ ØæÅ
Æ æÅ, ŒÆd ŒÆºŁø e b
e  q
r
ÆØ ÅÆE

‹æ , e b º Øe
ήa c
Œ Ø
c
æd ÆPH
I  ŁEÆ
O
ÆÆ
æ ƪ æıŁø YØ
. Bº
s
KΠH
NæÅ
ø
ܯ ήa c

F
ØÆæØ
ÆæÆ a 
Æ ıÆ
Ø ª
ŁÆØ, j ‹æ
j YØ
j ª
 j ıÅŒ . iii See Topiques, pp.LXXVI–LXXXIII. ii

318

Logical Matters

132b8–18, 132b19–34, 134a18–25, and 137a21–b2 (since æ   and ¼
Łæø  are the same — 133a30–32 — the example at 137a34–37 will conflict with the    at 135a9–19 unless weak properties are in play). The probable fifth case is 132a34–b7. In the remaining    Aristotle considers the fault of ‘giving the definition as property’, i.e. of asserting that I(A,B) when in fact D(A,B). D(A,B) entails E(A,B); hence Aristotle should say that, in the situation supposed, if ‘I(A,B)’ is read as ‘I1(A,B)’, then the claim is false, and if it is construed as ‘I2(A,B)’, then the claim is true. In fact he says that ‘the property will not be correctly laid down’ (131b38): he places the fault squarely among incorrect claims which he sharply distinguishes from false claims (132a22–26).i Here at least Aristotle does not simply fail to specify which property-relation he is thinking of: he positively conflates the two. Outside Book E the weaker sense certainly predominates and is perhaps universal; there is no occurrence of ‘YØ ’ where it must take the strong sense, and several in which it must take the weak sense. The most important of the weak instances appear in the passages where Aristotle discusses the relations holding between   Ø directed toward the different predicables. In Book ˙, arguing that definition claims are the easiest things to attack, he says: Again, it is possible to attack a definition by way of the other predicables too; for if the predicate is not proper, ... the definition is destroyed. (155a7–10)ii

Unless we suppose Aristotle to be confused, we must take ‘proper’ in the weak sense here. This section of H picks up a passage at the beginning of Z, where again ‘proper’ must bear the weak sense (139a31–32; b3–4). In Z Aristotle says that he has said all this before — the reference is most probably to ˜ 120b11–12, so that there too ‘proper’ is weak. Alternatively, Z may refer to A 102b27–35, [142] where again Aristotle sets out the connexions between the different batches of   Ø. However, in A Aristotle uses a slightly different, and I think more cautious, turn of phrase: it seems to me that he is carefully stating the relations between the groups of   Ø in such a way that he may use ‘proper’ in the strong sense which Book A has just assigned to it. Apart from that series of passages, there are two   Ø in Book ˘ in which Aristotle indicates that a definition must be proper to its subject i Sharply, but not clearly: see E 139a9–20; Alexander, in Top 385.21–22; Pflug, libro quinto, pp.8–12. ii Ø æe b
‹æ
K
åÆØ ŒÆd Øa H
¼ººø
KØåØæE
· Y ªaæ c YØ  › º ª , ... I
fi ÅæÅ
 ª
ÆØ › ›æØ .

Property in Aristotle’s Topics

319

(140a33–b15; b16–26), and where he must therefore be using ‘proper’ in the weak sense (see also 143a31; 148a35); and there are two further places in H (154b2; 155a23–27: cf 154b13, 16, 19; 155a13, 14, 15, 20) where reference is certainly made to weak properties — indeed 155a23–27 is tantamount to a formulation of (D2). When the word ‘YØ ’ occurs in logical contexts outside the Topics, it is regularly used in the weak sense (see e.g. APst B 91a15). In what follows I shall as a rule work in terms of weak properties, for the sake of simplicity. I shall sometimes use the sign ‘I’ to stand indifferently for the strong and the weak property relation.

Quasi-properties In the case of definition and genus Aristotle allows that his accounts are rough and asserts that ‘of the rest we must attach to each class the things which have affinity to it, calling them ›æØŒ and ª
ØŒ’ (A 103a1–4; cf 101a19–24; 102a2–10, 35–37). He does not make a parallel assertion about properties, but he does in fact discuss under the rubric of property a number of relations which I shall call quasi-properties. A 5 contains the following passage: No-one calls proper what can hold of something else ... , not even if for a while it actually holds of it alone. If something of that sort is to be called proper, it will be said to be proper not without qualification but at some time or relative to something; for being on the right may be called proper at some time and being two-footed proper relative to something, e.g. of man relative to horse and dog. (102a22–29)i

(

(

Thus parallel to (D2) there will be the formula for sometime properties: [143] (D3) I3(A,B) ¼ df ($t)((8x)(Ax at t Bx at t) & (8x)(Bx at t Ax at t)) and the formula for relative properties: (D4) I4(A,B,C) ¼ df (8x)(Bx ! Ax) & (8x)(Cx ! ¬Ax).

i PŁd ªaæ YØ
ºªØ e K
å 

¼ººfiø æåØ
, ... P i
åfi Å ŒÆ Ø
Æ åæ


fiø æå
: N  ¼æÆ Ø ŒÆd ºª Ø H
 Ø ø
YØ
, På ±ºH Iººa  b j æ  Ø YØ
ÞÅŁÆØ· e b
ªaæ KŒ ØH
r
ÆØ  b YØ
KØ, e b  ı
æ  Ø YØ
ıªå
Ø ºª 

, x
fiH I
Łæfiø æe ¥ 
ŒÆd Œ
Æ. — For the text at line 27, see Brunschwig, Topiques, p.7 n.3.

Logical Matters

320

(

(

(Note: (i) I have formulated (D3) and (D4) — and shall formulate subsequent definitions — on the model of (D2) rather than of (D1): a strong version of each quasi-property could be set beside my weak version — Aristotle himself expresses no preference. (ii) In (D3) the implications have to be weakened from strict to material in view of the temporal quantifier — cf E 129a3–4. (iii) In (D4) I have formulated being relatively proper as a triadic relation: there is no reason to restrict relative properties to triads, and it is simple to formulate a general definition for polyadically relative properties.) Aristotle also refers to a ‘now’ property (E 131b5–18): (D5) I5(A,B) ¼ df (8x)(Ax now Bx now) & (8x)(Bx now Ax now) (D5) is not equivalent to (D3); but Aristotle nowhere distinguishes the ‘sometime’ from the ‘now’ property and at least once appears to equate them (see E 129a28). (D3) and (D4) suggest the construction of omnitemporal and non-relative properties. The suggestion is taken up in the more systematic discussion of quasi-properties in chapter 1 of Book E. The book opens with a general classification: A property is given either in itself and always or relative to something else and sometime. (128b16–17)i

The accounts of relative and sometime properties which follow square with (D3) and (D4), though Aristotle adds considerable embellishments to his discussion of relative properties (128b22–33; 129a6–16). What is proper ‘in itself’ is then explained as the limiting case of a relative property: A property in itself is what is given relative to everything and separates it from everything. (128b34–35;ii cf 129a23–26)

Instead of contrasting B with C, D, ... , we contrast it simply with not-B. Thus: (D6) I6(A,B) ¼ df (8x)(Bx ! Ax) & (8x)(¬Bx ! ¬Ax) The right-hand sides of (D2) and (D6) are equivalent; hence I2(A,B) is equivalent to I6(A,B). Similarly, the omnitemporal or always property is given by: [144]

i ii

I  ÆØ e YØ
j ŒÆŁ Æe ŒÆd I, j æe æ
ŒÆd  . Ø b e b
ŒÆŁ Æe YØ
n æe –Æ
Æ I  ÆØ ŒÆd Æ
e åøæÇØ.

Property in Aristotle’s Topics

321

(

(

(D7) I7(A,B) ¼ df (8t)((8x)(Ax at t Bx at t) & (8x) (Bx at t Ax at t)) (See E 128b39–129a2.) At E 131b5–18 Aristotle sets out a    whose destructive part is aimed against the man who ‘gives the now property without announcing that he is giving the now property’ (131b5–6). That is bad practice because ‘everything running counter to common usage stands in need of special notice, and everyone is for the most part accustomed to give the property which always follows’ (131b7–9).i If Aristotle himself conforms to his counsel, the sort of property usual in the Topics — that is, (D1) or (D2) property — will in fact be an always property. Now I2(A,B) would be equivalent to I7(A,B) if the universal time-quantifier in (D7) were equivalent to the necessity operator which is implicit in the arrow of (D2). Notoriously, Aristotle sometimes confuses necessity with — or analyses it as — omnitemporality;ii and there are passages in Book E which commit Aristotle to the analysis. For example, the phrase ‘holding from necessity’ at 131b32 is picked up three lines later by ‘holding always’; and the    at 133a12–23 turns on the assumption that ‘Possibly P’ entails ‘P at some time’ (see also 129a3–4; 131a27–32). However, there are places in E in which Aristotle makes it plain that the terms ‘always’ and ‘in itself’ are not interchangeable: consider the contrasts at 128b17  128b19, 128b34  129a1, and 129a23  129a26. Moreover, Aristotle explicitly recognizes a class of property which is always and relative (129a6–16). If I7(A,B) is not to be read as equivalent to I6(A,B), then, since I6(A,B) is equivalent to I2(A,B), I7(A,B) cannot be equivalent to I2(A,B); but in that case Aristotle cannot consistently maintain his identification of necessity with omnitemporality, for that does make I7(A,B) and I2(A,B) equivalent. It is clear that Aristotle has not thought all this through: it looks as though he hoped, vainly, to hold on to the identification and yet still distinguish between always and in itself properties.

i Ø I
ÆŒıÇ
Æ b
N e
F
YØ
I Ø f c ØøæÆ ‹Ø e
F
YØ
I øØ
· P ªaæ ÆØ ŒÆºH Œ

e YØ
: æH
b
ªaæ e Ææa e Ł  ªØ


–Æ
Ø æØ F æ EÆØ· NŁÆØ  ‰ Kd e  ºf 
 e Id ÆæÆŒ º ıŁ F
YØ
I Ø
ÆØ. ii See esp K.J.J. Hintikka, ‘Aristotle on the realization of possibilities in time’, in his Time and Necessity (Oxford, 1973), pp.93–113 [the chapter is a revised version of ‘Necessity, universality and time in Aristotle’, Ajatus 20, 1957, 65–90]; cf J. Barnes, review of Hintikka, Time and Necessity, Journal of Hellenic Studies 97, 1977, 183–186 [reprinted as ‘The principle of plenitude’, in volume I, pp.364–370].

322

Logical Matters

At E 128b16 Aristotle cautiously reveals the possibility of four types of property: (a) what is always and in itself proper; (b) what is sometimes and in itself proper; (c) what is always and relatively proper; and (d) what is sometimes and relatively proper. Relative properties — types (c) and (d) — ‘must be considered by means of the   Ø concerning accidents’ (129a32–34) and hence are not suitable subjects for Book E. In a few places properties of type (b) appear to be in view (e.g. 131b5–18; 133a14); but [145] properties of this sort are also said to be ‘not correctly laid down’ (131a27–33), so that E is in agreement with A 5, which says that ‘sometime’ and ‘relative’ properties ‘may be called’ properties rather than ‘are’ properties, and which classifies them as special cases of accidents (102b20–26). That leaves type (a). According to Porphyry, ‘they say that these are proper in the strict sense [Œıæø]’ (Isag 12.20–21: so, for example, Alexander, in Top 373.6).i But it would be a mistake to conclude that the   Ø in Book E are aimed exclusively at type (a) properties, for two reasons. First, as we have already seen, Aristotle’s view as to the relation between what is always proper and what is in itself proper is obscure and perhaps inconsistent. Secondly, the conclusion would probably be anachronistic: the body of Book E betrays no knowledge of the systematic classification of E 1 (note especially 131a27–b19). I suspect that Aristotle worked out the classification after the bulk of Book E had been put together and probably, too, after he had written the general account of property in A 5.ii It may be that a further and distinct grouping of quasi-properties is sketched in one of the   Ø of E 5. The    is introduced like this: With certain sorts of property mistakes are generally made because of a failure to distinguish how and of what the property is being posited. (134a26–28)iii

Aristotle then lists and discusses five ways in which this sort of mistake can occur (134a28–135a8). The section is in parts highly obscure; in particular, it is unclear whether Aristotle thinks that these mistakes are failures to state unambiguously what is being said to be proper to what, or rather that they are failures to state what type of property-relation is being claimed to hold. In i On Porphyry’s thoughts about properties, see J. Barnes, Porphyry: Introduction (Oxford, 2003), pp.201–219. ii V. Sainati, Storia dell’ ‘Organon’ aristotelico, I: dai ‘Topici’ al ‘de Interpretatione’ (Florence, 1968), pp.118–120, infers that E 1 was not written by Aristotle; but the facts do not seem to me to warrant such a strong conclusion. iii ıÆ
Ø  K
K
 Ø H
Nø
‰ Kd e  ºf ª
ŁÆ Ø
Æ ±ÆæÆ
Ææa e c Ø æÇŁÆØ H ŒÆd 
ø
ŁÅØ e YØ
.

Property in Aristotle’s Topics

323

one case at least, namely failure to distinguish between what holds by nature and what holds tout court (134a29–31, b5–10), the latter is more likely; and in that case we should set up at least one further sort of quasi-property — namely, what is naturally proper (cf 129a7; 134a5–17). Aristotle made a series of attempts — bold but unsuccessful — to answer the important question: what is it for something to be the case ‘by nature’? But this is not the place to examine them. Yet another sort of property is mentioned in the last chapter of the Prior Analytics. Aristotle is talking about ‘physiognomy’ or the inference of mental from physical characteristics;i this, he says, is possible only if we can find pairs of [146] mental and physical features which are ‘proper to each genus’ (APr B 70b7–14). A few lines later he explains what he means: For the sign [i.e. the physical characteristic] is proper in this way: it is proper to the genus as a whole, and not proper to it alone as we are accustomed to say. (70b18–20)ii

Aristotle is not using the word ‘proper’ in its usual sense here; the phrase by which he indicates the usual sense — ‘proper to it alone’ — is presumably a somewhat inaccurate reference to the sense given by (D2). What does ‘proper to the genus as a whole’ mean? From the illustration Aristotle gives, we can infer the following definition (where ‘gl’, ‘g2’, ... are names for genera): (D8) I8(A,gl) ¼ df (8x)(x 2 gl ! Ax) & ¬($n)((n ¬ ¼ l & (8x)(x 2 gn ! Ax)) In other words, A is proper to g as a whole if g is the only genus all of whose members have A. Aristotle indicates that this is a peculiar sense of ‘proper’; he does not employ it in the Topics, and I do not known of any passage outside APr B 27 in which it occurs. The English phrase ‘X is proper to Y’ — and also the corresponding Greek — may suggest a further sort of quasi-property: if I say ‘A is proper to B’ or ‘A holds only of Bs’, I may be taken to mean no more than that only Bs are A. Thus: (D9) I9(A,B) ¼ df (8x)(Ax ! Bx)

i

See Ross, Analytics, pp.501–502. e ªaæ ÅE
oø YØ
KØ
‹Ø ‹º ı ª
ı YØ
KØ ŒÆd P 
ı YØ
, uæ NŁÆ
ºªØ
. ii

324

Logical Matters

(The relation I9 is the first of the three quasi-properties which Porphyry defines: Isag 12.12–22.) We could say on the basis of (D9) that being asleep is a property of animals, on the grounds that only animals can sleep. That example is based on a passage in Book A, 102a23. There Aristotle rejects the claim that being asleep is proper to men, and the way in which he does so suggests that he took being asleep to be proper to animals; if he did, then he must have had (D9) and not (D2) properties in mind. However, Aristotle nowhere shows interest in (D9) and perhaps 102a23 should not be squeezed. It is possible to guess why Aristotle did not pay any attention to (D9). In A 5 he is thinking more or less consciously of universal affirmative propositions. I say ‘more or less consciously’ because it seems probable that he had written down the bulk of the Topics before he had reflected much on quantification. In a few places, it is true, he does draw a distinction between universal and particular propositions (see B 108b34–109a26; 115b11–15; ˆ [147] 119a32–120b6; H 154b33–155a2). But even there the distinction is crudely and confusedly drawn, compared to what Aristotle writes in the Prior Analytics; moreover, it is probable that these passages represent fairly late additions to the text of the Topics;i and in any case Aristotle expressly says that the distinction holds only for accidents (B 109a11–12). Aristotle’s question in A 5, then, could be put like this: Given that everything B is A, what sorts of relation can hold between A and B? Aristotle answers that there are four such relations, namely the four predicables. If the schema of the predicables was devised to classify universal affirmative propositions, then the difference between (D2) and (D9) has no importance; for (D2) differs from (D9) only in making explicit the condition that everything B is A.

Singular propositions If Aristotle became clear on the difference between universal and particular propositions, he was never fully alive to the distinction between general and singular propositions.ii In some places in the Analytics it seems almost as if Aristotle is consciously construing proper names as a peculiar sort of general term, and so anticipating some fairly sophisticated modern manœuvres in i See Brunschwig, Topiques, pp.LIX–LXI, LXX–LXXII; id, ‘Observations sur les manuscrits parisiens des Topiques ’, in Owen, Dialectic, pp.3–21. ii See e.g. Cat 1b10–15 and 3a34–39, with the note by J.L. Ackrill, Aristotle’s Categories and de Interpretatione (Oxford, 1963), p.76.

Property in Aristotle’s Topics

325

this area;i but in the Topics at least the reduction is rather the other way about: propositions of the form ‘All/some Bs are A’ are read as though ‘A’ and ‘B’ in them were logically heterogeneous. This comes out in Aristotle’s terminology: in ‘A holds of B’, ‘A’ will be called the predicate or ŒÆŪ æ 

, the ‘account’ or º ª , or — in the context of Book E — the property or YØ
; and in contrast ‘B’ will be called the subject or  Œ

, the name or Z
Æ, the ‘thing’ or æAªÆ (see e.g. 132b22– 23; 132b9; 132b33 respectively). Porphyry does no more than make these suggestions explicit when he requires that if I(A,B) then B must be a species or r   and hence of a logically different type from A, the property (e.g. Isag 16.11). These facts help to explain a profound difference between Aristotle’s notion of predication and the notion of predication used by most logicians today. It is worth dwelling on this for a moment since it is often overlooked or ignored. Briefly, the difference is this: the Aristotelian subject of an Aristotelian subject–predicate [148] proposition is a modern predicate; Aristotelian subjects and Aristotelian predicates are alike modern predicates; modern subjects do not figure (or rather have no distinguishing name) in Aristotle’s analysis of Aristotelian subject–predicate propositions. Take, for example, the proposition ‘Every man is mortal’. That is an Aristotelian subject–predicate proposition; its Aristotelian subject is ‘man’ (not, of course, ‘every man’), and its Aristotelian predicate is ‘mortal’. In modern jargon, the proposition would be expressed in some such way as: ‘For all x: if x is a man, then x is mortal’, where both ‘man’ and ‘mortal’ (or better ‘ ... is a man’ and ‘ ... is mortal’) are predicative. I think that Aristotle’s careless treatment of the distinction between singular and general propositions led him to make mistakes in his account of properties in Book E. It is clear that in A 5 he is not thinking of singular propositions such as ‘Theaetetus is sitting’. Alexander explicitly stipulates that every property-claim must contain two terms (in Top 37.32–33) and hence that no singular proposition can constitute a property-claim (ibid, 39.2–7). Unfortunately, Aristotle did not observe Alexander’s stipulation: there are at least half a dozen places in Book E where properties are ascribed to individuals (128b20; 129a5; 131b12, 17; 134a30; b9; and perhaps 135a30; see also A 102a26; b23; cf 102b7; 103a30; 103b29–35). Moreover, many of i See esp APr A 47b29, 35, 40; cf Int 21a2 — but contrast Met ˜ 1018a3–4. See further J. Barnes, Truth, etc. (Oxford, 2007), pp.154–167.

326

Logical Matters

Aristotle’s examples are ambiguous between general propositions and singular propositions with an abstract subject. (Aristotle himself was aware of the danger of such ambiguities: E 134a31–32; 134b22–135a5.) That is unfortunate because no singular proposition can express the relations defined in (D1) and (D2), since I1 and I2 are relations between pairs of terms, and their definitions involve Aristotelian predications. Of course, it is easy enough to frame a definition involving singular propositions of what might reasonably be called a property relation: (D10) I10(A,a) ¼ df (8x)(Ax ! x ¼ a) & Aa That is analogous in some fairly obvious ways to (D2); but plainly it is not equivalent to (D2). What led Aristotle sometimes to countenance properties of individuals? He thought that his use of the word ‘proper’ reflected, at least up to a point, the ordinary Greek use of the word: as we have seen, he justifies (D1) by appealing to how people actually use the word ‘proper’ (A 102a22).i [149] It is certainly legitimate to talk of what is proper to an individual or of what marks him off from his fellows. In the formula ‘X is proper to Y’, or ‘Y alone is X’, either general or singular terms may be substituted for ‘Y’ without loss of sense: we can say ‘Men alone are rational’, and we can equally say (to adapt an example of Aristotle’s) ‘Socrates alone is walking in the market-place’. Exactly the same can be said of the Greek word ‘YØ ’. Introducing Aristotle’s non-technical use of the word, Bonitz writes: omnino vocc YØ , Nfi Æ ea, quae ad unum pertinent hominem rem genus ab iis distinguuntur, quae latius patent (Index, 339a32–34). (D1) is founded on ordinary usage, and ordinary usage admits individual properties: it may never have occurred to Aristotle to question whether (D1) and the subsequent definitions fit individual properties. It is worth adding two further points. (i) Aristotle is clearly wrong to claim that ordinary usage supports the necessity operator in (D1): usage is not offended if the arrow of entailment in (D1) — and in (D9) — is replaced by the horseshoe of material implication. (ii) There is a use of ‘proper’ and ‘YØ ’ such that in the formula ‘X is proper to Y’ ‘X’ as well as ‘Y’ may be replaced by a singular term. (Think of the things we normally claim as our i It has been supposed that the phrase ‘c
Œ Ø
c
O
ÆÆ
’ at A 101b22–23 marks an appeal to ordinary usage (see e.g. Verbeke, ‘Notion de proprie´te´’, p.260 n.3; G. Ryle, ‘Dialectic in the Academy’, in Owen, Dialectic, pp.69–79, on p.73); but Alexander’s reading of the phrase is the correct one (in Top 39.16–17: cf Brunschwig, Topiques, p.5 n.4; E. de Strycker, ‘Concepts-cle´s et terminologie dans les livres ii a` vii des Topiques ’, in Owen, Dialectic, pp.141–163, on p.145).

Property in Aristotle’s Topics

327

property.) In particular, Aristotle’s notion of a ‘proper sensible’ exploits this usage: a sensible quality Q is proper to a sense S if and only if (a) necessarily if Q is perceptible by any sense x then x is S, and (b) Q is perceptible by S (an B 418a11–12 — compare (D10)). The ordinary use of ‘YØ ’ is amply illustrated in Aristotle’s works (see Bonitz, Index 339a13–b53); but despite the claim at A 102a22, Aristotle’s technical use of the term is in more than one respect a refinement on its ordinary use. Failure to distinguish between (D2) properties and (D10) properties was responsible, I believe, for a further confusion in Aristotle’s account of properties. This can best be seen if we start from the    at E 132b19–34. The destructive part of the    is introduced like this: [150] Again, in attack see if he has given the subject as proper to what is said in the subject; for what is supposed to be proper will not be proper. (132b19–21)i

What does ‘is said in the subject’ mean? An example follows: e.g. since one who gives fire as proper to the lightest body has given the subject as proper to the predicate, fire will not be proper to the lightest body. (132b21–24)ii;

This shows that ‘is said in the subject’ means the same as ‘is predicated of the subject’. According to this   , then, if we are given that every A is B (if B is predicated of the subject A), we can deduce that ¬I(A,B). But that is absurd; for (D1) and (D2) alike license the inference of ‘Every A is B’ from I(A,B). Thus assuming I(A,B) we can deduce first ‘Every A is B’, and then ¬I(A,B) by the   . Hence I(A,B) entails ¬I(A,B); and there are no true propertyclaims. (That is so whether the indeterminate ‘I(A,B)’ is read strongly as ‘I1(A,B)’ or weakly as ‘I2(A,B)’.) I do not think that Aristotle can be extricated from this position: he is in a muddle which cannot be interpreted away. But I think that we can guess why he should have got into the muddle in the first place. He argues in the following way: The subject will not be proper to what is said in the subject for this reason: the same thing will be proper to many things of different sorts. For many things of different

i Ø I
ÆŒıÇ
Æ b
N e  Œ

YØ
I øŒ  F K
fiH  ί
fiø ºª 
ı· P ªaæ ÆØ YØ
e Œ

YØ
. ii x
Kd › I  f YØ
 F º æ ı Æ  e Fæ e  Œ

I øŒ  F ŒÆŪ æ ı
ı YØ
, PΠi
YÅ e Fæ Æ   F º æ ı YØ
.

328

Logical Matters

sorts hold of the same thing, being said of it alone; and the subject will be proper to all of these, if someone lays down the property in this way. (132b24–28)i

Each subject has many predicates true of it. (Aristotle appears to assert the stronger thesis that each subject has many properties: that is a thesis he asserts elsewhere: see e.g. E 138a25–29, b10–15; and the example at e.g. E 130a28 compared with that at e.g. 130b8; cf 130b23–25.) Suppose then that we have ‘Every A is B1’, ‘Every A is B2’, ... , ‘Every A is Bn’: if ‘Every A is B’ is compatible with I(A,B), then it will be possible that I(A,B1) and I(A,B2) and ... and I(A,Bn). But that is not possible. Therefore ‘Every A is B’ is incompatible with I(A,B). The argument is fallacious. But the question I want to raise about it is this: Why should Aristotle think that A cannot be proper to each of the Bis? He does not explain, but he repeats twice that a thing cannot be proper to more than one thing (E 137a17; 138a20 — the view is also implicit in the argument at 138b20). I suspect that he was confused by the apparently true and [151] innocent formula ‘If X is proper to Y, then X holds of Y alone’; and that the confusion stems from his failure to distinguish between (D2) and (D10) properties. If we suppose that the neutral variables ‘X’ and ‘Y’ in the apparently innocent formula range respectively over predicates and individuals, then we can represent the intention of the formula rather more clearly and rigorously like this: (1) I10(A,a) ! (8x)(Ax ! x ¼ a) If some predicate is proper to a give individual, then any individual which has that predicate is identical with the given individual. That is true — it is a trivial consequence of (D10). If ‘X’ and ‘Y’ in the formula are read alike as predicate variables, then there is a temptation to construe the formula by analogy with (1) as: (2) I(A,B) ! (8C)((8x)(Cx ! Ax) ! C ¼ B) That plainly entails: (3) I(A,B) ! (8C)(I(A,C) ! C ¼ B) and (3) is what Aristotle means when he says that nothing can be proper to more than one thing. But (2) does not follow from anything Aristotle has said about (D1) or (D2) properties; and he gives no independent reason for i Øa  F  PŒ ÆØ e  Œ

 F K
fiH  ί
fiø YØ
‹Ø e ÆPe ºØ
ø
ÆØ ŒÆd ØÆç æø
fiH YØ YØ
. fiH ªaæ ÆPfiH ºø Ø
a Øç æÆ fiH YØ æåØ ŒÆa 
ı ºª 
Æ, z
ÆØ 
ø
YØ
e  Œ

K
Ø oø ØŁBÆØ e YØ
.

Property in Aristotle’s Topics

329

accepting it. The apparently innocent formula is open to a true interpretation, namely: (4) I(A,B) ! (8x)(¬Bx ! ¬Ax) That bears the same relation to (D1) and (D2) as (2) bears to (D10). I suggest that indifference to the distinction between singular and general terms gave Aristotle confidence in (3) by allowing him to read the apparently innocent formula as (2), on analogy with (1), rather than as (4). The confidence was imprudent: in the case of at least one    it reduced Aristotle to absurdity. There is one place in Book E in which Aristotle comes close to rejecting proposition (2): at 134b2–4 he appears to admit that I(A,B) is compatible with the existence of some C distinct from B such that (8x)(Cx ! Ax). But he seems not to have reflected on the matter. Proposition (2) does not entail that the property relation is irreflexive — that ¬I(A,A) — but it seems improbable that anyone holding to (2) would be willing to allow that a thing might be its own property. In fact, Aristotle explicitly denies that a thing can be its own property (E 135a9–19). It should be said, however, that this denial is made for (D1) properties and is based on the assertion, ‘everything reveals its own being’, which presumably comes to E(A,A). He does not commit himself on (D2) properties. [152] There is an interesting passage in the Posterior Analytics which is germane to this issue. The passage occurs in the course of an involved argument aimed at showing that it is not possible to demonstrate definitions. I shall ignore the special difficulties caused by the context. Here is the text: The definition of something is both proper to it and predicated of it in the category of substance. But it is necessary that these things convert. For if A is proper to C, it is clear that it is also proper to B and B to C; so that all are proper to each other. (APst B 91al5–18)i

It is immediately clear that Aristotle is admitting a plurality of properties: each of the three terms A, B, C is proper to both the other two. By now, Aristotle has given up (3). For a closer understanding of the passage it is necessary to realize that Aristotle is imagining a syllogism in Barbara — A holds of every B, B holds of every C: A holds of every C — the conclusion of which is alleged to represent a definition of the term ‘C’. If the conclusion is a

i e b  KØ
YØ
 ήd K
fiH  KØ ŒÆŪ æEÆØ. ÆFÆ  I
ªŒÅ I
ØæçØ
. N ªaæ e `  F ˆ YØ
, Bº
‹Ø ŒÆd  F ´ ŒÆd  F  F ˆ, u 
Æ Iºººø
. — See J. Barnes, Aristotle’s Posterior Analytics (Oxford, 19942), pp.208–209.

330

Logical Matters

definition, Aristotle argues, then A must be proper to C. That shows that he is using the word ‘proper’ in the sense of (D2). But I2(A,C) together with the second premiss of the syllogism, ‘B holds of every C’, yields ‘B holds of every A’; and that plus the first premiss of the syllogism amounts to I2(A,B). It is easy to prove I2(B,A), I2(B,C), I2(C,A), and I2(C,B) along the same lines. The next step would be to add I2(A,A), I2(B,B), and I2(C,C), and to recognize the reflexivity of I2. Aristotle does not take it; but that may be only because it was not to the point in the context of his argument.

Appendix: E 7, 137a8–20 This    has caused a great deal of trouble.i This is the received text: Ø KŒ H
‰Æø Kå
ø
, I
ÆŒıÇ
Æ b
N e ‰Æø å
 F ‰Æø å
  c Ø
YØ
· Pb ªaæ e ‰Æø å
 F ‰Æø å
  ÆØ YØ
. N  Kd  F ‰Æø å
  e ‰Æø å
YØ
,   ı PŒ ÆØ YØ
y ŒEÆØ r
ÆØ YØ
. x
Kd ‰Æø åØ çæ
ÅØ æe e ŒÆºe
ŒÆd e ÆNåæ
, fiH KØÅ ŒÆæ ı ÆPH
r
ÆØ, PŒ Ø  YØ
çæ
ø e KØÅ
r
ÆØ ŒÆº F, PŒ i
YÅ YØ
çæ
ø e KØÅ
r
ÆØ ÆNåæ F. N  Kd
YØ
çæ
ø e KØÅ
r
ÆØ ŒÆº F, PŒ i
YÅ YØ
ÆPB e KØÅ
r
ÆØ ÆNåæ F· I
Æ
ªaæ r
ÆØ e ÆPe ºØ
ø
YØ
: ŒÆÆŒıÇ
Ø b Pb
y  ›    Kd åæØ · e ªaæ ‰Æø å
£
æe ºø ıªŒæ
ÆØ.

It is clear that Aristotle is proposing two rules for disestablishing propertyclaims; and that each rule is then illustrated by an example. The problem is to decide what Aristotle’s two rules are. Unless we are to suppose that the text is irredeemably obscure or corrupt, we must take Aristotle to be proposing, from the four following rules, either (R1) or (R3) and either (R2) or (R4): (R1) ($R)(R(A,B) & R(A,C)) & ¬I(B,A) ::
¬I(C,A) (R2) ($R)(R(A,B) & R(A,C)) & I(B,A) ::
¬I(C,A) (R3) ($R)(R(A,B) & R(A,C)) & ¬I(A,B) ::
¬I(A,C) (R4) ($R)(R(A,B) & R(A,C)) & I(A,B) ::
¬I(A,C) i See T. Waitz, Aristotelis Organon II (Leipzig, 1846), pp.492–493; G. Colli, Aristotele: Organon (n.p. 1955), pp.969–971; M. Soreth, review of W.D. Ross, Aristotelis Topica et Sophistici Elenchi (Oxford, 1958), Gnomon 34, 1962, 351–354; W. J. Verdenius, ‘Notes on the Topics ’, in Owen, Dialectic, pp.22–42, on pp.35–36; M. Soreth, ‘Zu Topik E 7, 137a8–20 und b3–13’, in Owen, Dialectic, pp.43–48.

Property in Aristotle’s Topics

331

[153] There are two questions raised by all four rules; namely: What is the range of ‘R? and: How should the implication sign ‘
’ be read? Those questions are independent of the problem I am going to discuss, and they are not peculiar to the    in E 7; so I shall say nothing more about them. The example illustrating Aristotle’s first rule looks like this: Since prudence is related in the same way to the fair and to the foul, inasmuch as it is knowledge of each of them, and being knowledge of the fair is not a property of prudence, then being knowledge of the foul will not be a property of prudence either. (137a12–16)

The example instantiates neither (R1) nor (R3), since the phrase ‘is knowledge of’ cannot function both as the value of ‘R’ (the relation holding both between wisdom and the fair and between wisdom and the foul) and also as part of the predicates substituted for ‘B’ (‘being knowledge of the fair’) and ‘C’ (‘being knowledge of the foul’). Aristotle was careless in illustrating the rule. That is unfortunate, but not singular. If we overlook this error (read ‘the fair’ for ‘knowledge of the fair’ and ‘the foul’ for ‘knowledge of the foul’), it is plain that Aristotle must be intending to illustrate (R1) rather than (R3). The first rule is formulated like this. Suppose that what is related in the same way is not a property of what is related in the same way: then what is related in the same way will not be a property of what is related in the same way either.

That has the air of an empty tautology; but you can see more or less what Aristotle was trying to say — and I incline to think that he was trying to express (R1) rather than (R3). At first sight, (R2) looks a better partner than (R4) for (R1): structural parallels hold between (R1) and (R2), and again between (R3) and (R4), which do not hold for the other cross-pairings. The second rule is illustrated like this: If being knowledge of the fair is a property of prudence, then being knowledge of the foul will not be a property of prudence. (137a16–18)

The error which infected the first illustration affects this one too; but that apart, the example answers to (R2) and not to (R4). Nonetheless, I doubt that Aristotle’s two rules are (R1) and (R2), for the following three reasons. (i) The second example is immediately followed by the sentence:

332

Logical Matters

(S) For it is impossible for the same thing to be a property of several things. (137a17–18) It is easy to see how (S) supports (R4), impossible to find any connexion between it and (R2). Of course, (S) could be excised or transposed, or otherwise manipulated.i [154] (ii) One scholar who backs (R1) and (R2) has proposed to emend (S) so that it reads: (S*) It is impossible for there to be several properties of the same thing.ii The change can scarcely be right since Aristotle expressly rejects the principle which (S*) expresses. But that fact works not just against (S*) but also against (R2) itself; for it is hard to see how Aristotle could have supported (R2) otherwise than by the principle expressed in (S*). (iii) Taken together, (R1) and (R2) yield: (R5) ($R)(R(A,B) & R(A,C)) ::
¬I(C,A) Aristotle can hardly have meant to commit himself to such a rule. If Aristotle did not intend (R2), he must have intended (R4). He expresses the second rule like this: If what is related in the same way is a property of what is related in the same way, then it will not be a property of what it is supposed to be a property of. (137a10–12)

That is, I think, compatible both with (R2) and with (R4); but in two respects it appears marginally better adapted to (R4): first, the structural contrast between (R1) and (R4) gives point to the difference in word order between Aristotle’s formulations of the first and second rules (the nominative ‘e ‰Æø å
’ before or after the genitive ‘ F ‰Æø å
 ’); secondly, (R4) provides a subject for ‘ÆØ’ in ‘e ‰Æø å
’. It might be thought that the structural parallelism between (R3) and (R4) gave a reason for preferring (R3) to (R1), granted that (R4) must be preferred to (R2). But just as (R1) and (R2) together yielded the impossible (R5); so (R3) and (R4) together yield: (R6) ($R)(R(A,B) & R(A,C)) ::
¬I(A,C)

i Excision was mooted by Waitz, Organon, p.493, and advocated by Soreth, review of Ross, and ‘Zu Topik E 7’; transposition was urged by Colli, Organon, p.971 (he placed the sentence after ‘åæØ ’ at 137a19 — cf 138a19–20). ii So Verdenius, in the typescript version of his ‘Notes’, pp.35–36; but the suggestion did not appear in the published version of the text.

Property in Aristotle’s Topics

333

I conclude that Aristotle’s two rules are (R1) and (R4). That was Alexander’s view (in Top 411.15–412.9). Aristotle’s second example is transmitted in this form: But if being knowledge of the foul is a property of prudence, then being knowledge of the fair will not be a property of it.

The example does not illustrate (R4). What is to be done with it? (i) Waitz was inclined to suppose that Aristotle had just made a mistake. (ii) The example as a whole might be cut from the text. (iii) The text can be emended in some such way as the following: N  Kd
YØ
çæ
ø e KØÅ
r
ÆØ ŒÆº F, PŒ i
YÅ YØ
 F KØÅ
r
ÆØ ÆNåæ F.

Emendation seems to me the least unpalatable option.

The property of prudence (by a triumvirate*) One of the rare puzzles which the text of the Topics presents is found in Book E, among the   Ø concerned with property.1 The passage is at 137a8–20.2 [80] It has been much discussed. We start out from the discussion by Barnes (in the previous section of this chapter): we shall follow his style, and we shall in the end accept the greater part of his contentions, while corroborating or correcting them on certain points. One curiosity of this    lies in its relation to its predecessor, at 136b33– 137a7: although the terms in which it is presented are very similar to those of its predecessor, its structure is completely different. Its predecessor invites us to consider terms which are [81] ‘similarly related [› ø å
Æ]’. Someone proposes that I(P1,S1).4 We look for terms ‘P2’ and ‘S2’ such that * This section is a lightly edited translation of ‘Le propre de la prudence’, an essay I wrote jointly with Jacques Brunschwig, and Michael Frede and first published in R. Brague and J.-F. Courtine (eds), Herme´neutique et ontologie: hommage a` Pierre Aubenque (Paris, 1990), pp.79–96. 1 This chapter is the collaborative product of its three authors. Most of the work was done in 1985 at the Wissenschaftskolleg in Berlin: it is with great pleasure that we offer it to the author of La prudence chez Aristote — in memory of an Aristotelian colloquium, held at the same place in the same year, at which all four of us were present. 2 Greek text above, p.[152]. 4 Aristotle defines properties in Book A like this: A property is that which, while not showing the essence of its subject, holds of it alone and is counter-predicated of the thing. (102a18–19) The distinction between a strong and a weak sense of ‘proper’ (see Brunschwig, Topiques, pp.LXXVI–LXXVII; Barnes, above pp.[137–142]) is not relevant to the present discussion.

334

Logical Matters

P1/S1 ¼ P2/S2. Then if ¬I(P2,S2), then ¬I(P1,S1) — and the    may be used in refutation of the proposal (136b33–137a1). Similarly, if I(P2,S2), then I(P1,S1) — and the    may be used to confirm the proposal (137a1–7). This schema with four terms, two subjects and two predicates, is common to all the   Ø in the near neighbourhood (cf 136b3, 15, 33) and to many others in the larger context of the passage (135b7, 17, 27; 136a14; 137b14, 28; 138a4, 30). But in the larger context Aristotle also uses other schemas in which only three terms occur. Sometimes the proposal that I(P1,S1) is confronted with a claim of the form I(P2,S1), sometimes with a claim of the form I(P1,S2). The first of those schemas, which compares two predicates applied to one subject, is found at 136a5, 138a21, and 138b6. The second, in which one predicate is applied to two subjects, is found at 136a29, 137b3, 138a13, and 138b16. Our   , or so the grammar of its initial presentation surely insinuates, should fit the schema of four terms, two predicates and two subjects: 137a8– 10 is exactly the same as 136b33–35, with ‘‰Æø’ substituted for ‘› ø’ — and 136b33–35 introduce a    with two subjects and two predicates. Nonetheless, it is perfectly plain that our    actually fits one or other of the three-terms schemas: first, the example at 137a12–16 (prudence related in the same way to the fair and the foul) shows that the schema is triangular; secondly, at the end of the passage Aristotle expressly states that ‘what is related in the same way is compared as one thing to more than one [e ªaæ ‰Æø å
£
æe ºø ıªŒæ
ÆØ]’ (137a19–20). [82] Which of the two three-term schemas is the pertinent one? There is no need to assume that only one of them is involved. It is plain, from the general structure of the paragraph, that the    offers two distinct rules, each of which may be used to refute a property-claim (at the end of the paragraph Aristotle states that the    cannot be used to confirm a property-claim, and he explains briefly why it cannot). The first rule for refutation is stated at 137a8–10 and illustrated by an example at 137a12–16; the second rule is stated at 137a10–12 and illustrated at 137a16–18. The essential difference between the two rules is that one of the hypotheses or premisses is negative in the first rule (137a8–9: N ... c KØ
YØ
) and affirmative in the second (137a10–11: N KØ ... YØ
). Multiply the two sorts of three-term schema by the two types of hypothesis or premiss, and there are four possible rules, namely: (R1) ($R)(R(A,B) & R(A,C)) & ¬I(B,A) ::
¬I(C,A) (R2) ($R)(R(A,B) & R(A,C)) & I(B,A) ::
¬I(C,A)

Property in Aristotle’s Topics

335

(R3) ($R)(R(A,B) & R(A,C)) & ¬I(A,B) ::
¬I(A,C) (R4) ($R)(R(A,B) & R(A,C)) & I(A,B) ::
¬I(A,C)5 In (R1) and (R2) we have one subject and two predicates. In (R3) and (R4) we have one predicate and two subjects. Aristotle must choose either (R1) or (R3), which each have a negative hypothesis, and either (R2) or (R4), which each have an affirmative hypothesis. The first rule and its illustrative example do not offer any serious problems, and as far as they are concerned we adopt the analysis proposed by Barnes. First, take the illustrative example: [83] Since prudence is related in the same way to the fair and to the foul, inasmuch as it is knowledge of each of them, and knowledge of the fair is not a property of prudence, then being knowledge of the foul will not be a property of prudence either. (137a12–16)

Strictly speaking, the example illustrates neither (R1) nor (R3): prudence is related in the same way to the fair and to the foul (the relation being ‘ ... is knowledge of —’), whereas the items which are said not to be proper to prudence are not the fair and the foul but rather knowledge of the fair and knowledge of the foul. Aristotle has been careless here: given that prudence is related in the same way to the fair and to the foul, inasmuch as it is knowledge of each, he thinks he may claim that prudence is, as it were by extension, similarly related to knowledge of the fair and knowledge of the foul, of which the fair and the foul are constituent parts.6 That minor difficulty apart, it is plain that the example illustrates (R1) rather than (R3): a single subject, prudence, is related in the same way to two predicates, knowledge of the fair and knowledge of the foul; since (by hypothesis) the first is not proper to the subject, neither is the second. The first rule, too, can be paraphrased in the sense of (R1), once we have rejected the suggestion, made by its surface grammar, that it has a four-term schema. Thus:

5 So Barnes, above, p.[152]. 6 Alexander is, to the best of our knowledge, the only commentator who has taken Aristotle au pied de la lettre. He says: ‘If prudence is thought to be similarly related to the fair and the foul inasmuch as it is thought to be knowledge of each of them, then if it is not a property of one of them, it will not be a property of the other either’ (in Top 412.1–2). Alexander arrives at this result by clumsily imposing the rule on the example, which he thereby completely distorts. In addition, it is hard to see why anyone would need advice on how to refute ‘I(prudence, foul)’.

336

Logical Matters

if that [¼ B] which is related in the same way is not proper to that [¼ A] which is related in the same way ; for in that case that [¼ C] which is related in the same way will not be proper to that [¼ A] which is related in the same way . [84]

The real difficulties begin with the second rule and the second example. Let us begin with the example. In the received text, the example translates like this: But if being knowledge of the foul is a property of prudence,7 then being knowledge of the fair will not be a property of it. (137a16–17)

The example, in that form, evidently answers to (R2) and not to (R4). From ‘I(knowledge of the fair, prudence)’ we infer ‘¬I(knowledge of the foul, prudence)’. And yet there are reasons for thinking that (R2) cannot be Aristotle’s second rule. Barnes offers three such reasons,* each of which seems to us to be solid. First, there is the sentence (S) For it is impossible for the same thing to be a property of several things (137a17–18) which might serve to justify or explain (R4), but which cannot do the same for (R2). [85] Secondly, in order to support (R2) Aristotle would presumably have had to appeal to something like (S*) It is impossible for there to be several properties of the same thing. But that is a thesis which he explicitly, and rightly, rejects. Thirdly, (R1) and (R2) together imply (R5) ($R)(R(A,B) & R(A,C)) ::
¬I(C,A) Not only is that a curious rule in itself, but in addition — and here we add to Barnes’ argument — (R1) and (R2) together imply the further rule (R5bis) ($R)(R(A,B) & R(A,C)) ::
¬I(B,A) That is to say, if a subject is ‘related in the same way’ (whatever that way may be) to each of two predicates, then neither of the predicates can be proper to it

7 This hypothesis, namely ‘I(knowledge of the fair, prudence)’, is the contradictory of the hypothesis in the first example, which was ‘¬I(knowledge of the fair, prudence)’. So at least this much is plain: (i) you may affirm or deny that knowledge of the fair is a property of prudence — each of the two contradictory propositions is 
 
; (ii) whether you affirm or deny, you can in each case use the    to refute a property-claim. According to the received text, you can use the    to refute the same ascription of a property. See below, n.13. * Above, pp.[153–154].

Property in Aristotle’s Topics

337

— contrary to the hypothesis of (R2). In that case, our    is selfdestructive.10 [86] And worse: suppose that we take ‘ ... having as predicate —’ for the relation in which A stands to each of B and C. Then by way of (R5) and (R5bis) it follows that no predicate can be proper to any subject. So Aristotle’s two rules cannot be (R1) and (R2). It may be added that, for similar reasons, the two rules cannot be (R3) and (R4). For, as Barnes has remarked, those two together yield the unacceptable: (R6) ($R)(R(A,B) & R(A,C)) ::
¬I(A,C) In addition, they yield (R6bis) ($R)(R(A,B) & R(A,C)) ::
¬I(A,B) — with disastrous consequences. Since Aristotle’s second rule cannot be (R2), it is reasonable to think that it must be (R4). For the moment let us leave the example to one side and look at the formulation of the rule itself. The received text is this: N  Kd  F ‰Æø å
  e ‰Æø å
YØ
,   ı PŒ ÆØ YØ
y ŒEÆØ r
ÆØ YØ
. (137a10–12)

As Barnes says, that is compatible both with (R2) and with (R4). We get (R2) if we take  F ‰Æø å
  for A, e ‰Æø å
for B, the subject of ‘ÆØ’ for C, and   ı ... y ŒEÆØ r
ÆØ YØ
for A again. We get (R4) if we take [87]  F ‰Æø å
  for B, e ‰Æø å
for A, the subject of ‘ÆØ’ for A again, and   ı ... y ŒEÆØ r
ÆØ YØ
for C. Two 10 That the    is in this way self-destructive has actually been accepted by C. Natali, ‘Virtu` o scienza? Aspetti della çæ
ÅØ nei Topici e nelle Etiche di Aristotele’, Phronesis 29, 1984, 50–72, on p.54. — Alexander also proposed a self-destructive interpretation of the   , but along different lines. In commenting on the second rule (in Top 412.7–9), he wonders how one and the same thing can be similarly related to different things and yet at the same time be proper to one of them and not to the other. His answer is that Aristotle here shows that what seems to be similarly related in not in fact similarly related: e  Œ F
› ø åØ
c › ø åØ
. In other words: ($R)(R(A,B) & R(A,C)) & I(A,B)
¬I(C,A) & ¬($R)(R(A,B) & R(A,C)) Or, simplifying: I(A,B)
¬($R)(R(A,B) & R(A,C)) — A property cannot have one and the same relation both to its subject and to a third item. — Note that Alexander’s argument, taken in the opposite direction, explains the variant found at 137a11–12 in the two best manuscripts of the Topics, A and B. A and B read ‘ÆØ ŒÆ’ where Du¸, followed by editors, offer ‘  ı PŒ ÆØ YØ
’. The copyist must have thought that ($R)(R(A,B) & R(A,C)) & I(A,B) ought to imply I(A,C); and so he excised the negation-sign — and ignored Aristotle’s statement that this    cannot be used to establish a property (137a18–20).

338

Logical Matters

arguments suggest that the text is marginally better adapted to (R4) than to (R2). First, there is a difference in the word-order between the formulations of the first and the second rule: the nominative ‘e ‰Æø å
’ comes before the genitive ‘ F ‰Æø å
 ’ in the formulation of the first rule (137a9) and after it in the formulation of the second (137a11). That difference might be deemed to reflect the structural difference between the hypothesis ‘¬I(B,A)’ of (R1) and the hypothesis ‘I(A,B)’ of (R4). Secondly, if (R2) is intended, then the subject of ‘ÆØ’ must be C, which has not yet been mentioned, whereas if (R4) is intended, then the subject is A, which has been mentioned under the description ‘e ‰Æø å
’. Of those two reasons in favour of taking the second rule to be (R4), the first is of little weight. Interchange the letters ‘A’ and ‘B’ in (R4) and you get: (R4bis) ($R)(R(B,A) & R(B,C)) & I(B,A) ::
¬I(B,C) (R4bis) is equivalent to (R4), but (R4bis) and (R1) do not reflect the structural difference between the hypotheses which was supposed to favour (R4). Nonetheless (R4bis) seems to fit Aristotle’s train of thought rather better than does (R4). In it, the second hypothesis, ‘I(B,A)’, is the contradictory of the second hypothesis of (R1), ‘¬I(B,A)’. In the examples which illustrate the two rules, Aristotle proceeds in just that way: ‘ PŒ Ø  YØ
çæ
ø e KØÅ
r
ÆØ ŒÆº F’ (137a14–15) is the contradictory opposite of ‘N  Kd
YØ
çæ
ø e KØÅ
r
ÆØ ŒÆº F’ (137a14–15). The difference in word-order between the formulation of the two rules might incline us to prefer (R4) to (R2); but it has no relevance to a choice between (R4bis) and (R2). On the other hand, (R4bis) has the same advantage over (R2) as does (R4) in the matter of the subject of ‘ÆØ’: in (R4bis) [88] the subject is B, which has been mentioned in the antecedent under the description ‘e ‰Æø å
’. We may go a step further by calling upon evidence from the manuscripts of the Topics which previous editors have not exploited. An important manuscript omits our text: it is C, the Coislinianus 330, which dates from the eleventh century, and which leaves out the whole of 132a18–138b33. The gap can be filled, at least to some degree, thanks to another manuscript which extensive samplings have shown to be in all probability a direct copy of C. This manuscript is Vaticanus graecus 244 (dating from the thirteenth century). We shall call it W. In our passage W offers some variant readings which are worth looking at.

Property in Aristotle’s Topics

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The first variant concerns the formulation of the second rule. At 137a11 W omits the words ‘e ‰Æø å
’ and gives this text: N  Kd  F ‰Æø å
  YØ
,   ı PŒ ÆØ YØ
y ŒEÆØ r
ÆØ YØ
.

In that version, the grammatical subject of ‘ÆØ’ is not mentioned in the antecedent; rather, it is the same as the subject of the preceding ‘K’ and so must be looked for in the formulation of the first rule: it is the ‘e ‰Æø å
at 137a9, which is thus the subject of the two opposite premisses ‘N ... c Kd
YØ
’ (137a8–9) and ‘N  Kd ... YØ
’ (137a10–11). The fact that the subject is not repeated — in the version of W — makes a strong connexion between the two rules, and thus confirms that the second rule should be written in the form (R4bis) rather than (R4). That ‘c K’ at 137a9, ‘K’ at a11, and ‘ÆØ’ at a12 all have the same grammatical subject shows up in the fact that the same letter, ‘B’, occurs in the second hypothesis of (R1) (namely ‘¬I(B,A)’) and in the second hypothesis and the consequent of (R4bis) (namely ‘I(B,A)’ and ‘¬I(B,C)’). That, we think, constitutes a good reason for preferring the reading of W at 137a11. The reading of the other manuscripts came about when a (correct) marginal gloss, namely ‘e ‰Æø å
’, was accidentally or mistakenly incorporated into the text. [89] We turn now to the example which is supposed to illustrate the second rule, and which provides the central difficulty of the passage. In the received text, the example fits neither (R4) nor (R4bis). For the second rule, whatever exactly it is, requires a comparison between two subjects connected to a single predicate: the example, in the form in which it is transmitted, compares two predicates (‘knowledge of the fair’ and ‘knowledge of the foul’) which are attached to a single subject. Several solutions have been suggested, none of them satisfactory: Waitz thought that Aristotle had made a relatively trifling mistake; Ross was inclined to delete the second example; and Pacius, more radically, wanted to delete both examples.* Ross also thought of changing ‘ÆPB’ to ‘¼ººÅ IæB’; but that introduces a four-term schema (prudence

* See Waitz, Organon, p.493; Ross, Topica, app crit ad loc ; J. Pacius, In Porphyrii Isagogen et Aristotelis Organum commentarius analyticus (Frankfurt, 1597), ad loc.

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and ‘another virtue’, knowledge of the fair and knowledge of the foul), and we have seen that such a schema is not compatible with the text.11 Barnes too thought that emendation was the answer, and proposed something more [90] adventurous: he excised ‘ÆPB’ and he changed the nominative ‘e KØÅ
r
ÆØ ÆNåæ F’ into a genitive, thus: N  Kd
YØ
çæ
ø e KØÅ
r
ÆØ ŒÆº F, PŒ i
YÅ YØ
 F KØÅ
r
ÆØ ÆNåæ F.

The conjecture has a point in its favour, and the world against it. The point in its favour is that it satisfies two demands made by the text. For if we start out from sentence (S), we shall say that the received text of the second example contains two anomalies. First, it mentions two different properties (knowledge of the fair and knowledge of the foul), whereas (S) concerns a single property (e ÆP : 137a18). Secondly, it mentions a single subject (‘çæ
ø’ in 137a16, which is taken up by ‘ÆPB’ in a17), whereas (S) concerns several (ºØ
ø
: 137a18). An emendation ought to remove both of those anomalies, and Barnes’ conjecture does so: his text mentions a single property (prudence) and two subjects (knowledge of the fair and knowledge of the foul). But the emendation meets an insuperable obstacle: it makes prudence, which in the first example was a subject, into a property, and it makes knowledge of the fair and knowledge of the foul, which were properties, 11 Ross’ view of the passage is strictly incoherent: his app crit says ‘16–18 N ... YØ
’ seclusi ’ — that is to say, he regards the second example together with sentence (S) as a foreign intrusion into the text; but the app crit also says ‘17 ÆPB an ¼ººÅ IæB?’ — that is to say, he regards the second example as Aristotelian but corrupt. In the first edition of his Topica (1958) Ross set the second example and sentence (S) between obeli, thereby marking it as corrupt; in later reimpressions (1971, 1979) he set the matter between square brackets, thereby marking it as extraneous. — However that may be, behind Ross’ conjecture there presumably lies the notion that knowledge of the fair and knowledge of the foul are one and the same piece of knowledge (in virtue of the principle that ‘contraries belong to the same science’) — and hence one and the same property. Although in the Topics Aristotle gives only guarded assent to that familiar principle about contraries (note ‘ºªÆØ’ at 110b20, ‘K
 Ø ...  ŒE’ at 142a24–25), it is in fact quite plausible to suppose that he took the expressions ‘knowledge of the fair’ and ‘knowledge of the foul’ to have the same reference. But he will also have taken the expressions to have different senses; and the difference in sense is enough to ensure that ‘I(knowledge of the fair,X)’ and ‘I(knowledge of the foul,X)’ are two different propertyclaims — hence in the first example Aristotle infers ‘¬I(knowledge of the foul, prudence)’ from ‘¬I (knowledge of the fair, prudence)’. That being so, it is difficult to see why, in Ross’ emended text, one and the same property, the identity of which is underlined by the expression ‘e ÆP ’, should be designated by one description in the apodosis of the sentence and by another in the apodosis. — It may be noted that knowledge of the fair and knowledge of the foul cannot possibly be understood as contraries (pace Verdenius, ‘Notes’, p.35 — who takes the suggestion from Verbeke).

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341

into subjects. The word ‘prudence’ is a name or Z
Æ, the expressions ‘knowledge of the fair’ and ‘knowledge of the foul’ are formulas or º ª Ø. According to Aristotle, properties, like definitions, contribute to the knowledge of their subjects (129b 7–8; 131a1), and that is why a property is usually expressed by a formula or º ª  — an expression composed of several O
ÆÆ —, whereas a subject is normally indicated by an Z
Æ (129b30– 33). It is true that an Z
Æ may, on a rare occasion, have a definitional status (›æØŒ
: 102a5); and no doubt, on a rare occasion, a property may be expressed by a single Z
Æ (see [91] the relative properties at 128b25, 129a9). But in none of the examples which Aristotle provides is the property expressed by an Z
Æ and its subject by a º ª . And it is no accident that that is so. At 132b18 Aristotle explicitly states that property-ascriptions do not convert — or rather, that if I(B,A), then ¬I(A,B). It is a property of fire to be a stuff composed of the finest particles: fire is not a property of such stuff. Aristotle offers a proof: if a subject A could be a property of its properties B, C, ... , then A would be a property of the several specifically different subjects B, C, ... .But the same term cannot be a property of several specifically different subjects. Hence Barnes’ conjecture must be rejected. The fact that, on the received text, there are two properties, knowledge of the fair and knowledge of the foul, is embarrassing; but the embarrassment may be removed without transforming the properties into subjects — it is enough to replace ‘ÆNåæ F’ in 137a17 by ‘ŒÆº F’. It is easy to imagine that a copyist might have suspected an error when he found the phrase ‘e KØÅ
 F ŒÆº F’ twice in his text, in a16 and then again in a17, and his suspicions must have hardened if he also read ‘ÆPB’. The received text was absurd, the correction obvious. And it may be noted that the manuscript W is once more a valuable witness: it gives ‘ÆNåæ F’ in a16 and ‘ŒÆº F’ in a17. So we shall imagine that an early text which contained ‘ŒÆº F’ twice and which appeared absurd because of ‘ÆPB’ was corrected in two different ways by two different copyists. In the tradition represented by most of the surviving manuscripts, ‘ŒÆº F’ was replaced by ‘ÆNåæ F’ in a17: in the tradition to which W belongs, the replacement was made in a16. By writing ‘ŒÆº F’ twice, we have a single property. But we must now get two distinct subjects out of ‘çæ
ø’ and ‘ÆPB’. We may suppose that ‘ÆPB’ has displaced some concrete term. The displaced term — call it ‘X’ — must be ‘related in the same way’ to the fair as prudence is related. From 137a14–15 we know that ‘ ... is knowledge of —’ is the relation which

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Aristotle has in mind. [92] So X, like prudence, must be knowledge of the fair — or rather, the claim that X is knowledge of the fair must be reputable or 
 
.13 Ross wondered if we might not read ‘¼ººÅ IæB’ instead of ‘ÆPB’. In the same spirit, we suggest simply ‘IæB’. Palaeographically, the conjecture is modest: replace a upsilon by the two letters rho and epsilon. But in order to commend the proposed text we need to say something in favour of the following proposition: (T) If [1] ([a] knowledge(prudence, fair) & [b] knowledge(virtue, fair) & [2] I(knowledge of the fair, prudence), then [3] ¬I(knowledge of the fair, virtue) We cannot, of course, here reopen the large question of what ethical views Aristotle embraces in the Topics. But we do not need to reopen it: quite generally, one should hesitate before assuming that the examples which Aristotle offers in what is essentially a handbook of dialectic express opinions to which he himself subscribed;* and in the particular case before us, the relation among çæ
ÅØ, virtue, and knowledge is a matter on which the Topics oscillates or hesitates.** (For example, in one place it is said that virtue and knowledge are two distinct genera, neither subordinate to the other (152a39–b2); and yet elsewhere it is suggested, at least tentatively, that prudence may, exceptionally, be both a virtue and a sort of knowledge (120a28–31; 121b26–38) — so that some modification would have to be made to the rule according to which nothing may fall under two genera neither of which is subordinate to the other (121b33–38).) [93] Now the elements of the antecedent of (T) are all of them 
 Æ, and we have no reason here to ask whether or to what extent Aristotle himself commended them or would have commended them. All we need show is that the 
 Æ, taken together, form a consistent set, and that the conclusion of (T) is validly inferred from its premisses according to rules which Aristotle himself acknowledges. So let us ask this question: if prudence is a virtue, and if we suppose — hypothetically — that being knowledge of the fair is proper 13 Our passage, like several others (e.g. 138a13, b16), shows how generous the notion of an 
 
is: two contradictory propositions, ‘Being knowledge of the fair is not proper to prudence’ and ‘Being knowledge of the fair is proper to prudence’ are each assumed as a premiss for a dialectical argument (in the first and the second of the examples), and hence are each taken to be 
 
. The disjunctive definition of ‘
 
’ at 100b21–23 shows how that can be so. * See I. Du¨ring, ‘Aristotle’s use of examples in the Topics, in Owen, Dialectic, pp.202–209. ** See Natali, ‘Virtu` o scienza?’

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343

to prudence, then what follows, according to Aristotelian rules, so far as the relation between virtue and knowledge of the fair is concerned? Well, it follows, first, that being knowledge of the fair holds — at least in one sense of the verb ‘æåØ
’ — of virtue. For if something is proper to a species, then a fortiori it holds of that species (155a28–31), so that being knowledge of the fair holds of prudence. But ‘everything which holds of a species holds also of the genus’ (111a27–28).14 Hence being knowledge of the fair, since it holds of the species prudence, holds also of the genus virtue. The hypotheses of (T) are thus mutually comforting: if [2] knowledge of the fair is a property of prudence, then [1a] knowledge of the fair holds of prudence; if [1a] knowledge of the fair holds of prudence, then [1b] knowledge of the fair holds also of virtue; if knowledge of the fair holds both of prudence and of virtue, then prudence and virtue are related in the same way to the fair, namely by the relation ‘ ... is knowledge of —’. Secondly, the rules of the Topics allow us to infer [94] [3] from the hypotheses of (T). The inference has been found puzzling. Alexander* is not the only commentator to have wondered how a term B could be related in the same way to A and to C and nevertheless be proper to A and not proper to C. But the puzzlement seems to depend upon the mistaken idea that if one relation to B is shared by A and C, then all relations to B must be shared by them — that if there is one relation R such that R(B,A) and R(B,C), then for any relation R, R(B,A) if and only if R(B,C). That is not so — and in fact Aristotle paid some little attention to the point (134a26–135a8). Consider a predicate B which may legitimately be proposed as a property of a subject A. By the rule we invoked a moment ago, together with the converse rule according to which what holds of a genus holds of the species, B must also hold (admittedly in different senses of the word ‘hold’) of a whole series of other terms — of those terms which are found above and below it in a genus– 14 On the difficulties in this passage, see Brunschwig, Topiques, pp.142–143; A. Urbanas, La notion d’accident chez Aristote (Montreal/Paris, 1988); Barnes, Porphyry, p.145 n.137. — It might be objected to the argument in the text that, on a plausible interpretation of the illustrative example at 111a28–29, the passage is concerned only with accidental holding, so that the rule which the passage endorses does not apply to the case which concerns us — in the hypothesis ‘I(knowledge of the fair, prudence)’ the predicate ‘knowledge of the fair’ does not hold accidentally of the subject ‘prudence’. But the example at 111a28–29 should not be looked at in isolation; and in fact another example in the same passage, at 111a26–27, shows that, according to Aristotle, if something holds nonaccidentally of a given species (of bird, say, or of quadruped), then it holds also of the genus (of animal). In other words, if the rule is to apply to all the cases to which Aristotle applies it, the verb ‘æåØ
’ cannot here signal a purely accidental holding. * in Top 412.7–9 — above, n.10.

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species hierarchy. But, perhaps despite initial appearances, that is not fatal to the proposal that I(B,A). All that it requires is that it should be specified ‘how and of what items [H ŒÆd 
ø
]’ the property is supposed to hold. It is impertinent to observe that B also holds of subjects other than A (ŒÆd ¼ºº Ø Ød
æØ e YØ
: 134b19). In this passage, in which he displays a subtlety and a taste for symmetry which sometimes lead him to paradox (see in particular 134b4), Aristotle usually tries to show that one and the same term B can be proper to a subject A in one sense and proper to another subject C in another sense, the two senses being as it were symmetrical or complementary. For example, someone might propose perception as a property of animals ‘by being shared [fiH åŁÆØ]’. You may not object that perception holds also of men, and that men and animals are two different subjects — for men perceive precisely insofar as they are animals or animal is ‘shared’ by them (134b1–4). Symmetrically, life may be proposed as a property of some species of animal15 ‘by sharing [fiH åØ
]’. You [95] may not object that life also holds of animal, which is a different subject from any species of animal; for the species of animal have life precisely inasmuch as they ‘share’ animal (134b4). Doubtless Aristotle would be ready to say, again symmetrically, that perception is a property of men ‘by sharing’ and that life is a property of animal by being shared. In any event, it is plain that one and the same term cannot be a property of the same sort for two different subjects. It follows that when we consider, as Aristotle does in our passage, a term B (knowledge of the fair) which is proper ±ºH (134a32) to a subject A (prudence) and which also holds of another subject C (virtue), B cannot be proper ±ºH to C. We have shown that (i) the hypotheses of (T) are consistent; that (ii) they do not imply that knowledge of the fair must be a property of virtue as well as a property of prudence (something which would be incompatible with sentence (S)); that (iii) they do not imply either that knowledge of the fair can be a property neither of prudence nor of virtue (something which would make the    self-destructive); and that (iv) they do imply — as our conjectural text has it — that knowledge of the fair is not proper to virtue.

15 At 134b4 and 21 ‘ F Ø
e Çfi ı’ must indicate a species rather than an individual, by symmetrry with ‘¼
Łæø ’ at b3. When he wants to indicate an individual, Aristotle writes ‘I
Łæ ı Ø
’ (134a30).

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345

Retractationes In the second volume of his magisterial edition of the Topics, Jacques Brunschwig returned to the    which the preceding pages have discussed.* Largely persuaded by Reinhardt’s analysis of the passage, he came to believe, first, that the former of the two rules set out in 137a8–20 must, after all, be (R3) rather than (R1); and secondly, that the two examples which purport to illustrate the rules must — as Pacius had proposed — be excised from the text. The trouble with (R1), as Reinhardt showed, is this. From (R1) ($R)(R(A,B) & R(A,C)) & ¬I(B,A) ::
¬I(C,A) there follows (R7) ($R)(R(A,B) & R(A,C)) & I(C,A) ::
I(B,A) Now (R7) is a rule not for refutation but for confirmation — it may be used to establish or to corroborate a property-claim which allows the establishment of a property. But Aristotle explicitly says that the    of 137a8–20 cannot be used to establish or confirm a property-claim. Since Aristotle can hardly have failed to see that (R1) implies (R7), he cannot have intended to advance (R1). And so — despite the arguments proposed in the earlier parts of this paper — he must have meant to advance (R3). The example at 137a12–16 is supposed to illustrate the first rule. As it is transmitted in the manuscripts, it might indeed serve to illustrate (R1) — that fact was a chief argument in favour of finding (R1) in the text; but — quite evidently — it does not illustrate (R3). Hence the manuscripts are in error. Since no reasonable emendation will produce an appropriate example, the lines had best be expunged. And once the first example is expunged, then the second example — and all its attendant problems — must go as well. For such reasons, Brunschwig’s text sets the two examples, 137a12–18, within square brackets. Although it would be rash to expect that that is the end of this long story, I confess that I find Reinhardt’s and Brunschwig’s arguments hard to resist. Nonetheless it may, I hope, be instructive, and diverting, to republish those earlier and now outmoded reflections on what Jacques Brunschwig has called ‘one of the most difficult passages in the Topics ’.

* Aristote: Topiques, livres V–VIII (Paris, 2007): text, apparatus and translation on p.32, notes on pp.185–190.

10 ‘Sheep have four legs’* I The difficult problem about which this chapter briefly flutters is simply posed: What is the meaning of the sentence ‘Sheep have four legs’? It is indisputable that the sentence is true; moreover, it expresses a scientific truth — an elementary theorem of the science of animal morphology. But, on the one hand, the sentence is not analytically true: a vet who amputates an ovine limb does not change the genus of his patient; and I have gazed at fivelegged sheep in dark booths on English fairgrounds. Nor, on the other hand, is it an accident that sheep have four legs: it does not simply happen to be the case that those creatures are quadrupeds rather than bipeds, like ducks, or octopods, like the black widow. The fact is that ‘Sheep have four legs’ is true because sheep have four legs by nature, or as a rule, or for the most part — or, as Aristotle puts it, ‰ Kd e  º. But what exactly do those qualifying phrases mean?

II One of Aristotle’s deepest scientific insights was his realization that things which, like the quadrupedality of sheep, hold ‘for the most part’ constitute a large part of the subject matter of all but the most abstract sciences. Aristotle divides the natural world into the things which happen always and of necessity and the things which happen for the most part or ‰ Kd e  º (e.g. Phys B 198b36; GC B 333b5; EE ¨ 1247a32–35; Rhet A 1369a34); and he says that in the case of things for which it is not impossible but possible to be other than they are, what is natural is what holds for the most part. (GA ˜ 777a19–20;** cf A 727b29) * First published in AA.VV., Proceedings of the World Congress on Aristotle (Athens, 1982), vol III, pp.113–119. ** K
ªaæ  E c Iı
 Ø ¼ººø åØ
Iºº’ K
å 
Ø e ŒÆa çØ
Kd e ‰ Kd e  º.

‘Sheep have four legs’

347

Thus what holds for the most part features largely in the social sciences (e.g. EN A 1094b21; E 1137b15; [114] Rhet A 1374a31), and in the sciences of life — psychology, biology, zoology (e.g. Mem 449b7; PA A 690a10; GA A 728a3; Rhet B 1392b22); and it is not wholly absent from more solid disciplines such as meteorology (e.g. Meteor B 197a19) and chemistry (e.g. Meteor A 387a8). Unlike chance events, things that happen for the most part can be explained or accounted for — they have a º ª  (e.g. Phys B 197a19); they are objects of scientific knowledge and of scientific proof, of KØÅ and of I ØØ (e.g. APr A 32b18–21; APst A 87b19–21; Met E l027a20–22). So we might hope to find in Aristotle’s writings some recognition of the ovine question, and some attempt to answer it. The corpus contains, alas, no sustained or systematic discussion of e ‰ Kd e  º; but scattered throughout it we find numerous incidental observations on the topic. Those observations can be roughly divided into two classes: those in the first class bear on the syntax or on the logic of e ‰ Kd e  º, and those in the second class deal with the semantics or meaning of the notion. In the following discussion I shall use a capital omega to abbreviate ‘‰ Kd e  º’, so that ‘For the most part, sheep have four legs’ is abbreviated to ‘( sheep have four legs’. In addition, ‘AxB’ will stand for the ‘indefinite’ sentential structure ‘A holds of B’; and ‘AaB’, ‘AeB’, ‘AiB’, and ‘AoB’ will be used, in what is now the orthodox fashion, to expresss the syllogistic propositions ‘A holds of every B’, ‘A holds of no B’, ‘A holds of some B’, ‘A does not hold of some B’.

I II Turning first to Aristotle’s remarks on the logic of e ‰ Kd e  º, I note that he explicitly asserts that arguments may have premisses of the form ‘(p’ (Rhet A 1356b17; B 1396a3; B 1402a15); and he states that if an argument validly concludes to a proposition of the form ‘(p’, then at least one of its premisses must also be of the form ‘(p’ (APr A 43b33–35; APst B 96a11–19). More particularly, Aristotle subscribes, implicitly or explicitly, to certain inference schemata involving propositions of the form ‘(p’. First, and most importantly, there is a sort of ‘( syllogism’:

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(1) (AxB, (BxC: so (AxC [115] Next, two less exciting rules: (2) (AxB: so AoB (3) (AxB: so it is not necessary that AxB Finally there is the curious schema: (4) (AoB: so (BxA I find (1) at APst A 87b22–27, and Rhet A 1357a27–30 (cf. EN A l094b21); for (2) see Top B 112b5–9, and Rhet B 1402b28; for (3) see APr A 13, 32b16. My text for (4) is APr A 25b16–25, which also appears to deny that (AeB entails (BeA; but the text is peculiarly difficult, and schema (4) is indubitably odd (indeed, some may wonder if ‘(AoB’ is an intelligible expression). Those texts indicate that Aristotle gave at least passing thought to the problems of ‘( logic’. They raise several interesting questions — which I shall ignore, in order to turn to the second group of observations.

IV At first sight, it appears that Aristotle suggests not one but four semantic interpretations of e ‰ Kd e  º. First, he occasionally construes ‘(’ as though it were an expression of the same sort as ‘ŒÆŁ º ı’ or ‘ŒÆa Æ
 ’, ‘universally’ or ‘of every’ (e.g. Rhet A 1356b17). Moreover, he frequently implies that ‘(AxB’ is true if most Bs are A (e.g. APst A 79a21; Rhet B 1390b23–24), and he will contrast ‘(AxB’ with ‘Few Bs are A’ (e.g. Cat 7b24). Such texts suggest that ‘(’ is a sort of quantifying phrase, belonging to the logic of plurality: ‘(AxB’, on this interpretation, means ‘Most Bs are A’, so that ‘Sheep have four legs’ is true if most sheep have four legs. Secondly, Aristotle often treats ‘(’ as though it were an expression of the same sort as ‘I’ or ‘always’ (e.g. APst B 96a9; Cael A 283b2; EN ˆ 1112b3–8; Rhet A 1369a34); and he sometimes couples and contrasts it with ‘K
 ’ or ‘sometimes’ (e.g. Top E 129a6–16; Rhet A 1362b37–38). Such passages suggest that ‘(’ means something like ‘ ººŒØ’ — ‘often’, or perhaps ‘very often’), and that it is a sort of temporal quantifier, belonging to chronological logic. On this second interpretation ‘(p’ means ‘Very often, p’, so that ‘Sheep have four legs’ is true if very often sheep have four legs. [116]

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349

The third and fourth interpretations read ‘(’ as a modal operator, on a level with the modal phrase ‘K I
ªŒÅ’ or ‘by necessity’. Aristotle frequently construes ‘(’ as though it were an expression of that type (e.g. Phys B 196b11; Mem 451b13; Met E 1026b27–35; Rhet A 1357a31; Poet 1450b30). In such contexts, Aristotle sometimes contrasts ‘K I
ªŒÅ’ with ‘NŒ ’, and implies that the latter term is equivalent in meaning to ‘(’ (e.g. Poet 1451a12, 1451a38). Moreover, he explicitly states that ‘what is likely is not what holds always but what holds for the most part’.* Thus we are apparently licensed to interpret ‘(’ as ‘NŒ ’ or ‘probably’, and to regard it as an operator belonging to the logic of probability. On the third interpretation, ‘(p’ means ‘It is likely that p’, so that ‘Sheep have four legs’ is true if it is probable that sheep have four legs. The fourth interpretation rests primarily on two difficult passages in the Prior Analytics. At A 25b14, Aristotle refers to ‘those things which are said to be possible inasmuch as they hold for the most part or are naturally so’;** and at A 32b4–7, he notes that of the two ways in which things are said to be possible, one is that ‘it comes about for the most part and there are gaps in the necessity’.*** Here Aristotle seems to offer ‘possibly’ or ‘K
åÆØ’ — in one of its uses —, as an interpretation of ‘(’ (cf Rhet A 1357a15; and perhaps APst A 88a7). Moreover, he explicitly says that ‘generally speaking, arguments and investigations are concerned with what is possible in this way’, while in the case of the other sort of possibility, ‘there can be syllogisms but they are not normally looked for’ (APr A 32b20–22).**** And that seems to imply that the sort of possibility about which Aristotle builds his ‘problematic’ syllogistic is precisely the possibility of what holds for the most part. Those passages suggest that ‘(’ is the familiar modal operator ‘K
åÆØ’ or ‘It is possible that’, in the more important of its guises; and the fourth interpretation has it that ‘(p’ means ‘It is possible that p’, and that ‘Sheep have four legs’ is true if it is possible that sheep have four legs.

* e b NŒe P e Id Iººa e ‰ Kd e  º: Rhet B 14023b21; cf APr B 70a4; and perhaps Int 19a21. ** ‹Æ b fiH ‰ Kd e  ºf ŒÆd fiH çıŒ
ÆØ ºªÆØ K
åŁÆØ. *** e ‰ Kd e  ºf ª
ŁÆØ ŒÆd ØƺØ
e I
ƪŒÆE
. **** ŒÆd åe
ƒ º ª Ø ŒÆd ƃ ŒłØ ª

ÆØ æd H
oø K
å 
ø
· KŒ
ø
’ KªåøæE b
ª
ŁÆØ ıºº ªØ
, P c
YøŁ ª ÇÅEŁÆØ.

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V Can those four interpretations be united into a single semantic system? Aristotle suggests once or twice that the first two interpretations should be taken as complementary parts of a single analysis; at least, he sometimes implies that ‘(AxB’ is true if most Bs are very often A (cf Cael ˆ 301a7; [117] GA A 727b28–30; Rhet B 1402b36) Again, he observes that a ºø ŒÆd  ººŒØ provide grounds for what is NŒ  (Rhet B 1402b36), so that probability is founded upon, and perhaps explained in terms of, frequency. In that case, the third interpretation of ‘(’ will be equivalent to the conjunction of the first two interprerations. As for the fourth interpretation, I am inclined to regard it as Aristotle’s ‘official’ semantics for ‘(’ — as an attempt to give a more rigorous structure to his other remarks. For the fourth interpretation has the signal merit of integrating what holds for the most part into Aristotle’s general theory of logic and knowledge. Aristotle’s modal syllogistic rests upon the two operators ‘K I
ªŒÅ’ and ‘K
åÆØ’: the former grounds ‘anankastic’ syllogistic, the latter ‘problematic’ syllogistic. Anankastic syllogistic underlies the apodeictic theory which is propounded in the main body of the Posterior Analytics, and which was designed to formalize those sciences whose objects hold always and of necessity. If ‘(’ is identified with one variety of possibility — and with precisely that variety about which ‘arguments and investigations’ are concerned —, then surely problematic syllogistic was intended to underlie a second branch of apodeictic theory, and to formalize those sciences whose objects hold only for the most part. Thus the modal syllogistic of APr A 8–22 as a whole supplies a unitary logic for the sciences, and a coherent apodeictic theory within which our knowledge of the natural world can be given a structured exposition.

VI There is, however, a serious objection to that construction. At APr A 32a29–33, Aristotle states a central thesis of his problematic syllogistic:

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351

It turns out that all propositions of possibility convert with one another ... for example, ‘possibly holds’ converts with ‘possibly doesn’t hold’.*

That is to say, (5) It is possible that p if and only if it is possible that not-p. Now it is plain that the corresponding conversion thesis for ‘(’ is false; it is not true that (6) (p if and only if ((not-p) (‘Sheep have four legs’ is not equivalent to ‘Sheep don’t have four legs’.) It follows that ‘K
åÆØ’, as that operator is construed in Aristotle’s [118] modal syllogistic, is not a possible reading of ‘(’; and hence that the fourth interpretation of ‘(’ is untenable. That objection may well seem both fatal and obvious; and it may encourage a certain scepticism. For surely Aristotle will have seen the objection, and appreciated its force? Surely, therefore, he can never seriously have construed ‘(’ by way of possibility? And surely the fourth interpretation of ‘(’, and the integrated apodeictic theory which it suggested, are figments of the modern imagination and no part of Aristotle’s philosophy? Such scepticism has its temptations; but it also has its difficulties. Moreover, it is not clear that the objection it starts out from must have seemed fatal to Aristotle; for it did not seem so to Theophrastus or to Eudemus. According to the Ammonian commentary on the Prior Analytics, Aristotle’s pupils took note of the non-convertibility of ‘(p’ with ‘((not-p)’: recognizing the falsity of (6), they determined to abandon thesis (5), and to construct an alternative logic of possibility.** That story implies that, in Peripatetic eyes, the primary function of problematic syllogistic was to provide an ( logic; and that Aristotle’s pupils took the falsity of (6) as an objection not to the fourth interpretation of ‘(’ but rather to their master’s problematic logic. Far from abandoning the fourth interpretation, they attempted to develop a logic of possibility which would accommodate it. Their attempt may have been quixotic (at any rate, it certainly failed); but it is an intelligible reaction to the problem posed by (6). Pseudo-Ammonius’ story is consistent with what little else we know of the history of Peripatetic modal logic. But it is, admittedly, an isolated story, of dubious provenance: sceptics may prefer to reject it, and to reiterate their * ıÆ
Ø b Æ a ŒÆa e K
åŁÆØ æ Ø I
ØæçØ
IºººÆØ. ... x
e K
åŁÆØ æåØ
fiH K
åŁÆØ c æåØ
. ** See [Ammonius], in APr 45.42–46.2 [¼ Theophrastus, 103C Fortenbaugh, and Eudemus, frag 13 Wehrli].

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doubts about the fourth interpretation of ‘(’. For the moment, I incline to believe pseudo-Ammonius, and hence to confide in the historicity of the fourth interpretation and of all it suggests.

VII In this short chapter I have scratched the surface of a fertile and largely untilled field. The texts I have cited need detailed analysis; other texts remain to be adduced; the notion of what holds for the most part should be set more firmly in the context of Aristotle’s concept of nature; the Platonic background could with advantage be explored (the end of the Philebus is of particular importance here); and the semantics of ‘(’ deserve philosophical study in their own right.* * My thoughts on this subject were first stimulated by the pioneering study of Albrecht Becker, Die aristotelische Theorie der Mo¨glichkeitsschlu¨sse (Berlin, 1933), chh.VIII–IX. I have already touched on the matter at pp.133–137 of ‘Aristotle’s theory of demonstration’, Phronesis 14, 1969, 123–152 [reprinted in volume III]. An earlier draft of this chapter was purged of at least two serious errors by the pertinent criticisms of Mlle Suzanne Mansion and M. Jacques Brunschwig. My understanding of the problem of e ‰ Kd e  º owed much to discussions in Oxford and in Thessaloniki with Mario Mignucci, whose own views, far more refined than mine, were published as ‘‰ Kd e  º et ne´cessaire dans la conception aristote´licienne de la science’, in E. Berti (ed.), Aristotle on Science: the Posterior Analytics (Padua, 1981), pp.173–203. I may also mention L. Judson, ‘Chance and ‘‘always or for the most part’’ in Aristotle’, in L. Judson (ed.), Aristotle’s Physics (Oxford, 1991), pp.73–99.

11 The law of contradiction* Section I presents an argument for a proposition which might reasonably be expressed by the sentence ‘The Law of Contradiction is a Law of Thought’. Section II examines a similar argument given by Aristotle in his Metaphysics. Section III sets out some propositions which the argument does not prove.

I The argument has three premisses, each of which is supposed to be necessarily true; in the case of each premiss I shall offer a few considerations designed to bring this out. The first premiss is this: (1) Anyone who believes a conjunction of two propositions believes each of the conjoined propositions, or: (1S) (8x)(xB:(P & Q)
(xB:P & xB:Q)).** That is a special case of: (1*) Anyone who believes a conjunction of propositions believes each of the conjoined propositions. I shall try to support the weaker thesis (1), which is all that the argument requires; but analogous points could plainly be advanced in support of (1*). To deny the necessity of (1) is to assert that a man may at one time both (a) believe that both P and Q, and also (b) either not believe that P or not believe that Q or both not believe that P and not believe that Q. And that is absurd: if a man does not believe, say, that Q, how can he possibly believe that both P and Q? * Originally published in Philosophical Quarterly 19, 1969, 302–309. ** The original version of this chapter set the steps of the argument out symbolically, and only symbolically: the present version gives all the steps in English, or in semi-English, adding in most cases a symbolic version (signalled by an adscript ‘S’). — ‘xB:P’ stands for ‘x believes that P’; ‘xD:P’ for ‘x disbelieves that P’; ‘C(F,G)’ means that the properties indicated by the predicate-terms ‘F’ and ‘G’ are contrary to one another; ‘RF’ indicates the range of the property indicated by ‘F’.

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Try to imagine circumstances in which someone says that he believes some conjunction and yet at the same time denies that he believes one of the conjuncts. Suppose that a foreign student reads in a digest of English literature the sentence ‘Pepys and Evelyn wrote diaries’, but does not meet with either of the sentences ‘Pepys wrote a diary’ and ‘Evelyn wrote a diary’; and suppose that this leads him in an examination to assert that he believes that Pepys and Evelyn wrote diaries and to deny that he believes that Evelyn wrote a diary. Could we make anything of his answer? We might conjecture that the candidate was making a curious joke or attempting to simulate lunacy; but if explanations of this sort were eliminated, I think we could only conclude that he did not understand the [303] conjunctive sentence he wrote and hence could not believe the conjunctive proposition he claimed to believe. (This might happen in more than one way: he might, for example, be ignorant of the meaning of the connective ‘and’; or think that Pepys and Evelyn were collaborators like Beaumont and Fletcher; or imagine that ‘wrote diaries’ was a predicate of the same sort as ‘corresponded with one another’.) In short, if anyone asserts that he believes that P and Q, and also asserts that he does not believe that P, one at least of his assertions is not true: either he is lying, joking, or otherwise unserious, or else he does not understand one of the sentences which express the propositions which he claims to believe. It is worth noting that the converse of (1): (1.1) Anyone who believes each of a pair of propositions also believes their conjunction, does not hold — it is possible to believe a number of propositions and yet be ignorant of the operation of conjunction. It is clear too that the disjunctive and conditional analogues of (1): (1.2) Anyone who believes a disjunction of two propositions either believes one of the disjoined propositions or believes the other, and: (1.3) If anyone believes a conditional proposition, then if he believes the antecedent he also believes the consequent are not true; and neither are the disjunctive and conditional analogues of (1.1). The notion of contrary predicates is deployed by Aristotle in the argument which I shall discuss in Section II; and although the notion is not necessary to the present argument, it is convenient to introduce it here before setting down the second premiss of the argument.

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Contrariety has a long, but not unambiguous, history. It is useful to distinguish among three relations, each of which Aristotle seems to have thought of as a type of contrariety. In the following definitions, the ‘range’ of a property is, roughly, the class of objects to which it can be ascribed without commission of a category mistake. First: (D1) Two properties are contraries1 if and only if they have the same range and nothing which possesses one of them can possess the other, or: (D1*) C1(F,G) ó ((RF ¼ RG) & (8x)(&(Fx
¬ Gx)). Then: (D2) Two properties are contraries2 if and only if they have the same range, and nothing which possesses one of them can possess the other, and anything in their range must possess the one of them or the other, or: (D2*) C2(F,G) ó ((RF ¼ RG) & (8x)(&(Fx
¬ Gx) & (8x)((x in RF)
&(Fx v Gx))). Thirdly: (D3) Two properties are contraries3 if and only if they have the same range, and nothing which possesses one of them can possess the other, and any other property with the same range is between the two of them, or: (D3*) C3(F,G) ó ((RF ¼ RG) & (8x)(&(Fx
¬ Gx) & (8H)(RH ¼ RF
H is between F and G))). Contrariety1 might be called incompatibility: paradigm contraries1 are red and green, hot and cold. Contrary2 predicates might be called contradictory predicates: typical contraries2 are odd and even, guilty and innocent. Contrariety3 might be called polar opposition: examples of contraries3 are black and white, bald and hirsute. Those definitions are not very satisfactory: some account is needed of what the range of a predicate is, and in (D3) the notion of ‘being between’ demands explanation. If I do not attempt to satisfy those requirements here, that is because nothing in Aristotle’s argument turns [304] on the more questionable features of the definitions. Moreover, in what follows I shall not be concerned with either contrariety2 or contrariety3, and henceforth I shall omit the subscripts and use ‘contraries’ and ‘C’ to refer to contraries1. The second premiss of the argument is this: (2) Anyone who disbelieves that P does not believe that P,

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or: (2S) (8x)(xD:P
¬ xB:P). That is a necessary truth if (but not only if) believing that P and disbelieving that P are contraries. The Oxford Dictionary asserts that disbelief is the state contrary to that of belief; and although that is not strictly true,1 it seems to me clear that belief and disbelief — like praise and blame, love and hate, approbation and disapprobation — do fulfil the defining conditions of the relation of contrariety.2 In particular, it seems indisputable that anyone who disbelieves that P must thereby not believe that P; for how could a man both disbelieve that P and also not not believe that P? Disbelieving is simply one way of not believing, just as loathing a person is simply one way of not liking him. And just as there are other ways of not liking a man — for example, feeling completely indifferent to him —, so there are other ways of not believing a proposition — for example, feeling uncertain about its truthvalue. This last point shows that the converse of (2): (2*) Anyone who does not believe that P disbelieves that P, or: (2*S) (8x)(¬ xB:P
xD:P) is not a necessary truth. The necessary truth of the third premiss, (3) Anyone who believes that not-P disbelieves that P, or: (3S) (8x)(xB:¬ P
xD:P) is evident. The conditional may be strengthened to a biconditional to give: (3*) Someone believes that not-P if and only if he disbelieves that P, a sentence which might serve as a definition of disbelief.* To disbelieve a man’s testimony just is to believe that his testimony is false; and in general, disbelieving that P just is believing that not-P. It might be objected against (3*) that ‘x doesn’t believe that P’ is compatible with ‘x doesn’t believe that not-P’ (x might be unsure whether or not P), so that the sentence: 1 (D1) gives no guarantee of uniqueness, and so does not warrant our talking of the contrary of a given property. 2 They might well fit (D3) on some satisfactory account of the relation of being between; and I suspect that Aristotle thought of them as contraries3. * Barnes’ argument ‘employs a notion of disbelief that simply slides ambiguously between not believing and believing that not’ (G. Priest, ‘To be and not to be — that is the answer. On Aristotle on the Law of Non-Contradiction’, Logical Analysis and History of Philosophy 1, 1999, 91–130, on p.94 n.9). No it doesn’t.

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If someone doesn’t believe that P, then he believes that not-P does not express a necessarily true proposition. That, of course, can only count as an objection against (3*) if ‘x doesn’t believe that P’ is synonymous with ‘x disbelieves that P’. But in fact ‘x doesn’t believe that P’ does, at least sometimes, mean the same as ‘x disbelieves that P’ — I can reject a story as well by saying ‘I don’t believe you’ as by the more ponderous ‘I disbelieve you’. Nonetheless, I think that the objection shows only that the everyday negative ‘doesn’t believe that’ is ambiguous. We can say both of the atheist and of the agnostic that he doesn’t believe that God exists; but when we say it of the [305] former we mean that it is the case that he believes that God does not exist, and when we say it of the latter we mean that it is not the case that he believes that God does exist. It is plain that if we take ‘x doesn’t believe that P’ in the atheist’s sense, then ‘x doesn’t believe that P’ is incompatible with ‘x doesn’t believe that not-P’; and if we take it in the agnostic’s sense, then ‘x doesn’t believe that P’ and ‘x doesn’t believe that not-P’ are compatible — but that their compatibility does nothing to show that (3*) is false. The argument from those three premisses can best be put in the form of a reductio ad absurdum. Let us assume, for example, that: (4) Priest believes that both Paris is south of London and Paris is not south of London, or: (4S) aB:(P & ¬ P). From premiss (1) and assumption (4) there follows (by universal instantiation and modus ponens): (5) Priest believes that Paris is south of London and Priest believes that Paris is not south of London, or: (5S) aB:P & aB:¬ P. Next, from that proposition, together with premiss (3), there follows: (6) Priest believes that Paris is south of London and Priest disbelieves that Paris is south of London, or: (6S) aB:P & aD:P. Finally, from (6) and (2), there follows: (7) Priest believes that Paris is south of London and Priest doesn’t believe that Paris is south of London,

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or: (7S) aB:P & ¬ aB:P. But that is a contradiction — it is a special case of (one version of) the Law of Contradiction, namely: (8) No proposition both is the case and is not the case, or: (8S) (8P)¬ (P & ¬ P). So the three premisses, together with the assumption, lead to a contradiction: given the premisses, the assumption cannot be correct. Nothing in the argument depends on the particular example used as the assumption: the scope of the proof is perfectly general. Thus its conclusion can be generalized: no one can believe of any proposition both that it is the case and that it is not the case. A slightly more dramatic way of expressing that is to say that the Law of Contradiction is a Law of Thought.

II The traditional doctrine of the Laws of Thought can be traced back to a passage in Aristotle. Aristotle does not recognize four Laws, but only one; and he does not advance dubious psychological claims (or use the vague phrase ‘a Law of Thought’): rather, he gives [306] a short and rigorous argument for a precisely formulated conclusion. Aristotle’s argument is similar to the one which I set out in Section I; since it is difficult to follow as it stands in his text, and since its ingenuity has not been appreciated by his commentators,* I shall set out the passage in translation and then offer a few explanatory remarks.3 (A) A principle is firmest4 of all if it is impossible to be mistaken about it ... What this principle is let us now say: It is impossible for the same thing at the same time both to belong and not to belong to the same thing and in the same respect (and let us

* That sentence was written forty years ago, since when gallons of ink have flowed. For a couple of recent examples, see Priest, ‘To be and not to be’ (who says ‘this is a hopeless argument’ — p.94), and W. Cavini, ‘Principia contradictionis: sui principi aristotelici della contraddizione’, Antiquorum Philosophia 1, 2007, 123–169, and 2, 2008, 159–187 (who takes the argument to be evidently probative — pp.180–181). 3 The numerals inserted in the translation link sentences of Aristotle’s text — hence the adscript ‘T’ — to formulas in the explanatory remarks. 4 The superlative implies that Aristotle thought only one logical law could be a Law of Thought.

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suppose added all the other qualifications which we should add to guard against the dialectical difficulties).5 This, then, is firmest of all the principles, (107T) for it answers to the definition given above. (106T) For it is impossible for anyone to believe that the same thing is and is not, as some think Heraclitus says — for it is not necessary that a man believe what he says.* If (102T) it is not possible for contraries to belong at the same time to the same thing (let us suppose the usual qualifications added to this proposition too), and if (103T) the opinion contrary to an opinion is the opinion of the contradictory, then (105T) it is evident that it is impossible for the same man at the same time to believe that the same thing is and is not; (104T) for the man who was mistaken about this would have contrary opinions at the same time. (Met ˆ 1005b11–12; 18–32)**

This passage may be supplemented by an extract from a later part of the same book: (B) Since (100T) it is impossible for contradictories to be true at the same time of the same thing, it is evident that (102T) it is not possible for contraries to belong at the same time to the same thing either. (101T) For of contraries one is in addition a privation — a privation of substance —, and a privation is a denial with regard to some determinate subject-matter.6 (1011b15–20)

The passages demand close reading; it may help if the steps of the argument are re-arranged somewhat and the proof set out more formally. The proof is conducted, Aristotle says (1006a4), by means of the Law of Contradiction; the Law appears here in the form of: 5 For these ‘dialectical difficulties’, which can be ignored in a modern presentation of Aristotle’s argument, see also: Int 17a35–37; Top A 166b37–167a35; and compare EE B 1221b4–7. * ‘That is quite true, but hardly sufficient to show that people such as I do not believe contradictions. People are not infallible about what they believe, but that someone sincerely asserts something (and is clear that what they assert is what they mean) is very strong prima facie evidence that they believe it’ (Priest, ‘To be and not to be’, p.94). Sincere assertion is not strong evidence for belief — it is not evidence at all. If someone sincerely asserts that P, it follows that he believes that P. ** ÆØ Å  Iæåc ÆH
æd m
ØÆłıŁB
ÆØ I
Æ
...   Ø
ÆoÅ a ÆFÆ ºªø
· e ªaæ ÆPe –Æ æåØ
 ŒÆd c æåØ
I
Æ
fiH ÆPfiH ŒÆd ŒÆa e ÆP (ŒÆd ‹Æ ¼ººÆ æ Ø æØÆŁ ’ ¼
, ø æ ØøæØ
Æ æe a º ªØŒa ıåæÆ), ÆoÅ c ÆH
Kd ÆØ Å H
IæåH
· åØ ªaæ e
NæÅ

Ø æØ
: I
Æ
ªaæ ›
Ø
F
ÆPe
 ºÆ
Ø
r
ÆØ ŒÆd c r
ÆØ, ŒÆŁæ Ø
b Y
ÆØ ºªØ
 ˙挺Ø
( PŒ Ø ªaæ I
ƪŒÆE
– Ø ºªØ ÆFÆ ŒÆd  ºÆ
Ø
). N b c K
åÆØ –Æ æåØ
fiH ÆPfiH I
Æ
Æ (æ ØøæŁø  E
ŒÆd Æfi Å fiB æ Ø a NøŁ Æ), K
Æ
Æ  Kd  Æ  fi Å

B I
Øçø, çÆ
æe
‹Ø I
Æ
–Æ  ºÆ
Ø
e
ÆPe
r
ÆØ ŒÆd c r
ÆØ e ÆP · –Æ ªaæ i
å Ø a K
Æ
Æ  Æ › Øłı
 æd   ı. 6 Kd  I
Æ
c
I
çÆØ
–Æ IºÅŁŁÆØ ŒÆa  F ÆP F, çÆ
æe
‹Ø Pb I
Æ
Æ –Æ æåØ
K
åÆØ fiH ÆPfiH
H
b
ªaæ K
Æ
ø
Łæ
æÅ KØ
På w
, PÆ b æÅØ
b æÅØ I çÆ KØ
I Ø
 侯
ı ª
ı. — The Greek is uncertain at b18–20: I have translated Alexander’s reading, which is followed by most editors.

360

Logical Matters (100) Nothing both possesses a given property and does not possess it,

or: (100S) (8x)¬ (Fx & ¬ Fx). From (100) and: [307] (101) Nothing which possesses one of a pair of contrary properties also possesses the other, or: (101S) (8x)(C(F, G)
(Gx
¬ Fx)).7 Aristotle infers (‘K’, 1011b15; ‘ªæ’, 1011b18): (102) Nothing can possess both of a pair of contrary properties, or: (101S) (8x)(C(F, G)
¬ (Fx & Gx)). That is the argument of passage (B). It is valid. Next let us take: (103) Believing that so-and-so and believing that not-so-and-so are contrary properties, or: (103S) C(B:P, B:¬ P). Aristotle does not argue for (103) in the Metaphysics; some commentators — among them Alexander of Aphrodisias (in Met 270.24-25) — have thought that he tries to prove it in the last section of the de Interpretatione; but that section is extremely obscure. From (102) there follows: (104) If believing that so-and-so and believing that such-and-such are contrary properties, then no one both believes that so-and-so and also believes that such-and-such, or: (104S) C(B:P, B:Q)
(8x)(¬ (xB:P & xB:Q). Next, (103) and (104) yield (‘N’, 1005b26; ‘ªæ’, 1005b31): (105) No one believes that P and also believes that not-P, or: (105S) (8x)¬ (xB:P & xB:¬ P) by substitution of ‘¬ P’ for ‘Q’ in (104) and modus ponens. Finally, Aristotle passes from (105) to: (106) No one believes that both so-and-so and not-so-and-so, 7 (101) is not a close representation of (101T). Aristotle seems to mean that if F and G are contraries, then G is a privation or lack of F; and that if G is a lack of F, then being G entails not being F. Aristotle has almost certainly said this before, at 1004a10–16 — but there too the text is uncertain.

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or: (106S) (8x)¬ (xB:(P & ¬ P)). It is not clear from the text what Aristotle thought the relation was between (105) and (106); indeed, it is not even clear that he saw any difference between the two propositions. However, (106) is the most natural reading of the Greek of (106T); and at the same time it is hard to suppose that Aristotle thought of (106) as an immediate inference from (103) and (104): so it seems reasonable to introduce (105) into the argument as a representation of (105T). To get from (105) to (106) Aristotle of course needs something like my premiss (1).

I II My account of Aristotle’s argument misrepresents the text on at least two counts;8 both concern the modal qualification of propositions. First, some of the steps in the argument are prefixed in the Greek text, but not in my account of it, by modal operators. For example, a stricter interpretation of (105T) would be: (105Sm) (8x)¬ ¤(xB:P & xB:¬ P). [308] The same applies to (100T), (102T), and (106T); but not to (101T), (103T), or (104T). However, that is probably trivial: I suspect that the function of these operators is simply to indicate that the steps in the argument are necessary truths; the indications are admittedly casual and sporadic, but that is in line with the carefree attitude towards modal operators which Aristotle displays in the rest of Metaphysics ˆ and elsewhere. At all events, I shall not pursue the point any further. The second point is more serious. Aristotle claims to have proved not merely (106) but (107T), or more fully: (107T*) It is impossible to be mistaken concerning the principle that it is impossible for the same thing at the same time both to belong and not to belong to the same thing. If we read ‘be mistaken concerning the principle that’ as ‘(wrongly) believe that it is not the case that’, this becomes: 8 It also ignores the recurrent phrase ‘at the same time’: see above, n.5.

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Logical Matters (107m) It is impossible for anyone to believe that it is possible for there to be anything which both possesses and does not possess a given property,

or: (107Sm) (8x)¬ ¤(xB:¤(&F)(&y)(Fy & ¬ Fy)). Let us consider a simpler proposition, namely: (107) No one believes that it is possible for a proposition both to be the case and not to be the case, or: (107S) (8x)¬ (xB:¤(P & ¬ P)). It is quite clear that (107m*) is neither equivalent to nor entailed by (106): in general, it is possible that, while no one believes that something is actually the case, there are nevertheless people who believe that the same thing may possibly be the case. Moreover, no argument analogous to Aristotle’s or to that of Section I could prove (107). We might perhaps accept the modal analogue of premiss (1), namely: (1m) Anyone who believes that a conjunction of two propositions is possible believes that each of the two propositions is possible, or: (1mS) (8x)(xB:¤(P&Q)
(xB:¤P & xB:¤Q)). But the required modal analogue of premiss (3), namely: (3m) Anyone who believes that it is possible that not-so-and-so disbelieves that it is possible that so-and-so, or: (3mS) (8x)(xB:¤¬ P
xD:¤P), is plainly false. Aristotle’s deduction of (107) is thus invalid. A similar fallacy would be committed if we tried to infer a quantified version of (107), namely: (107q) No one believes that there is a proposition which is both the case and not the case, or: (107qS) ¬ (&x)(xB:(&P)(P & ¬ P)). The fallacy turns on the fact that the quantifier ‘(&P)’ in (107q) falls within the intensional context ‘x believes that ... ’. If we quantify over ‘P’ in (106) to get: (106q) There is no proposition such that anyone believes that it is the case and also not the case,

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or: (106qS) (8P)(8x)¬ (xB:(P & ¬ P)), we can see that in the passage from this to (107q) the initial quantifier is captured by the intensional context ‘x believes that ... ’. An analogous point holds of the move from (106m) to (107); and it is possible that Aristotle’s willingness to make the move was due to his ignorance of the snares of intensionality. A further proposition which the argument does not prove is: (106u) Everyone believes that it is not the case that both so-and-so and not-so-and-so, or: (8x)(xB:¬ (P & ¬ P)). Nor does it prove the propositions similarly analogous to (107) and (107q): (107u) Everyone believes that it is impossible that both so-and-so and not-so-and-so, and: (107qu) Everyone believes that there is no proposition which both is the case and is not the case. Moreover, if, as I claimed, proposition (1*) is untrue, then (106) does not even yield: (106&) No one both believes that so-and-so and believes that not-soand-so, or: (106&S) (8x)¬ (xB:P & xB:¬ P). [309] Finally, there is an interesting proposition which is all but stated by Aristotle at 1005b13–17, a sentence which I omitted in my translation of passage (A). It is this: (108) Anyone who believes anything believes that no proposition is the case and also not the case. Neither (108) nor any modalized version of it follows from (106). Any of the propositions mentioned in the last three paragraphs might not unreasonably be glossed as the proposition that the Law of Contradiction is a Law of Thought; and there are certainly many more analogous propositions equally open to such a gloss. Furthermore, there are normative propositions about how all men ought to think and psychological propositions about how all men do think which might also claim the right to the gloss. Some of these propositions may well be true. My claim that the Law of Contradiction is a Law of Thought is meant as nothing more than the claim that (12) or (106) is a necessary truth.

12 Proofs and the syllogistic figures* Wolfgang Kullmann has made signal contributions to the study of that large and thorny subject, Aristotle’s philosophy of the sciences. One particularly thorny patch is the relation between the logical theory which Aristotle develops in the Analytics and the method which he practises in his scientific works. This relation can be construed as the product of two further relations: the relation between the syllogistic theory of the Prior Analytics and the demonstrative theory of the Posterior Analytics; and the relation between the demonstrative theory and the scientific method. It is a commonplace — and a truth — that the logic of the Prior Analytics is not adequate to the needs of scientific proof; that is to say, there are proofs the validity of which cannot be exhibited in Aristotle’s syllogistic. The truth was acknowledged in antiquity — Galen, for example, expressed it with vigour and clarity.1 But in Peripatetic circles, ancient and modern, the truth was suppressed or denied; and it was suppressed or denied on the authority of Aristotle himself — for a chapter in the Prior Analytics purports to establish, or appears to purport to establish, that categorical syllogistic is sufficient for the purposes of scientific proof. The following pages pass some remarks on that authoritative chapter. The remarks propose no exciting heterodoxy, and they fall far short of a commentary; but I hope that Wolfgang Kullmann will read them in the spirit in which they are written — as a token of admiration and of esteem. The chapter is Prior Analytics A 23. Aristotle begins by announcing his demonstrandum: That the deductions in these figures are completed by way of the universal deductions in the first figure and are reduced to these deductions is plain from what * First published in H.-C. Gu¨nther and A. Rengakos (eds), Beitra¨ge zur antiken Philosophie: Festschrift fu¨r Wolfgang Kullmann (Stuttgart, 1997), pp.153–166. 1 See e.g. lib prop XIX 39–40.

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has been said; that this will hold in general of every deduction will next be evident, once it is shown that every deduction comes about by way of one of these figures. (40b17–22)*

There follows a complex argument, at the end of which Aristotle concludes thus: If that is true, then necessarily every proof and every deduction comes about by way of the three figures earlier described; and if that is shown, it is plain that every deduction is completed by way of the first figure and is reduced to the universal deductions of this figure. (41b1–5)**

The demonstrandum proposes that every deduction can be reduced to Barbara and Celarent, the [154] two universal deductions in the first figure. The argument of A 23 offers the demonstrandum as the immediate consequence of two subordinate theses: that every deduction comes about by way of the three figures; and that every deduction in the three figures is reduced to Barbara and Celarent. The second of these theses has already been established.2 The body of A 23 aims to establish the first of them. I want a neutral name for this first thesis: I shall call it ‘the Thesis’. The demonstrandum, and hence the Thesis, are initially stated in terms of deductions or ıºº ªØ  (40b20). But a few lines later proofs are coupled with deductions (40b32);3 and at the end of the chapter Aristotle restates the demonstrandum with reference to ‘proofs and deductions’ (41b1–2). The reference to proofs serves, I suppose, to indicate the bearing of the demonstrandum: it is not merely a ‘metalogical’ theorem but also a doctrine about the nature of scientific demonstration. But the reference to proof does not complicate the argument of A 23; for, given that a proof is a type of deduction,4 if every deduction reduces to Barbara and Celarent, it follows trivially that every proof reduces to Barbara and Celarent. * ‹Ø b
s
ƒ K
  Ø  E åÆØ ıºº ªØ d ºØ F
Æ  Øa H
K
fiH æfiø åÆØ ŒÆŁ º ı ıºº ªØH
ŒÆd N   ı I
ª
ÆØ, Bº
KΠH
NæÅ
ø
· ‹Ø ’ ±ºH A ıºº ªØe oø Ø
F
ÆØ çÆ
æ
, ‹Æ
ØåŁfiB A ªØ

 Øa  ø
Ø
e H
åÅø
. ** N b  F IºÅŁ, AÆ
I ØØ
ήd 
Æ ıºº ªØe
I
ªŒÅ ª
ŁÆØ Øa æØH
H
æ ØæÅ
ø
åÅø
:   ı b ØåŁ
  Bº
‰ –Æ  ıºº ªØe KغEÆØ Øa  F æ ı åÆ  ŒÆd I
ªÆØ N  f K
 fiø ŒÆŁ º ı ıºº ªØ . 2 In fact, Aristotle established it in A 7, to which 40b17–20 refers: it has been supposed, plausibly and frequently, that in an earlier version of APr, A 23 followed immediately upon A 7, the chapters on modal syllogistic being a later insertion. 3 The ‘ŒÆ’, I take it, is genuinely conjunctive rather than epexegetic. 4 e.g. APst A 71b17–18.

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The term ‘deduction’ or ‘ıºº ªØ ’, as Aristotle uses it in A 23, doubtless bears the sense — technical or semi-technical — which Aristotle devised for it in A 1, at 24b18–22. The terms of that celebrated definition repay — and have often enough received — the closest scrutiny. But it is clear that the Greek word ‘ıºº ªØ ’, in the sense given to it in APr, means, roughly, ‘valid deductive argument’ (and hence that the English ‘deduction’ is a decent enough translation). At any rate, that rough synonymy will be enough for my purposes. Hence A 23 does not urge that every categorical syllogism is reduced to Barbara and Celarent; rather, it urges that every valid deductive argument is reduced to Barbara and Celarent. And in particular, the Thesis does not urge that every categorical syllogism comes about in the three figures; rather, it urges that every valid deductive argument comes about in the three figures. All that, I take it, is uncontroversial — if not banal. But the demonstrandum has thus far been only dimly expressed; in particular, the Thesis rests obscure. Aristotle says that every deduction ‘comes about by way of’ the three figures;5 or that it is ‘brought to a conclusion by way of’ them.6 The preposition ‘by way of’ gives little away; ‘come about’ is the most self-effacing of verbs; and it is not plain what force we should ascribe to ‘bring to a conclusion’.7 Alexander of Aphrodisias offers a gloss: ‘his aim is to show that no deduction comes about outside the three figures he has described but that every deduction is in one of these figures’ (in APr 255.20–21).* But Alexander’s ‘outside’ and ‘in’ scarcely improve on Aristotle’s ‘by way of ’. Aristotle’s statement of the Thesis is not ambiguous: it is indeterminate. That is to say, he has stated no thesis at all. But he surely intended to state a thesis: is [155] there a thesis which he intended to state? and if there is, what is it? In order to address those questions we need a little machinery. Any deduction may be set out, with modest formality, in a finite sequence of lines, the last of which carries the conclusion of the deduction and the first one or several of which carry the premisses from which the conclusion is deduced. Suppose that there are n lines in all, the conclusion being stated on the nth line. Suppose that there are m premisses, which therefore occupy lines 5 ª
ŁÆØ Ø: 40b21; 41a17, b2; cf r
ÆØ Ø: 41a37. 6 æÆ
ŁÆØ Ø: 41a21–22, 35–36. 7 Neutral, ‘reach a conclusion’, or technical, ‘be completed’ (a synonym for ‘ºØ FŁÆØ’ and ‘KغEŁÆØ’)? If the verb does bear that technical sense in A 23, then Aristotle implicitly claims that every deduction stands to the fourteen syllogistic moods as arguments in those moods stand to Barbara and Celarent. * æ ŁØ ÆPfiH EÆØ ‹Ø Åd ıºº ªØe ø H
NæÅ
ø
ª
ÆØ æØH
åÅø
Iººa A 
Ø
Ø H
åÅø
Kd  ø
.

Proofs and the syllogistic figures

367

1 to m. Line n, trivially, comes after line m: it may follow it immediately (if, as they say, the conclusion ‘follows immediately’ from the premisses), or there may be a number of intermediate lines. A proposition on an intermediate line will be either a supplementary hypothesis or else a conclusion from one or more earlier lines in the deduction — and in either case some later line in the deduction will be derived from it (together, perhaps, with other lines). To the right of each line we may indicate the status of the proposition which it carries: why is it there? what explains or justifies its appearance in the deduction? Against the first m lines we shall write the word ‘premiss’. Against each subsequent line, from m þ 1 to n, we shall need to write something else — for example, the name of a rule of inference or of a pattern of inference (‘modus ponens ’, ‘Barbara ’) which warrants the presence of that item on that line. Thus a deduction might contain the following line: (7) Every isosceles has an angle-sum of 1808 4, 6 Barbara The item on the seventh line of the deduction is derived from the items at lines 4 and 6 by virtue of Barbara. The item at line (7) has the form XaY; the items at (4) and (6) will have the same form; the inference of (7) from (4) and (6) will thus instantiate the pattern: XaY, YaZ, so XaZ.8 Among the possible labels for a line in a deduction are ‘Barbara ’ and ‘Celarent ’ and the names of the other categorical forms which Aristotle recognizes in the Prior Analytics. If a deduction has at least one line labelled with the name of one of the categorical forms, I shall say that it is at least partly categorical. If every line of a deduction is labelled either with the name of a categorical form or else with the word ‘premiss’, I shall say that the deduction is purely categorical. A deduction which is purely categorical is thereby at least partly categorical; but — so far as my stipulations go — there may be partly categorical deductions which are not purely categorical. Now to say that a deduction ‘comes about through’ the three categorical figures might, I suppose, be to say that it is purely categorical. Or it might rather be to say that it is at least partly categorical. Those two possibilities represent two ways of eliminating one indeterminacy in Aristotle’s presentation of his demonstrandum. There is a second indeterminacy. When Aristotle says ‘every deduction’ should we suppose that he means — ‘literally’ — every deduction? In that 8 Here and hereafter I use the ‘Patzig’ notation for categorical propositions: ‘XaY’ means ‘X holds of every Y’, ‘XeY’ means ‘X holds of no Y’, etc.

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case, he urges that, for any propositions P1, P2, ... , Pm, Q, if there is a deduction of Q from [156] the Pis, then that deduction is (purely or at least partly) categorical. But we might prefer a more liberal construal, thus: for any P1, P2, ... , Pm, Q, if there is a deduction of Q from the Pis, then there is a categorical deduction of Q from the Pis. The second construal leaves open the possibility that there are perfectly acceptable deductions which are not categorical; but it insists that anything which can be done by a non-categorical deduction can also be done by a categorical deduction. And let me mention a third construal. We might, at a pinch, take Aristotle to mean that, for any Q, if there is a deduction of Q from some set of Pis, then there is a categorical deduction of Q from some set of Pis. (If Frege’s theorems can be derived from his axioms by his rules of inference, then his theorems can be derived by categorical deductions from one set of axioms or another.) All that will produce six candidate versions of Aristotle’s Thesis. More versions might easily be excogitated; but six are enough for me. I give them rebarbative labels for later convenience. (XA) Every deduction of any Q from any Pis is purely categorical. (XB) Every deduction of any Q from any Pis is at least partly categorical. (YA) If there is a deduction of Q from certain Pis, then there is a purely categorical deduction of Q from those same Pis. (YB) If there is a deduction of Q from certain Pis, then there is an at least partly categorical deduction of Q from those same Pis. (ZA) If there is a deduction of Q from some Pis or other, then there is a purely categorical deduction of Q from some Pis or other. (ZB) If there is a deduction of Q from some Pis or other, then there is an at least partly categorical deduction of Q from some Pis or other. Each A-version entails the corresponding B-version, but not vice versa. Each X-version entails the corresponding Y-version, but not vice versa; and each Yversion entails the corresponding Z-version, but not vice versa. Which, if any, of the six versions should we identify with Aristotle’s Thesis? Aristotle’s explicit remarks about the Thesis seem to some commentators to favour an A-version and also an X-version — hence to point to (XA). I agree that the wording of A 23 rather suggests (XA). But I do not think that there is anything stronger than a suggestion. Abstract logical considerations seem to some commentators to favour (YB): the first three of the six items are far too strong to be plausible, and the last two are far too weak to be worth stating. The abstract considerations are weighty. But not, I think, heavy enough to settle the balance.

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Often enough, in order to decide what thesis a philosopher is advancing, it is useful to consider the way in which he argues: if an argument in fact — and pretty evidently — supports this thesis rather than that, then there is some reason to ascribe to our philosopher this thesis rather than that. In any event, it is worth looking at Aristotle’s argument in A 23 — or rather, at one or two features of that argument. [157] The argument is articulated by way of a pair of considerations which Aristotle sets down at the start: Necessarily, every proof and every deduction shows either something holding or something not holding (and this either universally or particularly), and again either deictically or from a hypothesis. (40b23–25)*

That is to say, in the case of any deduction of Q from the Pis, two things may be said: first, Q itself is either affirmative or negative and either universal or particular; secondly, the inference to Q proceeds either deictically or from a hypothesis. The first point is clear: the conclusion of any deduction must have one of the four categorical forms, XaY, XeY, XiY, XoY. The second point is obscure. In APr B 14, Aristotle explains that a ‘deictic’ proof ‘begins from agreed posits [K ‰ º ªÅ
ø
]’, whereas a reductio ad impossibile ‘posits what it wants to reject’ (62b29–32). Whatever the value of that explanation in the context of B 14, it cannot be applied to A 23; for there Aristotle expressly says that — in some cases at least — deductions from a hypothesis proceed ‘by way of an agreement [K › º ªÆ]’ (41a41). No other Aristotelian text9 seems to me to shed any light on the distinction between deictic arguments and arguments from a hypothesis. Various scholarly guesses have been made, some of them more plausible than others.10 Here I may leave the matter open.11 Aristotle next notes that ‘showing something by way of the impossible is a special case of showing something from a hypothesis’ (40b25–26); and he indicates his strategy: * I
ªŒÅ c AÆ
I ØØ
ήd 
Æ ıºº ªØe
j æå
Ø j c æå
،

ÆØ, ŒÆd  F j ŒÆŁ º ı j ŒÆa æ , Ø j ،،H j K  Łø. 9 See APr A 29a31–32; 45a23–24; b8–11; Rhet B 1396b22–27. 10 Alexander, in APr 256.11–14, says that here ‘،،H’ means ‘ŒÆŪ æØŒH’ — i.e. an argument is deictic if and only if all its component propositions are categorical propositions. And he adds that Aristotle uses ‘،، ’ rather than ‘ŒÆŪ æØŒ ’ here because he [I read ‘ÆPfiH’ at 256.14 for ‘ÆP E’] usually uses ‘ŒÆŪ æØŒ ’ in the sense of ‘ŒÆÆçÆØŒ ’ or ‘affirmative’. 11 Hence I transliterate (‘deictic’) rather than translate. As English translations I have seen ‘direct’, ‘probative’, ‘ostensive’, ‘affirmative’.

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First, then, let us discuss deictic deductions;12 for once it has been shown in their case, it will be evident too in the case of deductions to the impossible and generally of deductions from a hypothesis. (40b26–29)*

The first part of the argument ends at 41a20. The second part occupies 41a21–31. The first part runs, in outline, as follows.13 Given that we are to deduce a categorical conclusion, ‘it is necessary to assume something of something’ (40b30–31); that is to say, it is necessary to take a premiss which is in categorical form. The terms of that premiss cannot be the A and B of the [158] conclusion, for in that case we shall simply beg the question;14 so let us take, say, A and C (b31–33). Now one premiss is not enough, as — so Aristotle falsely claims — we have already shown; ‘so that we must assume in addition another proposition’ (b33–37). This second premiss must contain the terms B and C, ‘so that we must assume something intermediate between the two which will link the predications together’ (b37–41a11). The upshot is that one of our premisses must be of the form AxC or CxA, and the other of the form BxC or CxB. But ‘if it is necessary to assume something common to both, and this can be done in three ways ... , and these are the figures we have described, then it is evident that, necessarily, every deduction comes about by way of one of the figures’ (a13–18).** ‘It is necessary’, ‘we must’: the modal expressions which punctuate the argument (and which are picked up in the final statement of the conclusion at 41b2) are presumably deliberate; and they surely imply that Aristotle intends to establish an X-version of his Thesis: (XA) or (XB). For he does not argue that, if there is a deictic deduction of Q, then there is a deictic categorical deduction of Q; nor does he argue that, if there is a deictic deduction of Q from certain Pis, then there is a deictic categorical deduction of Q from those 12 æd H
،،H
[sc ıºº ªØH
]: it might be argued that we are not obliged to ‘understand’ ‘ıºº ªØH
’ (or anything else); and that there is some reason not to do so. But 41a21–23 picks up 40b27–29; and there, I think, we are bound to understand ‘ıºº ªØ ’ with ‘ ƒ ،، ’ (and equally with ‘ ƒ N e I
Æ
’). * ...  F  K  Łø æ  e Øa  F Iı
 ı. æH
s
Yø
æd H
،،H
:  ø
ªaæ ØåŁ
ø
çÆ
æe
ÆØ ŒÆd Kd H
N e I
Æ
ŒÆd ‹ºø H
K  Łø. 13 For a detailed analysis, based on an interpretation rather different from the one I presuppose here, see T.J. Smiley, ‘Aristotle’s completeness proof ’, Ancient Philosophy 14, 1994, 25–38. 14 Why? Suppose we want to show that AiB: why not take as a premiss AaB? ** I
ªŒÅ ºÆE
Ø ŒÆ Ø
. ... u æ ºÅ
ŒÆd æÆ
æ ÆØ
. ... ºÅ
Ø 
Iç E
n ı
łØ a ŒÆŪ æÆ ... N s
I
ªŒÅ 
Ø ºÆE
æe ¼çø Œ Ø

,  F  K
åÆØ æØåH ... , ÆFÆ  Kd a NæÅ
Æ åÆÆ, çÆ
æe
‹Ø 
Æ ıºº ªØe
I
ªŒÅ ª
ŁÆØ Øa  ø
Ø
e H
åÅø
.

Proofs and the syllogistic figures

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same Pis: he argues that if there is a deictic deduction of Q, then that deictic deduction must be categorical.15 And if that is what he upholds for deictic deductions, then he must uphold an analogous thesis for deductions in general; that is to say, he must maintain that any deduction of any Q from any Pis is a categorical deduction. I shall return to all that. Next, though, a look at the second part of Aristotle’s argument for his Thesis. In 41a21–b1 he first considers the special case of reductio ad impossibile. All deductions which conclude by way of the impossible deduce the falsity and show the point at issue from a hypothesis — when something impossible results if the contradictory is posited. e.g. a deduction that the diagonal is incommensurable inasmuch as odds come to be equal to evens if it is posited as commensurable. That odds are equal to evens it deduces; that the diagonal is incommensurable it shows from a hypothesis since a falsity results because of the contradictory. For this is what deducing by way of the impossible is: showing something impossible because of the initial hypothesis. Hence since there is a deictic deduction of the falsity in arguments which reduce to the impossible, the point at issue being shown from a hypothesis, and since we have already said that deictic deductions are brought to a conclusion by way of these figures, it is evident that deductions by way of the impossible will also occur by way of these figures. (41a23–37)*

In general, wishing to conclude from the Pis that Q, I hypothesize the contradictory of Q. From the contradictory of Q and the Pis I construct a deduction to R, where R is false (or perhaps impossible). Hence, I conclude that Q. All deductions of that sort can be displayed in the following way. The first m lines carry (as before) the premisses from which Q is to be deduced, or the Pis. The next line looks like this: (m þ 1) Contr(Q) hypothesis [159] 15 And I might add that he does not say that any deictic deduction of Q can be recast as a categorical deduction: the categorical or non-categorical status of a deduction is not determined on the casting couch. * 
 ... ƒ Øa  F Iı
 ı æÆ

 e b
łF  ıºº ªÇ
ÆØ, e  K IæåB K  Łø ØŒ
 ıØ
‹Æ
I
Æ
Ø ıÆ
fi Å B I
Øçø ŁÅ, x
‹Ø Iæ  Øæ  Øa e ª
ŁÆØ a æØa YÆ  E Iæ Ø ıæ ı ŁÅ. e b
s
YÆ ª
ŁÆØ a æØa  E Iæ Ø ıºº ªÇÆØ, e  Iæ
r
ÆØ c
Øæ
K  Łø Œ
ıØ
Kd łF  ıÆ
Ø Øa c
I
çÆØ
:  F ªaæ q
e Øa  F Iı
 ı ıºº ªÆŁÆØ, e EÆ Ø I
Æ
Øa c
K IæåB  ŁØ
: u Kd  F ł ı ª
ÆØ ıºº ªØe ،،e K
 E N e I
Æ
Iƪ 
Ø, e  K IæåB K  Łø Œ
ıÆØ,  f b ،، f æ æ
Y 
‹Ø Øa  ø
æÆ

ÆØ H
åÅø
, çÆ
æe
‹Ø ŒÆd ƒ Øa  F Iı
 ı ıºº ªØ d Øa  ø

ÆØ H
åÅø
.

Logical Matters

372

After a number of further steps we reach (n – 1) R i, j categ — where R is something false or impossible, and ‘categ’ indicates some categorical form of inference. Finally, (n) Q 1, 2, ... , m, m þ 1, n  1: reductio Aristotle states that the ‘intermediate’ deduction, as I shall call it, which leads to step (n – 1) is a deictic deduction and therefore (by the previous argument) will be categorical. And he concludes that the whole argument is categorical. Then comes the generalization: ‘so too all the other deductions from a hypothesis; for in all of them the deduction relates to something assumed in a different guise,16 and the point at issue is brought to a conclusion by way of an agreement or some other hypothesis’ (41a37–b1).* Aristotle’s ‘so too’ gives little away; but it is reasonable to ascribe to him the following notion. Any deduction from a hypothesis may be set out in the following fashion: (1) (2) . . . (m) (m þ 1) . . . (n  1) (n)

P1 P2

premiss premiss

Pm H

premiss hypothesis

R Q

i, j categ 1, 2, ... , m, (n  1), hypoth

The intermediate deduction is deictic, and therefore categorical. The final step, from (n  1) to (n), makes use of some hypothetical rule or procedure (a rule of reductio in the case of reductions; some other rules in the case of other arguments from a hypothesis).17 Since the intermediate deduction is categorical, the deduction as a whole is categorical. It must seem plain that Aristotle’s argument cannot warrant any conclusion about purely categorical deductions; and plain that Aristotle cannot 16 e ƺÆÆ


: for an explanation of the term, see Alexander, in APr 263.26–264.6. * ‰Æø b ŒÆd ƒ ¼ºº Ø 
 ƒ K  Łø: K
–ÆØ ªaæ › b
ıºº ªØe ª
ÆØ æe e ƺÆÆ


, e  K IæåB æÆ
ÆØ Ø › º ªÆ X Ø
 ¼ººÅ  Łø. 17 That rough sketch smudges several points: see esp G. Striker, ‘Aristoteles u¨ber Syllogismen ‘‘Aufgrund einer Hypothese’’ ’, Hermes 107, 1979, 33–50; J. Lear, Aristotle and Logical Theory (Cambridge, 1980), pp.34–53.

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have supposed it to do so. For, in skeleton, he reasons thus: ‘Every argument from a hypothesis contains a categorical deduction: therefore every argument from a hypothesis is a categorical deduction’. Quite evidently, such reasoning is valid only if the conclusion is taken to mean that every argument from a hypothesis is at least partly categorical. [160] Thus the second part of Aristotle’s argument in A 23 suggests that he intended to establish a B-version of the Thesis rather than an A-version. The first part indicated that he meant to establish an X-version rather than a Yversion or a Z-version. The two parts together thus indicate that he meant to establish version (XB): every proof and every deduction is at least partly categorical. To be sure, Aristotle does not establish (XB) — his arguments are not sound; to be sure, he could not have established it — it is false). But at least — or so we might gratefully conclude — he did not stick his neck out for anything stronger than (XB). Is that conclusion secure? First, is there any hope of ascribing to Aristotle something weaker than (XB)? Is the X-component inescapable? To consider that question, I return to the first part of Aristotle’s argument. The argument at 40b30–41a20 is full of holes. Some of them are readily patched, others not; and it is often supposed that there is a vast and irreparable puncture at the very start of the argument — or, less politely, that Aristotle cheats from the outset. He cheats when he asserts than any deduction — not just any deictic deduction, but any deduction whatsoever — concludes to something of the form XxY. For that assertion is simply and patently false. Deductions may conclude to propositions of innumerably many forms, of which the categorical forms are an inconsiderable subgroup. I may, for example, deduce that Aristotle was the founder of logic, that no prime is higher than every other prime, that either it is Monday or it is Tuesday, that if Theophrastus was right then Aristotle’s modal logic needed revision, ... I may thus deduce conclusions of the forms: Fa, ¬ (&x)(8y)Rxy, P v Q, P ! Q, ... Aristotle’s argument presupposes, absurdly, that no deduction may advance to conclusions of those forms: the argument is therefore worthless from the beginning — a` la poubelle. That sort of accusation is familiar enough. And there is a familiar defence. The defence runs like this. To be sure (it is conceded), a proposition such as ‘Either it is Monday or it is Tuesday’ has a disjunctive form, P v Q; and to be sure, that form is not a categorical form. But that does not in the least tell against Aristotle; for there is, in general, no such thing as ‘the’ form — ‘the’

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logical form — of a proposition: every proposition has several logical forms, and the fact that ‘Either it is Monday or it is Tuesday’ has the form P v Q does nothing to show that it does not also have one of the four categorical forms. Moreover — the defence concludes — with a little ingenuity and not a little artificiality, we may discover a categorical form for any proposition whatsoever: just as every proposition has the form P, so every proposition has one of the four forms XxY. (Thus ‘Either it is Monday or it is Tuesday’ may first be paraphrased as ‘Every day identical with today is either Monday or Tuesday’; and this may be ‘parsed’ as follows: ‘Being either-Monday-orTuesday holds of every day-which-is-identical-to-today’. Thus the proposition has the form XaY.) Let us accept, for the sake of argument, the claim that every proposition whatsoever has among its several forms a categorical form. (The claim may seem outrageous: I suspect that it is vacuously true.) The claim accepted, it might seem that the first assertion in the argument of A 23 must be accepted: Aristotle there [161] asserts that every conclusion of every deduction will have one of the four categorical forms, and we are now accepting (at least for the sake of argument) that every proposition has one or other of those forms. In a sense, of course, Aristotle’s assertion is vindicated. But not in a sense which can comfort his argument. For the argument presupposes not merely that every conclusion has a categorical form but also that its categorical form is deductively pertinent. An example will best show what I mean. Take the following trivial deduction: It is Monday. ————— Either it is Monday or it is Tuesday. The argument is valid, and formally valid: it exhibits the form P J P v Q, and every argument of that form is valid. The conclusion of the argument has a disjunctive form. It also, of course, has a categorical form — and so too does the premiss. Thus the argument also has the following form: AaB J CaB. Now that is a categorical form. But it is not a valid form. Consequently, the categorical form of the argument — the categorical form of its premiss and of its conclusion — is irrelevant to the validity of the argument. The argument has a categorical form. Every argument, if you like, has a categorical form. But, for the most part, those categorical forms have nothing to do with the logical structure of the argument — I mean, the arguments are not valid in

Proofs and the syllogistic figures

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virtue of their categorical form. (You might construct an argument parallel to the first argument of A 23, beginning as follows: ‘The conclusion of every deduction has the form ‘‘P’’ or else the form ‘‘not-P’’. Now ... ’. The initial assertion is true, and uncontroversially so. But it cannot begin to ground a claim about the structure of deductions.) One ancient reaction to considerations of that general sort was in effect to suggest that arguments like the disjunctive argument are logically elliptical: we must add a premiss or two in order to turn them into proper deductions. Suppose, for example, we add the proposition Being Monday-or-Tuesday holds of every Monday to the argument. Then we shall arrive at an argument the categorical form of which is: CaA, AaB J CaB, that is to say, we shall arrive at a deduction in Barbara. In general, we might consider the following suggestion: for any deduction which is not valid in virtue of its categorical form, there may be produced — by appropriate adjunction of premisses — an argument to the same conclusion which is valid in virtue of its categorical form. Or, a little more precisely, if there is a deduction of Q from P1, P2, ... , Pm, then [162] there is a categorical deduction of Q from P1, P2, ... , Pm, P*1, P*2, ... , P*k. That suggestion is a special case of a Z-version of Aristotle’s Thesis. So what? Well, in the argument at 40b30–41a20 Aristotle attends to no form but categorical form: he is exclusively concerned with deductions which are valid in virtue of their categorical forms. The modal expressions, ‘It is necessary’ and ‘we must’, which I earlier invoked in favour of an X-version of the Thesis, might therefore be construed relative to this restriction. That is to say, Aristotle does not mean to argue that the only possible way to construct a deduction to XxY is by way of premisses of a certain type: he means to argue that the only way to construct a deduction to XxY in which the form XxY is logically pertinent is by way of premisses of a certain type. If we want to produce a deduction of Q in which the pertinent form of Q is one of the categorical forms, then ‘we must’ start from premisses of a certain sort. In that case, the modal expressions in the argument do not tell in favour of an X-version of the Thesis. On the contrary, if they are embedded in the considerations which I have just rehearsed, they may rather suggest a Z-version. More specifically, the modal expressions might suggest the following theses:

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(ZA*) If there is a deduction of Q from P1, P2, ... , Pm, then there is a purely categorical deduction of Q from P1, P2, ... , Pm, P*1, P*2, ... , P*k. (ZB*) If there is a deduction of Q from P1, P2, ... , Pm, then there is an at least partly categorical deduction of Q from P1, P2, ... , Pm, P*1, P*2, ... , P*k. Some passages in Alexander suggest that he might have toyed with one or other of those two theses; and, from a logical point of view, the theses are neither evidently false nor patently vacuous. So shall we conclude that Aristotle in fact hoped to establish a Z-version of the Thesis rather than an X-version? The conclusion is tempting; but I incline to resist. Perhaps Aristotle ought to have aimed at a Z-version; perhaps he would have done well to aim at a Z-version. But nothing in the text of A 23 hints at a Z-version; and I remain persuaded that the modal expressions suggest an X-version. If the Thesis is not weaker than version (XB), is it perhaps stronger? Does the second part of Aristotle’s argument really show that he was intending to support a B-version? It will be useful to start with a glance at a later chapter in the Prior Analytics, A 44, where Aristotle returns to deductions from a hypothesis. At first blush, A 44 is disconcerting. For Aristotle begins by announcing that ‘we must not try to reduce deductions from a hypothesis’ (50a16–17). He adds that ‘the same goes for deductions which are brought to a conclusion by way of the impossible — it is not possible to analyse them either’ (50a29–30). He concludes by remarking that ‘many other deductions are brought to a conclusion from a hypothesis’; that these deductions will be investigated later on; and that ‘for the moment let this much be evident to us: it is not possible to analyse such deductions into the figures’ (50a39–b3).* In A 23 Aristotle argued that all deductions, including deductions from a hypothesis, ‘come about through the figures’ and hence ‘reduce’ to the figures. In A 44 he states that no hypothetical deduction can [163] be reduced or analysed into the figures. A flat contradiction.

* Ø b  f K  Łø ıºº ªØ f P ØæÆ
I
ªØ
: ... › ø b ŒÆd Kd H
Øa  F Iı
 ı æÆØ

ø
: Pb ªaæ   ı PŒ Ø
I
ƺØ
. ...  ºº d b ŒÆd æ Ø æÆ

ÆØ K  Łø ...
F
b   F
E
ø çÆ
æe
‹Ø PŒ Ø
I
ƺØ
N a åÆÆ  f  Ø  ı ıºº ªØ .

Proofs and the syllogistic figures

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The contradiction is there: it cannot be wished or washed away. But is it a deep contradiction? Or is there rather an underlying unity of thought, disguised by an inconsistent mode of expression? Like A 23, A 44 takes arguments from a hypothesis to have two components. Thus we are imagined to hypothesize that, if there is not a single capacity for contraries, then there is not a single science of contraries; and it is then to be argued that there is not a single capacity for contraries. Now that there is not a single capacity for contraries has been shown; that there is not a single science has not been shown. But it is necessary to agree to it — not from a deduction but from a hypothesis. Now it is not possible to reduce this; but that there is not a single capacity can be reduced — for that no doubt was a deduction, whereas the former is a hypothesis. (50a23–28)*

Again, in the case of arguments to the impossible, the reduction to the impossible can be reduced (for it is shown by a deduction); the other item cannot be (for it is brought to a conclusion from a hypothesis). (50a30–32)**

That is to say, in terms of my earlier schema, the intermediate deduction in any argument from a hypothesis is always categorical; but the final step is not a categorical deduction. Now that is perfectly compatible with the analysis offered in A 23 — indeed, it scarcely differs from that analysis. It is true that A 23 does not explicitly assert that the step from (n – 1) to (n) is non-categorical; but it implies as much — at any rate, no reader of A 23 has ever supposed that the final stage of an argument from a hypothesis might be another categorical deduction. In A 44 Aristotle insists that deductions from a hypothesis do not reduce to the categorical figures: that is to say, he insists that they are not purely categorical deductions. In A 23 Aristotle insists that deductions from a hypothesis do reduce to the categorical figures: that is to say, he insists that they are at least partly categorical deductions. In A 44 he explicitly rejects an A-version of the Thesis (and implicitly accepts a B-version). In A 23 he explicitly accepts a B-version (and implicitly rejects an A-version). He adopts * ‹Ø b
s
PŒ Ø Æ 
ø
H
K
Æ
ø

ÆØ, KØØŒÆØ, ‹Ø  KØÅ PŒ Ø
, P ØŒÆØ. ŒÆ Ø › º ªE
I
ƪŒÆE
: Iºº’ PŒ KŒ ıºº ªØ F Iºº K  Łø.  F
b
s
PŒ Ø
I
ƪƪE
, ‹Ø  P Æ 
ÆØ, Ø
: y  ªaæ Yø ŒÆd q
ıºº ªØ , KŒE
  ŁØ. ** c
b
N e I
Æ
Iƪøªc
Ø (ıºº ªØfiH ªaæ Œ
ıÆØ), Łæ
 PŒ Ø
(K  Łø ªaæ æÆ
ÆØ).

378

Logical Matters

a woefully misleading manner of expression, to the extent that he formally contradicts himself. But the contradiction is superficial; and the subtle reader will not be long misled. Thus A 44 in the end confirms the inference which was earlier drawn from A 23: Aristotle prefers a B-version of the Thesis to an A-version. Or does he? He distinguishes sharply, if not always clearly, between the two component stages of an argument from a hypothesis. Thus in reductio arguments he says that the falsity ‘is deduced’ (41a24), or that ‘there is a deictic deduction of the falsity’ (41a32–33), or that the impossibility ‘is shown by a deduction’ (50a31): that is to say, we reach step (n – 1) by deductions. In general, in arguments from a hypothesis, ‘the deduction is directed to something assumed in a different guise’ (41a38–39): there, in the intermediate stage of the argument, the deduction is to be found. As for the second stage of the argument, in A 23 Aristotle never says [164] that it is done by deduction; and he implies that it is not done by deduction — ‘for this is what deducing by way of the impossible is: showing something impossible because of the initial hypothesis’ (41a31–32). In A 44 he expressly says that it is not done by a deduction (50a17–18, 25). In A 23, the final step is ‘shown’ (41a25, 29, 34) or ‘brought to a conclusion’ (41a40). In A 44 the final step ‘is not shown’ (50a24–25); but it is ‘brought to a conclusion’ (50a16). There is a trifling discord between A 23 and A 44 over the question of what, positively speaking, is done in the final stage of an argument from a hypothesis: is the conclusion shown or not shown? But both A 23 and A 44 agree that the final conclusion is not deduced. Aristotle is content to speak of ‘deductions from a hypothesis’ (50a16); but it now appears that we should construe the phrase on the model of ‘decoy duck’ or ‘expectant mother’. ‘Deductions from a hypothesis’ are not a special kind of deduction — they are not deductions at all.18 If that is right, then we may look again at the second part of the argument in A 23. That argument has seemed to contain at least one gaping lacuna: it assumes that step (n – 1) will be reached by a deictic deduction. The argument depends on the assumption. But Aristotle offers no reason for it; and we may well wonder why the intermediate deduction could not proceed by some other method. The question is sharpened by a passage in A 44. At 18 So, explicitly, Alexander, in APr 265.19–23; 386.13–14; 390.9–19. — Alexander might have added that the phrase ‘deictic deduction’ becomes a pleonasm: every deduction is, trivially, deictic (just as every duck is a real duck).

Proofs and the syllogistic figures

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50a20–24 Aristotle hints at an illustrative intermediate deduction. The intended structure of this illustration is obscure; but Alexander, for one, supposes that it is not a deictic deduction: ‘if it is shown in this way, then not even this [i.e. the item at (n – 1)] will have been shown by way of a deduction, but this too from a hypothesis’ (in APr 387.10–11).* Alexander is not upset. On the contrary, he thinks that Aristotle implicitly allows that the intermediate argument need not be deictic; for he takes the word ‘Yø’ at 50a27 (which I have translated as ‘no doubt’) to mean ‘perhaps’, and he understands Aristotle to indicate that the intermediate argument is perhaps a deduction and perhaps not (387.27–388.12). After all, ‘Theophrastus, in the first book of his Prior Analytics, says that, the additional assumption [i.e. the item at line (n – 1)] is set down either by way of induction or it too from a hypothesis or by way of evidence or by way of a deduction’ (388.17–20).** But does not that undermine Aristotle’s argument? For the argument presupposes that every deduction from a hypothesis will contain a deictic deduction: Theophrastus evidently rejected the presupposition, and Alexander — purporting to explain Aristotle — follows Theophrastus. In fact Aristotle does not need to make the presupposition; nor does he need to show that every deduction from a hypothesis ‘comes about by way of’ the figures. To be sure, he wants to show that every deduction comes about by way of the figures; but in order to show that, he does not need to show that every deduction from a hypothesis comes about by way of the figures — for deductions from a hypothesis are not deductions. His interest, in A 23, in deductions from a hypothesis is limited: if such an argument includes a deduction, then he must show that the included deduction comes about by way of the figures. But if a deduction from a hypothesis includes no deduction [165] — if, say, its intermediate conclusion is established by induction, or is self-evident —, then the argument has no pertinence to the Thesis; for the Thesis is a thesis about deductions. In short, given that deductions from a hypothesis are not deductions, the argument at 41a21–31 is less bad than it seems to be. There is a further point. The reason for ascribing a B-version of the Thesis to Aristotle was this: that a deduction from a hypothesis includes a categorical

* Ka
b oøfi q ØŒ


, PŒ ÆØ Pb  F Øa ıºº ªØ F ت

Iººa ŒÆd ÆPe K  Łø. ** ŒÆd ¨ çæÆ  b K
fiH æfiø H
—æ æø
I
ƺıØŒH
ºªØ e æ ºÆÆ


j Ø KƪøªB ŁŁÆØ j ŒÆd ÆPe K  Łø j Ø K
ÆæªÆ j Øa ıºº ªØ F.

380

Logical Matters

deduction cannot, and evidently cannot, show that a deduction from a hypothesis is a purely categorical deduction. Hence Aristotle must hold that deductions from a hypothesis are at least partly categorical deductions. The premiss for this piece of reasoning remains good; but the word ‘hence’ is now seen to mark a non sequitur. Aristotle need not — or rather, cannot — hold that deductions from a hypothesis are at least partly categorical deductions; for he does not hold that they are deductions at all. Hence Aristotle’s Thesis may be — and probably is — an A-version. And, given the frailty of the argument against an X-version, the Thesis is probably version (XA). ‘But surely that cannot be right? Even if the argument at 41a21–31 is improved, the improvement is won at an enormous cost — first, the cost of ascribing the unlovely (XA) to Aristotle; secondly, the cost of attributing to him the grotesque idea that deductions from a hypothesis are not deductions at all?’ I agree that (XA) is unlovely; and no doubt the grotesque idea is grotesque. But Alexander certainly liked the idea; and Theophrastus probably did. So why not Aristotle? After all, the idea is not evidently false in the case of reductio arguments — the case which A 23 takes as paradigmatic. For what happens at step (n) in a reductio? In a deduction, as Aristotle defines the notion, something results by necessity from the fact that certain other items have been laid down. Now the item which ‘results’ at line (n) is the conclusion of the deduction, Q. What does Q ‘result from’? The only items which are posited in the argument and on which Q depends are the m premisses, the Pis. But — or so it is easy to think — Q does not result from the fact that the Pis have been laid down; rather — this is the essence of a reductio — it results from the fact that, if the Pis are laid down and the contradictory of Q is hypothesized, then something false (or impossible) follows. Hence — or so, again, it is easy to think — the inference marked at step (n) is not a dedution in the sense in which that term is used in the Prior Analytics.19 But whatever the value of the argument in the case of reduction to the impossible, it will not generalize to all deductions from a hypothesis. Consider, in schematic form, the illustrative argument which Aristotle hints at in A 44. [166] (1) P1 premiss (2) P2 premiss 19 That doesn’t mean merely that the reductio step cannot be a categorical syllogism: it means that it cannot be construed as a deduction of any type, given Aristotle’s definition of deduction.

Proofs and the syllogistic figures

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. . . (m) Pm premiss (m þ 1) If there is not a single capacity for contraries, there is not a single science of contraries hypothesis . . . (n  1) There is not a single capacity for contraries i, j categ (n) There is not a single science of contraries 1, 2, ... , m, m þ 1, hypoth What happens here at line (n)? The answer seems inescapable: given (m þ 1) and (n  1), (n) results — certain things being laid down, something else results. In other words, the step at line (n) is a deduction in Aristotle’s sense of the word. That is surely true. You may huff and puff a bit. You may tinker with the definition if you will. But in the end it will be allowed, I imagine, that the claim that all deductions from a hypothesis contain a non-deductive component — a component which is not a deduction in Aristotle’s sense of the word — must be rejected. And we shall also reject the idea that deductions from a hypothesis are not deductions. Shall we also conclude that Aristotle did not hold that all deductions from a hypothesis contain a non-deductive component? and that he did not hold that deductions from a hypothesis are not deductions? The conclusions are evidently tempting; but here again — and uncharacteristically — I incline to resist temptation. A 23 is vexingly indeterminate; but — all in all and alas and alack — the interpretation which Alexander (and perhaps Theophrastus) imposed on it seems the least implausible of several possibilities. That is to say, if we are to ascribe any Thesis at all to Aristotle, we should probably ascribe (XA) to him.20 20 Maddalena Bonelli and Ben Morison read through the text of A 23 with me. Ben Morison vetted a penultimate version of this chapter. I thank them both warmly. — Mario Mignucci has argued against my chief contentions in his ‘Syllogism and deduction in Aristotle’s logic’, in M. Canto-Sperber and P. Pellegrin (eds), Le Style de la pense´e: recueil de textes en hommage a` Jacques Brunschwig (Paris, 2002), pp.244–266. He holds that the syllogisms which APr A 23 is concerned to reduce are all and only those items which fall under the definition which Aristotle furnishes in A 2; and he holds, further, that the definition, by virtue of the ‘fiH ÆFÆ r
ÆØ’ clause, ‘includes the idea that what is defined is a deduction in which follows from in virtue of their being affirmative or negative, universal or particular or indefinite’ (p.263). In that case, Aristotle’s Thesis is something far weaker than (XA) — but it is, of course, still a far from trivial proposition (and one which Aristotle quite certainly does not prove).

13 Aristotle and Stoic logic* Were Aristotle’s logical writings known to the early Stoic logicians, and did Aristotle’s logical ideas have any influence on the development of Stoic logic? The evidence which bears on the question is perplexing: there are numerous pertinent texts which favour an affirmative answer; yet as we approach them they seem, like so many will-o’-the-wisps, to retreat — and we are left stumbling in a treacherous marsh. But the question is not without its fascination, inasmuch as it concerns the historical relations between two magnificent monuments to Greek philosophical acumen; and it may stand some discussion. Section I presents a few general ruminations. Section II deals with the preliminary question of whether the Stoics could in principle have read Aristotle. Section III assembles a sample of the evidence which suggests that the Stoics did in fact read and study their Aristotle. And the remaining sections try to assess the value of this evidence.

I The question is an historical one, and it invites consideration of a certain type of historical explanation. It is not merely a matter of whether the Stoics were aware of the Peripatetic achievement in logic: it is a matter of whether such an awareness influenced their own logical thoughts and caused them to think in this way rather than in that. Roughly speaking, it asks whether there are any truths of the form: [24] Chrysippus, in his logic, held that P because Aristotle, in his logic, had held that Q. Although I shall continue to speak in that rough way, it may be worth making a few moves in the direction of precision. * First published in K. Ierodiakonou (ed), Topics in Stoic Philosophy (Oxford, 1999), pp.23–53. The chapter was a substantially revised version of a talk which I gave at a conference in Cambridge. I owed much to the remarks made by my audience there; and I also had the advantage of Katerina Ierodiakonou’s perceptive comments on a penultimate draft.

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First, then, I shall use the names ‘Chrysippus’ and ‘Aristotle’; but I am really concerned with the possible influence of the Old Lyceum on the Old Stoa, and the names should be construed loosely. As a matter of fact, there was not very much serious logic done in the Stoa before Chrysippus and there were few advances made in the Lyceum after Aristotle;1 so that in this context there is little harm in using the names of the scholarchs to denote the schools. Secondly, in raising a question about Aristotle I do not mean to suggest that there can have been no other influence on the logic of Chrysippus — nor even that there can have been no other equally important influence. What is sometimes said about the significance of the ‘Dialectical School’ strikes me as exaggerated;2 but I suppose it certain that men such as Diodorus Cronus and Philo — Dialecticians or Megarics, call them what you will — had some effect on the logic of the Stoa. My question is not: Was it Aristotle rather than Diodorus who influenced Chrysippus? It is simply: Did Aristotle influence Chrysippus? And this paper has nothing at all to say on the entirely independent question: Did Diodorus influence Chrysippus? Next, I am concerned with influence of any sort, whether direct or indirect. The question ‘Did Chrysippus read this in Aristotle?’ is shorthand for the question: ‘Did Chrysippus (or some other Old Stoic) read this in an early Peripatetic work, or read it in the work of someone who had read it in a Peripatetic work, or hear it from someone ... ?’. There are, it is true, many different possibilities there; but our evidence is almost always too coarsegrained to allow us usefully to distinguish among them. Fourthly, if I say that Chrysippus said this because Aristotle had said that, I mean the ‘because’ in a generous sense. I mean, not that Chrysippus’ remark was wholly and completely fixed by what Aristotle had said, but rather — and, I suppose, evidently — that any complete explanation of why Chrysippus said what he said would [25] need to make reference to Aristotle’s having said what he had said. Aristotle’s remarks form ‘part of the explanation’ of Chrysippus’ remarks. Finally, I shall talk indifferently of Chrysippus’ saying that P or holding that P or hitting upon the idea that P or ... Here, again, there are many distinct questions which might be asked. It is, for example, one thing to ask how someone first came to entertain a particular thought and quite another 1 But note that one of the main texts I shall be examining concerns Theophrastus rather than Aristotle: below, p.[45]. 2 See J. Barnes, ‘A big, big D?’, CR 43, 1993, 304–306 [reprinted below, pp.479–484].

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thing to ask why they persistently accepted it as true. But, again, our evidence is too coarse-grained to make it profitable to insist on such distinctions. In sum, I am asking whether we can find any truths about the history of logic which take the following form: Chrysippus (or some other early Stoic logician) held — or came to hold or persisted in holding or hit upon the idea ... — that P because (no doubt among other reasons, and perhaps by an indirect route) Aristotle (or some other early Peripatetic logician) had said or held that Q. That is a mouthful, and tediously pedantic. Hence: Chrysippus held that P because Aristotle had held that Q. Questions of that general sort form the stuff of intellectual history; and in many cases they are easy enough to answer. Thus — to take an example from the later history of logic — we know that and how Frege influenced Russell. We know it from various biographical sources, for example from the correspondence of the two men. Russell himself tells us, explicitly and often, that Frege was on his mind. Again, and from antiquity, we can say a reasonable amount about the influences which led the young Galen to deal with logic in the way in which he did. And we owe our knowledge — or at any rate our plausible belief — to Galen’s own autobiographical writings. For example, Galen himself tells us, explicitly, why and how he came to reflect upon ‘relational syllogisms’.3 In the case of the early Stoics we have no pertinent biographical information at all. The meagre factual details at our disposal, and the unreliable anecdotes, do not allow us to reconstruct an intellectual biography of Chrysippus. Now influence and dependence in philosophical matters are always difficult to discover in the absence of positive [26] biographical evidence. And in logic, because of the nature of the subject, the problem is most severe. For in the absence of biographical evidence, we shall, I suppose, only hypothesize that X influenced Y if we suppose that the best explanation for Y’s saying that P is that X had said that Q. But in logic — and especially in formal logic — there is almost always a good explanation to hand in the subject-matter itself. Perhaps Y said that P because P pretty plainly follows from Q and it is pretty plain that Q. In the case of Frege and Russell we should have a powerful reason to posit influence even without the biographical evidence. For one of Russell’s main logical innovations is his theory of types; and the theory is intelligible solely as 3 See J. Barnes, ‘ ‘‘A third kind of syllogism’’: Galen and the logic of relations’, in R.W. Sharples, (ed) Modern Thinkers and Ancient Thinkers (London, 1993).

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a solution to the paradoxes which — as Russell proved — were the ruination of Frege’s system. Why does Russellian logic include the inelegant and barely comprehensible theory of types? — Because Frege’s typeless system was inconsistent. If Russell’s system is rediscovered after a thousand years of oblivion, then future historians of logic will have good reason to connect Russell with Frege, to hold that there are some truths of the form Russell held that P because Frege had held that Q. Clear cases of that sort are, I think, extremely rare. For Aristotle and the Stoics, the best we can expect is a few unclear cases.

II The first question must be this: could the Old Stoics have learned of Peripatetic logic? It was once orthodox to believe that, on the death of Theophrastus, the works of Aristotle — and of Theophrastus himself — went out of circulation and were not recovered by the philosophical world until the first century bc. Aristotle’s writings were not read by the Stoics, or by any other Hellenistic philosophers, because they were not there to be read; and in consequence Aristotle’s views were scarcely known to them. That orthodoxy is now generally rejected;4 but it is perhaps worth mentioning some of the evidence which indicates that Aristotle’s logical works were known in the Hellenistic period. [27] Theophrastus and Eudemus, in the first generation after Aristotle, certainly read the master’s works. And it is unreasonable to deny that later Peripatetics also conned them — thus Strato, who interested himself in ‘topics’, had surely read Aristotle on ‘topics’. Nor were the books seen only by cardcarrying Peripatetics. Epicurus referred at least once to Aristotle’s Analytics. A fragment of a letter preserved in a work by Philodemus indisputably contains the letters ‘ÆæØ ’ and ‘Æ
ƺı،ƒ — evidently ‘Aristotle’ and ‘Analytics’.5 This scrap proves little;6 but it demonstrates that Epicurus knew 4 For a full discussion, see J. Barnes, ‘Roman Aristotle’, in J. Barnes and M. Griffin (eds), Philosophia Togata II (Oxford, 1997), pp.1–69 [reprinted in volume IV]. 5 PHerc 1005, frag 111 9–10, from —æe  f . For text and commentary, see A. Angeli, Filodemo: Agli amici di scuola (Naples, 1988), pp.166–167, 233–240. 6 So, rightly, F.H. Sandbach, Aristotle and the Stoics, Proceedings of the Cambridge Philological Society suppt 10 (Cambridge, 1985), p.5; D.N. Sedley, Lucretius and the transmission of Greek wisdom (Cambridge, 1998), p.183 n.54 (who speaks of ‘a letter by a first generation Epicurean, not necessarily Epicurus himself ’, and who insists that ‘there is no indication’ whether or not the author of the letter has read the Aristotelian works).

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of the Analytics, and it probably indicates that Epicurus had read the Analytics or some parts of them.7 It is improbable that Epicurus, an enemy of formal logic, much liked what he read. Other enemies of Aristotelian logic, of a different stripe, also knew their onions: in his Reply to Maximus on the Second and Third Figures, a work preserved only in Arabic, Themistius remarks that if we number ourselves among those who reject conversion of the premisses, as Eubulides and Menelaus did, then we are obliged to deny that the two last figures are derived from the first.8

The Arabic text presents difficulties of every sort; but the sentence I have cited plainly implies that Eubulides and ‘Menelaus’9 were acquainted with the technicalities of Aristotelian syllogistic. That Eubulides, at least, was so acquainted is confirmed and elaborated by Alexander of Aphrodisias. In his essay On Conversion, also preserved only in Arabic translation,10 Alexander reports at some length Eubulides’ views on the conversion of negative propositions: Eubulides held — or at least, he argued sophistically against Aristotle — that E-propositions do not convert and that O-propositions do convert. (‘No A is B’ does not entail ‘No B is A’, ‘Some A is not B’ does entail ‘Some B is not A’.) The level of argument, insofar as I can judge it, was not high; but the text proves that Eubulides concerned himself with certain [28] technical matters which lie at the bottom of Aristotelian syllogistic, and that makes it plausible to suppose that he had studied Aristotle’s Analytics.11 If Eubulides had worked over Aristotle’s logic, then it must be a sporting guess that the logicians of the Megaric or Dialectical school were also familiar with it. But here, so far as I am aware, no text gives us positive reason for belief. Evidence of a more general sort comes from the book-list in Diogenes Laertius’ Life of Aristotle. That catalogue includes Categories (item 141 in Du¨ring’s numbering), de Interpretatione (142), Prior Analytics (49: in nine 7 Perhaps not the text which we now know under that title: see Barnes, ‘Roman Aristotle’, pp.44–45. 8 The Arabic text is printed in A. Badawi, Commentaires sur Aristote perdus en grec (Beirut, 1972). There is a French translation in A. Badawi, La transmission de la philosophie grecque au monde arabe (Paris, 19872), pp.180–194. — Marwan Rashed, who has made a new French version of the piece, generously gave me his advice on the passage in question. 9 Presumably Menedemus? 10 Text in Badawi, Commentaires; see J. Barnes, S. Bobzien, K. Flannery, and K. Ierodiakonou, Alexander of Aphrodisias: On Aristotle Prior Analytics 1.1–7 (London, 1991), p.3. 11 Once again (above, n.8), not necessarily in our modern version.

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books), and Posterior Analytics (50: the 
ƺıØŒa oæÆ ªºÆ). In addition, parts of the Topics — if not the Topics itself — are almost certainly referred to (52, 55a, 55b, 57, 58, 59, 60); and —æd KæØØŒB (27) perhaps has something to do with the Sophistici Elenchi. The origins of the list are controversial, and there are particular difficulties with some of the items I have just enumerated.12 But the most plausible view takes the list back to Hermippus and to the Alexandrian Library in the third century bc. And thus there is evidence that some Aristotelian writings on logic were available — available outside the Lyceum — in the Hellenistic age. A further piece of evidence about the Alexandrian library comes from Philoponus: They say that Ptolemy Philadelphus had a passion for the works of Aristotle (as indeed he had for books in general), and that he offered money to anyone who brought him any books by the philosopher. So various people, hoping to make a profit, brought him works on which they had written the philosopher’s name — and so it is that they say that the great library contained forty books of Analytics and two of Categories. (in Cat 7.22–28)*

The text is late, its source and origin are unknown, and the story has doubtless been embroidered — but embroidered, I suppose, on a tissue of fact. Such items indicate that texts of Aristotle’s logical works were available, in one form or another, in the Hellenistic period. No doubt Aristotle’s texts were conserved, along with the writings of Theophrastus and Eudemus and their successors, in the library of the Lyceum itself; and whether or not this library was restricted to members of the school, Peripatetic works could be read by outsiders. [29] Aristotle’s treatises never achieved the popularity or the dissemination of Plato’s dialogues; but they were not secret documents, and they were not unobtainable. None of that proves that all or any of the logical writings were available to Zeno or to Chrysippus. Yet it would be absurd to affirm that those writings were not available to the early Stoic logicians. And a plausible conclusion would read like this: ‘Our present evidence, such as it is, suggests that Aristotle’s 12 See Barnes, ‘Roman Aristotle’, pp.40–44. * — ºÆE
e
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ı K ıÆŒ
ÆØ çÆd æd a æØ º ı ıªªæÆÆ, ‰ ŒÆd æd a º Ø, ŒÆd åæÆÆ Ø
ÆØ  E æ çæ ıØ
ÆPfiH º ı  F çغ  ç ı. ‹Ł
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b åæÅÆÆŁÆØ  ıº 
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 ıªªæÆÆ fiH  F çغ  ç ı O
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ƺıØŒH
b
ÆæŒ
Æ º ı, ˚ÆŪ æØH
b  . — For a more sceptical view of this text, see J. Barnes, ‘Les cate´gories et les Cate´gories’, in O. Bruun and L. Corti (eds), Les Cate´gories et leur histoire (Paris, 2005), pp.11–80 [reprinted above, pp.187–265], on pp.30–31.

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logical writings could have been read by Zeno and by Chrysippus had they been concerned to get hold of them’. That is a modest conclusion, in that nothing whatever follows about the influence of Aristotle on Stoic logic. But if the conclusion is rejected, then there is little more to be said on the topic.

III The early Stoics could have read Aristotle’s logical writings. Did they in fact read them? Some may find attractive a general argument from probability. Chrysippus lived in Athens, a small enough township. He worked within a brief walk of the Lyceum. He knew that there were philosophers there and that those philosophers had done something in logic. He was himself deeply immersed in logical studies. Surely he must have tried to find out the Peripatetic view of the subject? Surely he must have cornered a contemporary Peripatetic and quizzed him? Surely he must have made some little effort to get a look at those celebrated works by Aristotle and Theophrastus and Eudemus? I confess that, for my part, I find that argument not merely attractive but seductive. But others, alas, are less easily seduced and in any case, particular evidence is preferable to general probability. There is — or so it seems — an abundance of particular evidence. The commentators on the Organon, from Alexander onwards, frequently advert to the Stoics, almost invariably contrasting their views unfavourably with those of the Peripatetic logicians. They refer to celebrated disputes over, for example, the question of whether logic is a part or an instrument of philosophy; over the ‘parts of speech’ and logical syntax; over the proper nomenclature for logical items. The disputes are frequently presented in a somewhat scholastic form. For example, is the nominative a case or not? According to Ammonius, there are two views on the matter. One is championed by [30] Aristotle and the Peripatetics, the other by the Stoics. The Stoics set out their thesis. The Peripatetics bring an objection to it. The Stoics reply to the objection. The Peripatetics retort to the reply ... And so on.13 Ammonius is, of course, primarily interested in the substance of the dispute, and only secondarily (if at 13 See Ammonius, in Int 42.30–43.20; other texts in K. Hu¨lser, Die Fragmente zur Dialektik der Stoiker (Stuttgart/Bad Cannstatt, 1987), pp.914–930.

Aristotle and Stoic logic

389

all) in its historical career. Nonetheless, his text naturally suggests that there was an historical reality behind the abstract dispute. And several texts are historically explicit. Thus in the introduction to his commentary on the Categories Dexippus asks: What caused the old philosophers to dispute with one another in so many and such varied ways about this work of Aristotle’s which we call the Categories? For I have observed that no other subject has given rise to more disputes or produced warmer controversies — not only on the part of the Stoics and the Platonists, who do their best to shake these categories of Aristotle, but also among the Peripatetics themselves, some claiming to have come closer to the intentions of the master, others believing that they can readily resolve the puzzles which others have proposed. (in Cat 5.16–25)*

Dexippus alludes to historical blasts and counterblasts; and he claims that certain Stoics had taken issue with Aristotle’s theory of categories. Again, according to Boethius, some people, among them the Stoics, thought that Aristotle meant that future contingents are neither true nor false. (in Int 2 208.1–3)**

The Stoics are implicitly taken to have read, and to have offered an interpretation of, Chapter 9 of the de Interpretatione. Or again, Alexander implies that the Stoics had read the Prior Analytics. Aristotle maintains that if B follows from A and A is possible, then B is possible; Chrysippus notoriously held that ‘the impossible may follow the possible’.14 Alexander reports that Chrysippus urges that nothing prevents the impossible from following the possible — he says nothing against the proof given by Aristotle but attempts to show that he is wrong by way of some falsely constructed examples. (in APr 177.25–27)*** *  s
  q
¼æÆ e  ØBÆ
 f ƺÆØ f çغ  ç ı  ØŒºÆ ŒÆd Æ
 Æa KåÅŒ
ÆØ æe Iººº ı æØÆ æd   ı  F æØ ºØŒ F ıªªæÆ  n c ŒÆº F
˚ÆŪ æÆ; åe
ªaæ ŒÆÆ

ÅŒÆ ‰ h º ı I
غ ªÆØ N æÆ
 ŁØ
ªª
ÆØ
h Ç ı IªH
 ŒŒ
Å
ÆØ P 

 E øœŒ E ŒÆd —ºÆø
ØŒ E ƺØ
KØåØæ FØ ÆÆ a æØ º ı ŒÆŪ æÆ Iººa ŒÆd ÆP E ª  E —æØÆÅØŒ E æe Æı ,  E b
Aºº
KçØŒ
EŁÆØ B ØÆ
Æ I
æe غÅç Ø,  E  P ææ
ºØ
N 
Ø a Ææ æø
I æ 
Æ. ** putaverunt autem quidam quorum Stoici quoque sunt Aristotelem dicere in futuro contingentes nec veras esse nec falsas. 14 See e.g. J. Barnes, Logic and the Imperial Stoa, Philosophia Antiqua 75 (Leiden, 1997), pp.96–98. *** æØ  b ºªø
Åb
ŒøºØ
ŒÆd ı
ÆfiH I
Æ
ŁÆØ æe b
c
 æØ º ı NæÅ
Å
EØ
Pb
ºªØ, ØæAÆØ b Øa ÆæÆتø
Ø
H
På ªØH ıªŒØ
ø
،

ÆØ  F c oø å
.

390

Logical Matters

Alexander does not explicitly state that Chrysippus had read Aristotle’s argument; but he plainly implies as much — and Philoponus, in the corresponding passage of his commentary, is yet plainer (in APr 165.27–29). Later on, and more strikingly, Alexander records a significant logical debt owed by Chrysippus to Aristotle. In Book A of the Prior Analytics, at 42a1, he finds a reference to the ‘so-called synthetic theorem’, which he expounds like this: When something is inferred from certain items, and what is inferred, together with one or several items, implies something, then the items which implied it, together with the one or several items with the help of which it implied something, will themselves imply the same item. (in APr 274.21–24)*

In other words: [31] If ‘A1, A2, ... , An: so B’ is a valid argument, and if ‘B, C1, C2, ... , Cm: so D’ is a valid argument, then ‘A1, A2, ... , An, C1, C2, ... , Cm: so D’ is a valid argument. The theorem, according to Alexander, was used by Aristotle to the extent that need demanded and so handed down; but the Stoics took it from him and divided it and constructed from it what they call the second, third and fourth themata. (in APr 284.12–15)**

The Stoics are thus reported to have read the Prior Analytics and to have developed from one of Aristotle’s discoveries a central feature of their own logical system. Nor were the Stoics limited to those logical works which found their way into our Organon: they could also consult items long since lost. Simplicius refers to a work in one book On Opposites: The Stoics pride themselves on their work in logic; but strive to show that both in other matters and in the case of opposites their starting-points were all provided by Aristotle in one book, which he entitled On Opposites and which contains a vast number of puzzles, a small proportion of which the Stoics set out. (in Cat 387.18–22)*** * ‹Æ
Œ Ø
ø
ı
ªÅÆ Ø, e b ı
ƪ 

a Ø
e j Ø
H
ı
ªfiÅ Ø, ŒÆd a ı
ƌ،a ÆP F, Ł y j Ł z
ı
Bª Ø KŒE
, ŒÆd ÆPa e ÆPe ı
Ø. — The explanation is repeated at 278.10–11; and the repetition allows us to correct the received text at 274.23, where the MSS apparently have ‘ı
ªÆØ KŒE
’ rather than ‘ı
Bª Ø KŒE
’. ** Text (and discussion) below, pp.[49–52]. *** H
ªaæ øœŒH
ªÆ çæ

ø
Kd fiB H
º ªØŒH
KæªÆfi Æ, 
  E ¼ºº Ø ŒÆd Kd H
K
Æ
ø
 ıÇ ıØ
،

ÆØ ‹Ø 
ø
a Iç æa › æØ ºÅ Ææå
K

d غfiø n —æd I
ØŒØ
ø
KªæÆł
K
fiz ŒÆd I æØH
KØ ºBŁ  IåÆ

z
OºªÅ
KŒE
Ø  EæÆ
ÆæŁ
 .

Aristotle and Stoic logic

391

In the following pages Simplicius reports some of the contents of the book and repeats the claim that the Stoics took their starting-points from it. And he explicitly names Chrysippus (389.22; cf 394.31). The title ‘On Opposites ’ or ‘—æd I
ØŒØ
ø
’ is known only from Simplicius; but other authors refer to an ‘On Contraries ’ or ‘—æd K
Æ
ø
’, which may well have been the same work. In any case, there is no reason to doubt that Aristotle wrote a work On Opposites,16 or that Simplicius reports its contents with a reasonable degree of accuracy. [32] Other passages could be adduced. If the scraps of evidence assembled in the previous section show that Aristotle’s logical writings were available to the Stoics, then the texts of the commentators — taken at their face value — assure us that within the shadow of the Porch those writings were perused and criticized and plundered. And if confirmation is needed, it appears to be supplied by Plutarch — or rather, by Chrysippus himself, whom Plutarch quotes verbatim.17 In the third book of his On Dialectic, in a section evidently designed to defend the study of dialectic against its many detractors,18 Chrysippus appealed to the practice of Aristotle: Aristotle took dialectic seriously, and we should rather sin with Aristotle than live virtuously with lesser men.19 It is a striking passage, and it impressed Plutarch. Chrysippus does not explicitly state that he had read Aristotle’s logical writings; but an ingenuous reader will surely form the opinion that he had indeed done so. A final Chrysippean straw for this brick of conjecture. The catalogue of Chrysippus’ logical writings, preserved by Diogenes Laertius and deriving from a sanitary source, includes several overtly polemical or critical pieces.20 16 P. Moraux, Les listes anciennes des ouvrages d’Aristote (Louvain, 1951), p.53, followed Valentin Rose in supposing that the work was a late forgery, designed to convict the Stoics of plagiarism. Sandbach remarks: ‘This seems to me a possibility not to be overlooked, but equally not to be accepted as certain’ (Aristotle and the Stoics, p.20). Moraux offers no evidence for his suggestion; and Sandbach is evidently right to state that it should not be ‘accepted as certain’. But what is the force of saying that forgery is ‘a possibility not to be overlooked’? No doubt forgery is a possibility, in the sense that the supposition of forgery involves no contradiction; but there is not the least reason to suppose that forgery is a fact. 17 Apart from this passage, no other early Stoic fragment mentions Aristotelian logic. 18 Logic, in one sense or another, had been attacked or rejected by the Epicureans and the Cynics and the Cyrenaics — and by Aristo from within the Stoic school: see Barnes, Logic and the Stoa, pp.7–10. 19 See M. Frede, Die stoische Logik (Go¨ttingen, 1974), p.29, who takes this passage as evidence for Peripatetic influence on Chrysippus’ theory of inference. 20 See J. Barnes, ‘The catalogue of Chrysippus’ logical works’, in K.A. Algra, P.W. van der Horst, and D.T. Runia (eds), Polyhistor: studies in the history and historiography of ancient philosophy, Philosophia Antiqua 72 (Leiden, 1996), pp.169–184 [reprinted in volume IV].

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Logical Matters

None of these refers explicitly to the Peripatetics; but two refer to ƒ IæåÆE Ø or ‘the ancients’.21 Now later texts frequently use this appellation to refer to the Peripatetics.22 It is tempting to think [33] that the later usage originated with Chrysippus. And in any event it is plausible to think that ‘the ancients’ to whom Chrysippus alludes may be the old Peripatetics — Aristotle and Theophrastus and Eudemus.

IV The text cited by Plutarch does not supply specific evidence for particular and determinate lines of influence — at most, it encourages us to look about for such evidence. And here seekers shall be finders; for the specific evidence is there, aplenty, in those passages from the Greek commentators which refer to Stoic views. It is those passages, some of which I have already cited, which are the crucial texts: on them the weight of the inquiry rests. It is appropriate, nonetheless, to start by looking more closely at the passage from Plutarch. I cite it in full. In the third book of his On Dialectic, having intimated that dialectic was keenly studied by Plato and Aristotle and their followers up to Polemo and Strato, and especially by Socrates, and having added that one would be happy to err in company with these numerous and talented men, he continues in these words: If they had spoken of these matters by the by, you might perhaps dismiss the subject. But since they spoke of them seriously, as though dialectic were one of the greatest and most indispensable of capacities, it is not plausible that they should have made so great a mistake — if they were in general men of the calibre we take them to have been. Why, then, Chrysippus — someone might say — do you yourself never cease battling with such talented and numerous men, and proving (as you take it) that they erred in the greatest and most important matters? For surely they did not write with studious care about dialectic while writing by the by and frivolously about first 21 Diogenes Laertius, VII 197 (¸Ø ŒÆa  f IæåÆE ı: Solution [sc of the Liar Paradox] according to the Ancients); 201 (—æd  F KªŒæ
Ø
 f IæåÆE ı c
ØƺŒØŒc
f
ÆE I Ø: That the Ancients admitted Dialectic as a reputable subject — along with proofs of this fact). On the latter work, see J. Brunschwig, ‘On a book-title by Chrysippus: ‘‘On the fact that the ancients admitted dialectic along with demonstrations’’ ’, in H.J. Blumenthal and H.M. Robinson (eds), Aristotle and the Later Tradition, OSAP suppt (Oxford, 1991), pp.81–85 — who takes the title in a different way. 22 Usually contrasted with ƒ
æ Ø, who are often Stoics: see J. Barnes, Porphyry: Introduction (Oxford, 2003), pp.317–319.

Aristotle and Stoic logic

393

principles and the ends of life and the gods and justice, areas in which you call their remarks blind and self-contradictory and full of a thousand other errors? (Stoic repugn 1045F–1046B)*

The passage is self-contained: the context adds nothing to our understanding of it. The first point to make is negative. Throughout his essay Plutarch is concerned to discover the ‘contradictions’ of the Stoics. He refers to Chrysippus’ views on the importance of dialectic solely because they introduce yet another ‘contradiction’. The alleged [34] contradiction is this: Chrysippus praises the Academics and the Peripatetics for their addiction to dialectic, and affirms that such illustrious men were unlikely to err on such an important matter; yet he attacks them ceaselessly on other matters which he regards as equally important.23 We may cavil, urging that that is not a formal contradiction; but we shall agree that it is at least an inconcinnity — and Chrysippus might reasonably be asked to explain why he thought it improbable that men would make errors in one important area and certain that they made errors in others. But it is plain — and it must have been plain to Plutarch — that a far more damaging inconcinnity would be revealed could Chrysippus be shown both to praise and to criticize his great predecessors for their views on dialectic: ‘Aristotle was a great logician’ — ‘Aristotle’s syllogistic is fundamentally mistaken’. Why does Plutarch not go for the throat? He was well read, and had the keenest of noses for Chrysippean contradictions. The fact that he does not say that Chrysippus both praised and criticized his great predecessors for their views on dialectic therefore suggests that he was not aware of a text in which Chrysippus had produced any such criticism: as far as Plutarch knew, Chrysippus did not criticize and reject Aristotelian logic, although he ceaselessly * K
fiH æfiø æd B ˜ØƺŒØŒB Øg
‹Ø —ºø
K Æ æd c
ØƺŒØŒc
ŒÆd æØ ºÅ ŒÆd ƒ Ie  ø
¼åæØ — ºø
 ŒÆd æø
, ºØÆ b øŒæÅ, ŒÆd KØçø
Æ ‹Ø ŒÆd ı
ÆÆæ
Ø
¼
Ø ŁºØ   Ø    Ø ŒÆd  Ø  Ø sØ
, KØçæØ ŒÆa ºØ
· N b
ªaæ KŒ Æææª ı æd ÆPH
NæŒÆ
, å ¼
Ø Øıæ e
 
 F
· oø  ÆPH
KغH NæÅŒ ø
‰ K
ÆE ªÆØ ı
Ø ŒÆd I
ƪŒÆØ ÆØ ÆPB hÅ, P ØŁÆ
e
Kd   F
ØÆÆæ
Ø
ÆP f K
 E ‹º Ø Z
Æ ¥ ı 
F
:  s
, çÆØ Ø ¼
, ÆPe I
æØ  Ø  Ø ŒÆd    Ø P  ÆfiÅ Æå 
 P Kºªåø
, ‰
ÇØ, K
 E ŒıæØø Ø ŒÆd ª Ø ØÆÆæ

Æ; P ªaæ  ı æd b
ØƺŒØŒB K ıÆ
ø ªæÆłÆ
, æd  IæåB ŒÆd º ı ŒÆd ŁH
ŒÆd ØŒÆØ 
Å KŒ Æææª ı ŒÆd ÆÇ
, K
x  ıçºe
ÆPH
I ŒÆºE e
º ª
ŒÆd Æå 

ÆfiH ŒÆd ıæÆ ¼ººÆ ±ÆæÆ å
Æ. 23 Plutarch’s text perhaps suggests a second ‘contradiction’: Chrysippus admires the Peripatetics for their dialectical prowess; yet he constantly condemns them for logical errors in other parts of their philosophy.

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attacked Aristotelian ethics. It does not follow that Chrysippus had not in fact criticized Aristotle’s logic, still less that he had not read Aristotle’s logic. But the negative point is still worth something. Consider, secondly, the subject which Chrysippus is defending. It is dialectic, or ØƺŒØŒ. I have thus far written as though ancient dialectic — or at any rate, ancient Stoic dialectic — were the same as modern logic; and in many contexts such an assimilation is harmless enough. But although Stoic dialectic certainly embraces what we call logic, it also embraces other matters — including epistemology.24 If Chrysippus praised the dialectic of the ancients, it does not follow that he praised their logic — it does not follow that he knew anything about their logic.25 [35] Thirdly, look at the witnesses whom Chrysippus summons in defence of dialectic. We have the list in Plutarch’s paraphrase rather than in Chrysippus’ own words; but there is no reason to doubt the accuracy of the paraphrase, at least as far as the names are concerned. The great dialecticians, then, were these: Plato and Aristotle; the Academy up to the time of Polemo; the Lyceum up to the time of Strato; ‘and especially Socrates’. If we were asked to give a list of the great logicians prior to Chrysippus, we should come up with exactly one name: Aristotle. Pressed to be more generous, we might add Theophrastus and Eudemus. (And doubtless also Diodorus Cronus and Philo.) We should never think of Plato as a logician; nor was any logic — in our sense — done in the Old Academy after Plato. As for Socrates, no one would dream of enrolling him among the logicians. Our list of logicians would be quite different from Chrysippus’ list of dialecticians. Aristotle is the single star on the former list: on the latter, he is merely one of several players, and not the most eminent. Did Chrysippus entertain perversely unhistorical views about the early career of logic? Surely not. His list of dialecticians differs from our list of logicians because he is not concerned to list logicians — he is not thinking about logic at all. Plato, who studied the topic of division, was thereby a professor of dialectic; Socrates, who pressed for definitions and insisted on questions and answers, was thereby a dialectical champion. As for Aristotle, his work in logic would indeed qualify him as a dialectician — but so too 24 The point is made by Sandbach, Aristotle and the Stoics, p.69 n.39. 25 Against that notion, it might be said that the opponents of dialectic generally accepted the value of epistemological investigations while rejecting precisely what we should call logic; so that insofar as Chrysippus may be assumed to be writing against such opponents, we may expect him to have been primarily concerned to vindicate the logical parts of dialectic.

Aristotle and Stoic logic

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would his interest in division and in definition and in sophisms and in dialectical debate. Such dialectical studies were doubtless continued in the Old Academy and the Old Lyceum. It is those dialectical studies, and not specifically logical studies, to which Chrysippus must be alluding. In honouring Aristotle as a master of dialectic, he was not thinking of syllogisms at all. Nonetheless, Plutarch’s text surely informs us that Chrysippus had at least read some Aristotle — perhaps some of the pieces in our Organon, surely something on logic or dialectic? Not so. If we ask to what writings Chrysippus is here alluding, the answer is plain: to none. Socrates wrote nothing, so that in citing Socrates as the dialectician par excellence Chrysippus cannot be covertly alluding to any written texts. The same is no doubt true of the other figures on the list: Chrysippus surely knew — it was common knowledge — that the men he names were in various ways dialectically inclined; but the text from On Dialectic does not allude to [36] any of their writings, nor does it imply that Chrysippus knew any of their writings.26 The passage from Plutarch, which seems to promise so much, tells us all too little. It certainly does not show that Chrysippus had read any of Aristotle’s logical writings. It does not even show that Chrysippus had any knowledge of or interest in Peripatetic logic. The most we can decently extract from the text is another appeal, which will seduce some and leave others unmoved, to general probability: given that Chrysippus thought that Aristotle was a philosopher of great talent, and that he knew him to have been devoted to dialectic, surely he would have made some effort to read Aristotle’s works? And surely such an effort would not have been thwarted?

V If the passage from On Dialectic gives no firm facts, surely the book-titles say something? They say something only if the expression ‘the ancients’, ‘ ƒ IæåÆE Ø’, refers to the Peripatetics. Does it? First, there is a further piece of evidence to adduce. For the expression occurs in one other Chrysippean text apart from the two titles. In the fourth book of his On Lives Chrysippus observed:

26 Note that he says ‘NæŒÆ
’ — ‘they spoke’, not ‘they wrote’. (In fact he says ‘æd ÆPH
NæŒÆ
’, where we cannot divine the reference of ‘ÆPH
’.)

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First of all, I hold, in accordance with what the ancients correctly said, that the theorems of the philosopher fall into three kinds: the logical, the ethical, the physical. (Plutarch, Stoic repugn 1035A)*

Now in the Topics Aristotle remarks that Roughly speaking, there are three sorts of propositions and problems: there are ethical propositions and physical propositions and logical propositions. (A 105b19–21)**

Surely Chrysippus must have this very text of the Topics in mind, so that ‘the ancients’, here at least, may be identified with Aristotle himself? And in that case, economy will encourage us to take ‘the ancients’ in the book-titles in the same way. What can be said against that delicious conclusion? A further passage may be summoned to the witness-box: Zeno: they say that concepts are neither somethings nor qualified items but as it were somethings and as it were qualified items, being representations made by the soul, and that they are called ideas by the ancients. (Stobaeus, ecl I xii 3)***

Zeno is surely thinking of Plato and surely not thinking of Aristotle: his ‘ancients’ are either Plato himself or else the members of the early Academy. And in that case, why not think that Chrysippus’ ancients too are Academics?27 [37] After all, the tripartition referred to in On Lives is not peculiarly Aristotelian: on the contrary, later sources ascribe it to the Old Academy — to Xenocrates, or even to Plato.28 The ‘ancients’ referred to in On Lives are in all probability Academic. And the same or something similar holds for at least one of the book-titles: in That the Ancients admitted Dialectic as a reputable subject Chrysippus will surely have appealed to those great men whom he mentions in the passage from On Dialectic — the ancients will be, or include, Plato and the Academics up to Polemo, Aristotle and the Peripatetics up to * æH
b
s
 ŒE  Ø ŒÆa a OæŁH e H
IæåÆø
NæÅ
Æ æÆ ª
Å H
 F çغ  ç ı ŁøæÅø
r
ÆØ, a b
º ªØŒa a  MŁØŒa a b çıØŒ. ** Ø  ‰ fiø æغÆE
H
æ ø
ήd H
æ ºÅø
æÅ æÆ· ƃ b
ªaæ MŁØŒÆd æ Ø N
, ƃ b çıØŒÆ, ƃ b º ªØŒÆ. *** ˘
ø
· a K

Æ çÆØ  Ø
a r
ÆØ   Ø, ‰Æ
d  Ø
Æ ŒÆd ‰Æ
d  Øa çÆ
ÆÆ łıåB· ÆFÆ b e H
IæåÆø
NÆ æ ƪ æŁÆØ. 27 See also Sextus, M XI 30, where ƒ IæåÆØ æ Ø (contrasted with the Stoics) are certainly Old Academics. 28 On the tripartition, see K. Ierodiakonou, ‘The Stoic division of philosophy’, Phronesis 38, 1993, 57–74.

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Strato, ‘and especially Socrates’. There is no reason to suspect a particular reference to Aristotle. That is persuasive to a point: it is persuasive insofar as the title That the Ancients ... is concerned. But no weight can be put on the extract from Stobaeus;29 and there is perhaps room for doubt about the text from On Lives. At any rate, it is worth remarking that Chrysippus does not there refer, broadly, to the familiar tripartition of philosophy — rather he refers specifically to a tripartition of philosophical theorems. To that the Topics does provide a close parallel, and no other text provides much of a parallel at all. Nonetheless, it would surely be absurd to insist that Chrysippus is thinking of the Topics; for it would be absurd to insist that he is thinking of any specific passage in the writings of the ancients — he is alluding generally to what he takes to be a commonplace. There remains the second book-title: Solution according to the Ancients. It is plain from its position in the catalogue that the book discussed a solution to the paradox of the liar.30 Now we know that Theophrastus wrote a work in three books On the Liar (Diogenes Laertius, V 49). We do not know of anyone else before Chrysippus who wrote on the subject. To be sure, others may have written volumes on lying — our information is patchy at best. And perhaps Chrysippus was [38] actually referring to an author of one of those hypothetical works. But speculation along those lines goes nowhere; and, given the surviving evidence, it is reasonable to believe that Chrysippus had read Theophrastus’ work on the Liar, and that he wrote about — and no doubt against — his solution. I do not infer that Chrysippus hungrily read the rest of Theophrastus’ logical œuvre, still less that he perused Aristotle’s sweet Analytics. But I do not believe that he had seen no Peripatetic material.

VI Thus far the skirmishing: the real battle takes place on the fields of the commentators. I incline — at any rate on Wednesdays and Saturdays — to 29 The text is uncertain: Diels added ‘ŒÆd H
I ÆP F’ after ‘˘
ø
’ in order to accommodate the plural verb ‘çÆØ’; and I suspect that ‘Z
Æ’ vel sim should be added before or after ‘çÆ
ÆÆ’. In any event Stobaeus does not purport to be citing Zeno verbatim (and he is generally taken to be citing Arius Didymus). 30 A. Ru¨stow, Der Lu¨gner (Leipzig, 1910), pp.64–65, proposed to add ‘ F łı 
ı’ after ‘ºØ’.

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think that Chrysippus had read some Peripatetic logic; but nothing I have yet said bears directly on the question: Did Chrysippus say that P because Aristotle had said that Q? As for the commentators, their texts are deucedly difficult to assess. A piecemeal approach is the only way. Here I shall make two general comments, and then consider three particular texts. The first general comment is a platitude: when the commentators refer to disagreements between Stoics and Peripatetics, often they are not — or need not be construed as — referring to genuine historical disputes. Ancient scholars, like modern scholars, find it pedagogically convenient to represent a theoretical difference of opinion as an historical debate: the pros and cons of abstract argument are represented by the cuts and thrusts of concrete discussion. But the concrete discussion is — or so we may often suppose — a pleasing and commodious fiction. ‘The Peripatetics say that ... The Stoics retort that ... ’. We need not construe the retort as an answer given, at some point in history, by some particular Stoic to some particular Peripatetic challenge. The retort is window-dressing: the commentator means only that a given Stoic view can be seen as rejecting a given Peripatetic position. It is, I suppose, uncontroversial that that sort of pseudo-history is a common component in ancient and modern scholarly writings. (And a perfectly reputable component — so long as it is not taken for the real historical McCoy.) If it is not always easy to be sure exactly when and where the fiction is present, [39] sometimes at least it is transparent. Thus in his commentary on Aristotle’s definition of what a syllogism is (APr A 24b18–20), Ammonius observes that he said that the conclusion must be ‘something different from the assumptions’ on account of the reduplicated or indifferently concluding syllogisms of the Stoics. (in APr 27.35–36)*

That is to say, Aristotle insisted that the conclusion of a syllogism be distinct from any of its premisses in order to ensure that certain arguments accepted by the Stoics were not classified as syllogisms. In other words, Aristotle formulated his definition with an eye to outlawing certain Stoic arguments.31

* e b
æ
Ø H
ί
ø
r 
Øa  f Ææa  E øœŒ E Øç æ ı
ı ıºº ªØ f j IØÆç æø æÆ

Æ. 31 Alexander, in APr 18.12–22, judges that Aristotle was right to include the clause in his definition; and he notes that the ‘reduplicated’ and ‘indifferently concluding’ arguments of ƒ
æ Ø are not properly regarded as syllogisms. Unlike Ammonius, he does not suggest that Aristotle included the clause in order to disbar such arguments from syllogistic status.

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We shall not suppose that this sentence in Ammonius’ commentary provides us with valuable evidence about Aristotle’s prescient reaction to Stoic logic. We shall not suppose that Aristotle said: ‘I’ll have none of those damnable Stoic arguments’. Nor does Ammonius expect us to construe his words in an historical fashion: the historical colouring in his text — admittedly pale in this case — is a cosmetic only.32 Ammonius’ technique — if that is not too grand a word — is the same elsewhere as it is here. Here we are not for a moment tempted to suppose that Aristotle reacted to the Stoics— nor that Ammonius intended us to suppose that Aristotle reacted to the Stoics. Elsewhere, then, we need not suppose — and we need not suppose that we were intended to suppose — that the Stoics reacted to Aristotle. The second general point is no less banal. Often the commentators refer, generically, to ‘the Stoics’: explicit references to particular Stoics, even to Chrysippus, are relatively rare. Now we have no general entitlement to construe an indeterminate reference to the Stoics as a reference to the Old Stoa. After all, our sources are all late — the earliest is Alexander, and by the time he wrote Chrysippus had been dead for centuries and Stoicism had developed in a variety of ways. Even if logic was a relatively stable part of Stoicism, there is evidence to show that the subject did not die with Chrysippus: there were later [40] Stoic logicians, and they did not simply parrot God’s own logician.33 A reference to ‘the Stoics’ may well depend on one of the works (more accessible and more modern) of these epigoni. Thus we know that a certain Athenodorus wrote a work entitled Against Aristotle’s Categories; and the celebrated imperial Stoic, Lucius Annaeus Cornutus, wrote Against Athenodorus and Aristotle and touched on the same issues in his Rhetoric.34 We learn from an Oxyrhynchus papyrus that Cornutus also wrote a —æd ŒH
— a work which will surely have touched on logical issues and on the dispute between Peripatetics and Stoics over the notion of a Ø.35 How much more — if anything — these men, and others like them, wrote on logic we do not know; nor do we learn very much about the logical studies of Posidonius, that most Aristotelian of Stoics. But the 32 What does Ammonius mean and mean us to believe? Merely (i) that Aristotle’s definition in fact excludes certain arguments which the Stoics would later classify as syllogisms? Or rather (ii) that the definition was formulated with the intention of excluding certain arguments (arguments which, as it turned out, the Stoics later classified as syllogisms)? Option (ii), I am pretty sure, was what Ammonius intended; but the text of APr warrants, at most, option (i). 33 For the evidence, see Hu¨lser, Fragmente, pp.192–198; cf Barnes, Logic and the Stoa, p.5 n.19. 34 Porphyry, in Cat 86.21–22; Simplicius, in Cat 62.25–26; cf Barnes, ‘Les Cate´gories ’, p.36. 35 See POxy 3649 (only the title-tag of the roll survives); on the issue, see the texts in Hu¨lser, Die Fragmente, pp.1058–1063.

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general point is plain: insofar as the disputes between Peripatetics and Stoics are genuinely historical disputes, their history may be later — perhaps much later — than 100 bc. To the extent that that is so, we cannot appeal to the disputes recorded by the commentators as evidence for the influence of Aristotle on the early development of Stoic logic. A dispute which reflects the thought of Posidonius or of Athenodorus or of Cornutus has no immediate relevance to the study of Chrysippus’ logic. Here I may cite a text from Alexander’s de mixtione, although it does not refer specifically to logical matters. Discussing the views of the Stoics on the subject of blending or ŒæAØ, Alexander observes that the opinion about blending which seems to enjoy most favour among them is that of Chrysippus. For of his successors some agree with Chrysippus, while others — although they later had the opportunity to hear Aristotle’s opinion — themselves repeat many of the things which he said about blending. These latter include Sosigenes, the friend of Antipater. (mixt 216.7–12)*

Whatever we make of the phrase ‘they later had the opportunity to hear’,36 Alexander’s message is plain: Chrysippus worked in ignorance [41] of Aristotle; later Stoics learned of Aristotle’s views — but did not profit from them. Any dispute between Stoics and Peripatetics over blending must — if we believe Alexander’s story — have arisen in the generation after Chrysippus at the earliest. What Alexander says of blending could, for all we know, be true also of logic. At the very least, we must bear in mind the fact that later Stoics discussed logical matters, were familiar with Aristotle’s writings, and were in their turn cited by the later commentators on the Organon.

VII The three particular texts which I shall examine all come from one work, Alexander’s commentary on the Prior Analytics. I choose the work because it * ... ºØÆ  Œ FÆ  Æ P ŒØE
Ææ ÆP E æd Œæ KØ
e æı ı ºª 
Å. H
ªaæ  ÆPe
ƒ b
æıfiø ıçæ
ÆØ, ƒ  Ø
 ÆPH
B æØ º ı  Å oæ
IŒ FÆØ ı
ÅŁ
  ººa H
NæÅ
ø
 KŒ
ı æd Œæø ŒÆd ÆP d ºª ıØ
z
x  KØ ŒÆd øت
Å ÆEæ  
Øæ ı. 36 oæ
IŒ FÆØ ı
ÅŁ
: (i) ‘IŒ FÆØ’ presumably means ‘read’ (see D.M. Schenkeveld, ‘Prose usage of IŒ Ø
‘‘to read’’ ’, CQ 42, 1992, 129–141); (ii) Alexander implies that Aristotle’s opinions were available to Sosigenes but not to Chrysippus — why should he have thought so?

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is the earliest, and probably the best, of the commentaries which are pertinent to my theme. Any difficulties which are to be found with Alexander increase rather than diminish with later and lesser authors. One of the little essays which Alexander inserted into his commentary concerns negation.37 At issue are simple name–verb sentences, such as ˚ƺºÆ æØÆE and their negations. Alexander reports and defends the familiar Peripatetic view, according to which the negation-sign modifies the verb, ‘æØÆE’. We might indicate that by positioning the sign immediately in front of the verb and holding it there with a pair of brackets, thus: P ˚ƺºÆ [ P æØÆE] — and in general we might represent the Peripatetic negation of ‘Fa’ as ‘[notF]a’. Alexander also reports a rival view which in effect takes the negationsign to modify the whole sentence. That might be brought out by writing: P [˚ƺºÆ æØÆE] — and in general we might use ‘not-[Fa]’ to represent that alternative understanding of the negation of ‘Fa’. [42] The second view — the rival view, as I shall call it* — is credited with three arguments. Each argument is examined in detail by Alexander — and declared unsound. The dialectical structure of the text is intricate. The first argument of the rivals is set out at 402.12–19. Alexander’s reply occupies 402.36–404.31, and it consists of six separate reasons for rejecting their argument. To the second of those reasons (403.11–14) Alexander reports a subtle counterargument (403.14–18), which he then rebuts (403.18–26) and which leads him to a positive defence of the Peripatetic view (403.26– 404.11). Alexander does not name his opponents. But scholars have treated the text as evidence for Stoic logic, and for early Stoic logic — indeed, it has been treated as evidence for Chrysippus’ views on negation.38 Now the three arguments by which the rivals support their own view work obliquely rather than directly — I mean that they argue for the truth of their view not 37 in APr 402.1–405.16; see J. Barnes, ‘Peripatetic Negations’, OSAP 4, 1986, 201–214 [reprinted above, pp.172–186]. * For Alexander takes it to rival the Peripatetic view — you might, of course, think that both views are correct and that there are (at least) two different ways of construing ‘Callias isn’t going for a walk’. 38 The text was not printed by von Arnim in SVF : it appears in Hu¨lser, Die Fragmente, pp.1162–1172.

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straightforwardly but rather by way of urging that the Peripatetic view is false. Their arguments are essentially arguments against the Peripatetic view, and they are only intelligible if they are construed in that way. If the arguments in Alexander’s text are Chrysippean, then we may infer that Chrysippus’ views on negation were formed — or at least were supported — by reaction against Aristotle’s views on negation. It follows at once that Chrysippus had studied the Aristotelian view. And in that case we may as well suppose that he had read some at least of Aristotle’s logical works. Does Alexander’s text warrant that heady conclusion? We might wonder, first, whether the debate recorded by Alexander was an historical debate at all. The dispute is not explicitly presented in historical terms: Alexander employs the present tense throughout, and he does not attempt to give any historical colour to his abstract unfolding of the debate. Yet it is plausible to suppose that there was at least a minimal historical reality behind the story. The rivals, we should surely suppose, were real men. For Alexander says ‘some people hold [NØ
x   ŒE]’: he does not report the opinion as one which might be or might have been advanced, but as one which is actually advanced. And if the rivals were genuine historical figures, then we may reasonably suppose that they used arguments at least roughly comparable to the arguments which Alexander assigns to [43] them; and it is reasonable to infer from this that they knew the Peripatetic view and were overtly reacting against it. Whether all the complexities of Alexander’s account are founded on historical reality I shall not decide; but at least it seems highly likely that at some point a group of logicians became aware of the Aristotelian view on the negation of simple sentences, that they argued against the view, and that they thought thereby to establish a different view. Then who were the rivals? In particular, were they Stoics? — were they Chrysippus? Alexander is not normally reluctant to name his opponents, nor does he always disguise his references to the Stoics or to Chrysippus. Here he names no one, offering an anonymous ‘some people’. That perhaps suggests that the phrase ‘the Stoics’ would not have fitted the bill, and hence that the rivals are not simply ‘the Stoics’ or some particular group of Stoics. A fortiori the rivals are not Chrysippus. Against that, scholars have appealed to the content of the passage. Their argument is simple enough: the rival view is a Stoic view, and an early Stoic view; hence the rivals must be Stoics, and early Stoics. But in that argument the inference is dubious and the premiss uncertain.

Aristotle and Stoic logic

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As to the inference, suppose for the moment that the view which the rivals defend is an Old Stoic view: it simply does not follow that the rivals were Old Stoics. They may, for example, have been later Stoics — Athenodorus or Cornutus, say — who determined to defend the Old Stoic doctrine against its resuscitated Peripatetic rival. Alexander may be referring to an attempt by Cornutus to support the Chrysippean view of negation — an attempt in which he deployed his own knowledge of Aristotelian texts. Even if the rival view is itself Chrysippean, there is no reason to infer that the supporting arguments within which it is embedded come from Chrysippus. And hence, of course, no reason to think that Chrysippus adopted his view in studied reaction to some Peripatetic ideas. And is the view Chrysippean? The heart of it is. According to Chrysippus — or so I think we may properly assume — negation is a sentence-forming operator on sentences, so that the negation of ‘Fa’ is ‘not-[Fa]’. That is the view which the rivals are defending. But the defence relies on a number of points which are not otherwise attested for Chrysippus — or indeed for the Stoa. The most remarkable of these points is the following. The second of the rivals’ three arguments turns about the sentence: [44] y  P æØÆE — a sentence which is supposed to imply that its subject exists and is male. The rivals affirm that the sentence is equivalent to, and perhaps analysable as: Ø
› ØŒ

 y  n P æØÆE. (See in APr 402.29–30.) I am not confident that I understand that sentence; but I suppose that it ought to mean something like this: This is the man being pointed to, and it is not the case that he is walking. More generally, perhaps, the negation of a sentence of the form F — where ‘’ is a demonstrative pronoun — is taken to be equivalent to something of the form  is the object demonstrated and not-[F(the object demonstrated)]. No text ascribes that equivalence to any Old Stoic. We know a certain amount about the Old Stoic view of negation and a certain amount about the Old Stoic view of ‘definite’ sentences (sentences of the form ‘F’):39 nothing there hints at the account which we read in Alexander; and although 39 Texts in Hu¨lser, Die Fragmente, pp.1150–1160 (definite sentences), pp.1160–1205 (negation).

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we can see how the equivalence might have been excogitated on the basis of Old Stoic ideas,40 we should doubt that the rival view is Chrysippean, even if it is derived from certain Chrysippean ideas — and even if it was developed in order to defend certain Chrysippean views. I cannot claim that the argument of the last paragraph will bear much weight. We know that Chrysippus wrote at vast length on various logical matters — among them the matters of negation and of definite sentences (see the catalogue in Diogenes Laertius, VII 190); and we can be sure that he explored these issues in far [45] subtler and more complicated ways than our surviving texts, which for the most part represent the thin pap of the handbooks, allow us to see. Thus it would be false to claim that the pages in Alexander contain material which is demonstrably post-Chrysippean. But, conversely, I do not believe that anything in the text shows — or even suggests — that the rivals whose view Alexander rehearses are Chrysippus and his friends. Everything is compatible with the hypothesis that the rivals date from the first or second century ad.

VIII Aristotle promised to write about syllogisms ‘based on a hypothesis’. He never did so; but, according to Philoponus, lengthy treatises were written on the subject by Aristotle’s pupils — Theophrastus, Eudemus, and the others — and also by the Stoics. (in APr 242.18–21)*

In ancient terminology, Peripatetic logic was categorical syllogistic, whereas Stoic logic was hypothetical syllogistic. Some of the Peripatetics did spend 40 Suppose that Callias no longer exists. Then P [˚ƺºÆ æØÆE] is true; and in general, according to the rival account, a negation of ‘Fa’ will be true when the object denoted by ‘a’ does not exist. Here, proper names differ from demonstratives, according to Chrysippus (see esp Alexander, in APr 177.26–32, with Barnes, Logic and the Stoa, pp.97–98): if ‘’ denotes nothing, then the sentence ‘F’ says nothing; hence ‘not-[F]’ says nothing — and a fortiori nothing true. Thus a Chrysippean view of demonstratives requires that negations of ‘F’ be treated differently from negations of ‘Fa’ — and the equivalence which the rival view patronizes is one way of showing up the difference. * N
ªaæ ‹Ø  ºıå ı æƪÆÆ æd  ø
ŒÆºº
 ¥  ÆŁÅÆd  F æØ º ı, ƒ æd ¨ çæÆ
ŒÆd ¯hÅ
ŒÆd  f ¼ºº ı, ŒÆd Ø ƒ øœŒ . — See J. Barnes, ‘Theophrastus and hypothetical syllogistic’, in J. Wiesner (ed), Aristoteles Werk und Wirkung — Paul Moraux gewidmet I (Berlin, 1985), pp.557–576 [reprinted below, pp.413–432], on pp.561–562.

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some time on some aspects of hypothetical syllogistic — and it is only natural to wonder if their first ponderings excited the Stoics and primed them for their own endeavours. Philoponus does not say that the Stoics borrowed from Aristotle’s pupils; but he perhaps suggests — and intends to suggest — as much. The corresponding passage in Alexander’s commentary (in APr 398.31–390.9) does not even mention the Stoics. But it does offer us some information about early Peripatetic forays into hypothetical syllogistic. Alexander gives a list of the sorts of hypothetical syllogism which Aristotle would have discussed had he fulfilled his promise. I have argued elsewhere43 that Alexander’s list in effect coincides with the list of syllogisms which Theophrastus had discussed. The list contains five items, the first three of which are here relevant. First, there are ‘arguments which proceed by way of a continuous proposition (or a connected proposition, as it is also called) together with an additional assumption’; in other words, arguments of the general form: (A) If A, then B; but C: therefore D. [46] Two particular instances of this form are: (i) If P, then Q; but P: therefore Q. (ii) If P, then Q; but not Q: therefore not-P. Secondly, there are arguments which ‘proceed by way of a separative or disjunctive proposition’ and an additional assumption: (B) Either A or B; but C: therefore D.44 For example: (iii) Either P or Q; but P: therefore not-Q. (iv) Either P or Q; but not-P: therefore Q. Finally, there are ‘arguments which proceed by way of a negated conjunction’ and an additional assumption: (C) Not both A and B; but C: therefore D. For example: (v) Not both P and Q; but P: therefore not-Q. Now (A)–(C) use thoroughly Stoic connectives. And examples (i)–(v) are the celebrated five unproveds or ‘indemonstrables’ which form the foundation of Chrysippus’ hypothetical syllogistic.45 Have we not discovered the historical 43 See Barnes, ‘Theophrastus’. 44 Note that disjunction must here be construed ‘exclusively’, so that a disjunction is false if both (or more than one) of its disjuncts are true. 45 Texts in Hu¨lser, Die Fragmente, pp.1528–1554; see S. Bobzien, ‘Stoic syllogistic’, OSAP 14, 1996, 133–192 (on pp.134–141).

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origins of Stoic logic? Chrysippus stole it from the Lyceum, from Theophrastus. It is plain that that conclusion46 is at best exaggerated. There is no evidence that Theophrastus developed a logical theory around schemata (i)–(v); no evidence that he took them as indemonstrable; no evidence that he thought of them as foundations for hypothetical syllogistic; no evidence that he thought of uniting (A)–(C) into a single system of logic — in short, no evidence that he anticipated any of the outstanding features of Chrysippean logic. But a whimper of doubt remains. Can the parallelism between Theophrastus’ first three types of hypothetical syllogism and Chrysippus’ unproveds [47] really be a mere coincidence? Chrysippus uses four logical particles — ‘not’, ‘or’, ‘if ’, ‘and’. Theophrastus’ forms (A)–(C) use the same four. How did Chrysippus hit on the very same logical particles which Theophrastus had hit upon? Surely Chrysippus chose the particles he did because those were the particles used by Theophrastus in the logical system which Chrysippus hoped to develop or surpass? And then the following story concerning the origins of Stoic logic tentatively suggests itself. The Stoics had done a little logic before Chrysippus, but it had not developed anything which could be called a system of logic: there was not yet such a thing as ‘Stoic logic’. Chrysippus changed all that. Aware that Aristotle had created a logical system of astonishing elegance and precision, and aware that Theophrastus had at least half invented a second and supplementary syllogistic, he resolved to produce a logic of his own. His system would take its start from some ideas sketched by Theophrastus. But the Stoic system would not be a supplement to Aristotle’s categorical syllogistic — it would outclass and supplant anything which the Peripatetic logicians had invented. It is a charming story, and the argument on which it is based is not contemptible. But neither the story nor the argument is compelling. Suppose that you were devising a hypothetical logic — what particles would you choose? No doubt your choice would be determined by the way in which hypothetical inferences are ‘naturally’ or commonly formulated. Plainly, the word ‘if ’ will immediately impose itself — without ‘if’ (or some semisynonym) there will be no system of hypothetical logic at all. Equally plainly, 46 See esp C. Prantl, Geschichte der Logik im Abendlande (Leipzig, 1855), I, p.379; cf e.g. I.M. Bochen´ski, La logique de The´ophraste (Fribourg, 1947), p.9. contra e.g. Sandbach, Aristotle and the Stoics, p.18: ‘Aristotle was aware of propositional [i.e. hypothetical] syllogisms but uninterested, and Theophrastus and Eudemus appear to have investigated them without any great commitment. There is no reason for supposing their work to have provided the stimulus for Stoic logic’.

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‘not’ is indispensable in any ‘natural’ logical system. And it is tempting to say that the same goes, if to a lesser degree, for ‘or’ and ‘and’: those particles will appear in hypothetical syllogistic for the simple and unexciting reason that they frequently figure in those ordinary arguments with which hypothetical syllogistic is formally concerned. Now if such mundane considerations indicate that the four particles will readily present themselves to anyone who makes a study of hypothetical syllogistic, then it is otiose to suggest that X may have adopted them because Y had adopted them. Theophrastus adopted them, and Chrysippus adopted them. There is no reason at all to think that Chrysippus adopted them because Theophrastus had adopted them. But that counterargument overlooks a point. Why do both hypothetical syllogistics, the syllogistic of Theophrastus and the syllogistic [48] of Chrysippus, make use of an exclusive disjunction? In ordinary English ‘or’ is often, perhaps normally, inclusive; and the same seems to be true of the Greek equivalent, ‘X’. At any rate, Greek disjunctions are not exclusively exclusive.47 Hence the choice of an exclusive ‘or’ in hypothetical syllogistic is not determined by ordinary usage; and we might think that, here at least, the fact that Chrysippus made the same choice as Theophrastus might plausibly be explained by hypothesizing that he followed Theophrastus. But why did Theophrastus adopt an exclusive ‘or’? The later Peripatetic logicians gave a reason, of a philosophical nature, for selecting exclusive disjunction — and the reason may derive originally from Theophrastus. Things, the later logicians said, are either dependent on or independent of one another, either connected to or separated from one another. Hence there are two fundamental forms of compound (or hypothetical) sentences: connecting sentences, which express a dependence and which will standardly employ the word ‘if’; and separating sentences, which express an independence and which will standardly call on the word ‘or’ (see Galen, inst log iii 1). And therefore ‘or’ must be exclusive. Now that argument cannot possibly have been adopted by Chrysippus. For it presupposes that there are only two basic sentential connectives, ‘if ’ and ‘or’. And in fact later Peripatetic logicians explicitly denied that ‘and’ was a genuine sentential connective, that it made a single sentence out of several.48 But Stoic 47 See e.g. Apollonius Dyscolus, conj 215.14–221.15, who discusses successively the exclusive and the inclusive use of ‘j ... j ... ’. 48 See e.g. Porphyry, apud Ammonius, in Int 73.19–33.

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logic recognized three basic connectives: ‘and’ was admitted — indeed, ‘and’ was an essential part of Chrysippus’ system of logic. Of course, Chrysippus might in principle have taken the exclusive ‘or’ from Theophrastus even though he rejected the argument which gave it its place in Theophrastus’ system. But if the Peripatetic argument did indeed derive from Theophrastus, then his hypothetical syllogistic will have employed only two connectives — and syllogisms depending on negated conjunctions will not have appeared in it.49 The old Peripatetic system of hypothetical syllogistic was thus very different from the Stoic system. And in that case Chrysippus is less likely to have bought his basket of particles at the Lyceum. [49] All that stuff is a little dizzying — and hopelessly conjectural. What is the least implausible conclusion to draw? I doubt if we need invoke Theophrastus’ forms (A)–(C) — or (A)–(B) — in order to explain anything in Stoic logic.50 There is no positive evidence that the Stoic connectives were taken from Peripatetic practice. We can imagine circumstances in which such borrowing would be plausible — and we can equally imagine circumstances in which it would be implausible. And we have no reason to find one such set of imaginary circumstances more likely than another.

IX The four ‘themata’ lie at the heart of Stoic logic: by means of them complex syllogisms are to be ‘reduced’ to the five unproved or indemonstrable syllogisms; and thus the ‘completeness’ of the Stoic system (whatever exactly its completeness was) can be shown. We are vexingly ill informed about the themata: our texts are few, obscure, and inconsistent; and there is no scholarly consensus on the matter.51 One main text appears in Alexander’s commentary on the Prior Analytics: In this way you can get three syllogisms from the three figures ... by virtue of the synthetic theorem which has been handed down. The theorem was used by Aristotle to the extent that need demanded; but the Stoics took it from him and divided it and constructed from it what they call the second, third and fourth themata, paying no attention to what is useful but zealously elaborating everything there is to be said in 49 In point of fact, the text of Alexander, far from opposing that notion, tends to favour it. See Barnes, ‘Theophrastus’, pp.566–567. 50 So e.g. Frede, Stoische Logik, pp.17–18. 51 Texts in Hu¨lser, Die Fragmente, pp.1606–1619; see Bobzien, ‘Syllogistic’, pp.142–180.

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this area of study, even if it is useless. That has been shown elsewhere. (in APr 284.10–17)*

An earlier passage explains what the synthetic theorem was, and explicitly states that Aristotle himself was its discoverer (in APr 274.19–24). Alexander’s claim is clear and unambiguous: Aristotle discovered the logical rule known to the Peripatetics as the synthetic theorem; the Stoics — and here Chrysippus must be meant — took the rule from Aristotle and formed three of their four themata out of it. Aristotle’s theorem was thus directly responsible for a central feature of Stoic logic. [50] As a matter of logic, could the three themata have been derived from the synthetic theorem? We have descriptions of the third thema in Alexander (in APr 278.12–14) and in Simplicius (in Cael 237.2–4). The rule they describe can probably best be given as follows:52 If ‘A, B: so C’ is a valid argument, and if ‘D1, D2, ... , Dn: so B’ is a valid argument, then ‘A, D1, D2, ... , Dn: so C’ is a valid argument. And that rule is indeed a special case of the synthetic theorem. For the second and fourth themata we have no direct description: indeed, Alexander’s assertion that they were derived from the synthetic theorem has been the major text on which reconstructions have been based. Hence we cannot test Alexander’s assertion against the rest of the evidence — there is no more evidence. Alexander was a competent logician, but he could make mistakes and he was biassed against the Stoics. I am not sure that we are bound to believe his assertion that the themata derive — logically speaking — from the synthetic theorem. And in that case, I am not sure that we can hope to reconstruct the themata themselves. But that is an issue which I leave to one side. More pressing is the question of the synthetic theorem itself. And first we might wonder if it is really Aristotelian. Alexander says this: * Iººa ŒÆd æE ıºº ªØ f Ø
oø ºÆE
KΠH
æØH
åÅø
... ŒÆa e ÆæÆ 

ı
ŁØŒe
ŁæÅÆ, n ƒ b
æd æØ ºÅ fiB åæfi Æ ÆæÆæÆ
 Ææ Æ
Kç ‹
ÆoÅ IfiØ, ƒ b Ie B  A Ææ KŒ
ø
ºÆ
 ŒÆd غ
 K ÅÆ
K ÆP F e ŒÆº 

Ææ ÆP E æ
ŁÆ ŒÆd æ
ŒÆd Ææ
, IºÆ
 b
 F åæÅ ı A
b e ›ø F
ı


ºªŁÆØ K
fiB  ØÆfiÅ Łøæfi Æ Œi
¼åæÅ
fi q KºŁ
  ŒÆd ÇźÆ
: ØŒÆØ b æd  ø
K
¼ºº Ø. — See above, pp.[30–31]. — I take the last sentence to mean that Alexander has discussed elsewhere (perhaps in his Notes on Logic : in APr 250.1–2) the question of the synthetic theorem; but I. Mueller, Alexander of Aphrodisias: On Aristotle, Prior Analytics 1.23–31 (London, 2006), p.141, takes Alexander to be referring to his earlier remarks about the uselessness of bits of Stoic logic at 18.12–20.29 and 164.23–165.8. 52 The two texts do not agree with one another, and there is considerable dispute over the correct formulation of the thema. But the details are here irrelevant.

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In what Aristotle says here he sketches for us more clearly the so-called synthetic theorem of which he himself is the discoverer. (in APr 274.19–21)*

The passage on which Alexander is commenting — ‘what Aristotle says here’ — is this: Or again, when each of A, B is obtained by way of a syllogism — e.g. A by way of D, E, and B by way of F, G. (APr A 42a1–4)**

Does that say what Alexander says it says? Aristotle has just stated that every proof involves precisely three terms. He quickly qualifies the statement. The sentence at 42a1–4 is the second qualification. What Aristotle has in mind is this: I have a proof of a theorem C from premisses A, B; but first I prove each premiss — A from D, E, and B from F, G. So here you might say that a proof involves more than three terms: [51] the proof of C involves precisely five terms.54 Aristotle allows that more than three terms are involved, and he allows that this is a reputable way to prove C. But he comments that ‘in this way there are several syllogisms’ (42a4). That is to say, the example does not show that a single syllogism or a single proof may contain more than three terms; it shows only — and trivially — that a chain of connected syllogisms may do so. (And it presupposes, perhaps less trivially, that you may prove something by producing not a proof but rather a sequence of proofs.) There, according to Alexander, Aristotle ‘sketches more clearly’ the synthetic theorem. It is perfectly plain, however, that Aristotle does not sketch or describe the theorem at all: no theorem of any sort is described or sketched or outlined in the text. But can’t Alexander at least make good the weaker claim that Aristotle implicitly uses the synthetic theorem? Presumably he supposes that Aristotle is considering the inference D, E, F, G: so C, and that he is implicitly justifying or validating it by appeal to the three inferences D, E: so A; F, G: so B; A, B: so C. Alexander assumes, finally, that the validation itself presupposes the synthetic theorem. * Ø z
b ºªØ
F
 ªæçØ E
çÆ
ææ
e ºª 

ı
ŁØŒe
ŁæÅÆ y ÆP  KØ
æ. ** j ºØ
‹Æ
ξ
H
` ´ Øa ıºº ªØ F ºÅçŁfiB ( x
e ` Øa H
˜ ¯ ŒÆd ºØ
e ´ Øa H
˘ ¨). 54 The letters in the Greek text here mark propositions, not terms. So suppose that C is a universal affirmative, XaY, and that it is proved from XaZ and ZaY (which are the premisses A and B). XaZ is proved from XaW and WaZ, and ZaY from ZaV and VaY. Thus the terms involved in the proof of C are these: X, Y, Z, W, V.

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Now it is far from evident that Aristotle has the inference ‘D, E, F, G: so C’ in mind: his words rather suggest that he is considering the chain of three syllogisms as together constituting a proof of C. Moreover, had he had his mind on the inference Alexander suggests, he need not have appealed to the synthetic theorem to support it: he might have appealed to nothing at all (in the text he does appeal to nothing at all); or he might have appealed to a different theorem. And finally, he could not properly have appealed to the synthetic theorem as that theorem is formulated by Alexander. The theorem is perhaps closely related to any rule which will validate the inference Alexander ascribes to Aristotle. But the theorem itself will not do so. The synthetic theorem not only is absent from Aristotle’s text — it ought to be absent. Alexander says that ‘he sketches for us more clearly the so-called synthetic theorem’. If the comparative, ‘more clearly’, is taken seriously, [52] then Alexander might be hinting at another and less clear sketch of the theorem elsewhere in Aristotle’s works.55 But Alexander cites no other text, and as far as I know no surviving passage in Aristotle’s works states or refers to the theorem. Indeed, apart from a couple of references in Alexander and two in Themistius, we know nothing at all about the history of the theorem. It is, I suppose, possible that Aristotle — or Theophrastus or Eudemus — discussed the theorem in a lost work, and that the lost work was eagerly read by Chrysippus. But we have not the slightest reason to believe that things were actually so. I am inclined to suspect that some later Peripatetic — Boethus comes to mind — had discussed the synthetic theorem and, perhaps, had noted its relation to the Stoic themata. Alexander may then have falsely inferred that the theorem must have been known to Aristotle — and that Chrysippus took his themata from that source. But that is idle speculation. The most I insist upon is this: we should not believe that Alexander’s remarks on the origins of the themata are historically accurate.

X The preceding sections justify no general conclusion: I have not discussed all the pertinent texts; and I have not discussed any of the pertinent texts in 55 But ‘çÆ
ææ
’ might rather mean ‘fairly clearly’, or simply ‘clearly’ (in later Greek the comparative form often lacks any comparative sense).

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sufficient detail. But I suspect that an exhaustive account would in the end warrant the following general conclusion: ‘In the present state of our evidence we have no compelling reason for affirming that Chrysippus was in any way influenced by the formal logic of the Lyceum. Scholars, and other incurable romantics, will tell pretty stories. Cynics, and other incurable anti-romantics, will tell the opposite tales. Sober historians — and inebriated historians too — must, if they care at all for evidence, reserve judgement.’ If we are ever to trace the external philosophical influences on Stoic logic, then we shall first need to unearth more evidence — in particular, we shall need to unearth some reliable biographical evidence. We shall only learn more when Oxyrhynchus or Herculaneum unrolls the papyrus biography of Chrysippus. That biography may [53] turn out to contain the sentence ‘Chrysippus loved and studied the Prior Analytics ’. It may, with equal probability, contain the sentence ‘Chrysippus never knew anything about Aristotelian logic’. The appearance of neither sentence ought to surprise us — and we should not, of course, be surprised if neither sentence appears.

14 Theophrastus and Stoic logic* I In chapter 44 of Book A of the Prior Analytics, Aristotle considers ‘arguments on the basis of a hypothesis’. He deals first with arguments which are ‘agreed to by way of a compact’, and then with those which ‘reach their conclusion by way of the impossible’. The chapter ends with a promise: Many other arguments reach their conclusion on the basis of a hypothesis. We should consider them and mark them out clearly. We shall say later what varieties of them there are and in how many ways arguments can rest on a hypothesis. (APr A 50a39–b2)**

Alexander of Aphrodisias comments on the passage as follows: Having talked about arguments on the basis of an agreement and arguments by reductio ad impossibile, he says that many others reach their conclusion on the basis of a hypothesis. He postpones discussion of them, as though intending to deal with them more carefully; but no book of his on the subject is in circulation. Theophrastus, however, refers to them in his own Analytics — and so do Eudemus and some others of Aristotle’s associates. Aristotle presumably has in mind those hypothetical arguments which proceed by way of a continuous proposition (or a connected proposition, as it is also called) together with the additional assumption, and those which proceed by way of a separative or disjunctive proposition — and perhaps also those which proceed by way of a negated conjunction, if they are indeed different from the ones already mentioned. [558] And in addition to those we have mentioned, there will also be arguments on the basis of proportion and those which they call ‘qualitative’ (i.e. arguments from what is more so or less so or equally so) and whatever other varieties of arguments based on a hypothesis there are (they have been discussed elsewhere). (in APr 389.31–390.9)1 * First published as ‘Theophrastus and hypothetical syllogistic’ in J. Wiesner (ed), Aristoteles Werk und Wirkung — Paul Moraux gewidmet I (Berlin, 1985), pp.557–576. **  ºº d b ŒÆd æ Ø æÆ

ÆØ K  Łø R KØŒłÆŁÆØ E ŒÆd ØÆÅB
ÆØ ŒÆŁÆæH. 
 b
s
ƃ ØÆç æÆd  ø
ŒÆd  ÆåH ª
ÆØ e K  Łø, oæ
Kæ F
... 1 Ng
æd H
K › º ªÆ ŒÆd H
Øa B N I
Æ
IƪøªB ºªØ ŒÆd ¼ºº ı  ºº f K  Łø æÆ
ŁÆØ æd z
æŁÆØ b
‰ KæH
Kغæ
, P c


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Those paragraphs are of some importance for the history of logic: the present chapter is a commentary upon them.

II Aristotle undertook to discuss the ‘other arguments on the basis of a hypothesis’. Alexander cautiously observes that no Aristotelian treatise on the topic ‘is in circulation’; Philoponus says that ‘Aristotle has taught us nothing about the subject’ (in APr 242.15), Boethius that ‘nothing was written on the matter by Aristotle’ (hyp syll I i 3). A curious passage in Al-Farabi’s commentary on the de Interpretatione contradicts those judgements.2 But whatever the precise [559] sense of the passage may be, Al-Farabi’s value as a witness is çæÆØ ÆP F ªªæÆÆ æd ÆPH
· ¨ çæÆ   ÆPH
K
 E N Ø 
ƺıØŒ E 
Å
Ø Iººa ŒÆd ¯hÅ  ŒÆ Ø
 ¼ºº Ø H
Ææø
ÆP F. ºª Ø  i
   Øa ı
å F, n ŒÆd ı
Å

ºªÆØ, ŒÆd B æ ºłø  ŁØŒ f ŒÆd  f Øa  F ØÆØæØŒ F  ŒÆd ØÇıª
ı, j ŒÆd  f Øa I çÆØŒB ıº ŒB N ¼æÆ y Ø æ Ø H
æ ØæÅ
ø
· Ææa b  f NæÅ
ı r 
i
ŒÆd ƒ K I
ƺ ªÆ ŒÆd R ºª ıØ ŒÆa  Ø ÅÆ,  f Ie  F Aºº
ήd w
ŒÆd › ø, ŒÆd Y Ø
 ¼ººÆØ H
K  Łø ØÆç æÆ NØ æd z
K
¼ºº Ø YæÅÆØ. — For the text, see below, nn.16 and 20. — The passage is F29 in A. Graeser, Die logischen Fragmente des Theophrast (Berlin/New York, 1973), frag 33c in L. Repici, La logica di Teofrasto (Bologna, 1977), and 111E in W.W. Fortenbaugh, P.M. Huby, R.W. Sharples, and D. Gutas (eds), Theophrastus of Eresus: sources for his life, writings, thought and influence, Philosophia Antiqua 54 (Leiden, 1992). See P.M. Huby, Theophrastus of Eresus: sources for his life, writings, thought and influence: Commentary 2 — Logic, Philosophia Antiqua 103 (Leiden, 2007), pp.135–144. 2 The passage is in Int 53 (see F.W. Zimmermann, Al-Farabi’s Commentary and Short Treatise on Aristotle’s de Interpretatione (Oxford, 1981), p.45) — it is 111C in Fortengaugh et al., Theophrastus. Professor Dimitri Gutas first drew my attention to certain difficulties in the paragraph and saved me from some serious misconceptions. Then Dr. Fritz Zimmermann, with great generosity, subjected the text to a fresh scrutiny and allowed me to benefit from his learning. He now translates the relevant lines as follows: [1] Aristotle does not consider the composition of hypothetical propositions in this book at all, though he does slightly in the Prior Analytics. [2] The Stoics, i.e. [?] Chrysippus and others of the Stoa, did do so with a vengeance: they exhaustively treated the subject of hypothetical syllogisms. [3] Similarly, Theophrastus und Eudemus after Aristotle. [4] They say that Aristotle wrote books on hypothetical syllogisms. [5] But in his logical writings we find no indication that he produced a separate account of hypothetical syllogisms. [6] That is only found in the commentators’ commentaries, [7] who relate them from Theophrastus. In clause [7], ‘them’ refers to hypothetical syllogisms. In sentence [6], ‘that’ is ambiguous in its reference: the sentence may mean either that an indication that Aristotle produced a separate account is found only in the commentaries, or else that a separate account is found only in the commentaries. In sentence [4], ‘they’ probably refers specifically to Theophrastus and Eudemus; but its reference may include the Stoics of sentence [2]. (Gutas’ translation, in Fortenbaugh et al., Theophrastus, p.239, makes ‘they’ refer exclusively to the Stoics.)

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slight, and we may reasonably assume that Aristotle wrote nothing on hypothetical syllogisms apart from the few paragraphs in the Prior Analytics.

I II By Alexander’s account, Theophrastus, Eudemus, ‘and some others of Aristotle’s associates’ considered the arguments which Aristotle had passed over. Philoponus echoes the report, adding that the Stoics also wrote on the subject (in APr 242.19–21). Boethius mentions only Theophrastus and Eudemus (hyp syll I i 3). Al-Farabi also drops the reference to Aristotle’s ‘other associates’, but like Philoponus he adverts to the Stoics. The identity of those ‘other associates’ is uncertain. Boethus of Sidon, the successor of Andronicus of Rhodes, devoted much attention to logic, and he is known to have discussed the relationship between hypothetical arguments and Aristotle’s categorical syllogistic (Galen, inst log vii 2). Aristo of Alexandria ‘and several of the younger Peripatetics’ are said to have studied logic (Apuleius, int xiii [213.5–10]), and they may have touched upon hypothetical syllogistic.3 But those men can scarcely be in Alexander’s mind: he is referring to the older Peripatetics, who might properly be called ‘associates’ of Aristotle, and not to the renascent Peripatetics of the first century bc.4 [560] The only early Peripatetics, apart from Eudemus and Theophrastus, whose names are connected with logical studies are Phaenias of Eresus and Strato of Lampsacus. Phaenias is said to have written an Analytics (Philoponus, in Cat It is sentence [4] which is the singularity in Al-Farabi’s account. Al-Farabi, unlike Alexander, Philoponus and Boethius, clearly thought that, in the view of some people, Aristotle had written a separate treatise on hypothetical syllogisms. He may perhaps be relying on some Greek source which we no longer possess; or he may perhaps have misunderstood the passage from Alexander. But even if the former is the case, we can put no weight on Al-Farabi’s report. Dr. Zimmermann writes: ‘First, Farabi being what he is — intelligent, perverse, ignorant — he is the worst possible kind of witness for a historian. Secondly, Farabi’s Arabic being what it is, it is normally necessary to construe his evidence in the light of his Greek sources in order to know what he means.’ 3 See P. Moraux, Der Aristotelismus bei den Griechen 1, Peripatoi 5 (Berlin, 1973), pp.164–169 (Boethus), pp.186–192 (Ariston). 4 Mario Mignucci suggests that ‘ÆEæ ’ may mean ‘follower’ rather than ‘associate’, so that Alexander could after all be referring to the renascent Peripatetics. If he is right, then the logical work which I place in the fourth or third century may actually have been undertaken much later. I do not think that the texts which Mignucci has thus far cited establish his point, and I have not yet come across any passage in which someone whose career did not overlap with the career of X is unequivocally called an ÆEæ  of X.

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7.20); but nothing is known about the work. Strato produced a few books on logical matters (Diogenes Laertius, V 59–60). None of their titles mentions hypothetical syllogistic (or, come to that, categorical syllogistic); but the work On the more and less finds an echo in Alexander’s description of ‘qualitative’ hypothetical syllogisms and conceivably dealt with them. On Eudemus we are better informed. He too wrote an Analytics, and his name is regularly coupled with that of Theophrastus in ancient references to early Peripatetic logic. Boethius asserts that his treatment of hypothetical syllogistic was fuller than that of Theophrastus (hyp syll I i 3). But only one text (ibid, I xii 5) ascribes a view on the subject to Eudemus without at the same time ascribing it to Theophrastus. In what follows I shall, for the sake of convenience, speak exclusively of Theophrastus, ignoring Eudemus and ‘the others’. Alexander appears to give Theophrastus a certain pre-eminence, and the most detailed information we possess about hypothetical logic in the Peripatos is connected specifically with him (Alexander, in APr 325.33–328.6). IV How extensive was Theophrastus’ work on hypothetical syllogisms? Alexander says that he ‘refers to [
Å
Ø]’ them in his Analytics. Elsewhere Alexander cites the first book of Theophrastus’ Prior Analytics (in APr 326.21–22). It was Theophrastus’ general practice, when writing on a subject already treated by Aristotle, to touch lightly on those aspects which Aristotle had discussed and to follow out in some detail those aspects which Aristotle had ignored (Boethius, in Int 2 12.3–16). No doubt his Analytics, at the place corresponding to Aristotle’s APr A 50a39–b2, contained some moderately expansive account of hypothetical syllogisms. [561] Alexander does not refer to any other work of Theophrastus’ in connexion with hypothetical arguments. The known titles of Theophrastus’ logical writings do not include On Hypothetical Syllogisms or anything similar. Alexander’s use of the verb ‘refer to’ perhaps suggests a treatment of relatively slight proportions. That suggestion is supported by a passage from Boethius. When he began his study of hypothetical syllogisms, he says, he discovered no Latin and few Greek treatments of the subject. Aristotle had written nothing. Theophrastus, a man of universal learning, only pursues the elements of the matter; Eudemus follows a broader path of scholarship, but in such a way

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that he seems to have, as it were, sown the seed yet not harvested the crop. (hyp syll I i 3)*

If Eudemus only sowed the seed and Theophrastus did even less, then Theophrastus did not do much. Against those deflationary testimonies there stands a passage from Philoponus. He says that lengthy treatises were written on the subject by Aristotle’s pupils — Theophrastus, Eudemus, and the others — and also by the Stoics. (in APr 242.18–21)**

That statement is unequivocal. Scholars customarily dismiss it: Philoponus is mistaken; Theophrastus wrote no ‘lengthy treatise’ on hypothetical syllogistic.5 But although it is easy to imagine ways in which Philoponus might have come to commit such a mistake, his text should, I think, be taken more seriously. Theophrastus is nowhere stated to have written a work entitled On Hypothetical Syllogisms. But there is no reason to believe that we have a complete list of his logical works. The catalogue in Diogenes (V 42–50) is certainly defective, and Philoponus may be referring to a treatise named in no ancient source. Alternatively, Philoponus may have in mind one or more of the books which do appear in Diogenes’ list: I shall suggest a little later on that Theophrastus’ essay On Reduced Commonplaces consisted of an account of one part of hypothetical syllogistic. Nor is Alexander’s evidence formally inconsistent with the testimony of Philoponus. Alexander reports that Theophrastus referred to hypothetical syllogisms in his Prior Analytics. That is compatible with the proposition that Theophrastus also discussed hypothetical syllogisms elsewhere. [562] The text of Boethius is the stumbling-block. But here three things may be said. First, the extent of Boethius’ knowledge is uncertain. No doubt he was a conscientious scholar. But there were Latin treatments of hypothetical syllogisms which he had not come across, and there were certainly Greek texts

* Theophrastus vero vir omnis doctrinae capax rerum tantum summas exsequitur. Eudemus latiorem docendi graditur viam, sed ita ut veluti quaedam seminaria sparsisse, nullum tamen frugis videatur extulisse proventum. — The text is 111A in Fortenbaugh et al, Theophrastus. ** N
ªaæ ‹Ø  ºıå ı æƪÆÆ æd  ø
ŒÆºº
 ¥  ÆŁÅÆd  F æØ º ı, ƒ æd ¨ çæÆ
ŒÆd ¯hÅ
ŒÆd  f ¼ºº ı, ŒÆd Ø ƒ øœŒ . 5 So e.g. M. Pohlenz, Die Stoa (Go¨ttingen, 1949), II p.29; I.M. Bochen´ski, La logique de The´ophraste (Fribourg, 1947), pp.110–111; Graeser, Fragmente, pp.92–93.

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with which he had no acquaintance.6 If Boethius discovered no extensive work on hypothetical syllogistic by Theophrastus, it by no means follows that Theophrastus wrote no such work. Secondly, Boethius’ words may be disingenuous. Internal evidence suggests that, in parts at least, his Hypothetical Syllogisms follows Greek sources closely;7 external evidence confirms the suggestion — certain correspondences between Boethius’ text and passages in an Arabic treatise seem to imply a common Greek original.8 Boethius’ uncharacteristic claim to novelty in hyp syll is not wholly convincing: his disparagement of Theophrastus’ work may be exaggerated. Finally, it needs observing that Boethius and Philoponus are not in formal opposition. Philoponus says that Theophrastus wrote at length on hypothetical syllogisms, Boethius that he only pursued the elements of the subject. Lengthy treatises may be elementary — and they may certainly be judged to be elementary. Perhaps Theophrastus wrote at length and Boethius judged — or affected to judge — that his long disquisitions were elementary. In sum, the case against Philoponus is not as strong as scholars have supposed. All the evidence we have about the quantity of Theophrastus’ work is formally compatible. I do not assert that Philoponus is to be believed; but I find no sufficient reason for disbelieving him. In any case, even if Philoponus is wrong, Theophrastus may have worked extensively on hypothetical syllogistic. Logic does not take up much space. Aristotle’s complex and sophisticated development of assertoric categorical syllogistic occupies no more than ten pages of the Oxford Text. A ten page treatment of hypothetical syllogisms could well be similarly elaborate. [563]

V What were the hypothetical syllogisms which Theophrastus discussed? A hypothetical syllogism is an argument at least one of whose premisses is a hypothetical proposition. A proposition is hypothetical if it is a compound of at least two propositions. In modern English the adjective ‘hypothetical’ 6 See L. Obertello, A.M.Severino Boezio: de hypotheticis syllogismis (Brescia, 1969), pp.15–66. 7 See G. Striker, ‘Zur Frage nach den Quellen von Boethius’ de hypotheticis syllogismis’, AGP 55, 1973, 70–75. 8 See M. Maro´th, ‘Die hypothetischen Syllogismen’, Acta Antiqua 27, 1979, 407–436.

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suggests the notion of conditionality: conditional propositions, of the form ‘If P, then Q’, are indeed hypothetical in the normal ancient sense of that term; but for the ancient logicians disjunctions equally count as hypothetical propositions.9 (The status of conjunctions was disputed.) Here I follow the ancient usage. Hypothetical syllogistic contrasts with categorical syllogistic; for a syllogism is categorical if all its component propositions are ‘simple’, i.e. if none is a compound of two or more propositions.* Modern logicians sometimes identify hypothetical syllogistic with (a part of ) the propositional calculus and categorical syllogistic with (a part of ) the predicate calculus. That identification is in some ways misleading. When ancient hypothetical syllogistic was rediscovered by Lukasiewicz he advertised it as Aussagenlogik: that puff was pardonable in the circumstances, but hypothetical syllogistic no longer needs the efforts of the admen and Lukasiewicz’s nomenclature is best abandoned.

VI Alexander supposes that in APr A 44 Aristotle ‘has in mind’10 an exposition of hypothetical syllogistic, and he proceeds to catalogue the arguments which Aristotle would have discussed had he kept his promise. Alexander was not in telepathic communication with Aristotle’s ghost: how, then, did he know what Aristotle had had in mind? Plainly, he inferred Aristotle’s intentions from the performance of Aristotle’s associates. Observing what arguments Theophrastus had discussed, he reasonably deduced that those were the arguments which Aristotle had intended to discuss. [564] Alexander does not state that the arguments he lists were discussed by Theophrastus. Modern scholars have insisted on that fact. They have inferred that Alexander gives us no information about the content of Theophrastus’ work.11 They are right in what they insist upon. But their inference is fallacious and their conclusion is at odds with Alexander’s text. For although 9 See e.g. Apuleius, int ii [190.9–16]; Alcinous, didask vi [158.16–17]; Galen, inst log iii 1; Boethius, hyp syll I i 5, xiii 2; cf M.W. Sullivan, Apuleian Logic (Amsterdam, 1967), pp.24–30. * That is what several ancient texts say. It is, at best, misleading: a proposition is categorical inasmuch as it says something of something — and a proposition can do that while being as complicated as you like (see J. Barnes, Truth, etc. (Oxford, 2007), pp.128–138. 10 That, I think, is the sense of ‘ºª Ø ¼
’. 11 So e.g. Bochen´ski, Logique de The´ophraste, p.110; Graeser, Fragmente, p.93; Repici, Logica di Teofrasto, p.143; Maro´th, ‘Hypothetischen Syllogismen’, pp.411–412.

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Alexander does not state that his arguments were discussed by Theophrastus, he unequivocally implies that they were. The gist of the passage from Alexander is this: ‘Aristotle does not discuss the ‘‘many other’’ hypothetical syllogisms. Theophrastus does. They are the following ... ’ The train of thought is a crass non sequitur except on the assumption that the arguments listed by Alexander are the arguments Alexander takes Theophrastus to have discussed. We can affirm with complete confidence that Alexander believed Theophrastus to have discussed the arguments which he catalogues. I see no reason to question his belief. Against the consensus of modern scholars, I share the view of Carl Prantl that in this passage from Alexander’s commentary we possess an account of the content of Theophrastus’ work on hypothetical syllogistic.12

VII Alexander’s catalogue divides into two sections. The first section (390.3–6) covers what were usually called ‘mixed’ hypothetical syllogisms, i.e. arguments one of whose premisses was not hypothetical but categorical.* The text reads as follows: ... those hypothetical arguments which proceed by way of a continuous proposition (or a connected proposition, as it is also called) together with the additional assumption, and those which proceed by way of a separative or disjunctive proposition — and perhaps also those which proceed by way of a negated conjunction.

It is clear that Alexander has three varieties of ‘mixed’ syllogism in mind.13 [565] The first variety contains a ‘continuous’ or ‘connected’ proposition and an ‘additional assumption’. A ‘continuous’ or ‘connected’ proposition is a conditional. ‘Connected’, or ‘ı
Å
’, is the standard Stoic term for ‘conditional’. Galen says that it is the terminology of the ‘more recent philosophers’ — the ‘old’ philosophers used the phrase ‘ŒÆa ı
åØÆ
’ (inst log iii 3). Since the ‘old’ are more ancient than the ‘more recent’, and the ‘more recent’ go back at least as far as Chrysippus, it is a compelling inference 12 C. Prantl, Geschichte der Logik im Abendlande (Leipzig, 1855), vol I, p.379. * Better: ‘i.e. arguments the pertinent form of one of whose premisses is ‘‘P’’ ’ — the premiss in question may, of course, be hypothetical, and as complicated as you care to make it. 13 contra, Bochen´ski, Logique de The´ophraste, pp.109–110.

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that the ‘old philosophers’ are the early Peripatetics: ‘ı
å’ or ‘ŒÆa ı
åØÆ
’ was Theophrastus’ term for ‘conditional’.14 The ‘additional assumption’ or æ ºÅłØ is the categorical premiss of the ‘mixed’ hypothetical syllogism. The term ‘æ ºÅłØ’ is standardly used thus in Stoic logic.* Alexander reports that ‘the old philosophers’ preferred the word ‘ºÅłØ’’; but he adds that ‘they also use ‘æ ºÅłØ’ instead of ‘ºÅłØ’ (in APr 263.26–264.5). The most general form of hypothetical syllogisms of the first variety can therefore be represented by the schema: (I) If A, then B; but C: therefore D where ‘If A, then B’ is the continuous or connected proposition and ‘C’ is the additional assumption. Two valid instances of that form are: (1) If P, then Q; but P: therefore Q (2) If P, then Q; but not-Q: therefore not-P Those two valid schemata later assumed prominence in Stoic logic. Mixed hypothetical syllogisms of the second variety contain a ‘separative or disjunctive’ premiss as well as the additional assumption. ‘Separative’, or ‘ØÆØæØŒ ’, is the term used by ‘the old philosophers’ for the propositions which the Stoics called ‘disjunctive’, or ‘ØÇıª
’, and which modern logicians call ‘exclusive’ disjunctions (Galen, inst log iii 3). A ‘separative’ proposition is true just in case one or the other, but not both, of its components is true. The most general form of hypothetical syllogisms of the second variety is thus: (II) Either A or B; but C: therefore D [566] where ‘Either A or B’ is the separative or disjunctive premiss and ‘C’ is again the additional assumption. Two valid instances of that form are: (3) Either P or Q; but P: therefore not-Q (4) Either P or Q; but not-Q: therefore P Those two schemata also played an important part in Stoic logic. VIII Alexander’s description of the third variety of mixed hypotheticals runs thus: ... and perhaps also those which proceed by way of a negated conjunction. 14 See Bochen´ski, Logique de The´ophraste, p.108. * Pace Bochen´ski, Logique de The´ophraste, pp.117–119, the word, as it is used here, has nothing to do with the so-called ŒÆa æ ºÅłØ
propositions and syllogisms.

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The most general form of this variety of syllogism will therefore be: (III) Not (both A and B); but C: therefore D A valid instance is (5) Not (both P and Q); but P: therefore not-Q — and that too is a fundamental schema in Stoic logic. Alexander’s presentation of (III) differs from his presentation of (I) and (II): he gives it in Stoic terminology, without any Peripatetic equivalent; and he introduces it not by a simple conjunction but by the word ‘X’, a disjunctive connector which I have rendered, tendentiously, by ‘and perhaps’.15 Moreover, he adds a caveat: ‘if they are indeed different from the ones already mentioned’.16 [567] Elsewhere, in the course of arguing that mixed hypothetical syllogisms can in a way be ‘reduced’ to categorical syllogisms, Alexander again casts doubt upon the independence of form (III). Having offered ‘reductions’ for arguments of form (I) (in APr 262.32–264.6) and then for form (II) (264.7–14), he continues thus: The same holds for arguments involving a negated conjunction — if indeed they are actually different from the forms already discussed and are not the same as those involving conditionals with affirmative antecedents and negated consequents, i.e. ‘If A, then not B’. (264.14–17)*

15 cf M. Frede, Die stoische Logik (Go¨ttingen, 1974), p.18. But it might be that Alexander uses only Stoic terminology because on this point Peripatetics and Stoics spoke the same language. As for the ‘X’, it would be easy to excise it from the text. 16 Here I accept a suggestion made by David Sedley. Wallies, in the CIAG edition, prints the lines in question as follows: ... j ŒÆd  f Øa I çÆØŒB ıº ŒB. N ¼æÆ y Ø æ Ø H
æ ØæÅ
ø
, Ææa  f NæÅ
ı ... The ‘N ¼æÆ’ sentence is at best ungainly and obscure. Sedley changes Wallies’ punctuation, putting a comma after ‘ıº ŒB’ and a full stop after ‘æ ØæÅ
ø
’. The result is better sense and better Greek — and it receives support from 264.15 (quoted in the following note). The new punctuation introduces an asyndeton, which I find — perhaps wrongly — disagreeable: I incline add ‘’ after (or ‘ŒÆ’ before) ‘Ææ’. — The jingle ‘ æ Ø H
æ ØæÅ
ø
, Ææa  f NæÅ
ı’ is disagreeable, however the passage is punctuated. It is perhaps eased if the sentence ‘j ŒÆd ... æ ØæÅ
ø
’ is put in parentheses, and read as a question. And I confess that I am tempted simply to cut the sentence from the text — perhaps it began life as a marginal note, referring to 264.14–17? * Iººa ŒÆd Kd  F K I çÆØŒB ıº ŒB Y ª ŒÆd ÆPe ¼ºº  H
æ ŒØ
ø
æ ø
ŒÆd c › ÆPe fiH Øa ı
Å
ı  F Iæå 
ı Ie ŒÆÆçÆØŒ F ŒÆd ºª
  N I çÆØŒe
x
KØ
e N e `, P e ´.

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Alexander thus suggests that ‘Not (both A and B)’ is another way of expressing the conditional ‘If A, then not B’; so that form (III) turns out to be a special case of form (I). What Alexander suggests, Galen positively affirms. According to Galen, there are just two kinds of hypotheticals, those which mark a connectedness and those which mark a separateness. Hypothetical propositions, correspondingly, are either conditional or disjunctive (inst log iii 1). The same view is defended by Boethius (hyp syll I iii 4), and the only hypotheticals admitted into Boethius’ syllogistic are disjunctions and conditionals.17 Alexander, Galen, and Boethius are each opposing, implicitly or explicitly, a feature of standard Stoic logic. For the Stoics in effect treated (III) as an independent form of mixed hypothetical syllogism. The debate to which these texts pertain may have had a long history; for Boethius may be drawing on Eudemus: his statement that there are only two varieties of hypothetical proposition follows immediately upon a direct citation of Eudemus. In that case, the early Peripatetics will have claimed explicitly that hypothetical syllogistic need concern itself only with forms (I) and (II). However that may be, Alexander does not give (III) the same status as (I) and (II). I suggest that his reference to (III) should be treated as in effect parenthetical. Theophrastus discussed forms (I) and (II), but he did not discuss (III); Alexander knew that the Stoics [568] gave independent status to form (III), and in his parenthesis he left open the possibility that Aristotle had intended to discuss (III) as well as (I) and (II).

IX The second section of Alexander’s catalogue refers explicitly to two types of hypothetical argument. Arguments of the second type are ‘those which they call ‘‘qualitative’’ ’. The rather obscure phrase which ‘they’ use is also used by Aristotle (APr A 45b17), and ‘they’ are surely Theophrastus, Eudemus, and Co. The phrase is glossed as ‘arguments from what is more so or less so or equally so’. Earlier Alexander had explained that 17 No doubt this view is connected with the thesis that conjunction is a purely linguistic operation (e.g. Porphyry, apud Ammonius, in Int 73.19–33). Inexpert logicians are perennially tempted to suppose that ‘P and Q’ is not a single compound proposition but a list of two propositions, distinguishable only linguistically from ‘P, Q’.

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arguments are called ‘qualitative’ if they prove from what is more so or less so or equally so: Since these things are thus and so, what is similar (or what is more so, or what is less so) has the same quality. These arguments too come about by virtue of an additional assumption. (in APr 324.19–22)*

The function of the ‘Since’ clause is to give a schematic representation of qualitative arguments. It is compressed, and not easy to understand. Alexander follows it with an example, which makes everything plain: If something which might seem more likely than another thing to be sufficient to produce happiness is not actually sufficient, then the other thing is not sufficient either; but health, which seems more likely than wealth to be sufficient to produce happiness, is not sufficient: nor, therefore, is wealth. (324.26–29)**

Some qualitative arguments ‘from what is more so’ thus contain a universal premiss of the form ‘If it is more likely that Fx than that Fy, and not Fx, then not Fy’: from that premiss and two singular propositions — ‘It is more likely that Fa than that Fb’ and ‘not Fa’ — they infer the singular conclusion ‘not Fb’. Arguments of that sort are discussed in Aristotle’s Topics. Their general form might be cumbrously represented as follows: (IV) For any x and any y, if R(Fx, Fy) and + Fx, then + Fy; but R(Fa, Fb) and + Fa: therefore + Fb There ‘R’ is a schematic letter the possible substituends for which are ‘more’, ‘less’, and ‘equally’; and ‘ + P’ can be replaced either by ‘P’ or by ‘not P’. In what sense is (IV) a form of hypothetical syllogism? According to Alexander, arguments from what is more so and equally so [569] and less so also count among arguments on the basis of a hypothesis; for in them one thing is hypothesized and another additionally assumed. (in APr 265.30–31)***

So Alexander construes the universal premiss in (IV) as a hypothetical proposition.

* ŒÆa  Ø ÅÆ b ºª
ÆØ ƒ Ie  F Aºº
ήd w
ŒÆd ›  ı ØŒ

· KØc ÆFÆ, e ‹ Ø
ŒÆd e Aºº
ήd e w
, fiH  ØfiH ÆæÆŒ º ıŁE. Q ŒÆd ÆP d ªª

ÆØ ŒÆa ºÅłØ
. ** N n Aºº
i
 ÆØ ÆhÆæŒ r
ÆØ æe PÆØ
Æ
 F  KØ
ÆhÆæŒ, Pb e w
KŒ
ı YÅ i
ÆhÆ挷 ªÆ b º  ı Aºº
 ΠF
r
ÆØ ÆhÆæŒ æe PÆØ
Æ
PŒ Ø
ÆhÆ挷 P ¼æÆ › º F . *** r 
 i
K
 E K  Łø ŒÆd ƒ Ie  F Aºº
ŒÆd  F ›  ı ŒÆd  F w
· ŒÆd ªaæ K
  Ø e b
 ŁÆØ, e b ƺÆ
ÆØ.

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X Before mentioning qualitative syllogisms Alexander refers to arguments ‘on the basis of a proportion [K I
ƺ ªÆ]’. Some scholars* suppose him to mean arguments of the general form: (V) If A, then B; if C, then D: therefore if E, then F For Theophrastus is reported to have named arguments of that form ‘hypotheticals in virtue of a proportion [ŒÆa I
ƺ ªÆ
]’ (Alexander, in APr 326.9). But Alexander’s own term for (V) is ‘thoroughly hypothetical [Ø ‹ºø
 ŁØŒ ]’; and it is unlikely that in our passage he would, without explanation, designate (V) by a variant on a nomenclature which he never elsewhere uses in propria persona. Elsewhere, Alexander analyses Aristotle’s argument to the effect that ‘He is not-white’ is not the contradictory of ‘He is white’. (See in APr 397.25– 398.15, on APr A 51b10–27.) The argument goes thus: ‘He is not-white’ stands to ‘He is white’ as ‘He is capable of not walking’ stands to ‘He is capable of walking’; but ‘He is capable of not walking’ is not the contradictory of ‘He is capable of walking’: therefore ‘He is not-white’ is not the contradictory of ‘He is white’. Alexander comments that ‘the proof is by way of proportion, and that too is a hypothetical proof ’ (in APr 397.27).** The general form of the argument is: (VI) As X is to Y, so Z is to W; but X is R to Y: therefore Z is R to W There can be no doubt that it is arguments of the form (VI) which Alexander means to designate in our passage by the phrase ‘on the basis of a proportion’.19 [570] XI Finally, Alexander refers to ‘whatever other varieties of arguments based on a hypothesis there may be’.20 We know of one form of hypothetical syllogism * So e.g. Bochen´ski, Logique de The´ophraste, p.110. ** b EØ Ø I
ƺ ªÆ lØ Kd EØ  ŁØŒc ŒÆd ÆP. 19 Alexander apparently takes the first premiss to be a hypothetical proposition (in APr 398.15–17); and it can readily be rewritten as a conditional. 20 The received text here is ‘Y Ø
 ¼ººÆØ H
K  Łø ØÆç æÆd æ ø
’: I excise ‘æ ø
’. The phrase ‘propositions based on a hypothesis’ is strange, and even if it may be allowed as a variant on ‘hypothetical propositions’, it is out of place — Alexander is enumerating types of hypothetical arguments, not types of hypothetical propositions.

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which Theophrastus discussed and which has not yet been mentioned by Alexander in our passage. That is the ‘thoroughly hypothetical’ form — form (V). It would be strange were form (V) completely ignored in our passage, and it seems safe to infer that it is one of the ‘other varieties’ of hypothetical syllogism to which Alexander generally alludes. Alexander himself has said something about form (V) at in APr 326.8–328.7. It is natural to construe ‘elsewhere’ as a reference to those pages.

XII The preceding paragraphs have determined which forms of hypothetical syllogism were discussed by Theophrastus and his Peripatetic associates. The catalogue is not long, but it includes several important forms of argument to which Aristotle had paid no official attention. What exactly did Theophrastus say about those argument forms? The question can be answered with confidence for only one of the six forms. Alexander writes at some length about the way in which Theophrastus treated arguments of form (V) or wholly hypothetical syllogisms (in APr 326.8–328.7).* It may be that we also know something about Theophrastus’ treatment of qualitative syllogisms, arguments of form (IV). The Florentine logical papyrus (PSI 1095) contains a brief fragment of what was apparently a comprehensive, formal, and systematic discussion of at least some varieties of qualitative syllogism.** The papyrus text is anonymous, but it is evidently of Peripatetic origin. If it would be rash to ascribe the text to Theophrastus himself, it is nonetheless plausible to suppose that it derives ultimately from a work by one of the early Peripatetic logicians — perhaps, indeed, from Theophrastus’ essay On Reduced Commonplaces, or —æd I
Ū
ø
 ø
. [571] Here I shall not analyse those two texts. Instead, I turn to forms (I) and (II). Certain arguments of those forms came to occupy a fundamental position inside Stoic logic: in fact, schemata (1)–(4) represent the first four

* On which, see J. Barnes, ‘Terms and sentences’, Proceedings of the British Academy 69, 1983, 279–326 [reprinted below, pp.433–478]. ** The text is printed as appendix 2 in vol I of Fortenbaugh et al., Theophrastus; see F. Solmsen, ‘Ancora il frammento logico fiorentino’, Rivista di filologia e d’istruzione classica 7, 1929, 507–510; Bochen´ski, Logique de The´ophraste, pp.119–120; Huby, Theophrastus: Logic, p.171.

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of Chrysippus’ five ‘unproveds’ or ‘indemonstrables’. Theophrastus’ treatment of the schemata is thus of peculiar historical interest; for we cannot help but wonder if the Peripatetics anticipated and influenced the logical studies of the Stoa.

XIII We possess no information whatsoever about Theophrastus’ treatment of the forms (I) and (II). A prudent scholar would stop there. But where evidence is lacking, speculation offers its seductive hand. There was a distinctively Peripatetic way of doing formal logic — an approach familiar from Aristotle’s account of categorical syllogistic, visible in the brief remains of Theophrastus’ treatment of ‘wholly hypothetical’ arguments, and exhibited at length in the works of Boethius, whose logic was fundamentally Peripatetic. The main feature of that approach is its use of the method of exhaustive survey: a general form of argument is isolated; its various subforms are classified; and each possible instance of those subforms is examined seriatim, it being determined whether the instance is valid or invalid. If we hypothesize that Theophrastus followed that approach in his study of forms (I) and (II), we can apprehend with some accuracy what he said on the subject. The hypothesis is speculative — but the speculation is not mere whimsy. It allows us to construct a paraphrase of part of Theophrastus’ lost discussion of forms (I) and (II). The next section presents a paraphrase of Theophrastus’ treatment of (I). A parallel paraphrase for (II) can readily be produced.

XIV ‘‘Arguments by way of a continuous proposition and an additional assumption have the general form: (I) If A, then B; but C: therefore D [572] Just as, in a categorical syllogism, the two premisses must be linked by a middle term, so in a hypothetical syllogism of form (I) the additional assumption must be linked to one of the terms of the hypothetical premiss; that is to say, C must be either A or not-A or B or not-B.

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‘‘Thus there will be two ‘figures’ under form (I), depending on whether the additional assumption takes up the antecedent or the consequent of the hypothetical premiss. We may represent those two figures by: (X) If + P, then + Q; + P (Y) If + P, then + Q; + Q (The notation ‘ + P’ indicates that we may have either ‘P’ or its negation ‘not-P’.) ‘‘Each figure generates a number of premiss-pairs or ıÇıªÆØ. The possible pairings in the first figure, (X), are these: (i) If P, then Q; P (ii) If P, then Q; not-P (iii) If not-P, then Q; P (iv) If not-P, then Q; not-P (v) If P, then not-Q; P (vi) If P, then not-Q; not-P (vii) If not-P, then not-Q; P (viii) If not-P, then not-Q; not-P The second figure, (Y), generates a similar eight pairings, viz: (ix) If P, then Q; Q (x) If P, then Q; not-Q (xi) If not-P, then Q; Q (xii) If not-P, then Q; not-Q (xiii) If P, then not-Q; Q (xiv) If P, then not-Q; not-Q (xv) If not-P, then not-Q; Q (xvi) If not-P, then not-Q; not-Q ‘‘Pairing (i) in the first figure yields the valid syllogism: (1) If P, then Q; P: therefore Q [573] Pairing (ii) admits no valid conclusion, as Aristotle has already observed.21 Pairings (iv), (v), and (viii) are analogous to pairing (i): in each case there is a valid syllogism (to Q, not-Q, and not-Q respectively). Pairings (iii), (vi), and (vii) are analogous to pairing (ii): they admit no valid conclusion. ‘‘As for the second figure, pairing (ix) admits no valid conclusion; but pairing (x) yields: (2) If P, then Q; not-Q: therefore not-P.

21 See APr B 57b1–2; Soph El 167b1–8; 181a22–29.

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Again, pairings (xi), (xiv), and (xvi) are analogous to (ix) and give no syllogism, while pairings (xii), (xiii), and (xv), being analogous to (x), admit valid syllogisms. ‘‘Thus form (I) contains two figures; each figure contains eight pairings; and of each set of eight pairings four yield, and four do not yield, valid hypothetical syllogisms.’’

XV Theophrastus, I suggest, said all that — if not in those words or in that order. Did he say more? Surely he did. In categorical syllogistic some syllogisms are ‘perfect’, others ‘imperfect’, and imperfect syllogisms are ‘perfected’ or justified by reduction to perfect syllogisms. Theophrastus’ treatment of wholly hypothetical syllogisms included such a reduction (Alexander, in APr 327.33–35). He will surely have wondered if a similar reduction is not possible for hypothetical syllogisms of form (I). It is — and evidently so. If syllogism (1) is taken as perfect, the seven remaining valid arguments can be perfected or justified by reference to (1). Consider, for example, argument (2). Theophrastus might have argued thus: ‘If if P, then Q, and also not-Q, then not-P. For suppose that not-P is not the case. Then P is the case. From P and the hypothetical premiss we infer Q, by syllogism (1). But that is impossible, since not-Q is given; hence not-P.’ Set out more formally, the reduction runs thus: (A) If P, then Q assumption (B) Not-Q assumption [574] (C) P hypothesis (D) Q from (A) and (C), by (1) (E) Q and not-Q from (B) and (D) (F) Not-P reductio Similar reductions can easily be performed for the remaining six valid syllogisms. No ancient author ascribes any such reductions to Theophrastus; but they are found in Boethius and are clearly Aristotelian in spirit. It does not seem temerarious to conjecture that Theophrastus advanced them.* A singular text * And perhaps he did yet more — perhaps he tried to reduce these hypothetical syllogisms to categorical syllogisms (see Alexander, in APr 388.17–20, with Barnes, ‘Terms’, p.286 n.3).

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in Galen (inst log viii 2) observes that of the five schemata (1)–(5) — the five unproveds of Chrysippus’ logic — four are primitive but one, schema (2), requires proof. According to Galen, then, argument (2) can be reduced. He surely has in mind the reduction of (2) to (1) which I have just rehearsed. He does not name a source. He may, of course, be drawing on a Stoic (not all Stoic logicians accepted the Chrysippean systematization of logic), but he is perhaps more likely to be using a Peripatetic source.* Boethus springs to mind. Galen may have drawn his observation from a treatise by Boethus. If so, I guess that Boethus himself was copying the earlier work of Theophrastus.

XVI What I have just offered is a generous — some will say risibly generous — interpretation of Theophrastus’ contribution to the theory of the hypothetical syllogism. If Theophrastus did all that, surely he must be regarded as the effective founder of what we misleadingly call Stoic logic?22 The thesis that Theophrastus had a profound influence on the work of Chrysippus and his colleagues presupposes, first, that there was intellectual contact between Theophrastus and the Stoa, and secondly that there is a strong connexion between the content of Theophrastus’ logic and the content of Chrysippus’ logic.23 The Peripatetics were not intellectual anchorites, nor were they obsessively secretive about their views. The Hellenistic schools were [575] all domiciled in Athens, they worked within a few miles of one another, and pupils moved easily from one school to another. There is no direct evidence in the biographical tradition that the great Stoics ‘heard’ their Peripatetic contemporaries. But it must be thought probable, on general grounds, that they were aware of the views promulgated in the Lyceum. And recent scholarship has argued with some cogency that various aspects of Stoic and Epicurean thought are best understood as reactions against Aristotelian positions. * But Bochen´ski, Logique de The´ophraste, p.20, appears to suggest that Galen may have discovered the thing for himself. (And why not?) 22 That view was stated by Prantl, Geschichte der Logik, vol I, p.379: it has been dismissed, almost unanimously, by later scholars — but for the wrong reasons. 23 It does not presuppose, what would be foolish, that there were no other influences upon Stoic logic. See, in general, Frede, Stoische Logik, pp.12–26.

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It seems to me excessively sceptical to suppose that Chrysippus knew nothing at all about Peripatetic logic.* If that is once granted, should we not forthwith declare that Theophrastus invented Stoic logic? After all, Chrysippus’ greatest contribution to logic was the theory of the five unproveds — the five basic argument-patterns on which all other syllogisms could allegedly be shown to depend. And the five unproveds — arguments (1)–(5) — had been discussed by Theophrastus. We might indeed go further. If Theophrastus attempted a reduction of the valid hypothetical forms, and if he showed that argument (2) can be derived from argument (1), then he improved upon Chrysippus’ theory before Chrysippus had stated it; for the Theophrastean reduction effectively proves that the second of Chrysippus’ unproveds is superfluous — it can be reduced to the first, and the five unproveds become four. That is hasty. First — a relatively trifling point — it is probably false that Theophrastus discussed all Chrysippus’ unproveds. For he probably did not treat arguments of form (III) — and hence did not recognize argument (5), the third of Chrysippus’ five unproveds. If that is so, then at the very least Chrysippus added something to Theophrastus’ account. But Chrysippus certainly did far more than that. Theophrastus may have published a thorough examination of forms (I) and (II); he may have singled out certain syllogisms of those forms as perfect and derived other syllogisms from them. But there is no reason to believe that he regarded his perfect syllogisms as the basis for arguments of different forms — that he took argument (1) to be a primitive basis not merely for all syllogisms of form (I) but also for syllogisms of other forms. Nor is there reason to believe that Theophrastus attempted a unitary theory of hypothetical syllogistic, that [576] he tried to find a single set of unproveds from which all other hypothetical arguments might be derived. The Peripatetics recognized that arguments come in different forms. They distinguished several types of form, and within each form they systematized and regimented the valid moods. But they did not conceive the notion of a logical system which would include arguments of different types, nor did they attempt a unitary and comprehensive regimentation of valid arguments. Their logic was systematic, rigorous, and formal; but it was piecemeal.

* See J. Barnes, ‘Aristotle and Stoic logic’, in K. Ierodiakonou (ed), Topics in Stoic Philosophy (Oxford, 1999), pp.23–53 [reprinted above, pp.382–412].

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It is just here that the originality of Chrysippus lies. His theory collects argument-forms of different logical types as its unproved basis, and it professes to comprehend within a single system all varieties of valid inference. Even if Theophrastus’ work was studied by Chrysippus, it can have had at most a superficial influence on his thought: it did not suggest to him his greatest achievement. Theophrastus invented hypothetical syllogistic; but he did not invent Stoic logic.*24 * The matter of this chapter has been discussed, with rare refinement, by Susanne Bobzien: see esp ‘The development of modus ponens in antiquity: from Aristotle to the 2nd century AD’, Phronesis 47, 2002, 359–394, and ‘Pre-Stoic hypothetical syllogistic in Galen’s institutio logica’, in V. Nutton (ed), The Unknown Galen, Bulletin of the Institute of Classical Studies supplement 77 (London, 2002), pp.57–72; see also ‘Wholly hypothetical syllogisms’, Phronesis 45, 2000, 87–137; ‘Why the order of the figures of the hypothetical syllogism was changed’, CQ 50, 2000, 247–251; ‘Some elements of propositional logic in Ammonius’, in H. Linneweber-Lammerskitten and G. Mohr (eds), Interpretation und Argument (Wu¨rzburg, 2002), pp.103–119; ‘A Greek parallel to Boethius’ de hypotheticis syllogismis’, Mnemosyne 55, 2002, 285–300; ‘Peripatetic hypothetical syllogistic in Galen — propositional logic off the rails?’, Rhizai 2, 2004, 57–102. 24 This chapter was read at a conference on Theophrastus held in Liverpool in March 1983. Earlier drafts had been presented to meetings in Oxford and in London. My audiences were very helpful. I am particularly indebted to Bill Fortenbaugh, Dimitri Gutas, Pamela Huby, Mario Mignucci, David Sedley, and Fritz Zimmermann.

15 Terms and sentences* I Formal logic has a double pedigree. One line or tradition supposes that the inferences which logic studies are grounded upon terms and upon certain relations holding among terms. The fundamental logical notion is that of predication, a relation which associates two items of the same logical category. At the heart of every proposition lies the form ‘S is P’, where S and P are terms and the copula ‘is’ makes the predicative association. Propositions are then differentiated according to quantity (universal or particular), quality (affirmative or negative), and modality (assertoric, apodeictic, problematic). The paradigm inference is an assertoric syllogism in Barbara, the schema for which runs thus: Every S is M Every M is P ———— Every S is P. The tradition for which Barbara is the paradigm may be called term logic. A second line or tradition discovers the basis of all inferences in sentences or sentential functions and in certain relations holding among sentences. The fundamental notion is that of sentential connection.1 Propositions, in this tradition, do not lack internal [280] articulation — indeed, this tradition too uses a notion of predication. But here predication is not a relation among items

* First published in Proceedings of the British Academy 69, 1983, 279–326. 1 See M. Dummett, Frege: Philosophy of Language (London, 1973), p.21: ‘The expressions which go to make up atomic sentences — proper names (individual constants), primitive predicates and relational expressions — form one type: sentence-forming operators such as sentential operators and quantifiers which induce reiterable transformations which lead from atomic to complex sentences form the other. ... Logic properly so called may be thought of as concerned only with words and expressions of the second type.’

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of the same category but a tie which associates items from different categories. Sentences which express predicative propositions conjoin items of different categories, and the difference is brought out by the standard symbolic notation. In formulas such as ‘Fa’ or ‘Rab’ the difference between upper- and lowercase letters reflects an underlying categorial difference. The paragon inference in this tradition is modus ponendo ponens, the schema for which is: If P, then Q P — Q The line or tradition for which modus ponens is the paragon I shall call sentence logic.1 The two lines are rivals, York and Lancaster.2 Each offers a distinct philosophy of logic, each presents a distinct understanding of the fundamental nature of the subject, each intends to develop a complete and exhaustive system of inference. There is, of course, a strong temptation to regard the two lines not as rivals but as collaborators. After all, standard modern treatments of formal logic divide the subject into two main parts, the propositional calculus and the predicate calculus; and it is tempting to regard term logic as an essay in the predicate calculus, and sentence logic as an essay in the propositional calculus. That temptation is to be resisted. Barbara, the paradigm inference of term logic, doubtless belongs in the predicate calculus; [281] but term logic presents — or hopes to present — a treatment of propositional inferences as well as of predicate inferences. Modus ponens, the paragon inference of sentence logic, belongs to the propositional calculus, but sentence logic embraces predicate as well as propositional inferences. The two traditions make rival claims to the whole domain of logic. 1 The label is not ideal, if only because the phrase ‘sentence logic’ may be confused with ‘sentential calculus’. 2 The rivalry is pervasive, but it perhaps shows most clearly at the basic level. According to term logic, every proposition has a kernel which is syntactically symmetrical: if ‘X is Y’ is well formed, then so too is ‘Y is X’. According to sentence logic, the fundamental form of the proposition is syntactically asymmetrical: if ‘X(Y)’ is well formed, then ‘Y(X)’ is ill formed. It is a further question how serious such syntactical disagreements are: they might be thought to reflect deep semantic disagreements and hence to mark a philosophical or metaphysical divide; they might be thought, at the other extreme, to amount to little more than squabbles about notation. I return briefly to this question at the end of the paper. (Note that even were the disagreements merely notational, the two traditions would remain rivals: the rivalry would perhaps be trifling or sham, but a sham rivalry is not the same thing as a real partnership.)

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II The modern hero of sentence logic is Gottlob Frege. Since Frege’s time, indeed, formal logic has been dominated by the sentence tradition, so that our current textbooks are almost all written within that tradition. Every tiro quickly learns how to reconstrue Barbara within the framework of sentence logic, and it is frequently supposed that a Fregean sentence logic, or at least a logic based on Frege’s system, is the only viable kind of formal logic. The modern hero of term logic is Leibniz. In logic Leibniz was less original than Frege, and he never produced the systematic treatment of logic which he had planned. But his numerous scattered thoughts can be collected into a coherent presentation of term logic.1 Moreover, a neo-Leibnizian system has recently been elaborated in technical detail and with considerable sophistication.2 Sentence logicians may refer to term logic as a dead Titan, but a requiem would be premature. I II Term logic was not born with Leibniz. It was two thousand years old when Leibniz wrote, and its original inventor was Aristotle. Although Aristotle’s syllogistic underwent various transformations and developments at the hands of his ancient and mediaeval followers, we may fairly name the theory championed by Leibniz Aristotelian or Peripatetic logic. Equally, Frege did not invent sentence logic. He too had Greek predecessors. Sentence logic was first developed by the Stoic logicians, of whom Chrysippus was the [282] chief, and the theory which Frege championed may reasonably be called Stoic or Chrysippean logic.1 1 See H.-N. Castaneda, ‘Leibniz’s syllogistico-propositional calculus’, Notre Dame Journal of Formal Logic 17, 1976, 481–500; F. Sommers, ‘Frege or Leibniz’, in M. Schirn (ed), Studies on Frege (Stuttgart, 1976), vol III, pp.11–34 [¼ ‘Leibniz’s program for the development of logic’, in R.S. Cohen, P.K. Feyerabend, and M. Wartofsky (eds), Essays in Memory of Imre Lakatos (Dordrecht, 1976), pp.589–615]; H. Ishiguro, ‘Leibniz on hypothetical truths’, in M. Hooker (ed), Leibniz: critical and interpretive essays (Manchester, 1982), pp.90–102. 2 F. Sommers, The Logic of Natural Language (Oxford, 1982). 1 Leibniz was, of course, familiar with his Greek predecessors, whereas Frege (to the best of my knowledge) was not. Where Leibniz developed, Frege reinvented. Nevertheless, we may properly set Frege in the Stoic tradition. — Or perhaps Frege learned something about Stoic logic from his Jena landlord, Rudolf Hirzel? See G. Gabriel, K. Hu¨lser, and S. Schlotter, ‘Zur Miete bei Frege — Rudolf Hirzel und die Rezeption der stoischen Logik und Semantik in Jena’, History and Philosophy of Logic 30, 2009, 369–388.

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In antiquity, Peripatetic and Stoic logic, Aristotle and Chrysippus, were treated as rivals. Each system had its supporters who debated with — and sometimes slanged — one another.2 Our knowledge of the dispute is partial in both senses of the word: the evidence we possess is fragmentary, and it derives mainly from the ancient commentaries on Aristotle’s Organon. But it is clear that the dispute was long drawn out, that it involved a number of difficult issues in logical theory, and that it was conducted — on occasion at least — with a remarkable subtlety. Modern scholars sometimes speak as though Aristotle invented the predicate calculus, Chrysippus the propositional: each having elaborated one part of logic, they should stand together as the twin inventors of the two complementary halves of standard modern logic. If that is right, then the ancient dispute was fatuous, each party ignorantly taking a fragment of logic for the whole. No doubt there is some truth in that idea; for the dispute was a complex one, and in part, like any other philosophical dispute, it surely turned on confusions and misapprehensions. But that is not all there was to the matter. It is more plausible historically, and more interesting philosophically, to regard the dispute as, at bottom, a confrontation between term logic and sentence logic. The disputants were partisans of different ideologies, and their disagreement reflected more than a trifling misconception of their own and each other’s views: it manifested a genuine puzzlement about the underlying nature of logical inference.

IV Term logicians hold that all formally valid inferences can be represented within the framework of term logic. The old Peripatetic logicians were committed to a somewhat stronger thesis; for they held that all formally valid inferences could be construed within an extension of Aristotelian syllogistic. The task of establishing that thesis constitutes what I shall call the Peripatetic programme. The Peripatetic programme, as the ancient Peripatetics were [283] aware, faced three chief objections.1 First, the terms of Aristotelian syllogisms are all 2 On the dispute, see I. Mueller, ‘Stoic and Peripatetic logic’, AGP 51, 1969, 173–187; M. Frede, ‘Stoic vs. Aristotelian syllogistic’, AGP 56, 1974, 1–32 [¼ Essays in Ancient Philosophy (Oxford, 1987), pp.99–124]. 1 Leibniz encountered the same difficulties: for a succinct account, see B. Russell, The Philosophy of Leibniz (London, 1900), pp.12–15; see also G. Englebretsen, Three Logicians (Assen, 1981), and the essays referred to on p.[281] n.1.

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general. But some inferences essentially involve propositions which contain singular terms (proper names, for instance). How can term logic deal with such inferences? Secondly, the terms of Aristotelian syllogisms correspond to monadic or one-place predicates. But some inferences turn essentially upon the presence of polyadic or relational predicates. How can term logic incorporate such relational inferences? Thirdly, the propositions in Aristotelian syllogisms are all simple or ‘categorical’. But some inferences turn essentially upon complex propositions (conditionals, disjunctions, conjunctions, etc). How can term logic encompass complex propositions?

V The later Peripatetics customarily stated the third difficulty, which concerns complex propositions, in the following form: How can hypothetical syllogisms be reduced to categorical syllogisms? A syllogism is categorical if each of its constituent parts — its premisses and its conclusion — is categorical.2 Categorical propositions are simple propositions, and a proposition is simple provided that it does not contain two or more propositions as components.3 In practice, the Peripatetics held that every [284] assertoric categorical proposition can be construed as having one of the four standard Aristotelian forms: ‘Every S is P’, ‘No S is P’, ‘Some S is P’, ‘Some S is not P’. A syllogism is hypothetical if at least one of its constituent parts is hypothetical. A proposition is hypothetical if it contains at least two propositions 2 The word ‘ŒÆŪ æØŒ ’ is usually translated — or transliterated — as ‘categorical’. It should properly be translated as ‘predicative’: the Peripatetics called simple propositions ‘predicative propositions’ because they all supposedly exhibit the predicative Ø ŒÆ Ø
 structure. But the word ‘categorical’ is so well entrenched in modern discussions of term logic that it would be futile to insist upon the correct translation. 3 Here I conflate the Peripatetic and the Stoic terminologies. My use of the word ‘categorical’ is Peripatetic. (The Stoics used ‘ŒÆŪ æØŒ ’ in a special sense of their own.) The distinction between simple (±º F) and non-simple is Stoic (e.g. Diogenes Laertius, VII 68; Sextus, M VIII 93), and so too is the account of simplicity I give in the text. But the Peripatetics called their categorical propositions ‘simple’ (e.g. Alexander, in APr 11.17–18), and their distinction between categorical and hypothetical propositions can — for present purposes — be assimilated to the Stoic distinction. Note that the negations of simple propositions are themselves simple; for if ‘P’ is simple, then ‘notP’ cannot contain two or more propositions as components. (What of ‘not-not-P’? Is that, too, simple, or does it contain both ‘P’ and ‘not-P’ as components? It is simple; for a component of a component of X is not itself a component of X. Similarly, propositions such as ‘Chrysippus believed that Heraclitus held that the world was periodically consumed by fire’ are presumably also simple. But I do not know of any ancient text that discusses such complicated simple propositions.)

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as components. To us the word ‘hypothetical’ suggests the notion of conditionality. Conditional propositions of the form ‘If P, then Q’ are indeed hypothetical; but so too are disjunctions, conjunctions, and — in principle, at least — propositions compounded by such connectives as ‘since’, ‘because’, ‘in so far as’, etc. In practice, Stoic logic, in its classical form, limited its attention to three sentential connectives: ‘if ’, ‘or’, ‘and’.1 And the Peripatetics normally divide hypothetical propositions into just two types, conditionals and disjunctions.2 I shall not discuss the reasons for those limitations; for the hypothetical propositions with which I shall be concerned are in fact all conditional in structure.*

VI The later Peripatetics observed with regret that Aristotle had said very little about hypothetical syllogisms.3 In two difficult [285] chapters of the Prior Analytics, A 23 and A 44, he passes some remarks on ‘syllogisms from a hypothesis’.1 At the end of A 44 he he says that 1 Stoic logic also uses the sentential operator ‘not’ or ‘it is not the case that’; but unlike modern logicians the Stoics did not treat ‘not’ as a sentential connective (see above, p.[283] n.3). 2 See, for example, Alexander, in APr 11.20; Galen, inst log iii 1–5; Apuleius, int ii [190.9–16]; Alcinous, didask vi [158.12–14); Boethius, hyp syll I i 5, iii 2 (cf M.W. Sullivan, Apuleian Logic (Amsterdam, 1967), pp.24–30). The issues here are intricate. The Peripatetics did not merely overlook the various connectives which the Stoic logicians recognized. Crudely speaking, the Stoics adopted a linguistic approach, recognizing as many compound propositions as there were distinct sentential connectives (but they used a loaded notion of distinctness). The Peripatetics regarded such an approach as superficial: they held that there were only two forms of hypothetical proposition because there were only two ways in which facts could in reality be connected. The dispute is again philosophical or ‘ideological’: that is to say, it reflects different underlying conceptions of the nature of logic. * Section V connives at certain traditional muddles. A proposition is categorical if it has at least one categorical form, hypothetical if it has at least one hypothetical form. No hypothetical proposition is simple. Some categorical propositions are simple — but, pace the tradition, there is no necessity that a categorical proposition be simple. And a categorical proposition may also be hypothetical — in other words, a proposition may have both a categorical and a hypothetical form. 3 Alexander, in APr 389.31–390.1; Philoponus, in APr 242.14–15, 359.30–32; [Ammonius], in APr 67.35. Later authors were not always so disappointed. John of Salisbury’s comment is amusing enough to bear transcription: sed forte ab Aristotile de industria relictus est hic labor, eo quod plus difficultatis quam utilitatis videtur habere liber illius qui diligentissime scripsit [i.e. Boethius]. profecto si hunc Aristotiles more suo exequeretur, verisimile est tante difficultatis fore librum ut preter Sibillam intelligat nemo (Metalogicon iv 21). 1 See G. Striker, ‘Aristoteles u¨ber Syllogismen ‘‘aufgrund einer Hypothese’’ ’, Hermes 107, 1979, 33–50; J. Lear, Aristotle and Logical Theory (Cambridge, 1980), chapter 3. Aristotle’s ‘syllogisms from a hypothesis’ should perhaps not be construed as hypothetical syllogisms, i.e. as arguments from hypothetical premisses. Aristotle’s successors, however, certainly discussed hypothetical syllogisms, and they certainly supposed that Aristotle himself had undertaken to discuss them.

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we shall discuss later the varieties of arguments of this kind and the number of ways in which things are said to be from a hypothesis. For the present let this much be clear to us — that it is not possible to analyse such syllogisms into the figures [of categorical syllogistic]. (50a40–b3)*

Aristotle did not keep his promise to discuss the things: advocates of the Peripatetic programme were disappointed — and they must have been depressed by the magisterial assertion that hypothetical syllogisms could not be analysed into the categorical figures. But if Aristotle was discouraging, his immediate successors lightened the gloom. According to Alexander of Aphrodisias, ‘Theophrastus mentions in his own Analytics, and so do Eudemus and certain others of Aristotle’s associates’ (in APr 390.2–3).2 Later, Philoponus and Boethius repeat the assertion, in slightly different forms.3 The reports have occasioned much comment. It is uncertain who the ‘other associates’ of Aristotle were: apart from Theophrastus and Eudemus, the early Peripatetics do not appear to have had much taste for logic. It is disputed exactly what sorts of hypothetical syllogisms Theophrastus and the rest discussed. It is not clear how extensively the early Peripatetics treated the subject — Philoponus speaks of ‘long treatises’ while Boethius appears to imply that the discussions were superficial and brief. Those general questions are of some importance to the history of formal logic; but they may be ignored here.4 For on one aspect of the matter we are in fact tolerably well informed. [286] VII One of the topics which Theophrastus certainly treated was that of ‘wholly hypothetical’ syllogisms. Our main source for that treatment is a long passage * 
 b
s
ƃ ØÆç æÆd  ø
ŒÆd  ÆåH ª
ÆØ e K  Łø oæ
Kæ F
·
F
b   F
E
ø çÆ
æ
, ‹Ø PŒ Ø
I
ƺØ
N a åÆÆ  f  Ø  ı ıºº ªØ . 2 ¨ çæÆ   ÆPH
K
 E N Ø 
ƺıØŒ E 
Å
Ø, Iººa ŒÆd ¯hÅ  ŒÆ Ø
 ¼ºº Ø H
Ææø
ÆP F. The passage is 111E in W.W. Fortenbaugh, P.M. Huby, R.W. Sharples, and D. Gutas, Theophrastus of Eresus: sources for his life, writings, thought and influence, Philosophia Antiqua 54 (Leiden, 1992). The texts on hypothetical syllogisms are collected as 111–113 on pp.237–253; they are discussed in P.M. Huby, Theophrastus of Eresus: sources for his life, writings, thought and influence — commentary 2: logic, Philosophia Antiqua 103 (Leiden, 2007), pp.135–154. 3 Philoponus, in APr 242.18–21 [¼ Theophrastus, 111B]; Boethius, hyp syll I i 3 [¼ 111A]. 4 See J. Barnes, ‘Theophrastus on hypothetical syllogisms’, in J. Wiesner (ed), Aristoteles Werk und Wirkung — Paul Moraux gewidmet I (Berlin, 1985), pp.557–576 [reprinted above, pp.413–432].

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in Alexander’s commentary on Aristotle’s Prior Analytics in which he draws on the first Book of Theophrastus’ Prior Analytics.1 The passage is not a quotation from Theophrastus, nor indeed does it purport simply to document Theophrastus’ views. Nonetheless, we can extract his views from Alexander’s commentary with reasonable confidence. The passage is formally devoted to an examination of APr A 45b19 (‘we must investigate and distinguish the number of ways in which arguments from a hypothesis ... ’). Alexander’s question is whether or not all hypothetical syllogisms can be ‘reduced’3 to [287] categorical syllogisms by what he has

1 in APr 325.31–328.7: the Greek text is printed in the Appendix. — Parts of the passage appear as Theophrastus, 113B. See also Philoponus, in APr 302.6–23 [¼ Theophrastus, 113C], which is, however, a highly condensed and somewhat inaccurate version of Alexander’s account. (But L. Obertello, A.M. Severino Boezio: de hypotheticis syllogismis (Brescia, 1969), p.45, says that ‘the account closest to the thought of Theophrastus seems to be that of Philoponus, whereas Alexander presents his own personal reworking of it’.) — On the passage in Alexander, see S. Bobzien, ‘The development of modus ponens in antiquity: from Aristotle to the 2nd century ad’, Phronesis 47, 2002, 359–394, on pp.380–396; ead, ‘Wholly hypothetical syllogisms’, Phronesis 45, 2000, 87–137, on pp.115–124. 3 ‘Reduce’ translates ‘I
ªØ
’, for which ‘I
ƺØ
’ is a virtual synonym; ‘reduction’ is ‘I
ƪøª’, which is interchangeable with ‘I
ºıØ’. Those terms are technical, or at least semitechnical, in Peripatetic logic, but they are not given any formal definition. Aristotle uses ‘I
ªØ
’ in two main contexts. (1) He speaks of ‘reducing’ one syllogism to another (e.g. APr A 29b1, the reduction to Barbara and Celarent of the other valid moods). The origin of this sense is to be found in the notion of ‘I
ªØ
N Iæå’, ‘reducing to first principles’. It corresponds closely to the notion of derivation in modern logic: an argument schema S is ‘reduced’ to a set of schemata S* just in case S is derivable from S*. (2) Aristotle also speaks of ‘reducing’ arguments ‘into the figures’ (e.g. APr A 46b40). Here the corresponding modern notion is that of formalization. An argument (expressed in natural language) is ‘reduced’ to a schema S just in case it is formalized as an instance of S. When the Peripatetics speak of ‘reducing’ hypothetical syllogisms, it is not always clear which usage, (1) or (2), they have in mind. And in fact it does not matter. For to ‘reduce’ modus ponens, in sense (1), to a set of categorical schemata is equivalent to ‘reducing’, in sense (2), to categorical form any ordinary language argument which, so to speak, invites formalization by way of modus ponens. I have spoken of the Peripatetic programme as involving the reduction of hypothetical syllogisms to categorical syllogisms. There is a hitch. Take modus ponens, a ‘mixed’ hypothetical syllogism. Alexander does not maintain that modus ponens inferences can be represented within categorical syllogistic (e.g. in APr 386.5–8, following APr A 50a16). Rather, he argues as follows. The categorical premiss of a modus ponens inference either is or is not the conclusion of a further inference. If it is the conclusion of a further inference, then that inference is either a categorical syllogism or a mixed hypothetical syllogism. If it is a categorical syllogism, then the original modus ponens inference is shown to depend upon, and hence to be reduced to, a categorical syllogism (see, for example, in APr 263.15–17). If the second inference is hypothetical, then its categorical premiss either is or is not the conclusion of a further inference — and the earlier argument is repeated (see in APr 387.5–11; cf Philoponus, in APr 241.31–242.13). If, finally, the categorical premiss of a modus ponens argument is not the conclusion of a further inference (because it is ‘evident’ or K
Ææª), then the modus ponens inference is not a syllogism at all (in APr 263.7–11; 265.5–10; 388.12–17).

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called ‘the method of selection’.1 A particular problem is caused by one sort of [288] hypothetical syllogism; ‘for wholly hypothetical arguments ... will be thought not to be amenable to proof by selection’ (326.8–10). What does the phrase ‘wholly hypothetical’ mean? Alexander does not explain it, but Philoponus says that wholly hypothetical syllogisms are so called because ‘all the propositions assumed are hypothetical’ (in APr 243.16; cf 302.9–12).1 They thus contrast with, say, modus ponens arguments, in which only one of the assumed propositions is hypothetical. (Arguments of that In all that, Alexander is probably following Theophrastus (see in APr 388. 17–20 [¼ Theophrastus 112B]). As Alexander presents the argument, it is confused. Most obviously, it cannot count as a reduction of modus ponens to categorical syllogistic. Three views of Alexander’s procedure are possible. (A) Alexander believes, mistakenly, that the procedure does reduce modus ponens, in sense (1), to categorical syllogistic. (B) Alexander realizes that he cannot produce a genuine reduction but thinks that his procedure is the nearest he can get to one. (C) Alexander is operating with a new notion of ‘reduction’: he thinks, perhaps, that his procedure shows that categorical syllogisms are in a sense prior to hypothetical syllogisms, and that that notion of priority can properly ground a new notion of reducibility. If we adopt (C), then we must infer that the Peripatetic programme is not, after all, one of reducing all formal inference to Aristotelian term logic. That is, perhaps, the most charitable way to construe Alexander’s procedure. But I am inclined to think that charity is misplaced. Alexander himself does not clearly state what he has in mind by a reduction: I suspect that, if pressed, he would acknowledge that he is really after a genuine sense (1) derivation. In that case, view (A) is correct and Alexander is in a muddle. (Something similar is certainly true of Alexander’s treatment of relational inferences: see e.g. J. Barnes, ‘Logical form and logical matter’, in A. Alberti (ed), Logica Mente e Persona (Florence, 1990), pp.7–109 [reprinted above, pp.43–146], on pp.83–118.) 1 Alexander is referring to the notion of ‘selection’ or KŒº ª which Aristotle employs in APr A 27–29 (KŒºªØ
, 43b11, etc., KŒº ª, 44b26 etc). For an example of the method of selection, see in APr 324.5–15. Alexander considers the mixed hypothetical syllogism: If the soul is always in motion, the soul is immortal? The soul is always in motion ———————————— The soul is immortal. He remarks that we shall take the terms in the ºÅłØ or æ ºÅłØ [i.e. the second, categorical, premiss] — they are soul and always in motion — and make the selection with regard to them. Iººa ºÅł ŁÆ  f K
fiB ƺłØ j æ ºłØ ‹æ ı (Nd b y Ø l  łıåc ŒÆd e IØŒ
Å
), ŒÆd Kd  ø
c
æ ØæÅ
Å
KŒº ªc
 ØÅ ŁÆ. (324.10–12) The selection picks on the term ‘self-moved’, and thus generates a categorical syllogism in Barbara: Every soul is self-moved Everything self-moved is always in motion —————————— Every soul is always in motion. By means of the selection we produce a categorical syllogism which establishes one of the premisses of the hypothetical syllogism, and the hypothetical syllogism is thus reduced to a categorical syllogism (see above, p.[286] n.3). 1 Philoponus actually uses ‘Ø ‹º ı’ rather than ‘Ø ‹ºø
’ (so too the documentum Ammonianum: [Ammonius], in APr XI 2).

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sort were customarily called ‘mixed’ hypothetical syllogisms.) According to Philoponus (302.9), Theophrastus himself used the phrase ‘wholly hypothetical syllogism’. But Alexander reports that Theophrastus called such syllogisms ‘arguments in virtue of an analogy’ (326.9) on the grounds that ‘the premisses are analogous to each other and the conclusion to the premisses — they all show a similarity’ (326.11–12). But that is at best a strained explanation, and we may wonder if Alexander has not misunderstood Theophrastus’ text.2 Philoponus adds that wholly hypothetical syllogisms are also called ‘hypotheticals with three components’ ‘because these syllogisms are inferred by way of at least three propositions’ (in APr 243.16–17).3 Alexander, however, appears to treat ‘hypotheticals with three components’ as a special kind of wholly hypothetical syllogism (326.9), and he is right to do so. In principle, then, a wholly hypothetical syllogism is an argument in which each premiss, and also the conclusion, is hypothetical or contains at least two propositions as components. In fact, we shall find that Theophrastus concerned himself with only one special sort of wholly hypothetical syllogism. [289] VIII Alexander’s first illustrative example of a wholly hypothetical syllogism is this: an argument of the following sort is wholly hypothetical: If A, then B If B, then C

————— If A, then C. (Here the conclusion too is hypothetical.) e.g.: If he is a man, he is an animal If he is a animal, he is a substance

———————————— If he is a man, he is a substance (326.22–25) 2 It is tempting to guess that Theophrastus wrote: ºªø b ÆP f ıºº ªØ f ŒÆa I
ƺ ªÆ
. He meant: ‘It is in virtue of an analogy [i.e. the analogy with categorical syllogisms] that I call them ‘‘syllogisms’’ ’. Alexander wrongly took his ambiguous sentence to mean: ‘I call them ‘‘syllogisms in virtue of an analogy’’ ’ — and he then concocted an implausible explanation for the nomenclature. That conjecture has the merit of associating the I
ƺ ªÆ at 326.9 with the I
ƺ ªÆØ which are invoked later in the passage. It has the demerit of imputing a surprising carelessness to Alexander. 3 cf e.g. Alexander, in APr 265.16; 390.19; [Ammonius], in APr XI 1; Boethius, hyp syll I vi 2.

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It is worth noting, in passing, that the argument — the wholly hypothetical syllogism — is contained in the last three lines of that extract. The lines using the letters ‘A’, ‘B’, ‘C’ do not present a wholly hypothetical syllogism because they do not present a syllogism at all: their function is to exhibit the skeleton or underlying structure of certain wholly hypothetical syllogisms. It is also worth noting that there is no warrant for introducing material implications into Alexander’s syllogism. Sophisticated scholars regularly replace Alexander’s ‘If ... , then —’ by the horseshoe of material implication. Now the Greeks knew something rather like material implication, and certain ancient arguments invite formulation by way of the modern connective. But the analysis of conditional propositions was hotly disputed among the ancient philosophers. Material implication was not the orthodox, let alone the only, variety of conditional which they recognized, and it is misleading to throw horseshoes casually into Greek texts. The ordinary Greek ‘N’ should be translated by the ordinary English ‘if ’; and unless there is some indication that a conditional should be given some particular technical analysis, we must be content with an informal and non-technical understanding.1 [290]

IX Alexander’s schema raises one difficult question. What is the syntactic status of the letters ‘A’, ‘B’, ‘C’? The grammar of 326.23 demands that they be sentential letters: like the ‘P’ and ‘Q’ of modern propositional calculus, they hold the place of complete sentences. No other replacement of ‘A’ and ‘B’ will make grammatical sense of the schema ‘If A, then B’. And it seems that Alexander does as a matter of fact replace ‘A’ and ‘B’ by complete sentences, namely by ‘He is a man’ and ‘He is an animal’. 1 Did the Peripatetics have an official or orthodox account of the truth-conditions of conditional sentences? (i) Theophrastus said something about the meaning ‘N’ — at any rate, in his APr he distinguished ‘N’ from ‘K’ (see Simplicius, in Cael 552.31–553.4 [¼ Theophrastus 112C]. (ii) Some scholars ascribe to the Peripatetics the account of conditionals in terms of çÆØ which Sextus preserves (PH II 110–112; cf Galen, meth med X 126). But the ascription is dubious (cf M. Frede, Die stoische Logik (Go¨ttingen, 1974), pp.90–93). (iii) Alexander may have held a special view about the nature of conditional sentences — see below, p.[308]. (iv) Parts of Boethius’ logic either commit serious blunders or else employ an unusual notion of the conditional. In the present state of research I do not think that we can interpret the hypothetical syllogistic of the Peripatetics with any confidence. But we can surely attain a partial understanding: when in the text I assert that such and such an inference is valid or invalid, I mean the assertion to hold whatever the proper analysis of Peripatetic conditionals should turn out to be.

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Yet most scholars hold that Alexander’s ‘A’, ‘B’, ‘C’ are term letters, having the status which they regularly have in Aristotle’s Analytics, where they hold the place of general terms like ‘man’, ‘animal’, ‘substance’.1 Now if ‘A’ and ‘B’ are really meant as term letters, we must plainly treat ‘If A, then B’ — ‘If man, then animal’ — as elliptical. And there are more ways than one of understanding the ellipsis. Philoponus, in his account of hypothetical syllogistic, perhaps intends ‘A’, ‘B’, ‘C’ as term letters,2 and if that is so he probably means us to construe ‘If A, then B’ as ‘If A, then B’: ‘If man, then animal’.3 It might be thought that Philoponus’ interpretation does not differ significantly from the sentential interpretation. After all, in Alexander’s text (327.12) the sentential interpreter, like Philoponus, will construe ‘If man, then animal’ as elliptical for ‘If he is a man, then he is an animal’. But there is an important difference: whereas Philoponus takes ‘man’ and ‘animal’ as proper replacements for ‘A’ and ‘B’ and holds ‘If A, then B’, no less than ‘If man, then animal’, to be elliptical, the sentential [291] interpreter takes ‘man’ to abbreviate the proper replacement for ‘A’ and does not regard ‘If A, then B’ as elliptical. In his work on hypothetical syllogisms, Boethius does not explicitly offer an interpretation of earlier Peripatetic treatments. But he was writing in the Peripatetic tradition and his own way of construing ‘A’, ‘B’, ‘C’ can be regarded as an implicit interpretation of Theophrastus and his followers. Boethius regularly refers to ‘A’, ‘B’, ‘C’ as termini; and he regularly writes ‘est A’, ‘est B’, ‘est C’, thus indicating beyond any doubt that he thinks that ‘If A, then B’ is elliptical and that ‘A’ and ‘B’ are term letters. He remarks that the terms of conditional propositions are usually expressed in the indefinite mode, and so I have judged it unnecessary to follow out a host of propositions determinate in quantity. (hyp syll I ix 2–3).*

‘If man, then animal’ is ‘indefinite’, that is to say it is marked neither as universal nor as particular — it is unquantified. In other words, Boethius in 1 So, for example, I.M. Bochen´ski, La Logique de The´ophraste (Fribourg, 1947), p.114; id, Formale Logik (Freiburg/Munich, 1956), pp.118–119; Obertello, Boezio, p.25. 2 in APr 302.22, where a hypothetical conclusion is expressed schematically by the words ‘N c e ` ¼æÆ, Pb d H
ˆ’. Here ‘ˆ’ can only be a term letter. But that may betoken no more than a minor slip on Philoponus’ part. 3 See in APr 244.7: N e æ Øe
¼
Łæø  KØ
, μ. * ... conditionalium termini propositionum indefinito maxime enuntiantur modo, atque ideo supervacuum iudicavi determinatarum secundum quantitatem propositionum quaerere multitudinem cum determinatae conditionales proponi non soleant.

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effect regards ‘If man, then animal’ as an open sentence — ‘If x is a man, then x is an animal’. In practice, he usually seems to treat the open sentences as equivalent to their universal closures, thus construing ‘If man, then animal’ (‘If A, then B’) as ‘If anything is a man, then it is an animal’ (‘If anything is an A, then it is a B’). More recently, scholars have offered a different interpretation. They read ‘A’, ‘B’, ‘C’, as term letters; they take Boethius’ ‘est A’, etc, as correct expansions of ‘A’, etc; and they then read ‘est ’ existentially. Hence they gloss ‘If A, then B’ as ‘If there are As, then there are Bs’: ‘If man, then animal’ thus represents ‘If there are men, then there are animals’.1 Those four interpretations of ‘If A, then B’ imply significantly different structures for the wholly hypothetical syllogism. The first interpretation, which makes ‘A’, ‘B’, ‘C’ sentential, suggests that a typical wholly hypothetical syllogism might have the form: If P, then Q If Q, then R ————— If P, then R. The second, Philoponan, interpretation suggests rather: If a is F, then a is G If a is G, then a is H ———————— If a is F, then a is H. [292] Boethius offers a third suggestion: If anything is F, then it is G If anything is G, then it is H ——————————— If anything is F, then it is H. Finally, from the moderns we have: If there are Fs, then there are Gs If there are Gs, then there are Hs ————————————— If there are Fs, then there are Hs. The second and the fourth of those illustrative forms are special cases of the first. The third is an argument form of a somewhat different type. 1 So e.g. A. Graeser, Die logischen Fragmente des Theophrast (Berlin, 1973), pp.98–99; L. Repici, La logica di Teofrasto (Bologna, 1977), p.149.

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The choice of interpretation is not a trifling matter. For it will determine the scope of Theophrastus’ treatment of wholly hypothetical syllogisms, and hence the truth or falsity of his views and theses on the subject.

X The fourth, modern, interpretation can be eliminated with some confidence. Were it right, then we should have to construe the illustrative syllogism which Alexander gives at 327.12–13 as follows: If there are men, there are animals If there are stones, there are no animals ——————————————— If there are men, there are no stones. I doubt if anyone would naturally take Alexander’s words in that way, or would readily suppose that such an argument would have struck any Peripatetic logician as an apt illustration.1 (Apart from its inherent asininity, the argument is unlike virtually all illustrative arguments in ancient texts: ancient logicians — like their modern successors — customarily illustrate schemata by arguments which are, or are assumed to be, sound. In many ways that is a bad custom. But it is deeply entrenched.) It is harder to decide among the other three interpretations. In favour of the second or the third is the fact that hypothetical syllogistic is almost invariably illustrated in our surviving texts by [293] examples which fit the specific argument forms which those interpretations determine. If the Peripatetics had intended the first and most general interpretation, why, it might pertinently be asked, did they always choose illustrations which were accommodated to the forms determined by the other two interpretations? But that question has, I suspect, a perfectly trivial answer. Alexander’s example at 326.24–25, which sets the tone for the remaining illustrations, is drawn from Aristotle: it appears at APr A 47a28–30. A Peripatetic logician would as a matter of course look to Aristotle for his first example of an argument form. Here that example happens to fit the second and the third interpretations as well as it fits the first. The subsequent examples, to preserve uniformity, will also have the same fit. Had Theophrastus wanted to discuss 1 cf Boethius, hyp syll II ix 7, whose informal comments on a similar concrete argument make it plain that ‘non est lapis ’ means ‘He is not a stone’ and not ‘There are no stones’. See also II xi 4: si homo est, non est irrationabile; si irrationabile non est, inanimatum EUM non esse necesse est.

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the argument forms determined by the first interpretation, he would, by virtue of his Aristotelian starting-point, have chosen as illustrative examples arguments which happen also to be accommodated to the second and third interpretations.1 There are at least two2 considerations which tell in favour of the first interpretation of ‘A’, ‘B’, ‘C’. First, when the Peripatetics discussed ‘mixed’ hypothetical syllogisms, such as modus ponens, they did not restrict themselves to specific forms. In other words, they discussed: If P, then Q P —— Q rather than If a is F, then a is G a is F ——— a is G [294] or If anything is F, it is G a is F ——— a is G.1 Given that the Peripatetics aspired to generality in the mixed cases, why should they have restricted themselves in the wholly hypothetical cases? Secondly, there are at any rate one or two Peripetatic illustrations of wholly hypothetical syllogisms which do not fit the second or the third interpretation. Thus the so-called documentum Ammonianum presents the following argument as a paradigm of wholly hypothetical inference:

1 Frede, Stoische Logik, p.9, says that ‘the Stoic truth-conditions for conditionals and disjunctions are so strong that examples of such propositions always seem to be true due to a certain relation between the terms, e.g. ‘‘If something is a man, he is a mortal’’, ‘‘If something is walking, then it is in motion’’. It is therefore not surprising that authors who, at least in logic, follow the Peripatetic tradition treat hypothetical arguments as if they depended on a relation between terms’. But one of the most common Stoic examples of a conditional proposition is ‘If it is day, it is light’, and that is not easily taken to exhibit the form ‘If a is F, a is G’. 2 One might also urge that the sentential interpretation is the obvious one, inasmuch as it does not suppose that Alexander’s formal account of the structure of a wholly hypothetical syllogism is elliptical. 1 Strictly speaking, that is not a special case of modus ponens; but see below, p.[313] n.3.

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If the sun is above the earth, then it is day If it is day, then it is light —————————— If the sun is above the earth, then it is light (See [Ammonius], in APr XI 2–3.) Again, an anonymous scholium on the Prior Analytics sketches a theory of ‘syllogisms from three conditional terms’ and then gives three concrete examples. The first is this: If it is day, it is light If it is light, visible things can be seen —————————— If it is day, visible things can be seen The other two examples are similar.* Thus at least one or two Peripatetic logicians implicitly endorse the first interpretation, construing ‘A’, ‘B’, ‘C’ as sentence letters.2 Not without hesitation I assume that the first interpretation represents Alexander’s — and Theophrastus’ — intention.3 If that is right, then we may

* Text and discussion in S. Bobzien, ‘A Greek parallel to Boethius’ de hypotheticis syllogismis ’, Mnemosyne 55, 2002, 285–300. 2 Boethius’ illustrations of hypothetical propositions in hyp syll are usually of the special form ‘If Fx, then Gx’. But they are not invariably or essentially of that form. He is happy to use the stock Stoic example, ‘si dies est, lux est ’ (e.g. I iii 4); his illustration of an ‘accidental’ hypothetical is ‘cum ignis calidus sit, caelum rotundum est ’ (I iii 5); and he shows what he means by a hypothetical in which ipsius consequentiae causam positio terminorum iacit by offering the sentence ‘si terrae fuerit obiectus, defectio lunae consequitur ’ (I iii 7). Note also Aristotle, APr B 57a36–b16, where the argument is illustrated by the sentences ‘If A is white, B is large’, ‘If A is not white, B is large’, etc. Theophrastus must have been aware that not all conditional sentences have the form ‘If Fx, then Gx’. 3 K. Du¨rr, The Propositional Logic of Boethius (Amsterdam, 1951), p.22, explicitly takes Boethius’ ‘est a ’, ‘est b ’, etc., to be propositional variables, thus construing Boethius in the same way as I construe Theophrastus. — T. Ebert, Dialektiker und fru¨he Stoiker bei Sextus Empiricus, Hypomnemata 95 (Go¨ttingen, 1991), p.17 n.16, rejects my arguments and denies that Theophrastus made any contribution to the founding of propositional logic. — Bobzien, ‘Wholly hypothetical syllogisms’, also rejects my arguments (p.122 n.80). Her paper offers a history of wholly hypothetical syllogistic, which may be roughly summarized as follows: Theophrastus’ syllogisms are ‘termlogical’; Alexander, at in APr 326–328, offers ‘an up-dated version of Theophrastus’ theory’ (p.116), which is still term-logical (pp.122–124); in the chief source of Boethius’ hyp syll the style is also term-logical; the earliest sentence-logical version of wholly hypothetical syllogistic is found in Alexander, at in APr 374.21–35 (pp.128–130); later Greek texts are predominantly sentencelogical. — It should be noted that the term-logical arguments in Alexander use propositions of the form ‘If anything is one of the As, then it is one of the Bs’, which is importantly different from ‘If anything is A, it is B’. — At in APr 330.29–30 Alexander says that according to Aristotle wholly hypothetical arguments, unlike genuine syllogisms, ‘do not prove any holding but only an implication [ PØA æø Z
Æ ØŒØŒ f Iººa IŒ º ıŁÆ 

]’. You might perhaps wonder how ‘If anything is one of the As, it is one of the Bs’ could fail to indicate a holding, given that ‘Each of the As is a B’, which is equivalent to it (if not synonymous with it), does indicate a holding.

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say that the wholly hypothetical arguments with which Theophrastus was concerned were of the general form: [295] (H) If A, then B If C, then D ————— If E, then F.4

XI Theophrastus developed an analytical account of syllogisms of form (H). The first step in his analysis is the observation that ‘here too [i.e. in hypothetical as well as in categorical syllogisms] there must be some middle term in virtue of which the premisses connect with one another’ (326.25–27). Philoponus repeats the point, speaking more exactly of a ‘middle hypothesis’ (in APr 243.17–21) rather than of a ‘middle term’.1 That amounts to the metatheorem that an inference of form (H) is valid only if the two premisses have a component in common. The metatheorem is worth stating a little more precisely. Since the component propositions of a hypothetical syllogism may be either affirmative or negative, we can reformulate (H) as: (H*) If + A, then + B If + C, then + D —————— If + E, then + F where ‘ + X’ indicates that ‘X’ may or may not be preceded by a negationoperator. Theophrastus’ metatheorem now amounts to this: if an argument of the form (H*) is valid, then either A ¼ C or A ¼ D or B ¼ C or B ¼ D. 4 Perhaps, to preserve full generality, we should rather write: (H*) If A1, then A2; If A2, then A3; ... ; If An-1, then An: therefore if B1, then B2 where n $ 2. For cases where n > 4 see below, p.[306]. Our texts never consider the possibility of cases in which n ¼ 2 (i.e. in which the hypothetical syllogism has a single premiss). Perhaps Theophrastus ruled that case out, just as Aristotle rules out categorical syllogisms with only one premiss (APr A 40b35–36). (‘But surely Theophrastus allows the validity of ‘‘If P, then Q; therefore, if not-Q, then not-P’’?’ Yes (see below, p.[299]). And Aristotle allows the validity of ‘Some A is B: therefore some B is A’. But those are ‘immediate inferences’, not syllogisms.) Chrysippus, too, rejected º ª Ø 
ºÆ Ø (e.g. Sextus, PH II 167). See, in general, J. Barnes, ‘Proof destroyed’, in M. Schofield, M.F. Burnyeat, and J. Barnes (eds), Doubt and Dogmatism (Oxford, 1980), pp.161–181, on pp.173–175 [reprinted in volume III]. 1 See also Boethius, hyp syll I ix 1.

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Alexander reports no argument for the metatheorem2 — perhaps Theophrastus took it to be self-evident.3 Any component of the premisses which is not a ‘middle’ [296] hypothesis we may call an ‘extreme’. By speaking of the middle hypothesis, Alexander implies that each syllogism contains a single middle hypothesis, and hence two extremes. Theophrastus probably also assumed that the two extremes were distinct from one another; and he certainly assumed that the extremes each appeared once in the conclusion. There is no direct textual evidence for those assumptions; but they are, I think, implicit in the Peripatetic treatment of wholly hypothetical syllogistic. They are best regarded as stipulative in nature: their function is to determine a special class of syllogisms within the general schema (H*).1 Let us use ‘M’ to designate the middle hypothesis, ‘E’ and ‘E*’ to designate the extremes. And let ‘IF [X, Y]’ be ambiguous between ‘If X, then Y’ and ‘If Y, then X’. Then Theophrastus’ wholly hypothetical syllogisms are arguments of the specific form: (H**)

IF [ + E, + M] IF [ + E*, + M] ————— IF [ + E, + E*].

2 In categorical syllogistic Aristotle offers an argument for the corresponding metatheorem that every valid inference must contain a middle term: APr A 40b30–41a20. Theophrastus might have translated that argument into the hypothetical mode. 3 Theophrastus’ metatheorem may seem not merely to be non-evident but actually to be false; but see below, p.[296] n.1. 1 Those assumptions exclude from the scope of wholly hypothetical syllogistic certain valid arguments of form (H*). Thus the assumption that there is just one middle hypothesis will rule out, e.g.: If A, then B; if B, then A: therefore, if A, then B. The assumption that the extremes are distinct will rule out, e.g.: If A, then B; if B, then A: therefore, if A, then A. (For similar assumptions implicit in Aristotle’s categorical syllogistic see P. Thom, The Syllogism (Munich, 1981), pp.27–29. There is a considerable ancient literature on the subject of ‘reduplicated’ propositions of the form ‘If A, then A’.) The assumption that only the extremes appear in the conclusion outlaws, e.g.: If A, then B; if A, then C: therefore, if not-C or not-B, then not-A. It also rules out: If A, then B; if A, then C: therefore, if A, then B and C — an argument which lacks a middle hypothesis (see above, p.[295] n.3).

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XII Alexander next remarks that the ‘middle term will be positioned three ways in pairings of this sort too’ (326.27–28). In categorical syllogistic, the three Aristotelian figures are determined by the ‘position’, or role, of the middle term:2 the middle term is either subject in one premiss and predicate in the other, or predicate in [297] both premisses, or subject in both premisses. The ‘position’ of the middle proposition in hypothetical premiss-pairings is similarly determined by its role as antecedent or consequent in the conditional premisses: it may be antecedent in one premiss and consequent in the other, or consequent in both premisses, or antecedent in both premisses. There are no other possibilities. The three possible pairings can be set down as follows: (P1) If + E, then + M; if + M, then + E* (P2) If + E, then + M; if + E*, then + M (P3) If + M, then + E; if + M, then + E* The three pairings determine the three possible ‘figures’ of wholly hypothetical syllogistic: a syllogism belongs to the first figure if its premisses have the structure (P1), and so on. Just as every categorical syllogism belongs to one of the three Aristotelian figures, so every wholly hypothetical syllogism belongs to one of the three Theophrastan figures.1 I have set down the three pairings in the order in which Alexander gives them. But Alexander notes that he has changed the original Theophrastan order: Alexander’s second figure was Theophrastus’ third, Alexander’s third was Theophrastus’ second (328.2–5). Alexander tentatively undertakes to discuss the question of the ordering ‘separately’ (328.6), but no such discussion survives. Philoponus follows Alexander’s order of the figures (in APr 302.15–22). Boethius follows Theophrastus.2 Neither author gives any hint that there is

2 For the notion of ‘position’ or ŁØ see G. Patzig, Aristotle’s Theory of the Syllogism (Dordrecht, 1968), pp.91–104. 1 There can be no fourth figure in hypothetical syllogistic — nor is there any room for a fourth figure in Aristotelian categorical syllogistic. The history of the fourth figure is the history of a muddle: the (stipulative) determination of the figures by way of the configurations of premisspairings establishes their number as three (see Thom, Syllogism, pp.24–27). 2 See hyp syll II ix 2; III i 1; iv 2. — And so too the anonymous scholium discussed by Bobzien, ‘A Greek parallel’.

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an alternative ordering; neither indicates that the matter is in the least controversial. The figures of wholly hypothetical syllogistic are also mentioned in the Didascalicus, an introduction to Plato’s thought ascribed to Alcinous by the manuscripts and to Albinus by several modern scholars.3 The Didascalicus notes that Plato uses all three figures of categorical syllogistic and then remarks that ‘we shall find hypothetical arguments propounded by him in many of his Books — and especially in the Parmenides ’ (vi [159.4–7]).* An illustration is produced: it belongs to the first figure, although the text does not [298] say so. Next: And in the second hypothetical figure, which most people call third (in which the common term is consequent for both extremes), he propounds the following argument... . And again in the third figure, called second by some, in which the common term is antecedent for both ... ([159.12–17])1

The Didascalicus thus adverts to the hypothetical figures casually, as though they were no less familiar than the categorical figures; it indicates that there was disagreement about the order of the figures — a disagreement which apparently involved several scholars; and it tacitly sides with the position favoured by Alexander. Albinus was active in about ad 150. If the Didascalicus is his work, then we have evidence for a dispute about the hypothetical figures before the time of Alexander. (We might reasonably guess that the disputants included Boethus and Ariston, participants in the Peripatetic revival of the first century bc who showed some interest in logic.3 If the Didascalicus is by the shadowy Alcinous, we can date neither it nor the dispute to which it refers.4) [299] 3 See C. Mazzarelli, ‘L’autore del Didaskalikos — l’Alcinoo dei manoscritti o il medioplatonico Albino?’, Rivista di filosofia neo-scolastica 72, 1980, 606–639; J. Whittaker (ed), Alcinoos: Enseignement des doctrines de Platon (Paris, 1990), pp.VII–XIII; J. Dillon, Alcinous: the Handbook of Platonism (Oxford, 1993), pp.ix–xiii. *  f b  ŁØŒ f K
 ºº E غ Ø æ 
Kæøø
ı  ÆP F, ºØÆ  K
fiH —Ææ
fiÅ  Ø  ı oæ Ø
i
º ª ı. 1 ŒÆa b e æ
 ŁØŒe
åBÆ, n ƒ ºE Ø æ
çÆ, ŒÆŁ n › Œ Ø
e ‹æ  Iç æ Ø  E ¼Œæ Ø ÆØ, oø Kæøfi A ... ŒÆd c
ŒÆd ŒÆa e æ
åBÆ, æ  Ø
ø
b æ
, ŒÆŁ n › Œ Ø
e ‹æ  Iç æø
ªEÆØ, ... — Alcinous’ first two illustrations come from the Parmenides, his third from the Phaedo. The surviving ancient commentaries on Parm and Pho do not, so far as I am aware, follow Alcinous and find wholly hypothetical syllogisms in Plato’s text. (Alcinous’ first example draws on Parm 137D: this text is analysed by Proclus, in Parm 1111.1–6, as a simple modus ponens argument.) 3 On Boethus and Ariston, see P. Moraux, Der Aristotelismus bei den Griechen I, Peripatoi 5 (Berlin, 1973), pp.164–169, 186–192. 4 The anonymous commentary on the Theaetetus has the following note on Tht 152BC:

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XIII Alexander discusses each of the three hypothetical figures in turn. He illustrates his first figure by the valid mood: (1) If A, then B If B, then C ————— If A, then C. And he observes that in the case of (1) ‘the conclusion can also be taken the other way about ... — the other way about not without qualification but including negation’ (326.37–327.1). Taking ‘If A, then C’ the other way about means converting it to ‘If C, then A’; taking it the other way about including negation means contraposing it to ‘If not-C, then not-A’. Thus Alexander recognizes, in addition to (1), the argument pattern: (2) If A, then B If B, then C ————— If not-C, then not-A. And he derives the validity of (2) from that of (1) by way of a rule of contraposition. Alexander gives no other illustrations of first-figure syllogisms. He considers no invalid moods. ‹Æ
Œ fiB ŒÆa e æ
åBÆ MæÅÆØ ÆPfiH › º ª · x Æ Œfiø çÆ
ÆØ,  ØÆFÆ ŒÆd Kd
ÆPfiH· ŒÆd x Æ çÆ
ÆØ,  ØÆFÆ ŒÆd ÆNŁ
ÆØ· K z
ı
ªÆØ x Æ ŒÆ  ÆNŁ
ÆØ,  ØÆFÆ ŒÆd Kd
ÆPfiH. (LXVI 11–22) (Text by G. Bastianini and D.N. Sedley, in Corpus dei papiri filosofici greci e latini III (Florence, 1995, pp.227–562). The first editors of the papyrus — H. Diels and W. Schubart, Anonymer Kommentar zu Platons Theaetet, Berliner Klassikertexte 2 (Berlin, 1905) — cited the Didascalicus and its references to the hypothetical figures. The date of the anonymous commentator is disputed. The papyrus itself is from the first half of the second century ad, and the first editors supposed that the work itself dated from the same period. But H. Tarrant urged a much earlier dating — the second half of the first century bc: ‘The date of anon. in Theaetetum ’, CQ 33, 1983, 161–187; and his thesis has been supported by Bastianini and Sedley, pp.254–246. For some reservations, see D.T. Runia, ‘Redrawing the map of early Middle Platonism: some comments on the Philonic evidence’, in A. Caquot, M. Hadas-Lebel, and J. Riaud (eds), Hellenica et Judaica (Leuven, 1986), pp.85–104 [¼ Exegesis and Philosophy: studies in Philo of Alexandria (Aldershot, 1990), chapter IX]). If the early dating is right, then it seems that a non-Theophrastan ordering of the hypothetical figures was current two centuries before Alexander. (And in any event, it seems that we have evidence for a non-Theophrastan ordering before the time of Alexander.) But that is a doubtful conclusion. The argument, as the commentator sets it down, is not explicitly hypothetical in form. Bastianini and Sedley suppose that ‘the third figure’ is the third figure of Aristotle’s categorical syllogistic (pp.550–551); and so too do Diels and Schubart, despite their citation of the Didascalicus. And perhaps they are right — though I confess that to me the hypothetical interpretation somehow seems more ‘natural’, or easier. (Of course, the argument is invalid, however it is formalized.)

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Turning to his second figure, Alexander reports that ‘the pairing is syllogistical if the consequent for the two antecedents is taken in contradictory fashion’ (327.7–8). That must represent the metatheorem that a premisspairing of form (P2) yields a conclusion by (H**) if and only if 2 it takes one or other of the forms: (Æ) If A, then C; if B, then not-C () If A, then not-C; if B, then C That observation is true, and Alexander truly remarks that in such cases ‘it will be concluded that if one of the antecedents holds, the other does not’. From (Æ) and (), then, we can produce four valid moods. Alexander contents himself with one: (3) If A, then C If B, then not-C ————— If A, then not-B. [300] (The schema of the mood is garbled in the manuscripts at 327.11–12, but the illustration at 327.12–13 proves that Alexander has mood (3) in mind.) The account of the third figure parallels that of the second. Alexander first remarks that premiss-pairings of the form (P3) yield a conclusion if and only if they take one of the forms: (ª) If A, then B; if not-A, then C () If not-A, then B; if A, then C He remarks that ‘it will be concluded that if one of the consequents does not hold, then the other does’ (327.17–18). He points to the two moods thereby generated from pairing (ª). He produces a concrete illustration of schema: (4) If A, then B If not-A, then C ————— If not-B, then C.2 2 At 327.7 Alexander’s ‘¼
’ is reasonably construed as implying equivalence: ‘if ’ is frequently so used in natural language. 2 Philoponus’ account of the second and third figures is puzzling. The published text reads: ª
ÆØ ºØ
æ
[sc åBÆ] ‹Æ
oø Yø· N e `, ŒÆd e ´· N c e ˆ, Pb e ´· N c e ` ¼æÆ, Pb e ˆ. › ø ŒÆd e æ
oø· N c e ´, Pb e `· N e ´, ŒÆd e ˆ· N c e ` ¼æÆ, Pb d H
ˆ. ı
Æe
b ŒÆd ŒÆŪ æØŒa ºÆE
Iç æÆ. (in APr 302.20–23) It is plain that Philoponus follows Alexander’s ordering of the hypothetical figures. But his two illustrations are both invalid. Now an invalid inference will serve just as well as a valid one to illustrate a figure — and Philoponus’ illustrations have the appropriate form. Yet it is difficult to avoid the suspicion that Philoponus supposes himself to have been producing valid illustrations (cf

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XIV Alexander does not claim to give an exhaustive account of the wholly hypothetical moods. He is content to characterize each of [301] the figures and to indicate one or two of the valid moods in each. As a matter of fact, in each figure there are four possible schemata for the first premiss and four for the second. (In the first figure they are: (1) If E, then M; If E, then not-M; If not-E, then M; If not-E, then not-M; (2) If M, then E*; If not-M, then E*; If M, then not-E*; If not-M, then not-E*.) Again, there are eight possible forms for the conclusion: If E, then E*; If E, then not-E*; If not-E, then E*; If notE, then not-E*; If E*, then E; If E*, then not-E*, If not-E*, then E; If not-E*, then not-E. Since there are three figures, there are 3  4  4  8 ¼ 384 moods. Of those 384 moods, forty-eight are valid.1 The fullest ancient treatment of wholly hypothetical syllogistic is found in Boethius. His de hypotheticis syllogismis 2 considers the three figures3 and p.[292]), a suspicion which is confirmed by the final note ‘
Æ
b Œº’. For Philoponus means, I take it, that in the third figure both elements in the conclusion may be affirmative. (In fact the syllogism ‘If not-A, then not-B; if A, then C: therefore, if B, then C’ is valid.) Hence we should paraphrase the note thus: ‘You can also by taking ... ’. It may be objected that ‘ºÆE
’ should refer to the premisses, so that Philoponus is alluding to the inference ‘If A, then B; if A, then C: therefore, if B, then C’. And that inference is invalid. But even if that uncharitable objection is correct, the final note still suggests that Philoponus imagines he is producing valid illustrations. Either the Greek text is badly corrupt or (more probably) Philoponus has made a logical howler. 1 Du¨rr, Boethius, p.52, observes that Boethius holds the premiss-pair ‘If A, then B; if A, then C’ to yield no conclusion. He then accuses Boethius of failing to see the validity of: If A, then B If A, then C ————— If A, then B and C. It is true that Boethius does not mention that inference. But it is not a wholly hypothetical syllogism as he and his Peripatetic predecessors understood the phrase, i.e. it is not an example of (H**). (See also above, p.[296] n.1). In a complete logic of conditionals (such as the Stoics perhaps tried to construct) inferences of that type have their place: the Peripatetics, however, make no claim to construct a complete logic of conditionals. 2 II ix 1–III vi 4: see Du¨rr, Boethius, pp.43–55; on Boethius’ logic, see also H. Chadwick, Boethius (Oxford, 1981), ch. 3; J. Barnes, ‘Boethius and the study of logic’, in M. Gibson (ed), Boethius (Oxford, 1981), pp.73–89 [reprinted below, pp.666–682]. 3 Boethius’ treatment of the first figure is odd, for his schemata are not, strictly speaking, instances of the form (H**). Thus in place of (1) he offers: (1*) (If A, then B) and (if B, then C) A —— C

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their constituent moods in a systematic [302] fashion: he describes the possible premiss-pairings and the possible conclusions; he determines the valid moods; he attempts to show, by formal proof or by counter-example, the invalidity of the invalid moods. In all he gives explicit and detailed attention to 192 of the 384 moods, and he comments summarily on a further 128.1 Boethius’ treatise is largely Peripatetic in content and in character. It is true that he claims originality for his work on the subject: hypothetical syllogistic, he says, is a study which I have found discussed briefly and confusedly by a very few Greek authors — and by no Latin authors at all. ... Aristotle wrote nothing on the matter. Theophrastus, a man of exhaustive learning, dealt only with the elements of the subject. Eudemus followed a broader path of study — yet even he seems as it were to have sown the seedbeds without seeing the fruit. (hyp syll I i 3)*

That is what Boethius says. But it is hard to believe his story, and it is likely that in hyp syll, as in his other logical writings, he is relying heavily In general, he conjoins the two hypothetical premisses of the Theophrastan syllogisms by the word ‘et ’ (but occasionally he omits to do so), and he supplies as an additional premiss the antecedent of Theophrastus’ hypothetical conclusion. His conclusions are then the consequents of the Theophrastan conclusions. He observes that (1*) and its congeners are ‘imperfect’ syllogisms, and says that ‘their proof is a demonstration through a syllogism’: the syllogisms in question are in fact (1) and its congeners (hyp syll II ix 4–5; cf 2). Thus Boethius’ first figure consists in fact of mixed hypothetical syllogisms, which he grounds on the wholly hypothetical syllogisms of the first figure. (Abelard, who follows Boethius closely, notices this point: see Petrus Abaelardus, Dialectica, ed L.M. de Rijk (Assen, 1956), p.517. But Abelard treats all the figures on the model of Boethius’ first figure.) In the second and third figures Boethius presents standard wholly hypothetical moods. (There are occasional traces of the first-figure style of treatment: III ii 6; iii 2; iv 6; vi 2.) Boethius gives no indication that he is aware of this lack of uniformity in his treatment: he purports to be giving a uniform account of wholly hypothetical syllogistic. The oddity is best explained by the hypothesis that Boethius made use of more than one immediate source (see below, n.2). Three further oddities in his treatment of the first figure point in the same direction. (i) The reference to the three figures at II ix 3 breaks the train of thought. (ii) The brief and unexplained allusions to ‘extra’ syllogisms at II x 7 and xi 1 suggest an idiosyncratic source for the account of the first figure. (iii) Sixty-four of the 128 moods of the first figure are wholly ignored (see below, n.1). 1 In the second and third figures Boethius lists the eight ‘equimodal’ premiss-pairings (i.e. the premiss-pairings in which the middle term is twice þ M or twice  M), and he observes that it is easy to show that none of them yields a valid syllogism (III iii 7–iv 1; ix 2–4); but he does not discuss the equimodal pairings individually. In the first figure he does not even mention the eight premisspairings which yield no valid syllogisms, and he thus ignores completely sixty-four moods. * quod igitur apud scriptores quidem Graecos perquam rarissimos strictim atque confuse, apud Latinos vero nullos repperi ... nihil est ab Aristotele conscriptum. Theophrastus vero, vir omnis doctrinae capax, rerum tantum summas exsequitur. Eudemus latiorem docendi graditur viam sed ita ut veluti quaedam seminaria sparsisse nullum tamen frugis videatur extulisse proventum. — See Barnes, ‘Theophrastus’, pp.560–562.

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on Greek sources.2 How far he introduced minor novelties we cannot yet [303] say.1 For my part, I am inclined to suppose that most of Boethius’ account was already in Theophrastus, and that Alexander was excerpting from a passage which Boethius reproduced, indirectly, in fuller form.2 However that may be, in Boethius’ hyp syll we possess a comprehensive account of wholly hypothetical syllogistic as the Peripatetics saw it.3 XV Having discussed the figures, Alexander turns to their ‘generation’.* Aristotle’s second and third categorical figures are generated from the first by conversion: similarly, Alexander’s second and third hypothetical figures are generated from the first by conversion. The point is trivial. The first categorical figure is determined by the pairing: AxB, BxC4

2 For Boethius’ sources, see Du¨rr, Boethius, pp.4–15; Obertello, Boezio, pp.15–66; G. Striker, ‘Zur Frage nach den Quellen von Boethius’ de hypotheticis syllogismis’, AGP 55, 1973, 70–75; M. Maro´th, ‘Die hypothetischen Syllogismen’, Acta Antiqua 27, 1979, 407–436; id, Ibn Sina und die peripatetische ‘Aussagenlogik’ (Budapest, 1989). — Some scholars may find it improper to accuse Boethius, as in effect I do, of a gross exaggeration, if not a downright lie, in his claim to originality. And they may observe that Quellenforschung, never a simple task, is peculiarly difficult in the case of formal logic, where, as the history of the subject shows, independent discoveries of the same facts are perfectly possible. Even if we had a text of Theophrastus which coincided in content with that of Boethius, we could not safely infer that Boethius had copied — at first or second hand — the earlier treatment: he might easily have hit upon it independently. The detailed study of Boethius’ style and method which is necessary for any serious Quellenforschung has not yet been carried out. But the preliminary work (by Striker and by Maro´th) strongly suggests that Boethius was basing himself on more than one Greek source. Perhaps I should add that there is nothing discreditable in that; nor does it imply that Boethius was a mere copyist. (See further Barnes, ‘Boethius’.) 1 Here again the Arabic commentators offer further intelligence: see Maro´th, ‘Hypothetischen Syllogismen’; Ibn Sina. 2 But I do not suppose that Boethius had a copy of Theophrastus: he reproduced Theophrastus at second or third hand, and by way of at least two distinct intermediary sources (see above, p.[301] n.3). 3 Boethius shows no interest in reducing hypothetical to categorical syllogisms; nor does he advert to the ‘analogies’ between the two types of syllogistic. (But Abelard does: Dialectica, pp.517–518, 522.) * Themistius says that neither Aristotle nor Theophrastus talked about the generation of the (categorical) figures: ad Max p.184 [¼ Theophrastus 94]. If he is right, then this part of Alexander’s account of wholly hypothetical syllogisms is an addition to what Theophrastus had left. 4 Here and hereafter I follow the convention established by Patzig, Aristotle’s Theory, p.296 n.2, whereby the predicate term precedes the subject term. Thus ‘AaB’ represents ‘A holds of every B’ or ‘Every B is A’.

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Conversion, in the present context, is the interchange of subject and predicate terms.5 Thus if we take the first-figure pairing and convert AxB we generate BxA, BxC [304] which is the pairing characteristic of the second categorical figure. By converting BxC we generate AxB, CxB which is the third figure. In hypothetical syllogistic, conversion is the interchange of consequent and antecedent. By converting the second premiss of the first-figure pairing If + E, then + M; if + M, then + E* we generate: If + E, then + M; if + E*, then + M which is Alexander’s second figure. Similarly, by converting ‘If + E, then þ M’ we generate: If + M, then + E; if + M, then + E* which is Alexander’s third figure.

XVI ‘Similarly, arguments in the second and third figures will be analysed into the first figure’ (327.33–34). This point, which Alexander does not elaborate, is not trivial; for analysis is a matter of reduction or derivation,1 and Alexander is claiming that the valid moods of the latter two figures can be derived from the valid moods of the first figure. The derivations are simple enough, requiring no more logical apparatus than a rule of contraposition (which we have already seen invoked within the first figure). Take syllogism (3), from the second figure. Its second premiss, ‘If B, then not-C’, gives by contraposition ‘If C, then not-B’; and that together with the first premiss, ‘If A, then C’, forms a first-figure 5 At in APr 29.23–27 Alexander distinguishes it from other sorts of conversion as I
Øæ çc H
‹æø
. Galen sensibly uses a separate term, ‘I
Ææ ç’, for the operation; and he warns against the danger of confusing I
Ææ ç with I
Øæ ç proper, or contraposition: inst log vi 3–4; simp med temp XI 500 (see J. Barnes, ‘Galen on logic and therapy’, in F. Kudlien and R.J. Durling (eds), Galen’s Method of Healing (Leiden, 1991), pp.50–102, on pp.81–84 [reprinted in volume III]. 1 For this sense of ‘I
ƺØ
’, in which it is a synonym of ‘I
ªØ
’, see in APr 7.25; cf, for example, APr A 50b33. (See above, p.[286] n.3.)

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pairing which yields the conclusion ‘If A, then not-B’.2 That derivation is given by Boethius (hyp syll III iv 3). His text contains many similar derivations.3 [305] Aristotle derives the valid moods of the second and third categorical figures from the valid moods of the first. Compared to Aristotle’s categorical derivations, the derivations required by hypothetical syllogistic are child’s play. Theophrastus’ account of wholly hypothetical syllogisms was clearly patterned on Aristotle’s account of categorical syllogistic. Theophrastus must surely have wondered if hypothetical logic allowed for the same sort of reductions as categorical logic. He can scarcely have avoided the correct answer: I suppose that the derivations we find in Boethius were discovered by Theophrastus.1

XVII ‘These, then, are the simple and primary so-called wholly hypothetical arguments. All the compound wholly hypothetical arguments will be shown to be constituted from them’ (328.1–2). Boethius offers as a type of compound hypothetical proposition the schema: If if A then B, then if C then D (see hyp syll I v 1). Compound hypothetical syllogisms may then have been those with compound hypothetical premisses — premisses in which the

2 More formally: (i) If A, then C Assumption (ii) If B, then not-C Assumption (iii) If C, then not-B (ii), Contraposition (iv) If A, then not-B (i), (ii), first-fig. syllog. 3 All of Boethius’ derivations rest upon the single application of a rule of contraposition which is, in effect, the following principle: From ‘If + A, then + B’, infer ‘If + B*, then + A*’ — where + X* is not-X if + X is X and X if + X is not-X. Usually his application of the principle is tacit; but sometimes he explicitly refers to it: III i 4, 6; ii 1, 2; 5; iv 5, 6, 7, 8; v 1, 2, 3, 4, 5, 6, 7; vi 1. Boethius never actually says that he is reducing second- and third-figure syllogisms to the first figure, but that is evidently what he is in fact doing (so, explicitly, Abelard, Dialectica, p.522). 1 What of reductions within the figures? Boethius does not consider them. Alexander, as we have seen, reduces (2) to (1) in the first figure. In fact all the valid hypothetical syllogisms can be reduced to syllogism (1). All that is required for a reduction is (i) the extended rule of contraposition (above, p.[304] n.3) and (ii) a rule of substitution: If (A) is a valid syllogism containing the component A, and (not-A) results from the uniform replacement in (A) of A by not-A, then (not-A) is valid.

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replacements for ‘A’ and ‘B’ in ‘If A, then B’, are themselves hypothetical propositions. It is of course true that any compound syllogisms of that sort are ‘constituted from’ — or are substitution instances of — the simple syllogisms we have been discussing. The Didascalicus, however, suggests another interpretation of compound hypotheticals. The passage in question offers three Platonic illustrations of hypothetical syllogisms, one from each figure. The text for the third figure is probably corrupt.2 The [306] first two illustrations present arguments of the following sorts: (5) If not-A, then either not-B or not-C or not-D If either not-B or not-C or not-D, then not-E If not-E, then not-F ———————— If not-A, then not-F. (6) If not-A, then not-B and not-C If D, then either B or C ————————— If not-A, then not-D. Argument (6) evidently supposes that ‘not-B and not-C’ is negated by ‘either B or C’. Given that supposition, the argument is a substitution instance of a third-figure hypothetical. Argument (5) is more interesting. It is a substitution instance of (7) If A, then B If B, then C If C, then D ————— If A, then D. And (7) is a compound hypothetical syllogism in a new sense: unlike the simple hypotheticals, it has more than two premisses. Plainly, (7) can be constituted from two simple first-figure hypotheticals. From the first two premisses of (7) we can infer, by argument (1), that if A, then C. From that conclusion and the third premiss of (7), argument (1) again yields the conclusion that if A, then D. It is possible that Alexander’s allusion to compound arguments is, or encompasses, a reference to syllogisms 2 didask vi [159. 4–19].—The received text cites two premisses (of the form ‘If not-A then B; if A then C’) and omits the conclusion: no doubt the text originally contained the conclusion — see Dillon, Alcinous, pp.81–83.

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like (7), and that he is claiming to be able to prove that all hypothetical syllogisms with a plurality of premisses can be reduced to sequences of twopremissed hypotheticals. We cannot be sure if that is his meaning, or if Theophrastus discussed such arguments. If the Didascalicus is by Albinus, then it seems probable that compound arguments like (7) had been noticed by Peripatetic logicians before Alexander.1 [307] XVIII A generous, but not wholly implausible, reconstruction of Theophrastus’ account of wholly hypothetical syllogisms would thus ascribe the following discoveries to him. He investigated inferences of the form (H**). He arranged them into three figures. Within each figure he discussed, systematically, the possible moods, singling out those which were valid. He asserted, if he did not prove, certain metatheorems about wholly hypothetical syllogistic. He showed that the second- and third-figure moods could be derived from the first figure. He produced some derivations within the figures. He may perhaps have said something about compound syllogisms. Modern logicians will not perhaps regard that achievement as particularly remarkable. Yet in its day it represented a definite extension of logical science beyond anything that is found in Aristotle.1 At the same time, it is clear that Theophrastus was relying upon his master’s work: Aristotle’s treatment of categorical syllogistic gave him a model and a pattern for his own treatment of wholly hypothetical syllogisms.

XIX Alexander discusses Theophrastus’ account of wholly hypothetical syllogisms in the context of the Peripatetic programme: ‘wholly hypothetical syllogisms will be thought not to be amenable to proof by selection’ (326.8–10) — are these arguments amenable to any other form of reduction? 1 Alexander does not mention the possibility of modal hypothetical syllogisms. Boethius does (hyp syll I viii 6–7); but he decides not to investigate them on the grounds that they are rarely used (I ix 3). 1 Wholly hypothetical syllogistic does not comprise the sum of Theophrastus’ achievement in non-categorical logic: see Barnes, ‘Theophrastus’, for further details (and for a brief argument against the tempting conclusion that Theophrastus the Peripatetic invented Stoic logic).

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Alexander first offers a suggestion of his own. ‘Perhaps these arguments are not syllogisms in the proper sense’ (326.12). The paragraph which that cautious sentence introduces has been widely misunderstood. Scholars have connected it with Alexander’s preceding explanation of Theophrastus’ phrase ‘in virtue of an analogy’. They have supposed Alexander to mean: ‘Perhaps Theophrastus called these arguments ‘‘arguments in virtue of an analogy’’ because they are not really syllogisms at all ... ’.2 That is mistaken. Alexander is introducing his own answer to the [308] question he posed at 326.8, a solution which will shortly be followed by Theophrastus’ answer to the same question.1 Alexander’s answer is this: ‘Wholly hypothetical syllogisms are not genuine syllogisms. For they do not prove anything. They do not prove anything because their conditional conclusions do not assert anything — they do not say that anything holds or does not hold. Hence the fact that they do not reduce to the categorical figures does not show that some syllogisms do not reduce to the categorical figures.’ Alexander says the same thing at 265.15–17. He thought that he was expressing Aristotle’s own view on the matter (see 390.18–19).2 That solution may seem to be a mere quibble. For surely the conclusion of a wholly hypothetical syllogism does assert something, namely a conditional proposition of the form ‘If P, then Q’. But in fact the standing of Alexander’s solution depends upon the nature of conditional sentences — or rather, upon the nature of those conditional sentences which feature in the conclusions of wholly hypothetical syllogisms.3 There are modern philosophers who have shared Alexander’s view that conditional sentences do not, in their primary use, express genuine propositions.4 Just as a conditional bet or a conditional promise is not (yet) a bet or a promise, so a conditional assertion is not (yet) 2 So, for example, H. Maier, Die Syllogistik des Aristoteles, I (Tu¨bingen, 1890), p.280; Bochen´ski, Logique de The´ophraste, p.116; W.C. and M. Kneale, The Development of Logic (Oxford, 1962), pp.110–111; Graeser, Logischen Fragmente, p.98; Repici, Logica di Teofrasto, p.148. 1 Philoponus understood Alexander correctly (in APr 302.12–15); but his own answer to the problem of reduction (302.23–32) is neither Alexander’s nor Theophrastus’. 2 cf, therefore, Striker, ‘Aristoteles u¨ber Syllogismen’; Lear, Aristotle. 3 Alexander’s solution also assumes that the conclusion of any syllogism must be a genuine assertion: were his implicit account of the nature of conditionals accepted, that assumption might be questioned. 4 See e.g. J.L. Mackie, Truth, Probability and Paradox (Oxford, 1973), p.93: ‘I want to offer, then, this general analysis: to say ‘If P, Q’ is to assert Q within the scope of the supposition that P ... abandons the claim that conditionals are in a strict sense statements, that they are in general any sort of descriptions that must either be fulfilled or be not fulfilled by the way things are, and hence that they are in general simply true or simply false.’

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an assertion. If the condition is fulfilled, the bet is on, the promise undertaken, the assertion made; but unless and until the condition is fulfilled, there is no bet, no promise, no assertion. Thus the conditional ‘conclusion’ of a hypothetical argument is not (yet) a genuine conclusion, and so the hypothetical argument is not (yet) a genuine syllogism. Whatever the merits of his own solution, Alexander appears to subscribe as well to the solution offered by Theophrastus. For ‘Theophrastus has proved in the first book of his Prior [309] Analytics ’1 that wholly hypothetical syllogisms ‘reduce, in another way, to the three figures’ of categorical syllogistic (326.21).2 By ‘another way’, Alexander means a way other than the ‘method of selection’.

XX At the heart of the Theophrastan method lies an analogy. Alexander repeatedly stresses that there are close analogies between hypothetical and categorical syllogistic: in each there are three figures, determined by the position of the middle term; in each the second and third figures are generated from the first; in each the syllogisms of the second and third figures analyse into those of the first. As it is in categorical syllogisms, so it is in wholly hypothetical syllogisms. The basis of that general analogy is a particular analogy to which Alexander draws attention at the beginning of his discussion. ‘Being a consequent or apodosis is analogous to being predicated, and being antecedent to being subject — for in a way it is subject for what is inferred from it’ (326.31–32).3 Consider the (indefinite) categorical proposition ‘Man is an animal’ in which animal is predicated of man, and compare it to the hypothetical proposition ‘If he is a man, he is an animal’. There is an analogy, Alexander maintains, between the relation in which man stands to animal in the categorical proposition and the relation in which he is a man stands to he is an animal in the hypothetical proposition. (And, trivially, there is an analogy between the converses of the two relations.) No doubt there is an analogy. It is presumably no accident that Aristotle occasionally used the word ‘follow’ as a synonym of ‘be predicated of ’ in his 1 cf Philoponus, in APr 302.5. 2 cf Philoponus, in APr 302.15; [Ammonius], in APr 67.24–30. 3 cf Philoponus, in APr 302.17–19.

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categorical syllogistic,4 or that the metalogical vocabularies of hypothetical and categorical syllogistic overlap. Modern sentence logicians are equally aware of the analogy. In his paper on ‘Logical Generality’, Frege observes that: We have various expressions for the same general thought: All men are mortal Every man is mortal If something is a man, it is mortal [310] The differences in the expression do not affect the thought itself. ... In the last mode of expression we have the form of the hypothetical compound sentence — a form we can hardly avoid using in other cases too ...1

Frege’s analysis of generality — which is the basis of his development of predicate logic — turns on his perception of an analogy between categorical and hypothetical sentences. Frege in effect appeals to the analogy to reduce categorical propositions to hypotheticals. Alexander had appealed to the same analogy with the opposite intention. XXI What is the weight of Alexander’s analogy? Precisely how is it supposed to ground a reduction of wholly hypothetical syllogisms to the three categorical figures? Alexander remarks that ‘the combinations in arguments, being similar in this way to those in the categorical figures, should reasonably reduce to them’ (327.20–21). He says no more: he does not actually carry out a reduction or even indicate how a reduction might be carried out; he merely says that it is reasonable, given the analogy, to suppose that a reduction is available.2

4 So ‘ ŁÆØ’ at, for example, APr A 43b3; 44b13; 56b20; ‘IŒ º ıŁE
’ at, for example, 26b2; 43b4 (see Alexander, in APr 55.10). 1 G. Frege, ‘Logical generality’, in his Posthumous Writings (Oxford, 1979), pp.258–262, on p.259. 2 Sommers’ investigations lead him to uphold ‘the parity and mutual independence of term and propositional logic’. He maintains that categorical and hypothetical propositions ‘must share a common structure’; he discovers ‘important formal affinities’ between the two; he talks of ‘isomorphism’ (Logic, p.160; see below, p.[317] n.3). The ‘affinities’ of Sommers are the ‘analogies’ of Alexander. But whereas Alexander takes his analogies as evidence that hypothetical syllogisms can be reduced to categoricals, Sommers eventually concludes that his affinities and isomorphisms indicate a common abstract structure of which hypothetical and categorical syllogisms are distinct specifications.

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Then did Theophrastus merely develop certain analogies and infer that a reduction was in principle possible? I think not.3 First, Alexander expressly says that ‘Theophrastus has proved’ that hypothetical syllogisms ‘reduce in another way’ to categorical syllogistic (326.21). That would be a remarkably inaccurate way of reporting the fact that Theophrastus had opined that some reduction was in principle possible. Secondly, there is reason to [311] think that the careful development of the analogy was the work of Alexander rather than of Theophrastus. Alexander’s ordering of the hypothetical figures is, as we have seen, different from Theophrastus’. And Alexander’s ordering was plainly chosen with an eye to the analogy with categorical syllogistic. The second categorical figure is determined by the pairing BxA, BxC in which the middle term, B, appears twice in predicate position. Given the analogy between predicate and consequent, the second hypothetical figure should be determined by the pairing If + E, then + M; if + E*, then + M. And that is indeed Alexander’s second figure. That point is entirely obvious. Had Theophrastus been concerned to stress the analogy between hypothetical and categorical syllogistic, he could hardly have failed to anticipate Alexander’s ordering of the hypothetical figures.1 The fact that he did not do so makes it unlikely that he was concerned to elaborate the Alexandrian analogies. It might be asked why Theophrastus originally chose the order he did. Some scholars have suggested that syllogisms in Theophrastus’ third (Alexander’s second) figure require more operations to reduce them to first-figure syllogisms than do syllogisms in Theophrastus’ second (Alexander’s third) figure. Theophrastus’ second figure is second because it is, so to speak, logically closer to the first figure.2 That is not a compelling argument, as a glance at Boethius’ derivations shows. All the reductions require one operation — an application of the extended principle of contraposition3 — and 3 Thus when Alexander says that hypothetical syllogisms ‘should reasonably reduce’ to the categorical figures, I take him to mean something like this: ‘In the light of the pervasive analogies I have drawn attention to, it is only reasonable that there should be a reduction of the sort which Theophrastus proved’. 1 Obertello, Boezio, p.143, wrongly says that Theophrastus follows the order of the Aristotelian figures. 2 So Bochen´ski, Logique de The´ophraste, p.115. 3 See above, p.[304] n.3.

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nothing more: second and third figures are on an equal footing, equally close to the first figure. I suspect that Theophrastus had no reason for choosing the order he did. The order of the second and third figures seemed logically indifferent to him, and no cunning thought lies behind his choice of arrangement.*

XXII I said that Frege perceived an analogy between categorical and hypothetical sentences. That is not quite accurate: Frege asserted [312] that certain categorical sentences express the very same thought as certain hypotheticals. He saw an identity, not merely an analogy, here. Frege’s view is an ancient one. It is found, for example, in the writings of Galen, who took a peculiar and justified pride in his knowledge of logic. Thus when he is criticizing an argument which draws on the two premisses ‘All pungent things produce hoarseness’ and ‘Oil produces hoarseness’, Galen comments that ‘from these it does not follow that oil is pungent, whether we make the premisses categorical or hypothetical’ (simp med temp XI 499).** He thus supposes that one and the same proposition can be ‘made’ either categorical or hypothetical. In other words, we may represent the thought expressed, informally, by the sentence ‘Oil produces hoarseness’ either by the categorical: Hoarseness-production holds of all oil or by the hypothetical: If it is oil, then it produces hoarseness. Consider, then, Alexander’s illustrative syllogism in the hypothetical mood (1). Its first premiss, If he is a man, then he is an animal could be taken as a formal version of the informal ‘Man is an animal’. And the same thought can be expressed equally well by the categorical: * But see Bobzien, ‘Wholly hypothetical syllogisms’, pp.104–105, 120–121; ead, ‘Why the order of the figures of the hypothetical syllogism was changed’, CQ 50, 2000, 247–251: the order was determined by ‘a superficial structural similarity’ between hypothetical and categorical premisses; and the order changed when categorical premisses came to be formulated no longer in the style ‘A holds of every B’ but rather in the style ‘Every B is A’. ** –Æ
b
ªaæ ‰ º ªÅÆØ e Œ

r
ÆØ Œæå
H, ‰ º ªÅÆØ b ŒÆd  hºÆØ
æåØ
Œæå
H· Iºº KŒ H
 ί
ø
 ø
P æÆ
ÆØ ÆŒ
H r
ÆØ  hºÆØ
, h ŒÆŪ æØŒa h  ŁØŒa H
 ØÅ
ø
a æ Ø.

Terms and sentences

467

Man holds of every animal. But then the first hypothetical mood reduces easily to categorical syllogistic. For the concrete illustration of (1) can be formalized indifferently as: (1H) If he is a man, he is an animal If he is an animal, he is a substance —————————————— If he is a man, he is a substance or as: (1C) Animal holds of every man Substance holds of every animal ———————————— Substance holds of every man. And (1C) is a categorical syllogism in Barbara. If that account can be generalized, then wholly [313] hypothetical syllogistic will reduce to categorical syllogistic in a strong sense: wholly hypothetical syllogisms will turn out on examination to be notational variants on categorical syllogisms.1 Whatever merits that reduction may possess, it was surely not the reduction Theophrastus had in mind.2 For neither Galen nor Frege supposes that conditional sentences in general express thoughts which are equally well expressed in categorical sentences. Rather, they both have in mind a particular form of conditional sentence, namely ‘If anything is F, it is G’.3 Thus the reduction will work, if at all, only for hypothetical syllogisms whose component propositions all have that particular form. In other words, it will only work if we construe Theophrastus’ wholly hypothetical syllogisms on what I earlier called the Boethian line. But that construe is probably wrong. Hence 1 Compare Galen’s remarks, inst log xix 1–3, on syllogisms ŒÆa æ ºÅłØ
. 2 At 326.32 Alexander says that the antecedent of a conditional ‘in a way ... is subject for what is inferred from it’. Without the qualifying phrase ‘in a way [ø]’ that sentence would constitute an endorsement of the Galen–Frege identity thesis; but we should not suppress the qualification (see below, p.[315] n.3). 3 Strictly speaking, propositions of the form If anything is F, it is G are not conditionals. They do not exhibit the general form ‘If A, then B’; they are not constructed by conjoining two propositions by way of the operator ‘If ... , then —’. Galen is nevertheless prepared to call such sentences ‘conditionals’ or ‘ı

Å
Æ’ (and so, I think, were most ancient logicians). Frege is more careful. When he says that ‘in the last mode of expression we have the form of the hypothetical compound sentence’ (see above, p.[310]), he does not mean that the last mode of expression is a hypothetical compound sentence: he means that it contains an embedded conditional, namely the open sentence ‘If x is a man, then x is mortal’.

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the reduction suggested by the Galen–Frege thesis is unlikely to have been Theophrastus’ reduction.4

XXIII Let us consider the desired reduction in more abstract terms. If hypothetical propositions are to be reduced to categorical form, then two — or perhaps three — requirements must be satisfied. First, the sentential operator ‘If ... , then —’ must somehow be translated into an operator on terms. Secondly, the sentential components of hypothetical propositions must somehow be reconstrued as terms.5 And perhaps, thirdly, the sentential operator [314] of negation must be displayed as a negation operator within term logic.1 The third requirement can be met in more ways than one. Categorical syllogistic has two modes of introducing negation into its propositions: you may use one of the two negative term-relations, E and O; and you may negate the terms themselves.2 Those two categorical modes of negativity will surely suffice for the reduction of sentential negation. 4 There is a further argument to that conclusion, derivable from the text of Boethius himself: see below, p.[316]. 5 See Leibniz, Generales inquisitiones de analysi notionum et veritatum, § 75 [in L. Couturat, Opuscules et Fragments ine´dits de Leibniz (Paris, 1903), p.377]: si, ut spero, possim concipere omnes propositiones instar terminorum, et hypotheticas instar categoricarum, et universaliter tractare omnes, miram ea res in mea characteristica et analysi notionum promittit facilitatem, eritque inventum maximi momenti. 1 Wholly hypothetical syllogistic does not consider negated conditionals of the form ‘It is not the case that (if A, then B)’. Negation only appears as an operator on the components of the hypothetical propositions. Thus we might decide to ignore the internal structure of the components of, say, ‘If not-A, then not-B’: we might be satisfied if we could reduce ‘not-A’ and ‘not-B’ to terms, and relinquish any hope of reflecting in categorical form the structural difference between ‘If not-A, then not-B’ and ‘If A, then B’. But in that case the principle of contraposition (above, p.[304] n.3) will have a peculiar status: it will have no formal perspicuity and will appear a puzzling oddity. For it will have the general form: ‘From ‘‘If A, then B’’ infer ‘‘If C, then D’’, when A, B, C, D, are of suchand-such a type’. 2 Negative terms are not treated in the formal development of Aristotle’s syllogistic in APr A 2–7. But they are extensively discussed in APr A 46, and elsewhere Aristotle propounds some rules concerning them. (See especially Int 20a20–23: if AaB, then AeB; if AiB, then AoB; Top B 113b15–26: if AaB, then BaA. See further Thom, Syllogism, pp.125–128.) Theophrastus is known to have evinced some interest in the matter: he coined the phrase ‘æ ÆØ ŒÆa ŁØ
’ (or ‘KŒ ÆŁø’) for propositions which predicate negative terms, a phrase which was generally adopted by the later Peripatetics (see Alexander, in APr 397.2–4 [¼ Theophrastus, 87A — other texts collected as 87B–F]). A theory of negative terms was extensively developed in later antiquity (see e.g. A.N. Prior, ‘The logic of negative terms in Boethius’, Franciscan Studies 13, 1953, 1–6): it is quite possible that the development originated with Theophrastus.

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The second requirement, similarly, can be satisfied by various devices.3 We might, for example, construct from any sentence ‘P’ the one-place predicate ‘ ... is such that P’. Like any one-place predicate, ‘ ... is such that P’ will generate a term. For example, from the sentence ‘Verdi is Italian’ we construct the [315] predicate ‘ ... is such that Verdi is Italian’, which generates the term being such that Verdi is Italian. I shall use bold type to mark such propositional terms: in general, P is the term (being such that P), produced from the sentence ‘P’. Plainly, P is true of any object just in case that object is such that P; and, trivially, an object is such that P just in case P. For example, Verdi is Italian is true of Berlioz just in case Berlioz is such that Verdi is Italian, and Berlioz is such that Verdi is Italian just in case Verdi is Italian.1 The first requirement demands the representation of the sentential connective ‘If ... , then —’ by means of some term relation. More precisely, ‘If ... , then —’ must in some fashion be reduced to the relation of term predication together with a sign of quantity. Within Aristotle’s syllogistic, that amounts to the requirement that the conditional connective be transmuted into one of the four relations A, E, I, and O.2 A moment’s thought shows that the only plausible candidate is A, the universal affirmative relation. Thus ‘If A, then B’ becomes ‘Everything such that A is a thing such that B’ or BaA.3 Consider, then, the first hypothetical mood, (1). That is reduced to:

3 What is needed is a function which makes terms from propositions in such a way that the semantic content of the term is the same as that of the proposition. Thus Sommers, who thinks that to every proposition there corresponds a (possible) state of affairs, introduces the term-forming function ‘[ ]’: where ‘p’ is a proposition, ‘[p]’ is the corresponding term — and ‘[p]’ should be read as ‘state of affairs in which p’ (Logic, p.153; cf Castaneda, ‘Leibniz’, p.491). 1 The term Verdi is Italian must seem highly artificial — a logician’s contrivance, analogous to the modem contrivance of treating a complete sentence as a zero-place predicate. The Peripatetics recognized the need to construct artificial terms, and they apparently felt no embarrassment at their contrived nature: see e.g. Aristotle’s discussion in APr A 36–38, and, for a good example, Alexander, in APr 344.9–355.12 (cf Thom, Syllogism, pp.75–76). For Leibniz, see Generales inquisitiones § 138 [Couturat, p.389]: nempe si propositio A est B consideretur ut terminus, ... oritur abstractum, nempe e A esse B, et si ex propositione A est B sequatur propositio C est D, tunc inde fit nova propositio talis: e A esse B est vel continet e C esse D, seu Beitas ipsius A continet Ceitatem ipsius D, seu Beitas ipsius A est Ceitas ipsius D. 2 I ignore two further possibilities, neither of which seems to me to repay close attention. (i) The translation of the conditional might involve a complex set of categorical propositions and a web of term relations. (ii) Categorical syllogistic might be enriched by the addition of further termconnectives — for example, by the connective m, where BmA is to be read as ‘B holds of most A’. 3 Thus, as Alexander says, the antecedent ‘in a way is subject for what is inferred from it’ (see above, p.[313] n.2). A, the term associated with the antecedent A, is subject for B, the term associated with the consequent B. So ‘in a way’ A is subject for B.

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(1*) BaA CaB —— CaA [316] which is a categorical syllogism in Barbara.1 Again, Alexander’s second illustration of first-figure hypothetical syllogisms becomes: (2*) BaA CaB —— == A a== C That schema is not to be found in Aristotle’s Analytics, since the Analytics does not discuss syllogisms with negative terms. But it is derivable from (1*), given that AaB entails == B a== A — an entailment which Aristotle states in the Topics.2 And so, it may seem, all the wholly hypothetical moods can be reduced to the categorical figures.

XXIV But there is a devastating objection to that reduction. It is implicit in a passage from Boethius’ discussion of hypothetical propositions. Boethius first observes that if someone asserts ‘Man is an animal’ and then again expresses it thus, ‘If he is a man, he is an animal’, those propositions are admittedly different in style but they do not seem to signify anything different. (hyp syll I i 6)*

But a little later he indicates that this seeming identity is misleading: In a categorical proposition we shall consider the fact that man himself is an animal, i.e. takes on the name of animal; in a hypothetical, we understand that should there be anything that is called a man, it is necessary for there to be something entitled animal. Thus the categorical proposition indicates that the thing it puts as subject takes on the name of the thing predicated; but the hypothetical proposition has this

1 cf Sommers, Logic, p.154. 2 See above, p.[314] n.2. * si quis ita proponat homo animal est, id si ita rursus enuntiet si homo est animal est, hae propositiones orationis quidem modo diversae sunt, rem vero non videntur significasse diversam.

Terms and sentences

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sense — something is the case if something else is (even if neither receives the name of the other). (hyp syll I ii 2)*

Boethius’ expression is muddled, but his intention is plain. The categorical proposition AaB implies that B ‘takes on the name’ of A; that is to say, it implies that there are Bs which are A. But the hypothetical proposition, ‘If it is B, it is A’, does not have that implication: it may be true even if there are no Bs at all. Boethius is adverting to a familiar — a notorious — feature of Aristotle’s syllogistic. Within Aristotle’s system AaB entails BiA (APr A 25a17–19), and BiA entails AiB (25a20–22); hence AaB entails AiB. (That last entailment is one of the so-called Laws of [317] Subalternation.1 Thus BaA entails BiA, and BiA says that some things such that A are such that B. But that is true only if there are some things such that A and some things such that B.2 BaA thus entails that A and that B. But evidently, ‘If A, then B’ entails neither that A nor that B. Hence BaA is not equivalent to ‘If A, then B’. The reduction fails.3

XXV If the old Peripatetic programme is unsuccessful, the underlying cause of its failure is to be found in the fact that AaB in Aristotle’s system entails AiB. It will perhaps cause little surprise that subalternation should prove the * in praedicativa igitur id spectabimus quod ipse homo animal sit, id est nomen in se suscipiat animalis, in conditionali vero illud intelligimus quod si fuerit aliqua res quae homo esse dicatur, necesse sit aliquam rem esse quae animal nuncupetur. itaque praedicativa propositio rem quam subicit praedicatae rei suscipere nomen declarat, conditionalis vero propositionis haec sententia est ut ita demum sit aliquid si fuerit alterum etiamsi neutrum alterius nomen excipiat. 1 The Laws of Subalternation can be stated as follows: (a) If AaB, then AiB (b) If AeB, then AoB Aristotle states both (a) and (b) in the Topics (A 109a3–6; cf ˆ; 119a34–36). He states (b), but not (a), in the Analytics (APr A 26b15–16). His syllogistic commits him to both laws. 2 BiA surely represents ‘A and B’ (see Sommers, Logic, p.153). ‘A and B’ is equivalent to ‘Not(not-A or not-B)’. ‘A or B’ is equivalent to ‘If not-A, then B’ (see Boethius, hyp syll III x 4). Thus: A and B ¼ Not-(if not-not-A, then not-B) ¼ Not-(BaA) ¼ BoA ¼ BiA. 3 Sommers, though generally friendly to the Peripatetic programme, eventually concludes that ‘the policy of analysing ‘‘if p then q’’ or ‘‘p and q’’ as a categorical subject–predicate proposition, even if it is a possible one, is not desirable ... . Our own standpoint is that ‘‘p and q’’ and ‘‘some A is B’’ ... share a common structure ... They are analytically autonomous and structurally isomorphous’ (Logic, p.159).

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stumbling-block; for that feature of Aristotle’s system has upset logicians of many persuasions and for many reasons. But categorical syllogistic is not irredeemably Aristotelian in that respect. Logicians have invented systems which, like Aristotle’s, are systems of term logic, but which, unlike Aristotle’s, do not countenance subalternation.4 One such system was devised by Franz Brentano.5 In Brentano’s syllogistic, the particular [318] propositions, AiB and AoB, retain their Aristotelian truthconditions: AiB is true just in case some B is A, and AoB is true just in case some B fails to be A. But the universal forms are given non-Aristotelian interpretations: AaB is held true just in case nothing both is B and fails to be A, and AeB is held true just in case nothing both is B and is A. Thus for Brentano, AaB may be true in circumstances in which AiB is false. For if nothing at all is B, AiB is false (for no B is A), but AaB is true (for nothing both is B and fails to be A). The syllogistic which results from these specifications is, of course, sensibly different from Aristotle’s: the moods Darapti and Felapton, for example, are not valid for Brentano.1 Given Brentano’s interpretation, the Peripatetic reduction is not open to the objection raised in the last section. For BaA does not imply BiA, so that it is, pro tanto, a possible construe of ‘If A, then B’. Indeed, it appears that wholly hypothetical syllogisms are generally reducible to Brentano’s categorical syllogistic. Thus we might conclude that the Theophrastan reduction can after all be carried out — provided that its categorical basis is sufficiently un-Aristotelian.

XXVI As far as we know, Theophrastus did not attempt to apply to mixed hypothetical syllogisms the method of reduction which he applied to wholly hypothetical syllogisms. There, we may suppose, he was content with 4 In Sommers’ TFL system, the Laws of Subalternation do not hold in any straightforward way. Sommers says that ‘in TFL‘‘every S is P’’ is defined as ‘‘no S is non-P’’ provided that ‘‘no S is P’’ is not also true’ (Logic, p.201). Later: ‘it appears that ‘‘every X is Y’’ is defined as equivalent to ‘‘no X is not-Y’’ only when it is the case that one of the two sub-contrary propositions, ‘‘some X is Y’’ or ‘‘some X is not-Y’’, is true’ (p.290). Otherwise, ‘every S is P’ is undefined. Sommers also holds analogously that ‘if p then q’ is undefined when ‘p’ is false (p.321 n.11). 5 See A.N. Prior, Formal Logic (Oxford, 19622), pp.166–168; id, The Doctrine of Propositions and Terms (London, 1976), pp.111–116. 1 See the formal discussion in Thom, Syllogism, pp.111–113, where Brentano’s system is an interpretation of Thom’s A f or B. (But strictly speaking it is Thom’s BN — see p.121 — which I advert to in the text: BN is B plus negative terms.)

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Aristotle’s ‘method of selection’. But it must seem desirable to extend the Theophrastan method to mixed cases; for if no extension is possible, the method will appear unpalatably ad hoc. The extension places a further requirement on reduction: we need some way of translating simple propositions into categorical form. Different translations can be dreamed up. We might, for example, determine to construe the simple proposition P by way of PiP.2 That is to say, ‘P’ is true just in case something which is such that P is such that P.3 Similarly, not-P may be construed as [319] PeP: ‘not-P’ is true just in case nothing is both such that P and such that P. Modus ponens inferences now assume the following form: BaA AiA —— BiB And modus tollens emerges as: BaA BeB —— AeA The second schema presents no difficulty: it is the categorical mood Camestres. The first schema is not itself a standard categorical mood; but it can be validated by way of the moods Darii and Datisi. From BaA and AiA infer BiA (by Darii ); from BaA and BiA, infer BiB (by Datisi ).

XXVII With ingenuity, further reductions of that sort can be effected. But it may well be wondered, at this point in the argument, what end such ingenuity might serve. Surely the end is no longer one of historical understanding; for it can hardly be supposed that the Brentanoesque manœuvres undertaken in the last sections have any direct historical application to the Peripatetic logicians. The later Peripatetics did not always follow Aristotle slavishly, and they 2 Sommers, Logic, p.156, translates ‘p’ by ‘a [p] obtains’: that could be represented as OiP, where O is the term obtaining. 3 Since BiA is equivalent to ‘A and B’ (above, p.[317] n.2), PiP is equivalent to ‘P and P’ — which is in turn equivalent to ‘P’.

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modified his system at various points;1 but they never considered a categorical syllogistic as un-Aristotelian as that of Brentano.2 Nor did they evince any interest in extending Theophrastus’ reductive techniques from wholly hypothetical to mixed hypothetical syllogisms.3 [320] If the further pursuit of reductions has no historical sense, it is presumably not without technical interest. Questions of reduction are after all at least semi-technical, and technical exercises have their own intrinsic value. But I believe that the debate between term logic and sentence logic involves more than purely technical issues. Formal logic may be studied for a variety of purposes and under a variety of aspects. Under one perfectly respectable aspect, it may be seen as an attempt to systematize and to explain informal patterns of inference — in other words, as an attempt to codify the laws of thought.1 There are several constraints on any such attempt. Formal logic must, for example, be adequate to ordinary inferential structures — it should, in principle, be capable of accounting for all the formally valid inferences which we normally recognize. It should also, I think, be homogeneous — that is to say, it should have a unified vocabulary, a cohesive set of rules, an organic structure: it should not be an aggregate of disjointed parts. Again, formal logic must be natural: it must reflect the underlying structure of ordinary discourse, and preserve and explain structural similarities and dissimilarities. These constraints are vague, perhaps essentially so; and they are flexible. But their general purport and their good sense are plain.

1 Theophrastus, who modified Aristotle’s categorical syllogistic in various ways, not all of them minor, did not question the Laws of Subalternation (see for example, Alexander, in APr 69.26– 70.21 [¼ Theophrastus 91A — other texts in 91B–E]): Theophrastus derives, for example, Baralipton from Barbara by converting the conclusion of Barbara, i.e. by inferring CiA from AaC). 2 But see Thom, Syllogism, p.128: ‘Aristotle’s logic of indefinite [i.e. negative] terms is ... fragmentary. ... The full system of which his system is a fragment is BCN, and hence a system with a Brentanoesque component.’ Perhaps we can say, after all, that the germs of a Brentanoesque system are present in Aristotle — though they did not sprout in the ancient Peripatetic tradition. 3 That is not, I think, an accidental fact about the history of Peripatetic logic, which was in a sense essentially piecemeal (see Barnes, ‘Theophrastus’). 1 There is nothing disreputable in the old notion that logic studies the laws of thought — provided that the notion is not mistaken for the thesis that formal logic is concerned with the ways in which men actually think, and provided, too, that we do not suppose such study to exhaust the scope of logical research. Aristotle was interested in codifying the laws of thought, but that was not his only reason for studying logic. The Topics show his interest in codification, the Analytics are, on the whole, less concerned with such matters: there, Aristotle’s primary desire is to develop a formal system suitable for the presentation of scientific proofs, and his enterprise is analogous to Frege’s in the Begriffsschrift.

Terms and sentences

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Sentence logic is often considered to do well on the score of adequacy and homogeneity, badly on the score of naturalness. Take, for example, the orthodox rendering in Fregean sentence logic of ‘Every A is B’. The formula ‘(8x)(Ax  Bx)’ imports a propositional connective into what is apparently a simple sentence. What is more, other sentences which apparently have the same structure as ‘Every A is B’ (for example, ‘Most As are B’), cannot be represented by any formula of the form ‘(Qx)(Ax  Bx)’. Term logic, on the other hand, or at least its Aristotelian core, is often granted a considerable degree of naturalness. But it is now [321] generally regarded as inadequate — that, indeed, is the chief reason for the modern triumph of sentence logic. The Peripatetic programme was an attempt to show that, despite various difficulties, term logic is after all an adequate logic. If the ancient Peripatetic programme was doomed to failure, it may still be worth investigating the feasibility of a neo-Peripatetic programme — a programme unconstrained by the particular features of Aristotelian term logic. For the modern term logician’s hope is to produce a system of logic which is adequate and homogeneous and which retains at least some of the naturalness of the Aristotelian core.1 Seen in that light, Theophrastus’ attempt to reduce wholly hypothetical syllogisms to categorical syllogistic is of more than technical interest. For it is an essay in the general philosophical problem of codifying the laws of thought. The essay may ultimately prove futile, and term logic may eventually be laid to rest. Sentence logic may justify its recent rude usurpation. Or perhaps, after the thesis of term logic and the antithesis of sentence logic, we should, in Hegelian vein, expect a new synthetic logic.2

APPENDIX: Alexander, in APr 325.31–328.7 Kpisje†xashai dº deE jad diekeEm posawHr oi“ Kn u“pohe† seyr.  F YæÅŒ
X Ø ‰ 
ø
H
K  Łø  Ø
ı
Æ
ø
fiB KŒŒØ
ށ H
‹æø
KŒº ªfiB  ŒÆd fiB Ø ÆPH
Ø (N ªaæ [35] KØŒ Ø Ø ŒÆd 1 The extended Brentanoesque term logic, however, contains several unnatural features: PiP is an odd rendering of ‘P’. Adequacy and naturalness are in tension, and a gain in one is often a loss in the other. 2 Rough versions of parts of this chapter were presented to seminars in Oxford, Go¨ttingen, and London. I am grateful to my audiences for numerous helpful criticisms. I owe particular thanks to Pamela Huby, Antony Lloyd, Mario Mignucci, and Timothy Smiley.

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Terms and sentences

477

¼æÆ e ` e ˆ. 
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Iæå 
ø
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· N ªaæ e ` e ˆ, N [323] e ´ P e ˆ, N ¼æÆ e ` P e ´, x
N ¼
Łæø  ÇfiH
, N ºŁ  P ÇfiH
, N ¼æÆ ¼
Łæø  P ºŁ . N  ª Ie  F ÆP F Iæå 
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ÆØ, x
N e ` e ´, N P e ` e ˆ· ı
ÆåŁÆØ ªaæ N c Łæ
H
ºÅª
ø
, Łæ
· N ªaæ P e ´ e ˆ, j N P e ˆ e ´, x
N ¼
Łæø  º ªØŒ
, N c ¼
Łæø  ¼º ª
, N c º ªØŒe
¼æÆ [20] ¼º ª
. ÆfiÅ  s
‹ ØÆØ Æƒ K
  Ø ıº ŒÆd ÆE K
 E ŒÆŪ æØŒ E åÆØ
sÆØ NŒ ø i
N KŒ
Æ I
ª Ø
 . ŒÆd Ø ª
Ø uæ K
 E ŒÆŪ æØŒ E fiH ıæfiø ŒÆd æfiø åÆØ Ie H
I
Øæ çH
H
K
fiH æfiø æ ø
, oø b ŒÆd K
  Ø· B b
ªaæ Ç
 I
ØæÆçÅ K
æfiø åÆØ æ ø e æ
[25] Kª
 åBÆ, B b Kº
 e æ
. Ø b  E  ŁØŒ E Çø
b
ıæÆ K
fi w ªEÆØ ›  , Kºø
b æÅ K
fi w ÆØ ›  · x


b
N e ` e ´ æÅ  ŒÆd Kºø
, b N e ´ e ˆ ıæÆ  ŒÆd Çø
. B b
s
N e ´ e ˆ I
ØæÆçÅ ÆØ K
Iç æÆØ e ´  

ήd c
åæÆ
[30] ºÆ

 F ŒÆŪ æ ı
ı, n YØ
 F ıæ ı åÆ · B b æÅ B N e ` e ´ I
ØæÆçÅ ÆØ ºØ
ª 

K
Iç æÆØ ÆE æ Ø e ´, n åæÆ
 ί
ı å
 ØE e æ
åBÆ. ÆæƺÅø b ŒÆd ƃ I
ƺØ H
K
fiH ıæfiø ŒÆd æfiø åÆØ N e æH

ÆØ åBÆ K y ŒÆd ƃ ª
Ø ÆP E uæ ŒÆd Kd H
ŒÆŪ æØŒH
. y Ø b
s
ƒ ±º E  ŒÆd æH Ø  ŁØŒ d [328] Ø ‹ºø
ºª 
Ø. KŒ  ø
b ŒÆd ƒ 
Ł Ø 
 c
ÆØ
å
 ØåŁ
ÆØ. ¨ çæÆ  
 Ø

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Logical Matters

K
fiH æ æfiø H

ƺıØŒH
æ
åBÆ ºªØ K
 E Ø ‹ºø
 ŁØŒ E r
ÆØ K
fiz Iæå 
ÆØ Ie  F ÆP F ƃ æ Ø ºª ıØ
N æÆ, æ
b K
fiz Ie [5] ØÆç æø
Iæå 
ÆØ ºª ıØ
N ÆP
. I
ƺØ
 E KŁŁÆ. Iººa æd b
 ø
Nfi Æ ŒÆØæe i
YÅ ºªØ
.
F
 KÆ
Ø
Kd c
B ºø KªÅØ
. 326.38 e ˆ addidi 327.11 e ˆ1 (Prantl)] e B codd 327.12 e ´ P e ˆ] e ˆ P e B codd

16 Logic and the dialecticians* ‘As Aristotle invented predicate logic, so Chrysippus invented propositional logic. Unlike Aristotle, Chrysippus had precursors; but his debt to them was slight — and in any event we know little or nothing about them.’ Thus, in caricature, an orthodoxy. Theo Ebert has urged heresy: Chrysippus, he suggests, owed a very great deal to his precursors — and we can itemize at least some parts of the debt. For substantial parts of Chrysippean logic were based, directly or indirectly, on the work of the Dialecticians (Diodorus Cronus, Philo, and their associates), and it is the Dialecticians whom we should honour as the inventors of propositional logic.1 In doing so we shall not merely pay just tribute to the eminent dead: we shall come to a better understanding of the course and career of logic itself. Ebert’s thesis is sustained by meticulous analyses of familiar texts, most of them in Sextus; and a thorough consideration of it would occupy a volume: here — OºªÆ Ie  ººH
— I voice two general doubts and sketch two particular disagreements. The first doubt concerns Ebert’s modus operandi. He takes a clutch of similar passages and scrutinizes their differences: the scrutiny indicates that the passages derive from different sources, for which it then suggests a chronology (and perhaps a clutch of authors). Thus Sextus, PH II 104–106, Sextus, M VIII 244–256 and [Galen], hist phil XIX 235–236 offer remarkably similar accounts of the theory of signs: the differences in detail persuade Ebert to ascribe M to Zeno the Stoic, PH to Cleanthes — and [Galen] to Philo. A minute illustration of the same method from a later context: at PH II 150 Sextus writes the phrase ‘d H
æe c
ı
ƪøªc
 F ıæÆ  åæÅØı
ø
’; in the parallel passage in M VIII 434, the corresponding clause is less cumbersome: ‘d H
ı
ƌ،H
ºÅø
’. Ebert invites us to * A review of T. Ebert, Dialektiker und fru¨he Stoiker bei Sextus Empiricus: Untersuchungen zur Entstehung der Aussagenlogik, Hypomnemata 95 (Go¨ttingen, 1991) originally published in CR 43, 1993, 304–306, under the title ‘A big, big D?’. (Some readers of which forgot that the answer to the question, is: ‘Well, hardly ever’.) 1 Ebert denies any share of honour to Theophrastus and the Peripatetics: pp.15–19, 73 n.8.

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Logical Matters

infer that Sextus used two different sources, the source of M being later than the source of PH in whose text it self-consciously replaced a periphrasis by a technical term (pp.138–139). Ebert thus supposes that Sextus preserves the characteristic flavour, and often the very wording, of his ultimate sources2 — ‘ultimate sources’, since (as Ebert allows: p.145) Sextus usually relied on secondary literature. Is it credible that the secondary literature was so scrupulous and scholarly? Ebert does not face the question until the end of his book — and then in a footnote. He suggests that Sextus depends on ‘a tradition which goes back ultimately to the circle of Arcesilaus’, or (as though it were the same thing) that Sextus read ‘texts from the Academy of Arcesilaus in which the doctrines of their contemporary philosophers from the Dialectical and Stoic Schools were preserved with a critical intent’ (p.307 n.2). One of these texts will have given a careful account of Zeno’s views on signs, another of Cleanthes’, a third of Philo’s. The three texts bobbed down the river of time: Sextus fished out first one and then another (without apparently noticing the difference); and [Galen] was left to fish out the third. Everything we know about the aims and methods of ancient doxography tells [305] against that romantic story. Moreover, the particular Sextan couplings on which Ebert relies have a thousand parallels. Karel Jana´cek has argued that we should not think of different sources — let alone of different ultimate sources. Rather, Sextus copied the same texts twice over, and the differences between PH and M mark changes in his own stylistic habits and intellectual concerns. Jana´cek’s hypothesis, which offers a uniform explanation for a common feature of Sextus’ writings, is preferable to Ebert’s hypothesis, which offers a special explanation for certain occurrences of the feature.3 A second doubt concerns the Dialecticians. Following David Sedley,* Ebert maintains that a group of philosophers, Diodorus at their centre, 2 In chapter 9 (which closely follows Brunschwig’s ‘Proof defined’, in M. Schofield, M.F. Burnyeat, and J. Barnes (eds), Doubt and Dogmatism (Oxford, 1980), pp.125–160), Ebert discerns the personalities of three different Stoics behind the three accounts of proof which Sextus reports. 3 Ebert takes Jana´cek to have established that PH is prior to M (p.300 n.10); but he does not reveal that Jana´cek’s arguments are based on a hypothesis which is incompatible with his own thesis. (See K. Jana´cek, Prolegomena to Sextus Empiricus (Olomouc, 1948); Sextus Empiricus’ Sceptical Methods (Prague, 1972); and the numerous articles collected in his Studien zu Sextus Empiricus, Diogenes Laertius und zur pyrrhonischen Skepsis, Beitra¨ge zur Altertumskunde 249 (Berlin, 2008); cf J. Barnes, ‘Diogenes Laertius XI 61–116: the philosophy of Pyrrhonism’, in W. Haase (ed), Aufstieg und Niedergang der ro¨mischen Welt II 36.6 (Berlin, 1992), pp.4241–4301, on pp.4268–4273 [reprinted in volume III]. * D.N. Sedley, ‘Diodorus Cronus and Hellenistic philosophy’, Proceedings of the Cambridge Philological Society 23, 1977, 74–120.

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were known in antiquity as ‘the Dialecticians’ — ‘ ƒ ˜ØƺŒØŒ ’;4 and he believes, further, that Sextus — and at least three other late authors5 — sometimes use the adjective ‘ØƺŒØŒ ’ as a School-name to refer to the group. Thus the classification of propositions at M VIII 93–129, which is standardly taken to be Stoic, should be ascribed to the Dialecticians; for Sextus himself attributes it to ƒ ØƺŒØŒ  — that is to say, to ƒ ˜ØƺŒØŒ  (VIII 93, 99, 108, 112, 118, 119: see p.84). The expression ‘ ˜ØƺŒØŒc ’ is indeed used, as a Schoolname, in four or five late and fuddled texts.* But the adjective ‘ØƺŒØŒ ’, which is of course enormously common in philosophical texts, is never, or hardly ever, used to indicate membership of a school or sect; and although the expression ‘ ƒ ØƺŒØŒ ’ might have been used to mean ‘the members of the Dialectical School’, it was so used at most once or twice.6 Certainly, ‘ ƒ 4 But (p.24 n.38) he does not commit himself to Sedley’s thesis that the Dialectical sect was an independent School (in some sense of the word) rather than a phase of the Megaric School, to which shadowy entity ante-Sedleians used to assign Diodorus and his chums. 5 [Galen], hist phil XIX 230 (see p.67); Apuleius, int xii [210.5] (see below); anon, proleg in Herm stat 295.21 Rabe (see p.196 n.17). * Diogenes Laertius, I 18; II 106; Suda, s.vv. ¯PŒºÅ, øŒæÅ; [Galen], hist phil XIX 230 (where the text is uncertain). The texts are not mutually consistent, some saying that ‘Dialectical’ was another name for the Megaric School (or perhaps for one phase in the career of the Megaric School), others distinguishing between the Dialectics and the Megarics. Against Sedley’s claim that the Dialectical School was a distinct entity see K. Do¨ring, ‘Gab es eine Dialektische Schule?’, Phronesis 34, 1989, 293–310 — to which there is a reply in T. Ebert, ‘In defence of the Dialectical School’, in F. Alesse, F. Arondaio, M.C. Dalfino, L. Simeoni, and E. Spinelli (eds), Anthropine Sophia: studi di filologia e storiografia filosofica in memoria di Gabriele Giannantoni (Naples, 2008), pp.275–293, on pp.277–283. — I should perhaps note that doubts about the Dialectical School do not touch the main contention of Sedley’s paper; for whether or not Diodorus was a Dialectician (and the issue is of marginal significance), he was surely a consummate dialectician. 6 Almost always a phrase of the form ‘X › ØƺŒØŒ ’ is parallel to e.g.‘X › ÞÅ æØŒ ’ rather than to e.g. ‘X › —æØÆÅØŒ ’. There are, I think, only two texts in which the adjective might plausibly be construed as an indication of school-membership. (1) Philip of Megara apud Diogenes Laertius, II 113: Ææa b
ªaæ ¨ çæ ı Åæ øæ
e
ŁøæÅÆØŒe
ŒÆd )Øƪ æÆ
e
ˆºH
IÆ
[sc ºø
], Ææ æØ º ı b  F ˚ıæÅ
ÆŒ F ˚ºÆæå
ŒÆd ØÆ
, Ie b H
ØƺŒØŒH
—ÆØ
Ø
b
I æØ ı, ˜çغ
b e
´  æØÆ
e
¯Pç
 ı ... Stilpo enticed some people away from Theophrastus, other from Aristotle the Cyrenaic and others from the ØƺŒØŒ  — in that context, you might take ‘ØƺŒØŒ ’ to indicate a sect rather than a profession, the Dialecticians rather than the logicians. But, pace Ebert, pp.24–25, it is not clear that the sentence has to be construed in that sense (and it is worth observing that in two places the received text is pretty certainly corrupt). (2) Seneca, ep cxvii 11–12: Peripateticis placet nihil interesse inter sapientiam et sapere cum in utrolibet eorum et alterum sit ... dialectici veteres ista distinguunt. ab illis divisio usque ad Stoicos venit. Is wisdom the same as being wise? Yes, say the Peripatetics. No, say the old dialectici and the Stoics after them. The context favours taking ‘dialectici ’ as a School-name, parallel to ‘Peripatetici ’ and

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ØƺŒØŒ ’ in Greek — like ‘dialectici ’ in Latin — is standardly used as a vague and general denotation: ‘The logicians say ... ’. Ebert acknowledges this last fact (see p.146); but he supposes that sometimes, and without any signal, Sextus — who himself never refers to the Dialectical School — intends his readers to fit out ‘˜ØƺŒØŒ ’ with a capital delta and to understand it as a School-name. I find that hard to believe. And so does Ebert. For, under textual pressure, he suggests that Sextus ‘was not clear’ about the use of the word as a School-name (p.146 n.13). Later, he conjectures that the word was marked, or at least intended, as a proper name in Sextus’ source but that Sextus either misconstrued it as a general term or else was unsure in what way to construe it.7 In either case, the answer to the question of whether Sextus intended to use the word as the proper name of the members of a School is No; and our texts of Sextus should print the word ‘ØƺŒØŒ ’ with a small delta. So far as I can see, that explodes Ebert’s chief reason for ascribing Sextan passages to the Dialecticians. The first particular disagreement bears on M VIII 93–129. In sections 112–119 Sextus retails the disagreement — ‘ØÆçø
Æ’ — among ƒ ØƺŒØŒ  over the analysis of conditional propositions. He names only Philo and Diodorus, both of whom were in fact Dialecticians with a capital delta.8 Hence — so Ebert argues — in sections 112, 118, and 119 we must print ‘˜ØƺŒØŒ ’ with a capital delta; and since we cannot suppose a change in use within sections 93–129, we must print the capital throughout and ascribe the whole section to the Dialecticians.9 The argument is frail, its consequences bizarre. The views of Philo and Diodorus [306] are offered as illustrations, ÆæƪÆÆ (118), of the Ø among ‘all the ØƺŒØŒ ’ (112). If 112 refers to the Dialecticians, we must infer that Sextus knew the views of other members of the Dialectical School — and we shall find the inference confirmed by Sextus’ remarks in 119. So according to Ebert, Dialecticians other than Diodorus and Philo held views on conditionals, views which were known to Sextus (although he chose not to report them) and which have left no trace elsewhere in the ancient literature. ‘Stoici ’. (Ebert does not adduce the passage. Rudolf Hirzel had noticed it — as I learn from G. Gabriel, K. Hu¨lser, and S. Schlotter, ‘Zur Miete bei Frege: Rudolf Hirzel und die Rezeption der stoischen Logik und Semantik in Jena’, History and Philosophy of Logic 30, 2009, 369–388, p.383 n.38.). But again, it is not clear that the sentence has to be taken in that sense — and I think that the presence of the word ‘veteres ’ tells rather against it. 7 See pp.181–182, where these two conjectures are presented as though they were the same. (The second is supported by a misreading of ‘Yø’ at PH II 245.) 8 Ebert takes this to be uncontroversial; myself, I am sceptical. 9 Except, it seems, for II 108–109, which form a Chrysippean pocket in the text: p.110 n.3.

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Again, if the dispute which Sextus describes in M VIII 110–119 is intrasectarian, then it is not the same dispute as the one to which he refers a little later in the same book, at M VIII 265 and which he rehearses in PH II 110–112. For this dispute is intersectarian, not intrasectarian — it is the dispute to which Cicero refers at Luc xlviii 143, and which he says took place among the dialectici. Sextus, of course, drops no hint that he knows of two different ØÆçø
ÆØ, one intersectarian and the other intrasectarian. That is not a reductio ad impossibile of Ebert’s interpretation — but it is a reductio ad absurdum. Plainly, M VIII 112–119 gives a truncated report of the debate rehearsed in PH and Luc. (No doubt Sextus’ source was a Stoic introduction to logic: M VIII 428.) Hence at M VIII 112 ƒ ØƺŒØŒ  are certainly ‘the logicians’ rather than ‘the Dialecticians’; and thus Sextus ascribes the classification of propositions in M VIII 93–129 not to a particular school but, vaguely enough, to logicians in general.10 The second particular disagreement touches Apuleius — I mean, the author of the de Interpretatione which ascribes itself to Apuleius. At int xii [209.9–210.11] he discusses a modus or rule for ‘reducing’ one syllogism to another. He ascribes the rule to the dialectici. Ebert claims that ‘beyond any doubt’ Apuleius is referring to the Dialecticians (p.213); so that the propositional logic which they invented was developed into an axiomatized system of inference-schemata (p.217). Apuleius gives first a Stoic formulation of the rule and then one which he ascribes to the veteres.11 He alleges that the rule was introduced in order to deal with certain impudent logicians. And he concludes with a comment, of which this is the syntactical skeleton: nec frustra constituerant dialectici eum verum modum esse ... ; at Stoici quidem ... , veteres vero ... [210.4–11]

Ebert maintains that the adversative particle ‘at ’ contrasts the Stoics with the dialectici, and that the contrast would be unintelligible unless the word ‘dialectici ’ picked out a School — that is to say, unless it meant ‘the Dialecticians’. But ‘at ’ does not contrast the Stoics with the dialectici. Rather, it indicates that the double-barrelled sentence (quidem/vero: 
=) which it introduces is a qualification of what has just been said: ‘The logicians were 10 So which logicians originated the classification? Sextus’ text gives no answer. But the orthodox view, that the Stoics are behind it all, is surely true. 11 209.14: the veteres are, of course, the older Peripatetics, pace p.214 n.2.

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quite right to introduce their rule; but whereas the Stoics formulated it thus and so, the Peripatetics preferred a different version’. In sum, Ebert has not yet converted me to his heresy.* Nonetheless, I give his book four hearty cheers. It is a rattling good read; it is lucid and open and honest; it essays sharp and subtle interpretations of texts which other scholars have merely blustered through; and in the course of discussing the theories of signs and of proof, the classification of types of proposition, the analyses of fallacies and sophisms, it often throws new and brilliant light on a portfolio of documents which are central to our understanding of Hellenistic logic. * He has replied to the chief parts of this review on pp.283–293 of his ‘Defence’.

17 The Logical Investigations of Chrysippus* In the third century bc the Stoics developed a subtle logical theory. The chief architect of the theory was Chrysippus, the third head of the School: if the gods had needed logic, it was said, then they would have used the logic of Chrysippus. There have been three giants in the history of logic: Aristotle, Chrysippus, Frege. Chrysippus wrote more than three hundred books on logical subjects.** All are lost. Lost too are all the works written by Chrysippus’ Stoic successors. Modern attempts to reconstruct the logic of Chrysippus rely on three kinds of evidence: first, there are a few fragments of Chrysippus’ own works, some preserved on papyrus and others surviving as quotations in later authors; secondly, there are various handbooks and summaries (Galen’s Institutio logica, the account of Stoic logic in Diogenes Laertius’ Lives of the Philosophers, ...); finally, there are critical and polemical notices and discussions in later texts (notably, in Alexander of Aphrodisias’ commentary on Aristotle’s Prior Analytics). The difficulties which any reconstruction must meet and overcome are daunting. Two of them are sometimes overlooked and deserve particular mention. There is first the problem of dating the information we find in our sources. Although Chrysippus was indisputably the greatest figure in the history of Stoic logic, so that we may properly speak of Chrysippean logic, nevertheless his followers were not mere parrots. We know that some of them in some respects modified his views or added to them.*** Thus when a [20] late source speaks of ‘the Stoics’ — and such indeterminate forms of reference * First published in Wissenschaftskolleg zu Berlin: Jahrbuch 1984/5 (Berlin, 1986), pp.19–29. — I have revised my text in the light of the new edition of the Logical Investigations published by Livia Marrone, ‘Le Questioni Logiche di Crisippo (PHerc 307)’, Cronache Ercolanesi 27, 1997, 83–100. ** See J. Barnes, ‘The catalogue of Chrysippus’ logical works’, in K.A. Algra, P.W. van der Horst, and D.T. Runia (eds), Polyhistor: studies in the history and historiography of ancient philosophy, Philosophia Antiqua 72 (Leiden, 1966), pp.169–184 [reprinted in volume IV]. *** See J. Barnes, Logic and the Imperial Stoa, Philosophia Antiqua 75 (Leiden, 1997).

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are the rule — it is often quite uncertain whether it is reporting old Chrysippean doctrine or adverting to some subsequent theory. In general scholars are, I think, too prone to ascribe things to Chrysippus. Secondly, there is a difficulty caused by the gross disparity between the handbooks and summaries on the one hand and the fragments and polemical discussions on the other. The summary material is introductory, superficial, uninspiring: the fragments and the discussions indicate something sophisticated, detailed, profound. Scholars tend to put too much emphasis on the summary material. And it is in any case hard to combine evidence of two such disparate types and to form a convincing story of Chrysippus’ original logic. It is as though our understanding of Shakespeare’s plays depended on a handful of quotations and a Guide to Hamlet of the sort produced for American college students.1 The surviving fragments of Chrysippus, spare and sparse though they are, thus assume an enormous importance. And the most important single fragment is the burnt and battered papyrus text of Chrysippus’ Logical Investigations — the ¸ ªØŒa ˘ÅÆÆ — which was discovered in the lava of Herculaneum. What follows here is a preliminary discussion of two columns of that invaluable and puzzling papyrus.2 I offer an English translation (which is in places very uncertain) and a brief commentary. The Appendix prints the Greek text which the translation presupposes; to the Appendix are relegated a few notes on matters of detail.

Translation col XII ... is shown in these cases too — for example ‘Go for a walk — otherwise sit down’. For everything falls under the command, [15] but it is not possible to 1 This chapter was the basis for a talk I gave at the Wissenschaftskolleg zu Berlin. I should like to record my profound gratitude to that splendid institution for electing me to a Fellowship, and for providing ideal conditions in which to work. I owed a particular debt to the Library, whose staff were unfailingly helpful, and to the Sekretariat, whose patience and skill were unsurpassable. It was peculiarly pleasant to have as colleagues in Berlin my friends Jacques Brunschwig, Michael Frede, and Gu¨nther Patzig. Our regular Tuesday meetings were always profitable and often thrilling. The topic of the present chapter was discussed on a Tuesday afternoon, and the chapter itself in effect reports a collaborative effort to understand a difficult text. 2 The papyrus — PHerc 307 — has been published more than once. In the first version of this chapter I relied principally on the text in K. Hu¨lser, Die Fragmente zur Dialektik der Stoiker (Konstanz, 1982) — that is to say, on the preliminary version of Hu¨lser’s collection. I was also able to use Livia Marrone, ‘Nuove letture nel PHerc. 307 (Questioni Logiche di Crisippo)’, Cronache

The Logical Investigations of Chrysippus

487

take any predicate in its place; for no object is shown by such a thing as ‘He is going for a walk — otherwise sitting down’. Now [20] we do use such things for the sake of brevity, in the place of (say) ‘Go for a walk, but if you don’t do that, sit down’, and (say) ‘Please do go for a walk, but if you don’t [25] do that, sit down’. And that can be extended still further — indeed, endlessly, like this: ‘Please do go for a walk — otherwise [30] sit — otherwise go to bed’, and ‘Please do this — otherwise that, otherwise that’, and so on ad libitum. But when we say that in this way we have commanded the whole thing (namely, to go for a walk — otherwise to sit down), nothing shows that what is commanded exists ...

col XIII ... commanded ‘Don’t do it’. But this, ‘Either to go for a walk or to sit down’, will be taken in two senses: in one way [10] we show that one of the items signified is not commanded; and the other is ‘This — otherwise this’. Then do we say this [15] — or should we say that here too what is commanded does indeed exist (in the way in which there is an assertible of the sort ‘Dio is going for a walk — otherwise sitting down’), and that [21] it is plausible that there is a predicate [20] of the sort: to go for a walk — otherwise to sit down; and if that is so, it is also plausible that things of this sort are commanded. Next, there is another [25] matter of this sort worth attention: perhaps those who command in the following way, ‘Take whichever of these’ and ‘Take any one of these’, command nothing. [30] For it is not possible to find any predicate which is being commanded, nor anything else of that sort at all. Similarly, if you say ‘Take [35] whichever of these’, in this way. In this way ... will be said to have taken or to take whichever of these ... saying that we seem to have commanded nothing ...

Commentary The Stoic theory of ºŒ or ‘sayables’ distinguished between complete and incomplete sayables. The latter included predicates or ŒÆŪ æÆÆ. The Ercolanesi 12, 1982, 13–18; and in addition, Livia Marrone had the kindness to answer a multitude of questions about disputed passages in the two columns which concerned me.

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former came in a variety of sorts — statements, questions, commands, oaths, etc. We find eight lists of complete ºŒ, no two of them identical, in the ancient sources.* The IøÆ or assertible was naturally the most important of the complete ºŒ from the point of view of logical theory; but there is evidence that the old Stoics also discussed the logical properties of other types of complete sayables — for example, oaths (Stobaeus, ecl I xxviii 18). The Greek grammarians took the Stoic list to be tantamount to a list of the grammatical moods. Modern scholars tend to treat it rather as a list of speechacts. Neither interpretation is correct; but it is not my intention here to discuss such general issues. Columns XII–XIII of Chrysippus’ Logical Investigations deal with a particular problem within the logic of commands. (The command, æ ƌ،
, features in most of the lists of complete ºŒ.) The problem is discussed in terms of the imperative utterance: (1) Go for a walk — otherwise sit down. But it is raised generally by all imperatives of the form ‘Do this — otherwise do that’. The end of column XIII introduces a new problem of the same sort. One of the problematical imperatives there is: (2) Take whichever of these. The problem raised by (2) is plainly stated. Sentence (2) appears to be a perfectly intelligible imperative; yet there is here no predicate which is commanded. The Stoics use the infinitive of the verb to designate a predicate, so that ‘to go for a walk’ designates the predicate I ascribe to Arthur when I say ‘Arthur is going for a walk’. No predicate is commanded in case (2) inasmuch as ‘to take whichever of these’ scarcely designates a predicate; and it scarcely designates a predicate inasmuch as the putative indicative sentence ‘He is taking whichever of these’ does not express an assertible. The problem with (1) is entirely analogous. Sentence (1) appears to be an intelligible imperative — it is in use (XII 20). Yet ‘it is not possible to take any predicate in its place’ (XII 15–17), since ‘to go for a walk — otherwise sit down’ does not seem to designate a predicate. And it does not seem to designate a predicate because ‘no object is shown by’ the [22] putative indicative sentence ‘He is going for a walk — otherwise sitting down’ (XII 17): the putative sentence fails to signify an ‘object’ or æAªÆ — that is to say, a ºŒ
— and hence cannot be used to assert anything, or indeed to say anything at all. * See D.M. Schenkeveld, ‘Stoic and Peripatetic kinds of speech act and the distinction of grammatical moods’, Mnemosyne 37, 1984, 291–353.

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That exposition of the problem raised by (1) and (2) implicitly invokes two semantic principles. First, it is assumed that if ‘!!(a)’ commands anything, then ‘to !’ designates a predicate. (I use ‘!P’ to represent the imperative sentence ‘Let it be the case that P’. ‘! you go for a walk’ represents ‘Go for a walk’.) The idea is surely this: a command is issued only if there is something which counts as obedience (or disobedience) to it; but to obey a command expressed by the imperative ‘!!(a)’ is to bring it about that a possesses the predicate designated by ‘to !’. Hence commands presuppose corresponding predicates: the predicate can indeed be said to be what is commanded. Secondly, it is assumed that if ‘to !’ designates a predicate, then the indicative sentence ‘!()’, where ‘’ is a demonstrative, expresses an assertible, an IøÆ. For every predicate there is a corresponding definite assertible. Both those semantic principles seem eminently reasonable. Given the two of them, the imperative sentences (1) and (2) must come to seem puzzling. Chrysippus’ solution to the puzzle raised by sentence (1) occupies the central portion of column XIII (lines 15–24): at all events, the phrase ‘or should we say that ... ’ appears intended to introduce his solution. Between the statement of the puzzle at XII 12–19 and the statement of its solution at XIII 15–24 occur two difficult sections of text. It is unfortunate that the end of column XII and the beginning of column XIII are both mutilated beyond repair. XII 20–36 divides at line 25. In the later section (‘And that can be extended ... ’), Chrysippus seems to be contemplating an extended version of the problematical sentence. As well as ‘! — otherwise +’ we may find ‘! — otherwise + — otherwise X ’, and so on without end. The last lines of the column, which are in an extremely fragmentary state, appear to say that, in the extended cases too, there is no appropriate predicate underlying the command. It is not clear what role the extended cases play in the argument — whether, for example, they require and receive a special solution, or whether they are thought somehow to help with the simple case. Nor are things much clearer with XII 20–25, where the text contains gaps at crucial points and where the grammar of what can be read is highly uncertain. Two different interpretations of the lines seem in principle to be possible. First, the point of the lines may simply be to insist that the imperative (1) has an intelligible use: it is a short form of the imperative: (1*) Go for a walk — but if you don’t do that, then sit down.

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[23] Since (1*) is surely acceptable, and (1) is merely a short version of (1*), then (1) — whatever the problems it raises — must be an intelligible imperative; and hence it must somehow command something. That interpretation is unexciting; but it fits the lines into their context and it may well be correct. It is perhaps nonetheless worth sketching a second and more ambitious interpretation; for whether it is right or wrong, it will help to bring out a further aspect of the puzzle. According to the second interpretation, then, we should see in XII 20–25 a proffered solution to the problem — a solution which may seem initially plausible but which Chrysippus himself does not accept. For if (1) is a short version of (1*), then we shall have dissolved the problem which (1) appears to raise if we can show that there is no genuine problem with (1*). And it might well be thought that (1*) is not at all problematical. Sentence (1*) is a complex complete ºŒ
. Its form is perhaps given by the schema: ‘(!!(a) and (if not !(a), then !+(a))’. That is a conjunction. It will be unproblematical if each of its conjuncts is unproblematical. The first conjunct is plainly unproblematical: it is a command, and what is commanded is the predicate designated by ‘to !’. The second conjunct is a conditional. Its first member is a statement which embeds the predicate designated by ‘to !’, and its second member commands the predicate designated by ‘to +’. There is no difficulty here in finding the predicates which legitimate sentence (1*) and show how it is intelligible. Thus it remains true that there is no (single) predicate commanded by (1). But that is because (1) is, so to speak, a disguised conjunction. Once the disguise is removed, the apparent difficulty disappears with it. That solution is certainly suggested by XII 20–25 even if the original point of the lines was not to advance it. It is not the solution which Chrysippus eventually gives. Why did Chrysippus reject it? (Or why would he have rejected it?) And should it be rejected? At XII 13–15 Chrysippus says that in the case of (1) ‘everything falls under the command’; and the remark is taken up at the end of the column, in lines 33–35. The remark contains two important points. First, the whole content of (1) must be construed as being commanded. In my notation (1) has the form ‘!P’, where the command indicator, ‘!’, governs the whole sentence. Secondly, sentence (1) expresses a single command — in my notation it will be expressed by means of a single indicator ‘!’. Neither of those things is true of sentence (1*), as I have construed it: it is neither a single command nor nothing but a command. Hence (1*), so construed, cannot express the same

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thing as (1), and the fact that (1*) is unproblematical does not show that (1) is unproblematical. The Chrysippean objection to the proposed solution seems correct. At all events, it is implausible to construe (1) as issuing two conjoined commands — the more so in that the two cannot be simultaneously obeyed. In fact (1*), construed as I have construed it, begins itself to look a little strange once you reflect upon it: if it is indeed synonymous with (1), then it must be [24] understood by way of our understanding of (1) and it cannot be used to shed light on (1). It is precisely the fact that (1) issues a single command which is puzzling: it surely does issue a single command — and yet there appears to be no single predicate which it commands. It might be thought that the problem with (1*) is that it is conjunctive. Perhaps we should replace it by a disjunctive imperative? That, it seems, is the suggestion which was canvassed at the beginning of column XIII. For line 14 (‘Then do we say this ... ’) refers back, with implicit dismissal, to a preceding attempt at solving the puzzle. From line 9 it is clear that the solution had something to do with the disjunctive imperative: (1**) Either go for a walk or sit down. The simplest way of discovering a putative solution in (1**) is this: sentence (1) may be taken to be synonymous with (1**); but (1**) is unproblematical; hence the apparent problem with (1) is only apparent. Sentence (1**) would clearly be unproblematical if it were construed as having the form ‘(!!(a)) or (!+(a))’, for then it would involve the two ordinary predicates designated by the infinitives ‘to !’ and ‘to +’. But I suppose that the sentence, rather than being a disjunction of commands, is the command of a disjunction: ‘!(!(a) or +(a))’. In that case, we shall have to countenance a disjunctive predicate — a predicate expressed by ‘to ! or +’. But presumably disjunctive predicates are not particularly puzzling items. Chrysippus’ rejection of this solution apparently involved the objection that (1**) will turn out to be ambiguous. One sense of (1**) is given at XIII 13: (1**) will have the sense of (1). The other sense is explained in the difficult lines 10–12: ‘we show that one of the items signified is not commanded’. If the sentence is taken to express the command of a disjunction, then the disjunction is exclusive; and so Chrysippus can characterize it, partially, by saying (I think) that in that sense one of the disjuncts is prohibited. (Why such a curious and partial characterization? — Because that brings out one of the differences between (1**), so construed, and (1).) If that is what Chrysippus had in mind, then it constitutes a rejection of the proposed solution of the puzzle. For if (1) is not synonymous with (1**)

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in its normal sense, then nothing is gained by appealing to a synonymy between the two sentences; for any puzzles which (1) may raise will equally be raised by (1**) when it is construed in its non-standard sense. And it is, of course, plain that (1) is not synonymous with (1**) in its normal disjunctive sense. For example, (1**) is equivalent to: Either sit down or go for a walk. But (1) does not convert in that way. Equivalently, you satisfy (1**) equally well by walking and by sitting down, but that is not the case with (1). It is in this difference between (1) and (1**) that the unity or singleness of (1) consists. There remains Chrysippus’ own suggested solution to the puzzle; and that solution emerges without ambiguity from the text. Sentence (1), he claims, does express a command (XIII 15–16, 22–24). There is a predicate designated by ‘to go for a walk — otherwise sit down’ (XIII 19–22). There is an assertible of the form ‘Dio is going for a walk — otherwise sitting down’ (XIII 17–19). It is clear how that does, in a way, constitute a solution to the problem raised by (1). The [25] problem arose because there seemed to be no predicate commanded by (1): Chrysippus now decides that there is an appropriate predicate — and the problem disappears. In another way, that seems to be no solution at all. Why does Chrysippus now think that there is a predicate of the relevant sort? How is it that the difficulties with such a putative predicate have suddenly vanished? For a solution, we need more than Chrysippus’ bland assertion that, after all, the predicate is there to be commanded. It is, of course, possible that Chrysippus said more in some lost part of the papyrus — perhaps after his discussion of the analogous problem which is raised at XIII 24. And it is tempting to think that XIII 15–24 contains a hint or two toward the content of Chrysippus’ hypothetical explanation of his solution. For strict1y speaking Chrysippus does not say that there is a predicate of the sort in question — he says that it is plausible that there is such a predicate. And, secondly, the assertible corresponding to the predicate is not a ‘definite’ assertible (‘This man is going for a walk — otherwise sitting down’) but what the Stoics called an ‘intermediate’ assertible (‘Dio is walking — otherwise sitting down’). Perhaps those two facts are hints? The second of the two semantic principles presupposed by the puzzle was this: if ‘to !’ designates a predicate, then the definite indicative sentence ‘!()’ can express an assertible. Perhaps Chrysippus is now hinting at a weaker version of this principle: if ‘to !’ designates a predicate, then some intermedi-

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ate indicative sentence of the form ‘!(a)’ — where ‘a’ is a proper name — can express an assertible. Now even though ‘This man is going for a walk — otherwise sitting down’ does not express anything, ‘Dio is going for a walk — otherwise sitting down’ does express an assertible, and hence it is at least plausible that the expression ‘to go for a walk — otherwise sit down’ designates a predicate. If that was Chrysippus’ line of thought, then he must have seen a crucial difference between the definite sentence: This man is going for a walk — otherwise sitting down and the intermediate sentence: Dio is going for a walk — otherwise sitting down. Now we know that the Stoics did think, correctly, that there were important logical differences between definite sentences of the form ‘!()’ and intermediate sentences of the form ‘!(a)’. But I have been unable to think of any sensible way of applying these differences to the case before us: I do not see how, in this particular case, the difference between definite and intermediate statements is, or could be thought to be, of any significance. If that is right, then the use of an intermediate sentence at XIII 18–19 is of no importance. And when Chrysippus says that it is plausible that a predicate of the required sort exists, he means just what he says: given that (1) seems to be an intelligible single command, then there surely must [26] somehow be a predicate which it commands. Perhaps it is difficult to see what that predicate could be; but exist it plausibly will. On this view of the text, Chrysippus is not really purporting to solve the puzzle raised by (1). The Logical Investigations are, after all, inquiries and not solutions, ÇÅÆÆ and not ºØ. The goal is the raising of problems and their discussion — it is not, save incidentally, their solution. Finally, it might be wondered if there is really a problem to be solved. Both Chrysippus’ semantical principles may well seem sound; yet together they raise a problem with sentence (1) only if we are inclined to believe that ‘to go for a walk — otherwise sit down’ does not designate a genuine predicate, and that ‘He is going for a walk — otherwise sitting down’ is not an intelligible indicative sentence. But why should we be suspicious about the predicate or the sentence? They are, perhaps, a little odd; but that is not to say that the predicate does not exist and the sentence signifies nothing. Well, I myself am inclined to think that Chrysippus was right to see a small puzzle. We might well think that we can understand an imperative sentence only if we grasp the conditions under which it is obeyed. (Obedience

Logical Matters

494

conditions stand to imperatives as truth conditions stand to indicatives.) Yet it is curiously difficult to express the obedience conditions of sentence (1) — and if it has no obedience conditions, then it is not a genuine command. If you address (1) to me and I go for a walk, then I have clearly obeyed you. And equally, if I do not go for a walk but sit down, I have obeyed you. But there is more to the command than just that. (Compare the advice: ‘Fly via Hannover — or better fly direct’. If I fly direct, I have taken your advice. So too if I fly via Hannover. Yet that is not all there is to the advice, and someone who knew only that it could be followed or obeyed in either of those two ways would not have understood it.) It is what the command has over and above these two features which gives it its unity and which constitutes the problem which Chrysippus addresses.

Appendix The text I print here is taken from Marrone, ‘Questioni Logiche ’. In one or two places I have ventured to prefer a different reading — such places are all indicated in the notes. In matters of punctuation I have gone my own way — in particular, I have not inserted any quotation marks into the Greek text. Square brackets indicate gaps in the papyrus: the letters enclosed by them have been divined by the various editors of the text. I have marked all these gaps, even where it is perfectly obvious what the filling must be: the result in ugly — but it gives some idea of the state of the papyrus. In fact, it gives an optimistic idea, on two counts. First, Marrone, like any other honest papyrologist, places a dot under a letter when the papyrus shows not a whole letter but only a fragment of one — I have not transcribed the dots. Secondly, the papyrus is very hard to make out, and different papyrologists will sometimes see different letters. So, for example, at XIII 6 I print ‘ Ø’. Marrone prints the same word — but with a dot under every letter. Cro¨nert thought he could see ‘[ ØE]
’ — he put a dot under the pi, and after a gap of four letters he saw the whole of a nu.

col XII K[
çÆ]
ÆØ ŒÆd [Kd]  ø
, ¥ [ ]
æØ[Ø N ]b  Œ[Ł ı]. 
-

The Logical Investigations of Chrysippus Æ b
ªaæ e c
æ Ø
Ø, ŒÆŪ æÅÆ 15 ]b ƺÆE
PŁ
KØ
. PŁb
ªaæ K
çÆ[
]Ø  Ø F æAªÆ y  []æØÆ]E N b  ŒŁÅÆØ. []Ø
ª åæÆ  ØÆÅ Øa  F 20 å ı x
æØØ Ka
b  F c KŒ ØfiB ŒŁ ı, ŒÆd x
ºØÆ b
-[27] æØØ, Ka
b  F c KŒ ØfiB ŒŁ ı: 
ÆÆ[Ø ]b  F25  ŒÆd Kd º
KŒ[]ؽ
ŁÆØ ŒÆd
c ˜Æ IŒÆÆÆø[] {N b } fiH [æ] fiø  fiø æØØ b [º]ØÆ, {YØŁØ} N [b]  ŒŁı, ŒÆd ºØÆ  Ø 30  F , N b   F N b   F , [Œ]Æd oø Kç › [
F
· ‹Æ
b oø ºª[ø[]
æ []Æå
ÆØ e ‹º
 F æØÆE
[N b 35  ŒÆŁBŁÆØ, Pb
çÆ
Ø [e ]r
ÆØ e æ Æ[ 

K]
YØ  E
[... ... ήd i
ºªø
‹[Ø ...

col XIII æ [[][Ł]ÆØ c  Ø: e b  [Ø] F [Ø]åH ÞÅ[Ł]ÆØ j ]æØÆ[E
] j [Œ]ÆŁB[]ŁÆØ, e [b
K][Ø]
 Ø F H
[ÅÆØ]
10 
ø
 ø
Ø K
çÆ[]
[ 
P æ ŁÆØ, [e b  Ø F  F N b   F :  []æ
F
ÆFÆ ºª[ 
j ÞÅ
ŒI
ÆFŁÆ r 15
Æ[Ø ]c e æ Æ 



495

496

Logical Matters ‹
æ 
Kd  Ø F IøÆ æØÆE ˜ø
N b c ŒŁÅÆØ, ŒÆd ŒÆŪ æÅÆ ØŁÆ
e
r
ÆØ  Ø F 20 æØÆE
N b  ŒÆŁBŁÆØ; N b  F ŒÆd æ ]ŁÆØ [ Ø] F ØŁÆ
e
r
ÆØ; a b ÆFÆ ŒÆd ¼ººÅ æ]Ø
KÆØ  [Ø]Æ- 25 Å·   ŒÆd ƒ oø æ 
 ‹ ıå  ø
ºÆ, ŒÆd › Ø
F
[] ø
ºÆ PŁb
æ  ıØ
. h ªaæ ŒÆŪ æÅÆ  K30 Ø
æE
e æ []Æ 

h’ ¼ºº  Ø F
PŁ
. › ø b ŒÆd i
oø YfiÅ › Ø
F
 ø
º
Æ
. hH b
e
35 ... ] I  F
ÆØ[ ........ ÞÅŁ]ÆØ [b]
› Ø
F
 ø
º]ÆE
j ºÆ

Ø
[ ... ºª[ ]
 PŁb
ç
Æ[ŁÆØ æ []Æå
ÆØ[ ..... 40

Notes XII 12: In the first eleven lines of the column a few words are decipherable; but they yield no continuous sense, and they do not — so far as I can see — help with the understanding of the following text. [28] 17: Livia Marrone takes ‘ PŁ
’ as subject and ‘ Ø F æAªÆ’ as object of ‘KçÆ
Ø’ (‘Nothing shows an object of such a sort as ... ’). But ‘ y  Œº’ is not a æAªÆ or ºŒ
. So I construe ‘ Ø F ’ as subject and ‘ PŁb
... æAªÆ’ as object of ‘KçÆ
Ø’ (which then has the sense of ‘ÅÆ
Ø’, as it often does in e.g. Apollonius Dyscolus); ‘ y  Œº’ is then in apposition to ‘ Ø F ’. That is anything but easy. Michael Frede wondered if ‘KçÆ
Ø’ can be taken in a middle sense (‘No such object as y  Œº reveals itself ’). However that may be, the general sense of the Greek is uncontroversial.

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497

20–21: Earlier editors printed: Øa [] F [å] ı  x
. I supposed that that was largely correct — but that the delta before ‘ x
’, which will not construe, was a scribal error. Marrone prints: Øa « F’» å ıÆ x
. She translates: ‘There exists in fact a linguistic usage which by way of ‘‘this’’ determines, for example, ... ’. I do not understand what that means; and I do not see what sense Marrone’s Greek (with or without the quotation marks) could bear. So I have stuck to my earlier text. I suppose — perhaps optimistically — that whatever Chrysippus may have written here, what he meant was that the problematical sentence either has or might be thought to have the same sense as the two sentences which follow. 25–30: Marrone prints this text: 
ÆÆØ b « F » ŒÆd Kd º
KŒ
ŁÆØ ŒÆd
c ˜Æ IŒÆÆÆø «N b » fiH æ fiø  fiø «æØØ b ºØÆ, YŁØ, N b  ŒŁı». She translates: ‘This’ can be extended still further, and ‘otherwise’, by God, can be extended endlessly, like this: ‘Above all go for a walk, come on, otherwise go to sleep’. I doubt if her Greek can mean that — or anything else; and in any event, it makes no sense in its own right. First, it is not the word ‘this’ which is to be extended but rather a command of the form ‘A otherwise B’. Secondly, the word ‘otherwise’ is not extended either — though it is repeated. Nor will it construe in any even semi-satisfactory way — hence I excise it from the text. Thirdly, ‘YŁØ’, which is apparently written as ‘ØØŁØ’, is out of place — I excise that too. Fourthly, the illustrative example — ‘Above all go for a walk ... ’ — is not an example of the sort Chrysippus has promised: we expect an example with more than two clauses. I therefore assume that a third clause has dropped from the text. The result is this: 
ÆÆØ b  F ŒÆd Kd º
KŒ
ŁÆØ ŒÆd
c ˜Æ IŒÆÆÆø fiH æ fiø  fiø æØØ b ºØÆ, N b  ŒŁ ı, N b  ŒŁı. That surely gives what Chrysippus ought to have written. Whether it gives what he wrote is perhaps less certain. 28–30: Earlier editors wrote ‘ŒÆŁØ’. Hence the first clause should be the indicative ‘æØÆE’ rather than the imperative ‘æØØ’. In the first version of this paper I therefore supposed that Chrysippus was providing a putative

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example of the sort of indicative to parallel the problematical imperative. Marrone has seen a space after ‘ŒÆŁı’, which she therefore prints as an imperative. 32: Marrone prints ‘Kç’ ‹ [Ø]
F
’, translating the clause thus: ‘and it can be thus extended in any way you like’. I doubt if her Greek can bear that sense; and in any event, the gap is better filled by a sigma than by an iota. 34: Marrone takes ‘e ‹º
’ adverbially (‘in general’): better, I think, to suppose that it picks up the point made in lines 13–15, namely that the whole of what is said is within the scope of the command. 36–38: I print Marrone’s text, which she translates thus: ‘nothing shows that the command is of the form ‘‘Go for a walk’’ ’. I can’t see how her text could mean that — or anything else. I have invented a semi-translation of the first words and left the last two or three in the dark. XIII 1–5: There are some traces of these lines, among them the word ‘[]ØåH’; but nothing helps with what follows. 15: Marrone translates ‘ŒI
ÆFŁÆ’ by ‘in this case too’; and that ought to be right. But then what is (or was) the other case — what are (or were) the other cases — in which we ought to say such-and-such? The question has no answer — and like a coward I have left the ‘ŒÆ’ untranslated. 30: Marrone prints ‘ŒÆŪ æÆØ’ rather than ‘ŒÆŪ æÅÆ ’ (that is to say,’ she takes the sequence of twelve letters to constitute one word rather than two). But I cannot see that the dative makes any sense (Marrone’s translation is at best dubious). 33: ‘Similarly, if ... ’: in my English translation, it appears to be not a similar case but exactly the same case. In Greek, the former case uses the aorist imperative, ‘ºÆ’, whereas the ‘similar’ case used the present, ‘ºÆ
’. Lines 37–38 show that that distinction is the pertinent one; but what could or should be made of it, I do not know. 35–40: The last lines of the column are too broken to be interpreted; but it seems that they may have said that, in the case of ‘Take whichever you like’, nothing can be commanded — that is to say, there seems to be no predicate in the neighbourhood.

18 —ØŁÆ
a ı

Å
Æ* I Chrysippus wrote a work in four books under the title ‘ØŁÆ
a ı
Å
Æ’ (Diogenes Laertius VII 190). It was addressed to Dioscurides, and it appears as the sixth and last item in the first section of the catalogue of Chrysippus’ logical works. No fragments of the work have survived, and there are no other ancient allusions to it. Speculation about its purpose and content is tempting but idle. We might think that at least we know what the title means. The word ‘ı
Å

’ is the standard Stoic term for ‘conditional’: a ı
Å

is a proposition of the form ‘If P, then Q’. And ‘ØŁÆ
’ means ‘plausible’ (or ‘persuasive’ or ‘convincing’). So ØŁÆ
a ı
Å
Æ are propositions which (1) are plausible and (2) have the form ‘If P, then Q’. Diocles of Magnesia offers as an illustrative example of what the Stoics called ‘ØŁÆ
a IØÆÆ’ or ‘plausible assertibles’ the proposition that if someone bore something, then she is its mother (Diogenes Laertius VII 75). Since that proposition is also — at any rate, on a Stoic view of the matter — a conditional, we might take it to be a paradigm ØŁÆ
e
ı
Å

. David Sedley has argued that such a simple-minded view of the thing is mistaken.1 He holds that ‘ØŁÆ
e
ı
Å

’ was a name given [454] by Chrysippus to a special kind of negated conjunction: a ØŁÆ
e
ı
Å

is a propositı´on of the form ‘It is not the case both that P and that not-Q’. An example might be: ‘It is not the case both that someone bore something and that she is not its mother’.2 * First published in Elenchos 6, 1985, 453–467: I have made a few modifications to the original text in the light of a commentary which David Sedley generously sent to me. 1 See ‘Diodorus Cronus and Hellenistic Philosophy’, Proceedings of the Cambridge Philological Society 23, 1977, 74–120 (on p.91 with notes 96 and 97); ‘On signs’, in J. Barnes, J. Brunschwig, M.F. Burnyeat, and M. Schofield (eds), Science and Speculation (Cambridge, 1982), pp.239–272, on pp.253–255); ‘The negated conjunction in Stoicism’, Elenchos 5, 1984, 311–316. I shall refer to these papers as Sedley [1], [2], and [3]. Sedley’s view has undergone certain modifications during the seven years covered by the three publications. 2 Chrysippus also wrote a book on º ªØŒa ı
Å
Æ (Diogenes Laertius, VII 194). In [2], p.253, Sedley contrasts º ªØŒa ı
Å
Æ with ØŁÆ
a ı
Å
Æ, and suggests that º ªØŒa ı
Å
Æ are genuine Chrysippean conditionals — propositions of the form ‘If P, then Q’ which are true if and

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Sedley’s suggestion is more than a matter of nomenclature. Conditionals and negated conjunctions are two of the three main types of complex proposition which figure in Chrysippean formal logic: any suggestion which touches upon them touches upon a central part of Stoic logic. Moreover, the suggestion has some bearing on the Stoic attitude to the so-called sorites argument; and, as recent studies have emphasized,3 that paradoxical argument was closely connected to central problems in Stoic epistemology. [455] I think that Sedley’s suggestion is both important and mistaken. This short paper belongs to the unlovely genre of negative polemic. I hope that the lustre of its opponent may justify its own somewhat dismal existence.

III The first difficulty with Sedley’s suggestion is this. If he is right, then no ØŁÆ
e
ı
Å

is a ı
Å

. For no ØŁÆ
e
ı
Å

has the form ‘If P, then Q’. In general, the Stoics defined compound propositions in terms of the connectives by means of which they are compounded. In particular: only if there is a conflict between the antecedent and the negation of the consequent. In [3], p.312 n.6, he finds confirmation for the suggestion in Alexander, fat 209.31–210.1. Alexander, adverting to a Stoic argument which he set out at 207.5–21, refers to IŒ º ıŁÆ ... ŒÆa e
º ª
. Sedley takes the phrase to mean ‘the implication according to reason’ or ‘the logical implication’, and hence to be equivalent to ‘º ªØŒe
ı
Å

’; but I am more inclined to take ‘ŒÆa e
º ª
’ in the sense of ‘according to their argument’ (so R.W. Sharples, Alexander of Aphrodisias on Fate (London, 1983), p.90). In any event, what might º ªØŒa ı
Å
Æ be? I mean, what is the sense of the adjective ‘º ªØŒ ’ there? The title in the catalogue reads like this: º ªØŒa ı
Å
Æ æe )Ø ŒæÅ
ŒÆd !غ ÆŁB N a æd º ªø
ŒÆd æ ø
. It occurs in the section devoted to º ª Ø and æ  Ø, and it is tempting to imagine that ‘º ªØŒ ’ is linked here to ‘º ª ’ in the sense of ‘argument’. Then you might guess that a ‘logical’ conditional is a conditional which corresponds to a (valid) argument, a conditional of the form ‘If P1 and P2 and ... and Pn, then Q’, where ‘P1, P2, ... , Pn: so Q’ is a valid argument. ‘Logical conditionals’ will then be Chrysippean conditionals, as Sedley contends (though not all Chrysippean conditionals will be logical conditionals). But that does not seem to me to be particularly pertinent to the question of ØŁÆ
a ı
Å
Æ: after all, the two titles ‘º ªØŒa ı
Å
Æ’ and ‘ØŁÆ
a ı
Å
Æ’ appear in two very different parts of the catalogue; the adjectives ‘º ªØŒ ’ and ‘ØŁÆ
’ normally indicate attributes of very different varieties; and there is no reason to think that the logical conditional and the plausible conditional together form an antithetical pair. 3 See J. Barnes, ‘Medicine, Experience and Logic’, in J. Barnes, J. Brunschwig, M.F. Burnyeat, and M. Schofield (eds), Science and Speculation (Cambridge, 1982), pp.24–68 [reprinted below, pp.538–581]; M.F. Burnyeat, ‘Gods and Heaps’, in M. Schofield and M.C. Nussbaum (eds), Language and Logos (Cambridge, 1982), pp.315–338.

—ØŁÆ
a ı

Å
Æ

501

Among non-simple propositions, ı
Å
Æ — as Chrysippus says in his Dialectics and Diogenes in his Art of Dialectic — are those which are compounded by means of the conditional connector ‘if’. This connector announces that the second follows from the first — e.g. If it is day, it is light. (Diogenes Laertius, VII 71)*

That rather ‘formalistic’ approach to logic was a notorious feature of the Stoic system: the Stoics were often criticized for it. In particular, they were criticized for failing to see that negated conjunctions of the form ‘It is not the case both that P and that not-Q’ were ‘really’ conditionals in disguise.4 If Sedley is right, the Stoics gave the name ‘ØŁÆ
e
ı
Å

’ to a type of proposition to which they notoriously refused the name ‘ı
Å

’. The expression ‘ØŁÆ
e
ı
Å

’ would be, in that respect, like the expression ‘Dutch courage’ or ‘Bombay duck’ — or, according to Alexander, the expression ‘ıºº ªØe  ŁØŒ ’. Such expressions are not absurd, nor even particularly surprising;** but they are not normal — and there is, on the face of it, no reason why the phrase ‘ØŁÆ
e
ı
Å

’ should be, or should have been taken by the Stoics to be, in that way abnormal. By the same token, if Sedley is right, then no ı
Å

which is ØŁÆ

is a ØŁÆ
e
ı
Å

; for no ı
Å

has the form ‘It is not the case both that P and that not-Q’.5 Diocles’ illustrative [456] ØŁÆ

is not a ØŁÆ
e
ı
Å

even though it is a ı
Å

. That is surely strange. * H
 På ±ºH
IØøø
ı
Å


KØ
, ‰ › æØ  K
ÆE ˜ØƺŒØŒÆE çÅØ ŒÆd ˜Ø ª
Å K
fiB ˜ØƺŒØŒfiB å
fiÅ, e ı
e Øa  F N ı
ÆØŒ F ı
 ı. KƪªººÆØ  › 
  y  IŒ º ıŁE
e æ
fiH æfiø, x
N æÆ K, çH KØ. 4 See e.g. Alexander, in APr 264.14–17; Galen, inst log iii 1; Boethius, hyp syll I iii 4; cf Porphyry, apud Ammonius, in Int 73.19–33. ** As David Sedley forcibly reminded me. 5 Sedley sometimes refers to propositions of the form ‘It is not the case both that P and that notQ’ as ‘material implications’. This technical term of modern propositional logic must be used with care. One way of defining material implication is this: a proposition is a material implication if and only if (1) it is of the form ‘C(P, Q)’, where ‘C( , )’ is a two-placed sentential connective, and (2) ‘C (P, Q)’ is true if and only if either P is false or Q is true. Then ‘It is not the case both that P and that not-Q’ is a material implication. On the so-called Philonian interpretation, a ı
Å

or proposition of the form ‘If P, then Q’ is true whenever either ‘P’ is false or ‘Q’ is true. According to Philo, then, ı
Å
Æ are something like material implications. (Only something like: the ‘whenever’ in Philo’s interpretation has a genuinely temporal sense, whereas temporal notions do not enter into the definition of the modern material implication.) There is evidence that the Stoics themselves sometimes used conditionals with the Philonian interpretation in mind. Sometimes, then, Stoic propositions of the form ‘If P, then Q’ will be something like material implications. But being a material implication is a semantic and not a syntactic property: it is a matter of truthconditions, not of logical structure or form. Thus to say that negated conjunctions of the relevant sort are material implications is to say nothing about their form, and the fact that Stoic ı
Å
Æ are sometimes material implications does nothı´ng to support the view that negated conjunctions are ı
Å
Æ.

502

Logical Matters IV

There is a second difficulty with Sedley’s view. If he is right, then not all ØŁÆ
a ı
Å
Æ are ØŁÆ
. For it is plain that not all propositions of the form ‘It is not the case both that P and that not-Q’ are plausible. Many such propositions are grossly implausible, and some such propositions are certain rather than (merely) plausible. In general, the plausibility of a proposition is not determined by its logical form: any logical form (unless it is tautological or self-contradictory) will have both plausible and non-plausible instances. The suggestion that the phrase ‘ØŁÆ
e
ı
Å

’ picks out propositions of a particular logical form implies that the Stoics were confused on this issue, that they supposed that the logical form of a proposition might determine its epistemic status. [457]

V Sedley is aware of these difficulties. I find his reaction to them unsatisfactory. In [2] he says: I mean that if one wanted to assert the truth of a conditional which one found convincing but recognised as fallible, the material formulation [i.e. the formulation by way of a negated conjunction] would be appropriate; not that the Stoics would recommend the same formulation for those pithana, like the hen–egg example, whose truth they did not wish to assert. (p.253 n.36)

In [3] he writes: The negated conjunction cannot, of course, in itself express the epistemological status of a proposition. But it is properly called pithanon insofar as it is the appropriate form for an implication which you recognise that you do not know for certain and which you, at most, feel justified in asserting. (p.312)

I take the point to be something like this: ‘If you think that it is plausible [ØŁÆ

] that if P then Q, then the appropriate thing for you to assert is that it is not the case both that P and that not-Q’. Now that is odd. After all, if you find it plausible that if P then Q, why not say ‘It’s plausible that if P then Q’?* Why say something of a different form * David Sedley has explained that, on his view, you produce a ØŁÆ
e
ı
Å

not when you think that it’s plausible that if P then Q but rather when you believe that it is not the case that if P then Q — but still think that ‘there are good grounds for not expecting Q to be false while P is true’.

—ØŁÆ
a ı

Å
Æ

503

and with a different sense? Perhaps it is true — the matter is a long-standing topic of dispute — that ‘If P, then Q’ is stronger than ‘It is not the case both that P and that not-Q’, that the former entails the latter and the latter does not entail the former. In that case, the latter will sometimes be assertible when the former is not, and it will sometimes be ‘appropriate’ to use the latter rather than the more adventurous former. But it is not the case that whenever it is plausible that if P then Q, then it is true that it is not the case both that P and that not-Q. If you think it plausible that if P then Q, it will always be appropriate to utter ‘It is plausible that if P then Q’, and it will only sometimes be appropriate to utter ‘It is not the case both that P and that not-Q’. In any case, even if Sedley’s point were true, that would constitute no reason for calling negated conjunctions ØŁÆ
a ı
Å
Æ. [458] Sedley is implicitly offering the Stoics the following line of thought: ‘We shall give to negated conjunctions of the form ‘‘It is not the case both that P and that notQ’’ the name ‘‘ØŁÆ
a ı
Å
Æ’’, even though none of them is a ı
Å

and not all of them are ØŁÆ
; and we shall do so because when you think that a (genuine) ı
Å

of the form ‘‘If P, then Q’’ is ØŁÆ

, then it is appropriate to express your conviction in the form ‘‘It is not the case both that P and that not-Q’’.’ It should be plain that that line of thought is a muddle. But surely, it will be said, Chrysippus himself sometimes counsels the use of negated conjunctions rather than conditionals? He does, and in one case we know why: Here Chrysippus becomes agitated. He hopes that the Chaldaeans and the rest of the seers are mistaken, and that they will not use conditionals (such as ‘If anyone is born at the rising of the dog-star, he will not die at sea’) to express their theorems — they should rather express them like this: ‘It is not the case both that someone was born at the rising of the dog-star and that he will die at sea’. (Cicero, fat viii 15)*

Chrysippus thought the Chaldaeans should abandon conditionals and use negated conjunctions in their place. He thought so not because he believed that the conditionals were plausible, but because he believed that they were false. Thus Chrysippus’ recommendation does not support, or illustrate, Sedley’s thesis — indeed it has nothing to do with ØŁÆ
a ı
Å
Æ. * hoc loco Chrysippus aestuans falli sperat Chaldaeos ceterosque divinos neque eos usuros esse conexionibus ut ita sua percepta pronuntient: si quis natus est oriente canicula is in mari non morietur, sed potius ita dicant: non et natus est quis oriente canicula et is in mari morietur.

504

Logical Matters VI

Thus far I have argued that if Sedley’s suggestion were right, then Chrysippus’ notion of ØŁÆ
a ı
Å
Æ would have been horribly muddled. It does not follow that Sedley is wrong, for great philosophers are capable of great muddles. But it does follow that we should not accept Sedley’s view unless there is good evidence in its favour. [459] In [1] Sedley expresses his view briefly and offers no argument for it. In [2] and [3] he produces the evidence. In [2] he characterizes his suggestion as a ‘tempting guess’; and he finds ‘strong support’ for it in a passage from Philodemus’ de signis.6 The passage reads (in Sedley’s translation) as follows: Again, when our people [the Epicureans] say that according to them even freaks bear resemblances in some respects ... he [Dionysius] says ... that ... it is sufficient, concerning these things and concerning those which derive from experience, for us to be convinced in accordance with probability, just as when we sail in summer we are convinced that we will arrive safely. (VII 26–38)*

The text is in parts uncertain, and the translation is also difficult; but I shall not question Sedley’s version. How does this passage bear upon ØŁÆ
a ı
Å
Æ? The English ‘for us to be convinced’ translates the Greek ‘ E
... EŁÆØ’. Sedley says that ‘there can be no doubt that the reference here is to the pithanon, or ‘‘convincing’’ ’. Thus the passage is about ØŁÆ
. Now the realm of the ØŁÆ

— of the convincing — is here determined by the phrase ‘concerning these things and those which derive from experience’. The two areas mentioned are, according to Sedley, ‘inference from similarity and inference from empirical generalisation about conjunctions of events’. But those inferences are expressed by way of conditional propositions. Thus the subject matter of the passage is convincing conditionals, ØŁÆ
a ı
Å
Æ. It is not clear to me that, because Philodemus uses the verb ‘EŁÆØ’, he must have ‘the pithanon’ in mind. The emphasis in the passage is on the phrase ‘ŒÆa c
Pº ªÆ
’: Dionysius says that in certain areas we should be 6 Sedley also refers to Sextus, M IX 139 ([2], p.253 n.36), and to Galen, PHP V 502 ([2], p.252 n.33). I can see nothing in either text which supports his suggestion. * Ø b ºª
[ø]
‰ ŒÆd a æÆÅ æ  [Ø
‹] ØÆ ŒÆ ÆP f ... çÅ[
... ] KÆæŒ[E
]

E
[ ] EŁÆØ æd [ ]ø[
ŒÆd ]æd H
KŒ B []æÆ ŒÆ[a c
] Pº ªÆ
n
æ 
‹Ø [ª
Å] ŁÆ º
 Łæ[ ı] K
IçƺE.

—ØŁÆ
a ı

Å
Æ

505

satisfied with probabilities [460] and need not strive for certainty. And although there may well be a close connexion between plausibility and probability, the two notions (as Sedley recognizes) are not identical. I doubt if the notion of plausibility is present in the Philodemus passage at all. Nor is it clear that Philodemus has conditional propositions in mind. I am far from sure what he does have in mind; but it seems to me that he is talking about the conclusions of certain inferences and about judgements based upon experience. The illustration bears this out. It is on grounds of probability that we are persuaded that in summer we shall travel safely; that is to say, the judgement ‘It’s safe to sail’ is probable. The judgement is not conditional. Thus even if we accept Sedley’s text and his translation, it is far from clear that the passage says anything about ØŁÆ
 or anything about ı
Å
Æ. But let us grant, for the sake of argument, that Sedley is right, and that Philodemus is here reporting a Stoic view to the effect that in certain areas we incline to accept, or ought to incline to accept, plausible conditional propositions. How does that support the suggestion that plausible conditionals are appropriately expressed in the form ‘It is not the case both that P and that not-Q’? Sedley observes that in some other Stoic passages negated conjunctions are used in connexion with inferences from similarity and in connexion with inferences based upon empirical generalization. The two areas which, according to Philodemus, are the location of ØŁÆ
a ı
Å
Æ are two of the areas in which the Stoics used negated conjunctions of the specified form. Sedley’s observation is correct; but the argument he constructs about it is unsound. The Philodemus passage contains no negated conjunctions. The passages where negated conjunctions appear never refer to ØŁÆ
a ı
Å
Æ. Suppose (what is not the case) that the Philodeman passage said explicitly that if someone utters ‘If you sail to Rhodes, you will arrive safely’, then he makes a ØŁÆ
e
ı
Å

. And suppose that some other text remarked that it is not the case both that you sail to Rhodes and that you do not arrive safely. It would be bizarre to infer from the conjunction of those two imaginary texts that the remark in the second passage gave an instance of a ØŁÆ
e
ı
Å

. Not only is there nothing to be said in favour of the inference: there is a [461] strong argument against it — for the sentence in the second passage is not a ı
Å

at all. I conclude that even if the passage from the de signis is construed (as it probably should not be) in the way most favourable to Sedley’s thesis, it does nothing to support that thesis.

506

Logical Matters VII

In [3] Sedley offers what he calls confirmation of his suggestion. The confirmation comes from a passage in the papyrus fragments of Chrysippus’ Logical Investigations. Sedley quotes two columns of text. I need only cite the beginning of the first column: It will be possible to progress convincingly from these also to those, saying that it is not the case that while there are plurals of plurals (by a kind of [extension] of what we have said in relation to singulars) there are not pasts of pasts and passives of passives, nor that while an infinite regress occurs in these it does not occur in those (and viceversa). (PHerc 307, I 15–26)7

(Again, I use Sedley’s translation.) The Greek for ‘progress convincingly’ is ‘ØŁÆ
H æ ºŁE
’, and the way in which we progress, or express our progression, involves negated conjunctions of the form ‘It is not the case both that P and that not-Q’. Chrysippus does not explicitly state that these negated conjunctions are ØŁÆ
 — it is our progress which is ØŁÆ

, not what we state as we progress. But it is surely quite reasonable to surmise, as Sedley tacitly does, that Chrysippus holds the negated conjunctions to be themselves plausible propositions. But the text does not say that these propositions are plausible conditionals. The propositions have the form of the negated conjunction. The text thus gives evidence that Chrysippus thought that there were plausible propositions of the form ‘It is not the case both that P [462] and that not-Q’. It gives no evidence that Chrysippus thought that such propositions were plausible conditionals. Unlike the Philodeman passage, this text is wholly clear in its import. And it is wholly clear that it says nothing whatsoever about conditionals.

VIII I conclude that, in the present state of scholarship, we have no reason to accept Sedley’s view of ØŁÆ
a ı
Å
Æ. New texts, or new readings of old 7 Ie  ø
[b] ŒÆd æe KŒE
Æ ÆØ ØŁÆ
H æ ºŁE
, ºª
Æ c ºÅŁı
ØŒa b
º[ÅŁı
،]H
r
ÆØ, æ 
Ø
[a.].ª . . . H
æe a 
ØŒa [NæÅ]
ø
, ÆæºÅºıŁ Æ b ÆæºÅºıŁ ø
c r
ÆØ ŒÆd oØÆ ø
, Å K[d]  ø
b
c
I[]ØæÆ
ª
ŁÆØ, K KŒ
ø
’ ¼æÆ , ŒÆd [ h]ƺØ
. — I cite the text as Sedley cited it. The later edition by Livia Marrone (‘Le Questioni Logiche di Crisippo (PHerc 307)’, Cronache Ercolanesi 27, 1997, 83–100) reads ‘æ 
Ø
[Ie º] ªø
H
’ at lines 19–20, and replaces the last word by ‘I
[]ƺØ
’.

—ØŁÆ
a ı

Å
Æ

507

texts, may always appear; and we cannot rule out a priori that such texts may in the end provide evidence for Sedley’s thesis. But as things stand there is none. And since the thesis involves ascribing a great deal of confusion to Chrysippus, we should reject it, and return to the simple-minded view that ØŁÆ
a ı
Å
Æ are plausible conditionals.

IX As Sedley notes, the Stoics tended to formulate sorites arguments by way of negated conjunctions rather than by way of conditionals. They would write: (A) One is few. It is not the case both that one is few and that two are not few. It is not the case both that two are few and that three are not few ... rather than (B) One is few If one is few, then two are few. If two are few, then three are few. ... [463] Why did they prefer form (A) to form (B)? Sedley rejects an answer I once suggested, and offers two answers of his own. In [3] he writes that ‘J. Barnes ... suggests that the negated conjunction was chosen as the stronger form’ (p.311). On the contrary, I suggested that the negated conjunction was chosen as the weaker form. (It is, of course, the weaker form — if either form is weaker than the other.) I argued that the Stoics used the weaker form for the premisses of the sorites argument in order to present the argument in its strongest possible form. Because the premisses of (A) are weaker than the premisses of (B), argument (A) is stronger than argument (B): anything which rebuts (A) will rebut (B), but not vice versa.8 In [2] Sedley understood me aright, and offered three counterarguments against my view (p.255 n.41). (1) ‘This formulation [i.e. (A)] of the sorites is used only by the Stoics, who hold the argument fallacious, and never by Carneades, who treats it as valid and therefore has something to gain from a dialectically more resilient version’. — There are several things which might 8 On the assumption that both arguments are valid, so that if they are to be rejected then one or more of their premisses must be rejected.

508

Logical Matters

be disputed there, but the chief point to be made is this: the Stoics have an excellent reason for putting the sorites in ‘a dialectically more resilient version’. In general, any philosopher who is worried by a paradoxical argument should consider the strongest version of the argument — otherwise his attempt to deal with the paradox will not be successful. (2) ‘What ground would the Stoics offer for holding that ‘‘not (both p and not-q)’’? Either that ‘‘if p, q’’, in which case there is no gain in stating this as a supplementary premiss rather than incorporating it directly into each step. Or, as I hold, some weaker ground than the strict conditional, in which case the ‘‘if ’’ formulation is not available to them anyhow.’ — That is not to the point. The Stoics must solve the paradox. For them, then, the question is not about grounds for accepting the premisses but about grounds for rejecting them. Hence they need to consider the weakest premisses which will give rise to the paradox. (3) ‘If they saw negated conjunction as dialectically more [464] powerful than their regular conditional, why did they not use it more widely?’ — I did not say that they thought negated conjunctions were ‘dialectically more powerful’ than conditionals. I said that the sorites is more daunting in form (A) than in form (B). Whether negated conjunctions should be used on similar grounds elsewhere is an open question: Sedley does not suggest any contexts in which they should be used and were not.

X The first of Sedley’s two9 reasons for the Stoic preference for (A) is this: ‘The justification of each premiss [sc. in form (A)] must be considered on its own merits, there being no repeatedly applicable universal principle that ‘‘n is few’’ entails ‘‘n þ 1 is few’’.’10 — As Sedley’s own formulation shows, that is rather confused. The availability of a suitable universal principle does not depend on the logical form of the premisses in a sorites. If the premisses 9 In [2], p.253, Sedley might appear to be offering a third reason when he says that ‘the point of the weaker formulation is to allow for the fact, not that there are exceptions, but at most that there could in theory be exceptions’. Sedley holds (wrongly, I think — but that is another story) that Chrysippean conditionals are ‘strict implications’. Then a Chrysippean ‘If P, then Q’ will be equivalent to ‘Necessarily it is not the case both that P and that not-Q’. And so ‘It is not the case both that P and that not-Q’ will be, as it were, ‘If P, then Q’ minus the necessity. That, I take it, is what Sedley means. If so, then when he says that this is ‘the point’ of the weaker formulation, he can hardly mean that this is the reason why the weaker formulation is used. He presumably means that this is the distinguishing mark of the weaker formulation. 10 Sedley ascribes this view to Burnyeat, ‘Gods and heaps’.

—ØŁÆ
a ı

Å
Æ

509

involve propositions of the form ‘n is few’, then there will be universal principles available, whether the premisses are conditionals or negated conjunctions. (‘If n is few, then n þ 1 is few’; ‘It is not the case both that n is few and that n þ 1 is not few’.) If the premisses involve propositions of different sorts (for example, propositions of the form ‘x is a god’), then there will be no universal principles available in either case. [465]

XI Sedley’s second reason runs like this: ‘As Chrysippus certainly recognised in another context, transitive properties are not transmitted through a chain of negated conjunctions in the way that they are through a chain of strong conditionals’ ([3], p.313; cf [2], p.255). The phrase ‘transitive properties’ is not very clear. But what Sedley means to say can perhaps be explained as follows. Consider the inference schemata (C) f(P) It is not the case both that P and that not-Q Therefore: f(Q) (D) f(P) If P, then Q Therefore: f(Q) Sedley holds that there are values of ‘f( )’ for which (D) is valid and (C) is not;11 and that Chrysippus recognized such cases. In particular, if ‘f( )’ is replaced by ‘It is certain that ... ’, then inferences of form (C) will be invalid while inferences of form (D) will be valid. It seems to me that the thesis which Sedley here ascribes to Chrysippus is false; for both (C) and (D) are invalid when ‘f( )’ is replaced by ‘It is certain that ... ’. From (1) It is certain that P and (2) If P, then Q we cannot infer (3) It is certain that Q 11 There are instances where both (C) and (D) are valid (e.g. ‘It is true that ... ’) and instances in which both are invalid (e.g. ‘It is asserted that ... ’).

510

Logical Matters

From (1) and [466] (2*) It is certain that if P, then Q we can, I suppose, infer (3). But here (C) and (D) seem to behave in the same way. For from (1) and (2a*) It is certain that it is not the case both that P and that not-Q it does seem that (3) follows. Moreover, it is not clear that Chrysippus held the view which Sedley ascribes to him. The text to which Sedley alludes is Cicero, de fato vii 14. There Cicero considers the prediction: ‘If you were born at the rising of the dog-star, you will not die at sea’. He says that if the first element in the conditional is necessary, then the consequent is also necessary.*

He implies that Chrysippus accepts this proposition; and he indicates that Chrysippus wanted predictions to be couched in negated conjunctions precisely in order to avoid commitment to this proposition. Thus Chrysippus held that for the case of ‘It is necessary that ... ’ (D) holds and (C) does not. But from this nothing follows about his attitude to ‘It is certain that ... ’; and that is the only ‘transitive property’ which has any bearing on Sedley’s concerns. Finally, even if Sedley is right about Chrysippus’ view, that is only indirectly relevant to the sorites. For sorites arguments do not start from premisses of the form (1) and they do not aim at conclusions of the form (3). Sedley acknowledges this: This would not solve the sorites itself, but it would blunt its attack on the crucial notion of cognitive certainty, which was thought particularly vulnerable to it (M VII 415–21). ([2], p.255; cf [3], p.313)

But it is not clear how blunt the sorites becomes in this respect: the certainty attaching to the first step will attach itself to later steps, even in the negated conjunction version, unless the negated conjunctions are themselves not certain. Chrysippus cannot blunt the attack on cognitive certainty merely by insisting on version (A) rather than version (B); he must also show how the steps in (B) are not certain. [467] * si ... quod primum in conexo est necessarium est, fit etiam quod consequitur necessarium.

—ØŁÆ
a ı

Å
Æ

511

XII Chrysippus sometimes used propositions of the form ‘It is not the case both that P and that not-Q’ in preference to the corresponding propositions of the form ‘If P, then Q’. Chrysippus had good reason to formulate the premisses of a sorites argument in the form ‘It is not the case both that P and that not-Q’. Chrysippus thought that some propositions of the form ‘It is not the case both that P and that not-Q’ were ØŁÆ
. There is no reason to think that the ØŁÆ
a ı

Å
Æ about which Chrysippus wrote were propositions of the form ‘It is not the case both that P and that not-Q’.

19 What is a disjunction?* Stoic logicians attended to words rather than to things: so claimed Galen, a dozen times or more; and so claimed Alexander of Aphrodisias. Galen and Alexander meant the claim as an accusation and a criticism: it was because they thought not of things, but of words, that the Stoics made fundamental errors in their logic. Nineteenth-century historians of logic echoed the ancient claim, and they too thought that Stoic logic was ruined by its passion for words. Twentiethcentury historians of logic also echoed the ancient claim. But for them it was not a criticism. On the contrary, it was a sign that the Stoic logicians were ‘formalists’ — and it is good thing for a logician to be a formalist. But whether it is bad or good to attend to words rather than to things can scarcely be decided until we know what it means to attend to words rather than to things. In the following pages I shall discuss one or two aspects of the ancient claim and one or two of the texts pertinent to it. The texts concern complex propositions — conditionals, conjunctions, disjunctions. Such items form the foundations of Stoic logic. According to Galen and Alexander, the Stoics made fundamental errors about those fundamental items: they did so because they attended to words rather than to things, because their misdirected gaze encouraged them to misclassify compound propositions. A contemporary logician, asked to explain what — say — a disjunction is, might begin his answer by invoking an artificial language; and he might end by saying something like this: a sentence expresses a disjunction if and only if it is synonymous with an expression of the form ‘P v Q’. Such a logician might be said to ‘pay attention to words’ in classifying compound propositions. But that fashion of attending to words was not Stoic — if only because neither they nor any other ancient logician ever considered inventing an artificial language for the use of logic. [275] * First published in D. Frede and B. Inwood (eds), Language and Learning (Cambridge, 2005), pp.274–298.

What is a disjunction?

513

Another contemporary logician, asked to explain what a disjunction is, might appeal to canonical expressions rather than to artificial languages. Taking, for example, ‘Entweder P oder Q’ as the canonical form of a disjunctive sentence, specifying the sense of the connector ‘Entweder ... oder ... ’, and indicating what expressions may replace ‘P’ and ‘Q’, he will suggest that a sentence expresses a disjunction if and only if it is synonymous with such a canonically disjunctive sentence. Such a logician might also be said to ‘attend to words’. Perhaps the Stoics attended to words in that way? In his account of Stoic logic, Diogenes Laertius gives an illustrated list of compound statables or IØÆÆ. Of disjunctions he says this: A disjoined statable is one which is disjoined by the disjunctive connector ‘X Ø’; for example, X Ø æÆ Kd
j
f K
This connector announces that one of the statables is false. (VII 72)1

The account certainly ‘attends to words’ inasmuch as it explains or defines disjunctions in terms of a connector — or, almost, in terms of a canonical expression: ‘X Ø  j ,’. And the account appears to have some weak points. For example, it explains disjunctions by means of a connector which is — or was taken to be — ambiguous. Again, it suggests that a disjunctive statable contains exactly two disjuncts; but the Greek connector is polyadic, capable of linking an indefinite number of disjuncts. Again — and more evidently — the connector ‘X Ø’ is a Greek word, so that the account implies that all disjunctions are Greek, or expressed in Greek. (Moreover, Greek itself has other connectors — most obviously, the simple ‘X’ — which appear to be capable of producing disjunctions.) Again, Stoic statables are not linguistic entities but items expressed by such entities: they are a sort of sayable or ºŒ
, not a sort of expression or ºØ. How can a connector, which is a linguistic entity, disjoin, or otherwise attach itself to, items which are not themselves linguistic? And again, why refer specifically to disjunctive statables? There are other types of complete ºŒ — questions, for example, or commands — which can be compounded. But Diogenes’ account apparently leaves no room for them. 1 ØÇıª

 KØ
n e  F X Ø ØÆÇıŒØŒ F ı
 ı ØÇıŒÆØ, x
X Ø æÆ Kd
j
 KØ
: KƪªººÆØ  › 
  y  e æ
H
IØøø
łF  r
ÆØ.

514

Logical Matters

Diogenes is offering his readers a summary based on an epitome. His account of disjunction — like his accounts of most other things — is best construed as what the ancients called an  ªæÆç, as a sketch or delineation [276] rather than as a formal definition. Then what did the Stoics say when they were asked to go beyond an introductory sketch of the matter? They might have started from the last clause of Diogenes’ delineation, a clause which I have thus far neglected: ‘This connector announces that one of the statables is false’. Something similar, and less cryptic, may be found in the following passages, the first from Sextus and the second from Apollonius Dyscolus: A sound disjoined item announces that one of the items in it is sound and other or others false (together with conflict). (PH II 191)2 That ... it is disjoined by what is indicated by the connector will become clear from ‘Either it is day or it is night’. For only one of the objects thought of can be accepted at any one time: the announcement of disjunctives announces the holding of one and the removal of the remaining one or ones. (conj 216.11–16)3

There are significant differences between the two passages; and in truth neither Sextus nor Apollonius says that he is rehearsing a Stoic thesis — the Sextan passage is part of an argument addressed generally to ‘the dogmatists’ (II 185), and Apollonius is explaining in propria persona how it is that a connecting particle may disjoin the items it allies. Nonetheless, the passages have an important thesis in common, namely the thesis that a disjunction is true provided that exactly one of its disjuncts is true.4 And it is reasonable to take the thesis to be Stoic — even if it was not peculiarly Stoic. The thesis implicitly addresses some of the criticisms which Diogenes’ sketch of disjunction aroused. Thus there is no invocation of an ambiguous connector — indeed, Sextus’ version invokes no connector at all. Nor is there any restrictive reference to Greek, or to any other language. Again, disjunctions are expressly allowed to contain more than two disjuncts. Again, 2 e ªaæ ªØb ØÇıª

KƪªººÆØ £
H
K
ÆPfiH ªØb r
ÆØ, e b º Øe
j a º Øa łF  j łıB a åÅ. — It is tempting to delete the first ‘ªØ’, which is logically offensive; but I suppose that the fault lies with the author, not with his copyist. 3 ‰ b ... ØÆǪ
ıÆØ ... e  F ź ı
ı  F Ie  F ı
 ı, Æçb ª
ÆØ KŒ  F j æÆ Kd
j
 KØ
: 

ªaæ £
Ø H

ı
ø
æƪø
ŒÆa e ÆPe ÆæƺÆ
ŁÆØ. KƪªºÆ H
ØÆÇıŒØŒH

e oÆæØ
KƪªººÆØ,  F   ºØ 
ı j H
 ºØ 
ø
I
ÆæØ
. — The text depends at several points on scholarly conjecture, the unique manuscript being in places unreadable; but the general sense is plain. 4 Disjunction is thus taken ‘exclusively’ rather than ‘inclusively’: so it was, almost invariably, in ancient logic, and so it will be throughout the following pages.

What is a disjunction?

515

Apollonius, who is speaking of disjunctive sentences, does not mingle linguistic entities with ºŒ. It might perhaps be said that there is an implicit confusion in Sextus, who is speaking of statables (IØÆÆ: II 189). For it is linguistic items, and not ºŒ, which ‘announce’ things, so that Sextus improperly says of the disjunctive ºŒ
what Apollonius (and Diogenes) properly say of the disjunctive connector. But that is cavilling. [277] Finally, does the thesis limit disjunctions to statables? Sextus, at least, is expressly considering statables and not compound complete ºŒ in general. And perhaps that is significant — perhaps the Stoics, when they distinguished among types of compound complete ºŒÆ, in fact limited their remarks to statables? After all, so it is throughout the pertinent passage in Diogenes (VII 68–76); and so too, for example, in Sextus, M VIII 95. Yet Apollonius at least has excellent reasons for exceeding the limit. And in fact it is easily exceeded. For example, start with the notion of a canonically disjunctive sentence, defined thus: ‘S is a canonically disjunctive sentence if and only if S has the form D(S1, S2, ... , Sn)’ — where D is a polyadic disjunctive sentential connector and each Si is a sentence. Next, define the connector: ‘A polyadic connector D is disjunctive if and only if a sentence of the form D(S1 þ , S2 þ , ... , Sn þ ) expresses a truth if and only if exactly one of the Si þ s expresses a truth.’ Note that the Si þ s must be, roughly speaking, indicative sentences — sentences which express, or can express, something true or false; but that the Sis may be sentences of any type — interrogatives, say. Thus ‘Is he in heaven or is he in hell, that d****d elusive Pimpernel?’ is (perhaps) a canonically disjunctive sentence. To be sure, the disjunctive connector is here defined in terms of truth. But it does not follow that it can only be used to conjoin sentences which are either true or false. You might define the word ‘dagger’ by saying: ‘ ‘‘dagger’’ is true of an item if and only if that item is a dagger’; and the definition, given in terms of truth-conditions, will give the sense of the word ‘dagger’ in such sentences as: ‘Is that a dagger which I see before me?’ The fact that the Stoics define disjunctives in terms of ‘holding’ or of truth does not show that disjunction is defined only for statables. But the account of disjunction is not yet complete. Next, then, introduce the general notion of a disjunctive sentence: ‘S is a disjunctive sentence if and only if there is a canonically disjunctive sentence synonymous with S’. It follows trivially that every canonically disjunctive sentence is a disjunctive sentence. A disjunction is a sort of ºŒ
, not a sentence; so, finally, explain disjunctions in terms of disjunctive sentences: ‘An item is a disjunction if and

516

Logical Matters

only if in saying it you can say something disjunctively. You say something disjunctively if and only if you can say it in uttering a disjunctive sentence.’ That such an account works modestly well for disjunctive statables is plain. That it also works for other types of complete ºŒ — to disjunctive questions, for example — may be seen by way of the schema: [278] X In uttering S, you say that — where the demonstrative pronoun ‘that’ refers to X. Consider a particular instance of the schema: Is he in heaven or is he in hell, that d****d elusive Pimpernel? In uttering ‘Is he in heaven or is he in hell, that d****d elusive Pimpernel?’ I said that. What is said in the first line — in the replacement for ‘X’ in the schema — is a disjunction; it is an interrogative disjunction.5 An account of disjunction along those lines is readily adapted to other complete compound ºŒ. It requires philosophical refinement; and it has certain consequences which might be judged unwelcome. In addition it seems to be defective as a version of what ancient logicians intended by disjunction; for it seems to contain nothing which corresponds to the last clause in the passage from PH II 191: ‘together with conflict’. Apollonius Dyscolus’ essay On Connectors — or On Conjunctions to give it its normal and misleading English title — survives in a single mediaeval manuscript. Time has been unkind to the book. Apollonius’ Greek is unfriendly, and his argument is usually contorted. The essay presents the most abominable difficulties. A substantial part of it is devoted to disjunctions — and primarily (for such is Apollonius’ design) to Greek disjunctive connectors. At one stage in his argument Apollonius makes this remark: Let us not omit what the Stoics say: they make a distinction within naturally disjoined items between what conflicts and what contradicts. Something conflicts if it cannot be accepted at the same time ... : Either it is day or it is night Either I am speaking or I am silent 5 A decent account of interrogative disjunctions would need to distinguish among at least: (a) the questioning of a disjunction — ‘Is it the case that (P or Q)?’, which invites the answers ‘Yes’ and ‘No’, and (b) the disjoining of questions — ‘Is it the case that P or is it the case that Q?’, which invites the answers ‘P’ and ‘Q’. And there are other neighbouring phenomena. (‘Stands the church clock at half past three, and is there honey still for tea?’: a conjunction of questions, or the questioning of a conjunction?)

What is a disjunction?

517

and the like. Something contradicts if it exceeds by a negation (and so is in effect conflicting): Either I am speaking or I am not speaking Either it is day or it is not day For the second sentence exceeds by a negation. (conj 218.20–27)6 [279]

The distinction between conflict and contradiction is found in a few other texts (Sextus, PH I 190, 198; Ammonius, in Int 91.9–10). Apollonius explicitly ascribes it to the Stoics. He may be suspected of imprecision — for he is talking of sentences whereas any Stoic distinction presumably concerned ºŒ. But although the ascription is unique, there is no reason to regard it as factitious. That Apollonius was familiar with Stoic logical and linguistic theories is certain; and it is equally certain that he sometimes adopted some parts of those theories. How Stoic he is in the piece on connectors is a nice question. Near the beginning of the essay he criticizes certain of his predecessors — according to the standard edition of the text — in the following words: Some, actually using words alien to those which contribute to the science of grammar, introduce Stoic doctrines, the tradition of which is not particularly useful for the technique which contributes to the science of grammar. (conj 213.7–10)7

That reads like an outright rejection of Stoic doctrine. But the word ‘Stoic’ does not appear in the manuscript (nor is there a blank space on the page): it was added by Bekker. He was presumably relying on Apollonius’ next remark: The observation of language is a long and arduous business. By it all dialects and all formations which contribute to the tradition of readings in Greek are corrected — a subject on which the work of the Stoics on language does not touch at all. (conj 213.11–15)8 6 Åb e æe H
øœŒH
ºª 

Ææƺø
Ææ x  K Ø ØÆç æa K
 E ŒÆa çØ
ØÇıª
Ø Æå 
ı ŒÆd I
ØŒØ
ı: ŒÆd q
Æå 

e c ı


ŒÆa e ÆPe ÆæƺÅçŁB
ÆØ bæ y ŒÆd K
 E æ ŒØ
Ø YæÅÆØ: æÆ Kd
j
 KØ
, j çŁªª ÆØ j تH, ŒÆd Ø a   Ø ‹ ØÆ: I
،

b e º
Ç
I çØ ‹æ ı
Ø ºØ
Æå 

: j çŁªª ÆØ j P çŁªª ÆØ, j æÆ Kd
j PŒ Ø
æÆ. › ªaæ æ  º ª  Kº
Æ fiB I çØ. — The text is doubtful in more places than one; but nothing will hang on any of the doubtful parts. 7 ƒ b ŒÆd O
ÆØ
Iºº æ Ø æ åæÅ
Ø Xæ  E N ªæÆÆØŒc
ı

ıØ, øœŒa ÆæØçæ ıØ  Æ z
Ææ Ø PŒ ¼ªÆ
åæØÅ æe c
N ªæÆÆØŒc
ı

ıÆ
å
º ªÆ
. 8 Ø ª F
 ºº Ø ŒÆd ıæºÅ  æd a çø
a æÅØ ŒÆ æŁ FÆØ AÆ ØºŒ , A åÅÆØe ı

ø
N  ¯ººÅ
ØŒc
Ææ Ø
I
ƪ
øø
, w Pb ŒÆ Oºª
KØłÆØ › Ææa  E øœŒ E æd çø
B º ª .

518

Logical Matters

Apollonius is not there complaining of the insinuation of Stoic doctrine into grammatical theory — on the contrary, he is grumbling that the Stoics do not touch on the particular issue he has in hand. Thus the passage does not support Bekker’s supplement. It is not clear that any supplement is needed; and if an adjective must be introduced, why ‘Stoic’ rather than any of a dozen others? However that may be, a few lines later Apollonius observes that in composing his essay he will take over various items from his predecessors, [280] and, having in addition thought some things up for ourselves, we shall set matters out with the necessary clarity, not going wholly outside the doctrine of the Stoics: Posidonius, in his On Connectors, says ... (conj 214.1–5)9

Apollonius will not depart completely from Stoic doctrine — and he at once proceeds to cite the Stoic Posidonius. (No one, I think, any longer takes seriously the suggestion that ‘Posidonius’ here designates someone other than the celebrated Stoic philosopher.) Some have taken the passage in a strong sense: they gloss ‘not going wholly outside’ as ‘not departing a whit from’ — so that Apollonius declares himself a thorough Stoic for the course of the essay. But the Greek can hardly carry that meaning; and in any event the obvious sense — ‘not being wholly unStoic’ — is surely right. I return to 218.20–27. Apollonius says that the Stoics make a distinction among ‘natural’ disjuncts. The distinction is clear to the extent that the notion of conflict is clear. It is plainly a necessary, but not a sufficient, condition for a conflict to hold between two items that it be impossible for both of them to hold at the same time — more generally, if the members of a group of items are in mutual conflict, then it is impossible that more than one of them be the case. It seems, too, that contradiction is a special sort of conflict, as Apollonius stumblingly states. There is a contradiction between two items if and only if one ‘exceeds the other by a negation’, i.e. by a negative particle. Contradiction holds between pairs of items and not among larger groups. The expression ‘exceed by a negation’ needs a careful gloss (see Sextus, M VIII 89–90); but it is plain that if two items contradict one another they are in conflict, but not vice versa. Contradiction is a special case of twoparty conflict. 9 æe x  ŒÆd ÆP  Ø KØ
Æ
 a B  Å ÆçÅ
Æ ÆæÆ 
, PŒ KŒe ªØ

Ø ŒÆa e Æ
ºb B H
øœŒH
 Å. — Ø
Ø  K
fiH æd ı
ø
...

What is a disjunction?

519

All natural disjuncts, then, involve conflict. That ties Apollonius’ text to the clause in the Sextan passage: disjunctions ‘are together with conflict’. That might be glossed as follows: ‘A disjunction is true if and only if one of its disjuncts is true and it is impossible for more than one to be true’. But it seems likely that the right gloss is rather this: ‘A disjunction is true if and only if, necessarily, exactly one of its disjuncts is true’. To see the difference between the two theses, consider, say: ‘Either it’s Monday or it’s Tuesday’. However that may be, Apollonius offers a touch which is missing in Sextus: he speaks of natural disjuncts. What are they? Apollonius introduces them in 216.16–218.19, a text of stunning difficulty. I take it in spasms.10 [281] Again, some of them [i.e. some disjoined items] have received their disjoining naturally and others have not accepted their disjoining naturally.

The adverb ‘naturally [ŒÆa çØ
]’, at both occurrences, has been supplied by editors: the manuscript is blank. Some have preferred ‘true’ as a supplement, a word which occurs in the next sentence. The length of the blank favours ‘naturally’; but those who prefer ‘true’ probably understand it in the sense of ‘genuine’, and between ‘genuine’ and ‘natural’ there is no pertinent difference. For the remark Either it is day or it is night stands in a true disjoined item; for these circumstances will never occur at the same time. But the remark Either Apollonius will be present or Tryphon will announces the disjoining as relative to an occasion.11 Thus the first example, even if it does not take the disjunctive connector, will still be in a disjoining: It is day. It is night. The one is true — if we were to say thus, it being day: It is day.

‘The one is true’ here means ‘One and only one is true’ — so too a few lines later on. Apollonius asserts that items naturally disjoined are ‘in a disjoining’ whether or not they take a disjunctive connector: this feature is a mark of natural disjunction — but it is, for the moment, the murkiest of marks. And the last clause, ‘if we were to say ... ’, is hardly pellucid.

10 For the Greek see Appendix A. 11 For ‘relative to an occasion [æe ŒÆØæ
]’ in contrast to ‘naturally’, see Sextus, PH II 97–99; M VIII 145–150: the phrase is not found elsewhere in Apollonius.

520

Logical Matters

But in the other, things are certainly not so: Tryphon will be present. Apollonius will be present. For such items are not disjoined if they do not take the disjunctive connector.

Here ‘the other [e ... æ
]’ corresponds not to the preceding ‘e æ
’ but rather to ‘e ... æ æ
’ in line 11/12; and the phrase ‘ P 
ø’ here means ‘certainly not’, whereas later it will mean ‘not certainly’. Neither clear nor elegant — but that is how Apollonius writes. And what is the function of the double example? In these cases you can also set down the connectors which conflict with the disjunctive ones — Both Apollonius will be present and Tryphon will be present. If Tryphon will be present, Apollonius too will be present. But in the case of items naturally disjoined you cannot; for ‘Both it is day and it is night’ will not cohere; nor will ‘If it is day, it is night’. [282]

This is a second mark of natural disjunction: naturally disjoined items cannot be linked by connectors which conflict with disjunctive connectors. Presumably ‘Both ... and ... ’ conflicts with ‘Either ... or ... ’ inasmuch as any sentence of the form ‘Both P and Q’ conflicts with its counterpart of the form ‘Either P or Q’; that is to say, the two cannot be true at the same time — though in some cases, where the disjunction is not natural, they will each be true at different times. But why think that ‘Either ... or ... ’ conflicts with ‘If ... then ... ’? And why is it only in natural cases that you cannot set down the conflicting connectors? And what does Apollonius mean when he says that certain sentences ‘will not cohere [ P ... ıÆØ]’? So there are some sentences disjoined or conjoined by the connectors, and also some so colligated; and there are some which do not perforce announce the colligation by way of connectors but actually indicate it in themselves — or again, some which are disjoined do not indicate the disjoining by the disjunctives but in themselves.

‘Colligation’ is ‘e ı
Æç’ — connected with the verb ‘ı
Ø
’, whence ‘ı
Å

’, the standard Stoic term for a conditional ºŒ
. So a colligation is a link of conditionality. Just as there are naturally disjoined items, so there are naturally colligated items. Apollonius does not say that there are also naturally conjoined items; and I suppose that there are not. In these cases, exchanges will not take place. Let us set out some examples. Someone who says ‘It is day’ has indicated that it is also light. In this case the following will not be possible:

What is a disjunction?

521

Either it is day or it is light. If am alive, I am breathing — for ‘Either I am alive or I am breathing’ will not be possible. For the colligating of breathing and being alive does not admit the disjunctive, as we have already said. And because its being day and its being night are disjoined, the one is true. In that case the colligative will not cohere since at the same time as you say It is day it has been indicated that it is not night, and what stands in a colligation must also stand in a sequence.

The two marks of natural connections are here put together: if certain items indicate a connection in themselves, without the need of connectors, then ‘exchanges will not take place’; that is to say, as the examples make plain, you will not be able to replace one connector by another conflicting connector: if ‘If P, then Q’ is true, then ‘Either P or Q’ is never true, cannot be true. Such items ‘do not admit’ certain connectors; certain compound sentences ‘will not be possible’ or ‘will not cohere’. The latter mark is taken as a consequence of the former. [283] And the former mark becomes a little less dark. An earlier phrase seemed to suggest that if you utter the two sentences, ‘It’s day. It’s night’ just like that, without linking them by any connector, you have thereby said something disjunctively. But the suggestion was misleading; for we now learn that Apollonius is thinking of someone who utters just ‘It’s day’. That was the point behind the obscure expression ‘if one were to say thus ... ’; and that indicates the way to take the double examples — they are, precisely, a pair of examples (and not a single disjunctive or conjunctive example). Someone who utters just ‘It’s day’ thereby indicates that it is not night. In the same way, if you say ‘It’s day’, it is thereby indicated that it is also light. The colligation is implicit in the sentence ‘It is day’ — there is no need to construct a colligation by way of a colligative connector. It is not that the utterance of ‘It’s day’ is the saying of a disjunction or of a colligation. ‘It’s day’ is not short or elliptical for ‘If it’s day, it is light’, in the way in which some thought ‘ªæçø’ to be elliptical for ‘Kªg ªæçø’.12 After all, there is a world of difference between saying ‘It’s day’ and saying ‘Either it’s day or it’s night’, or ‘If it’s day, it’s light’. And neither Apollonius nor any

12 See Apollonius, synt II 51 [165.4] — Apollonius rejects the thesis.

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logician can have missed that evident fact. Rather ‘It’s day’ indicates the disjunction and the colligation in itself.* In general, ‘Q’ is naturally colligated to ‘P’ if and only if, in uttering affirmatively ‘P’, you thereby indicate that Q. And ‘P’, ‘Q’, ‘R’, ... are naturally disjoined if and only if, in uttering affirmatively one of them you thereby indicate that none of the others holds. Why or how do you indicate such things? You indicate them — or they are indicated — by the very sentence you utter. That is to say, the sense of ‘It is day’ is such that, necessarily, if it is day it is not night and if it is day it is light. And so certain sentences are impossible, do not cohere. The text continues. The remaining sentences — I mean those which do not fall into this class — undergo disjoining and colligating by the connectors themselves. As when you say: Either pillage or divide all in two. Both pillage and divide all in two.

At the beginning the ink has been washed off the manuscript, and the traces are baffling. But the general sense of the lines is clear: one who says ‘Pillage’ does not thereby say ‘Don’t divide all in two’. Hence any disjoining or conjoining must be fabricated by the use of the appropriate connectors. [284] And just as it is not possible to assign an article to every declinable word, but only to one which can take it on, in the same way it is not possible to link every connector to every sentence. I mean a sentence which in itself announces a colligating — for where the disjunctive connector applies, the colligative does not; and where the colligative applies, the disjunctive does not.

Articles, in Greek, do not attach to every declinable expression: ‘Iººº ı’, for example, does not take the article (synt II 70 [59.12–60.12]); nor does ‘Iç æ Ø’ (II 71 [60.13–61.23]).13 Thus, in English, I say ‘It’s hard to lose either when you have both’. I do not say ‘It’s hard to lose either when you have the both’. The latter sentence is not possible, it does not cohere. Elsewhere, Apollonius produces other examples of impossibilities and incoherences. Thus it is not possible to apply ‘ y ’ to a feminine or to a plural noun — not even at night (synt III 9 [274.7–12]). Thus ‘We talked to us’ does not cohere (III 5 [271.2–4]); nor does ‘Dio is a philosopher * For a different way of understanding this elusive matter, see J. Barnes, Truth, etc. (Oxford, 2007), pp.239–241. 13 Similarly nouns in the vocative take no article, the definite article having no vocative: see the long discussion at synt I 73–79 [62.6–67.8]. For other related phenomena, see e.g. synt I 135 [111.4–9]; adv 182.27–183.4.

What is a disjunction?

523

converses’ — unless you put an ‘and’ in front of the last word (I 107 [90.7– 10]). And in just the same way ‘Both it is day and it is night’ and ‘If it is day, it is night’ are not possible, do not cohere. The cases do not seem to be parallel. ‘The both’ or ‘We talked to us’ are impossible inasmuch as they are ill formed, ungrammatical. But ‘If it is day, it is night’ is grammatically impeccable and beautifully formed. Moreover, such sentences have their uses — for example, as conclusions to reductio ad absurdum arguments. But it need not be supposed that Apollonius means to brand ‘If it is day, it is night’ as ungrammatical. (Indeed, he does not operate with anything like the notion of grammaticality.) Rather, that expression, like ‘The both’ or ‘We talked to us’, does not cohere insofar as it offends against the rules of language, insofar as its very linguistic form rules it out of court. The expressions are all — as we or Wittgenstein might put it — nonsense. This category of nonsense, you might object, is too general — and perhaps too indeterminate — to be of any utility. At any rate, a logician must distinguish among different types or different causes of nonsense. But it is easy enough to do so. ‘If it is day, it is night’ is nonsense inasmuch as, given the meaning of its constituent terms, it cannot ever express a truth. And that is so inasmuch as ‘It is day’ and ‘It is night’ are naturally disjoined. On the other hand, although ‘Either Apollonius will be here or Tryphon will be here’ may well be true, ‘Apollonius will be here’ and ‘Tryphon will be here’ are not naturally disjoined, so that both ‘Both Apollonius will be here [285] and Tryphon will be here’ and also ‘If Apollonius will be here, Tryphon will be here’ cohere and are not impossible — the two sentences are sometimes true. If that is Apollonius’ conception of a natural disjunction, is it also a Stoic conception? Did the Stoic logicians distinguish, as Apollonius does, between natural and occasional disjunctions? Apollonius does not say so. He says only that the Stoics made a distinction, between conflict and contradiction, which applies within the class of natural disjunctions. On the other hand, he surely gives his readers the impression that the Stoics spoke of natural disjunctions. No other text attributes the conception to the Stoics. To be sure, at conj 214.8–10, Apollonius says that Posidonius set out ‘the natural connectors’. But it is not clear that the expression ‘natural connector’ comes from Posidonius; and in any case, a theory of natural connectors has nothing to do with a theory of naturally connected sentences. Perhaps, then, the theory came from some other philosophical party? Boethius, for example, distinguishes between two sorts of conditional proposition, ‘the one so by accident,

524

Logical Matters

the other being such as to have a certain consequence by nature’ (hyp syll I iii 6). The distinction is presumably Peripatetic: it perhaps goes back to Theophrastus and Eudemus, and it surely was developed before Apollonius’ day. True — but it is not the same distinction as the one in Apollonius, and there is no reason to torture it into a spurious conformity. Perhaps, then, the theory comes from the grammarians rather than from the philosophers? After all, Apollonius himself is always concerned to distinguish what is natural in language from what is not. True — but he never elsewhere distinguishes the natural from the occasional. In short, there is some gentle reason to ascribe the theory to the Stoics; and no reason to attribute it to others. In any event, it is tempting to imagine that the disjunctions which interested the Stoics are Apollonius’ natural disjunctions: after all, Sextus insists that disjunctions come ‘together with conflict’, and in natural disjunctions the component disjuncts are in conflict with one another. But all natural disjunctions are true. Hence if Stoic disjunctions are natural disjunctions, then all Stoic disjunctions are true. And that is absurd. Then perhaps a Stoic disjunction is true if and only if it is natural? All natural disjunctions are true, and perhaps all true disjunctions are natural.14 False disjunctions abound. They fall into two discrete classes. A false disjunction may disjoin items which are not disjoined at all — for example, [286] ‘Either Geneva is in Switzerland or Hamburg is in Germany’. And there are false disjunctions in which the items are disjoined, but not naturally — for example ‘Either Apollonius will be here or Tryphon will be here’. For there is no conflict between those disjuncts. That may seem absurd: surely the first of the two sentences I have just adduced is true, and surely the second may have been true? Well, anyone who holds that a disjunction is true if and only if it is natural has a choice here: either those two sentences are not true or else they do not express disjunctions. If you choose the latter option, then you will presumably have an account of disjunctions which does not pay attention to expressions rather than to things. If you choose the former option, you will need to explain why those sentences are so easily taken for true. There is a further feature of Apollonius’ discussion which may be considered. He holds that, when ‘P’ and ‘Q’ are naturally disjoined, then both ‘Both P and Q’ and also ‘If P, then Q’ are impossible. The former contention 14 So at conj 217.2 (and perhaps at 216.16 and 217.1) perhaps after all ‘true’ means ‘true’ rather than ‘genuine’?

What is a disjunction?

525

is unremarkable. Not so the latter. Sentences such as ‘If it is odd, it is even’ have their uses. One sort of case is particularly striking. Presumably, for any ‘P’, ‘P’ and ‘not-P’ are naturally disjoined: whatever ‘P’ may be, ‘P’ and ‘not-P’ are contradictory and therefore in conflict. But sentences of the form ‘If not-P, then P’, far from being universally impossible, are used and used as truths in a number of ancient arguments. According to Sextus, the Dogmatic philosophers produce an argument for the existence of signs which runs thus: If there are signs, then there are signs. If there are no signs, then there are signs. Either there are signs or there are no signs. Therefore: there are signs. (See PH II 131.) A parallel argument, with the word ‘proof’ substituted throughout for ‘sign’, supposedly established the existence of proofs (PH II 186). The Dogmatists who offered those arguments, and who are frequently taken to be Stoics, cannot consistently suppose that if ‘P’ and ‘Q’ are naturally disjoined then ‘If P, then Q’ is impossible. At PH II 132 Sextus criticizes the Dogmatic argument by producing a parallel to it: If there are no signs, then there are no signs. If there are signs, then there are no signs. Either there are no signs or there are signs. Therefore: there are no signs. [287] The argument, he claims, is as good as the Dogmatic argument — and so the Dogmatic argument cannot establish the existence of signs. At PH II 189 he launches a different attack: the Dogmatic argument cannot be advanced by the Dogmatists; for ‘it is impossible, according to them, for a conditional composed of conflicting statables to be sound’. The Dogmatists’ own principles prove that their argument is unacceptable.*

* If there is conflict between two statables, then neither implies the other. Equivalently, if one statable implies another, then the two statables are not in conflict. Roughly: If if P, then Q, then not impossible both P and Q. The principle has been much discussed: see e.g. J. Barnes, ‘Boethius and the study of logic’, in M. Gibson (ed), Boethius (Oxford, 1981), pp.73–89 [reprinted in below, pp.666–682]; M.R. Stopper, ‘Schizzi pirroniani’, Phronesis 28, 1983, 265–297; L. Castagnoli, ‘ı
æÅØ crisippea e tesi di Aristotele’, in M. Alessandrelli and M. Nasti de Vincentis (eds), La logica nel pensiero antico (Naples, 2009), pp.105–163; M. Nasti de Vincentis, ‘Dalla tesi di Aristotele alla tesi di Boezio: una tesi per l’implicazione crisippea?’, in Alessandrelli and Nasti de Vincentis, Logica, pp.167–247.

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Logical Matters

It has been claimed that Sextus is foisting a principle on the Dogmatists. When he says that the principle holds ‘according to them’, then he means not that they have enunciated the principle but rather that they are committed to it. And it has been claimed, further, that Sextus is mistaken: the commitment which he purports to discern does not exist. In other words, the principle is no principle of the Dogmatists. And all the better — for the principle is false. But Apollonius provides a parallel to Sextus, proving that the principle had some life outside Sextus’ brain. Moreover, if Apollonius is reporting or paraphrasing Stoic doctrine, then we must agree with those Sextan exegetes who have construed the passage as a straightforward and truthful document in the history of Stoic logic. Moreover, Apollonius offers an argument in favour of the principle. Sextus says that the Dogmatists must accept the principle, since a conditional announces that if its antecedent is the case, then so too is its consequent, whereas conflicting items announce the contrary — that if either one of them is the case, it is impossible for the other to hold. (PH II 189)*

It is hard to see why that should have been thought a reason in favour of the principle. Apollonius has something different: In this case the colligative will not cohere since at the same time as you say It is day it has been indicated that it is not night, and what stands in a colligation must also stand in a sequence.

What is in colligation must also be in sequence: natural disjuncts are not in sequence — hence they cannot be colligated. What does Apollonius mean by ‘sequence [IŒ º ıŁÆ]’? The answer comes in the last lines of the text which we are examining: And it is clear from the case before us that the announcement of the colligatives conflicts with that of the disjunctives, and so also does that of the conjunctives — although in one way the conjunctives do not differ. For the disjunctives are not in sequence, and neither are the conjunctives. For if we assert thus Either it is day or it is night, or again by inversion Either it is night or it is day, [288] it makes no difference. So too: * e b
ªaæ ı
Å

KƪªººÆØ Z
   F K
ÆPfiH ª ı
ı r
ÆØ ŒÆd e ºBª
, a b Æå 
Æ  P
Æ

, Z
   F æ ı ÆPH
› Ø ı  I
Æ
r
ÆØ e º Øe
æåØ
.

What is a disjunction?

527

Both Apollonius will be present and Tryphon will be present Both Tryphon will be present and Apollonius will be.

Conjunctions and disjunctions are not in sequence: that is to say, the order of their elements is indifferent, they are commutative — ‘Both P and Q’ means the same as (or at least is equivalent to) ‘Both Q and P’, and ‘Either P or Q’ as ‘Either Q or P’. Conditionals, on the other hand, are not commutative: ‘If P, then Q’ is not equivalent to ‘If Q, then P’. Grant all that to be true — what follows? Apollonius infers that if ‘Either P or Q’ is true, then ‘If P, then Q’ is not true. The inference is fallacious.* Galen’s Institutio logica, like Apollonius’ On Connectors, survives in a single manuscript; and the single manuscript is in a miserable state. On the other hand, Galen’s Greek is not Apollonian, and his argumentation is usually semi-transparent. There are two pertinent and parallel texts, one in chapter iv, where Galen discusses conflict, and the other in chapter xiv, where he turns to the use of hypothetical syllogisms in proofs.15 It will be best to follow the latter text. The development of the argument in xiv 3–8 is at first sight perplexing. § 3 opens with the following assertion: That not a single syllogism by way of a negated conjunction is useful for proof ... has been demonstrated elsewhere.

Galen has his sights on the ‘third indemonstrable’ of Stoic logic: Not both P and Q; P: so not-Q For § 4 begins thus: Therefore a third indemonstrable which the Chrysippeans think to conclude from a negated conjunction and one of its elements to the opposite of the other element ... ‘ ... is of no use at all’, we expect Galen to say. Not a bit of it; the sentence continues as follows:

* Nasti de Vincentis, ‘La tesi di Aristotele’, p.191 n.13, says that this statement is ‘an oversight’: for (he says) I recognize that Apollonian conditionals satisfy the principle that if one statable implies another, then the two cannot be in conflict; and the inference in question, far from being fallacious, is an immediate consequence of that principle. But I don’t think that Apollonian conditionals satisfy the principle. I don’t think there are any ‘Apollonian conditionals’. Apollonius takes himself — of course — to be talking about ordinary conditionals, about what we mean when we say things like ‘If it doesn’t rain soon, we shall have to water the lawns’. He wrongly thinks that ordinary conditionals satisfy the principle. 15 Greek in Appendix B.

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Logical Matters

... we have shown to be useful for numerous proofs in ordinary life, even in the lawcourts.

Thus Galen first denies that syllogisms based on negated conjunctions are useful, adding that this is not the place to discuss useless or superfluous parts of logical theory. And then, paradoxically, he indulges in a lengthy [289] discussion of these allegedly useless syllogisms, claiming to have shown that they are, after all, useful for proofs. In § 9 he apologizes for the protracted nature of the discussion. The text of § 4 is risibly corrupt; but no emendation will do away with the paradox, and the summary which I have just given answers, grosso modo, to what Galen intended to say. The way out of the paradox is this. First, the word ‘ s
’ at the start of § 4, which I translated as ‘therefore’, must be given a resumptive rather than an inferential force: ‘I shall not discuss useless syllogisms. Well then, to get back to business ... ’. Secondly, when Galen says that ‘the Chrysippeans think’ that a third indemonstrable starts from a negated conjunction, he means just that: they think so — but, as we shall see, they are wrong to think so. So § 4 introduces a form of hypothetical syllogism which, Galen claims, the Stoics had misclassified. Then what is the syllogism in question? Galen offered an illustrative example: ‘as in the following sort of case’. The manuscript offers us the sentence: ‘Dio is both in Athens and at the Isthmus’. Evidently, that will not do. Equally evidently, the example which Galen had in mind was the following: It is not the case both that Dio is in Athens and that Dio is at the Isthmus. Dio is in Athens. So: Dio is not at the Isthmus. Whether the whole syllogism should be inserted into the text may be doubted;16 but that this was Galen’s syllogism is undeniable. And its legal potential is also plain. His client charged with armed robbery at the Isthmus, the defending counsel puts forward Galen’s syllogism: ‘I rest my case, M’Lud’. Yet if any syllogism uses a negated conjunction, surely that syllogism does? For who could deny that ‘It is not the case both that Dio is in Athens and that he is at the Isthmus’ is a negated conjunction? It carries its form on its face. 16 There are numerous cases in Galen’s writings where — in the received text — a single proposition, or a pair of propositions, stands in for a whole syllogism; and it is not clear that all these cases need to be emended away.

What is a disjunction?

529

But Galen claims that, pace Chrysippus, his syllogism does not start from a negated conjunction. He explains himself in § 5, which recalls and elaborates the account of conflict given in chapter iv. There are perfect and complete conflicts, when two items cannot both obtain and cannot both fail to obtain; and there are defective or half conflicts, when two items cannot both [290] obtain but may both fail to obtain.17 Now in iv 4 Galen had stated that in the case of defective conflict, the Greeks customarily speak like this: It is not the case that Dio is both in Athens and at the Isthmus And you will take this expression to be indicative of defective conflict.

That is to say, ‘not both ... and ... ’, in cases of this sort, signifies, according to Greek usage, a defective conflict. And so, in xiv 6, Galen announces, of defective conflicts, that in the case of items of this sort, the syllogism we described is useful. It uses the same expression as Chrysippus, but it is constructed not on a conjunction but on conflicting elements.

Galen is at any rate half right: given that Athens and the Isthmus are two separate places, then there is a defective conflict between Dio’s being in Athens and his being in the Isthmus. He might be in neither place; but if he is in one, he can’t also be in the other. But surely Galen is also half wrong; for even though its components are in conflict, ‘It is not the case both that Dio is in Athens and that he is at the Isthmus’ is a negated conjunction. Galen demurs. After all, ‘many disputes come about in connection with conjoined statables’.18 And his reason emerges in § 7. Again, the text is difficult; but there is no doubt about what Galen intended to say: There are three differences among items: one, a difference in respect of conflict, applying to items which never obtain together; a second, in respect of sequence, applying to items which always obtain together; and those items which possess neither a necessary sequence nor a conflict constitute conjunctive statables.

In Galen, ‘sequence’ has its normal logical sense of ‘implication’, and not Apollonius’ sense. So Galen means that a pair of items, X and Y, may be such that 17 Conflict need not be bilateral; but it is easier — and undeceptive — to conduct the discussion in terms of the simplest case. 18 Text and interpretation of this sentence are uncertain. My version supposes that the word ‘ØÆç æ’ is used in different senses in successive lines. That is unwelcome — but other interpretations seem me to have even greater disadvantages.

530

Logical Matters

(A) X conflicts with Y (B) X implies or is implied by Y (C) X does not conflict with Y and neither implies nor is implied by Y There are obscurities there. But it is plain, first, that the three classes are intended to be jointly exhaustive: any pair, X and Y, must fall into one or other of the classes. That is guaranteed by the definition of class (C). [291] Secondly, and for the same reason, no pair can be in (A) and also in (C), nor in (B) and also in (C). And it is a safe bet that Galen thought that no pair can belong both to (A) and to (B), even though he neither explicitly says nor strictly implies so. The distinction between (A) and (B) is an ancient commonplace. Items exclude one another or embrace one another, they conflict or they imply, they disjoin or they colligate: conflict and implication, Æå and IŒ º ıŁÆ, are the two logical relations par excellence. Every schoolboy, and every orator, knew that. And it is easy enough to think that the two relations are mutually exclusive: how on earth could one item both exclude another and also imply it? Galen tacitly supports the principle which Sextus ascribes to the Dogmatists and which Apollonius affirms on his own behalf. It is reasonable to infer that the principle was not a special theorem of Stoic logic, supported by some subtlety which we no longer know. Rather, it was taken to be an obvious corollary of a logical commonplace: in logic we are interested in conflict and implication, in incompatibilities and entailments — two relations which are quite different and (or so anyone will unreflectingly suppose) mutually exclusive. Odi et amo may do for poetry, but it will not wash in logic. Let me return to the text of Galen. Of class (C) he says that those items which possess neither a necessary sequence nor a conflict constitute conjunctive statables.

That is to say, as Galen had put it in iv 4, if the expression [sc ‘Not both ... and ... ’] is said of other cases, which possess neither mutual sequence nor conflict, we shall call such a statable a negative conjunction, as in the case of Dio is walking and Theo is talking. For these possess neither conflict nor sequence and are expressed by way of conjunction.

Conjunctions unite items which belong to class (C).

What is a disjunction?

531

And in xiv 7–8 Galen discusses syllogisms based on what are indeed negated conjunctions. Among items in class (C), he says, are the following: Dio is walking and Theo is talking. Clearly, the negation will be: It is not the case both that Dio is walking and that Theo is talking. [292] There are two additional premisses: But Dio is walking and again, But Theo is talking. The conclusion for the one additional premiss is Therefore Theo is not talking and for the other Therefore Dio is not walking. This sort of material has been shown to be utterly useless for proofs.

Galen does not repeat here his proof that such arguments are useless for proofs; and I shall refrain from speculation — for there is no proof to be found. However that may be, Galen is evidently right on one point: the two illustrative arguments are based on negated conjunctions. On the other hand, Galen holds that ‘It is not the case both that Dio is in Athens and Dio is at the Isthmus’ is not a negated conjunction. For ‘Both Dio is in Athens and Dio is at the Isthmus’ is not a conjunction. For a proposition is a conjunction if and only if it has the form ‘D(X1, X2, ... , Xn)’, where the Xis all belong pairwise to class (C), and D is a conjunctive connector. And a connector D is conjunctive if and only if ‘D(X1, X2, ... , Xn)’ is true if and only if every Xi is true. Perhaps that is an idiosyncratic account of conjunction (though Galen does not think so). But it appears to be a coherent account. Nor should we be worried by the question: If ‘Both Dio is in Athens and Dio is at the Isthmus’ is not a conjunction, then what on earth is it? It is sui generis. Galen’s remarks about conjunction presumably hold, mutatis mutandis, for disjunction and for colligation: just as class (C) produces conjunctions, so classes (A) and (B) produce disjunctions and colligations. Galen does not explicitly say that class (B) grounds colligation; but at xiv 5 he does state that ‘items in complete conflict I have decided to call by the name of disjunction’. Apollonius associated natural disjunction with class (A) in general. Galen divides class (A) in two: items in class (Ai), complete conflict, support disjunction; items in (Aii), deficient conflict, support a different type of

532

Logical Matters

compound statable. Perhaps Galen’s verb ‘I have decided [MøŒÆ]’ records a departure from standard usage. Whither all this? Here is a simplified version of Galen’s general position: Compound statables are to be classified according to the type of connector which governs them and the class of items which the connector connects. Suppose that we have an implicative connector DI, a disjunctive connector DD, a connector of partial conflict, DP, and a conjunctive connector DC. Then: [293] (1) A statable is an implication if and only if it has the form ‘DI(X,Y)’ and X and Y are in class (B). (2) A statable is a disjunction if and only if it has the form ‘DD(X,Y)’ and X and Y are in class (Ai). (3) A statable is a partial conflict if and only if it has the form ‘DP(X,Y)’ and X and Y are in class (Aii). (4) A statable is a conjunction if and only if it has the form ‘DC(X,Y)’ and X and Y are in class (C). No doubt that has a certain charm and coherence. But it does not take much reflection to show that it provides a curious basis for logical theory. For example, if X and Y are in (Ai), then exactly one of them is true. Hence their disjunction is true. So that there are no false disjunctions. Galen is in a mess. Why did he get into it? The answer — or at least, a part of an answer — is to be found in iv 6: But here too the Chrysippeans give their attention to expressions rather than to objects, and they call a conjunction anything which is constructed by way of the socalled conjunctive connectors, even if it is constructed from conflicting items or from sequential items.

The Stoics identify disjunctions by way of certain Greek connectors; they hold that a ºŒ
is disjunctive if and only if it is expressible by way of a sentence of the form ‘X Ø ... j ... ’. But that is absurd: it is not the vocables ‘X Ø ... j ... ’ which make something a disjunction — it is the objects themselves. The negative part of Galen’s complaint is correct: the presence of ‘X Ø ... j ... ’ is neither a necessary nor a sufficient condition for a sentence’s expressing a disjunction. (It is another question whether any Stoic logician ever thought that it was.) The positive part of the criticism is less easy to fathom: ‘Look at the objects, the æªÆÆ’ — what objects?

What is a disjunction?

533

Galen does not urge us to consider how things lie in the world, to look for the facts of the matter. The æªÆÆ in question are, to put it crudely, the meanings of the sentences. In other words, Galen’s exhortation is this: ‘If you want to determine what sort of compound ºŒ
is expressed by a given sentence, do not look only at the vocables which connect its parts — look also at what its parts mean’. Suppose you have a sentence with the structure ‘D(X,Y)’, and you are wondering whether the thing expresses a disjunction. What must you do? It is not enough, according to Galen, to note that ‘D’ here is ‘X Ø ... j ... ’. True — but will it not be enough to determine what ‘D’ means? After all, if ‘D’ is a disjunctive connector, then surely it follows that the sentence is a disjunction? I suppose — or hope — that Galen would have agreed. [294] But he might also have added a further point: he might have said that in order to determine what ‘D’ means, you must look at it in its context; and its context is given, in part, by the senses of the items which it conjoins. That is to say, instead of (2) A statable is a disjunction if and only if it has the form ‘DD(X,Y)’ and X and Y are in class (Ai), he might have written something like (2*) A statable is a disjunction (in a given context in which it is stated) if and only if it has the form ‘DD(X,Y)’ and the context indicates that the utterer of the sentence which expresses it means to say that X and Y are in class (Ai). It is in that sort of way that the senses of ‘X’ and of ‘Y’ will help to fix the sense of ‘D’. And that is the message of iv 4: in order to determine whether a sentence of the form Påd ŒÆd X ŒÆd Y, uttered in a given context, expresses a negated conjunction, you must determine the sense, in the given context, of the connectors; and you will not determine that sense unless you attend to ‘X’ and to ‘Y’.19

19 This chapter was presented to the Hamburg Symposium Hellenisticum. I am indebted to the members of the Symposium, whose questions and comments helped me to avoid several crass errors. I am also grateful to Tad Brennan, for a sheaf of written remarks; to Mauro Nasti, who made me see the pertinence of the Apollonian passage to the dispute over PH II 189; and to Susanne Bobzien, who scrutinized a penultimate version and suggested several substantial ameliorations.

534

Logical Matters

APPENDIX A: Apollonius, conj 216.16–218.19

5

10

15

20

25

ŒÆd Ø ºØ
ÆPH
L b
ŒÆa çØ
c
ØÇıØ
I
ƪ
Æ, L b P ŒØ ŒÆa çØ
c
ØÇıØ
ÆæغÅç Æ. e ªaæ ºª 

j æÆ Kd
j
 KØ
K
IºÅŁE ŒÆŁÅŒ ØÇıª
fiø: ÆFÆ ªaæ a ŒÆÆÆÆ P  ŒÆa ÆPe ª
ÆØ. e b ºª 

j  ºº
Ø  ÆæÆØ j )æçø
‰ æe ŒÆØæe
c
ØÇıØ
KƪªººÆØ. e ª F
æ æ
 تÆ, Œi
c ºfi Å e
ØÆÇıŒØŒe


, ºØ
K
ØÆÇØ ÆØ

æÆ K,
 KØ. e æ
IºÅŁ: N çÆÅ
oø, æÆ hÅ,

æÆ K. e b æ
P 
ø )æçø
ÆæÆØ,  ºº
Ø  ÆæÆØ: P ØÆǪ
ıÆØ ªaæ a  ØÆFÆ Ka
c ºfi Å e
ØÆÇıŒØŒe


: Kç z
Ø ŒÆd  f Æå 
ı  E ØÆÇıŒØŒ E ı
 ı ÆæÆŁŁÆØ ŒÆd  ºº
Ø  ÆæÆØ ŒÆd )æçø
ÆæÆØ. N )æçø
ÆæÆØ, ŒÆd  ºº
Ø  ÆæÆØ. Kd 
 Ø H
ŒÆa çØ
ØÇıª
ø
PŒØ· P ªaæ ıÆØ e ŒÆd

æÆ Kd ŒÆd
 KØ
, Pb e N æÆ K,
 KØ
. ‰ N Ø
 º ª Ø e H
ı
ø
ØÆÇıª

Ø j ıºŒ 
Ø, Ø
b b ı
Æ 
Ø, Ø
  P 
ø e H
ı
ø
e ı
Æçb Kƪªºº 
Ø Iººa ŒÆd Ø ÆH
ź F
· j ŒÆd ØÆÇıª

Ø ºØ
På e H
ØÆÇıŒØŒH
Iºº K ÆH
c
ØÇıØ
ź F
, Kç z
PΠK
ƺºÆªÆd ª

ÆØ: KŒŒŁø b  ªÆÆ: › ºªø
e æÆ K ºøŒ
‹Ø ŒÆd çH K
. Kd   ı PŒØ  F KªåøæØ X Ø æÆ Kd
j çH KØ. N ÇH I
Æ
ø. P ªaæ Ø KªåøæØ e X Ø ÇH j I
Æ
ø. ı
çØÆ ªaæ K
fiH ÇB
 F I
Æ
E
IÆæŒ  KØ  F ØÆÇıŒØŒ F, ŒÆŁg æ  
. Øa b e

Letters printed in grey are supplements where the MS is blank. All supplements are due to Bekker unless otherwise indicated. . 1 suppl Lehrs; IºÅŁB suppl Bekker . 2 suppl Lehrs; Œ IºÅŁB suppl Bekker . 13  ºº
Ø  þ P cod, del Brennan . 15  f Æå 
ı ... ı
 ı (Bekker)]  E - E ... Ø cod . 20 X add Bekker . 25 KŒŒŁø suppl Schneider þ Dalimier . 25 suppl Dalimier . 27 supplevi; ŒÆd ÇH ŒÆ suppl Bekker . 29 IÆæŒ  KØ  F ØÆÇ suppl Schneider

What is a disjunction?

5

10

15

20

535

ØÇFåŁÆØ æÆ
r
ÆØ ŒÆd
ή r
ÆØ, e æ
IºÅŁØ. Kd  F  Ø  ı e ı
ÆØŒe
P ıÆØ, Kd –Æ fiH ºªØ


æÆ K
ºøÆØ ‹Ø P
. e  K
ı
Æçfi Æ E ŒÆd K
IŒ º ıŁfi Æ ŒÆŁÆŁÆØ. a 
 Ø  ºØ 
Æ ÆFÆ H
º ªø
, ºªø a c  
Æ e e  Ø F
r  ,  ÆPH
H
ı
ø
ÆØ e ØÇFåŁÆØ j ı
BçŁÆØ. ‰ Y Ø ºª Ø Mb ØÆæÆŁØ
j ¼
ØåÆ 
Æ ÆŁÆØ. ŒÆd ØÆæÆŁØ
ŒÆd ¼
ØåÆ 
Æ ÆŁÆØ. ŒÆd n
æ 
På x
 Æ
d øØŒfiH ¼æŁæ
æ 
Ø
, fiH b ı
Æ
fiø KØÆŁÆØ, e
ÆPe
æ 
På x
 KØ Æ
d º ªfiø 
Æ 

ı
Ø
. ºªø b º ª
e
Ø Æı F Kƪªºº 

ı
çØÆ
. Kç y ªaæ › ØÆÇıŒØŒ , KŒE På › ı
ÆØŒ : ŒÆd ‹ ı › ı
ÆØŒ , KŒE PŒØ › ØÆÇıŒØŒ . ŒÆd Æçb KŒ  F æ ŒØ
ı ‰ åÆØ l  H
ı
ÆØŒH
KƪªºÆ ŒÆd Ø H
ıºŒØŒH
æe c
H
ØÆÇıŒØŒH
, ŒÆŁ
Æ æ 
H
ıºŒØŒH
IØÆç æ 
ø
. ‰ ªaæ ƒ ØÆÇıŒØŒ d PŒ K
IŒ º ıŁfi Æ, P ƒ ıºŒØŒ . N ªaæ z I çÆØ
ŁÆ X Ø æÆ Kd
j
 KØ
j ήd ήa I
Ææ ç
X Ø
 KØ
j æÆ K
IØÆç æE, ‰ N ŒÆd  ºº
Ø  ÆæÆØ ŒÆd )æçø
ÆæÆØ; ŒÆd )æçø
ÆæÆØ ŒÆd  ºº
Ø .

1 b e ... r suppl Schneider + Dalimier .  F  Ø  ı  suppl Schneider . 3 suppl Schneider . 4 suppl Schneider . 5 
Æ ÆF suppl Schneider þ Barnes . e e  Ø F suppl Schneider 12 º ª
add Schneider

536

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APPENDIX B: Galen, inst log

(1) iv 4–6 [4] Kd b
s
B KººØ Å åÅ K
ŁØ  E ¯ ººÅ
KØ
oø ºªØ
PŒ Ø
Ł
Å  ŒÆd Ł E ˜ø
· K
،،
 Ø c
 ØÆÅ
çø
c
B KººØ F åÅ: N b Kç æø
ºª Ø çø
c L  IŒ º ıŁÆ
åØ æe ¼ººÅºÆ  åÅ
, 5 I çÆØŒe
ıºª

ŒÆº 
e  Ø F
IøÆ, ŒÆŁæ Kd  F ˜ø
æØÆE ŒÆd ¨ø
ØƺªÆØ: 10 Æıd ªaæ h åÅ
h IŒ º ıŁÆ
å
Æ ŒÆa ıº Œc
æÅ
ÆØ. [5] Øe ŒIØa
I çŒø
ÆP, e
º ª
KŒE

X Ø ª I çÆØŒc
ıº Œc
j I çÆØŒe
r
ÆØ ıºª

ç 
. ( Pb
ªaæ æe e Ææe
ØÆçæØ ıºª

ºªØ
I çÆØŒe
j ıº Œc
I çÆØŒ
, å
  ª  ı Œ e
K
±fi Å ºØ e źHÆØ ÆçH 15  E ºÆ ‹Øæ i
ÆPe K

fiB.) [6] Iºº ƒ æd æØ
ŒI
ÆFŁÆ fiB ºØ Aºº
j  E æªÆØ æ å
 e

F
–Æ
Æ a Øa H
ıºŒØŒH
ŒÆº ı
ø
ı
ø
ı
Ø
Æ, Œi
KŒ Æå 
ø
j IŒ º Łø
fi q, ıºª
Æ ŒÆº FØ
. (2) xiv 3-8 20 [3] ‹Ø b Ø I çÆØŒ F ıºª
ı ıºº ªØe N I ØØ
åæØ  Pb x  KØ, ŒÆŁæ ª ŒÆd N  fi Å ª Œ  KØ
j    j Zª  j 
Æ  X Ø ¼ºº  ‰ KŒE
Ø ºª ıØ ıºº ªØ , I ØŒÆØ Ø æø
. Iººa
F
æ ŒØÆØ a åæØÆ 

ØæåŁÆØ ÆæƺØ
Æ

1 s
add Kalbfleisch . 2 PŒ Ø
add Kalbfleisch . 3 Ø (Irvine)] Ø cod . çø

þ ‹ Ø cod . 4 çø
 (von Arnim)] çø

cod . – add Kalbfleisch . 5 I çÆØŒ
] -
cod; del Kalbfleisch . 10 æÅ
ÆØ (Kalbfleisch)] -Ø cod . 13 I çÆØŒ
add Mynas . 15 ÆP  (Mynas)] ÆP
cod . 17 æ å
 (Kalbfleisch)] - ıØ cod . 18 fi q addidi . 20 ‹Ø (Mynas)] ‹ cod . ıºº ªØ  (Kalbfleisch)] - ı cod . 21 N  fiB ª (Irvine)] e c › cod, ‹Ø  Kalbfleisch . Œ  þ  cod; þ  Kalbfleisch . 23 

þ ÆP cod

What is a disjunction?

5

10

15

20

25

30

537

 f Kºªå ı H
æØH æ ØŁ
ø
. [4] æ
s
I
Æ ØŒ
H
æd e
æØ
ª ı
ø
K I çÆØŒ F ıºª
ı ŒÆd ŁÆæ ı H
K
ÆPfiH e I
،

 F º Ø F æÆ

Æ, ‰ Kd H
 Ø ø
Påd ŒÆd Ł
Å
KØ ŒÆd  Ł E ˜ø
, ήd 
 KÆ
N  ººa H
ήa e

I Ø r
ÆØ åæØ
¼åæØ ŒÆd H
ØŒÆÅæø
. [5] Kd b H
Æå 
ø
Iººº Ø æƪø
 ŒÆd º ªø

ØÆ b
›º ŒºÅæ
 ŒÆd ºÆ
åØ c
åÅ
Ł æåØ
–Æ  På æåØ
ı

Æ, Ø
a b K   æåØ
b
–Æ c ı

Æ, c æåØ
b –Æ ı

Æ, Øa  F a b
ήa c
ºÆ
åÅ
c
 F ØÇıª
ı æ Ū æÆ
ŒÆºE
MøŒÆ, a b ŒÆa c
KººØB c
B åÅ ±ºH j ŒÆd a æ ŁŒÅ. [6] K
  Ø s
 E æªÆØ
› NæÅ
 ıºº ªØe åæØ  KØ fiB b
ÆPfiB ºØ åæ
fi w æØ , P c
Kd ıºª
fiø ı
Ø
 Iºº Kd  E Æå 
Ø. fi‰Ð ŒÆd ØÆç æÆd  ººÆØ ŒÆa e ıºª

IøÆ ı
Æ
ÆØ. [7] æØH
ªaæ PH
ØÆç æH
K
 E æªÆØ, ØA b
B ήa c
å Å
Kd H
Å  ı
ıÆæå
ø
, æÆ b B ŒÆa c
IŒ º ıŁÆ
Kd H
Id ı
ıÆæå
ø
, ‹Æ  c
IŒ º ıŁÆ
I
ƪŒÆÆ
åØ c
åÅ
e ıºª

IøÆ ı
ÅØ
, › EÆ a  ØÆF KØ ˜ø
æØÆE ŒÆd ¨ø
ØƺªÆØ. Bº
b ŒÆd e I çÆØŒe
ÆP F  Ø F
K 

Påd ŒÆd ˜ø
æØÆE ŒÆd ¨ø
ØƺªÆØ. ƃ b æ ºłØ  : Iººa c
˜ø
æØÆE, [8] Ø b Iººa c
¨ø
ØƺªÆØ. ıæÆÆ b ŒÆa b
c
æÆ
æ ºÅłØ
PŒ ¼æÆ ¨ø
ØƺªÆØ; ŒÆa b c
æÆ
PŒ ¼æÆ ˜ø
æØÆE: æe I ØØ
b  ØÆÅ H
ºH
ØŒÆØ ŒÆd Æ
ÆØ
¼åæÅ  sÆ.

. 1 ıºª
ı (Kalbfleisch)] ıæÆ  cod . ŁÆæ ı (Kalbfleisch)] ŒÆŁ æ ı cod . 4 På] åØ cod; åØ På Kalbfleisch . 5 
KÆ
(Kalbfleisch)]  F ÆØ

cod . ŒÆ] ŒÆŁ º ı cod; ŒÆŁ ‹º
Mynas . 6 K (Kalbfleisch)] K cod . 8 Ł (Kalbfleisch)] –Æ cod . 11 ŒÆ add Prantl . 12 æ ŁŒÅ þ KººØ F åÅ cod . 18 I þ  cod . 24–25 ŒÆd ¨ø
...  post Kalbfleisch addidi

20 Medicine, experience, and logic* And he said, Oh let not the Lord be angry and I will speak yet but this once: Peradventure ten shall be found there. And he said, I will not destroy it for ten’s sake.

I turn now to tell you of what has become clear to me on reflexion and investigation, viz that the examination of a thing very many times does not admit of a final decision. Reflect upon my words and study them to see if I do an injustice or if I am a master of the principles on which the proof is based, either as regards the opinion that I hold and am convinced of or as regards the things which they support and are convinced of. And that is that they say that a thing which has been seen only once is not accepted nor reliable, and similarly for what has been seen a few times. They think that a thing is only acceptable and reliable if it has been seen a great number of times — and moreover in the same manner on each of the times. Then I ask them concerning that which has been seen ten times whether it is included among that which has been examined a great many times; and their answer to that is No. Then I say to them: And that which has been seen eleven times? And they say No. Then I ask them also concerning that which has been seen twelve times; and they say No. Then I say to them: And that which has been seen thirteen times? And they say this also has not reached that limit. I continue in this vein: I extend the question one by one until I reach a large number. The necessity for the respondent is inevitable: either he does not admit at any one time that the number has already reached the limit of that which is said to be a very large number; or, if he does admit it, he has already reduced himself at that time to the status of a laughing-stock, since he is asking that people allow him a number and a limit according to a usage fixed by himself and an opinion contrived for himself. And the speaker might say to him: Why has what has been seen fifty times, for example, become as if it has been seen a great many times, and that which has been seen forty-nine times is not among that which has been seen a great many times? Your assertion is the assertion of one who asserts two mutually contradictory issues. And that is that you have affirmed that what has been seen once is not therefore acceptable or [25] reliable. Then we see now that you have admitted that it is acceptable and * First published in J. Barnes, J. Brunschwig, M.F. Burnyeat, and M. Schofield (eds), Science and Speculation (Cambridge, 1982), pp.24–68.

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reliable, because if what has been seen forty-nine times and in all those times has been unacceptable and unreliable has only to be increased by one time to become acceptable and reliable, then it is clear that in fact it ends up acceptable and reliable by one examination only. Then it must be, from that, that the examination of the thing once — which has already been, from the beginning of the issue, unacceptable and unreliable — has acquired at this time the power that, when it was added to the thing that was already unacceptable and unreliable, makes it acceptable and reliable. And if it is curtailed and removed, it makes the thing which was already acceptable and reliable unacceptable and unreliable. This, then, is what the Dogmatists argue against the Empiricists with regard to the examination of the thing very many times; and they are arguments which ought to be remembered by heart and borne in mind.

Galen’s treatise On Medical Experience,1 from which that passage is taken, is a dramatic account, in dialogue form, of the disputes between the Empirical doctors and the Dogmatic or Logical doctors — disputes which ran on for several centuries and which dealt with numerous issues in the philosophy of science. Galen wrote the work when he was a young man of twenty: in his later Outline of Empiricism he refers to it for a fuller discussion of one of the major problems faced by the Empirical School: And just as the art as a whole is put together from several experiences, so again individual experiences of this sort are put together from many experiences. But this, viz the question ‘From how many?’, is indeterminable, and falls into the puzzling sort of argument which some call ‘soritical’: I have spoken more fully about that in another book, entitled On Medical Experience. (subf emp 38.12–17)2

[26] The Empirical doctors hold that the art of medicine is a congeries of ‘experiences’, and that an ‘experience’ is made up of many particular 1 Apart from two short passages of Greek, the treatise survives only in an Arabic translation. The Arabic is (as usual) at two removes from the original, being a translation of a Syriac translation. Although the Arabic is not sufficiently literal to permit a ‘back-translation’ into Greek, comparison with the surviving Greek fragments suggests that it provides a reliable account of Galen’s arguments. The Arabic has been edited and translated by R. Walzer, Galen on Medical Experience (Oxford, 1947). For discussion of the text and content, see the introduction to that edition, and also R. Walzer, ‘Galens Schrift u¨ber die medizinische Erfahrung’, Sitzungsberichte der preussischen Akademie der Wissenschaften phil. hist. Kl. (Berlin, 1932), pp.449–468; id, ‘Uno scritto sconosciuto di Galeno’, Rivista di storia critica delle scienze mediche e naturale 19, 1938, 258–265; K. Deichgra¨ber, Die griechische Empirikerschule (Berlin/Zurich, 19652), p.400. — The passage I have quoted is Med Exp VII 8–VIII 1. I am indebted to Adam Bruce-Watt of Balliol College, who has been kind enough to check Walzer’s translation against the Arabic and to suggest several improvements. 2 sicut autem ex pluribus emperiis componitur tota ars, ita rursus singula huiusmodi emperiarum ex multis emperiis. hoc autem — scilicet ex quot — indeterminabile est et subincidit in ambiguam rationem quam quidam nominant soriticam. — The Outline survives only in a Latin translation, for which Deichgra¨ber, Empirikerschule, pp.42–90, proposes a Greek ‘back-translation’.

540

Logical Matters

observations; but the ‘soritical’ argument rehearsed in On Medical Experience threatens the central notion of an ‘experience’ with incoherence. The concept of ‘experience’ has a long history, going back through Aristotle to the Presocratic philosophers.3 I shall not attempt to write that history, nor to give an account of the precise way or ways in which the concept was understood by the Empirical doctors who took their sobriquet from it. I assume that an experience is a piece of general knowledge (‘Pomegranates cure diarrhoea’),4 based upon a series of particular observations (‘Pomegranates were good for Dio when he had diarrhoea’); and I assume, further, that in the eyes of the Empiricists the general knowledge was justified by its observational basis.5 In effect, then, the Empirical doctors were committed to the acceptability of certain inductive inferences; and the soritical argument — or the sorites, as it is now customarily called — was used by the Dogmatists to cast doubt upon induction. The argument between Dogmatist and Empiricist in On Medical Experience is not a literary fiction: Galen says that he is recording, in a more orderly form, a conversation which took place between two eminent physicians, Pelops (Galen’s own Dogmatist teacher) and Philippus;6 and Pelops and Philippus themselves claim to be [27] reviewing a much older debate — Pelops’ case is ‘similar to Asclepiades’ view’, while Philippus’ argument is to be thought of as ‘laid down by a representative of the Empiricists, Menodotus, if you like, or Serapion, or Theodosius’.7 Thus the argument I am about to consider actually exercised medical practitioners, and considerations of an

3 See e.g. P.H. and E.A. de Lacy, Philodemus: On Methods of Inference (Naples, 19782), pp.165– 182. (The connexion between Empiricist doctors and Epicureans requires some examination.) 4 The knowledge may be universal (‘All sufferers ... ’), but it need not be: experience, or general knowledge, is sometimes a matter of what happens as a rule (‘Most sufferers ... ’), or IçØ ø (‘For half the time, sufferers ... ’), or rarely (‘A few sufferers ... ’). In what follows I shall usually have universal knowledge in mind; but most of the arguments are readily generalized to cover all varieties of experience. 5 Both assumptions are questionable. (1) Many texts imply that ‘experience’ is no more than the possession of numerous bits of particular information: no process of generalization — and hence no inference — is involved at all. (2) Even if ‘experience’ is general knowledge which arises from a multitude of observations, it is not clear that the relation between experience and observation need be one of inference: perhaps, rather, a multitude of observations simply produces or causes a piece of general knowledge. — Any discussion of the nature of medical Empiricism would have to look closely at those issues. I pass them by for two reasons: first, it is clear that sometimes — and notably in Med Exp — the question of justifying claims to general knowledge is uppermost in the minds of the disputants; secondly, my discussion of the sorites is largely independent of such issues. 6 See Galen, libr prop XIX 16–17. 7 Galen, Med Exp II 3. The elements of the argument thus go back to the second century bc.

Medicine, experience, and logic

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abstract and logical nature were an integral part of a debate which bore directly upon therapeutical practice and affected the welfare of patients. The sorites was no invention of the physicians, nor was it peculiar to medical disputations. Elsewhere, discussing the question of the time at which a disease may be said to commence, Galen observes that for present purposes, we are not affected by the argument from little-by-little, which they also call soritical; for the puzzle arising from it is common to many matters of everyday life, about which philosophers and doctors before my time have talked and argued. (loc aff VIII 25)*

Who were those doctors and philosophers? and how did they argue? What was the history of the sorites? How were its puzzles solved? Before turning to those questions, I shall first attempt to give a clear account of what constitutes a soritical argument.

I Galen’s Dogmatist presents his case informally, by posing a series of questions: Are ten observations many? are eleven? are twelve? ... And other authors who parade soritical arguments often do so in the same interrogative fashion. But we can — and the ancients did — see a logical structure behind that dialectical facade. A reasonably formal account of the argument can be found at the end of Diogenes Laertius’ survey of Stoicism, where he lists the ‘puzzling arguments’ traditionally discussed in Stoic logic.8 The text of Diogenes is corrupt; but the description of the sorites can be rescued intact: It is not the case that two are few and three are not also; it is not the case [28] that these are and four are not also (and so on up to ten thousand). But two are few: therefore ten thousand are also. (VII 82)9 * Pb
A N a Ææ
Æ  F Ææa ØŒæe
º ª ı ºı F
 , n
ŒÆd øæÅ
O
Ç ıØ
· Œ Ø
c ªaæ K ÆP F æe  ººa H
ήa e

I æÆ æd z
YæÅÆØ ŒÆd ØŒÆØ  E æe K F çغ  ç Ø  ŒÆd NÆæ E. 8 For similar references to the sorites as a standard º ª  ¼ æ  in Stoicism, see Cicero, div II iv 11; Gellius, I ii 4; Lucian, Symp 23; Fronto, eloq ii 13 [p.140 van den Hout]; Martianus Capella, IV 327. 9 Påd a b
 OºªÆ K
, Påd b ŒÆd a æÆ, Påd b ŒÆd ÆFÆ 
, Påd b ŒÆd a ÆæÆ ŒÆd oø åæØ H
ŒÆ· a b  OºªÆ K· ŒÆd a ŒÆ ¼æÆ. — There are lacunae before and after the passage quoted (see Menagius ad loc); but there is no doubt that the passage describes the sorites. With U. Egli, Zur stoischen Dialektik (Basel, 1967), pp.8, 55), I read ‘ıæø
’ and ‘æØÆ’ for ‘ŒÆ’ and ‘ŒÆ’ (cf Sextus, M VII 416–421). Sillitti’s proposal to insert a lot more

542

Logical Matters

Strictly speaking, the argument Diogenes describes contains 9,999 premisses; but the figure of 10,000 is a conventionally vast number, and nothing hangs upon it: we may generalize and give the argument n premisses, where n will be pretty large. One of the n premisses is simple (‘Two are few’, in Diogenes); the remainder are negated conjunctions, of the form ‘Not both P and not-Q’ (‘It is not the case that two are few and three are not also’). In many ancient presentations of soritical arguments, we find conditionals instead of negated conjunctions, ‘If P, then Q’ instead of ‘Not both P and not-Q’; and, on the weak or ‘material’ interpretation of ‘If ... , then ... ’ which is customary among modern logicians, ‘If P, then Q’ is logically equivalent to ‘Not both P and not-Q’. We know that Chrysippus would sometimes replace conditionals by negated conjunctions when he supposed that the conditional would be true only if it were given a weak or ‘material’ interpretation;10 and since Diogenes’ account of the sorites is Stoic in origin, it is plausible to suspect that Chrysippus did the same thing here. Why might he have done so? Soritical arguments are in no sense ‘weaker’ when formulated with negated conjunctions than they are when formulated with some tough form of conditional proposition. On the contrary, they are ‘stronger’, [29] inasmuch as their premisses assert less and are thus easier to sustain and harder to reject. Chrysippus needed to show that soritical arguments — or rather, those soritical arguments which furnished paradoxes — were not sound. If you want to refute a position, then you had best consider it in its strongest form — and in formulating soritical arguments by way of negated conjunctions, that is just what Chrysippus was doing.12 In my own formulations of soritical arguments, I shall prefer an overtly conditional form of proposition; but I shall use the artificial symbol ‘’, rather than the English ‘If ... , then ... ’, in order to make it clear that the conditionals in question are to be construed as weak or material.11 into the text is based upon a misunderstanding of the logic of the argument (see G. Sillitti, ‘Alcune considerazioni sull’ aporia del sorite’, in G. Giannantoni (ed), Scuole socratiche minori e filosofia ellenistica (Bologna, 1977), pp.75–92, on pp.77, 83). 10 See Cicero, fat vi 12. The Stoics generally preferred a strong interpretation of ‘if ... , then ... ’: discussion in M. Frede, Die stoische Logik (Go¨ttingen, 1974), pp.80–93. 12 For criticism of this paragraph (which was written in reaction to certain remarks in D.N. Sedley, ‘Diodorus Cronus and Hellenistic philosophy’, Proceedings of the Cambridge Philological Society 23, 1977, 74–120 — see p.91 and n.97) see D.N. Sedley, ‘On signs’, in J. Barnes, J. Brunschwig, M.F. Burnyeat, and M. Schofield (eds), Science and Speculation (Cambridge, 1982), pp.239–272, on pp.253–255); id, ‘The negated conjunction in Stoicism’, Elenchos 5, 1984, 311–316. See also J. Barnes, ‘—ØŁÆ
a ı
Å
Æ’, Elenchos 6, 1985, 453–467 [reprinted above, pp.499–511]. 11 The argument does not require formulation in terms of material implication: it works for any conditional for which modus ponens holds good, i.e. for any conditional at all.

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Stated most generally, then, the logical structure underlying any soritical argument will look like this: P1 P1  P2 P2  P3 ... ... Pn  1  Pn —— Pn There is nothing esoteric or obscure about that argument pattern; nor — at any rate on the surface — does there seem to be anything fallacious about the sorites. Rather, the argument pattern seems evidently valid; and even if its validity is not perfectly evident, it can be reduced to a pattern which must count as evidently valid if any argument pattern does. For the first two premisses yield, by the inference known as modus ponens, the proposition P2; P2 and the third premiss yield, again by modus ponens, P3; and so, by a series of modus ponens inferences, to Pn — however large n may happen to be.* The logical simplicity of the argument is to be emphasized. The sorites is often connected with, and held to produce puzzles for, the complex inference pattern known as ‘mathematical induction’.13 That may be so; but if it is so, it is not because the sorites has the form of a mathematical induction. If the argument produces puzzles for any inference pattern, it produces puzzles for [30] modus ponens; if the argument sheds doubt on any principles of logic, it

* M. Mignucci, ‘The Stoic analysis of the sorites’, PAS 93, 1993, 231–245, on pp.234–239, urges — on the basis of Galen’s example in Med Exp — that the original form of the sorites was in effect a sequence of modus ponens arguments, of which the argument pattern I here present (his pattern I*) is an abbreviated or derived version. 13 The rule of mathematical induction can be formulated as follows: Given (i) F(0) and (ii) For any n, if F(n) then F(n þ 1) infer: For any n, F(n) Informally speaking, the principle behind the rule is this: if zero possesses a given property; and if the successor to any number has that property provided that the number in question has the property: then every number has the given property. For the connexion between this and modus ponens, see e.g. M. Dummett, ‘Wang’s paradox’, Synthe`se 30, 1975, 301–324, on pp.303–306 [¼ Truth and other Enigmas (London, 1978), pp.248–268].

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sheds doubt on one of the most simple and fundamental of all logical principles. Next, we may observe that each Pi in the argument pattern — at any rate, in the simplest and most common cases — will be a singular proposition ascribing a predicate to a subject, predicating ‘F( )’ of a. The specific structure of the argument is thus: Fa1 Fa1  Fa2 Fa2  Fa3 ... ... Fan–1  Fan ————— Fan That is — or will here count as — the logical form of a sorites argument. Is any argument of that form a sorites? Some logicians, or historians of logic, use the term ‘sorites’ in such a way that the answer to the question is ‘Yes’. In that case, there is nothing wrong with soritical arguments in general; for evidently, any number of perfectly unproblematical arguments have that form. Other logicians, or historians of logic, use the word ‘sorites’ in such a way that every soritical argument is essentially paradoxical; and I shall here follow that second use of the word. (Nothing whatever hangs upon that choice.) For an argument to be soritical — paradoxically soritical — it must have the form I have just described, and in addition its subjects — the ais — and its predicate — ‘F( )’ — must satisfy certain conditions. The conditions are not demanding. First, the ais. Diogenes’ text uses the numerals ‘2’, ‘3’, ... , ‘10,000’; but he is not talking about the numbers 2, 3, ... , 10,000 (it is nonsense to say that the number 2 is few). Rather ‘2 are few’ stands for ‘Two so-and-sos are few’ (as it might be, ‘Two experiences are few’), and is thus implicitly general. If we take Diogenes strictly, we shall suppose that the ais are always groups or sets of things; but that supposition is unduly pedantic, and it has the unwelcome consequence that the most notorious of ancient sorites (Carneades’ argument against the gods) are not soritical. The subjects of a sorites must form an ordered set:

The use of numerals in Diogenes’ general description of the sorites need indicate no more than that the ais are thus ordered.

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Secondly, ‘F( )’. Diogenes uses ‘few’; the sorites in On Medical Experience can readily be formulated in terms of ‘few’; and indeed the term was standardly employed in ancient accounts of the argument. But the sorites is not about fewness, and ‘few’ is not the unique soritical predicate: ‘few’ may [31] be paradigmatically soritical, but the ancient texts provide us with plenty of sorites which do not use ‘few’. In Diogenes, then, ‘few’ stands as the representative of a general class of predicate: how can that class — the class of soritical predicates — be characterized? A predicate ‘F( )’ will be soritical — rather: will be soritical relatively to a given sequence of subjects 14 — if it satisfies three conditions. First, ‘F( )’ must, to all appearances,15 be true of a1, the first item in the sequence of subjects. Secondly, ‘F( )’ must, to all appearances, be false of an, the last item in the sequence of subjects. Finally, each adjacent pair of subjects in the sequence must, to all appearances, be indistinguishable with respect of ‘F( )’; that is to say, given any two adjacent subjects, ai and ai þ 1, it must be the case, to all appearances, that either ‘F( )’ is true of both of them or else it is false of both. The first of those three conditions makes plausible the first premiss of soritical arguments; for if ‘F( )’ is true of a1, then it is true that Fa1. The second condition indicates that the conclusion of the argument is false; for, if ‘F( )’ is false of an, then it is false that Fan. The third condition validates all the hypothetical premisses of the argument: unless ‘F( )’ is true of a1 and false of a2, it is true that Fa1  Fa2 is true; unless ‘F( )’ is true of a2 and false of a3, it is true that Fa2  Fa3; and so on, down to an  l and an. Thus soritical 14 The qualification is necessary: ‘F( )’ may satisfy the soritical conditions for some sequences of subjects but not for others. (‘Small’ might be soritical for the sequence but not for the sequence .) A predicate might be called unqualifiedly soritical if it satisfied the following condition: for any object, x, if ‘F( )’ is to all appearances true of x, then there is some sequence of which x is a member and for which ‘F( )’ is soritical. If a predicate is soritical relative to some sequence, does it follow that it is unqualifiedly soritical? 15 Why ‘to all appearances’? Not every argument of the logical form set out above is a sorites — not every predicate will produce puzzles if it is substituted for ‘F( )’ in the schema. Hence it seems necessary to give some general characterization, however vague, of those predicates which do produce puzzles. Plainly, it will not do to say that ‘F( )’ is soritical if it is actually true of a1, actually false of an ... — no predicate could satisfy such conditions. I might have said that a1 should be a ‘paradigm instance’ of ‘F( )’ (cf Carneades’ formula: N  ª qÆ
Ł , ŒÆd › ˘f i
YÅ Ł  — Sextus, M IX 184); or that it should be ‘eminently plausible’ to predicate ‘F( )’ of a1, etc.; or that ‘anyone would grant’ that ‘F( )’ is true of a1, etc. I hope that the general thrust of such phrases is plain: ‘to all appearances’ has the same general thrust; and that is all that matters about the phrase. (It may be worth adding that ‘to all appearances’ is used only in the characterization of soritical predicates: it is not a part of those predicates themselves, nor does it appear in the premisses of soritical arguments.)

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predicates, and soritical arguments, are paradoxical in the following sense: if ‘F( )’ is soritical, then by the second condition it does [32] not, to all appearances, hold of an and by the first and third conditions taken together, it does, to all appearances, hold of an. It is perfectly obvious that not-Fan; but evidently valid moves from evidently true premisses lead to the conclusion that Fan. Soritical arguments were sometimes called arguments from ‘little-bylittle’;16 for they proceed little by little from palpable truth to palpable falsity.17 But their standard ancient name was ‘øæÅ’.18 The Greek 16 › Ææa ØŒæe
º ª : Galen, loc aff VIII 25; Med Exp XVI 2; Sextus, M I 68–69; Chrysippus, ¸ ªØŒa ˘ÅÆÆ [PHerc 307] IX 19–20; Diogenes Laertius, VII 197; Plutarch, Stoic rep 1084AC; cf Aspasius, in EN 57.5; Simplicius, in Phys 1117.2; gradatim: e.g. Cicero, Luc xvi 49; cf Seneca, ben V xix 9 (paulatim). A. Ru¨stow, Der Lu¨gner (Leipzig, 1910), p.77 n.2, argues that ‘› Ææa ØŒæe
º ª ’ is a highly generic expression (‘Kleine Ursachen, grosse Wirkungen’), of which the sorites and the Liar are both specifications. Certainly, ‘Ææa ØŒæ
’ is used in logical contexts where soritical arguments are not in question (Ru¨stow cites Aristotle, Soph El 169b11, 15; APr A 47b38); but the evidence shows, I think, that ‘› Ææa [or: ŒÆa] ØŒæe
º ª ’ was also used specifically of the sorites. 17 natura cavillationis quam Graeci øæÅ
appellant haec est, ut ab evidenter veris per brevissimas mutationes disputatio ad ea quae evidenter falsa sunt perducatur (Ulpian, dig I xvi 177; cf Julian, ibid, xvii 65); › ... øæÅ  çØØŒ  KØ
º ª  KŒ B Ææa ØŒæe
Kæøø Iªø
ήa c
ŒºıØ
H
çÆ
Æø
K ¼ź
j łF  KŒçÆ
 (Simplicius, in Phys 1177.2–4 ¼ Scholiast to Lucian [vol IV p.254 Jacobitz]). 18 In Greek, the standard nomenclature is ‘› øæÅ º ª ’ (or simply ‘› øæÅ’); ‘ øæØØŒc I æÆ’ and ‘ øæØŒc I æÆ’ are also found, in Sextus and in Galen. Latin authors normally use ‘sorites ’. (The form ‘soritam ’ is found in the MSS of Nonius, 329.19 [¼ Cicero, Hortensius, frag 26 Grilli]; but the text should be emended, with Ru¨stow, to ‘soritas ’.) Cicero, div II iv 11, proposes ‘acervalis [sc ratio]’ as a suitable Latin translation of ‘øæÅ ’; but he adds that ‘sorites ’ is already well established in Latin so that there is no need for ‘acervalis ’. (The word ‘acervalis ’ was apparently never taken up, although Latin writers will often use ‘acervus ’ in connexion with the sorites.) Words ending in ‘-Å’ are common in Greek: C.D. Buck and W. Petersen, A Reverse Index of Greek Nouns and Adjectives (Chicago IL, 1944), pp.544–573) list some 4,500, of which about 750 are in ‘-Å’. The termination is ancient (e.g. ‘›Å’ from Homer onwards), and ‘its most common and probably oldest use was as an agent suffix’ (Buck and Petersen, p.544). ‘øæÅ’ is formed from ‘øæ ’, ‘heap’ (cf e.g. ‘ŒÆźÅ’ from ‘Œź ’), and it is naturally taken in an ‘agentive’ sense: ‘heaper’, ‘accumulator’. (For the adjectival use of such ‘agentives’ cf e.g. ‘›ºÅ’.) Admittedly, some words in ‘-Å’ are ‘agentive’ only in an extended sense, and others have no ‘agentive’ force at all (e.g. ‘IŒÅ’, a form of disease; or ‘çÆæƌŒ, which is apparently used exclusively as an adjective, usually in the sense of ‘drugged’); but the general truth about ‘-Å’ terminations makes it reasonable to suppose that ‘øæÅ’ was originally intended in the ‘agentive’ sense of ‘accumulator’. Chrysippus is the first author we know to have used the word ‘øæÅ’; but it is plausible to think that it was coined by Eubulides to name his argument. Sedley, ‘Diodorus Cronus’, p.115 n.132, points out that the titles of the ancient paradoxes often have a double sense — ‘the KªŒŒÆº
 is a veiled argument about a veiled man’. In the same way, the øæÅ may be seen as an accumulating argument about an accumulating man: the argument adds premiss to premiss (or question to question) as the man adds grain to grain. The term ‘sorites’ is long established as the English for ‘øæÅ’. We speak of the Master argument, not of the Cyrieuon, of the Liar, not of the Pseudomenus: why not translate ‘øæÅ’

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word is an adjective cognate with the noun ‘Hæ ’, which means ‘heap’ or ‘pile’; and the adjective was [33] applied to the argument because the original soritical argument was about a heap or pile. ‘There are some Dogmatists and logicians who call the argument expressing this doubt a sorites, after the matter which first gave rise to this question, I mean the heap’.19 The original sorites is expounded as follows in Galen’s Medical Experience: Wherefore I say: tell me, do you think that a single grain of wheat is a heap? Thereupon you say No. Then I say: What do you say about 2 grains? For it is my purpose to ask you questions in succession, and if you do not admit that 2 grains are a heap then I shall ask you about 3 grains. Then I shall proceed to interrogate you further with respect to 4 grains, then 5 and 6 and 7 and 8; and I think you will say that none of these makes a heap. Also 9 and 10 and 11 grains are not a heap. For the conception of a heap which is formed in the soul and is conjured up in the imagination is that, besides being single particles in juxtaposition, it has quantity and mass of some considerable size... . I for my part shall not cease from continuing to add one to the number in like manner, nor desist from asking you without ceasing if you admit that the quantity of each single one of these numbers constitutes a heap. It is not possible for you to say with regard to any one of these numbers that it constitutes a heap. I shall proceed to explain the cause of this. If you do not say with respect to any of the numbers, as in the case of the 100 grains of wheat for example, that it now constitutes a heap, but afterwards when a grain is added to it, you say that a heap has now been formed, consequently this quantity of corn becomes a heap by the addition of the single grain of wheat, and if the grain is taken away the heap is eliminated. And I know of nothing worse and more absurd than that the being and not-being of a heap is determined by a grain of corn. And to prevent this absurdity from adhering to you, you will not cease from denying, and will never admit at any time that the sum of this is a heap, even if the number of grains reaches infinity by the constant and gradual addition of more. And by reason of this denial the heap is proved to be non-existent, because of this pretty sophism.20

The sequence of subjects is a series of collections of grains. The first item, a1, [34] consists of one grain, a2 of two, and so on. The soritical predicate is ‘ ... . does not constitute a heap’. You can never make a heap of grain, however many sackfuls of wheat you pour out. instead of transliterating it? In the first version of this chapter, I used ‘heap’ and ‘heap-like’ for ‘øæÅ’ (‘heaper’ would have been better); in a second version I tried ‘accumulator’ and ‘accumulative’. But although both translations have the merit of giving the sense of ‘øæÅ’, they are unpleasing — and my friends told me that they would never catch on. So I have returned to orthodoxy, and write ‘sorites’ and ‘soritical’. 19 Galen, Med Exp XVI 2. Sillitti’s suggestion (‘Alcune considerazioni’, p.76 n.2) that the application of the sorites to heaps of grain may be post-Aristotelian is implausible. 20 Galen, Med Exp XVII 1–3; cf Aspasius, in EN 56.27–57.7.

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Some ancient texts say that soritical arguments may proceed either ‘by adding’ or ‘by subtracting’.21 The original sorites, as Galen reports it, proceeds ‘by adding’: each successive ai is obtained by adding one grain to its predecessor. The heap example can also be presented in a ‘subtracting’ form: let a1 be a collection of 1,000,000 grains, a2 a collection of 999,999 grains, and so on; and let ‘F( )’ be replaced by ‘ ... constitutes a heap’. Then the argument shows that even a single grain constitutes a heap — or, for that matter, that a collection of no grains constitutes a heap; and the reasoning proceeds by successively ‘subtracting’ one grain from the previous collection. In general, if ‘F( )’ is soritical for , then ‘not-F( )’ is soritical for ; and vice versa. And one of each pair of such soritical arguments may be regarded as proceeding ‘by addition’, the other as proceeding ‘by subtraction’. The sorites would be little more than an amusing conundrum if only such relatively tedious predicates as ‘ ... does not constitute a heap’ were soritical. But in fact, as Galen says, ‘the puzzle arising from it is common to many matters of everyday life’ (loc aff VIII 25); and the argument’s ancient exponents tricked it out with philosophical as well as with quotidian predicates. For according to what is demanded by the analogy, there must not be such a thing in the world as a heap of grain, a mass or satiety, neither a mountain nor strong love, nor a row, nor strong wind, nor city, nor anything else which is known from its name and idea to have a measure of extent or multitude, such as the waves, the open sea, a flock of sheep and herd of cattle, the nation and the crowd. (Med Exp XVI 1)

Cicero, two centuries earlier, had generalized the case: The nature of things has provided us with no knowledge of boundaries so that in any case we could determine how far to go; nor is this so only in the case of the heap of grain, from which the name derives; but in no case at all if we are questioned by degrees — is he rich or poor? [35] famous or obscure? are they many or few, great or small, long or short, broad or narrow? — do we know how much is to be added or subtracted before we can answer definitely. (Luc xxix 92)*

Virtually all predicates are soritical. 21 e.g. Cicero, Luc xvi 49; Scholiast to Persius, ad VI 80 [p.350 Jahn]; Galen, Med Exp XVII 4 (‘I wish to capture you ... from two sides’). If we are to believe Galen, the original sorites was an ‘adding’ argument. But there is no interesting difference between the ‘adding’ and the ‘subtracting’ arguments. * rerum natura nullam nobis dedit cognitionem finium ut ulla in re statuere possimus quatenus. nec hoc in acervo tritici solum — und nomen est — sed nulla omnino in re minutatim interrogati, dives pauper, clarus obscurus sit, multa pauca, magna parva, longa brevia, lata angusta, quanto aut addito aut dempto certum respondeamus non habemus.

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After centuries of comparative neglect, philosophers have recently begun to pay serious attention to the sorites. Some are worried by the fact that certain epistemologically basic predicates are soritical. Take, for example, the observational predicate ‘ ... is red’. Construct a band of colour, dark red at the lefthand end and shading by degrees through light red and orange to yellow at the right-hand end; and mark off a series of points, a1, a2, ... , an, from left to right. Now a1 is patently red; and an is patently not red. But any two adjacent points are indistinguishable in respect of colour: if ai is red, then so too, to all appearances, is ai þ 1, and vice versa. Thus ‘ ... is red’ is a soritical predicate; and all our colour-predicates — and, in general, all our observation-predicates — are threatened by soritical paradoxes.22 Other philosophers have considered predicates associated with ordinary middle-sized objects. Take, for example, ‘ ... is a table’. Tables, we know, are made up of millions of minute particles; and plainly if you remove just one particle from a table, what is left will still be a table. It is clear, then, that tables — and in general, all material objects — provide us with matter for soritical arguments: we can show that a single atom is a table, if anything is a table — and hence conclude that there are no tables at all. Ordinary predicates of everyday life are infected by soritical paradox.23 The sorites must be taken seriously: the Dogmatic doctors were on to a good thing.

II Galen reports that soritical arguments had been discussed by ‘philosophers and doctors’ before his time: the particular debate which he records took place in about ad 150; but at that time the dispute between Empirical and Logical doctors was already centuries old, and the sorites had no doubt entered their debates at an early stage. And, as I have observed, the sorites is also found [36] outside medical contexts: it was closely associated with the Stoics, and it functioned as a powerful weapon in the battle between the Stoa and the Sceptical Academy; it was familiar enough, as we should expect, to philosophers of other schools — to the Peripatetics and to the Pyrrhonists. 22 See e.g. C. Wright, ‘On the coherence of vague predicates’, Synthe`se 30, 1975, 325–365; id, ‘Language-mastery and the sorites paradox’, in G. Evans and J. McDowell (eds), Truth and Meaning (Oxford, 1976), pp.223–247. 23 See e.g. P. Unger, ‘I do not exist’, in G.F. Macdonald (ed), Perception and Identity (London, 1979), pp.235–251.

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More interestingly, it was known outside strictly philosophical circles. Horace uses it in his mocking attack on the laudatores temporis acti: old poets are best, but who counts as old? A poet who lived a century ago, perhaps; well then, let us subtract a month from that century: surely a poet who lived that long ago was old? And subtract a further month; and a further month. All poets are old if any are; and our opponent collapses, ‘overcome by the argument of the diminishing heap’.24 Persius urges someone to ‘sell his soul for cash’: he doubles his money, trebles it, quadruples it — but where should he stop? when will he be rich? Persius ironically comments: ‘We have found someone to put a limit to your heap, Chrysippus’.25 In antiquity, the sorites was as notorious as the Liar.26 The discovery of the sorites is usually ascribed to Aristotle’s contemporary, Eubulides.27 According to Diogenes Laertius, he proposed many arguments in logic — the Liar, the Elusive Man, the Electra, the Veiled Man, the Sorites, the Horns, the Bald Man. (II 108)

Diogenes does not actually say that Eubulides invented those arguments;28 and some scholars have attempted to push the origins of the sorites back a century or so, ascribing it to Zeno of Elea.29 In his paradox of the Millet Seed, Zeno argued that since a [37] bushel of seed makes a noise as it falls to the ground, any individual seed must also make a noise on falling. Now it is 24 Epistles II i 36–49: ‘the demonstration is deliberately presented in terms of hackneyed school logic’ (E. Fraenkel, Horace (Oxford, 1957), p.387 n.2). (Tacitus, dial 16, asks the same question, ‘Who are the old writers?’; but he does not allude to the sorites.) 25 Satires VI 75–80; see the scholiast to line 80 [p.350 Jahn]. Persius was a friend of the Stoic Cornutus, who became his literary executor (see the ancient Life, ed Jahn, pp.233–234). For ‘rich’ as a soritical predicate, see e.g. Cicero, Luc xxix 92 (quoted above, p.[35]); Aspasius, in EN 56.29–32; for the indeterminacy of the money-grubber’s desires, see the passages cited by Jahn, p.229. 26 See the Appendix. Not every occurrence of the word ‘Hæ ’ alludes to the sorites: scholars regularly refer to e.g. Tatian, adv Graec 27; but when he asks   i
TçºØ ºØ ØŒc ŒÆd çغ  çø
øæÆ ŒÆd ıºº ªØH
ØŁÆ
Å ... ; he means ‘a gaggle of philosophers’, not ‘the sorites of the philosophers’. Again, ‘acervus ’ is frequently used in Latin texts without any reference to the sorites — though it is tempting to see such a reference in passages like Horace, Epistles I vi 35. 27 On whom, see K. Do¨ring, Die Megariker (Amsterdam, 1972), pp.102–114; R. Muller, ‘Euboulide`s de Mile´t’, DPhA III, pp.245–248. 28 And in fact the ancients were not unanimous about the authorship of the paradoxes: some ascribed some of them to Diodorus (see Diogenes Laertius, II 111), some ascribed some of them to Chrysippus (id, VII 187). — Abraham got there first: Genesis XVIII 23–33. 29 See e.g. G. Grote, Plato and the Other Companions of Sokrates (London, 18672), III p.490 n.e.; E. Zeller, Die Philosophie der Griechen (Leipzig, 19225), II i, p.265 n.1; H.J. Kra¨mer, Platonismus und Hellenistische Philosophie (Berlin, 1971), pp.59, 75; Do¨ring, Megariker, p.111. contra e.g. J. Moline, ‘Aristotle, Eubulides, and the sorites’, Mind 78, 1969, 393–407, on p.393 n.3; Sedley, ‘Diodorus Cronus’, p.112 n.85; Sillitti, ‘Alcune considerazioni’, p.393 n.3. It has been suggested that the Millet Seed, though not soritical, gave Eubulides the idea of the sorites (Moline, loc cit; G. Reale, Storia della filosofia antica (Milan, 1976), III p.67): the suggestion is attractive, but untestable.

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certainly possible to get from Zeno’s premiss (‘A bushel makes a noise’) to his conclusion (‘An individual seed makes a noise’) by way of a soritical argument. But our evidence, such as it is, indicates that Zeno did not proceed in that fashion; rather, he derived his conclusion by the aid of a principle of proportionality which has nothing to do with the sorites.30 Our texts do not present the Millet Seed in soritical form, and there is no reason to think that Zeno himself gave it a soritical twist: so far as we can tell, Eubulides was the first man to hit upon the sorites. Diogenes mentions the sorites as one of seven paradoxes.31 According to Sextus (M VII 13), Eubulides was exclusively interested in logic; and we might well suppose that for him the sorites was a logical puzzle and nothing more.32 After all, logical puzzles are captivating things: they divert partyguests, and they delight logicians even when they have no serious moral to convey; and the evidence of Plato’s Euthydemus and of Aristotle’s Sophistici Elenchi shows that puzzles of that sort were found as entertaining in the fourth century BC as they are now. Nevertheless, many scholars have searched for a philosophical context within which to set Eubulides’ paradoxolatry.33 Of the [38] several suggestions which 30 For the Millet Seed, see Aristotle, Phys H 250a19–22; Simplicius, in Phys 1108.18–28. The ‘principle of proportion’ Zeno relies upon is something like this: if a weight w makes a sound of volume v on falling a distance d, then for any n a weight w/n will make a sound of volume v/n on falling a distance d. (See further, below n.43.) 31 There is no suggestion that the seven paradoxes formed a systematic set, nor that Eubulides generalized them (the occurrence of the Bald Man alongside the sorites is good evidence that he did not — for the Bald Man is simply an instance of a soritical argument, as later authors recognized: e.g. Galen, Med Exp XX 3; Aspasius, in EN 56.32–34). See also W.C. and M. Kneale, The Development of Logic (Oxford, 1962), p.114, who reduce the seven paradoxes to four. 32 So e.g. K. von Fritz, ‘Megariker’, RE Suppt V (1931), coll 707–724, in col 710; Do¨ring, Megariker, p.107. 33 e.g., H. Ritter, ‘Bemerkungen u¨ber die Philosophie der Megarischen Schule’, Rheinisches Museum 2, 1828, 295–335, on p.332 (a refutation of das Werden); D. Henne, E´cole de Me´gare (Paris, 1843), p.172 (an attack on perceptual experience); T. Gomperz, Greek Thinkers (London, 1905), II p.190 (‘a new proof of the contradictory nature of empirical concepts’); C.M. Gillespie, ‘On the Megarians’, AGP 24, 1911, 218–241, on p.234 (a refutation of the Principle of NonContradiction); A. Levi, ‘Le dottrine filosofiche della scuola di Megara’, Rendiconti della Reale Accademia Nazionale dei Lincei, VI 8, 1932, 483–488, on pp.483–484 (an attack on pluralism); E.W. Beth, ‘Le paradoxe du ‘‘Sorite’’ d’Eubulide de Me´gare’, in AA.VV., La Vie, la pense´e, Actes du VIIe Congre`s des Socie´te´s de Philosophie de langue franc¸aise (Paris, 1954), 237–241; id, The Foundations of Mathematics (Amsterdam, 19642), pp.21–23 (against Aristotle’s notion of infinity); Kneale and Kneale, Development of Logic, p.114 (‘it is incredible that Eubulides produced in an entirely pointless way, as the tradition suggests. He must surely have been trying to illustrate some theses of Megarian philosophy, though it may be impossible for us to reconstruct the debates in which he introduced them’); Moline, ‘Aristotle’ (see below); Reale, Storia della filosofia, p.68 (‘against all doctrines which admit plurality’); Sillitti, ‘Alcune considerazioni’, pp.91–92 (against Plato’s mathematical analysis of the sensible world).

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have been made, only one has even a morsel of ancient testimony in its favour; and that is the suggestion that we associate Eubulides’ sorites with some aspect of Aristotle’s philosophy. For Eubulides is known to have attacked Aristotle; and what is more natural than to suppose that he directed his paradoxes — in particular, the sorites — against an item of Aristotelian thought?34 Now Eubulides’ attacks on Aristotle were, sometimes at least, scurrilously personal; and scholars have doubted whether they had any philosophical content.35 But the sorites is at least once connected with a piece of Aristotelian doctrine. In the Nicomachean Ethics Aristotle observes that it is not easy to determine by reason how far and to what extent a man may go before he is blameworthy — for that is not easy in the case of any other perceptible thing either. (EN B 1109b20–22)

In their notes on that sentence, Aspasius and the anonymous commentator both refer to soritical arguments: it is because of the sorites, they say, that perceptible things cannot be determined by reason; and hence perception — or, in the case of feelings and actions, çæ
ÅØ — must act as judge and arbiter.36 Perhaps, then, Aristotle’s doctrine of the Mean, with its deliberate refusal to specify precise conditions for virtuous and vicious actions, was the original target of Eubulides’ sorites?37 Perhaps. But the commentators do not say so: they do not mention Eubulides or imply that the sorites had been originally directed against the Mean. (Nor do they state or imply that Aristotle was aware of the sorites and recognized that it was directed against his doctrine.38) Moreover, the sorites has no peculiar relevance to the specific point Aristotle is making. He is stressing, as he often does, that universal prescriptions can never offer more 34 So e.g. Henne, Beth, and Moline (references in n.33). 35 See Aristocles, apud Eusebius, PE XV ii 3; Diogenes Laertius, II 109; Themistius, orat xxiii 285C; Suda, s.v. Þ   ºÅŁæÆ; Athenaeus, 354C; cf I. Du¨ring. Aristotle in the Ancient Biographical Tradition (Go¨teborg, 1957), pp.373–388. Pace Moline, ‘Aristotle’, pp. 394, 394 n.3, and 399, Diogenes does not say that Eubulides got the better of the dispute; he remarks simply that ‘Eubulides actually was at odds with Aristotle and slandered him a great deal’. — But there is evidence that Eubulides also engaged with Aristotle on logical issues — in particular, that he argued against the validity of E-conversion and in favour of O-conversion (Themistius, Max p.186; Alexander, conv p.69 — the two texts survive only in Arabic translation: A. Badawi, Commentaires sur Aristote perdus en grec (Beirut, 1971); see J. Barnes, S. Bobzien, K. Flannery, and K. Ierodiakonou, Alexander of Aphrodisias: On Aristotle Prior Analytics 1.1–7 (London, 1991), pp.84–85, nn.11 and 12). 36 Aspasius, in EN 56.27–57.7; anon in EN [CIAG XX] 140.6–12. 37 So Moline, ‘Aristotle’. But he allows, p.395, that there may have been other Aristotelian doctrines under attack too. 38 pace Moline, ‘Aristotle’, p.396.

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than rough and approximate guides to action: [39] circumstances alter cases, and circumstances are indefinitely various. A philosopher may propose a number of generalizations; but he must leave it to individual agents in individual circumstances to determine what individual courses of action they should take. The sorites has no special bearing on that line of thought, and I do not imagine that Eubulides thought it had.39 Some later commentator, perhaps Aspasius himself, was the first to connect soritical arguments with the Mean. However that may be, we may still wonder if Aristotle had any knowledge of Eubulides’ argument, and if he thought of it as part of a philosophical manoeuvre. Two passages have been adduced in evidence. At Physics ¨ 253b14–26 Aristotle refers to ‘the argument about the drop of water rubbing away the stone and growing plants dividing stones’. Both examples can be reconstructed on soritical principles;40 and the waterdrop example was sometimes used by later authors as an illustration of the sorites. (One drop can have no effect on a stone; if one drop has no effect, two cannot; and so on.41) In his commentary on the passage, Simplicius explicitly raises the question of whether Aristotle is adverting to a soritical argument: after a long discussion he sides with Alexander, who took the argument to be based on a principle of proportion — if a long sequence of drops has a large effect, each individual drop must have had a proportionally smaller effect.42 And Alexander is certainly correct: Aristotle’s answer to the argument proves that he, at least, had nothing soritical in mind; for he thinks that, like Zeno’s Millet Seed, it rests upon a false principle of proportion.43 The second Aristotelian passage comes from the Sophistici Elenchi — and we should expect to find the sorites in that work if it was considered by Aristotle at all. Before quoting the passage, let [40] me observe that even if the sorites is to be found in the Sophistici Elenchi that will not give it any 39 Of course you can use a soritical argument in connexion with virtuous action: is giving away £50 generous? Yes. £49.99? And so on. But that is not an argument against anything specifically Aristotelian; and there is no peculiarly Aristotelian doctrine in EN to combat which Eubulides might specially have designed the sorites. 40 See e.g. C. Prantl, Geschichte der Logik im Abendlande (Leipzig, 1855), I, p.55. 41 See Simplicius, in Phys 1177.4–9. 42 Simplicius, in Phys 1197.35–1199.5. 43 Phys ¨ 253b14–26 is similar in both language and argument to Phys H 250a19–28, where Aristotle discusses Zeno’s Millet Seed; and in both cases Aristotle argues that the error lies in a mistaken principle of proportion. Simplicius’ discussion of the waterdrop argument suggests that in antiquity the sorites had been assimilated to, or at least closely associated with, Zeno’s Millet Seed and its congeners. (See above, n.30.)

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particular philosophical importance or prove that Eubulides advanced it as part of some philosophical campaign: the Sophistici Elenchi is a book of logical puzzles, some serious, some trivial; a few of the puzzles are connected by Aristotle with philosophical issues, but most appear merely as puzzles. If the sorites is there, its inclusion will be adequately explained by the simple fact that it is a puzzle. The Sophistici Elenchi does not cite the sorites by name; but it has been discerned in the following lines:44 Those who solve it by saying that every number is few make a similar mistake to that of those we have described; for if, though it does not follow, they overlook this and say that a truth is inferred (for every number is both many and few), they make a mistake. (179b34–37)*

Aristotle is discussing a sophism the conclusion of which reads: ‘Every number is both many and few.’ What sophism has he in mind? He tells us himself a few lines earlier:45 All the following sorts of arguments depend on the accidental: ‘Do you know what I am going to ask you?’, ‘Do you know the man who is approaching (or: the veiled man)?’, ‘Is the statue your work? (or: is the father-dog yours?)’ ‘Are few times few few?’ For it is evident in all these cases that what is true of the accident need not also be true of the thing. (179a32–36)**

The argument Aristotle alludes to at 179b34–37 evidently started from the question ‘Are few times few few?’, and led to the conclusion that every number is both many and few. What is the connexion between that argument and the sorites? The premiss of the argument (‘Few times few are few’) has nothing to do with the soritical form; the conclusion (‘Every number is many and few’) is not a conclusion of any known soritical argument. Moreover, Aristotle’s classification of the argument (it ‘depends on the accidental’) does not fit the sorites in any 44 ‘This appears to be an unmistakable allusion to the Sorites’: Moline, ‘Aristotle’, p.399; ‘Aristotle alludes unequivocally to this last form of the sorites, even though he does not explicitly mention it’: Sillitti, ‘Alcune considerazioni’, p.84; cf Prantl, Geschichte, p.54 n.94. * › ø  ±Ææ
ıØ ŒÆd ƒ º
 ‹Ø –Æ IæØŁe Oºª  uæ R Y 
· N ªaæ c ıæÆØ

ı  F ÆæƺØ
 IºÅŁb ıæ
ŁÆØ çÆ (
Æ ªaæ r
ÆØ ŒÆd  ºf
ŒÆd Oºª
), ±Ææ
ıØ
. 45 Neither Moline nor Sillitti appears to notice that 179b34–37 refers back to 179a33–36. ** Nd b 
 ƒ  Ø  H
º ªø
Ææa e ıÅŒ · pæ r Æ n ººø  KæøA
; pæ r Æ e
æ Ø
Æ, j e
KªŒŒÆºı

; pæ › I
æØa 
KØ
æª
, j e › Œø
Ææ; pæÆ a OºØªŒØ OºªÆ OºªÆ; çÆ
æe
ªaæ K
–ÆØ   Ø ‹Ø PŒ I
ªŒÅ e ŒÆa  F ıÅŒ   ŒÆd ŒÆa  F æªÆ  IºÅŁŁÆØ.

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way. It is, admittedly, uncertain just what argument Aristotle alludes to at 179a35, and it is uncertain what the reflexions of 179b34–37 imply.46 But it is plain that the sorites is not referred to in those lines. [41] Aristotle, I conclude, either did not know the sorites or else kept his knowledge to himself. In either case, there is no reason to look for a philosophical debate between Eubulides and Aristotle (or, I might add, between Eubulides and anyone else) based upon soritical arguments and puzzles. Eubulides, I imagine, posed the puzzle in its original and particular form: he did not generalize it, and he did not find any philosophical employment for it.47 After Eubulides, the most celebrated name associated with the sorites is that of Chrysippus. Numerous texts connect the puzzle with the Stoics in general or with Chrysippus in particular; the sorites became a standard part of Stoic logical teaching; and it was doubtless its Stoic connexion which gave it such wide currency in later antiquity. Chrysippus is credited with three books On Soritical Arguments against Words,48 and with two books On the Argument from [42] Little-by-Little, to 46 The only evidence we have for the form of the argument is found in pseudo-Alexander, who offers the following expansion: ºØ
pæ ª a OºØªŒØ OºªÆ OºªÆ; —
Æ. — Iººa 
a ήe
æe  ŒŒØ æØÆ OºØªŒØ K
OºªÆ· a KŒÆe
¼æÆ OºªÆ· Iººa 
ŒÆd  ºº (in Soph El 161.18–20). If we take that seriously, the argument moves from ‘100 are few times few compared to 10  10,000’ to ‘100 are few times few’; and that is the move which Aristotle stigmatizes: it transfers a predicate from the ıÅŒ  (‘100 compared to 10  10,000’) to the æAªÆ (100). But it is hard to believe that pseudo-Alexander’s interpretation is right: it makes the argument peculiarly obscure. And it may be that pseudo-Alexander’s text is corrupt: Jim Hankinson suggests ‘a ŒŒØ ŒÆ’ for ‘a ŒÆe
æe a ŒŒØ æØÆ’, which gives a simple and intelligible gloss on Aristotle’s text. ‘Few fews are few; ten tens are few fews; so 100 are few’. Aristotle tackles the argument by attacking the first premiss; but instead of simply dismissing it as false (few fews are sometimes but not always few), he brings the argument under the head of ‘Ææa e ıÅŒ ’. I am not sure what he means; but perhaps it is this: ‘When you say ‘n  m are few’ you may be truly predicating ‘are few’ of the accident — it may be true that what is taken m times is few, just in the sense that m times is not many times. But you cannot infer — as your argument requires — that ‘are few’ is truly predicated of the æAªÆ n  m’. The men Aristotle mentions at 179b34–37 ignore this error in the argument, and try to ‘solve’ the puzzle by admitting that its conclusion is true: Aristotle criticizes them for passing over the error, but he seems to imply that he accepts their suggestion that the conclusion is true. If that is so, then he will no doubt explain how the conclusion can be true by reference to his notion of the relational status of ‘many’ and ‘few’ (see Cat 5b12–25). (For a different interpretation of these passages, see G. Colli, Aristotele: Organon (n.p., 1955), pp.1025–1026.) 47 Was the sorites originally a serious piece of logic or a divertissement? Grote, Plato, p.484, is sure that Eubulides offered his puzzles ‘not to impose upon anyone, but on the contrary, to guard against imposition’. Why should Grote think that? We know nothing of Eubulides’ motives. 48 Diogenes Laertius, VII 192. The title is puzzling: someone had presumably directed soritical arguments against words (çø
Æ); but who? and how? Sedley, ‘Diodorus Cronus’, p.91, plausibly suggests an Academic author (Arcesilaus?), and supposes that he was ‘led to question the validity of

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Stesagoras.49 No doubt it was also discussed elsewhere in Chrysippus’ voluminous writings: it was at least mentioned in the Logical Investigations;50 and Plutarch records that in his Use of Argument Chrysippus attacked ‘Megarian reasoning’, alleging that it had become ‘in part somewhat clumsy, in part evidently sophistical’ (Stoic rep 1036F) — that would have been a suitable place for a few comments on the sorites. But why did Chrysippus bother with the sorites? and what had happened to the argument between the days of Eubulides and those of Chrysippus? Among Eubulides’ pupils was Apollonius Cronus; and Apollonius taught his skills, and bequeathed his surname, to Diodorus, that ´eminence grise of Hellenistic philosophy (Diogenes Laertius, II 111). Diodorus was a master of paradox; he probably discussed the sorites;51 and he used something very like a soritical argument to sustain his paradoxical views on motion.52 We may well imagine that it was Diodorus who transferred Eubulides’ sorites from its original home in Christmas-cracker eristic to the lecture-halls of philosophy; and from Diodorus we may find two paths leading to the Stoa. First, we know that Zeno, the founder of the Stoa, studied for a time under Diodorus (Diogenes Laertius, VII 5), and that he himself ‘used to solve sophisms and to order his pupils to learn logic since it was capable of solving them’ (Plutarch, Stoic rep 1034F). Logic was a part of [43] the Stoic Stoic terminology by exposing the lack of adequate definitions’. But the title appears among Chrysippus’ writings on language, not among his logical treatises; and we should expect that the soritical arguments had a linguistic rather than a logical target. (See below, n.60, for a sorites in a grammatical context.) 49 Diogenes Laertius, VII 197. — The next title reads in the MSS: æd H
N a  ºłØ º ªø
ŒÆd ıåÇ
ø
æe ˇ
 æÆ . The text is scarcely sound, and two titles seem to have been conflated. (æd H
N a  ºłØ º ªø
[ŒÆd ] ıåÇ
ø
æe ˇ
 æÆ ?) Several scholars have supposed that the ıåÇø
is the same as the sorites (see Reid on Luc xxix 93; Do¨ring, Megariker, p.107; Sedley, ‘Diodorus Cronus’, p. 113 n.94; cf Menagius on Diogenes Laertius, VII 197). The ıåÇø
is mentioned also by Epictetus, diss II xviii 18, and by Gellius, I ii 4; but neither author implies that it is the sorites under a different name — if anything, they suggest that it is a distinct argument, and from its name we should expect it to be a paradox connected with silence (The Silent Man). The only, and insufficient, reason for identifying it with the sorites is the fact that Chrysippus counselled ıåÇø
to those faced by soritical arguments (below, pp.[49–54]). 50 PHerc 307, IX 17–22: text below, n.68. 51 Fronto, eloq ii 13 [p.140 van den Hout], urged Marcus Aurelius to give up the frivolities of dialectic: discere te autem ceratines et soritas et pseudomenus ... hoc indicat loqui te quam eloqui malle ... Diodori tu et Alexini verba verbis Platonis et Xenophontis et Antisthenis anteponis? Fronto’s rhetoric is vague: he does not say that Diodorus wrote about the sorites — but it seems a pretty safe assumption that Diodorus did. — On Diodorus, see Sedley, ‘Diodorus Cronus’ (for the sorites, pp.89–94), to which I am greatly indebted; cf R. Muller, ‘Diodoros, dit Cronos’, DPhA II, pp.779–781. 52 The argument in question is to be found at Sextus, M X 112–117: it refers to heaps (see § 114), and it is, in a loose sense, soritical in tone; but it is not, strictly speaking, a sorites.

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curriculum from the beginning; and the study of paradoxes was a part of logic. Zeno will have heard of the sorites, among other such puzzles, from Diodorus; and thenceforward the sorites will have been an item in Stoic teaching. The fact that Chrysippus was a logician who inherited some of the interests of Diodorus would in itself be a sufficient explanation of his concern with the sorites: there is no need to seek any more profound motivation for his work on the paradox. But, secondly, there is in fact another, indirect, route by which the sorites may have impressed itself upon Chrysippus. Arcesilaus, who converted the Academy to scepticism, had some association with Diodorus: in the celebrated parody by Ariston the Stoic, he was ‘Plato in front, Pyrrho behind, Diodorus in the middle’ — and Diodorus in the middle ‘because he used the logic of Diodorus’.53 Now Arcesilaus devoted much of his energy to attacking Stoic epistemology and the fundamental Stoic conception of an apprehensive presentation or çÆ
ÆÆ ŒÆƺÅØŒ. If Arcesilaus both used Diodoran logic and attacked Stoic presentations, perhaps he used Diodoran logic in his attack on Stoic presentations; perhaps, more specifically, he used the soritical form of argument which he had learned from Diodorus in order to reveal flaws in Zeno’s notion of an apprehensive presentation; and perhaps, finally, that attack gave Chrysippus an urgent philosophical reason for tackling the puzzles set by the sorites. That string of perhaps’s smacks of idle conjecture. But the conjecture can be backed up by evidence. In the course of his discussion of apprehensive presentation, Sextus adverts to an argument which brought soritical armour to bear upon the Stoic conception. The argument is complex;54 but [44] for the moment it is enough to cite a single clause from it: 53 
Ł
ήd e
æø
Æ NE
æd ÆP F æ Ł —ºø
, ZØŁ
—ææø
,   ˜Ø øæ  Øa e æ åæBŁÆØ fiB ØƺŒØŒfiB fiB ŒÆa e
˜Ø øæ
, r
ÆØ b ¼
ØŒæı —ºÆø
،
(Sextus, PH I 234; cf Numenius apud Eusebius, PE XIV v 13; Diogenes Laertius, IV 33). 54 M VII 401–435 considers the Stoic claim that ‘apprehensive presentation’ is a criterion of truth; §§ 415–423 contain one sceptical argument against the Stoics. The argument claims that ‘since apprehensive presentation attaches closely to non-apprehensive presentation, apprehensive presentation will not be a criterion of truth’ (415), and §§ 416–423 are designed to show that apprehensive presentation does ‘attach closely’ to non-apprehensive presentation: the proof starts, in § 416, from reflexions upon Chrysippus’ attempt to answer a soritical argument against apprehensive presentation; and in §§ 418–423 a sorites is developed to prove the close attachment of apprehensive to nonapprehensive presentations. Thus there are three distinguishable layers. in §§ 415–423: first, the initial sorites against which Chrysippus argued; secondly, Chrysippus’ argument; thirdly, the sorites developed against Chrysippus. In the text, I ascribe the first layer to Arcesilaus; it is tempting to suppose that the third layer comes from Carneades. (See further below, n.70.)

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In the case of the sorites, when the last apprehensive presentation lies next to the first non-apprehensive one ... , Chrysippus and his school say that ... (M VII 416)*

Chrysippus himself 55 thus replied to a soritical argument directed against apprehensive presentation. It follows that the argument is at least as old as Chrysippus; and if we want an author for the argument, who is there but Arcesilaus?56 Chrysippus’ interest in the sorites was overdetermined: as a logician, he will have found it a fascination in its own right; as an epistemologist, he will have had it forced upon his attention by the sceptical attacks of Arcesilaus.57 The large question remains: what was Chrysippus’ attitude to the sorites? In particular, did he attempt to resolve the puzzle? And if so, how? But before turning to those matters, let me complete this brief history of the argument.58 After Chrysippus, the sorites is always closely associated with Stoicism; and the majority of references to it are by Stoics or in Stoic contexts.59 For all that, there is no evidence that any later [45] Stoic studied the argument or attempted to improve upon Chrysippus’ discussion of it — the sorites At Luc xvi 49–50, Cicero records an argument against apprehensive presentation which he calls a sorites. The argument is quite different from the one at M VII 415–423, and it does not have the form which I described in Section I. Rather, it uses a single subject and an ordered sequence of predicates: ‘F1( )’ is to all appearances true of a; ‘Fn( )’ is to all appearances false of a; for any i, if ‘Fi( )’ is true of a, then, to all appearances, ‘Fi þ 1( )’ is true of a. The argument is, as it were, a sorites with subjects and predicates interchanged; but I shall not attempt a precise analysis of the relationship between the sorites proper and Cicero’s argument. Other arguments of the same form: Cicero, fin IV xviii 50 (iam ille sorites est quo nihil putatis esse vitiosius — for a defence of the text, see Madvig ad loc); Plutarch, Stoic rep 1039C; Lactantius, inst div I xvi. * Text below, p.[49]. 55 For ‘ ƒ æd e
æØ
’ (cf PH II 253), see S.L. Radt, ‘Noch einmal Aischylos, Niobe Fr. 162 N2. (278 M)’, ZPE 38, 1980, 47–58: ‘ ƒ æd ’ (almost) always denotes either x and his colleagues or x alone — it does not mean ‘the colleagues of x’. 56 So e.g. Zeller, Philosophie der Griechen, III i, p.520 n.5; Sedley, ‘Diodorus Cronus’, p.92. — Arcesilaus was an Academic: did the sorites receive any Academic colouring? According to Kra¨mer, Platonismus, pp.75–76, Plato’s Theory of Principles, and especially his notion of The Great and Small, had a bearing upon the Academic history of the sorites; but I cannot see how that theory could have had any relevance to the sorites, which neither requires nor readily takes on any such metaphysical clothing (see Sedley, ‘Diodorus Cronus’, p.113 n.102; J. Glucker, Antiochus and the Late Academy (Go¨ttingen, 1978), p.34 n.79). A. Weische, Cicero und die neue Akademie (Mu¨nster, 1961), p.69, connects the rise of the sorites with Theophrastus’ botany, which self-consciously avoids the use of any precise concepts — a pretty conceit, and implausible. 57 The Stoics themselves, as Plutarch observed (comm not 1084ac), used arguments of the same logical form as the sorites: that fact too might have stimulated Chrysippus to attend to the problems raised by soritical arguments. 58 Clement, strom V i 11.6, seems to imply that Timon mentioned the sorites, among other paradoxes; if that is right, then the argument may have been a weapon of early Pyrrhonian as well as of Academic Sceptics. 59 I know of no reference to the sorites in an Epicurean context.

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seems to have become a part of the Stoics’ logical curriculum, but it does not seem to have been an object of controversy within the Stoa. Perhaps the later Stoics thought that Chrysippus had said the last word on the subject? Perhaps — but not everyone thought so. The Dogmatic doctors, who used the sorites against their Empirical opponents, presumably thought that soritical arguments — or rather, that some instances of the sorites — were sound arguments; at least, there is no reason to think that the Dogmatists were consciously advancing what they took to be incorrect arguments. It is not clear when or how the sorites entered the medical debates; but Galen suggests that the doctors were using it as early as the second century bc,60 and we may imagine that they learned about it — as about so much else — from their Stoic contemporaries. However that may be, the later members of the Sceptical Academy thought little of Chrysippus’ retort to Arcesilaus. For Carneades explicitly disputed — indeed, mocked — Chrysippus’ advice about the sorites (Cicero, Luc xxviii 90–xxix 92); and he himself brought forward a celebrated series of soritical arguments. Carneades propounded certain arguments in a soritical fashion, which his friend Clitomachus recorded as being most excellent and conclusive. (Sextus, M IX 182)

Sextus transcribes five of Carneades’ arguments, adding that there were more. In each case, the conclusion is that there are no gods, and Sextus construes them as general arguments for atheism. Cicero also reports Carneades’ arguments, and more numerously; but he says that they were propounded not in order to do away with gods (for what could be less fitting for a philosopher?), but to prove that the Stoics explain nothing about the gods. (nd III xvii 43)61

Cicero is certainly right about Carneades’ aims:62 they were not positive and atheistical but negative; Carneades was engaged in an attack on Stoicism, and 60 On the date of the arguments of Med Exp see above, p.[26]. — At M I 68–69, Sextus uses a sorites against Dionysius Thrax’s definition of grammar; and in the same context (I 72) he reports that Asclepiades had attacked the definition. But I think Sextus implies that Asclepiades’ attack did not involve the sorites. 61 On the arguments, see e.g. C. Vick, ‘Karneades’ Kritik der Theologie bei Cicero und bei Sextus Empiricus’, Hermes 37, 1902, 228–248, on pp.240–224; P. Couissin, ‘Les sorites de Carne´ade contre le polythe´isme’, Revue des E´tudes Grecques 54, 1941, 43–57; M. dal Pra, Lo scetticismo greco (Milan, 1950), pp.148–155; M.F. Burnyeat, ‘Gods and heaps’, in M. Schofield and M.C. Nussbaum (eds), Language and Logos (Cambridge, 1982), pp.315–338. 62 Carneades appeals to Stoic doctrines to support the conditional premisses of his arguments, which are thus ad hominem; and in general, Carneades was given to ad hominem — ad Stoicum — argumentation: see e.g. Cicero, Luc xlii 131; div II lxxii 150; fin II xiii 42. Sextus adapts Carneades’ arguments to his own Pyrrhonian ends.

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he [46] felt able to use in his attack a weapon that Chrysippus had hoped to render obsolete. One of the arguments reported by Clitomachus and transcribed by Sextus runs like this: If the sun is a god, the day will be a god — for the day is nothing else than the sun above the earth. And if the day is a god, the month will be a god; for it is a collection of days. And if the month is a god, the year will be a god; for it is a collection of months. But that is not so; nor, therefore, is the original supposition. (M IX 184)*

Carneades’ arguments are sometimes cited as paradigms of the soritical form; but the one I have just quoted differs in certain ways from a classical sorites.63 First, the subjects of Carneades’ propositions do not form an orthodox ordered sequence; for there is no obvious ordering relation that fixes the members of the sequence. In standard soritical arguments the subjects can be imagined as points along a continuum, or as successive steps in a single journey, or the like. In Carneades’ arguments that is not so: his sets of subjects are ordered and there is an ordering relation (trivially so); but in a plain enough sense his subjects do not form a natural succession of items. Again, Carneades provides arguments for at least some of his conditional premisses — and different arguments for different premisses. In standard sorites, the conditional premisses are not supported — and do not need to be supported — by argument; and if they were argued for, the argument would be quite general, applying equally to any adjacent pair of subjects. The fact that Carneades’ subjects do not form a ‘natural succession’ perhaps explains why he uses different arguments for different premisses; but it does not explain why he uses arguments in the first place. It is tempting to suppose that the provision of arguments reflects Carneades’ response to Chrysippus’ criticism of the sorites: while rejecting that criticism as inadequate, Carneades may have felt that it required him to modify the presentation of his own soritical arguments. In order to assess the merits of that suggestion we must go back to Chrysippus and attempt to discover his answer to the soritical paradoxes. [47] * ŒÆd c
N › lºØ  Ł  KØ
, ŒÆd æÆ i
YÅ Ł · P ªaæ ¼ºº Ø q
æÆ j lºØ  bæ ªB. N  æÆ Kd Ł , ŒÆd › c
ÆØ Ł · ÅÆ ªæ KØ
K æH
. N b › c
Ł  KØ, ŒÆd › K
ØÆıe i
YÅ Ł · ÅÆ ªæ KØ
KŒ Å
H
› K
ØÆı . Påd  ª  F ·  
ı
Pb e K IæåB. 63 One might also wonder if the subjects of the constituent propositions of the arguments are individuals: by ‘the day is a god’ does Carneades mean ‘daytime is a god’ or rather ‘each day is a god’? If the latter, then his argument contains universal propositions. And by ‘the month is a god’ he surely means ‘every month is a god’. But that is niggling: let us suppose that he does mean to provide an ordered set of subjects, say the set: .

Medicine, experience, and logic

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III What should be said about the sorites? how is the paradox to be resolved? I shall first make a brief general remark about the matter, then look at Chrysippus’ discussion of the paradox, and finally return to my startingpoint and consider what the Empirical doctors had to say about the sorites. If the conclusion of an argument is false, there are in principle two things that may have gone wrong: the argument may be invalid, its conclusion may fail to follow from its premisses; or the argument may be false, one or more of its premisses may fail to be true. And so it is with soritical arguments: if the conclusion of a soritical argument is false (if, for example, it is false that 10,000 observations are few), then either the conclusion does not follow from the premisses or at least one of the premisses is false. (Of course, the argument may be wrong in both ways at once: it may be both invalid and false.) Anyone who maintains that (at least some) soritical arguments are wrong by virtue of being invalid I shall call a radical opponent of the sorites: a radical opponent is committed to rejecting the validity of modus ponens inferences; he may hold either that modus ponens is simply an invalid form of reasoning, that from ‘P’ and ‘P  Q’ it does not follow that Q; or else that modus ponens must be restricted to certain types of proposition (say to propositions which do not contain soritical predicates). In either case he will be involved in a radical reformation of classical propositional logic, and good luck to him. Anyone who maintains that a soritical argument is wrong in virtue of being false I shall call a conservative opponent of the sorites: a conservative opponent may hold that all soritical arguments are wrong, or he may hold that only some are wrong; in either case he will have no quarrel with the logic of the sorites, but he will argue — differently in different cases — that in all or some soritical arguments at least one premiss is false. Chrysippus was, I assume, an opponent of the sorites: he thought he had solved the problems it raised.64 But was he a radical or a conservative 64 The sorites remains an ¼ æ
in the Stoic handbooks; the Stoic Seneca refers to it as ‘sorites ille inexplicabilis ’ (ben V xix 9); and the obnoxious youth who almost ruined one of Herodes Atticus’ dinner-parties claimed that ‘he alone could unravel the Master and the Silent Man and the Sorites and other riddles of that sort’ (Gellius, I ii 4). But that scarcely suffices to show that Chrysippus did not think he had solved the paradox — at very most, it shows that some later Stoics still found the sorites puzzling. (And paradoxes may remain puzzling even when they are known to have been definitively solved.) — S. Bobzien, ‘Chrysippus and the epistemic theory of vagueness’, PAS 102, 2002, 217–238, remarks, truly, that ‘it is possible for someone to hold certain views about the Sorites-paradox without believing that they have solved it’; she thinks that ‘this is likely to have been

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opponent? [48] We might hope to answer the question by considering the fourfold typology of fallacy which the Stoics invented (or at any rate, accepted): The dialecticians say that an argument is inconclusive either because of incoherence or because of deficiency or because of being propounded in an incorrect form or by redundancy. (Sextus, PH II 146)65

If the sorites is logically mistaken, it must presumably be mistaken in one (or more) of those four ways. Soritical arguments will scarcely have been accused of redundancy: if they had been, the proponent of a sorites, merely by omitting one or more of his premisses, would have been able to confront Chrysippus with an argument he could not fault.66 Again, soritical arguments will hardly have been accused of incoherence: in ‘incoherent’ arguments the premisses are unconnected in content with one another and with the conclusion. (‘If it is day, it is light; wheat is being sold in the market-place: therefore Dio is walking’: Sextus, PH II 146.) In the sorites, premisses and conclusions are connected as closely as you could wish. Nor, at least on the face of things, is Chrysippus likely to have argued that soritical arguments were propounded in a wrong form, or that they were not formally valid. After all, as Plutarch pointed out, the standard form of the sorites is thoroughly in accordance with Stoic principles of logic: the Stoics explicitly recognized the general form as valid, and they more than once proposed arguments which have the logical form of the sorites.67 So is the sorites inconclusive ‘through deficiency’? Sextus’ example of a deficient argument is this: Wealth is either good or bad; it is not bad: therefore it is good. And the Stoics’ objection is that the first premiss is deficient — it should read: ‘Wealth is either good or bad or indifferent’ (PH II 150). Deficiency is a disease of the premisses of an argument, and it marks a species of falsity. Now the Chrysippus’ situation. There is no positive evidence that he thought that he had provided a solution’, and the fact that ‘the Sorites ... was classified by the Stoics as insoluble (aporos) ... suggests at least that no solution was found that made the aporia disappear completely’ (p.218 and n.7). But Carneades thought that Chrysippus had proposed a solution. 65 ¥ ª c
ØƺŒØŒ  çÆØ
I
ƌ
º ª
ªª
ŁÆØ X Ø Ææa ØæÅØ
j Ææa ººØłØ
j Ææa e ŒÆa  åŁÅæe
MæøBŁÆØ åBÆ j ŒÆa Ææ ºŒ
(cf M VIII 429: here ‘the dialecticians’ are, or at any rate include, the Stoics: see M VIII 435). 66 On redundancy, see J. Barnes, ‘Proof destroyed’, in M. Schofield, M.F. Burnyeat, and J. Barnes (eds), Doubt and Dogmatism (Oxford, 1980), pp.161–181, on pp.164–75 [reprinted in volume III]. 67 Plutarch, comm not 1084AC; cf e.g. Alexander, fat 207.5–21; 210.15–28.

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conditional premisses of a sorites might be replaced by disjunctive premisses — at any rate, the material conditional ‘P  Q’ is equivalent to ‘P v¬Q’. So perhaps Chrysippus thought that some (or all) of the conditional premisses of a sorites were deficient in the sort of way in which ‘Wealth is either good or bad’ is deficient? Perhaps — but it is not easy to see how that might be so. In short, the fourfold typology is not illuminating. [49] So let us look at the texts in which Chrysippus’ stance on the sorites is actually described. There are three passages to consider. And if Chrysippus and his fellow dogmatists say that when the sorites is being propounded one should, while the argument is proceeding, stop and suspend judgement in order not to fall into absurdity, how much more appropriate it is for us Sceptics to suspend judgement in such cases. (Sextus, PH II 253)* For in the case of the sorites, when the last apprehensive presentation lies next to the first non-apprehensive presentation and is hard to distinguish from it, Chrysippus and his school say that in the case of presentations where the difference is small in this way, the wise man will stop and fall quiet, but in cases where it strikes him as greater, he will assent to the one as being true. (Sextus, M VII 416)** ‘But sorites are vicious.’ — Then destroy them, if you can, lest they be harmful; for they will be unless you are careful. ‘We have already been careful’, he says; ‘for Chrysippus holds that when you are being [50] questioned step by step, e.g. as to whether three are few or many, you should fall quiet a little while before you come to many’ (that is what they call ıåÇØ
). (Cicero, Luc xxviii 92)***

Those three texts certainly do not contain all that Chrysippus said about the sorites;68 and indeed, since they were selected by enemies of the Stoa — by * Yª ƒ æd e
æØ
 ªÆØŒ d K
fiB ı
æøØ  F øæ ı æ œ
   F º ª ı çÆd E
¥ ÆŁÆØ ŒÆd KåØ
¥
Æ c KŒøØ
N I Æ
,  ºf  ı Aºº
i
E
±æ Ç
YÅ ŒØŒ E sØ
. ** Kd ªaæ  F øæ ı B KåÅ ŒÆƺÅØŒB çÆ
ÆÆ fiB æfiÅ IŒÆƺfiø ÆæÆŒØ
Å ŒÆd ıØ æ ı åe
Ææå Å, çÆd
ƒ æd e
æØ
‹Ø Kç z
b
çÆ
ÆØH
OºªÅ Ø oø Kd ØÆç æ, ÆØ ›  çe ŒÆd ıåØ, Kç z
b ºø
æ Ø, Kd  ø
ıªŒÆÆŁÆØ fiB æfi Æ ‰ IºÅŁE. *** at vitiosi sunt soritae. — frangite igitur eos si potestis ne molesti sint: erunt enim nisi cavetis. — cautum est, inquit; placet enim Chrysippo cum gradatim interrogetur (verbi causa) tria pauca sunt anne multa, aliquanto prius quam ad multa perveniat quiescere, id est quod ab his dicitur ıåÇØ
. 68 I should also cite the brief remarks in Chrysippus’ ¸ ªØŒa ÇÅÆÆ (PHerc 307, IX 17–22): [  ] ø 
 E [Æh Ł ÆŒ [Ø]
ÆæØ KÆØ
ήa e
Ææa ØŒæe
º ª
ƒ
  [F
] E æd B I Œæø E
; ØŁÆ
e
b Å[b]  F æåØ
.

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Pyrrhonists or Academics — there is no reason to believe that they represent the best of what Chrysippus said.* But they are all that we have to work with. Chrysippus recommends us to ‘stop’ and to ‘fall quiet’ while the soritical argument is in full flow. He is thinking of a sorites in its informal, interrogative, version; and he means that at some stage in the questioning we should simply refrain from giving any answer. ‘Is a1 F?’ Yes. ‘And a2?’ Yes... . ‘And ai?’ Silence. (In the formal version of the argument, the questions are replaced by hypothetical propositions; and in terms of that version Chrysippus recommends us to decline to comment on one or more of the hypothetical premisses: if the question ‘And ai?’ should be passed over in silence, then the premiss ‘Fai–1  Fai’ should neither be accepted nor rejected.) By ‘fall quiet’ or ‘be silent’ Chrysippus means what he says: he is recommending us to keep mum.69 But at what point should we keep mum? and why should we do so? Let us take the former and easier question first. Sextus, in M VII, distinguishes two types of case. In the first, the subjects of the successive propositions — the ais — are fairly far apart: the difference ‘strikes him as greater’; i.e. adjacent ais are in fact distinguishable with regard to Fness. In those cases you will not ‘stop’: the right answer is clear, and you will reject as false the first hypothetical premiss which links an ai which is F to an ai which is not F.70 In such cases, the argument is not soritical in the sense in which I am (Text in L. Marrone, ‘Le Questione Logiche di Crisippo 9PHerc 307’, Cronache Ercolanesi 27, 1997, 83–100.) — The first sentence is relatively clear: ‘And up to what point one should continue giving the same answers will cause perplexity in virtue of the little-by-little argument’. The second sentence is problematical: there are two holes in the papyrus at crucial places; the sense of the verb ‘
Ø
’ is uncertain (its occurrence in the book titles at Diogenes Laertius, VII 197, is intriguing but unenlightening); and the second clause, ‘ØŁÆ
e
b ... ’ is doubtful in syntax and in sense. I wonder if ‘E
’ refers to finding a cut-off point along the ais between Fs and non-Fs, so that the sentence might read: ‘And similarly, if you must make a cut-off point in your answer, but it is plausible that not even this is possible’. That fits well (of course) with the view which I am about to ascribe to Chrysippus; but I do not offer the papyrus lines as evidence in favour of the ascription. (I might add that further information about the papyrus will not help: the reference to the sorites was very short, and the context surrounding the lines I have quoted deals with different paradoxes.) * Bobzien, ‘Chrysippus and vagueness’, p.223, argues that Chrysippus may have taken ‘borderline cases’ to be neither true nor false — not, of course, because the sentence ‘51 is few’ (say) expresses a proposition which is neither true nor false, but because it expresses no proposition — no IøÆ — at all. Perhaps so — but the old question will then return in a new dress: How can you think that ‘50 is few’ expresses a proposition and that ‘51 is true’ does not? 69 I take it that ‘ ıåÇØ
’ is being used in its normal sense of ‘be silent’, and not as a term of art; for the verb in logical or dialectical contexts, see e.g. Sextus, M VIII 115, 350; Plutarch, Stoic rep 1047C; adv Col 1124A; Simplicius, in Cat 24.13–20. 70 M VII 418–420 (see above, n.54) begins from a case of this first type: offered ‘Fifty are few’ and ‘10,000 are few’, the sage will assent to the former, since the difference between the two is great. But if he assents to ‘Fa50’ he will also assent to ‘Fa51’ — and so, ultimately, to ‘Fa10,000’. In effect, Sextus (i.e. Carneades?) is arguing that cases of the first type, where the ais are far apart, will always

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using the term; for the predicate ‘F( )’ does not satisfy the second condition on soritical predicates — it is not the case that, to [51] all appearances, if ‘F( )’ is true of one of a pair of adjacent subjects, then it is true of the other. In the second type of case, ‘the difference is small’; and then you must ‘stop’. Where? According to Cicero, you stop ‘a little while before you come to many’: suppose that ‘F( )’ is plainly false of aj; then at some point before aj — say at ai — you fall into silence. And presumably you start talking again when the interrogator reaches aj. But Cicero’s ‘a little while before’ is vague, and we may properly demand greater precision from Chrysippus. Cicero does in fact provide us with that precision in a passage which reports Carneades’ objections to Chrysippus’ views. For so far we have had nothing from Chrysippus but a piece of advice — and vague advice at that. What we expect — or hope — from him is not simply a recommendation about how to deal with soritical questions, but a solution to soritical problems; and a recommendation will be philosophically interesting only insofar as it is grounded on a solution.71 Carneades, for one, thought that Chrysippus’ recommendation was a trifling evasion of the problem: ‘As far as I’m concerned,’ says Carneades, ‘you can snore as well as fall quiet. But what good does that do? Someone will come along and wake you from your sleep and question you in the same way: ‘‘Take the number you fell silent at — if I add one to that number, will they be many?’’ — and you will go on again for as long as you think good. Why say more? You confess that you can tell us neither which is last of the few nor which is first of the many. And that sort of error spreads so widely that I do not see where it may not get to.’ ‘That doesn’t hurt me’, he says; ‘for, like a clever charioteer, I shall pull up my horses before I get to the end, and all the more so if the place where the horses are coming to is steep. Thus’, he says, ‘I pull myself up in time, and I don’t go on answering your captious questions’. If you’ve got hold of something clear but won’t answer, you’re acting arrogantly; if you haven’t, then not even you see through the matter. If that is because it is obscure, I agree; but you say that you don’t go as far as what is obscure — so you stop at cases that are clear. If you do that simply in order to be silent, you gain nothing; for what does it matter to the be convertible into cases of the second type; so that if the sage does not suspend judgement in the first type of case, he will never suspend judgement. 71 Prantl, Geschichte, p.489, speaks of ‘eine Politik des Zuwartens und Ruhigbleibens, ... eine Taktik ... ’; Sedley, ‘Diodorus Cronus’, p.91, suggests that ‘perhaps, to be charitable, this was intended less as a logical solution than as a procedural recommendation’. There is nothing charitable about taking the thing to be a recommendation — it plainly is a recommendation. The question is: did Chrysippus back the up ‘procedural recommendation’ with a ‘logical solution’?

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man who’s after you whether he catches you silent or talking? But if up to nine, say, you answer without hesitation that they are few, and then stop at the tenth, [52] you are withholding assent from what is certain and perfectly plain — and you don’t let me do that in cases that are obscure. So your art doesn’t help you at all against the sorites, since it does not tell you what is first or last in the increasing and the decreasing sequence. (Cicero, Luc xxix 93–94)*

According to Carneades, then, Chrysippus does not simply say, ‘Stop a little while before’; he says ‘Stop at cases which are clear’.72 Let us suppose, with Carneades, that Chrysippus assents up to the ninth case and falls silent at the tenth: then we are to suppose, first, that Chrysippus will not say that ‘F( )’ is true of a10 — he will not assent to ‘Fa10’ — and, secondly, that ‘F( )’ is clearly true of a10. That is, indeed, more precise advice than we have hitherto received; but it is, as Carneades forcefully asserts, highly perplexing advice. Moreover, if we want to know the grounds for the advice, we are given nothing more than a simile: stop before the horses reach the precipice. But perhaps we can make something of the simile. For if the horses really are approaching a precipice, not merely trotting down a slippery slope, they are heading for a sharp and sudden change in direction; and, outside the simile, such a sharp and sudden change can only be a change from F to non-F — the change will occur at an ai which is F but the successor to which is not F.** Thus if we press the simile, we shall conclude that according to * per me vel stertas licet, inquit Carneades, non modo quiescas. sed quid proficit? sequitur enim qui te ex somno excitet et eodem modo interroget: quo in numero conticuisti, si ad eum numerum unum addidero multane erunt? progrediere rursus quoad videbitur. quid plura? hoc enim fateris neque ultimum te paucorum neque primum multorum respondere posse; cuius generis error ita manat ut non videam quo non possit accedere. — nihil me laedit, inquit: ego enim ut agitator callidus prius quam ad finem veniam equos sustinebo eoque magis si locus is quo ferentur equi praeceps erit. sic me, inquit, ante sustineo ne diutius captiose interroganti respondeo. — si habes quod liqueat neque respondes, superbe; si non habes ne tu quidem percipis. si quia obscura concedo; sed negas te usque ad obscura progredi: illustribus igitur rebus insistis. si id tantum modo ut taceas nihil adsequeris: quid enim ad illum qui te captare vult utrum tacentem irretiet te an loquentem? sin autem usque ad novem (verbi gratia) sine dubitatione respondes pauca esse, in decimo insistis, etiam a certis et illustrioribus cohibes adsensum. hoc idem me in obscuris facere non sinis. nihil igitur te contra soritas ars ista adiuvat, quae nec augentis nec minuentis quid aut primum sit aut postremum docet. 72 illustribus ... rebus insistis; a certis et illustrioribus cohibes adsensum: Cicero plainly means that the tenth case is clearly and certainly one to which ‘F( )’ applies — his words cannot be taken to mean that the Stoic will stop after the last clear case. — Mignucci, ‘Stoic analysis’, pp.244–245, proposes to explain clarity by way of ‘degrees of truth’; and he argues that, so construed, the soritical argument pattern is invalid. That may be a fruitful approach to the philosophical problem; but I cannot think that it is exegetically plausible — there is, so far as I can see, no trace of any degrees of truth in the ancient texts on the sorites. ** For a more subtle interpretation of the precipice, see Bobzien, ‘Chrysippus and vagueness’, pp.225–226.

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Chrysippus one of the conditional premisses of the sorites must be false: for some i, ‘Fai’ is true, ‘Fai þ 1’ false. That may seem an absurdly strong conclusion to draw from a simile — a simile, moreover, which may not go back to Chrysippus at all.73 Then let us turn back to Sextus. According to M VII 417, ‘when the last apprehensive presentation lies next to the first non-apprehensive presentation and is hard to distinguish from it, Chrysippus and his school say ... ’. The when-clause is the one to watch; for it assumes that there is a last apprehensive presentation and a first non-apprehensive presentation, and that they lie next to one another. In other words, it assumes that for some i, ai is apprehensive or commands assent, and ai þ 1 is non-apprehensive or does not command assent. More generally, Chrysippus seems [53] to assume that, in some cases at least, ‘F( )’ will be true of ai and false of ai þ 1; in other words, that one of the hypothetical premisses, ‘Fai  Fai þ 1’, will be false. The when-clause in Sextus thus reinforces Cicero’s simile. In that case, Chrysippus is a conservative opponent of the sorites, who is inclined to consider that one of its hypothetical premisses will be false.74 We know that Chrysippus and the Stoics could insist on cut-off points where others incline to see a continuous gradation: there are, notoriously, no degrees of virtue in Stoicism — a man may ‘progress’ towards virtue, but his progress is a matter of steadily approaching a distinct goal, not of gradually acquiring more virtue; the man who has reached the goal is virtuous, everyone else — however close he may be — is still vicious.75 That notion of virtue, which some critics find strangely paradoxical, has rightly been connected with soritical phenomena:76 it evidently coheres well with the attitude to the sorites which I have just ascribed to Chrysippus. Again, it is now easy to see why Carneades modified his soritical arguments in the way I described at the end of Section II. If Chrysippus’ general strategy was to consider the hypothetical premisses and to divine falsity in some one of them, then Carneades was obliged to make those premisses as cogent as possible: he had to argue for them — and what better arguments could he hope to find than principles taken from Stoic philosophy itself ? 73 But it certainly goes back to Carneades: see Cicero, ad Att XIII xxi 3 (below, n.77). 74 Certainly, the Stoics did sometimes reject particular soritical arguments on the grounds that they contained false hypothetical premisses: Cicero, Luc xvi 49; fin IV xviii 50 (cf Galen, loc aff VIII 25). 75 e.g. Plutarch, comm not 1063AB; Diogenes Laertius, VII 120; cf Seneca, ep cxviii 12–16. 76 See E.G. Schmidt, ‘Eine Fru¨hform der Lehre vom Umschlag Quantita¨t-Qualita¨t bei Seneca’, Forschungen und Fortschritte 34, 1960, 112–115; Sedley, ‘Diodorus Cronus’, pp.93–94.

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Suppose, then, that our subjects run from a1 to a30. We discovered earlier that Chrysippus is going to keep mum about a10, even though it is clear that ‘F( )’ is true of a10. We have now seen that, according to Chrysippus, there will be some precipitous ai, roughly in the middle of the sequence, let us suppose, such that ‘F( )’ is true of it but not of ai þ 1. The precipitous ai will be after a10, and although ‘F( )’ is true of it, ‘F( )’ is not clearly true of it: that, plainly, is why Chrysippus bids us to stop at a10 rather than at the precipitous ai — we know that there is a precipitous ai, but we do not know [54] which ai is precipitous. The various things to which Chrysippus seems to be committed can best be expressed by way of a diagram. F

a1

aw

non-F

ak

aj

a30

STOP clearly F

not clearly F

Here, aj is the last F item, whose exact position is unknown; ak is the last clearly F item; and aw is the point at which Chrysippus keeps mum. Such was Chrysippus’ view: were Carneades’ criticisms of it just? Carneades concentrates his criticisms on aw; he asks, in effect, why Chrysippus distinguishes aw from ak: Does Chrysippus stop at aw ‘simply in order to be silent’? does he believe that ‘F( )’ holds of aw, yet stubbornly refuse to admit as much? Surely not; that would indeed be absurd, as Carneades indicates, and we must suppose — with Sextus in PH 77 — that when Chrysippus keeps silent at aw, that is a sign that he suspends judgement about aw — he judges neither that Faw nor that not-Faw. But how can that be? Chrysippus appears to be claiming both that ‘F( )’ is clearly true of aw and that he does not believe that Faw; and that claim has a contradictory air to it. Even if the air can be dispelled, the claim remains paradoxical: why ever should we suspend belief about aw if aw is a clear case? 77 PH II 253: E
¥ ÆŁÆØ ŒÆd KåØ
. The same point is implicit in Cicero; for when the Stoic replies to Carneades ‘I pull myself up [me ... sustineo]’ (Luc xxix 94), he means ‘I suspend judgement’. A letter to Atticus discusses this passage in Luc: Atticus had suggested ‘inhibeo’ as the Latin for ‘Kåø’; Cicero accepted the suggestion and had it written into the text of Luc; but he then discovered that ‘inhibeo’, a term taken from the technical vocabulary of rowing, did not give quite the right sense, and he asked Atticus to replace his original term, ‘sustineo’, in the text. After all, ‘sustineo’ has the authority of Lucilius behind it, and semper ... Carneades æ  ºc
pugilis et retentionem aurigae similem facit K åfiB (ad Att XIII xxi 3).

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Why should we not proceed happily up to ak, the last clear case, and only suspend belief at ak þ 1? [55] I do not know how to answer those Carneadean questions on Chrysippus’ behalf; but possible answers fall into two classes. First, it might be wondered whether we are entitled to place ak on the diagram at all: no text explicitly ascribes to Chrysippus the view that there is a last clear case, an ak: perhaps Chrysippus held that there was no last clear case — he does not advise us to stop at ak just because in his view there is no such item to stop at. After all, adjacent ais are supposed to be indistinguishable with regard to Fness; and if that is so, how could ak be clearly F, ak þ 1 not clearly F? If, to all appearances, ai is F if and only if ai þ 1 is F, then surely ai will be clearly F if and only if ai þ 1 is clearly F. That line of reasoning is plausible; but Chrysippus follows it at his peril. For if there are any clear cases but no last clear case, then all the ais are clearly F: if a1 is clearly F, a2 is clearly F; if a2 is clearly F, a3 is clearly F; and so on — for no ai is the last clear case. Thus Chrysippus’ advice to stop at a clear case is vacuous: we could follow it — and not stop until we reached a30. Secondly, we might revert to the supposition that there is a last clear case: just as there is a last ai which is actually F, so there is a last ai which is clearly F. Perhaps Chrysippus thought that although there is a last clear case, we cannot tell which that case is: we should stop at ak if we could recognize ak as the last clear case; but in fact we cannot, hence we must stop sooner, at aw. It has been thought that that is unsatisfactory; for is it not easy to show that if there is a last clear case, then we can recognize it as such? And in that case, we can have no cause to stop at aw, since we can readily identify ak. But in fact it is not clear that any last clear case can readily be recognized.78 However that may be, we may of course always wonder if Carneades has not misrepresented Chrysippus’ advice. Perhaps Chrysippus did not say that we should stop before the last clear case: perhaps he advised us to stop at the last clear case. Now it is doubtless possible that what is a clear case to one observer is not clear to another: a Stoic sage will be better equipped than the rest of us, and for him (I suppose) even aj may be a clear case; but for us obscurity sets in sooner — and at different points for different men. Suppose, then, that Chrysippus said something like this: ‘Stop at the first case that is not clear to you — even if others [56] may find it clear to them’. Then we can imagine Carneades representing Chrysippus as saying ‘Stop among the clear cases’. 78 This is the argument. Consider any ai between aw and aj: is it clearly F or not? You may answer ‘No’, ‘Yes’, or ‘I don’t know’; but if you don’t know whether ai is clearly F, then it is not clearly clearly F and hence not clearly F. Hence you can always answer ‘No’ or ‘Yes’ to the question ‘Is ai F?’: hence ak, if it exists, is recognizable. — But why suppose that if something is clearly F then it is clearly clearly F?

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The past few paragraphs have been highly speculative: I incline towards the last of the answers I have offered to Chrysippus, but I have no clear notion of where the truth may lie. In any event, perplexity over ak should not distract us from the fundamental part of Chrysippus’ solution of the sorites, viz his postulation of aj. How good is that solution? Is Chrysippus right in supposing that there will be a last ai of which ‘F( )’ is true? It is worth stressing that Chrysippus was entirely correct to insist that the hypothetical premisses of any soritical argument should be carefully scrutinized; and that he was entirely correct to suspect that apparent truth might there conceal actual falsity. Moreover, the conservative approach to the sorites is surely at least methodologically prior to any more radical attack: we should not toy with the idea of rejecting or restricting modus ponens until we are entirely sure that the sorites admits of no other solution. But a serious doubt remains: it is one thing to say that there is a precipitous ai in a sorites, another thing to show that there is; one thing to assert that there is a swift and sharp divide between Fness and non-Fness, another thing to prove the fact. As far as we know, Chrysippus did nothing to demonstrate his claim that, where ordinary men saw continuous gradation, there was in reality a determinate cut-off point; and to that extent he did not, so far as we know, answer the sorites: at best he sketched a project for a possible answer. Moreover, Chrysippus’ project is surely doomed to failure for very many soritical predicates. Can we really imagine that one grain, unknown to us, miraculously turns a mere collection into a genuine heap? or that one heartbeat, yet to be determined by science, makes an adult from a child? Such suppositions are patently ridiculous: there are no undiscovered facts of the sort which Chrysippus’ solution would postulate. To some soritical arguments, Chrysippus’ proposal is plainly inapplicable; and about those arguments he has nothing to tell us. To other soritical arguments — and, it should be added, to those arguments which will have mattered most to him79 — his proposal is, in principle, worth considering; but it remains a proposal for a solution, not a solution. [57] So much for Chrysippus and the Stoics; I turn now to the Empirical doctors. Galen’s Empiricist replies to the Dogmatist at considerable length; but his argument is repetitious, and its core can be briefly expressed. The Empiricist observes that the sorites is an argument 79 It seems to me at least that for such Stoically crucial predicates as ‘ ... is virtuous’ or ‘ ... commands assent’ Chrysippus’ proposal has more initial plausibility.

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which opposes the whole of the arts in general and, furthermore, rejects what is obvious to the eye, and contradicts all habits and customs of life adopted by mankind. (Med Exp IX 1)80

That observation is elaborated by detailed examples running to several pages of text (XVI–XX), with the result that the sorites has been discredited and exposed and found to be unreliable to the extent that what is most convincing in it is opposed to the things which manifestly lie open to perception by the senses. (XXI 1)

Now if you say of something which people see very many times under the same conditions throughout their lives, that it is non-existent, you will not be helped at all. For you reject it and declare it to be invalid only by argument and not in reality ... Since, however, any argument which is contradicted even by one thing among those seen and found is bad, consequently it is a bad and a wrong argument. And how should this not be the worst and most erroneous of all arguments, since so many facts contradict it? (XVII 8)

But where does the sorites go wrong? The Empiricist does not care to know: Of two points, the first is that things are discovered by observation alone — and that I want and you admit, even though you do so reluctantly; the second is how this occurs, which I say it is neither possible nor useful to discover, while your remaining task is to discover it. So in proving it puzzling by your sophism, you destroy yourself but do no harm to us. (XV 6)

After all, I am no sophist, and do not belong to those whose business, aim and intention it is to confute fallacious arguments and reject them. (XX 6) [58]

The sorites is certainly a bad argument, since it contradicts evident truths; and no self-respecting Empirical doctor will waste time trying to show why it is bad. 80 The Empiricist adds: ‘And it also opposes him who speaks and him who argues with it’; and later he says to the Dogmatist: ‘you only contradict yourself and prove yourself in the wrong’ (XVII 8). But that is not the exciting claim that soritical arguments are self-refuting, but the ad hominem observation that even those Dogmatists who pretend to reject ‘experience’ because of the sorites do in fact frequently rely upon ‘experience’ (see e.g. XII 1–11). — R.J. Hankinson, ‘Self-refutation and the sorites’, in D. Scott (ed), Maieusis: essays in ancient philosophy in honour of Myles Burnyeat (Oxford, 2007), pp.351–373, on pp.364–371, plausibly urges (with reference to Cicero, Luc xxix 92–93) that self-refutation was sometimes associated with the sorites; and he constructs an ingenious sorites the conclusion of which is that there are no sorites arguments.

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At first glance, that is a stout, no-nonsense argument;81 but on closer inspection it may seem less impressive. There are two things which the Empirical man ignores. He imagines that if one soritical argument succeeds, all must — if his own ‘experiences’ are shown to be incoherent, then so too are heaps, waves, and cities. He thus ignores the possibility of a conservative approach to the sorites: if we had to accept all sorites or none, then there might be something to be said for the blunt assertion that we should accept none and let logic go hang; but we do not have to accept all or none. The second point overlooked in the Empirical argument is this: unlike certain other sceptical arguments, the sceptical sorites does not reach its unpalatable conclusion by devious and subtle ratiocinations; indeed, the argument does not, in any obvious way, oppose reason to perception, logic to everyday experience. The only bit of reasoning involved in soritical arguments is modus ponens: the rest of the argument consists of observationally plausible premisses. The Empirical doctor presents us with a choice between accepting ‘argument’ and accepting what is ‘plain to the senses’; but the sorites does not press that choice upon us. Rather, the senses tell both for the sorites (they yield its premisses) and against it (they reject its conclusion). The choice which the sorites requires us to make — if we are determined to avoid a conservative approach — is this: either give up modus ponens or else confess that very many ordinary concepts are incoherent or paradoxical. And it is by no means obvious that, given such a choice, reason in the shape of modus ponens should be abandoned. But perhaps that interpretation of Galen’s Empiricist is unsympathetic: let us try to find a better strand of thought in his reply to the Dogmatist. In the Outline of Empiricism Galen sums up that reply by observing that ‘the question ‘‘how many?’’ is indeterminable’ [59] (subf emp 38.15). In Medical Experience the point is made more fully: Do you impute this against us because we cannot state with exactitude the precise number contained in each of these, but are only able to give a general notion of what they are and of what is formed of each of them in the mind or in the imagination? Since each has always been capable of expansion and augmentation and without limit or end at which its being stops, it is therefore impossible for us to say how large is the number of each one of them. (XVII 7) 81 Compare the Pyrrhonists’ attitude to sophisms: Sextus, PH II 229–259, esp. § 250: ‘If, then, when an argument is propounded in which the conclusion is false, we know at once that the argument is not true nor concludent from the fact that it has a false conclusion we shall not assent to it even if we do not know wherein the error lies’, etc.

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How many grains make a heap? — A large number. — But how large? — There is no answer to that: the number is indeterminable. The appeal to indeterminacy seems to be an important part of the Empiricist’s view, and it is something which was given no place in the first interpretation of his position. But how are we to understand indeterminacy? One answer springs to mind at once; and although that answer will prove ultimately to be unsatisfactory, it is worth developing. ‘How many hours make a day?’ — Quite a few. — ‘Exactly how many?’ — Well, 24 to be precise. ‘How many weeks make a vacation?’ — Not enough. — ‘Exactly how many?’ — There is no answer to that question: different vacations last different lengths of time. The interpretation of indeterminacy which those dialogues suggest is this: when the Empirical doctors say that no precise answer is forthcoming to the Dogmatist’s soritical questions, they are adverting to a perfectly familiar matter of fact. Our notions of various quantitative items are necessarily not precise; we are only able to give a ‘general idea of what they are and of what is formed of each of them in the mind or in the imagination’. We cannot make the notion precise because different specifications of the notion introduce different quantities: the notion of a vacation is quantitative; it is the notion of a period of time between terms. But it is not a precise quantitative notion, in the way that the notion of a day or a year is precise; it is not the notion of a six-week period or an eight-week period or a sixteen-week period. For although every vacation has a precise duration, there is no precise duration common to every vacation. Now that point was explicitly made by the Empiricists; for to the Dogmatist’s question, ‘Can you tell us, Empiricists, how many times is very many times?’, they reply: Idiot, there is no one measure for all things, but different measures for [60] each: you were asking me your question as though someone were to ask a shoemaker to tell him what last will shoe everyone. For in his case there is no one measure for all feet (they are unequal), and in our case there is none for all things (they are different). (Med Exp VI 5)82 82 This passage occurs in one of the surviving Greek fragments: t øæ, çÅd ªºÆ, £
PŒ Ø
±
ø
æ
Iººa ŒÆŁ ŒÆ
¼ºº · f  ‹ Ø
KŁ ı ‰ N ŒÆd Œı  
Ø IØ E ØÆØ ÆPe
e
ŒÆº Æ    KØ
fiz 
Æ  E. h ªaæ KŒE H
 H
£
æ
· ¼
Ø Ø ªæ· h K
Ł H
æƪø
· Øç æÆ ªæ. — In the first sentence, the received text has ‘ ... ªºÆ, e K
ÆP E £
PŒ Ø
... ’, which will make no sense. Deichgra¨ber changed ‘K
ÆP E’ to ‘£
ÆNE’, and Walzer followed him (accidentally omitting the semi-colon). Scho¨ne had suggested ‘K
Æ檒 for ‘K
ÆP E’. He had also wondered whether ‘e K
ÆP E’ should not be

574

Logical Matters

Asking ‘How many observations make an experience?’ is as silly as asking ‘What size of last will make a shoe?’ If that is what the Empiricist means when he adverts to indeterminacy, then he is making a sound point. But is the point relevant to soritical arguments? We could make it relevant, in the following way. We could suppose that the Empiricist was accusing the Dogmatist of seeking a single, universal answer where there are in fact many distinct specific answers; the Dogmatist expects to be told, in general, how many grains make a heap or how many observations make an experience — but there is no general answer. If the Dogmatist condescends to be specific in his questions — how many weeks make an Oxford long vac? how many men make a Roman legion? how many observations are needed for such-and-such a sort of experience? — he will always get a definite answer. The general question, ‘How many observations make an experience?’ gets only a general, imprecise, answer: ‘Very many’. Any specific question, ‘How many observations make such-and-such a sort of experience?’, gets a particular, precise answer: ‘243’, as it might be. The Empirical doctor could thus be seen as supplementing Chrysippus’ answer to the sorites. Chrysippus had asserted that one of the hypothetical premisses in (some or all) soritical arguments will be false; the Empiricist adds that this will be so when the arguments deal with specific cases, and he explains the meretricious fascination of the sorites by suggesting that it arises from a confusion between the general and the specific.83 [61] One specific experience in the Empirical doctor’s art will be that expressed by the general proposition that pomegranates cure diarrhoea. The Empirical excised: the Arabic has nothing answering to ‘e K
ÆP E’; and in my translation I have followed the Arabic and Scho¨ne. 83 It is tempting to find the same point in Aspasius and in the anonymous commentator on EN. The anon says that ‘the addition of a little does not make a heap; for a heap comes about at some time from the addition of more, but it is not possible to determine by reason when [reading ‘ ’ for ‘ æ
’] this is — for it is not reason but perception which judges perceptibles’ (in EN 140.9–12). Perception answers the question ‘Is this a heap?’, and perception deals with particulars: we might conclude that, according to anon, there is no universal answer to the question ‘How many grains make a heap?’ (reason offers no answer) but there is always an answer in particular cases (perception is a judge). Aspasius is a little different: he simply says that ‘it is not possible to say when it is first not a heap; for no perceptible thing can be grasped accurately [IŒæØH] but only broadly and in outline [ºØ ŒÆd fiø]. And it is the same with actions and passions ... That is why one needs çæ
ÅØ to discover the mean in passions and actions’ (in EN 57.2–7). The argument seems to be this: ‘Things cannot be grasped accurately; therefore çæ
ÅØ must grasp them accurately’. But that, of course, is absurd; and unless Aspasius is simply muddled, he must mean that ‘no perceptible thing can be grasped accurately ’.

Medicine, experience, and logic

575

doctor claims that his experience is grounded on a number of particular observations; and he holds, on the view we are now giving him, that some precise number of observations suffices to ground that experience. (He need not claim to know the precise number; but he must be able to make it plausible that there is a precise number.) He might have supported that contention by observing that patients differ in their constitutions and that diseases differ in their types. Suppose that there are a hundred varieties of constitution and four varieties of diarrhoea: then might not the Empiricist suggest that a total of four hundred observations will suffice to ground his experience? — if pomegranates prove successful in each possible set of circumstances, he will then be in a position to claim that they cure diarrhoea.84 Starting from the notion of indeterminacy, we have managed to construct a reasonably sophisticated answer on behalf of the Empiricist. But the answer will not serve as a defence of experience against the sorites; nor in fact is it the answer which the Empiricist gave.85 It will not serve for the following reason. We were supposing that the Empiricist came by his general knowledge about the effects of pomegranates by considering their effects in specific cases; but those specific cases are themselves examples of general knowledge or experience — they will be experiences expressed by sentences of the form ‘Pomegranates [62] cure C-constituted patients of T-type diseases’. And how does the Empiricist gain those experiences? — On the basis of observations. — How many observations? — Very many. — But how many? Inductive inference is apparently required at the specific level; and the sorites is back in action again. And the Empiricist was in fact well aware of that problem — the view I have been developing for him over the last few pages was not, historically speaking, his view. For the distinction between the general and the specific levels, between questions about experience as such and questions about specific experiences, was actually made at a very early stage in the argument. 84 I have in mind here something akin to Mill’s Methods of Induction; for ancient anticipations of Mill — not, alas, brought into connexion with the sorites — see Philodemus, sign XIX 12–19; XX 31–XXI 16 (cf XXXV 15–35). Philodemus is asked how many cases he needs to inspect before drawing a general conclusion: all, or only some? He answers: ‘not all; but a wide variety of cases’. 85 There are other problems too, not the least of which concerns the individuation of constitutions and types: one of the charges frequently made by the Dogmatic doctors against the Empiricists was that they could give no theory-free account of what circumstances were relevant to their observations; they could not, without reliance upon reason, determine what should count as a ‘set of circumstances’. See e.g. Galen, Med Exp III 1–6, VI 1–8.

576

Logical Matters

The Dogmatist accepts the distinction, and his soritical arguments are not, irrelevantly, directed at the general question ‘How many observations make an experience?’. Rather, he says this: Perhaps they haven’t even got anything determinate in any particular case? It’s clear to everyone that their position has already gone to pot. But next, just as we argued with them at the beginning, now too we will kindly inquire of one case at a time whether, though it is unknown to them, there is in the nature of things some measure of the ‘very many times’, or whether there cannot in any way at all be a measure of the ‘very many times’. (Med Exp VII 7)86

The sorites is thus deliberately aimed at specific experiences; and when the Empiricist asserts that the answer to the Dogmatist’s question is ‘indeterminable’, the indeterminacy lies at the specific level, not at the level of generality. Can we understand the imputation of indeterminacy at the specific level? I end by briefly indicating two ways — one dull, one exciting — in which such indeterminacy might be explained. First, the Empiricist may have in mind a move analogous to that from the general to the specific — I mean, the move from the specific to the particular. If we ask ‘How many observations are needed to ground the experience that pomegranates cure diarrhoea?’, we get the vague answer ‘Very many’; but we can expect no precise answer. Precision is to be sought at the particular level: ‘How [63] many observations did Serapion (or Menodotus, or Philippus) need?’ — ‘Very many’. — ‘How many?’ — ‘434’. The circumstances and the background knowledge of different physicians are different; and those differences are acutely relevant to the acquisition of particular experiences. For every particular question of the form ‘How many observations did physician x at time t require in order to achieve the experience E?’ there is a precise particular answer; but there is no unique and precise answer to the question ‘How many observations are required — by anyone at any time — to ground experience E?’ The specific question is indeterminable; but every particular question is wholly determinable. 86 The Greek survives:   s
P å ı Ø ŒÆŁ ŒÆ
侯

; ‹Ø b
s
ŒÆd XÅ ÆPH
ææØ a æªÆÆ, Æ
d Bº
. Iºº KçB i
YÅ, ŒÆŁæ IæåBŁ
ÆP E غåŁÅ
, Pª
ø
ø Ø ŒÆd
F
A KØŒłÆŁÆØ ŒÆa 
Æ  æ
KŒ
Ø b
Iª
EÆØ e  F ºØŒØ æ
Ø  K
fiB çØ H
æƪø
, j P ‹ºø ıB
ÆØ ı
Æe
æåØ
Ø æ
Kd  F ºØŒØ. — For ‘ÆP E غåŁÅ
’ the received text has ‘ÆP E غåŁÅ
æ ÆÆ
’. Scho¨ne, followed by Deichgra¨ber, prints ‘ÆP E < x > غåŁÅ
æ ÆÆ
’; Walzer suggests either correcting ‘æ ÆÆ
’ to ‘æ ÆÆ
’ or else excising ‘غåŁÅ
’. The Arabic has only one verb corresponding to the pair in the Greek, and the verb corresponds to ‘غåŁÅ
’. I follow the Arabic.

Medicine, experience, and logic

577

Although there is no positive evidence that the Empiricists had that sort of thing in mind when they spoke of indeterminacy, the line of thought may be worth further examination; for, like Chrysippus’ response to the sorites, it is not an answer to soritical puzzles but rather a programme for the construction of possible answers. The second way of understanding indeterminacy is very different. It supposes that there genuinely is no true answer to the question ‘How many observations did Serapion require to justify his belief that pomegranates cure diarrhoea?’ The question is indeterminable in a strong sense: although Serapion was justified in his belief, and justified on the basis of very many observations, there was no precise number of observations which together constituted his justification. He had to make between, say, 400 and 450 observations; and it was those observations on which his experience was based. But his experience was not based on any determinate number of observations. Take the sequence . The predicate ‘F( )’ is true of a400 and false of a450: falsity as it were enters the sequence between a400 and a450; but there is no precise point at which it enters — there is no ai which is the first ai of which ‘F( )’ is false. Falsity begins at some point within the sequence; but there is no member of the sequence such that falsity begins at it. At some point, ‘F( )’ ceases to apply; but no point can be picked out as the point at which ‘F( )’ ceases to apply.87 [64] That suggestion may seem quite absurd: surely it is incoherent and selfcontradictory? In a sense, it is; for it requires us to abandon certain deeply entrenched logical notions — to give up (or at least, to restrict the scope of) standard logic, and perhaps to embrace some new and unspecified logic.88 Thus the suggestion is necessarily incoherent when looked at from the standpoint of normal logic: it urges us to depart from that standpoint. Does the existence of such incoherence render the suggestion absurd? That, 87 This proposal does not involve the introduction of a ‘third truth-value’: the introduction of such a value — call it ‘indeterminate’ — would do nothing to explain or establish the indeterminacy the Empiricist is after; for the point at which ‘truly F( )’ ceased and ‘indeterminately F( )’ commenced to apply could be perfectly determinate, for all that the third truth-value could show (and similarly for the point where ‘indeterminately F( )’ gave way to ‘falsely F( )’). In general, the introduction of multi-valued logic is no aid to the resolution of soritical puzzles. 88 It requires us, in effect, to explain quantification in such a way that ‘(9x)(!(x)’ can be true for a (finite) domain D even though ‘!( )’ is not true of any y in ˜. Again, consider the hypothetical premisses of the sorites: on the suggestion canvassed in the text, the disjunction of their negations will be true even though no one of them will be determinately false. Thus we need an account of disjunction such that ‘either P or Q’ may be true even though ‘P’ is not true and ‘Q’ is not true. See Dummett, ‘Wang’s paradox’, pp.309–311.

578

Logical Matters

I think, is a peculiarly elusive question: it is part of the general question of whether the search for ‘alternative logics’ is intrinsically misguided; and I shall only say that it is hasty to dismiss such a search out of hand. Coherence apart, is it at all plausible to suppose that the Empiricists had some logical revolution in mind when they talked of indeterminacy? In a sense the answer is obvious: of course not; the Empiricists had no inclination to study logic, no inkling of the possibility of ‘alternative logics’, not the remotest idea of developing a logic of vagueness. We should take them at their word: they knew the sorites was a mistake; they did not know why it was a mistake; and they did not care. But that need not be quite the last word; and there is an interesting sense in which we can, with some semblance of plausibility, suggest that the Empiricists were anticipating a non-standard logic of vagueness. What I mean is this: the Empiricists in effect say: ‘These are the facts; if your logic disagrees with them, so much the worse for your logic. You must invent a new logic, if you will, to cope better with things as they are. We ourselves do not care a fig for logic; but we do know that it is a condition on the acceptability of a logical system that it does not lead to soritical arguments.’ What is fundamentally at issue here is a question about the nature of logic: is logic in a way prior to science and to experience, is it something which gives shape to experience and which cannot be modified by experience? or is logic rather parasitical upon [65] science, constrained by the observed facts and open to modification in the light of empirical discovery? Those questions still exercise us — quantum physics gave them new life not so long ago. I think that they are at the bottom of the dispute between Galen’s two doctors.89

Appendix: Texts Section 1 purports to be comprehensive; but I cannot claim to have scoured the whole of Greek and Latin literature in search of sorites. Sections 2 and 3 are far from exhaustive — they simply mention certain commonly cited texts. 89 An early draft of this chapter was presented at the 1980 Symposium Hellenisticum, where it benefited from a lengthy discussion. I received much help from many participants; but I may perhaps offer particular thanks to Mario Mignucci, David Sedley, and Eike von Savigny. Myles Burnyeat carefully vetted a revised version of the chapter: as always, his comments were of the greatest value. I am indebted to Jim Hankinson for several useful remarks. And I am especially grateful to Joe Incigneri: it was he who first interested me in the sorites; and his acute criticisms enabled me to make substantial improvements to my discussion of Chrysippus’ answer to the puzzle.

Medicine, experience, and logic

1.

579

Texts explicitly adverting to soritical argument:

[Acro], Scholia on Horace, ad Ep II i 45 Alexander, frag I Vitelli* anonymus, in EN 140.6–12 Aspasius, in EN 56.27–57.7 Augustine, c Acad II v 11 Chrysippus, ¸ ªØŒa ÇÅÆÆ, PHerc 307, IX 17–22 Cicero, Luc xvi 49–50 [but see n.54] xxviii 92–94 xxxiii 107 xlviii 147 div II iv 11 fin IV xviii 50 [but see n.54] Hortensius frag 26 Grilli [= Nonius, 329.19] nd III xvii 43–xx 52 Clement, strom V i 11.6 Diogenes Laertius, II 108 VII 44 82 192 197 Fronto, eloq ii 13 [p.140 van den Hout] [66] Galen, loc aff VIII 25 in Hipp progn XVIIIB 254 Med Exp VII 8–VIII 1 XVI–XXI subf exmp 38.12–17 Gellius, I ii 4 Horace, Ep II i 36–49 Jerome, adv Ruf 30 in Amos I i 5 Julian, dig lxvii 65 Lucian, symp 23 Marius Victorinus, in Cic rhet II 27 [285.8–11 Halm] * G. Vitelli, ‘Due frammenti di Alessandro di Afrodisia’, in AA.VV. Festschrift Theodor Gomperz (Vienna, 1902); English version in R.W. Sharples, Alexander of Aphrodisias: Quaestiones 2.16–3.15 (London, 1994), pp.90–92, 143–144. — cf Psellus, opusc theol iii [152–158 Gautier].

Logical Matters

580

Martianus Capella, II 122 IV 327 423 Persius, VI 75–80 Philoponus, apud Simplicius, in Phys 1175.23–26 Plutarch, comm not 1084AD Proclus, in Parm 834.8–20 prov 66 [p.170 Boese] Psellus, opusc theol iii [129–183 Gautier] scholiast to Lucian, volume IV p.254 Jacobitz scholiast to Persius, p.350 Jahn Seneca, ben V xix 8–9 Sextus Empiricus, PH II 253 III 80 M I 68–69 80 VII 416–421 IX 182–190 Sidonius, carm xxiii 119 Simplicius, in Phys 1176.34–1177.10 1197.35–1199.5 Suda s.v. hØ Ulpian, dig lxvi 177

2.

Other pertinent texts

Cicero, nd II lxvi 164–166 Lactantius, inst div I xvi 11–17 Plutarch, Stoic rep 1039C Seneca, ep cxviii 12–17 Sextus Empiricus, PH III 260–263 M V 65–67 X 112–117 [above, n.52]

3.

Some impertinent texts

Aristotle, Phys H 250a19–28 [above, n.30] ¨ 253b14–26 [above, p.[39]]

Medicine, experience, and logic

Pol E 1307b35–37 SEl 179a32–39 [above, p.[40]] 179b34–37 [above, p.[40]] Cicero, Tusc V xv 45 Iamblichus, in Nic viii 1 [Iamblichus], theol arith 21.9 Nemesius, nat hom xliii [129.9–14 Morani] [67] Seneca, ep lviii 12–16 Simplicius, in Phys 1108.18–28 [above, n.30] Tacitus, dial 16 [above, n.24] Tatian, adv Graec 27 [above, n.26]

581

21 Meaning, saying, and thinking* I There were three ancient theories of meaning: according to the Peripatetics, words mean thoughts, and thoughts stand for things; according to the Epicureans, words directly mean things; according to the Stoics, words mean sayables,1 and sayables stand for things. The Stoics agree with the Peripatetics and disagree with the Epicureans in maintaining that a semantic theory must be three-tiered. The Stoics disagree with the Peripatetics insofar as the intermediate items in their three-tiered theory are sayables and not thoughts. Thus far, mere caricature: each of the theories I have sketched requires further elucidation; and each of the sketches would be regarded as wildly inaccurate by some scholars. I shall not attempt to replace the caricatures by professional portraits; rather, I want to address one particular problem which the caricatures raise. If the Peripatetic and Stoic theories differ insofar as thoughts differ from sayables, then — we may well wonder — what exactly is the difference between sayables and thoughts, and how is Stoic saying related to Stoic thinking? Several scholars, both ancient and modern, have denied that there is any substantive difference between the Peripatetic and the Stoic theories of meaning on the grounds that sayables are simply thoughts under a different name. Thus according to Simplicius, some people held that the argument is about thoughts; for Aristotle plainly says that it is about things which are said, and things which are said, or sayables, are thoughts, as the Stoics too held. (in Cat 10.2–4)2 * First published in K. Do¨ring and T. Ebert (eds), Dialektiker und Stoiker (Stuttgart, 1993), pp.47–61. 1 I use the unlovely word ‘sayable’ for the Greek ‘ºŒ
’. 2 ... æd
Åø
i
YÅ › º ª : ‹Ø c æd H
ºª 
ø
K
, ÆçH r 
› `æØ ºÅ, a b ºª 
Æ ŒÆd ºŒa
Æ KØ
, ‰ ŒÆd  E øœŒ E K ŒØ. — Simplicius does not himself subscribe to this view of ºŒ (pace A.A. Long, ‘Language and thought in Stoicism’, in A.A. Long (ed), Problems in Stoicism (London, 1971), pp.75–113, on p.80):

Meaning, saying, and thinking

583

More recently it has been maintained that a sayable is ‘that which is merely an expressed thought’; for sayables ‘exist only insofar as they are thought and expressed in words. As ideas in the mind ... the ºŒ ... should be interpreted ... as something ... akin to the ideas of, for instance, classical British empiricism — as a kind of mental images which precede and accompany our words and give them meaning’.3 [48] A weaker thesis has also found favour: sayables are not to be identified with thoughts, but they are logically dependent upon the activity of thinking. For ‘every species of ºŒ
requires the utterance of some expressible object present to the mind. Does this entail that ºŒ only persist as long as the sentences which express them? ... there is no evidence to show that ºŒ, as distinct from the speaker and his reference, persist outside acts of thought and communication’.4 Those theses about sayables and thoughts are not mere conjectures. For there are several ancient texts which associate sayables with thoughts, and the texts have been taken to support either the strong view that sayables actually are thoughts or the weaker view that sayables are parasitic upon thoughts. The issues are complicated, both from a philosophical and from an exegetical point of view. I shall first make a few abstract remarks; then look at the Peripatetic theory of meaning; and finally turn to the texts which associate thoughts with sayables.

II I am concerned with meaning and saying and thinking. That is to say, sentences of the forms ‘x means ... ’ and ‘x says ... ’ and ‘x thinks ... ’ demarcate the realm of the investigation. It is easy to construe the verbs in such sentences as expressing ordinary two-placed relations. Then, if you are wondering about meaning, you may take the formula ‘x means y’ and ask what sort of items are referred to by the terms which can be substituted for ‘y’, and you will explain that ‘y’ is replaced by names of thoughts (if you are a Peripatetic) or by names of objects (if you are an Epicurean) or by names of sayables (if you are a Stoic). he ascribes it to unnamed interpreters of Aristotle’s Categories, and at e.g. in Cat 397.10–12 he implicitly distinguishes ºŒ from ØÆ
ÆÆ. 3 G. Nuchelmans, Theories of the Proposition (Amsterdam, 1973), pp.52, 55. 4 Long, ‘Language and thought’, pp.97, 98.

584

Logical Matters

But once you construe the verbs as expressing ordinary two-placed relations, you have lost any chance of saying anything sensible about the subject. And here lies my first main difficulty. For on the one hand, no discussion of the ancient theories will have any value unless it is conducted in moderately precise and rigorous terms; and on the other, no rigorous and precise semantic terminology was known in the ancient world. If I insist on precision, I shall be guilty of anachronism. If I stick to the ancient formulations, I shall be guilty of incoherence. I prefer anachronism. In particular, I shall use formulations which no ancient text uses, or at any rate uses consistently. Moreover, I shall restrict the range of my discussion in a way which is false to the ancient texts. As for the anachronistic restriction, I take it that meaning is best discussed, in the first instance, in terms of the meaning of indicative sentences. The ancients did indeed talk about the meaning of sentences; but they also talked about the meaning of words — and their theories are usually stated in terms of word meaning. As for anachronistic formulations, I take it that the best way to discuss sentence meaning is by way of formulas of the form: [49] S means that P (where ‘S’ is to be replaced by a name or description of an indicative sentence); or better, by way of formulas of the form: S, as uttered by x in circumstances C,5 means that P. A theory of meaning will thus concern itself initially with formulas of the form: (S, as uttered by x in C, means that P) if and only if Q. And a semantic theorist is engaged, initially, in the task of discovering the appropriate sort of substitutions for ‘Q’ in such formulas.

III At the beginning of the De interpretatione Aristotle passes a few remarks on words and meanings. These remarks were — or became — the Peripatetic semantic theory:

5 i.e. at a time t, in a place p, ... .

Meaning, saying, and thinking

585

Uttered items are symbols of affections in the soul, and written items of uttered items. Just as the written forms are not the same for all, so the utterances are not the same either. But the items of which they are primarily signs — affections of the soul — are the same for all; and the things of which these are likenesses — the objects — are also the same. Now we have discussed these matters in On the Soul ... (Int 16a3–9)*

The reference to the De anima is vague,6 and it has puzzled the commentators.7 But whatever Aristotle may mean, our version of the De anima does not discuss semantic matters. It is fashionable to read a semantic theory into the Posterior Analytics and parts of the Metaphysics; but the texts were not seen in that light by the ancient commentators, and they have no bearing on Peripatetic semantic theory. There are some semantic remarks in the Poetics; for in chapter 20 Aristotle distinguishes among various ‘parts of speech’ — and he does so in what seem to be primarily semantic terms. Yet if the chapter presupposes some semantic thought, it does not contain a semantic theory.8 There is one other pertinent text — half a sentence from the end of the De interpretatione: If matters stand thus with belief, and if uttered affirmations and negations are symbols of those in the soul, then it is clear ... (24b1–2)**

Uttered affirmations and negations are uttered sentences; and ‘those in the soul’, i.e. affirmations and negations in the soul, are clearly here to be construed as beliefs. Hence if I utter the sentence ‘Lions [50] roar’, that will (under certain conditions) be a ‘symbol’ of the belief that lions roar. Plainly, the sketchy theory of Int l is here being applied to indicative sentences.

* Ø b
s
a K
fiB çø
fiB H
K
fiB łıåfiB ÆŁÅø
 ºÆ ŒÆd a ªæÆç 
Æ H
K
fiB çø
fiB. ŒÆd uæ Pb ªæÆÆ AØ a ÆP, Pb çø
Æd ƃ ÆPÆ: z

 Ø ÆFÆ ÅEÆ æø
, ÆPa AØ ÆŁÆÆ B łıåB, ŒÆd z
ÆFÆ › ØÆÆ æªÆÆ XÅ ÆP. æd b
s
 ø
YæÅÆØ K
 E æd łıåB ... 6 The phrase ‘æd  ø
’ is indeterminate in its reference. 7 It led Andronicus to declare Int spurious: see Ammonius, in Int 5.28–6.4. Ammonius himself assembles a number of tangentially relevant passages in de An (in Int 6.4–7.14). 8 Aristotle frequently talks about the sense or senses of this word or that; but none of his discussions suggests any elaborated theory — and in particular, none alludes to the theory of Int 1. ** Yæ Kd  Å oø åØ, Nd b ƃ K
fiB çø
fiB ŒÆÆçØ ŒÆd I çØ  ºÆ H
K
fiB łıåfiB, ...

586

Logical Matters

So far as we know, Aristotle’s early successors did little to develop the embryonic ideas of Int.9 But one brief text merits mention. Having rehearsed the Stoic theory of meaning, Sextus adds that Epicurus and Strato the physicist allow only two items, what signifies and what obtains ... (M VIII 13)*

Thus Strato apparently rejected the view expressed at the beginning of the De interpretatione in favour of a more parsimonious theory. But apart from that reference we hear nothing of Strato’s ‘semantic theory’: we do not know whether he detected shortcomings in Aristotle’s view and articulated a rival of his own, or whether he merely indicated en passant that a more austere theory would do the semantic trick.10 9 Philoponus remarks that Theophrastus and Eudemus and Phanias also wrote On Interpretation — in which case they will doubtless have said something about meaning (in Cat 7.20: the report has been doubted, without good reason). But we know little enough about these works. Theophrastus’ —æd ŒÆÆçø certainly dealt with some of the material discussed by Aristotle in his Int; and a remark by Boethius, in Int 2 12.3–16 [¼ Theophrastus, 72A Fortenbaugh] suggests that the —æd ŒÆÆçø was in fact Theophrastus’ Int (cf A. Graeser, Die logischen Fragmente des Theophrast (Berlin, 1973), pp.50–51; M.G. Sollenberger, Diogenes Laertius’ Life of Theophrastus, diss Rutgers (Trenton NJ, 1984), pp.386–387); P.M. Huby, Theophrastus of Eresus: sources for his life, writings, thought and influence: commentary volume 2 — logic, Philosophia Antiqua 103 (Leiden, 2007), pp.24–26. Eudemus’ Int has been identified with (part of) his —æd ºø (F. Wehrli, Eudemos von Rhodos, Die Schule des Aristoteles VIII (Basel, 1955), p.79); but Theophrastus also wrote a —æd ºø (e.g. Diogenes Laertius, V 47) which there is no reason to think contained semantic matter. (But note PHamburg 128 [B. Snell (ed), Griechische Papyri IV (Hamburg, 1954) pp.36–51]: the papyrus, written in about 200 bc, deals with the same sort of things which Aristotle had discussed in Poet 20. It is a tempting conjecture that it is a fragment of Theophrastus’ —æd ºø; and in any event it is a relatively early Peripatetic text. (The piece is printed as appendix 9 in W.W. Fortenbaugh, P.M. Huby, R.W. Sharples, and D. Gutas, Theophrastus of Eresus: sources for his life, writings, thought and influence, Philosophia Antiqua 54 (Leiden, 1992).) Yet although the papyrus proves that stylistic issues continued to be discussed in the Lyceum, it does not provide any evidence for interest in strictly semantic theory.) Porphyry’s reference to Theophrastus’ On the Elements of Speech (apud Simplicius, in Cat 10.22–-11.1) is intriguing; but, again, the contents of the work (which is sometimes identified with the —æd ºø) will have been at best incidentally semantic. There is also a general remark in Boethius: The Peripatetics, here too deriving their views from Aristotle, quite rightly maintained that there are three sorts of speech (one which can be written in letters, another which can be expressed by utterance, a third which can be put together by thought), and that one is contained in thoughts, a second in utterance, a third in letters. (in Int 2 29.16–21) But that is vague in content and in chronology. * ƒ b æd e
¯Œ ıæ
ŒÆd æø
Æ e
çıØŒe
 

I º
, ÅÆE

 ŒÆd ıªå

, ... 10 At least one later Peripatetic adopted, and argued for, the view here ascribed to Strato: see the discussion of Sosigenes’ remarks about meaning by Dexippus, in Cat 7.1–8.23 (see P. Moraux, L’Aristotelismo presso i Greci II I (Milan, 2000), pp.324–326).

Meaning, saying, and thinking

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IV The De interpretatione does not straightforwardly offer a three-tiered account of meaning. First, Aristotle mentions not three but four tiers: written words, utterances, affections of (or in) the soul,11 things. We shall come to a threetiered theory only if we choose to ignore the first of the four tiers. Secondly, Aristotle is not exclusively concerned with meaning. Thus when he says that utterances are ‘symbols’ of [51] affections in the soul, he is not indicating what utterances signify; for written words are symbols of utterances and written words do not signify utterances — rather, they stand in for utterances, performing their function in a more endurable medium. Similarly, utterances are symbols of affections insofar as they stand in for them in the public domain. None of that has anything directly to do with meaning.12 But, thirdly, utterances are signs of affections; or rather, utterances are primarily signs of affections and, by implication, secondarily signs of things. That claim does appear to constitute a sort of ‘semantic theory’ — and hence Int 1 was the Urtext for the later Peripatetic account of meaning, the account which is standardly compared and contrasted with the Stoic and the Epicurean accounts. At the heart of that account is the thesis that names and verbs, which constitute sentences, and also sentences themselves, have meaning insofar as they signify — primarily — affections in the soul. Thus in the sentence ‘Lions roar’, the words ‘lion’ and ‘roar’ are meaningful insofar as they signify certain affections in the soul, and what they mean is determined by which affections they signify; and the whole sentence ‘Lions roar’ signifies something in the soul, and what it there signifies determines its meaning. What are these affections in the soul? Aristotle himself implies that sentences, sometimes at least, symbolize beliefs or judgements,  ÆØ; and since he holds that beliefs are compounded from thoughts or
ÆÆ, he should hold that names and verbs, sometimes at least, symbolize thoughts. That conclusion is supported, if not established, by the references to
ÆÆ at Int 16al0 and 14; and although there was a dispute among later scholars, some holding and others denying that the pertinent affections of the soul included çÆ
ÆÆ,13 the standard view took the phrase ‘affections in the soul’ simply to denote thoughts. Thus Ammonius: 11 He can intend no difference between ‘B łıåB’ and ‘K
fiB łıåfiB’. 12 In this paragraph I am indebted to Walter Cavini. 13 See e.g. Boethius, in Int 2 27.22–29.16; al-Farabi, in Int [24].

588

Logical Matters

Since names and verbs differ from the non-significant utterances insofar as they are significant of something, Aristotle first tells us what items are properly and directly signified by them, viz that thoughts are — and that objects are signified by way of intermediary thoughts. (in Int 17.22–26)*

(It should be added that the thoughts were usually envisaged as images or pictures of things.14) But are the pertinent beliefs and thoughts to be considered as mental events or states, as items currently in the soul of the utterer? Or are they rather generic beliefs and thoughts? If I say ‘Lions roar’, does the word ‘lion’ mean or refer to the particular thought (the ‘mental image’) of a lion which is currently in my soul, or does it rather mean or refer to the general thought or concept of a lion? And does the sentence signify my current thought that lions roar, or rather the general thought that lions roar?15 [52] Better, let us ask how a Peripatetic semantic theorist would replace ‘P’ and ‘Q’ in the formula: ‘Lions roar’, as uttered by x in C, means that P if and only if Q. I assume that he would offer us something along the following lines: ‘Lions roar’, as uttered by x in C, means that lions roar if and only if ‘Lions roar’, as uttered by x in C, expresses x’s thought in C that lions roar. Meaning is thus explained in terms of thinking; that is to say, ‘secondary’ signification is explained in terms of ‘primary’ signification. But should the last clause here — the clause which replaces ‘Q’ — be glossed by, say: (A) ‘Lions roar’, as uttered by x in C, expresses the fact that at t x is entertaining the thought that lions roar or rather by, say: * Kd ... ØÆçæ ıØ a O
ÆÆ ŒÆd a ÞÆÆ H
Iø
çø
H
ŒÆa e ÅÆ
ØŒ Ø
ø
r
ÆØ, æ æ
A › `æØ ºÅ ØŒØ Øa  ø

Æ Kd a æ Ū ı
ø ŒÆd æ åH  ÆPH
ÅÆØ

Æ, ŒÆd ‹Ø a
ÆÆ, Øa b  ø
ø
a æªÆÆ. 14 e.g. Dexippus, in Cat 10.19–23; Ammonius, in Int 18.29-30; Boethius, in Int 2 11.28-30 (from Alexander); al-Farabi, in Int [28]. The idea depends on Aristotle’s remark that the affections are likeness, › ØÆÆ, of the objects: Int 16a7. 15 Roughly speaking, the former option is Lockean: linguistic items have Ideas and compoundings of Ideas as their meanings; and the latter option is Fregean: linguistic items have Gedanken and their parts as their meanings. These rough parallels may (or may not) be found helpful; but they must not be pressed — and I am not suggesting that Peripatetic thoughts must be identified either with Lockean Ideas or with Fregean Gedanken.

Meaning, saying, and thinking

589

(B) ‘Lions roar’, as uttered by x in C, expresses the thought that lions roar?16 According to option (A), meaning depends on something peculiar to x and relatively transitory, namely a particular thought which x happens to be entertaining in C.17 According to option (B), meaning depends on something neither peculiar to x nor transitory: it depends on a thought which is impersonal and atemporal. The ancient commentators do not explicitly consider (A) and (B); but they implicitly opt for (A) rather than for (B).18 One reason for their doing so may perhaps19 be found in a passage from Alexander of Aphrodisias20 which is reported by Boethius: Alexander asks: If names are of things, then what is the reason why Aristotle says that utterances are primarily signs of thoughts? For it is things to which names are given — e.g. when we say ‘man’ we do indeed signify a thought, but the name is of a thing, i.e. of a rational mortal animal. Then why are utterances not primarily signs of the things to which they are given, rather than of thoughts? Perhaps (Alexander says) Aristotle says so for this reason: although utterances are names of things, nevertheless we use utterances in order to signify not things but those affections of the soul which are produced in us by the things. (in Int 2 40.30–41.11)* [53]

Alexander raises a pertinent question; and his tentative answer is curt. It perhaps relies on the following line of argument. If I utter the sentence 16 Perhaps the Peripatetics held that S, as uttered by x in C, expresses the thought that P only if x in C is thinking that P. In that case we might elaborate (B) thus: (B*) ‘Lions roar’, as uttered by x in C, expresses the thought that lions roar, and in C x is thinking that lions roar. 17 Note that in (A) — and also in (B*) — we must say ‘thought’ rather than ‘belief ’; otherwise we could not say things which we did not believe. In (B) the case is different. 18 See e.g. Dexippus, in Cat 8.15–18 (a ºª 
Æ persist only so long as someone is speaking); Ammonius, in Int 21.13–16 (cf e.g. 18.5–7, where
ÆÆ are the causes of çø
Æ; 18.30–35, where çø
Æ announce our (current)
ÆÆ). 19 I say ‘perhaps’: as Andreas Schubert pointed out to me, it is not clear that Alexander’s argument must be construed with (A) rather than (B) in mind. 20 Presumably from his lost commentary on Int — on which, see M. Bonelli, ‘Alexandre d’Aphrodise et le de Interpretatione ’, in S. Husson (ed), Interpre´ter le de Interpretatione (Paris, 2009), pp.51–67). * quaerit Alexander si rerum nomina sunt quid causae est ut primorum intellectuum notas esse voces diceret Aristoteles. rei enim ponitur nomen ut cum dicimus homo significamus quidem intellectum rei tamen nomen est id est animalis rationalis mortalis. cur ergo non primarum magis rerum notae sunt voces quibus ponuntur potius quam intellectuum? sed fortasse quidem ob hoc dictum est, inquit, quod licet voces rerum nomina sunt, tamen non idcirco utimur voces ut res significemus sed ut eas quae ex rebus nobis innatae sunt animae passiones.

590

Logical Matters

‘Lions roar’, then my primary purpose is to inform you of the affections in my soul, of my current thought that lions roar; and in general, when I use words, my primary intention is to indicate what I am currently thinking. Hence the primary meanings of my utterances must be constituted by my thoughts — that is to say, by what I am currently thinking. The argument is unsatisfactory on at least two counts. First, it is false that, in general, my primary purpose in speaking is to indicate what I am thinking. If I say to you ‘Lions roar’, then it is most probable that I want to let you know something about lions. Only in special circumstances will my primary intention be autobiographical confession. Secondly, even if my primary purpose is to communicate my thoughts, it by no means follows that my words must signify those thoughts. Suppose I indicate what my current thoughts are by saying straightforwardly ‘I am now thinking of Catherine Deneuve’: it is plain that the words ‘Catherine Deneuve’ in my sentence refer to Catherine Deneuve, and not to any thought of mine. In order to say what I am thinking, I must refer to the objects of my thought — to what I am thinking about and not to my thinking about it. However that may be, the Peripatetics did implicitly opt for (A). And they will surely have supposed that Aristotle’s use of the phrase ‘affections of the soul’ indicated that he too had particular thinkings in mind. It would seem odd to refer to an impersonal thought — such as the thought that lions roar — as an affection of the soul; for such thoughts are not mental states or events. Rather, we would incline to construe an affection of the soul as a state or event in the soul or mind of the utterer, as a particular, datable, thought or thinking.21

V Various texts connect Stoic sayables in one way or another with thought and thinking; and some of these texts have been taken to ascribe something like a Peripatetic theory of meaning to the Stoics. My main discussion will concern two groups of passages; but I begin with three general remarks. 21 On the other hand, Aristotle says that the affections in the soul, like the items in the world, are ‘the same for all’. If the affections are particular thinkings, then they can only be generically the same for all men — they will not be the same in the way in which the objects are the same. The parallel between the sameness of the affections and the sameness of the objects suggests something like this. When I say ‘Lions roar’ and you say ‘Die Lo¨wen bru¨llen’, then the objects to which I refer are the very same as those to which you refer — we both refer to lions; and similarly, the thought which I express is the very same as the thought which you express — we both express the thought that lions roar. And then the ÆŁÆÆ must be impersonal thoughts rather than particular thinkings.

Meaning, saying, and thinking

591

First, non-Stoic authors are frequently vague or careless or cavalier or downright wrong in their remarks about sayables. Thus when pseudoAmmonius, in APr 68.6, and Philoponus, in APr 243.4, assure us that the Stoics used the word ‘ºŒ
’ to designate çø
Æ or utterances, we should dismiss their reports without [54] ado.22 When Clement, strom VIII iii 13.1, remarks that ‘what is signified by the word ‘‘embryo’’ ... is incorporeal and a sayable and an object and a thought’, we should not take that as a serious historical report of Stoic doctrine.23 When Simplicius reports that some interpreters of Aristotle’s Categories affirm that sayables are thoughts (in Cat 10.2–4),24 we need not pay attention to the report — unless it is corroborated by other evidence. When Ammonius, in Int 17.27–28, observes that the Stoics hypothesize items in between thoughts and objects, which they call ºŒ, we should not take him to mean that the Stoics themselves said that sayables occupy such an intermediate position.25 Secondly, any philosopher, whatever his semantic theory, will from time to time state or imply that people sometimes say what they think. Consider the following brief passage: The Stoics say that the nominative has fallen from the thought in the soul; for when we want to express the thought of Socrates which we have within us, we utter the name ‘Socrates’. (Ammonius, in Int 43.9–12)26

The content of the last sentence is a commonplace. If you are thinking of Socrates and want to say who you are thinking of, you may reasonably utter the name ‘Socrates’. The Stoics, like anyone else, will have taken it for granted that producing the name of someone you are thinking about is in general a pretty good way of saying who you are thinking about. In taking that for granted, they commit themselves to no semantic theory. Even if Ammonius 22 The grammarians occasionally use the word ‘ºŒ
’ as a synonym for ‘çø
’ (e.g. Apollonius, pron 59.1; adv 158.20): that may have contributed to later confusions over the Stoic theory. Sextus, M I 78, explicitly notices the difference between the Stoic and the grammatical usage. 23 Clement himself does not pretend that it is. 24 The text is quoted above, p.[47]. 25 ‘So we should discard most of the texts which inform us about Stoic sayables?’ — Yes. — ‘Surely that is methodologically indefensible?’ — Not in the least. 26 ... I Œæ

ÆØ ƒ Ie B  A ‰ Ie  F
Æ   F K
fiB łıåfiB ŒÆd ÆoÅ øŒ
: n ªaæ K
Æı E å 
e øŒæ ı
ÅÆ źHÆØ  ıº 
Ø, e øŒæÅ Z
Æ æ çæ ŁÆ. — The question was: Is the nominative a case, a HØ? No, according to the Peripatetics; for whereas the oblique cases ‘fall’ from the nominative, the nominative does not fall from anything. Yes, according to the Stoics; for the nominative does indeed fall from something, viz from the thought.

592

Logical Matters

in this passage is referring to the Old Stoa (which is not clear), and even if he is reporting Stoic views with fidelity (which cannot be taken for granted), nevertheless his report has nothing to do with any theory of meaning. In general, we should not read philosophical theories into platitudes. Thirdly, the Stoics said surprisingly little about thought and thinking — or rather, our surviving evidence ascribes surprisingly few theses about thought to them. But we do know enough to rule out, from the very start, a Peripatetic interpretation of the Stoic account of meaning. The argument is simple. One of the salient facts about Stoic sayables is their incorporeality: any number of texts state that the Stoics took their sayables to be bodiless (e.g. Sextus, M VIII 258–261). Why they did so may be wondered, and the wisdom of their doing so may be questioned; but that they did so is uncontroversial.27 Thoughts, on the other hand, are corporeal; or [55] rather, thinkings,
Ø, are bodies (Diogenes Laertius, VII 51). For thinkings are a special kind of çÆ
ÆÆØ, namely rational çÆ
ÆÆØ, and çÆ
ÆÆØ are corporeal items. Unless the Stoics fell into an evident contradiction, they cannot have held that sayables were particular thoughts. In other words, they cannot have accepted anything like option (A) of the previous section, and they cannot have advanced anything like the Peripatetic theory of meaning. It does not follow that the Stoics did not accept option (B) of the previous section. For
ÆÆ are not
Ø, and their ontological status is not determined by the ontological status of
Ø. As a matter of fact, it is unclear to me what ontological status the Stoics ascribed to
ÆÆ — if indeed they gave the matter any consideration at all.

VI There is a celebrated Stoic description of sayables28 which makes an intimate connection between saying and thinking — and which has been thought to support the suggestion that Stoic sayables are Peripatetic thoughts under a different name. The Stoics claimed quite generally that the true and the false are found in sayables. And they say that a sayable is that which subsists in accordance with a rational 27 But see below, n.33. 28 The description is generally referred to as a definition; but, as Andreas Schubert rightly observed, no text formally so characterizes it.

Meaning, saying, and thinking

593

presentation, and that a presentation is rational if what is presented can be set out in language. (Sextus, M VIII 70)29

The crucial phrase, to which there are several parallels in other texts,30 is this: ‘a sayable is that which subsists in accordance with a rational presentation’. Rational presentations, as I have said, are thinkings,
Ø (Diogenes Laertius, VII 51). Hence they are mental events of some sort. Now sayables subsist ŒÆ or in accordance with such events: does not that mean that they subsist in virtue of such events? and hence that they depend for their subsistence on the occurrence of a certain type of mental event? So understood, the text establishes at least the weaker of the two theses which I rehearsed in section I. Although it does not follow that sayables are thoughts, one way of explaining how they depend on thoughts would be to identify them with thoughts; and in that case, the text would establish the strong thesis of section I. But that way of understanding the preposition ‘ŒÆ’ is not mandatory — and a different interpretation makes better philosophical sense and better exegetical sense. On this different interpretation, the force of ‘ŒÆ’ is given not by ‘in virtue of’ but rather by ‘corresponding [56] to’, ‘answering to’.31 Thus a sayable is not what depends on a rational presentation but what answers to a rational presentation. Rational presentations are presentations which are expressible in language — that is how we should understand the phrase ‘º ªfiø ÆæÆBÆØ’. Hence a sayable is what you say when you give linguistic expression to such a rational presentation. It seems to me now that there is a tapir in the garden. Here is a çÆ
ÆÆ. It is a rational çÆ
ÆÆ; that is to say, I can express it (or its content) in language — I can say what çÆ
ÆØ. I can do so by saying, for example: ‘There’s a tapir in the garden’. The sayable in question is what corresponds to

29 M ı
ƒ øœŒ d Œ Ø
H K
ºŒfiH e IºÅŁb r
ÆØ ŒÆd e łF . ºŒe
b æåØ
çÆd e ŒÆa º ªØŒc
çÆ
ÆÆ
çØ

, º ªØŒc
b r
ÆØ çÆ
ÆÆ
ŒÆŁ m
e çÆ
ÆŁb
Ø º ªfiø ÆæÆBÆØ. 30 See Diogenes Laertius, VII 63 (the same phrase as in M VIII 70); Suda, s.v. ŒÆŪ æÅÆ (the same phrase again); cf Sextus, M VIII 12 (what is signified is that y E I
غÆÆ
ŁÆ fiB

æfi Æ ÆæıçØÆ
ı ØÆ
fi Æ); Diogenes Laertius, VII 43. 31 At Diogenes Laertius, VII 43 (a passage to which Woldemar Go¨rler drew my attention) we read of e
æd H
çÆ
Æø
 
ήd H
KŒ  ø
çØÆ
ø
ºŒH
. Here it seems that ‘KŒ  ø
’ must correspond to the ‘ŒÆa çÆ
ÆÆ
’ in our text. But ‘KŒ  ø
’ can scarcely mean ‘answering to these’: the preposition must express some sort of dependence. Thus one text at least does express the view which I am declining to discover in M VIII 70. To that I can only reply — truly but lamely — that the whole paragraph at VII 43 is pretty confused.

594

Logical Matters

the çÆ
ÆÆ which I have just expressed in language; in other words, the sayable is precisely what I have said, namely that there is a tapir in the garden. In the light of that, consider the formula: ‘Lions roar’, as uttered by x in C, means that lions roar if and only if Q. Plainly, the Stoic replacement for ‘Q’ must somehow include a reference to a sayable, i.e. to what is said by uttering the sentence. I take it that the Stoic view amounts to something like this: ‘Lions roar’, as uttered by x in C, means that lions roar if and only if in uttering ‘Lions roar’ in C x thereby says that lions roar. That thesis makes no reference to thinking at all.32 The thesis is not the Stoic theory of sayables. It is at best a part of their theory; for it applies only to those sayables which correspond to (typical uses of ) indicative sentences. The theory itself must cope, in addition, with the sayables which correspond to non-indicative sentences (e.g. to imperative or to interrogative sentences) and also with the ‘incomplete’ sayables which correspond to certain parts of sentences. I shall say nothing about those matters; but my remarks will of course have no value unless they can eventually be extended to cover all sayables.33 [57]

VII In his pioneering monograph on Stoic grammar, Rudolf Schmidt supposed that there was the closest connection between sayables and thoughts.34 He cited four texts in evidence. One is a passage from Sextus, M VIII 80, which I

32 The ºŒ
may thus be identified with the content of an utterance, and hence it may equally be identified with the thought (the impersonal thought) which the utterance expresses: if a ºŒ
is what I say when I say that P, then — and trivially — it is also what I think when I think that P. But ºŒ are not thoughts in the sense of particular thinkings; nor does the subsistence of a ºŒ depend on the occurrence of any particular thinking. 33 But we are already in a position to understand the Stoic claim that sayables are incorporeal (see above, p.[54]). When I say that lions roar, is what I say corporeal or not? It is plain, I suppose, that that is a silly question. It might be rephrased thus: does ‘that lions roar’ denote something corporeal or not? Well, it does not denote anything corporeal — because it does not denote anything at all. Insofar as the Stoics suggest that it denotes something incorporeal, they are mistaken; but it is reasonable to take their claim that ‘sayables are incorporeal’ as an attempt to deny that e.g. ‘that lions roar’ denotes. The Stoics also, of course, hold that sayables are ‘things’; but to say that is only to say that there are such things as sayables, i.e. to say that we can say things. 34 See R. Schmidt, Stoicorum Grammatica (Halle, 1839) [German translation, ed K. Hu¨lser (Braunschweig/Wiesbaden, 1979)], pp.20–21 [p.50].

Meaning, saying, and thinking

595

shall discuss a little later on. Another is Diogenes Laertius VII 57, which does not mention thought or thinking at all. A third is a snippet from Ammonius, in Int 13.7–18: here Ammonius is presenting an interpretation of Aristotle; he does not refer to the Stoics and his remarks have no bearing upon any Stoic theory. The remaining text is more pertinent. It is a piece of Varro. loqui derives from locus. Because someone who is said to utter for the first time says names and other words before he can say each in its own place, Chrysippus says that he does not speak but only as it were speaks. Hence, just as a picture of a man is not a man, so in the case of ravens and crows and children who are first beginning to utter, their words are not words because they do not speak. Thus someone speaks if he knowingly places each word in its own place, and he has only spoken out when by speaking he has produced what he had in his mind. (ling Lat VI vii 56)*

The final sentence of the passage connects speaking and thinking. Yet how much of the passage comes from Chrysippus is hard to say: certainly the play on ‘locus’ and ‘loqui ’, essential to Varro’s etymological purpose, cannot be Chrysippean (for the etymology does not work in Greek); and a minimalist might claim that the only part of the text which surely comes from Chrysippus is the clause distinguishing ‘loqui ’ from ‘ut loqui ’ Hence the final sentence cannot with any great assurance be ascribed to a Stoic source. But there are other, and far better, texts which parallel the Varro passage and which Schmidt might rather have cited. For Galen quotes both Chrysippus and Diogenes of Babylon verbatim on the matter. Here are the texts in full. Speaking, and speaking within oneself, and thinking, and going through an utterance within oneself, and emitting an utterance, must all come from the intellect. (Chrysippus, De anima, apud Galen, PHP V 345)35 It is reasonable that that to which the significations in speech go and from which speech comes should be the sovereign part of the soul. For there is not one source of speech and another of thought, nor one source of utterance and another of speech;

* loqui ab loco dictum. quod qui primo dicitur iam fari vocabula et reliqua verba dicit ante quam suo quique loco ea dicere potest, hunc Chrysippus negat loqui sed ut loqui. quare ut imago hominis non sit homo, sic in corvis cornicibus pueris primitus incipientibus fari verba non esse verba quod non loquantur. igitur is loquitur qui suo loco quodque verbum sciens ponit et is tum prolocutus cum in animo quod habet extulit loquendo. 35 Ie ªaæ B ØÆ
Æ ... E ºªØ
ήd K
ÆıfiH ºªØ
ŒÆd ØÆ
EŁÆØ ŒÆd K
Æı E çø
c
ØØ
ÆØ ŒÆd KŒe KŒØ
. — The text is uncertain, but the uncertainties do not matter here. I follow de Lacy’s edition.

596

Logical Matters

nor, in general, is the source of utterance one thing and the sovereign part of the soul another. For in general, whence speech is emitted, there must reasoning and thinking and the preparation of saying reside, as I have said. But these evidently occur about the heart, since utterance [58] and speech are emitted from the heart through the windpipe. It is also persuasive that whither what is said conveys signification, there should it be given signification, and that utterances should come thence in the manner I have already described. (Chrysippus, apud Galen, PHP V 243)36 Whence utterance is emitted, thence articulated utterance is emitted. Now significant articulated utterance, i.e. speech, is also emitted thence. Therefore speech is emitted whence utterance is emitted. But utterance is emitted not from the regions around the head, but rather — and evidently — from the lower parts; for it evidently passes through the wind-pipe. Therefore speech is not emitted from the head, but rather from the lower parts. But it is also true that speech is emitted from the intellect. Indeed, some people actually define it as significant utterance emitted from the intellect. Again, it is plausible that speech is emitted when it has been given signification and has as it were been stamped by the notions in the intellect, and that it lasts for the same time as thinking and the activity of speaking. Therefore the intellect is not in the head, but in the lower parts — and in particular about the heart. (Diogenes of Babylon, apud Galen, PHP V 242)*

A final text37 is worth setting down alongside those citations from the Old Stoics themselves:

36 hº ª
b N n ªª

ÆØ Æƒ K
 fiø ÅÆÆØ ŒÆd K y º ª , KŒE
r
ÆØ e ŒıæØF
B łıåB æ . P ªaæ ¼ººÅ b
Ūc º ª ı Kd
¼ººÅ b ØÆ
Æ, Pb ¼ººÅ b
çø
B Ūc ¼ººÅ b º ª ı, Pb e ‹º
±ºH ¼ººÅ çø
B Ū KØ
¼ºº b e ŒıæØF
B łıåB æ . ... e ªaæ ‹º
‹Ł
› º ª  KŒÆØ KŒE E ŒÆd e
Øƺ ªØe
ªª
ŁÆØ ŒÆd a ØÆ
Ø ŒÆd a ºÆ H
Þø
, ŒÆŁæ çÅ
. ÆFÆ b KŒçÆ
H æd c
ŒÆæÆ
ªª
ÆØ, KŒ B ŒÆæÆ Øa çæıªª  ŒÆd B çø
B ŒÆd  F º ª ı KŒ 
ø
. ØŁÆ
e
b ŒÆd ¼ººø N n K
ÅÆ
ÆØ a ºª 
Æ, ŒÆd ÅÆ
ŁÆØ KŒEŁ
ŒÆd a çø
a I KŒ
ı ªª
ŁÆØ ŒÆa e
æ ØæÅ

æ 
. — Perhaps read ‘ÅÆ
ÆØ’ for ‘K
ÅÆ
ÆØ’ and ‘K
ÅÆ
ŁÆØ’ for ‘ÅÆ
ŁÆØ’? * ‹Ł
KŒÆØ çø
, ήd 
ÆæŁæ : PŒ F
ŒÆd ÅÆ
ıÆ 
ÆæŁæ  çø
c KŒEŁ
,  F b º ª . ŒÆd º ª  ¼æÆ KŒEŁ
KŒÆØ ‹Ł
ŒÆd çø
. b çø
c PΠKΠH
ήa c
Œçƺc
 ø
KŒÆØ Iººa çÆ
æH KŒ H
ŒøŁ
Aºº
: KŒçÆ
c ª F
KØ Øa B IæÅæÆ ØØ FÆ. ŒÆd › º ª  ¼æÆ PŒ KŒ B ŒçƺB KŒÆØ Iººa ŒøŁ
Aºº
. Iººa 
ª ŒIŒE
IºÅŁ, e e
º ª
KŒ B ØÆ
Æ KŒŁÆØ: 
Ø Ø ª F
ŒÆd ›æØÇ 
Ø ÆP
çÆØ
r
ÆØ çø
c
ÅÆ
ıÆ
Ie ØÆ
Æ KŒ 
Å
: ŒÆd ¼ººø b ØŁÆ
e
e H
K

ØH
K
ÅÆ

H
K
fiB ØÆ
fi Æ ŒÆd x
KŒıø

KŒŁÆØ e
º ª
ŒÆd ÆæŒ
ŁÆØ fiH åæ
fiø ŒÆ  e ØÆ

BŁÆØ ŒÆd c
ŒÆa e ºªØ
K
æªØÆ
. ŒÆd Ø
ØÆ ¼æÆ PŒ Ø
K
fiB ŒçƺfiB Iºº K
 E ŒÆøæø   Ø, ºØ ø æd c
ŒÆæÆ
. 37 See also Diogenes Laertius, VII 49; Stobaeus, ecl I iii 55; Cicero, nd II lix 149; Philo, somn I 28; Diomedes, ars gramm [GL I 300.7–12] (the last three texts reflect Stoic thought but do not refer explicitly to the Stoics).

Meaning, saying, and thinking

597

Animal utterance is air struck by an impulse; but human utterance is air which is articulated and emitted from the mind, as Diogenes says; and that is perfected after fourteen years. (Diogenes Laertius, VII 55)*

The texts plainly make a close connection between saying and thinking. Moreover, although they do not explicitly mention sayables, they explicitly refer to signification. The texts deal with physiological psychology, and their primary concern is physiological. (Thus the reference to fourteen years in the passage from Diogenes Laertius alludes to the change in voice which occurs in human males at puberty.) The Stoics were concerned to show that the ª
،
or ‘ruling part’ is lodged in the heart and not in the head. The ª
،
is, among other things, the locus of thinking. Hence the following simple argument: (1) The ª
،
is lodged where thinking takes place. (2) Speech is emitted from the place where thinking takes place. (3) Speech is emitted from the heart. Therefore: (4) The ª
،
is lodged in the heart. The argument demands no stronger connection between speaking and thinking than the connection claimed in premiss (2). [59] The Stoics were also concerned to explain the difference between adult human utterance on the one hand and animal utterance (and the utterance of human infants) on the other. Ravens may utter Greek sentences (see e.g. Sextus, M VIII 275); and the crows on Callimachus’ rooftop cawed on about conditionals; but crows and ravens do not say anything. Why not? According to the Stoics, human utterances depend on the human mind: human speech is air formed and articulated by the mind, and hence by the heart. When ravens utter, the sounds they produce do not come from the heart. That explanation of the difference between human and animal utterance does not simply invoke the fact that speech comes from the heart. More specifically, it relies on the claim that speech is caused by thinking; and it is this claim which lies behind premiss (2) of the Stoic argument about the location of the ª
،
. Thus we may ascribe to the Stoics some such thesis as this:

* Çfi ı 
KØ çø
c Icæ e ›æB ºÅª
, I
Łæ ı  Ø

ÆæŁæ  ŒÆd Ie ØÆ
Æ KŒ 
Å, ‰ › ˜Ø ª
Å çÅ
, lØ Ie ŒÆæø
KH
ºØ FÆØ.

598

Logical Matters

In uttering S in C, x says that P only if 38 in C x’s entertaining the thought that P causes39 x to utter S. I utter the sentence ‘Lions roar’, and so does a nearby raven. In uttering the sentence I say that lions roar — but the raven says nothing at all. I say that lions roar because my sentence was articulated by and emitted from my heart. And in particular, I say that lions roar inasmuch as my utterance of the sentence ‘Lions roar’ was caused by my entertaining the thought that lions roar. The Stoic thesis may seem plausible; but as it stands it is false — for we can, and often do, speak without thinking. Just as I ride my bicycle into College without thinking of what I am doing, so I give my standard lecture of Plato’s Idea of the Good without thinking of what I am saying — I have, after all, given the lecture any number of times before. In the course of the lecture I utter S and thereby say that P; but while uttering S I am not entertaining the thought that P. I may be thinking of nothing at all; or, more likely, I am thinking of lunch and a stiff gin and tonic. ‘Automatic’ speaking of this sort is a common enough phenomenon. Insofar as the Stoic thesis denies that it can occur, the thesis is false.40 But that is irrelevant to the present purpose. The vital question is this: Does the Stoic thesis have any semantic implications? Two elements in the Stoic texts suggest that it has. First, Diogenes remarks that ‘some people actually define as significant utterance emitted from the intellect’. Are these people not Stoics? And do they not hold that speech is significant insofar as it signifies what is in the intellect? It is true that Diogenes does not embrace the definition himself, nor indeed does he say that it was a Stoic definition. But a passage from Sextus gives [60] supplementary information. In the course of arguing against the existence of ºŒ, Sextus urges that every ºŒ
must be said (ºªŁÆØ), and that saying, e ºªØ
, is impossible — hence there are no ºŒ. In order to show that saying is impossible, he first explains what saying is, thus: 38 Not ‘if and only if’: see below, n.43. 39 Instead of ‘causes’ I should properly write — as Michael Frede urged — something rather more cumbersome: ‘is an element in the set of factors which together cause’. The cause will be a ‘containing’ cause, ÆYØ
ı
ŒØŒ
, if (as Diogenes suggests) ‘speech ... lasts for the same time as thinking and the activity of speaking’ (see e.g. Sextus, PH III 15). 40 No doubt the thesis can be amended, in one way or another, to cope with this objection — but I shall not here attempt any such amendment.

Meaning, saying, and thinking

599

For to say something, as the Stoics themselves assert, is to emit the utterance which signifies the object thought of. (M VIII 80)41

That is not identical with the definition cited by Diogenes; but it is sufficiently near to allow us to infer that the definition was a Stoic definition (or at any rate closely related to a Stoic definition). And we must admit that the definition has some semantic content. But may we infer that ‘speech is significant insofar as it signifies what is in the intellect’? We need not — and we should not. First, the definition cited by Diogenes actually suggests the possibility of significant utterance which is not emitted from the intellect; utterers who do not speak from the heart do not say anything — but what they utter may surely have significance. Secondly, the Sextan passage does not say that words signify thoughts or any other mental items. It says that words signify the thing which is being thought of. I suppose that Sextus is here using the word ‘thing’ or ‘æAªÆ’ in the semitechnical sense which it has in the Stoic theory of meaning, and hence that æªÆÆ are to be identified with sayables.42 Thus we reach something like the following thesis: In uttering S in C, x says something if and only if S means that P and in C x is thinking that P. The thesis tells us a little more — and a little less — than the causal thesis which I extracted from the texts a moment ago.43 Secondly, there are other references to meaning or signification in our texts. The references are far from clear in detail; but their general drift is intelligible enough. Thus when Chrysippus remarks that ‘the significations in speech go’ to the heart, he means — I take it — that we do not understand an utterance when it reaches our ears: for understanding to take place, the utterance must (somehow) affect the sovereign part of the soul, i.e. the heart. Although that in itself tells us nothing about meaning. Chrysippus also observes that ‘whither what is said conveys signification, there should it be given signification’. Diogenes presumably says more or less the same when he

41 ºªØ
ªæ KØ, ŒÆŁg ÆP  çÆØ
ƒ Ie B  A, e c
 F
ı
ı æªÆ  ÅÆ
ØŒc
æ çæŁÆØ çø

. 42 I suppose further, that when Sextus speaks of e


æAªÆ he does not mean ‘the object of which we are thinking’ but rather ‘the object which we are thinking’. For when I say ‘Lions roar’ I am thinking (perhaps) of lions and not of any ºŒ
. 43 A little more inasmuch as it offers an ‘if and only if’ rather than an ‘if’; a little less inasmuch as it makes no reference to any causal connection.

600

Logical Matters

remarks that ‘speech is emitted when it has been given signification and has as it were been stamped by the notions in the intellect’. Now to say that our utterances are given meaning by our hearts, or by the notions in our intellects, might seem to amount to something like this: [61] In uttering S in C x says that P if and only if (i) in C x is entertaining the thought that P and (ii) S means that x in C is entertaining the thought that P. And that comes pretty close to a Peripatetic theory of meaning. But this interpretation is not imposed upon us by the texts. Chrysippus and Diogenes hold that the thoughts in my mind give meaning to the words and sentences which I utter. It does not follow that the meanings of the words and sentences are the thoughts. My thoughts may give sense to my words not insofar as they constitute their sense but rather — and simply — insofar as I intend the words to carry that sense. Thus when I utter the sentence ‘Lions roar’, I then say that lions roar provided that I am entertaining the thought that lions roar and intend to express this thought by uttering the sentence ‘Lions roar’. My thoughts ensure that my utterance has a sense, and they determine which sense it has; but they do not constitute its sense. My intellect picks out a sayable and pairs it with an appropriate sentence; I then utter the sentence — and thereby say something. In other, and less picturesque, language: I entertain the thought that P; I rehearse a sentence, S, which I intend to express the thought that P; I utter S — and (with luck) I thereby say that P. Here again is the causal thesis — or rather, a somewhat elaborated version of that thesis.

VIII From the various texts in which Stoic saying is associated with Stoic thinking, I have extracted two theses. The first thesis, which connects saying and meaning, was this: S, as uttered by x in C, means that P if and only if in uttering S in C x thereby says that P. The second thesis connects saying and thinking; it was this:

Meaning, saying, and thinking

601

In uttering S in C, x says that P only if in C x’s entertaining the thought that P causes44 x to utter S. The two theses, I have suggested, were constitutive parts of the Old Stoic theory of meaning, saying, and thinking. How far they are true, by what means they can be afforced and enlarged into a comprehensive theory, and what modifications they imply to the three-tiered caricature with which this paper started, are questions which I leave to other occasions.45 44 For a gloss on this word, see above, n.39. 45 This chapter is revised version of a paper which I gave at a conference held at Bamberg and organized by Klaus Do¨ring and Theo Ebert. The chapter owes much to the numerous criticisms and comments which it received at Bamberg; and more to later discussions with Michael Frede.

22 Epicurus: meaning and thinking* I Sextus says of the Epicureans that they ‘did away with the existence of sayables [ºŒ]’ (M VIII 258). Elsewhere he asserts that ‘Epicurus and Strato the physicist admit only two items: items which signify and items which obtain (M VIII 13). They reject the third member of the semantic triad.1 In both passages an Epicurean view is characterized by contrast with and in the terminology of a Stoic theory. The Stoic theory, as Sextus presents it,2 is roughly this. There are three types of item which are linked to one another: items which signify, items which are signified, and items which obtain. Items which signify or ÅÆ

Æ are utterances (çø
Æ — spoken words and sentences). Items which are signified or ÅÆØ

Æ are incorporeal sayables or ºŒ — they are the things we say when we utter utterances. Items which obtain or ıªå

Æ are ordinary ‘external objects’ — the items we talk about and make reference to when we say something by uttering an utterance. When I utter the sentence ‘That’s a cow’ (which is a corporeal string of sounds), I may thereby say that that is a [198] cow (and what I say — that that is a cow — is not itself corporeal), and I talk about that cow (which is a bovine body). In general, when anything meaningful is said, three items are linked: by uttering an utterance, U, I thereby say a sayable, S, and talk about an object, O; and U means S. * First published in G. Giannantoni and M. Gigante (eds), Epicureismo greco e romano (Naples, 1996), pp.197–220. 1 ›æH
b ‰ N Ø
 ƒ I
fi ÅæÅŒ  c
oÆæØ
H
ºŒH
, ŒÆd På ƒ æ   Ø 

x
ƒ ¯ØŒ æØ Ø Iººa ŒÆd ƒ øœŒ d ‰ ƒ æd e
´ÆغÅ
... ƒ b æd e
¯Œ ıæ
ŒÆd æø
Æ e
çıØŒe
 

I º
, ÅÆE

 ŒÆd ıªå

... — Phrases of the form ‘ ƒ æd ˛’ are notoriously ambiguous (see J. Barnes, ‘Diogenes Laertius IX 61–116’, in ANRW II 36.6, pp.4241–4301, on p.4266 n.132 [reprinted in volume IV]); but here the translation I have given must be right. 2 See especially M VII 11–12. I am not here concerned with the reliability of Sextus’ account of the Stoic theory.

Epicurus: meaning and thinking

603

The later Peripatetic view, which was founded on the first chapter of Aristotle’s de Interpretatione, also had three tiers to it. But the Peripatetics did not like ‘sayables’: in their view, what my utterances mean are not sayables but rather ‘passions of the soul’ or, more specifically, thoughts [
ÆÆ]. Thus in uttering U, I thereby express a thought T, and talk about O; and U means T.3 The Epicureans, according to Sextus, in effect agreed with the Peripatetics in rejecting sayables; but, unlike the Peripatetics, they did not think it necessary to replace sayables with some other sort of item: it is not merely that sayables have no place in an account of meaning — rather, there is no place there for anything to have. Thus only two tiers and two types of items are left: in uttering U, I talk about O; and U means O. The two doxographical notices in Sextus are confirmed by a polemical passage in Plutarch: If even this sort of error4 subverts life, then who goes more wrong about language than you Epicureans? You do away entirely with the class of sayables, which gives speech its very being: you admit only utterances and items which obtain, and you say that the intermediate items which are signified — through which learning and teaching and preconception and thought and impulse and assent come about — do not exist at all. (adv Col 1119F)*

[199] Plutarch’s style is rhetorical; but he evidently ascribes to the Epicureans the thesis which Sextus ascribes to them. We may wonder what exactly lay behind those texts, what remarks by Epicurus or his followers were their ultimate source. Certainly, nothing in the texts obliges us — or even authorizes us — to speak of an Epicurean ‘theory of meaning’; for there is no reason to suppose that Sextus and Plutarch are offering a skeletal summary of what had once been a fleshy semantic theory.5 3 That is a caricature of the Peripatetic view, just as Sextus’ account of the Stoic view is at best a rapid sketch. 4 i.e. error concerning words rather than objects. * ‰ Y ª ŒÆd ÆFÆ e

I
ÆæØ, 
 Aºº
H
ºÅº FØ æd c
غŒ
, Q e H
ºŒH
ª
 PÆ
fiH º ªfiø Ææå
¼æÅ
I
ÆØæE, a çø
a ŒÆd a ıªå

Æ 

I ºØ
, a b Æf ÅÆØ

Æ æªÆÆ Ø z
ª

ÆØ ÆŁØ ØƌƺÆØ æ ºłØ
Ø ›æÆd ıªŒÆÆŁØ e ÆæÆ
P r
ÆØ ºª
; 5 ‘There really is no such thing as Epicurean semantics’ (D. Glidden, ‘Epicurean semantics’, in AA.VV., ,˘˙)˙: studi sull’ epicureismo greco e romano offerti a Marcello Gigante (Naples, 1983), pp.185–226, on p.204 — but Glidden ascribes more in the way of theory to Epicurus than I am inclined to do). I might add that there is no such thing as Peripatetic semantics either — although Aristotle and his followers said a few things about meaning. The only ancient school to which we could plausibly ascribe a semantic theory is the Stoa — and even there we should be using the word ‘theory’ in a fairly generous sense.

604

Logical Matters

Nor do the texts invite us to imagine that Epicurus affirmed that there were no sayables; for sayables were not there to be dismissed until after Epicurus’ death.6 But should we imagine that Epicurus had explicitly rejected ‘intermediate’ items, saying something to the effect that ‘there are no items intermediate between words and things, nor does the phenomenon of meaning require us to postulate such items’? Or should we rather imagine that he had only implicitly dismissed the putative intermediates, perhaps by saying something to the effect that ‘words mean objects — that’s all there is to it’? Again, should we imagine that he had made some general statement about meaning like the two statements which I have just invented for him? Or should we rather imagine that he had said something particular — say, ‘ ‘‘Cow’’ means an animal of such-and-such a shape’7 — and that the remark was later generalized on his behalf? However we may choose to answer those questions, [200] Sextus and Plutarch are clear that Epicurus had no truck with intermediates, whether thoughts or sayables: on Epicurus’ view — explicit or implicit, generalized or particular — words mean things, U means O.

II And yet there are texts which tell — or which have been taken to tell — a different story. Among these texts is one in Epicurus’ own fist. First, then, Herodotus, we must grasp the items which are collected under the sounds, so that we may refer what is believed or investigated or puzzled over to these items and may thus come to a judgement, and so that it may not be the case either (if we offer proofs ad infinitum) that everything is unjudged or yet that we make empty sounds. For the primary concept must be looked at in connexion with each sound and must need no proof, if we are to have something to which to refer what is investigated or puzzled over and believed. (ad Hdt 37)*

6 Of course, later Epicureans may have explicitly denied the existence of sayables. 7 See Sextus, PH II 25; M VII 267: the Epicurean ‘definition’ of man. * æH
b
s
a  ƪ
Æ  E çŁ ªª Ø, t  ˙æ  , E NºÅç
ÆØ ‹ø i
a  ÆÇ 
Æ j ÇÅ 
Æ j I æ 
Æ åø
N ÆFÆ I
ƪƪ
 KØŒæ
Ø
ŒÆd c ¼ŒæØÆ 
Æ E
fi q N ¼Øæ
I ،
 ıØ
j Œ
f çŁ ªª ı åø
· I
ªŒÅ ªaæ e æH
K

ÅÆ ŒÆŁ ŒÆ
çŁ ªª
ºŁÆØ ŒÆd ÅŁb
I ø æ EŁÆØ Yæ  
e ÇÅ 

j I æ 

ŒÆd  ÆÇ 

Kç n I
 
.

Epicurus: meaning and thinking

605

The details are obscure; but one thing may seem reasonably plain: the ‘primary concepts’ are the same as the ‘items collected under the sounds’ (for both the concepts and the items are characterized as the objects to which what is investigated and believed and puzzled over is to be referred); but the items which are collected under the sounds are surely the meanings of the sounds: ergo it is the primary concepts which are the meanings of the sounds we utter. In this passage, then, Epicurus is maintaining that meaningful sounds mean concepts: in uttering U, I thereby make use of a concept, C, and talk about O; and U means C. A second passage, from Diogenes Laertius’ account of Epicureanism, sits well enough with that interpretation: Now the items which are primarily collected under any name are evident; and we should not be investigating the [201] things which we do investigate unless we already knew these items. e.g. what is standing some distance away is a horse (or a cow) — we must at some point have known by a preconception the form of a horse and a cow; and we would not even have named anything if we had not first learned its shape by a preconception. Thus preconceptions are evident; and what is believed depends on something prior which is evident and to which we refer it when we speak — e.g. how do we know that this is a man? (Diogenes Laertius, X 33)*

Again, the details of the text are obscure; again, one aspect of its interpretation may seem reasonably plain: the ‘items primarily collected under names’ are the same as ‘preconceptions’ (both are characterized as evident); but the items are surely the meanings of the names under which they are collected: ergo it is preconceptions which are the meanings of the words we utter. The primary concepts of the Letter to Herodotus are presumably the same as the preconceptions of this second text. Once again, in uttering U, I thereby make use of C and talk about O; and U means C. The idea that preconceptions are meanings seems to be implicit in other Epicurean texts. Thus when Philodemus says that ‘according to our teachers, the Sage will become angry not in accordance with this preconception but in accordance with the more common one’ (de ira XLV 1–6),** he means that * Æ
d s
O
ÆØ e æø  ƪ

K
Ææª KØ· ŒÆd PŒ i
KÇÅÆ
e ÇÅ 

N c æ æ
Kª
ί
ÆP ; x
e  ææø g ¥   Kd
j  F· E ªaæ ŒÆa æ ºÅłØ
Kª
øŒ
ÆØ  b ¥  ı ŒÆd  e  æç
: P i
T
Æ
Ø c æ æ
ÆP F ŒÆa æ ºÅłØ
e

ÆŁ
. K
ÆæªE s
NØ
ƃ æ ºłØ, ŒÆd e  Æe
Ie æ æ ı Ø
e K
Ææª F XæÅÆØ Kç n I
Æçæ
 ºª 
x
 Ł
Y
N  F KØ
¼
Łæø ; ** IæŒØ b ŒÆd  E ŒÆŁÅª Ø
P e ήa c
æ ºÅłØ
ÆÅ
ŁıøŁŁÆØ e
 çe
Iººa e ŒÆa c
Œ Ø
æÆ
.

606

Logical Matters

the Sage will become angry not in this sense of the word ‘angry’ but rather in the more common sense of the word. (Indeed, the right English for ‘ŒÆa c
æ ºłØ
ÆÅ
’ is surely ‘in this sense (of the word)’.) More generally, several texts ascribe to Epicurus the idea that there can be no investigation and no inquiry without preconceptions — and that is the idea which underlies the view of meaning apparently presented in the Letter.8 [202]

III The Letter, the passage from Diogenes, and the several supporting texts, have been taken to show that the Epicureans offered what is in effect a modified version of the Peripatetic account of meaning. Between words and the world there lie certain mental items, usually characterized as preconceptions, which give meaning to the words which we utter. The passages from Sextus and Plutarch ascribe a different and more austere view to the Epicureans: there are no items between the words which I utter and the world which I describe, and what I say has its meaning without the interposition of any mental entities. Most scholars, I think, have supposed that these two sets of texts are mutually inconsistent: we must choose between Sextus and Plutarch on the one hand and Diogenes and Epicurus himself on the other. And most scholars have further supposed that the choice is easy: evidently we should prefer Epicurus’ own considered statement to the doxographical asides in Sextus and the polemical sneers of Plutarch. Moreover — or so it has been thought —, the view which Sextus and Plutarch ascribe to Epicurus is so crude, and open to such immediate and devastating objection, that even in the absence of counter-evidence we ought to be reluctant to attribute it to a rational being. No doubt we shall want an explanation of how Sextus and Plutarch made their egregious error. But that need not delay us: Epicurean theories were always traduced by their opponents, who, ignoring the subtle and sophisticated reality, represented Epicureanism in terms of rude and risible slogans: ‘All perceptions are true’, ‘The only good thing is pleasure’ — ‘Words mean things’.9 [203] 8 See Sextus, M I 57; VIII 331a; XI 21; Cicero, nd I xvi 43; Plutarch, frag 215f Sandbach; Clement, strom II iv 16. 9 For versions of the orthodox view which I vaguely ascribe to most scholars, see e.g. A.A. Long, ‘Aisthesis, prolepsis, and linguistic theory in Epicurus’, Bulletin of the Institute of Classical Studies 18, 1971, 114–133, on pp.120–122; D.N. Sedley, ‘Epicurus, On Nature book XXVIII’, Cronache Ercolanesi 3, 1973, 5–83, on pp.20–21; A.A. Long and D.N. Sedley, The Hellenistic Philosophers

Epicurus: meaning and thinking

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IV A word first about the way in which the error in Sextus and Plutarch is to be explained. The putative explanation which I have just rehearsed is limp. For the view which Sextus and Plutarch express is not a rude simplification of the true and sophisticated Epicurean view. ‘All perceptions are true’ is a simplistic slogan, and, like all philosophical slogans, it suppresses the subtleties of the thesis which it represents. Nonetheless, the slogan does recognizably represent an Epicurean thesis — and it is true to that thesis insofar as slogans may be true at all. The case of ‘Words mean things’ is quite other. This slogan — on the orthodox view — is not a rude but recognizable caricature of an Epicurean thesis: on the contrary, it is a rude caricature of a thesis which the Epicureans definitely did not hold. Epicurus’ first instruction in the Letter to Herodotus urges us (on the orthodox view) to make sure that preconceptions stand between our words and what we want to talk about: the slogan proclaims that there is nothing between the words and the world. If the orthodox are right, the slogan is no mere simplification. The error which the orthodox ascribe to Sextus and Plutarch is more serious — and therefore perhaps more surprising — than most of the errors which those two authors habitually make. Evidently, the orthodoxy is not thereby refuted; for Sextus and Plutarch do occasionally make gross errors which we can no longer explain.10 Nonetheless, it is [204] perhaps worth looking a little more closely at the credentials of the orthodox position.

V Next, then, consider the suggestion that the notion of meaning which Sextus and Plutarch attribute to Epicurus is so evidently silly that we should not ascribe it to any rational animal, not even to an Epicurean swine. (Cambridge, 1987), I, p.101. There are further references in Glidden, ‘Epicurean semantics’, p.168 n.8: Glidden, like me, is a heretic; but we confess different heresies. 10 For example, one might consider the possibility that the thesis underlying the reports was not originally a semantic thesis at all but rather a piece of Epicurean metaphysics: the thesis maintained that there are no incorporeal entities floating behind our sayings and thinkings, it did not maintain that there are no intermediate items involved in thinking and meaning — but later authors unsurprisingly construed it in this false fashion. It might still be thought odd that Sextus and Plutarch should independently make the same error. But perhaps the two authors drew ultimately from a common source.

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First, let us remember that most philosophers have held views of quite staggering absurdity and that most philosophers have entangled themselves in the most elementary confusions. (By ‘most philosophers’ I mean most great philosophers.) Why that should be so I do not care to ask, but that it is so I take to be beyond serious dispute. It follows that we must be extremely reluctant to argue that since such-and-such a view is thumpingly silly, old soand-so could never have held it; for old so-and-so did, in all probability, hold thumpingly silly views. Before arguing in that fashion, we need to be sure either that the view is so absurd that no one at all could conceivably have held it (and I doubt if any view is as absurd as that) or else that the type of absurdity which the view illustrates is simply not the sort of idiocy in which old so-and-so indulged. But, secondly, in the case before us — the case of ‘Words mean things’ — we are not obliged to engage in any such melancholy inquiry; for the view which Sextus and Plutarch ascribe to Epicurus, far from being crude and patently false, is in fact far closer to the truth than the quasi-Peripatetic view which the orthodox hang on him. Why has the view seemed patently false? (It seemed risibly false, or enragingly false, to Plutarch.) One main reason, I suppose, has been this. The view implies that, say, the word ‘cow’ means cows, the word ‘horse’ means horses, and so on. Hence the word ‘unicorn’ means unicorns. But there are no unicorns for the word ‘unicorn’ to mean. Therefore the word ‘unicorn’ — and every other term to which nothing in the real world corresponds — [205] means nothing at all; which is absurd. Suppose, on the other hand, that words mean concepts or preconceptions: then the word ‘unicorn’ will have a perfectly good meaning even though there are in reality no unicorns — for I may have a concept or preconception of unicorns whether or not unicorns exist. That argument is a terrible muddle. Whatever else may be obscure, it is pre-eminently clear that the word ‘unicorn’ does not mean a concept or a preconception or any other mental item. If it did, then in uttering the sentence ‘There aren’t any unicorns’ I would be denying the existence of certain concepts or preconceptions or other mental items. And evidently that is not what I am doing. It may be puzzling to imagine what the word ‘unicorn’ means or how it can have any meaning at all; but there is no difficulty at all in seeing that it does not mean a mental item. Of course, some words do mean mental items — the word ‘preconception’, for example, presumably does. But not all words mean mental items. And the view

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which the orthodox ascribe to Epicurus (and which another orthodoxy ascribes to Aristotle) is patently silly. (Of course I do not mean to insinuate that that is in itself a sufficient reason not to attribute it to Epicurus ... ) And yet, it will be demanded, how can the word ‘unicorn’ mean unicorns if there are no unicorns for it to mean? Well, it means unicorns in the sense that it applies to or is true of things precisely if they are unicorns. The word ‘London’ means London: that is to say, the word ‘London’ truly applies to an item if and only if that item is London. The word ‘Valhalla’ similarly means Valhalla: that is to say, the word ‘Valhalla’ truly applies to an item if and only if that item is Valhalla. The word ‘cow’ means cows: that is to say, the word ‘cow’ is true of an object if and only if that object is a cow. The word ‘unicorn’ means unicorns: that is to say, the word ‘unicorn’ is true of an object if and only if that object is an unicorn. [206] The sort of propositions with which we are here dealing are propositions of the form: A word w is true of an item x if and only if x is F. And it is plain that propositions of that form may be true whether or not there are in fact any items which are F. I do not know if there are any abominable snowmen; but I know that the word ‘yeti’ is true of an object if and only if that object is an abominable snowman. Now since the formula w is true of x if and only if x is F constitutes the core of the idea intended by the formula w means Fs, it follows that a proposition of the latter form may be true whether or not there are any items which are F; and in particular it may be true that ‘unicorn’ means unicorns even if there are no unicorns for it to mean. In short, the view which Sextus and Plutarch ascribe to Epicurus may reasonably be regarded as a crudely expressed version of the thoroughly modern view that meaning should be explained in terms of truth-conditions. You know the meaning of a sentence when you know the conditions under which it is true; you know the meaning of a common noun when you know what sort of item it is true of; you know the meaning of the word ‘unicorn’ insofar as you know an appropriate truth of the form: ‘unicorn’ is true of an object x if and only if x is F. The ‘thoroughly modern view’ to which I am alluding is, of course, far more sophisticated than the preceding sentences have indicated; and I am not claiming that — on the [207] account given by Sextus and Plutarch — Epicurus anticipated the thoroughly modern view. (Nor, I should perhaps

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add, am I claiming that the view is a thoroughly true view.) Rather, I am making the following, very modest, claim: the view which Sextus and Plutarch ascribe to Epicurus may plausibly be seen as a crude adumbration of a thought which is central to the most respectable modern theory of meaning. And this modest claim is enough to unseat one of the jockeys who ride for the orthodox stables: there are no philosophical grounds for thinking — or for hoping — that Epicurus did not hold the thesis which Sextus and Plutarch ascribe to him.

VI The orthodoxy, if it has any philosophical talent, should be shaken by that last reflection. But it will not be stirred; for it rests, after all, on the best of all possible evidence, the evidence of Epicurus’ own words; and if those words express a thesis which is less respectable than the thesis found in Sextus and Plutarch, tant pis. The thesis in Sextus and Plutarch is inconsistent with the thesis in Epicurus’ own text; and it would be wild to prefer the evidence of secondary sources to evidence which comes from the horse’s mouth. Yet it would be pleasing to believe Sextus and Plutarch; and there are at least two ways in which we might find ourselves able to do so. One way is simple enough. Allow that the two theories are inconsistent — and then look for an explanation of the inconsistency. A first explanation is banal: the two sets of sources are inconsistent because Epicurus himself was inconsistent — he had flashes of insight, which Sextus and Plutarch have preserved for us; and he also had moments of darkness, which we read in his own words and in Diogenes. Most philosophers have been inconsistent, and inconsistency is damnably difficult to avoid. A second explanation is more subtle: the two sets of sources are inconsistent because [208] Epicurus changed his mind, at one time advocating the benighted view of the Letter and at another time advancing the enlightened thesis which we find only in Sextus and Plutarch. And we might then like to imagine that Epicurus not only changed his mind but changed it for the better — that he came to see that the view expressed in the Letter was a bad view and that the view preserved by Sextus and Plutarch should replace it. Neither of those explanations is particularly seductive: it is never satisfactory to suppose, without compelling evidence, that a philosopher has contradicted himself in a fundamental manner; and it is never satisfactory to

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postulate a change of mind for which there is no evidence apart from an inconsistency in the sources. Nonetheless, I suppose that neither explanation can be excluded in principle; and I offer them here to anyone who may be convinced by what I have thus far said and who will not be convinced by what I am about to say. For there is a second option available to those who want to believe Sextus and Plutarch: we may deny that the two sets of sources are inconsistent with one another.

VII Consider more nearly the texts from the Letter and from Diogenes. They are both primarily concerned with what we might roughly call epistemological matters; and from them we may deduce at least the following four points. If you are to investigate or puzzle over anything — and again, if you are to hold beliefs or to talk about anything — , then: (1) you must have a concept or a preconception of that thing; (2) you must ‘refer’ your inquiry or aporia or belief or remark to that concept or preconception; (3) the concept or preconception must be true; and (4) the concept or preconception must be ‘primary’ or ‘evident’; it must not stand in need of ‘proof ’. The first point is simple enough, and true. If I am to ask ‘Is that thing over there a cow?’, then I must already know [209] what a cow is; for if I have no conception of what a cow is, then evidently I cannot ask or say anything at all about cows. If I am to believe that the thing over there actually is a cow, then I must have some idea of what it is to be a cow; for if I have no idea of what a cow is, then a fortiori I cannot believe of that thing — or of anything else — that it is a cow. (The point is connected with ‘Meno’s paradox’, and it was surely so connected by Epicurus himself: the language of the passage in Diogenes suggests as much; and Plutarch (frag 251f Sandbach) explicitly cites the view as the Epicurean answer to the paradox.) Next, consider two implications of the fourth point. The fourth point implies that preconceptions and concepts, æ ºłØ and K

ÆÆ, must be construed as or associated with propositional items: my concept or preconception of a cow can be expressed by a sentence such as ‘A cow is an animal of that shape’. For in saying that the concepts ‘must need no proof ’, Epicurus implies that they are items of a sort which could in principle be proved — they are items which, so far as their form goes, could admit of

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proof but which in fact do not need to be proved. Now the sorts of items which can be proved — the sorts of items which may feature as conclusions of probative arguments — are propositional items; and so concepts or preconceptions must possess or admit a propositional structure.11 The fourth point also implies that concepts and preconceptions must be true propositional items; for what is evident and not in need of proof is true. (There may indeed be evident falsehoods; but an evident falsehood is not, contradictorily, something which is both evident and false — it is [210] something which is evidently false.) Thus point (4) entails point (3), something which is not explicitly noticed in our texts. Before considering the substance of points (3) and (4) it will be well to address the second point. Epicurus and Diogenes both say that we must ‘refer’ or ‘reduce’ our beliefs to concepts or preconceptions (the verb is ‘I
ªØ
’); and Diogenes remarks that the beliefs ‘depend’ on the preconceptions (his word is ‘XæÅÆØ’). It is easy to suppose that Epicurus’ primary items play the role which first principles or axioms play in Aristotle’s theory of science: they are the primary truths upon which all other truths (in the science in question) depend and from which all other truths (of the science in question) are deduced, and they are themselves indemonstrable or not in need of proof. Diogenes’ example seems to support the supposition: How do I know that this item is a man? Well, I know that a man is something of that form (this is my preconception of man); I see that this item is a thing of that form: ergo ... My belief that this is a man is deduced from my preconception of what a man is (together, of course, with a further premiss). The parallel with Aristotle may be useful; but it is not adequate. For Epicurean preconceptions are objects of reference not simply for known truths (the truths of a science) but for every belief and every assertion, and for everything we inquire into and puzzle over — and in most of these cases there can be no question of deducing one truth from another basic truth or axiom. Then what is it for a belief or an object of inquiry to depend upon or be referred to a preconception? In order to inquire into cows, I must have some idea of what a cow is: my inquiry depends upon my concept inasmuch as the inquiry presupposes that 11 So e.g. G. Striker, ˚æØæØ
B IºÅŁÆ, Nachrichten der Akademie der Wissenschaften zu Go¨ttingen phil.-hist. Klasse 1974 (Go¨ttingen, 1974), pp.59–82, on pp.71–72. But note that most upholders of the orthodox view have taken æ ºłØ and K

ÆÆ to be concepts in a modern sense — and they have often identified them further as mental images.

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I know what a cow is and that I am deploying that knowledge — in inquiring into cows I am using my preconception of a cow. And I refer my inquiry to the concept inasmuch as I will or can allude to it if the object of my inquiry is put in question. ‘I [211] hear that you’re inquiring into cows?’ — ‘Yes indeed, fascinating creature the cow’. — ‘And what do you take cows to be?’ — ‘Oh, animals of that shape’ (pointing). What, then, of the third point? Why must the concept to which I refer my inquiries and beliefs be true? A chartered accountant (the story is not my own) went to the Labour Exchange and said that he wanted a new and more challenging position; when asked by his interviewer if he had anything particular in mind, he said: ‘I want to be a lion-tamer’. The interviewer took it that he had a desire to be a lion-tamer. But some of his subsequent remarks aroused suspicion, and a series of probing questions revealed that he thought that lions were small hairy animals equipped with long snouts and enjoying a diet of ants. The accountant was ready to refer his desire to his preconception of a lion; but his preconception was false — lions are not animals of that sort. The interviewer concluded, with reason, that the accountant did not nourish a desire to be a lion-tamer: if he wanted anything at all, he wanted to be a tamer of ant-eaters. The inquiries which he pursued at the Labour Exchange were not inquiries into lion-taming: if they were genuine inquiries at all, they were inquiries into the taming of ant-eaters. And when he uttered the words ‘I want to be a lion-tamer’ he did not thereby say that he wanted to be a lion-tamer: if he said anything at all, he said that he wanted to be a tamer of ant-eaters. What, finally, of the fourth point? Why must we refer our inquiries and beliefs to primary or evident concepts, to items which do not need to be proved and to which nothing is prior? If I am to believe that cows are ruminants, then I must possess the concept of a cow (and also, no doubt, the concept of rumination); and so I must believe that cows are animals of that sort. But then if I am to hold this latter belief, surely I must know what it is to be an animal of that sort, surely I must believe that animals of that sort are such-and-such. But then if I am to hold this latter belief, I must [212] surely know what it is to be such-and-such ... And the regression of beliefs which has thus begun will continue ad infinitum.12 But we cannot hold infinitely many beliefs; or at any rate (and this is all the argument requires) 12 Epicurus refers explicitly to an infinite regress; but he does not explain how a regress would come about, and the explanation which I suggest here is merely one of several possible glosses on his text.

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we evidently do not hold infinitely many beliefs of the relevant type. Hence the regress must be stopped: one of the beliefs — say the belief that cows are animals of that sort — must be self-sufficient, independent, primary.13 That argument deserves extended analysis. But what I have said should be enough to reveal at least the general tenor of Epicurus’ thought in the passages which are in question: he is thinking of the presuppositions of inquiry, of belief, of affirmation — in general, of intellectual activity. Take in particular the case of affirmation; and suppose that I utter the sentence ‘That’s a cow’ and thereby affirm that that is a cow. Then: (1) I must possess a concept of a cow, I must know what a cow is — otherwise I cannot say anything about cows; (2) I must refer my utterance to that concept — otherwise I will not, by that utterance, have said anything about cows; (3) my concept must be true — otherwise I will not say anything about cows; and (4) my concept must be primary — otherwise I will not yet have said anything about cows.

VIII None of those four points is a semantic point, and none says anything directly about the meaning of the word [213] ‘cow’ or of the sentence ‘That’s a cow’. But it is easy to suppose that there is a semantic thesis implicit in or underlying the four epistemological points; for such a thesis is suggested by at least two particular words in our texts, namely the adjective ‘empty’ or ‘Œ
’ and the verb ‘collect under’ (‘range under’, ‘subordinate to’, ... ) or ‘ Ø
’. The verb ‘ Ø
’ is not common in Epicurean texts; but it does occur twice in the fragments of Book XXVIII of the —æd !ø, and in contexts which are clearly concerned with words and utterances. Neither text is easy to understand; but in one of the two passages it is explicitly stated that what is ‘collected under’ an utterance is a belief, a  Æ,14 and that usefully confirms my earlier claim that the concepts and preconceptions which lie behind our beliefs and inquiries are propositional items — indeed, are themselves 13 Just as there is at least a rough parallel between primary preconceptions and Aristotelian first principles, so there seems to be a similarity between this argument of ad Hdt and a celebrated argument in Aristotle’s APst. Epicurus referred to, and presumably had read, the Analytics (PHerc 1005, frag 111.9–10: see A. Angeli, Filodemo: Agli amici di scuola (Naples, 1988), pp.166–167, 233–240). It is tempting to suppose that the parallel and the similarity are not casual. 14 PHerc 1479/1417, frag 6, I.5–13, in line 13. The other text is frag 13, VIinf 2–VIIsup 5 (text and references after Sedley, ‘Epicurus On Nature’).

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beliefs.15 The fragments do not help us further; in particular, they do not tell us what it is for a belief to be ‘collected under’ an utterance. And yet — as I have already indicated — it is not difficult to make a sporting guess: to be collected under a word is surely the same as to be meant or signified by it; and in saying that certain beliefs — concepts or preconceptions — are, or should be, ‘collected under’ our words, Epicurus is stating that our words mean those particular mental items.

IX Again, Epicurus does not say what he means by an ‘empty’ utterance; but again, a sporting guess requires no imaginative powers: a word or phrase is surely empty if it means nothing. This suggestion gives a reasonable sense to [214] the word ‘empty’, and it fits perfectly with the interpretation of ‘ Ø
’ which I have just offered; for no doubt a word is empty if nothing is collected under it, and if nothing (that is to say, no mental item of the appropriate sort) is collected under it, then it has no meaning. With those sporting guesses in mind, we may outline an argument which will take us from the epistemological matter explicit in the texts to the semantic thesis which lies behind them and which is apparently incompatible with the thesis found in Sextus and Plutarch. Thus: (I) If I utter the sentence ‘That’s a cow’ and do not refer my utterance to an appropriate concept, then I do not thereby say that that is a cow. (II) If, in such circumstances, I do not say that that is a cow, then the words which I then utter have no meaning. (III) If, in such circumstances, the words which I utter have no meaning, then when an utterance is referred to an appropriate concept, the concept determines the meaning of the uttered words. And given (III), shall we not readily conclude that, when I utter the sentence ‘That’s a cow’ and do thereby say that that is a cow, then the word ‘cow’ there signifies my concept of a cow — that U means C?

15 Glidden, ‘Epicurean semantics’, pp.188–199, argues that in ad Hdt 37 a  ƪ
Æ and e æH
K

ÅÆ are in fact objects in the world — ordinary, flesh-and-blood, cows and horses: the text does not speak of mental items at all, and so it is perfectly compatible with the reports in Sextus and Plutarch. That heroic proposal does not fit the Greek.

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That argument could surely be squared up a little; but I do not believe that it could be transformed into a sound proof. I shall say a little about each of its three stages, in reverse order. Suppose that I utter the sentence ‘That’s a cow’ and that, because I fail to associate an appropriate concept with the utterance, my words have no sense: does it then follow, as stage (III) of the argument supposes, that when my words do have a sense, their sense is determined by the associated concept? Well, it may not strictly follow, but it does seem highly plausible. I utter a sentence S. That sentence, as uttered [215] now by me, has a meaning (we are granting) only insofar as I refer it to an appropriate concept. Suppose, then, that I do refer it to an appropriate concept and that it does thereby have a meaning: what does it mean? Surely, what it means will be determined by the content of the concept to which I refer it: if the sentence ‘That’s a cow’ has a meaning insofar as I appropriately range it under my concept of a cow, then surely it must mean that that is a cow (and not, say, that that is a tapir). My concept of a cow will determine the sense of my utterances insofar as I refer the utterance to the concept or associate the concept with the utterance. What does reference or association amount to in this case? Here is one reasonably plausible answer. Consider those concepts which are expressible by sentences of the form ‘Gs are F’ (‘Cows are animals of that shape’): call them concepts of Gs, concepts of cows. Suppose too that the sentences which I utter are of the form ‘That’s a G’ (‘That’s a cow’): call them demonstrative sentences. Then we might say that I ‘associate’ an appropriate concept with a sentence when, by uttering the sentence, I appropriately intend to say that that is an F. More properly: a speaker, S, associates his concept of Gs with a demonstrative sentence U if and only if in uttering U S appropriately intends to say that that is an F. Meaning is determined by concepts in this sense: U, as uttered by S, means that P if and only if in uttering U, S appropriately intends thereby to say that P; or — for the case of words — W, as uttered by S in the context of a demonstrative sentence U, means Gs if and only if in uttering U, S appropriately intends thereby to say that that is an F. That account would of course need modification and generalization before it could be offered as a decent version of stage (III) of our argument. But it will do as it stands for my present purposes. For it should be clear that the account, and any modified generalization of it, is wholly consistent [216] with the thesis which Sextus and Plutarch ascribe to Epicurus. The latter thesis, it is true, will need to be relativized to utterers (and also, of course, to

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times), so that instead of saying ‘W is true of x if and only if ... ’ we shall say ‘W, as uttered by S at t, is true of x if and only if ... ’. And, putting the two theses together, we shall infer that W, as uttered by S at t, is true of x if and only if in uttering U at t, S appropriately intends thereby to say that x is an F. That may be an odd view, and it may be a false view;16 but it is at least a coherent view — and that is all I want to maintain. The main point can perhaps be stated more straightforwardly. The thesis that ‘meanings are determined by concepts’ need not be taken to imply that ‘words mean concepts’ in any serious sense: it need not be taken to imply that the word ‘cow’ signifies a mental item, that when I say ‘That’s a cow’ I am thereby talking about my concepts. And since it is perfectly plain that in saying ‘That’s a cow’ I am talking about cows (say) and not about my own concepts (nor about my own beliefs),17 we should not take the thesis to have that implication. But if we do not take it to have the implication, then it is consistent with the thesis in Sextus and Plutarch. We may, if we wish, advance to stage (III) of our argument and still believe what Sextus and Plutarch tell us. [217] What about stage (II) of the argument? If I utter a sentence without the appropriate conceptual backing and thereby say nothing, does it follow that the sentence — as uttered by me then — has no meaning? A parrot may be trained to utter the sentence ‘That’s a cow’; and in the presence of a beautiful Jersey I may utter the same sentence and merely parrot the words. I will do so if I do not refer to my concept of a cow or if, worse, I have no preconception of a cow to refer to, no idea in the world of what a cow is. In uttering his sentence the parrot says nothing, and in uttering my sentence I say nothing (in particular, we do not say that there is a cow over there). But do my words and do the parrot’s words therefore have no meaning? Surely not. There seems to be nothing at all wrong with the sentence ‘That’s a cow’ as the parrot and I uttered it: it was a recognizable English sentence, with a familiar syntax and a familiar sense. The fault lies in me rather than in the words I utter. 16 Judgement here will depend on how we construe the adverb ‘appropriately’ (an adverb which I have smuggled into the argument precisely in order to make the whole thing less odd). Suppose that I utter the sentence ‘L’acqua e` calda’ to the chambermaid of my hotel and thereby mean to say that the water is cold. If (as may seem plausible) I thus associate an inappropriate concept with the utterance, then the sentence, as uttered by me on this occasion, will not mean that the water is cold. 17 Of course, in saying ‘That’s a cow’ I may be expressing a belief of mine (e.g. the belief that that is a cow) — but equally of course I need not be expressing any belief of mine at all (e.g. I may be trying to mislead you). Again, I can of course talk about my concepts if I want to; and I might do so by using, for example, a sentence of the sort ‘My concepts are all perfectly articulated’.

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Suppose that that were not so, and that the two sentences, mine and the parrot’s, had no meaning. Then what is Epicurus to say if we ask him what, if anything, the English sentence ‘That’s a cow’ means? It seems that he can offer no general answer: whether or not the sentence has a meaning will depend on who or what utters it. Sometimes ‘That’s a cow’ means something and sometimes it means nothing: it does not mean anything in itself. Instead of saying ‘X means such-and-such’ (where ‘X’ is to be replaced by the name of a word or phrase), we should say ‘X, as uttered by so-and-so at this particular time, means such-and-such’. I do not say that that is a false thesis, let alone that it is an absurd thesis; but I do think that it is an odd thesis.18 [218] At any rate, it is certainly not a thesis whose truth is patent to the eye; and so we should not ascribe it to Epicurus unless we have some serious reason to do so. And if we do not ascribe stage (II) of the argument to Epicurus, then a fortiori we shall not attribute stage (III) to him. Then why go beyond stage (I) of the argument? Why not suppose that Epicurus, in the Letter, is warning us against the dangers of psittacosis? Epicurus is saying: Make sure that, when you utter words and sentences, you thereby say something. He is not saying: Make sure that the sentences and words which you utter have a meaning. He is saying: Make sure that you are not a parrot. He is not saying: Make sure that you are not a nightingale. The warning is apt enough, inasmuch as the danger is real enough — at any rate, very many people, and virtually all philosophers, fail to avoid it. We often babble: we utter strings of words and thereby say nothing at all; for we have no idea of what we are talking about. The phenomenon is familiar enough to any teacher of philosophy. A student reads an article on Tarski’s theory of truth. In his essay he writes: ‘So we see that a sentence is true if it satisfies every sequence’. The student’s sentence is meaningful — and it rapidly emerges that the student has said nothing at all in uttering it. In such cases it seems quite natural to say that the student’s words — the sounds he utters — are empty. They are empty not because they have no meaning: they are empty because the student says nothing by uttering them. In the same way, the parrot utters empty sounds when he chuckles ‘That’s a cow’, even though the sounds which he emits form a meaningful English

18 Or could Epicurus claim that neither the parrot nor I uttered an English sentence? We produced noises which had the same sound as a standard English sentence, but we did not produce any sentences at all. The English sentence ‘That’s a cow’ has a meaning in itself, and neither I nor the parrot proves anything to the contrary. But that ingenious suggestion has little in its favour.

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sentence. Again, we might say that the student does not collect anything under his utterance, and neither does the parrot. The metaphors of emptiness and of collection seem to me to be perfectly [219] appropriate to stage (I) of our argument: they do not give us sufficient reason to advance to stage (II) — and nothing else apart from them even seems to offer us any such reason.

X Here are two quite distinct questions. (1) What does the word ‘cow’ mean? Or in general, what does an expression E mean? (2) When I utter the sentence ‘That’s a cow’, how is it that I may thereby say something about cows? Or in general, how, by uttering E, can I thereby say something? One answer to the former question — the supposedly Peripatetic answer — might be this: ‘The word ‘cow’ signifies the thought or concept of a cow; and in general, E means some concept C’. Another answer — according to Sextus and Plutarch, the Epicurean answer — might be: ‘The word ‘cow’ signifies an animal of such-and-such a sort; and in general, E signifies a thing’. Those are utterly different answers to the same question. Moreover, the Epicurean answer, so far as it goes, is immeasurably superior to the Peripatetic answer. (Cows, after all, are not mental items.) One answer — Epicurus’ answer — to the latter question is this: ‘In uttering ‘That’s a cow’ I thereby say something about cows only if I have a true preconception of what a cow is, i.e. only if I truly believe that cows are animals of such-and-such a sort; and in general, in uttering E, I thereby say something only if I truly believe that P. I am suggesting that Sextus and Plutarch report Epicurus’ answer to question (1), whereas the passage from the Letter and the text from Diogenes give Epicurus’ answer to question (2). There are not two incompatible answers to one question. There are two compatible answers to two questions. But the two questions are presumably not completely unconnected one to the other. How, then, might their answers be related? Crudely speaking, there are two options. First, you might suggest that the answer to the first question depends on the answer to the second question in the following [220] way: what a word or phrase means is just what people (all people, most people19)

19 All or most people in the relevant linguistic community, of course.

620

Logical Matters

use it to mean. That is to say, the word ‘cow’ will mean cows just in case all or most people, when they utter the sentence ‘That’s a cow’, intend thereby to say that that is a cow. The meaning of the word is, so to speak, constructed out of the meanings of the utterers of the word. Secondly, you might suggest that the answer to the second question depends on the answer to the first question in the following way: what you can intend to say in uttering W is fixed by what W means. If you utter ‘That’s a cow’, then you have said that that is a cow only if you associate your cowconception with the utterance of the sentence; but if you associate your conception of Gs with a sentence, it does not follow that you have thereby said that that is a G (or that you have thereby said anything at all). The accountant associated a conception of an ant-eater with the sentence ‘I want to be a lion-tamer’; but he did not thereby say that he wanted to be a tamer of ant-eaters — he did not say anything at all. (He was confused: perhaps there was something which he meant to say — but there was nothing which he did say.) Which of these options is the more Epicurean? Plainly, the second; for Epicurus insists that your preconceptions must be primary, and hence true. The accountant associates with his sentence the belief that lions are friendly creatures which eat ants. The belief is false. Hence, so far as we can judge, Epicurus should say that the accountant’s sentence lacks the necessary backing, and that the accountant says nothing. And that, I confess, seems to me to be quite correct.

23 Ammonius and adverbs* I In chapter 12 of the De interpretatione, at 21a34, Aristotle turns his attention to modality. Ammonius, in whose edition 21a34 opens the fourth chapter or ŒçºÆØ
of the work,1 observes that Aristotle proposes to discuss ‘sentences with a mode [a a æ  ı æ Ø]’ (in Int 214.7–8). Such sentences constitute the third of the three species of simple sentence which Ammonius had distinguished in the preface to his commentary.2 First, and treated in the second chapter of the de Interpretatione, come sentences which contain only a subject and a predicate, such as: øŒæÅ æØÆE. Secondly, and treated in the third chapter, are sentences which include a æ
ŒÆŪ æ 

, such as: øŒæÅ ŒÆØ  KØ
— where the copula, ‘KØ
’, is the ‘third item additionally predicated’. Thirdly, sentences ‘with a mode’, such as: øŒæÅ  ıØŒe
r
ÆØ K
åÆØ — where the æ   or mode is ‘K
åÆØ’.3 [146] According to Ammonius, Aristotle considers only two features of sentences with a mode, namely the I
ØŁØ or oppositions and the IŒ º ıŁÆØ or consequences which hold among them. But he adds that, * First published in the Festschrift for Anthony Lloyd: OSAP supplementary volume 1991, pp.145–163. — Versions of the chapter were read at an Oxford seminar organized by David Charles and Stephen Everson, and at a meeting of the Southern Association for Ancient Philosophy. I am indebted to both audiences, and also to Manuela Tecusan. 1 For Ammonius’ capitulation of the work see in Int 7.15–8.23 (on the status of chapter 14, see 251.25–252.10). (All unspecified references are to Ammonius, in Int: I cite by page- and linenumber of Busse’s CIAG edition.) 2 See 7.29–8.19; cf 79.1–3; 157.7–10. 3 Each species is named after its ‘governing’ element (e ŒFæ  å
, e ŒıæØÆ
): sentences of the first type are predicative or ŒÆŪ æØŒ , since in them the predicate governs (70.4–10; 87.12–13); sentences of the second type are KŒ  F æ ı ŒÆŪ æ ı
ı, since the copula governs (160.14–16 — we might call them ‘copulative’); and sentences of the third type are a æ  ı, since the æ   governs (218.8–10 — we might call them ‘modal’).

622

Logical Matters

for our part, if we are to have an articulated knowledge of the sentences here under discussion and if we are to follow with any ease what Aristotle has to say about them, then before we give an interpretation of the text, we must grasp (1) what modes are, (2) whether their number is finite and knowable by us, (3) how many and which modes Aristotle selects for his exposition of these sentences, (4) why these and not others, (5) how the modes he introduces differ from what are called ‘matters’ although they are called by their names, (6) whether he has omitted any of the modes which ought to have been introduced in the present treatment of sentences, (7) how we make negations from affirmations in the case of such sentences (this, as I said, is the first point which Aristotle considers about them), and finally, (8) how we may grasp by way of a division the total number of these sentences. (214.11–24)*

Ammonius’ eight preliminary questions4 are answered in the next five pages of his commentary.5 I shall discuss Ammonius’ answers to questions (1), (6), and (4). I shall deal in passing with (2) and (3). I shall say nothing about (5), which leads Ammonius to distinguish neatly between modal sentences and the modality of states of affairs;6 nor about (7), to which Ammonius offers a lucid and uncontroversial answer;7 nor about (8), in tackling which Ammonius computes that there are exactly 3,024 different types of sentence.8 [147]

* A b N ºº Ø
ØÅæŁæø
Å
åØ
c
H

F
ÆæÆØ 
ø
æ ø
ª
HØ
ŒÆd Þfi A
ÆæÆŒ º ıŁE
 E e  F çغ  ç ı æd ÆPH
ºª 
Ø æ ºÆE
åæc B H
ÞÅH
KŪø   KØ æ   ŒÆd N æÆ
 ÆPH
› IæØŁe ŒÆd E
ª
æØ ,   ı  ŒÆd   ı KŒºªÆØ æ  ı › æØ ºÅ æe c
ØƌƺÆ
H
 H
æ ø
ŒÆd Øa 
Æ ÆNÆ
  ı ŒÆd PŒ ¼ºº ı, ŒÆd fiB H
ŒÆº ı
ø
ºH
ØÆçæ ıØ
ƒ ÆæƺÆÆ

Ø æ  Ø  E O
ÆØ
ÆPH
O
ÆÇ 
Ø, ŒÆd N Åd ÆæƺºØÆØ æ   H
Oçغ
ø
K
fiB æ ŒØ
fi Å H
æ ø
Łøæfi Æ ÆæƺÅçŁB
ÆØ, 
Æ  æ 
Kd H
 Ø ø
æ ø
KΠH
ŒÆÆçø
 Ø F
a I çØ, ‹æ çÆ
æH
KØŒłÆŁÆØ æd ÆPH
e
æØ ºÅ
, ŒÆd Kd AØ H i
KŒ ØÆØæø º Ø
ŒÆd  ø
H
æ ø
ÆH
e
IæØŁ
. 4 cf the preliminaries to the second and third chapters: 86.28–29; 159.24–29. 5 Question (1) at 214.25–29; (2) at 214.29–31; (3) at 214.31–215.7; (4) at 215.2–3 (i.e. in the course of the answer to (3)); (5) at 215.7–28; (6) at 215.29–218.2; (7) at 218.3–23; (8) at 218.23–219.23. 6 See also 88.12–28; and cf e.g. Alexander, in APr 27.27–28.30; Philoponus, in APr 43.18–44.1; al-Farabi, in Int 164.9–15 [pp.158–159 Zimmermann]. At 88.17–18 Ammonius refers to those who have concerned themselves with the å
º ªÆ of these matters: see perhaps 181.30–31, where Proclus is praised for his ŒÆ

 
ı å
ØŒ  (cf 223.18–19). 7 In general, you negate a sentence by attaching a negative particle to its governing element (see n.3 above and n.24 below). 8 See the earlier computations at 88.4–91.3 and 159.24–160.32.

Ammonius and adverbs

623

II The concept of a mode, and the distinction between sentences with a mode and sentences without a mode, are not idiosyncratic to Ammonius. The thing is a commonplace in the later logicians9 — and it was no doubt a commonplace before Ammonius. The earliest extant reference to modes is in Alexander’s commentary on the Prior Analytics (in APr 26.15–18). But Alexander mentions the things as though they were familiar to his audience: he sees no need to explain the word ‘æ  ’,10 and he evidently uses it as a standard piece of logical jargon. Yet the word is not found (in the relevant sense) in Aristotle.11 Nor does it occur in any non-Peripatetic text: the Greek grammarians, who might be expected to have mentioned this meaning of ‘æ  ’ in their catalogue of the different grammatical senses of the word,12 ignore it completely. I conjecture that the notion was developed in the renascent Peripatos, some time after the middle of the first century bc. But all we can safely say is that it was current before Alexander’s time and that it seems to have been peculiar to Peripatetic logic.

I II Ammonius’ first question about modes is the primary question: What is a mode? He answers: A mode is a word which signifies how the predicate holds of the subject, e.g. ‘quickly’, when we say ‘The moon completes her revolution quickly’, or ‘well’ in ‘Socrates converses well’, or ‘very much’ in ‘Plato loves Dio very much’, or ‘always’ in ‘The sun in always moving’. (214.25–29)13 [148] 9 See e.g. Philoponus, in APr 26.11–16; 120.12–13; Boethius, in Int1 166.24–167.4; in Int 2 377.4–14; al-Farabi, in Int 17.13–19 [pp.1–2]; anonymus Heiberg, § 22; Blemmydes, Epitome Logica 27.12–13 [PG CXLII 897]. 10 Even though he also uses it in several other senses, both technical and non-technical. 11 Nor — for what that is worth — does it not appear in the surviving testimonia to early Peripatetic logic. 12 See the scholium to Dionysius Thrax, GG I iii [456.27–457.13]; cf ibid [13.19–14.12]; [567.21–30]. 13 æ   b
s
KØ çø
c ÅÆ
ıÆ ‹ø æåØ e ŒÆŪ æ 

fiH  ί
fiø, x
e Æåø ‹Æ
ºªø
º
Å Æåø I ŒÆŁÆÆØ, j e ŒÆºH K
fiH øŒæÅ ŒÆºH ØƺªÆØ, j e 
ı K
fiH —ºø
˜ø
Æ 
ı çغE, j e Id K
fiH › lºØ  Id ŒØ
EÆØ. — cf 8.8–12; Stephanus, in Int 53.10–11; al-Farabi, in Int 163.8–10 [p.158]; 164.9 [ibid].

624

Logical Matters

The examples of modes are all adverbs. It is easy to suppose that the term ‘æ  ’ means the same as — or at least is extensionally equivalent to — the term ‘adverb’. Among the parts of speech recognized by the Greek grammarians there were KØææÆÆ; Ammonius, in his essay on the parts of speech at 11.7–15.13 offers a swift typology of KØææÆÆ, a typology which evidently derives from a grammar book.14 In his monograph on the subject Apollonius Dyscolus offers the following definition: An KææÅÆ is an indeclinable expression which is predicated of verbal inflexions, either universally or particularly, without which it does not complete a thought. (adv 119.5–6)15

Apollonius insists that KØææÆÆ modify verbs. And he observes that, just as adjectives or O
ÆÆ KØŁØŒ always demand nouns, so KØææÆÆ always demand verbs.16 Thus — or so we might quickly infer — an KææÅÆ is a verb-forming operator on verbs; it takes a verb and makes a verb; it belongs to the syntactic category V:V.17 In other words, an KææÅÆ is an adverb — and ‘adverb’ is, of course, the customary translation of ‘KææÅÆ’.

IV But whatever may be true of Apollonian KØææÆÆ,18 Peripatetic modes cannot be identified with adverbs. First, Ammonius subdivides [149] the 14 The typology at 11.15–12.4 shows close connections, in terminology and in illustrative example, with the typology in Dionysius Thrax, 19 [72.3–86.1]; cf the scholia in GG I iii [95.4–102.3]; [271.27–283.2]; [427.10–435.27]; [561.32–564.7]; [582.24–584.20]. Apollonius follows a different path in his adv. 15 Ø
s
KææÅÆ b
ºØ ¼ŒºØ , ŒÆŪ æ FÆ H
K
 E ÞÆØ
KªŒºø
ŒÆŁ º ı j æØŒH, z
¼
ı P ŒÆÆŒºØ Ø
ØÆ
. — cf Dionysius Thrax, 19 [72.4–5], with Uhlig’s note ad loc., and Schneider’s note on the Apollonian text in GG II i [137–138]. (For a full commentary on the definition, see I. Sluiter, Ancient Grammar in Context (Amsterdam, 1990), pp.70–105. Sluiter’s study was published after I had finished this chapter.) On ‘either universally or particularly’, see below, pp.[161–162]. 16 See adv 120.19–122.34; cf the scholia in GG I iii [91.15–19]; [95.21–31]; [427.21–28]. 17 A derived syntactic category C:C* consists of items which take a C* and make a C. Thus (intransitive) verbs form the category S:N (they take a name and make a sentence); two-place sentential connectives form the category S:S,S. And so on. I see no harm in deploying such fancy modern notions when discussing ancient texts; but it should be observed that the sharp distinction between syntax and semantics which they imply, and the formalistic treatment of syntax which they invite, were things quite alien to the ancients. 18 Neither the grammarians not the commentators offer us ‘clean’ syntactical definitions of KØææÆÆ — or of any other of the parts of speech. Syntactically speaking, KØææÆÆ belong,

Ammonius and adverbs

625

category of KØææÆÆ, and he indicates that the most significant subdivision consists of ‘those which indicate a certain relation between predicate and subject and so contribute to the generation of declarative sentences’ (in Int 12.6–9).* The description shows that this subdivision of KØææÆÆ corresponds exactly to the Peripatetic notion of a mode. Hence modes are at best a subclass of adverbs. Secondly, and more importantly, Ammonius implicitly rejects the view that KØææÆÆ — or at least, that those KØææÆÆ which are modes — are to be parsed as members of the category V:V Having argued, against Alexander, that the mode ‘ÆçH’ or ‘clearly’ is not a noun (13.19–14.2 — Alexander took it to be an ‘epithetic’ noun or adjective), he adds this: Nor shall we say that a sort of compound predicate is formed from ‘clearly’ and that about which ‘clearly’ is said — e.g. ‘clearly explains’. (14.2–4)**

Now if ‘clearly explains’ is not a V, then ‘clearly’ is not a V:V. In general, if ‘F’ is not a V and ‘F’ is a V, then ‘’ is not a V:V. Ammonius has an argument for his view. Compound predicates behave under negation in the same way as simple predicates. But sentences with modes behave differently. Thus the negation of: øŒæÅ ÆÇØ is: øŒæÅ P ÆÇØ But the negation of: øŒæÅ ÆÆØ ı
Æ
is not øŒæÅ c ÆÆØ ı
Æ
[150] but rather øŒæÅ ÆÆØ P ı
Æ
(See 14.2–17.) according to the grammarians, to the category V:V; but not every member of that category will satisfy the further semantic conditions in the definition. Note, too, that both Ammonius and the grammarians classify as KØææÆÆ items which we should hardly reckon to be adverbs or to belong to the category V:V: e.g. the conjunction ‘‹’ (68.20–27; cf Apollonius, adv 148.6–8; 158.28; scholia in GG I iii [274.8]; [583.27]), the words ‘Yes’ and ‘No’ (11.28–30; cf Dionysius Thrax, 19 [78.1–3]; Apollonius, adv 122.13–15). Despite the official definition of KØææÆÆ, it is difficult to see how such items could be construed as members of V:V. The ancient category of KØææÆÆ was a dustbin. (See also below, n.30.) * ÆFÆ b
s
, ‹æ Kºª 
, åØ
Ø
a  F ŒÆŪ æ ı
ı æe e  Œ

ź F
Æ ıººŁÆ Ø  Œ FØ æe c
ª
Ø
H
 Ø ø
I ç
ø
. ** P c
Pb 
Ł
Ø ŒÆŪ æ 

K ÆP F  ŒÆd  F æd y e ÆçH ºªÆØ ª
ŁÆØ ç 
, x
e ÆçH KŪEÆØ.

626

Logical Matters

Ammonius is right about his negations. But his argument fails to prove his conclusion; for why may we not construe: øŒæÅ ÆÆØ P ı
Æ
as denying of Socrates the compound predicate ‘ ... possibly walks’? Nonetheless, we may agree with Ammonius, at any rate with regard to modal æ  Ø. For even if the modal æ  Ø can sometimes be parsed as adverbs, that parsing is not always available. If I say: There may be a rabbit in the hutch my remark has the structure: :(&x)Fx. And there ‘’ cannot be a V:V.

V Then what are modes, syntactically speaking? Ammonius’ definition makes it clear that he takes them to modify the connection between subject and predicate (214.25–27; cf 11 30–32): he implicitly construes them as operators on the copula. They are ‘adcopulas’ rather than adverbs: they take a copula and make a copula they belong to the category C:C. The category of adcopulas is no doubt legitimate enough. But the examples of modes which Ammonius offers do not belong to it. Consider: øŒæÅ ŒÆºH ØƺªÆØ Ammonius expressly says that here ‘ŒÆºH’ signifies the way in which the predicate attaches to the subject (11.30–32, 214.25–27): he expressly maintains that ‘ŒÆºH’ is an adcopula. The supposition is bizarre: ‘ŒÆºH’ is surely an adverb modifying the verb ‘ØƺªÆØ’. The sentence does not say that conversing belongs in a fine way to Socrates. It says that conversing in a fine way belongs to Socrates.19 [151] Nor does the difficulty affect only examples like ‘ŒÆºH’ and ‘ÆçH’. Consider the modal æ  Ø, which are Ammonius’ central concern. Ammonius in effect invites us to understand the sentence: (1) K
åÆØ øŒæÅ ÆÇØ
as equivalent to: 19 Ammonius recognizes some of the difficulties his view encounters when he discusses the use of ‘ÆçH’ in a sentence such as: 
Ø  ÆçH KŪEÆØ. See 225.16–28.

Ammonius and adverbs

627

(2) øŒæÅ ÆÇØ K
å 
ø — where the mode ‘K
å 
ø’ indicates the way in which walking attaches to Socrates. So construed, the sentence might be Englished as: (2E) Socrates walks contingently or, perhaps more perspicuously, as: (2E*) It is a contingent fact that Socrates walks. And that plainly entails the non-modal sentence: Socrates walks. It is therefore not the construe which Aristotelian modal logic intends. For it is a fundamental feature of this logic that ‘K
åÆØ P’ does not entail ‘P’. In short, if we parse the modal æ  Ø as members of the category C:C, then we shall run the risk of misconstruing the whole of modal logic. Yet Ammonius certainly did parse the modal æ  Ø in that way. And, sometimes at least, he — like Alexander before him20 — did thereby fall into error. It may be said, and truly, that the Ammonian syntax does not [152] positively oblige us to read (1) as (2E*). We could maintain that ‘K
åÆØ’ in (1) says how the predicate applies to the subject without thereby maintaining that (1) implies that the predicate does in fact apply to the subject. And often, of course, the commentators show themselves aware of this. But the danger of a misconstrual remains; and even if the modal æ  Ø may sometimes be parsed as members of C:C, they may not always be so parsed. Thus the sentence: Necessarily not every competitor wins the race has the form: :not-(8x)(if Fx, then Gx). And there ‘’ is not a C:C. VI In his discussion of modi, Peter of Spain first distinguishes adjectives, which modify nouns, from adverbs, which modify verbs. He then distinguishes various classes of adverb. Of these, the first consists of 20 Alexander, like Ammonius and Philoponus, frequently uses the adverb ‘K
å 
ø’ to express what are intended to be ‘problematic’ modal propositions; and sometimes he plainly intends the adverb to have the force of ‘It is a contingent fact that ... ’. See e.g. in APr 38.6; 147.18–19; 149.4–7; 329.20–21; cf Philoponus, in APr 59.10; 162.14; 204.22; in APst 328.25; in Phys 262.23.

628

Logical Matters

adverbs which determine the verb in respect of its composition, e.g. ‘necessarily’, ‘contingently’, ‘possibly’, ‘impossibly’, ‘truly’, ‘falsely’.

In the second class come adverbs which determine the verb in respect of the matter of the verb, e.g. ‘acts bravely’, ‘runs fast’.21

Adverbs in Peter’s first class are words which modify the whole of the sentence to which they are attached. William of Ockham, in his discussion of modal propositions, observes that a proposition is called modal because of the addition of a mode to the proposition. But not any mode is sufficient to make a proposition modal. Rather, it is necessary that the mode be predicable of a whole proposition.22

Ockham’s modes are Ammonius’ æ  Ø. They fall within Peter’s first class of adverb, but they are not adverbs in the narrow sense. They [153] take sentences and make sentences. They belong to the category S:S. They are neither adverbs nor adcopulas but adsentences. What of ‘ŒÆºH’ and ‘ÆçH’? They are no more adsentences than adcopulas: it is to Peter’s second class of adverbs — to the class of genuine adverbs — that we should naturally assign such words.23 Is that natural view demonstrably right? Negation may help. If ‘’ is an adsentence, then we should be able to distinguish between ‘not-(:P)’ and ‘:not-P’. Thus there is a clear difference between: It is not necessary that Socrates walks and: It is necessary that Socrates does not walk. The point is not merely that, syntactically speaking, the negative particle may govern either the whole sentence or the core sentence.24 Rather, the negative particle may make a semantic contribution in either of two ways. 21 Tractatus, I 19 [ed L.M. de Rijk (Assen, 1972), pp.9–10]. 22 Summa Logicae, II 1 [P. Boehner, G. Gal, and S. Brown (eds), Opera philosophica I (St Bonaventure NY, 1974), p.242]. 23 According to Boethius, in: Socrates bene loquitur ‘the mode contains the whole sentence’ (in Int 2 397.6–22). But earlier, at 377.4–14, Boethius had said that in: Socrates velociter ambulat the mode is added to the walking of Socrates; i.e. here he takes ‘velociter’ to be a V:V. 24 Ammonius and others regularly say that to negate ‘:P’ you must attach the negative particle to the mode. They ought to mean that the negation must be attached to ‘:P’ as a whole. But Boethius, for one, sometimes gets into a tangle by — in effect — construing the negation of ‘:P’ as ‘[not-]:P’.

Ammonius and adverbs

629

Then consider: KŪEÆ Ø ÆçH Suppose ‘ÆçH’ is to be parsed as an S:S, thus: :(&x)Fx. Then look at: :not-(&x)Fx. [154] If ‘Clearly no one interprets’ makes any sense at all,25 then it must mean the same as ‘No one interprets clearly’. Hence it must be taken as equivalent to: not-(:(&x)Fx). Hence there is no distinction between ‘not-(:P)’ and ‘:not-P’. Hence ‘ÆçH’ is not an adsentence.26 In sum, the category of modes is defined by Ammonius as the category C:C. But some of Ammonius’ examples plainly belong to the category V:V; and others — including the centrally important examples — belong to the category S:S. The modal æ  Ø are best parsed as adsentences.27

VII In his On Adverbs Apollonius remarks that ‘åæ’ and ‘E’ require our closest attention — for pretty well everyone has taken them to be adverbs. (adv 128.10)*

Thus the negation of ‘Socrates walks quickly’ comes out as ‘Socrates walks non-quickly’, which entails ‘Socrates walks’ (in Int 2 380.12–382.8). Boethius seems content with this — but it implies that a proposition and its negation may both be false (e.g. if Socrates is standing still). 25 Of course, ‘clearly’ can sometimes be parsed as an S:S — e.g. in ‘Ammonius is clearly confused’. But I am not concerned with the use of ‘clearly’ to mean ‘It is clear that ... ’. 26 Boethius holds that with some modes there is no difference between ‘not-(:P)’ and ‘:not-P’, but that it is prudent to preserve uniformity among modes by stipulating that even in these cases ‘not-(:P)’ shall be the negation of ‘:P’ (in Int 2 379.12–380.11). That gets things back to front: the dissimilarity shows that Boethius’ modi (and Ammonius’ æ  Ø) do not form a single category. 27 Are all adsentences modes? Surely not. ‘There is honey still for tea and ... ’ is an impeccable adsentence; but it is not a mode. More modestly, ‘It is not the case that ... ’ is an adsentence but not a mode. (But it is an KææÅÆ according to the grammarians: e.g. Apollonius, adv 124.8–14; scholia in GG I iii [100.21–27]; [563.13–17]. Ammonius probably agreed (see 11.30) — but he cannot have taken it for a mode without destroying the distinction between sentences with a mode and sentences without a mode.) Modes are not the same as adsentences. Thus — and lamely: Ammonian æ  Ø are a subclass of adsentences; but the subclass is not defined, and Ammonius muddles its membership. * ŒÆd e åæ b ŒÆd e E IŒæØ F KØø EÆØ, Kd e º
ª æe ±
ø
ºçŁÅ KØææÆÆ.

630

Logical Matters

Apollonius then argues at length that the two words are not adverbs but verbs (128.10–133.12).28 But whoever held them to be adverbs, and why? ‘åæ’ and ‘E’ are surely modes. They are not explicitly mentioned by Ammonius. But he takes the sentence: [155] øŒæÅ ªØÆ
Ø
I
ƪŒÆE
as a paradigm ‘sentence with a mode’ (215.22–23), construing ‘I
ƪŒÆE
’ as a mode. There can be no doubt that he regarded ‘åæ’ and ‘E’ in the same light. And they surely are adsentences. It is tempting to infer that the champions of the view which Apollonius scouts were Peripatetic logicians. But although Apollonius does not name the champions, he does report their arguments. Those arguments contain nothing which is specifically Peripatetic. Rather, they are technical linguistic arguments, invoking the grammatical forms and constructions in which ‘åæ’ and ‘E’ may appear. Apollonius’ opponents were rival grammarians — from whom, perhaps, the Peripatetics took their cue. However that may be, the Apollonian text serves to introduce a further point about modes. In the sentence K
å 
ø øŒæÅ æØÆE any grammarian will recognize ‘K
å 
ø’ as an adverb. In ı
Æ
KØ øŒæÅ æØÆE
some grammarians will insist that ‘ı
Æ
’ is not an adverb but a verb or a noun. Ammonius regards ‘K
å 
ø’ and ‘ı
Æ
’ as exactly on a level; and he sees no significant difference between the two sentences.29 It is tempting to say that Ammonius is not in the same trade as Apollonius: he is concerned with semantic structure whereas Apollonius is interested in syntactic structure. But that would be at best misleading: better say that Ammonius is interested not in ‘surface’ grammar but in ‘deep’ or ‘logical’ grammar. These are choppy waters. Yet the main idea is simple: a sentence need not wear its mode on its sleeve.30 [156]

28 cf Apollonius, synt 234.23–235.12; Etym Mag s.v. åæ; Etym Gud s.v. åæ. 29 My example is actually drawn from Philoponus, in APr 28.13–16. But Philoponus’ commentary on APr is taken from the lectures of Ammonius (but see n.37 below). 30 Note that Ammonius takes verbal forms in ‘-
’ (e.g. ‘ªÆÅ
’, ‘ºı
’) to be KØææÆÆ (9.14–15; 11.25–26; 13.27–29; cf Stephanus, in Int 2.23–28). More precisely, they are ŁØŒa KØææÆÆ, and ‘ªÆÅ
’ etc. are equivalent to ‘E ªÆE
’ etc. (A connection with those who take ‘E’ and ‘åæ’ to be adverbs?) Typically Ammonian ‘logical’ grammar? No; for here (as often) Ammonius is lifting his terminology and his examples from the professional grammarians. See e.g. Dionysius Thrax, 19 [85.2]; cf the scholia in GG I iii [101.32–36]; [282.15–21].

Ammonius and adverbs

631

VIII Ammonius’ second preliminary question inquired after the number of modes. He answered: Their number is not by nature infinite, but it cannot be grasped by us — just like the number of universal subjects and predicates, which are themselves unnumberable. (214.29–31)31

Ammonius does not explain why the modes are unnumberable; but presumably it is because there is no method or algorithm for determining their number. He plainly thinks — although he does not explicitly say — that there is a vast number of them. Why? The parallel with subjects and predicates may offer a hint. There is a vast number of simple predicates. To every simple predicate there corresponds an adverb.33 And if — as perhaps Ammonius mistakenly thought — every adverb formed from a simple predicate is a mode, then there is a vast number of modes. How many of these innumerable modes concerned Aristotle? This was Ammonius’ third question, and it is easily answered: Aristotle introduces only four modes into his study of sentences with a mode: the necessary, the possible, the contingent, and in addition to these the impossible. (214.31–215.2)*

Aristotle’s modes are the four modal operators. (And in fact the four reduce to three.34) Ammonius spends more time on his sixth question: Are any relevant modes omitted from the de Interpretatione? He considers two candidates. I take the second first. 31 IæØŁe b ÆPH
çØ b
PŒ Ø
¼Øæ , P c
b æºÅ  ª E
, uæ Pb › H
ŒÆŁ º ı  ŒØ
ø
j ŒÆŪ æ ı
ø
, I
ÆæØŁø
b ÆPH
Z
ø
. — cf 230.8–13, where Ammonius takes int 22a13 to show that Aristotle took the modes to be unnumberable (see nn.44 and 48 below). For the contrast between what is infinite and what is ungraspable by us, between what is ¼Øæ
and what is IæºÅ
, see e.g. Epicurus, ad Hdt 42. 33 In particular, an KææÅÆ  Å : see 11.13; cf e.g. the scholium in GG I iii [97.31–98.5]. * ÆæÆ b 
ı › æØ ºÅ ÆæƺÆ
Ø æe c
ŁøæÆ
H
a æ  ı æ ø
, e
I
ƪŒÆE
e
ı
Æe
e
K
å 

ŒÆd Kd   Ø e
I
Æ
. 34 The contingent (marked by ‘K
åÆØ’) and the possible (marked by ‘ı
Æ
’) are to be identified: see 215.3–7 (cf Stephanus, in Int 55.8–12; Boethius, in Int 2 382.14–384.7). Later the list was reduced to two, the necessary and the possible: e.g. Philoponus, in APr 46.6–7; al-Farabi, in Int 163.16–18 [p.158].

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Logical Matters

Nor is ‘only’ — as when we say ‘Only animals perceive’ or ‘Only animals walk’ — a mode, as some people think ... (216.31–33)* [157]

Ammonius offers an analysis of such sentences, concluding that ‘only’ should be regarded as a complex quantifier or æ Ø æØ , rather than as a mode. ‘Only animals perceive’ means the same as ‘Every animal perceives and no non-animals perceive’ (216.33–217.12). We do not know who took the contrary view, but we may guess why they did so. For although ‘

’ is a quantifier when it is taken strictly (Œıæø ºÆÆ


: 217.19–21), it may also be used adverbially (KØææÅÆØŒH) as equivalent to ‘
ø’ — and then it is indeed a mode (217.25–26). The adverbial use of ‘

’ is rather rare. Ammonius glosses it by ‘purely [NºØŒæØ
H]’, explaining that ‘it signifies that the subject shares the predicate purely and not together with its opposite’ — as when we say that the gods are 
ø, immortal, whereas rational souls are immortal in essence but mortal in activity (217.26–34).35 Ammonius’ opponents presumably took this adverbial use of ‘

’ to be its primary or paradigmatic use.

IX No doubt it is obvious that ‘only’ is not a mode. The case is less clear with the other item which Ammonius discusses. He begins his answer to the sixth question like this: Now that this is clear, let us next consider whether there is any other mode ... of the same kind [as the modal æ  Ø] which has been introduced by Aristotle into the theory of propositions elsewhere and has been omitted in the work before us. Most of Aristotle’s commentators say that there is one, namely the mode of holding, and that it is enumerated in the Analytics before necessity and possibility. (215.29–216.1)**

* P c
Iºº Pb e 

, › Æ
ºªø


e ÇfiH
ÆNŁÅØŒ
j 

ÆØØŒ
, æ   i
YÅ Ø, uæ çÆ Ø
. 35 For such a use of ‘
ø’ in Ammonius himself, see e.g. in APr 10.7, 37; 27.4 (a nice example in Porphyry, in Cat 107.13–17). **  ø
b çÆ
æH
Z
ø
B KØŒłŁÆ  æ
Ø Ø ŒÆd ¼ºº  Ææa   ı æ  , ıªª
c b
 E NæÅ
Ø ŒÆd K
¼ºº Ø e  F æØ º ı K
fiB H
æ ø
Łøæfi Æ ÆæغÅ
 K
b fiB
ı
d æ ŒØ
fi Å æƪÆfi Æ ÆæƺºØ
, j PÆH· IØ FØ b
ªaæ ƒ ºE Ø H
KŪÅH
 F æØ º ı  F
r
ÆØ e
æå
Æ ŒÆd K
 E 
ƺıØŒ E æe  F I
ƪŒÆ ı ŒÆd  F K
å 
ı ŒÆÅæØŁÅ

.

Ammonius and adverbs

633

‘Most of Aristotle’s commentators’ certainly include Alexander.36 Ammonius dissents: neither in the Analytics nor in truth, he claims, is there a mode of ‘holding’ or of ‘actuality’. [158] What exactly was the view of ‘most of Aristotle’s commentators’? Perhaps they supposed that, in addition to the non-modal sentence: (1) Socrates walks there is also a different, modal, sentence: (1A) Socrates actually walks. Ammonius seems to construe their view in this way. For one of his arguments against it is this: were the view true, then both the de Interpretatione and the Prior Analytics would be incomplete — the former because it ignores sentences like (1A), the latter because it ignores sentences like (1). But the truth is rather that Ammonius’ opponents took sentence (1) itself to be modal. They maintained, in other words, that sentence (1) contains, implicitly, a mode, namely the mode of actuality which is explicit in (1A). Thus all sentences are modal — all contain, explicitly or implicitly, a modal æ  .39 An analogy may make the point clear. The later commentators followed Aristotle in recognizing something in the verb ‘walks’ in sentence (1) over and above its function as a predicate. For verbs ‘additionally signify time’: ‘walks’ in (1) is, or contains, a sign of time, and of the present time. Hence the semantic structure of (1) could be partially represented thus: 36 See e.g. in APr 26.25–27.6; 117.28–29; 123.29–124.1; 172.5; 197.2; 202. 6–7; 329.12–14; 330.12. Note too Alexander’s common use of the adverb ‘Ææå
ø’: e.g. 124.27; 129.24; 130.16, 18, 20; 132.8. (I shall speak of a mode of actuality, and I shall use ‘actually’ as a translation of ‘Ææå
ø’. That is not wholly felicitous; and the reader must forget the nuances of the ordinary English adverb ‘actually’ (and also the technicalities associated with the word ‘actuality’ in modern modal logic).) — Stephanus follows Ammonius, as ever (in Int 53.24–54.2). Philoponus professedly follows Ammonius (see in APr 42.35–45.20); but at in APr 46.7 he says ‘For clarity let us speak of a mode of actuality’ — and so he does throughout the rest of the commentary (e.g. 60.8; 61.2; 117.26; 121.2; 126.5). (He also uses ‘Ææå
ø’ some 80 times.) According to [Ammonius], in APr 38.1–33, ‘actually’ is a mode in the modal section of APr but not elsewhere (see e.g. 65.5). (‘Ææå
ø’ is also common in [Ammonius]. It never occurs in the genuine writings of Ammonius — but the modal part of Ammonius’ commentary on APr is lost.) Boethius simply states that there is a mode of actuality, and that Aristotle recognizes it in Int (in Int 2 382.16). In the Treatise al-Farabi recognizes a mode of actuality alongside necessity and possibility (75–76 [p.242]); and he seems to describe as old-fashioned the view, which he falsely ascribes to Alexander, that there is no mode of actuality (77 [p.243]). But in in Int there are just two (primary) modes, and actuality is ignored (163.16–18 [p.158]). 39 So Alexander, in APr 119.22–28: you can tell the modal differences among sentences by attending to their æ  Ø; ‘for each sentence and each syllogism will have the appropriate mode additionally predicated of it’.

634

Logical Matters

. [159] Ammonius’ opponents hold that modality runs parallel to time: a fuller account of the semantic structure of (1) will include a mark of modality, viz: . Thus ‘walks’ in (1) has three semantic functions.40 Then compare the following sentences: (1) Socrates walks. (2) Socrates possibly walks. (3) Socrates walks today. The opponents hold — and it is a commonplace — that in (1) ‘walks’ has the semantic function of referring to the present time; so in effect (1) is taken as equivalent to: (1N) Socrates walks now. Thus there is a pleasing symmetry between (1) and (3). Each sentence has a semantic core, which could be represented by a timeless ‘Socrates walks’, and an added time-operator. The opponents also hold that in (1) ‘walks’ has the semantic function of introducing a modality; so in effect (1) is equivalent to: (1A) Socrates actually walks. Thus there is a pleasing symmetry between (1) and (2). Each sentence has a semantic core, the non-modal ‘Socrates walks’, and an added modal operator. The two symmetries combine. Each of the sentences (1)–(3) has the same fundamental structure, namely: . How neat. An opposite theory would deny both symmetries. On this theory (1) is semantically pellucid. In it ‘walks’ does not covertly perform different operations. It performs the single operation of predicating walking of its subject. In (3) the word ‘today’ superadds something to the whole sentence (1). It does not replace an implicit element of (1) by another element from the same semantic category. In (2) the mode [160] ‘possibly’ similarly superadds something to (1). It does not replace an implicit element of (1) by another element of the same type.

40 ‘But is there a mode of actuality in sentence (1)?’ — Yes: just as ‘ªÆÅ
’ is a mode (see n.30 above), without presumably ceasing to be a verb, so in sentence (1) ‘walks’ is itself (among other things) a mode.

Ammonius and adverbs

635

Ammonius prefers a hybrid theory: he implicitly denies the analogy between modality and time. For time, he accepts the view which sees (1N) as a proper representation of (1). For modality, he accepts the view which finds (1) semantically pellucid.41

X Which theory should we prefer? Ammonius argues for his view (see 216.1–29); but he is more concerned to show that Aristotle does not countenance a mode of actuality than to prove that there is no such mode; and his arguments are obscure. I discern two main lines of thought. One line suggests that a mode of actuality would be somehow redundant — to say that something ‘holds holdingly [æåØ Ææå
ø]’, if it is not nonsense, is to say no more than that something holds.42 The second line invokes negation — and this line, which connects with an argument I used earlier, is worth developing a little.43 If a sentence consists of a mode and a core sentence — if it has the form ‘:P’ — then we should be able to distinguish between ‘not-(:P)’ and ‘:notP’. It is plain that there are two such ways of negating: (2) Socrates possibly walks. Are there also two analogous ways of negating: (1) Socrates walks? If the semantic structure of (1) is somehow made explicit in (1A), then we might try to find two distinct negations in the following sentences: It is not actual that Socrates walks. It is actual that Socrates does not walk. [161] There is a clear syntactic difference there; but is there any semantic difference? Surely not. It is plain that ‘not-(A:P)’ will be true just in case ‘A:not-P’ is true; and it is hard to see how there can be any difference between the truthconditions or the senses of the two sentences. If that is right, then ‘actually’ is not a mode — and hence (1A) does not explain the semantic structure of (1). Like ‘It is the case that’, ‘actually’ shows 41 Of course, he need not deny that (1) is equivalent to (1A). He must accept the equivalence but deny that (1A) makes explicit the structure of (1). It is the other way about: in (1A), ‘actually’ is a vacuous element — the structure of (1A) is given most perspicuously by (1). 42 See 216.19–21; cf Philoponus, in APr 44.6. 43 See 216.5–13 — but I claim here to be ‘developing’ rather than interpreting what Ammonius says.

636

Logical Matters

the syntax of an adsentence. Like ‘It is the case that’, ‘actually’ is semantically vacuous: it may play a rhetorical or a stylistic role — but it serves no semantic end. That, I take it, is Ammonius’ position. I am not confident that the Ammonian argument which I have just developed is in fact strong enough to sustain Ammonius’ position; nor am I confident that his position is correct.

XI Aristotle does not omit the modes ‘actually’ and ‘only’, for there are no such modes. But there are other modes which he does omit: ‘ÆçH’, ‘ŒÆºH’, ‘
ø’, ... And that brings us, finally, to Ammonius’ fourth question, which he answers thus: Aristotle introduces only four [sc modes] into his study of sentences with modes: the necessary, the possible, the contingent, and in addition the impossible. For these are both most universal and most appropriate to the nature of things. (214.31–215.3)44

That is pretty obscure. In what sense is the necessary ‘most universal’ and ‘most appropriate’? And why should that have anything to do with logical theory? I do not understand the force of ‘appropriate’. But Apollonius provides a clue to ‘universal’. He remarks that adverbs may be either universal or particular (adv 119.5–6); and he explains that some adverbs may intelligibly qualify any verb while others are restricted in their range of application. (Thus you may not say ‘It will rain [162] yesterday’.45) The modal æ  Ø are ‘most universal’ in the following sense: if ‘’ is a modal æ  , then for any sentence ‘P’, ‘:P’ is semantically well formed. And so what? ‘Well, logic is a science, and sciences deal with the universal. So the modal æ  Ø, being universal, are a proper object of logical study.’ 44 ÆæÆ b 
ı › æØ ºÅ ÆæƺÆ
Ø æe c
ŁøæÆ
H
a æ  ı æ ø
, e
I
ƪŒÆE
e
ı
Æe
e
K
å 

ŒÆd Kd   Ø e
I
Æ
, ‰ Z
Æ ŒÆŁ ºØŒø ı  ŒÆd ÆPfiB fiB çØ H
æƪø
NŒØ  ı. — Philoponus, in APr 304.28–31, says that ‘in the de Interpretatione it was said that the modes are infinite but are included in the three’ — that is quite false. Stephanus, in Int 53.14–24, argues that all the unnumberable modes really reduce to Aristotle’s three (thus ‘ŒÆºH’, for example, signifies contingency) — that is quite absurd. Al-Farabi holds that the modal æ  Ø are primary and that ‘once you know about these, you know about all the other modes’ (in Int 18.18–21 [pp.2–3]; 163.16–23 [p.158]) — that is wildly optimistic. 45 See adv 123.1–125.5; the remark does not appear in Dionysius Thrax, but see the scholia at GG I iii [96.4–9]; [272.17–31].

Ammonius and adverbs

637

That thought may be true. But it is jejune. Alexander offers more substantial fare. He too answers Ammonius’ fourth question (in APr 27.27–28.30). The heart of his answer is this: the addition or subtraction of modal æ   makes a difference to syllogisms. Necessarily A holds of every B B holds of every C So: necessarily A holds of every C is valid (according to Aristotle). A holds of every B Necessarily B holds of every C So: necessarily A holds of every C is not. The modal æ  Ø make a logical difference, inasmuch as there are formally valid inferences involving modal sentences which cannot be reduced to inferences involving non-modal sentences. In short: there is such a thing as modal logic. Equivalently: the modal æ  Ø are logical constants. Then why does Aristotle discuss only the modal æ  Ø? — Because only the modal æ  Ø are logical constants, only they sustain a logic.

XII Now that would be a good answer were it true. But is it true? Well, what other logical modes might there be? It is not difficult to come up with candidates. Thus al-Farabi reproduces the standard Ammonian definition of what a mode is, but he illustrates it with un-Ammonian examples: There are many ways in which a predicate can hold of a subject, as in ‘Laudably, Zayd is just’, ‘Deplorably, ‘Amr is unjust’. ‘Laudably’ and ‘deplorably’ signify how the predicate holds of the subject. Similarly, words expressing illegitimacy and legitimacy, as in ‘Zayd is forbidden to take away someone else’s money’, and ‘Zayd is entitled, or allowed, to do this and that’. Similarly, words like ‘ought to’, ‘must’, ‘makes a good job of’.47 [163]

Those are good examples of modes — and no doubt they were found in alFarabi’s Greek source. Earlier, Alexander had characterized ‘IºÅŁ’, ‘łı’, ‘
 
’, ‘¼ 
’, ‘Bº
’, ‘¼ź
’, ‘‰ Kd e ºE
’, ‘ŒÆa 47 in Int 163.8–15 [p.158]; see also Treatise, 70–71 [p.240].

638

Logical Matters

çØ
’, and ‘ŒÆa æ ÆæØ
’ as modes alongside ‘ı
Æ
’ and ‘I
Æ
’ (and ‘ŒÆºH’ and ‘Tçºø’).48 Now there is — or so many philosophers believe — such a thing as deontic logic. The deontic modes, which al-Farabi mentions, have been taken for logical constants. There is also such a thing as epistemic logic. Moreover, Alexander might surely have contemplated the possibility of an ‘endoxic’ logic. For just as ‘I
ƪŒÆE
’ marks off apodeictic inference, so ‘
 
’ marks off dialectical inference. And if the mode ‘I
ƪŒÆE
’ breeds a logic appropriate to the former, why should not the mode ‘
 
’ father a logic suitable to the latter? Alexander did not raise the question.49 Nor did Ammonius. Why not? Aristotle’s commentators were learned men, and they were sometimes acute. But they lacked imagination and they lacked a sense of intellectual adventure. At bottom they were conservative creatures, dull dogs. 48 See in APr 270.10–28 and 329.30–330.5 (330.3 refers back to the earlier passage); cf 411.35–37, where Alexander again classifies ‘IºÅŁ’ as a mode (no doubt with tacit reference to Int 22a13). 49 Perhaps ‘‰ Kd e ºE
’ and ‘ŒÆa çØ
’ were regarded as variants on ‘ı
Æ
’ and therefore did not call for special treatment. Perhaps ‘IºÅŁ’ was uninteresting, given that ‘IºÅŁ: P’ is equivalent to ‘P’ (e.g. Alexander, in APr 411.32–35). But the other modes remain — and they cry for investigation.

24 Priscian and connectors* Book XVI of Priscian’s Institutions concerns coniunctiones — conjunctions, in the standard translation, or connectors, as I shall call them. Priscian begins with a general characterization (XVI i 1 [93.2–8]).1 Then he lists the ‘accidents’ of connectors — form, species, order ([93.9–10]). He next discusses form, in a couple of lines ([93.11–12]), species, in eleven pages (i 2–ii 15 [93.13–104.13]), and order, in a single page (ii 16 [104.14–105.14]). There is pretty well nothing novel in Book XVI — or elsewhere in the Institutions, as Priscian himself more than once insists. So there are deliciously delicate questions about Priscian’s sources. But such questions I leave aside: the following remarks deal not with what Priscian took from his predecessors but with what he left to his successors — and to Western grammatical science. Connectors first appear in the Institutions in Book II, which introduces the parts of speech. Priscian states that non aliter possunt discerni a se partes orationis nisi uniuscuiusque proprietates significationum attendamus. the parts of speech can only be distinguished one from another if we pay attention to the properties of their meanings. (II iv 18 [55.4–5])

And he explains that proprium est coniunctionis diversa nomina vel quascumque dictiones casuales vel diversa verba vel adverbia coniungere. [366] it is proper to connectors that they connect different nouns (or other words which take cases) or different verbs or adverbs. (iv 21 [56.21–22]) * A version of ‘Quelques remarques sur la caracte´risation des connecteurs chez Priscien’, published in M. Baratin, B. Colombat, and L. Holtz (eds), Priscien: transmission et refondation de la grammaire de l’Antiquite´ aux modernes. Studia Artistarum 21 (Turnhout, 2009), pp.365–383. — The remarks on Priscian supplement, and occasionally compete with, chapter 3 of J. Barnes, Truth, etc. (Oxford, 2007). 1 References are by book-, chapter-, and section-number; and the square brackets enclose pageand line-number in the volumes of Grammatici Latini.

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Logical Matters

Is that a definition? Priscian says that he is stating a property — that is to say, something which holds of every connector and of no other part of speech. The ancients sometimes distinguished between a delineation or  ªæÆç, which gives a property of a thing, and a definition in the strict sense, which gives its essence. But the distinction is not always regarded, and often enough an author will offer a property as though it were a definition. However that may be, the characterization of connectors in Book XVI is rather more elaborate: coniunctio est pars orationis indeclinabilis, coniunctiva aliarum partium orationis quibus consignificat, vim vel ordinem demonstrans. A connector is an undeclinable part of speech which connects the other parts of speech, with which it co-signifies, and which indicates a force or an order. (inst XVI i 1 [93.1–2])

Four clauses, the second of which (stating that connectors connect the other parts of speech) corresponds grosso modo to the property given in Book II. Before looking at the characterization, a third text may be noticed. In a passage in the Partitions which analyses the first line of Book I of the Aeneid, Priscian has to explain the ‘que’ in ‘arma virumque cano’. He begins thus: que quae pars orationis est? — coniunctio. — quid est coniunctio? — pars orationis conectens ordinansque sententiam. What part of speech is que ? — A connector. — What is a connector? — A part of speech which connects and orders a thought. (part i 26 [465.37–39])2

That account of the matter, which is repeated three times, is not only less rich than the characterization in Book XVI of the Institutions: it appears to conflict with it. For according to the Partitions, connectors connect thoughts (whereas in the Institutions they connect parts of speech); and they serve to order the thoughts (whereas in the Institutions they signal either an order or a force). But the [367] conflict is only apparent. It will emerge that connecting a thought and connecting the parts of speech is one and the same operation; and the ordering to which the Partitions refers is not the order which the Institutions links with force but rather the order which the Institutions lists as one of the accidents of connectors. Back, then, to Book XVI. Does the characterization of connectors which Priscian offers there count as a genuine definition? Perhaps it does. On the 2 Exactly the same words (but with ‘adnectens ’ instead of ‘conectens ’) at iv 85 [478.15–16]; vi 125 [488.16–17]; vii 142 [493.2–3]; cf ii 65 [474.1]; iii 77 [476.34]; ix 170 [500.6].

Priscian and connectors

641

other hand, you might incline to judge that its four constituent clauses are not all on the same level. According to the first clause, connectors are undeclinable. No doubt that is true — at least, it is true for Latin and for Greek. But it is hard to believe that it marks an essential fact about connectors, hard not to believe that it marks a contingent fact about (Latin and Greek) connecting words. According to the third clause, connectors ‘co-signify’. That is no doubt more important than the first clause — and it is also more obscure. Nonetheless, if it indicates a feature which is found in all connectors, and is in that sense essential to them, it is far from evident that it is a part of the definition of what it is to be a connector — it looks more like what traditional logicians would call an ‘essential accident’, a feature which derives from but does not inhere in the definition. The fourth clause notes that a connector indicates a force or an order. The formula is opaque. Priscian offers a gloss (XVI i 1 [93.4–8]), which might be put like this: Take a connector, C, and two connected items, x and y. To say that C indicates a force (in Latin the word is ‘vis ’, for which Priscian sometimes substitutes ‘essentia’ and sometimes ‘substantia’) is to say that the proposition that Cxy implies the truth of both x and y: if Cxy, then x is true and y is true. And to say that C indicates an order is to say that ‘Cxy’ is not equivalent to ‘Cyx’ — that it is not the case that Cxy if and only if Cyx. There are some connectors which indicate a force: for example ‘et ’ or ‘and’ — if P and Q, then it is true that P and it is true that Q. There are some which indicate an order: for example, ‘si ’ or ‘if ’— it is not the case that if P then Q if and only if if Q then P (see i 3 [94.15–20]). And some indicate both a force and an order: for example, ‘quia’ or ‘because’ — if P because Q, then it is true that P and it is true that Q; and it is not the case that P because Q if and only if Q because P (see i 3 [94.22–25]). It might be added — though Priscian does not — that there are connectors which indicate neither a force nor an order: for example ‘aut ’ or ‘or’. Now that is all good stuff and true; but it is scarcely part of a definition of what a connector is. The second clause remains: connectors connect. The clause might be construed as in itself constituting a definition. Certainly — or so you would think —, it expresses something essential to connectors; and an Aristotelian philosopher would recognize in it the structure of a good definition — a connector is a part of speech (that is the genus) which connects parts of speech (there is the differentia). [368]

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In sum, the four-part characterization of connectors in Book XVI would make a pretty bad definition; and since Priscian doesn’t himself describe it as a definition, we need not treat it as one. To be sure, the matter is hardly of much importance. What does the characterization of connectors characterize? It characterizes connectors, of course. But that tautological answer requires three miscellaneous comments. First, a connector is a part of speech; and all parts of speech are dictiones, or semantically simple expressions (see II iii 14 [53.8–12]).3 The expression ‘elephant’ is a dictio: it has no semantically active parts. The expression ‘Indian elephant’ is not a dictio: its sense is fixed (at least in part) by the sense of its parts. In the same way, the expression ‘if and only if ’, which contemporary logic treats as a connector, is not a dictio — and hence is not a connector in Priscian’s book. That raises a couple of questions. First, if the expression ‘if and only if ’ isn’t a dictio, then what is it? The answer to that question (to which I shall return) is disappointing: ancient grammarians recognized no category of expression to which ‘if and only if ’ might belong. Secondly, suppose we write ‘iff’ instead of ‘if and only if ’ — have we then got hold of a connector? I think the answer is Yes — strange though that may seem. For ‘iff ’ has no semantically active parts. So it is a dictio. So it is some part of speech or other. And if it is any part of speech, then surely it is a connector. The second of the three comments starts by recalling that in the preface to the Institutions Priscian boasts that he has drawn on texts both in Greek and in Latin (praef 2–3 [2.7–9]) — he dedicates the Book to Julian, who is doctus utriusque linguae (praef 4 [2.30–31]). True, the vast majority of his illustrative examples are Latin. But there are also some Greek examples — and occasionally Priscian will discuss a linguistic phenomenon which occurs in Greek but not in Latin. That means that he is not writing a Latin grammar: he is writing a grammar — that is to say, a general grammar, a grammar which in principle and at any rate in outline applies to any and every actual language. To be sure, Priscian’s observations are [369] always fixed by the properties of the two languages which he knows, so that his grammar will not in fact apply to other languages without fairly serious modification. Nonetheless, the Institutions offers a general grammar. Thus when he characterizes 3 I am not sure that Priscian ever states explicitly that connectors are dictiones; but he implies it in several places — see e.g. XVII i 10 [114.9–22].

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connectors, Priscian is not saying something about Latin connectors (nor about Greek connectors): he is saying something about connectors. The third gloss demands a more elaborate presentation. At first blush, it must seem plain that the characterization ought to help us answer questions of the sort ‘What part of speech is the expression x?’, that it ought to help us to classify expressions according to certain semantic and syntactic features. Just as the word ‘horse’, say, is a noun, so the word ‘if ’, say, is a connector. That is the sort of information you will find in a modern dictionary: ‘horse, n’; ‘if, conj ’. But that is not quite what Priscian is up to — or at any rate, he is not always up to quite that. First, when he distinguishes among different sorts of connector, he doesn’t classify expressions but rather uses of expressions. Near the beginning of Book XVI he says that inveniuntur ... multae tam ex supra dictis quam ex aliis coniunctionibus diversas significationes una eademque voce habentes. many connectors — both among those we have already discussed and among others — are found to have different meanings in one and the same word. (XVI i 2 [93.20–22])

He says the same thing again at the end of the Book (ii 16 [105.4–6]); and between the two general affirmations he mentions many particular cases. For example, nam est quando ªæ, est quando  Graecam coniunctionem completivam vel affirmativam significat. nam sometimes means ªæ, sometimes  (the Greek connector which is expletive or affirmative) ... (ii 15 [104.5–6])

Is the Latin word ‘nam’ a causal connector or an expletive connector? The question has no answer: the word is sometimes the one and sometimes the other. That is to say, there are causal uses and expletive uses. So, in the same sort of way, one and the same expression is sometimes a connector and sometimes another part of speech. Thus inveniuntur ... nomina vel pronomina vel etiam praepositiones vel adverbia quae loco causalium accipiuntur coniunctionum: pronomina ut [370] ideo, eo; nomina: qua causa, qua gratia, qua propter, quam ob rem, et quas ob res. we find nouns and pronouns — and even prepositions and adverbs — which take on the role of causal connectors. Among pronouns there are ideo and eo; among

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nouns qua causa, qua gratia, qua propter, quam ob rem, and quas ob res. (XVI i 5 [95.26–96.1])4

It is true that the examples of ‘nouns’ are strange (they are not dictiones). It is true too that Priscian does not expressly say that ‘ideo’ (for example) is sometimes a pronoun and sometimes a connector, and he might rather be taken to mean that ‘ideo’ is in itself and always a pronoun and yet will sometimes function as a connector. But look at what he says about the word ‘ne ’, which he classifies as a causal connector: hoc autem, id est ne, quando  vel 
ı significat adverbium est. invenitur tamen etiam verbum pro adversativa coniunctione cum adverbio ut quamvis pro quamquam et pro etsi, quomodo et licet et licebit. This word — I mean ne — is an adverb when it means  or 
ı. (And you actually find verbs for contrastive connectors when they are with an adverb — quamvis, for example, for quamquam or for etsi. Similarly licet and licebit.) ([96.13–16])

In the same way, ‘quam’ is a preferential connector; but est ... quam et accusativus quae infiniti nominis et adverbium similitudinis. quam is also the accusative of the indefinite noun quae — and in addition an adverb of comparison. (i 9 [99.3–4])

Are the words ‘ne’ and ‘quam’ connectors? The question has no answer: sometimes they are connectors, sometimes they are not. If we take such texts seriously, then we shall say that Priscian’s theory of parts of speech does not classify words or expressions: it classifies uses or functions of words or expressions. A connector is an expression which connects other parts of speech — better, an expression functions as a connector when it serves to connect other parts of speech. That seems simple enough; and there is a standard interpretation — an interpretation which applies equally to the similar formulas which are found in other ancient grammatical texts, both Latin and Greek. In Book II Priscian indicates that a connector connects different nouns, or different pronouns, or different participles, [371] or different verbs, or different adverbs (II iv 21 [56.16–21]). So it seems that a connector may connect any part of speech save prepositions and connectors themselves. In Book XVI, Priscian says that connectors connect ‘the other parts of speech’; in other words — or so it seems — they may connect any parts of speech save connectors. 4 cf XI ii 7 [552.7–8]: loco coniunctionis tam nomen quam praenomen: quare, ideo.

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It is hard to find reasons for excluding prepositions and connectors from the range of operation of connectors. After all, there are any number of expressions in which a connector connects — or appears to connect — two prepositions (‘with or without your consent’) or two connectors (‘if and only if ’). It would be odd had Priscian really intended to outlaw such things. Better suppose that the list in Book II is illustrative and does not pretend to be exhaustive; and to think that in Book XVI the phrase ‘the other parts of speech’ is inexact. In any event, it seems that a connector will tie a noun to a noun, a verb to a verb, and so on, and that it will not tie a noun to a verb or a verb to an adverb, and so on. A connector connects syntactically homogeneous items — it connects two (or perhaps more) items which belong to the same part of speech. (That is what II iv 21 suggests. But in Book XVII of the Institutions, which discusses the construction of connectors, Priscian is less strict: he recognizes, for example, that a noun and a pronoun may be connected, as in ‘et Apollonius et ego ’ (see XVII xv 95 [160.18]).) A connector may tie a noun to a noun but not a noun to a verb. Why not? Priscian does not offer any explanation. But it is readily imagined that a noun and a verb stick together, so to speak, by nature: they are made for one another, and they do not need any third item to cement their union. The same goes for adverbs and verbs, for prepositions and nouns, ... On the other hand, two verbs won’t stick together without some sort of cement; and in general, in order that a couple of expressions of the same category may hold together, they need something to unite them — they need a connector. ‘Dionysius ’ and ‘loquitur ’ go together, without needing any sort of cement, to make ‘Dionysius loquitur ’. ‘Dionysius ’ and ‘Trypho ’ don’t go together. ‘Dionysius Trypho ’ is not grammatical: you must add a connector — say ‘et’, to reach ‘Dionysius et Trypho’. (See XVII xv 95 [160.16–18].) No doubt things are a little more complicated than that; but the general idea is clear enough, and it may seem to be at bottom sound.5 [372] That is, I think, the standard interpretation of what Priscian and his colleagues mean when they say that connectors connect parts of speech. But the thing is not without its difficulties. 5 It is worth noting that Priscian didn’t himself like the metaphor of cementing. It is one of a number of similar metaphors which, he claims, were introduced by ‘certain philosophers’ in order to indicate that connectors (like prepositions, adverbs, ... ) are not genuine parts of speech — and that is a view which Priscian vigorously rejected (XI ii 6–7 [551.18–552.14]).

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For example, when a connector unites a noun and a noun, what is the result of the operation? In Book II we find — or we seem to find — expressions such as ‘et Terentius et Cicero’, ‘vel Terentius vel Cicero’ (II iv 21 [56.17–18]): the result of the connecting operation appears to be a nominal phrase or a complex noun — something which has the syntax of a noun although it does not possess the simplicity demanded of a dictio and therefore is not a genuine noun. More generally, a connector will take two (or more) expressions of a given class to make an expression which has the same syntactical properties as the expressions it takes. But as I have already said — and it is a commonplace — ancient grammar never recognized complex items of that sort. The linguistic hierarchy, established by Plato and maintained unflinchingly (despite its oddities) until the end of antiquity, starts with letters, moves up to syllables, mounts to words, and culminates with orationes or º ª Ø. Thus sentences stand immediately on words — there is no sort of entity in between. Now it may be said that an oratio or º ª  is not necessarily a sentence. Rather, any semantically complex expression counts as an oratio or º ª : sentences are just one, particularly important, kind of oratio or º ª  — they are items which are ‘complete’ or which express a ‘complete’ thought. There are inklings of that notion in some of the ancient texts; but so far as I know, there are no more than inklings. And Priscian doesn’t even inkle: he says explicitly that oratio est ordinatio dictionum congrua, sententiam perfectam demonstrans an oratio is a sequence of words which is well formed and which presents a complete thought. (II iv 15 [53.28–29])

In other words, in Priscian an oratio is a sentence. Since for Priscian there is nothing between a semantically simple word and a complete sentence, a sequence of words such as et Terentius et Cicero is not a linguistic unity. On the one hand, then, a connector like ‘et ’ may serve to connect two nouns. On the other hand, it cannot produce an expression such as et Terentius et Cicero since there are no such sorts of expression. It will be said that that is not Priscian’s problem — rather, it is a problem common to ancient grammar as such. All we can do is note it, lament it, and

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pass on. [373] Perhaps. And yet there is in Priscian — and, so far as I know, nowhere else — a hint of something better. In one passage, where he is explaining the difference between prepositions and connectors, Priscian has this to say: praepositiones vero ... non coniungunt duas substantias cum uno accidente, quod est proprium coniunctionis ut ego et tu facimus, homo et taurus arant, vel duo accidentia cum una substantia ut scribit et legit homo vel iustus et fortis homo. Prepositions ... do not connect two substances to an accident, which is proper to connectors — for example ego et tu facimus, homo et taurus arant — or two accidents to a substance — for example scribit et legit homo or iustus et fortis homo. (XIV i 2 [25.1–5])

The formulation is scarcely correct — connectors don’t connect substances and accidents: they connect expressions, which may (perhaps) mean substances or accidents. But incorrectness of that stripe is a common phenomenon in ancient grammatical texts (as it is in modern grammatical texts). And we can see what Prisican means to say. The word ‘et ’ in Cicero et Brutus eunt ad forum conjoins the two names (of substances) ‘Cicero’ and ‘Brutus’ and it connects them to a single verb (which signifies an accident). In other words, the connector doesn’t produce a new nominal expression, ‘Cicero et Brutus’: it functions in the context of a sentence; and although what it connects are the two names, what it produces is a single well-formed sentence. The sequence of dictiones Cicero Brutus eunt ad forum is ungrammatical, it is not an oratio. But the sequence Cicero et Brutus eunt ad forum is well formed. And it is the connector which is responsible for its fine fettle. Priscian says that connectors connect the other partes orationis. Thus far I have used the stock translation of the Latin phrase: ‘parts of speech’. A pedantic translator might prefer — at least in the context of the Institutions — the phrase ‘parts of a sentence’; for in the Institutions the world ‘oratio ’ means not ‘speech’ but ‘sentence’. What we call parts of speech, Priscian and his colleagues called parts of sentences. What difference does that make? Little or none, in the case of most ancient grammarians. But in Priscian’s case it is tempting to believe that there is more to the matter than translator’s pedantry. Priscian’s colleagues say that connectors connect parts of speech or parts of a sentence: Priscian says that they

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connect the other parts of speech or the other parts of a sentence. Suppose we take the word ‘other’ not as a minor inexactitude but as a significant precision: then when Priscian says that a connector connects the other parts of a sentence, he doesn’t mean that a [374] connector connects a noun to a noun, a verb to a verb, and so on — he means that a connector connects the other parts of the sentence in which it occurs. For example, in the sentence et Dionysius loquitur et Apollonius there is the connector ‘et ’ (or perhaps the pair of connectors ‘et ... et ... ’). This connector serves to connect the other parts of the sentence — the other parts of that particular sentence. Priscian will no doubt say that here the connector connects the two names ‘Dionysius ’ and ‘Apollonius ’. But the product of that connecting operation is not the sequence et Dionysius et Apollonius. The product is the well-connected sentence et Dionysius loquitur et Apollonius. That, I think, is precisely what Priscian means when, in the Partitions, he explains that a connector is ‘a part of a sentence which connects and orders a thought’. In truth, the connector connects and orders the sentence which expresses the thought rather than the thought itself — but once again, that is no more than a familiar and widespread incorrectness. To say that a connector links the parts of a sentence and to say that it connects the sentence is to say the same thing twice over. Does the string tie up the bundle or tie up the sticks? Thus understood, Priscian’s characterization of what a connector is avoids certain difficulties; and it would be agreeable to believe that the interpretation is correct. But it must be allowed that it ascribes to Priscian, on the basis of a single word (namely, the word ‘aliarum’), a certain independence from the whole ancient grammatical tradition — an independence which he never claims for himself. In any event, the interpretation does not get Priscian clear of all the difficulties which the characterization confronts. A connector connects the parts of the sentence in which it occurs? Surely connectors also connect other linguistic units — and most evidently, they connect sentences to one another. In the trenches they sang ‘We’re ’ere because we’re ’ere because we’re ’ere because we’re ’ere’. They used the connector ‘because’. They didn’t use it to link ‘we’ to ‘we’ nor ‘are’ to ‘are’ nor ‘here’ to ‘here’: they used it to connect ‘we’re ’ere’ to ‘we’re ’ere’.

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Modern logicians agree with the PBI: the connectives of modern propositional logic are expressions which take one sentence or more to make a sentence. (Thus ‘if ’ takes a couple of sentences to make a new, conditional, sentence.) The ancient logicians took the same view. At any rate, Stoic logic turns about a few connectors whose function plainly is to produce [375] new sentences from old. So, for example, ‘if ’ may take ‘It’s day’ and ‘It’s light’ to make If it’s day, it’s light. Despite what the grammarians say, and despite some of the things which the Stoics themselves say, it is difficult not to think that the connector ‘if ’ serves there to connect sentences and not parts of sentences. It may be added that the ancient grammarians themselves had excellent reasons for attributing such a role to connectors. For example, they all scratched their heads over the question: How can prepositions be distinguished from connectors? If the function of a connector is to connect the parts of a sentence so that ‘et ’ connects the names of Terence and of Cicero in the sentence et Terentius et Cicero ibant in forum, then surely the word ‘cum’ does exactly the same in the sentence Terentius cum Cicerone ibat in forum? The Stoics, as Priscian knew (XIV ii 18 [34.23–35.3]), took prepositions and connectors to constitute two sub-classes of a single class of words; and there was a certain coherency to their view. For despite the plain implications of their logic, they too said that connectors connect the parts of sentences. The grammarians, Priscian among them, wanted to distinguish prepositions from connectors, and they developed a battery of arguments to do so. (See II iv 21 [56.21–27]; XIV i 2–3 [24.23–25.22]; ii 13 [31.16–20]; 18 [34.23–35.3].) The battery had little fire-power: it would have been easy to make the distinction by remarking [376] that connectors connect sentences and prepositions do not. Again, the fourth clause in the characterization of connectors implies that the connected items are sentences. For a connector to indicate a force is for it to imply that the connected items are true; to indicate an order is to signal that the compound sentence can’t be converted. Force and order are explained in terms of sentences, and the explanations have sense only if the connected items are taken to be sentences.

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Again, when the grammarians want to explain the sense of a connector, what they say frequently presupposes that the connected items are sentences. Thus Priscian explains disjunctive connectors as follows: disiunctivae sunt quae quamvis dictiones coniungunt sensum tamen disiunctum et alteram quidem rem esse alteram vero non esse significant. Disjunctives are those which, although they connect words, signify a disjoined sense and indicate that one of the items is and the other is not. (XVI i 6 [97.17–19])

(His example: vel dies est vel nox.) That is to say, to grasp the sense of a disjunctive connector is to recognize that a complex phrase which the connector connects is true if and only if exactly one of the items which it connects is true. So the ancient grammarians had excellent reasons — and reasons which were scarcely concealed — for thinking that the primary function of a connector is not to join words into sentences but to join sentences into sentences. Yet they did not so think. Someone might seek to defend their position along the following lines. Start from a sentence such as Dionysius loquitur et scribit. There it is initially plausible to say that the connector ‘et ’ connects two verbs and not two sentences — for there are no two sentences for it to connect. Next take this: Dionysius loquitur et Dionysius scribit. Why not say that there too it is the two verbs which are connected by the connector? Of course, the connector produces a compound sentence, a sentence compounded from two sentences. But if the connector connects the two sentences, it does so in a secondary or accidental way: it is because it connects the two verbs that the connector connects the two sentences. Finally, why not say the same for Dionysius loquitur et Apollonius scribit? No doubt the connector ‘et ’ connects the two sentences ‘Dionysius loquitur ’ and ‘Apollonius scribit ’; but it does so in an accidental or secondary way — it does so insofar as it connects the words which make up the sentences. Against such an analysis several objections might be brought. First, it is forced and arbitrary. Why ever say that in Dionysius loquitur et Apollonius scribit the connector connects the two verbs rather than the two nouns? Well, perhaps it connects, at one blow, both the two verbs and also the two

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nouns? But then why not say that it connects the two sentences? And why not add a fifth clause to the characterization of the connector, so that a connector connects either the parts of the sentence in which it occurs or else the sentences which constitute the sentence in which it occurs? In that case, the connecting of sentences is not accidental on the connecting of words: the two sorts of connecting are on a par, neither being prior to the other. But that is still unsatisfactory, for several reasons. For example, [377] consider the two sentences (1) Terentius et Cicero ibant in forum. (2) Terentius ibat in forum et Cicero manebat domi. Presumably one and the same connector, namely ‘et ’, appears both in (1) and in (2). How is its sense to be explained? Crudely speaking, like this. (a) You grasp the sense of a sentence of the form ‘! et !*’ if and only if you know that it is true if and only if both ‘!’ and ‘!*’ are true. (b) You grasp the sense of a sentence of the form ‘F(a et b)’ only if you know that it is true if and only if ‘Fa et Fb’ is true. So if you understand sentence (1), then by (b) you know that it is true if and only if Terentius ibat in forum et Cicero ibat in forum is true. And you understand that sentence by way of (a). In other words, the sense of the word ‘et’ in (1) is fixed by its sense in (2). In general, if you start from the notion that connectors connect sentences, it is easy to explain their other uses. (But it should be allowed that there are some uses of some connectors which resist such explanation.) If you try to reverse the direction of explanation, tackling (2) by way of (1), you will get nowhere; and if you attempt to give independent explanations for (1) and for (2) you will be obliged to hold that there are two different connectors in the two sentences. For those reasons, among others, priority should be accorded to the connection of sentences. A connector is an item which takes sentences and makes sentences. If it sometimes appears that a connector takes words to make sentences (or subsentential phrases), such cases are in one way or another secondary and derivative. When Priscian characterized connectors as items which connect the other parts of the sentence, he was mistaken. The mistake was both serious and easily avoided. To be sure, it was not his own. But we are responsible for the errors we borrow from others as well as for those we fabricate ourselves. It is perfectly obvious, you may think, that a connector connects — that it ties one item to another. Otherwise how could it be called a connector? And yet Priscian appears to countenance connectors which connect nothing.

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He notices that a sentence, in Latin and also in Greek, will sometimes contain an unnecessary connector: [378] coniunctiones quoque tam apud nos quam apud illos modo abundant, modo deficiunt. Connectors too, both with us and with them, are sometimes superfluous and sometimes missing. (XVII xxiii 171 [196.7–8])

Superfluity is not peculiar to connectors — it is a completely general phenomenon. Thus Priscian says that at Aeneid XI 42 the verb ‘inquit’ is superfluous, given that ‘fatur ’ appears in the preceding line; and he comments that nec mirum cum expletivae coniunctiones quantum ad sensum plerumque supervacue ponuntur. there is nothing remarkable in that — after all, expletive connectors are usually inserted superfluously as far as the sense goes. (XVII i 4 [110.6–8])

So not only do some sentences contain connectors which don’t connect: in addition, there is a class of connectors — the ‘expletive’ connectors — which normally connect nothing. Priscian discusses the first line of Book VII of the Aeneid twice, once in the Partitions and once in the Institutions: tu quoque litoribus nostris Aeneia nutrix ...

In the Partitions he says this: quoque quae pars orationis est? — coniunctio: accipitur enim pro et tu. What part of speech is quoque? — A connector. It is used for et tu. (part vii 142 [492.32–33])

So the word ‘quoque’ — in this passage — is a connector because it is equivalent to ‘et ’, and ‘et ’ — in a context of this sort — is a connector. In the Institutions he says the same thing, adding that quoque quando pro etiam vel et accipitur copulativa est. when quoque is used for etiam or et it is conjunctive. (XVI ii 15 [103.16])

And a little earlier, in i 2 [93.17–18], ‘quoque’ was duly listed among the connectors which ‘copulate’ or conjoin. But if ‘quoque’ at Aeneid VII 1 is a copulative connector, what on earth does it copulate or connect? Priscian doesn’t say. Moreover, the text of the Institutions continues as follows: [379]

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quando autem supervacua ponitur completiva est, ut Virgilius in I: multa quoque et bello passus dum conderet urbem. non egeret enim ea sensus si dixisset multa et bello passus. nisi quod quidam existimant pro adverbio similitudinis accipiatur quomodo item. But when quoque is inserted superfluously, it is expletive — e.g. Vergil, Book I: multa quoque et bello passus dum conderet urbem. For the sense would not be lost if Vergil had written multa et bello passus. True, some people think that it ought to be construed as an adverb of comparison, like item. ([103.19–23])6

Now it seems clear that ‘some people’ are right: here — and not only here — ‘quoque’ is an adverb. It is not any sort of connector — not even an expletive connector. What perplexes is not only the analysis which Priscian offers of Vergil’s ‘quoque’: it is the whole idea of there being a class of expletive connectors. This is what Priscian says about them: completivae sunt vero autem quidem equidem quoque enim nam namque; et fere quaecumque coniunctiones ornatus causa vel metri nulla significationis necessitate ponuntur hoc nomine nuncupantur. The expletives are vero, autem, quidem, equidem, quoque, enim, nam, namque — and indeed almost all the connectors which are inserted for stylistic or metrical reasons and without any semantic need are called by this name. (XVI ii 13 [102.12–14])

The illustrative examples are strange, but the general notion is plain: an expletive connector makes no contribution to the meaning of the sentence in which it appears — that is why it is called expletive. (And why expletives can always be deleted with no harm to the sense.) But if a word makes no contribution to the sense of a sentence, how can it be treated as a part of the sentence or as a part of speech? Or, more exactly, how can it be called a connector? It connects nothing, it does not play the part of a connector, it has no title to the name of connector. Nonetheless, Priscian speaks about expletive connectors without any sign of embarrassment. The text continues in this way:

6 Aeneid I 5 is quoted again at XVII xxiii 171 [196.9]: again to give an example of a superfluous connector.

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omnes tamen hae inter alias species inveniuntur. ut si dicam Aeneas vero et pius et fortis fuit completiva est, quia et si vero tollatur significatio integra manet; sin autem dicam Aeneas quidem pius fuit Ulixes vero astutus, pro copulativa accipitur, quia utriusque rei simul sententiam significat cum substantia. However, all these cases are found among the other species of connector. For example, if I say Aeneas vero et pius et fortis erat, the connector is expletive — for if vero is removed the sense remains complete. [380] On the other hand, if I say Aeneas quidem pius fuit, Ulixes vero astutus, it is understood as a conjunctive connector; for it means the thought and the existence of the two things at the same time. ([102.14–19])

In the first sentence, ‘vero ’ contributes nothing and can be removed without affecting either syntax or sense. In the second sentence, ‘vero’ has a conjunctive sense: ‘it means the thought and the existence of the two things’ — that is to say, the second sentence is true if and only if its two sentential components are true. Priscian thinks that every connector which belongs to the class of expletives sometimes functions as an ordinary connector of one kind or another. That is why expletives are classified as connectors: a connector is a part of a sentence which connects the other parts, and expletives all do that — at least part-time. But then why speak of a class of expletive connectors? Why not simply say that the members of any class of connector — like any other part of speech — are sometimes used superfluously or expletively? There is no answer to that question. Expletive connectors should be deleted from the grammar books. Expletives apart, Prisican sometimes confers the status of connector on an item which, at first blush, has no title to it. Perhaps the most striking case is that of the so-called ‘abnegative’ connectors: abnegativae sunt apud Graecos Œ
et ¼
quae verbis connectae posse fieri rem ostendunt sed propter causam aliquam impediri ne fiat ... nos autem sine coniunctionibus subiunctivis utimur verbis in huiuscemodi sensibus. Abnegatives, in Greek, are Œ
and ¼
which, when they are connected to verbs, show that the thing might happen but has been prevented from happening for some reason or another ... In Latin, we indicate this sense without any connector, by putting the verb into the subjunctive. (XVI ii 1 [100.5–10])

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It is noteworthy that Priscian recognizes a class of connectors which has no Latin members. It is more remarkable that the two Greek particles are plainly not connectors at all — and that the description of the abnegatives as a class plainly shows they are adverbs. There are other more ambiguous, and therefore more interesting, cases. Here are two rather different examples. First, the ‘approbative’ connectors, among them the word ‘equidem’. Priscian cites Aeneid XII 931: equidem merui nec deprecor, [381] inquit.

(See XVI i 6 [97.4–5].) A little later he cites the same line in the course of his discussion of expletive connectors: completivam esse etiam Sallustius ostendit in Catilinario: verum enim vero is demum mihi vivere et frui anima videtur. hic enim ornatus causa vero adiuncta est, quamvis possit etiam approbativa esse. similiter Virgilius in XII: equidem merui nec deprecor, inquit. poterat sensus etiam sine equidem stare si dixisset ego merui nec deprecor; sed sive metri causa sive ornatus addidit equidem. That is expletive is shown by Sallust in his Catiline: verum enim vero is demum mihi vivere et frui anima videtur — for vero is added here for stylistic reasons (although it could also be approbative). Similarly Vergil, Book XII: equidem merui nec deprecor, inquit. The sense would remain the same without equidem — if he had said ego merui nec deprecor, inquit. He added equidem either for the metre or for stylistic reasons. (ii 13 [102.20–26])

The word ‘equidem ’, in this Vergilian line, is either expletive or approbative — and it is not easy to see how Priscian (or anyone else) might have chosen between those two options. But why think that ‘equidem’ is a connector at all? Surely it doesn’t function as a connector in the Vergilian line? For if it were a connector, it would have to connect one thing to another; but here it connects nothing with nothing: it certainly does not connect the four words which follow it — and nothing at all precedes it since it is the first word in Turnus’ last speech. The second example concerns the word ‘nam’. Although Priscian lists it among the expletives, he also treats it as a causal connector: et proprie causales sunt quae causativa, id est res ex causa antecedente evenientes, significant, ut doctus sum nam legi.

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Causal in the strict sense are those which mean something causative — that is, something coming about by an antecedent cause. For example: doctus sum nam legi. (XVI i 6 [96.23–24])

He says the same about ‘enim’, a synonym or near synonym of ‘nam’: enim quoque cum sit causalis e ªæ significat ... invenitur tamen etiam completiva quando  significat Graecam coniunctionem. enim too is, when it is causal, means ‘ªæ’ ... but it is also found as an expletive, when it means the Greek connector . (ii 15 [103.23–25])

According to Priscian, the words ‘nam’ et ‘enim’ are connectors. [382] In the case of ‘equidem’ it was difficult to find anything for it to connect. The same difficulty does not arise here. For Priscian surely thinks that in doctus sum nam legi the word ‘nam’ connects the two verbs ‘sum’ and ‘legi ’; and if you don’t like that, you may say that it connects the two sentences ‘doctus sum’ and ‘legi ’. Nonetheless, you may wonder if ‘nam’ and ‘enim’ really are connectors — for the following reason. If ‘nam’ is a connector in doctus sum nam legi then doctus sum nam legi is itself a sentence. But it isn’t: it is two sentences, namely doctus sum followed by nam legi. The word ‘nam’ is not a connector which connects the parts of a sentence (or which connects two sentences): it is an adverb. To be sure, the word ‘nam’ makes a connection between the sentence which it introduces and the preceding sentence. To be sure, you might express that connection by using a connector — by saying, for example, doctus sum quia legi. But that doesn’t show that ‘nam’ is a connector, and it isn’t — because doctus sum nam legi isn’t a sentence. Or is it? Priscian says that a sentence is a sequence of words which expresses a complete thought. But he doesn’t explain how we should count sentences or decide if a given sequence of words is one sentence, or two sentences, or three sentences, ... When Julius Caesar announced veni vidi vici,

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did he express a complete thought? I mean, did he express one single complete thought? or did he rather express three complete thoughts, one after another. Priscian supplies no material for an answer to the question. Perhaps the question is trifling? Perhaps the answer to it is a matter of taste or of typography? One sentence or three? — One if you add a couple of commas, and three if you add a pair of full stops. And which should you add? — It is up to you, it makes no difference to Julius Caesar or to anyone else alive or dead. Punctuation is surely a matter of taste. But I am not sure that it is a matter of taste whether Caesar said one thing or three. At any rate, there are familiar tests which seem to supply objective answers — taste-free answers — to questions of this sort. One such test appeals to embedding. The general form of the test is this: A sequence of words  (in a language L) is a sentence if C() is well formed. A simple case of that formal schema concerns negation: [383] A sequence of words  (in a language L) is a sentence if the sequence neg þ  (where neg is an expression in L which means ‘It is not the case that’) is well formed. Another case, of a type of which there are numerous particular examples, concerns expressions which express ‘propositional attitudes’. For example: A sequence of French words  is a sentence if the sequence ‘Priscien affirme que’ followed by  is well formed. Such tests apply only to indicative sentences; but it is easy to adapt them to imperatives and interrogatives and the rest. A sequence of words  is a sentence if and only if it passes at least one of the embedding tests. So apply the tests to some Latin sequences. The expression ‘veni ’ turns out to be a sentence inasmuch as (say) dixi quod veni is well formed. On the other hand, veni vidi vici isn’t a sentence — I mean, isn’t one single sentence. What about doctus sum nam legi? That sequence isn’t a sentence either. True, you can construe the sequence dico quod doctus sum nam legi; but on condition that ‘legi ’ is co-ordinate with ‘dico’. In other words, [dico quod doctus sum] nam legi

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is well formed, but dico quod [doctus sum nam legi] is not. (The same goes, mutatis mutandis, for ‘enim’.) In Book XVI, ‘nam’ and ‘enim’ are causal connectors. In Book XVIII, at xxi 173 [287.8–10], they are classified as causales vel rationales. The class of rational connectors, as it is described in Book XVI, includes ‘ergo’, ‘itaque’, ‘igitur’, ... (ii 11–12 [100.15–101.8]); and the rational connectors — that is to say, the connectors which signal the articulation of an argument — are all in the same case as ‘nam’ and ‘enim’. But ‘ergo’, say, is not a connector. According to the embedding tests, the Latin sequence cogito ergo sum is not a sentence. For sequences such as non cogito ergo sum or ego Cartesius dico quod cogito ergo sum are ill formed. So Priscian is mistaken: what he classifies as rational connectors are not connectors at all. The word ‘itaque’ is not a connector: it is an adverb, a deictic sentential adverb, a deictic adsentence. But that is another story.

25 Late Greek syllogistic* The history of logic in late antiquity has not been a favourite subject of scholarly inquiry. The texts are imagined to be long, dull, and repetitive: they are perhaps quarries for information about earlier logicians, but their own content is unoriginal and unexciting. Anyone who holds that view should read Tae-Soo Lee’s monograph on the subject. Late Greek syllogistic emerges from Lee’s study as a subject well worth examination. Admittedly, it is not original in any strong sense. But it does offer numerous clarifications, developments, and modifications in Aristotle’s doctrines, many of which are intelligent and some of which are subtle. Lee takes as his primary texts the three surviving commentaries on the Prior Analytics — the commentaries of Alexander, of Ammonius, and of Philoponus. He examines their general conception of the nature of logic, explaining in what sense logic for them is genuinely ‘formal’ and in what sense it is nevertheless only an ‘instrument’ or ‘tool’ — an ZæªÆ

— and not a proper part of philosophy. He scrutinizes their notion of a proposition or æ ÆØ, their complex classification of ıÇıªÆØ or pairs of propositions, and their accounts of the operation of conversion or I
Øæ ç. He looks at their definition of what a syllogism is, and at their ideas about a systematic development of syllogistic. In sum, he describes a version of categorical syllogistic which stands midway between the original theory of Aristotle and the traditional logic of the mediaeval and modern schoolmen. As we should expect from a study prepared in Go¨ttingen, Lee’s monograph is admirable in its execution. He writes lucidly and he avoids cant. His analyses are acute and rigorous. He knows modern logic but he does [93] not clutter his text with anachronistic symbols. His arguments are almost always clear. In the course of his discussion Lee incidentally sheds light on a number of obscure parts of the Aristotelian tradition. For example, he has an excellent * First published in Phronesis 30, 1985, 92–98, as a review of Tae-Soo Lee, Die griechische Tradition der aristotelischen Syllogistik in der Spa¨tantike, Hypomnemata 79 (Go¨ttingen, 1984).

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account of the Greek idea of ‘form’ in logic; he gives a lucid explanation of what is involved in the idea that logic is (only) an instrument or tool of philosophy; he is illuminating on the dark topic of conversion. He also has wise words to say about the nature of his own enterprise: ‘I think that the main task of an historian is not simply to exclaim: ‘‘Look here — they already knew such and such’’ (usually adding: ‘‘but somewhat imperfectly and not with complete clarity’’). On the contrary, if an ancient author is worth our attention, that is not only because he already knew something which we too now know, but also — and more importantly — because his mode of thinking was different from ours’ (p.22). Lee does not purport to give a complete or definitive account of the later history of the categorical syllogism, so that it would be impertinent to criticize him for ignoring certain aspects of the subject. But it is not, I think, inappropriate to question his choice of texts. First, it needs to be noted that Ammonius and Philoponus are separated from Alexander by some three centuries — and by the development of late Platonism. It is far from plain that the three commentaries can properly be collected under the rubric of ‘syllogistic in late antiquity’. Certainly, the commentatorial tradition, perhaps especially in logic, was extremely conservative. But even so there are notable differences, as Lee himself regularly reports, between Alexander and the two later men. Lee’s monograph is in effect a study of two distinct phases in the history of syllogistic. Secondly, Lee might with advantage have adduced a few texts from the same epoch as Alexander’s commentary on the Prior Analytics. There is also Alexander’s long commentary on the Topics, a less talented work, perhaps, but one which contains much excellent stuff, particularly in its earlier pages. Or there are Galen’s Institutio Logica and Apuleius’ de Interpretatione. Both are short introductory text-books, and neither is comparable in scope or depth to Alexander’s commentaries. But they are roughly contemporary with Alexander, and they are similar in doctrine. It is a pity that Lee makes virtually no reference to them. Thirdly, there is a remarkable omission at the other end of Lee’s time-span: Boethius, whose works on categorical syllogistic constitute the longest and most systematic essay on the subject to survive from late antiquity, is barely mentioned. There is a reason for this. Lee thinks that Boethius’ [94] importance in the history of logic has been greatly exaggerated. ‘As far, at any rate, as the logic of the Prior Analytics is concerned, almost everything in Boethius comes from his Greek predecessors, while much that does not appear in

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Boethius (nor in Apuleius or Martianus Capella or Isidore) but does appear in the mediaeval and traditional logic texts can be found in the Greek commentators’ (p.19 n.13). That is a strong claim, and one which Lee does not attempt to substantiate in his monograph. But even if it is true, Boethius remains, for us, a major figure in the history of late Peripatetic logic, and that in itself is sufficient reason for setting him alongside Ammonius and Philoponus. Ammonius’ commentary on the Prior Analytics must strike even the most casual reader as inferior to Alexander’s. That impression is confirmed by Lee’s detailed comparisons: where Ammonius and Alexander differ, the difference is almost always to Alexander’s advantage. Lee records a single striking exception to this general truth. In his definition of ‘perfect’ syllogisms Aristotle uses the word ‘çÆ
B
ÆØ’ and not ‘ª
ŁÆØ’: a perfect syllogism is one which needs nothing adventitious ‘in order that the necessity be apparent’. The verb is crucial: Alexander does not comment upon it, Ammonius does — and his explanation is very plausible (see pp.130–131). More interesting, and perhaps more surprising, is the comparison between Philoponus and Ammonius. Philoponus was a pupil of Ammonius. In his commentary on the Prior Analytics he followed his master closely. He does not appear to have intended an independent interpretation of Aristotle’s text: rather, he aimed to produce an expanded version of Ammonius’ work. Since Ammonius’ commentary has not survived intact, Lee is obliged to use Philoponus in certain parts; and he might well have supposed that he would find there, in effect, a magnification of Ammonius’ lost work. Magnification indeed — but also distortion. Where Ammonius’ text survives we can see that Philoponus has often misunderstood it. And he frequently misunderstands Aristotle. Time and again he errs. He makes gross mistakes and falls into hopeless confusions. He is perhaps at his worst in his account of conversion. After a careful analysis of the discussion, Lee — who generally and deliberately refrains from critical comment — allows himself a summary judgement: ‘the passage discussed here is one of the numerous proofs of the highly suspect character of Philoponus’ writing. Carelessness conjoined with ignorance — and also prolixity — are the features of his style’ (p.83). For other examples of the ‘numerous proofs’, see pp.29, 31, 42, 43, 53, 61, 76, 81–84, 88, 89–92. On only one point — and [95] that a trifling question of terminology — does Philoponus improve upon Ammonius (see p.105). In short, Philoponus was a duffer at logic. In some quarters

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Philoponus is enjoying a sort of renascence: his champions must read Lee’s depressing chronicle with attention. There are places where Lee is open to criticism. His grasp on logical matters is usually firm, but it occasionally slips. Thus he seems to confuse identity with biconditionality or equivalence (p.82). In order to illustrate the difference between a declarative sentence and a non-declarative sentence — between a º ª  which is I çÆ
ØŒ  and one which is not —, he observes that ‘today every good student of logic recognizes the importance of the distinction between e.g. ‘A is B’ and ‘jj— A is B’ (p.30); but in fact — and whatever any good student of logic may make of Frege’s assertion sign — that distinction is not to the point. Again, he applauds Ammonius’ attempt to explain the difference between necessitas consequentiae and necessitas consequentis (p.104). But Ammonius’ attempt is thoroughly confused: he explains necessitas consequentiae as necessity of the sequence of expressions or IŒ º ıŁÆ H
ºø
, necessitas consequentis as necessity of the holding of things or oÆæØ H
æƪø
. I don’t know what that might mean; but in any event it is plain that Ammonius has no inkling of the notion of scope distinction, without which the distinction cannot be explained (and with which it is immediately clear). Again, I should be inclined to question Lee’s interpretation of the Greek texts at certain points. Thus his way of classifying in systematic fashion all possible pairs or propositions or ıÇıªÆØ (pp.66–68) inevitably introduces a fourth figure of syllogisms; but as Lee himself notes (p.71), the commentators did not recognize a fourth figure any more than Aristotle had done, and in fact their way of dealing with ıÇıªÆØ — which is essentially Aristotle’s way — excludes the possibility of more than three syllogistic figures. Here Lee is more schematic than the ancient schematizers, and he misrepresents their intentions. Then, on p.108 he concludes that ‘Alexander seems to believe that syllogistic necessity is something more than formal validity, and hence that the syllogism has a special status compared to certain other sorts of valid inference’. Certainly, Alexander thinks that categorical syllogisms have a special logical status; but I do not believe that he ascribes to them something more than formal validity. He says, following Aristotle, that there are arguments in which the premisses yield the conclusions necessarily but not syllogistically. His examples, and his brief theoretical remarks, indicate that necessary but non-syllogistic arguments are arguments which are valid but not formally valid. He does not mean that they are formally valid but not ‘superformally’ valid — an idea which in any case is near to

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nonsense. And although his views about what arguments are formally valid are misconceived, we should congratulate him on formulating the important distinction between validity and formal validity. Those criticisms are minor, local and disputable. In only one passage am I inclined to suspect Lee of more serious error. The passage is significant, if [96] only because it is the sole case in which Lee ventures to find fault with Alexander. It concerns Alexander’s views on the relation between the ‘generation’ of the syllogistic figures and the ‘analysis’ of the syllogistic moods. The notion of analysis is familiar from Aristotle: the moods of the second and third figures are ‘analysed’ into, or (equivalently) ‘reduced’ to, those of the first figure, and are thereby proved. To say that a schema A ‘analyses’ into a schema B is to say that A can be logically derived from B. The notion of generation is less familiar — it is not found in Aristotle — but it is equally simple. The second and third figures are ‘generated’ from the first in the following sense. The first figure is determined by the ıÇıªÆ PxM, MxS (I use the standard Patzig notation.) That is to say, a syllogism belongs to the first figure if and only if the term common to its two premisses is subject in one of them and predicate in the other. If you interchange the terms in PxM you get: MxP, MxS which is the ıÇıªÆ which determines the second figure. Similarly, interchange the terms in MxS and you get PxM, SxM which is the ıÇıªÆ for the third figure. (The Greek for ‘interchange the terms of ’ is ‘I
ØæçØ
’ or ‘convert’. The word is unfortunately used in several distinct logical senses: Philoponus characteristically confuses them, but Alexander explains them carefully and does not let himself be misled by the ambiguities.) The generation of the figures has some prominence in Alexander’s commentary. Lee asserts that ‘to all appearances, Alexander believes that the reductions undertaken in A 4–6 can be justified as proofs precisely because they rely, in a logical sense, on the procedures of figure generation’ (p.121). As Lee is aware, the thesis which he is ascribing to Alexander is worse than false — it is horribly confused. For, according to Lee, the generation of the figures has a metaphysical or ontological significance for Alexander, so that Alexander wants to ground the purely logical operation of analysis on some half-baked metaphysical notion of generation.

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Is Lee’s accusation just? In support of his interpretation he cites only one text from Alexander: Each of the figures is generated from the first figure by the conversion of a premiss. When this premiss is converted again, they are analysed into, or reduced to, the first figure, and this analysis proves their formal validity. (in APr 97.27–30)*

For Lee’s interpretation, Alexander’s use of the word ‘again’ is crucial. It shows, he thinks, that in Alexander’s view generation is logically prior to analysis, and hence that analysis is probative precisely because it has generation to back it up. [97] But I can see no reason to follow Lee here. The word ‘again’ does not in itself carry any suggestion of logical priority. (Had Alexander wanted to stress the priority of generation he could readily have done so: he cannot have used ‘ºØ
’ merely for want of a better word.) Nor does the context of the passage contain any hint that he was thinking of grounding analysis on generation.** Later, in his discussion of ‘wholly hypothetical’ syllogisms, Alexander again alludes to the connexion between analysis and generation, and he expressly compares the hypothetical with the categorical case (in APr 327.32–35). Here too there is no hint that ontological generation is supposed to be the basis of logical analysis. Lee also cites a passage from Boethius (p.127 n.16); but I cannot see the offensive thesis in that passage either — nor yet in the parallel from Apuleius (int x [207.7–9]) which Lee does not cite. He does cite a passage from Themistius’ Reply to Maximus (p.121 n.10). The Reply exists only in an Arabic translation. The relevant sentence reads like this: The experts in these matters say that the syllogisms of the two last figures are reduced in the direction of the first figure because their truth cannot come from themselves but from the first figure.***

Themistius means, I suppose, that the ‘truth’ — that is, the validity — of second- and third-figure syllogisms derives from the ‘truth’ or validity of firstfigure syllogisms; and that is why second- and third-figure syllogisms are * Iç’ w ªaæ æ ø ŒÆæfiø H
åÅø
I
ØæÆçÅ KŒ  F æ ı åÆ  ª
Ø, ÆÅ I
Øæç 
Å ºØ
ήd I
ºıØ ŒÆd I
ƪøªc ÆPH
N e æH
ª
ÆØ åBÆ, Ø’ w I
ƺø Œ
ı
ÆØ e ıºº ªØØŒe
å
. ** Even so, Alexander is not above all criticism: he is at any rate trying to make some sort of correlation between generation and analysis; and to do so he must slide over the fact that it is figures (not syllogisms) which are generated, and syllogisms (not figures) which are analysed. *** I translate from the unpublished French translation of Marwan Rashed. Lee used the French version in A. Badawi, La transmission de la philosophie grecque au monde arabe (Paris, 1968 [19872]),

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reduced to the first figure (rather than, say, first- and second-figure syllogisms being reduced to the third figure). So far as I can see, that remark does not allude to the generation of the figures. Lee concludes that ‘Alexander ... has no clear understanding of the logical structure of the proof procedures in the Prior Analytics’ (p.124). The passage he cites does not support that conclusion. On the contrary, it shows that Alexander has understood a fairly simple logical truth about the proof procedures. If a second- or third-figure syllogism can be proved from a first-figure syllogism by conversion, then the second or third figure can be generated from the first figure by interchange of terms. For example, Cesare II is proved from Celarent I as follows: 1 2 1 1, 2

(1) (2) (3) (4)

MeP MaS PeM PeS

assumption assumption 1, conversion 3,2 Celarent

Given that proof by conversion, we can see that the first figure must generate the second by interchanging the terms of PxM; for otherwise the conversion of MeP into PeM at step (3) of the proof could not yield the premisses of the first-figure syllogism Celarent. Alexander’s remarks in the passage are certainly not faultless. He must be criticized for using the same word, ‘I
ØæçØ
’ in successive lines to [98] designate the two completely different operations of term interchange and premiss conversion. But, as I have already remarked, he is aware of the ambiguity of the word and is not himself misled by it. Again, we might doubt whether the operation of generation has the importance which Alexander seems to ascribe to it. And if Lee is right in ascribing some metaphysical or ontological significance to the notion, then we should weep. But however that may be, I do not think that Alexander can rightly be convicted of logical misdemeanours on this particular point. pp.166–180 [pp.180–194]: the sentence in question is on p.176 [p.190]. There are no significant differences, on this point, between Badawi and Rashed.

26 Boethius and the study of logic* I When Theoderic was asked by the king of the Burgundians to send him a mechanical waterclock-cum-sundial, it was Boethius who was invited to supervise the commission. The letter of invitation, purple with panegyric, rehearses Boethius’ qualifications for the task: From far away you entered the schools of Athens; you introduced a Roman toga into the throng of Greek cloaks; and in your hands Greek teachings have become Roman doctrine. For you have shown with what profundity speculative philosophy and its parts are studied, and with what rationality practical philosophy and its branches are investigated; and whatever wonders the sons of Cecrops bestowed upon the world, you have conveyed to the senators of Romulus. Thanks to your translations, Pythagoras the musician and Ptolemy the astronomer may be read as Italians; Nicomachus the arithmetician and Euclid the geometer speak as Ausonians; Plato the theologian and Aristotle the logician dispute in the language of the Quirinal; Archimedes the physicist you have restored to the Sicilians as a Latin: it is by your sole exertions that Rome may now cultivate in her mother tongue all those arts and skills which the fertile minds of Greece discovered.1

Boethius, according to Theoderic, had brought the civilization of Greece to Rome, and naturalized it there. And Boethius himself encouraged such a view of his intellectual labours: writing in the year of his consulship, he boasts that ‘I shall not deserve ill of my fellow citizens if, after the virtue of men of old has brought power and [74] empire over all other cities to this one republic, I shall perform the task that remains and instruct our state in the arts of Greek wisdom’ (in Cat 201B). One of those arts — one of the wonders bestowed on * First published in M. Gibson (ed), Boethius (Oxford, 1981), pp.73–89. 1 Cassiodorus, Variae i 45; cf i 10 (Boethius, as an expert arithmetician, is asked to give his advice on matters of the coinage); ii 40 (Boethius, as an expert on music, is consulted when the king of the Franks asks Theoderic to send him a musician).

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the world by the sons of Cecrops — was philosophy; and Boethius devoted himself to the wisdom of Plato and of Aristotle: I shall translate into Latin every work of Aristotle’s that comes into my hands, and I shall write commentaries on all of them: any subtlety of logic, any depth of moral insight, any perception of scientific truth that Aristotle has set down, I shall arrange, translate, and illuminate by the light of a commentary; and I shall also translate and comment upon all Plato’s dialogues and put them into Latin. (in Int2 79.16–80.1)2

The first part of Aristotle’s philosophy is logic. According to Cassiodorus, Boethius ‘was so eminent in translating the art of logic or dialectic, and in the mathematical disciplines, that he equalled or excelled the ancient authors’.3 And it was Boethius’ early plan to present Peripatetic logic to the Latin world: Fabius, the fictional interlocutor in Boethius’ first commentary on Porphyry’s Isagoge, announces at the end of the dialogue that ‘I shall never grow weary of these studies, with you as my teacher; and I shall perhaps learn, if life allows, the whole discipline of Aristotle’s logic’ (in Isag1 13.126–132.2).* Within the audacious policy of making Greek wisdom available to the Latins lies the grand project of turning Aristotle into a Roman; within the grand project lies the ambitious plan of composing a Peripatetic logic in Latin. The policy could never have been more than a dream; the project would have taxed Boethius’ powers, even had he survived the suspicions of Theoderic; but the plan was realistic — and largely realized. Boethius’ design was, as both he and Cassiodorus emphasize, a design for translation; but translation has a broad and a narrow sense: Peripatetic logic was to be transferred from Greece to Rome, made audible to Latin ears; and the means by which that transference or translation was to be achieved was translation in the narrower sense.4 2 ego omne Aristotelis opus quodcumque in manus venerit in Romanum stilum vertens eorum omnium commenta Latina oratione perscribam ut si quid ex logicae artis subtilitate ex moralis gravitate peritiae ex naturalis acumine veritatis ab Aristotele conscriptum est id omne ordinatum transferam atque etiam quodam lumine commentationis inlustrem; omnesque Platonis dialogos vertendo vel etiam commentando in Latinam redigam formam. — On Boethius’ intellectual plans, see A. Kappelmacher, ‘Die schriftstellerische Plan des Boethius’, Wiener Studien 46, 1928, 215–225. 3 See anecdoton Holderi, 4. * ego numquam deficiam ab his studiis te praesertim docente a quo totam fortasse logicae Aristotelis — si vita suppetet — capiam disciplinam. 4 For Cassiodorus’ concern to get Greek texts, both sacred and secular, done into Latin, see e.g. inst I ix 5; xxiii 2 (note too II iv 7, which refers to Boethius’ translation of Nicomachus, and also to an earlier version by Apuleius); in general, see P. Courcelle, Late Latin Writers and their Greek Sources, trans H.E. Wedeck (Cambridge MA, 1969).

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Boethius’ logical œuvre contains works of three types. First, and at the centre, there are the Latin translations of the Greek texts: Boethius put into Latin the Categories, the de Interpretatione, the Prior and Posterior Analytics,5 the Topics, the Sophistici Elenchi; and he prefaced his Latin Organon with a version of Porphyry’s Isagoge, the standard Greek introduction to Peripatetic philosophy.6 Secondly, there are the commentaries: Boethius planned commentaries on the [75] Isagoge and on each book of the Greek Organon, and he added, as a supplement, a commentary on Cicero’s Topics.7 The commentaries on Aristotle’s Topics and Analytics have not survived; and some scholars doubt if Boethius lived to complete his commentatorial task.8 Thirdly, there are the treatises: On Division covered much of the ground tilled in the Categories; On Categorical Syllogisms and the unfinished Introduction to Categorical Syllogisms correspond in part to the de Interpretatione and the Prior Analytics. On Hypothetical Syllogisms has no counterpart in Aristotle’s works, but answers to a fixed feature of later Peripatetic logic. On Topical Differences matches Aristotle’s Topics.9 Thus on three distinct levels Boethius translated Peripatetic logic from Greece to Rome. His achievement is remarkable by any reckoning; and his work in logic stands as a paradigm of sustained and systematic scholarship. The next three sections will discuss separately the translations, the 5 The translation of the Posterior Analytics has not survived; but see Aristoteles Latinus iv 1–4, pp.XII–XV. 6 For the status of the Isagoge, see in Isag1 14.8–25. Boethius regarded the Organon, prefaced by the Isagoge, as a unitary — but not a fully comprehensive — treatment of logic. 7 At first blush, the commentary on Cicero seems anomalous; but in fact Cicero presents his Topics as a version — indeed, as a translation — of Aristotle’s Topics, and Boethius regarded Cicero’s work as forming an integral part of Peripatetic logic (see in Cic Top 272.4–26 — but in truth Boethius is there paraphrasing Cicero). 8 (i) Topics: Boethius states categorically that he has written a commentary (top diff 1191A; 1209C; 1216D). Nothing is known to have survived. (ii) Prior Analytics: we possess only preliminary notes (published in Aristoteles Latinus iii 1–4); at syll cat 829D Boethius says that he will comment on the Analytics, but he nowhere asserts that he has composed such a commentary. (iii) Posterior Analytics: a note to a thirteenth-century commentary on the Sophistici Elenchi quotes from Boethius’ commentary on Book I of the Posterior Analytics: see S. Ebbesen, ‘Manlius Boethius on Aristotle’s Analytica Posteriora’, Cahiers de l’Institut du Moyen-Aˆge Grec et Latin, 1973, 68–69. If we believe the note, then — contrary to orthodox opinion — Boethius did write such a commentary. 9 The dating of Boethius’ logical works is to some extent conjectural: see L.M. de Rijk, ‘On the chronology of Boethius’ works on logic’, Vivarium 2, 1964, 1–49, 125–162. — His first opus was in Isag1, composed in 504/5; he was probably working on int syll cat and in APr in 523; in Cat is dated to 510. There is not much awry with the following ordering: in Isag1; syll cat; div; trans Isag; in Isag2; trans Cat; in Cat; trans de Int; in Int1; in Int2; trans Top; trans Soph El; syll hyp; in Top; in Cic Top; trans An; top diff; int syll cat; in APr.

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commentaries, and the treatises; but it should not be forgotten that, for Boethius, those three types of scholarly production were complementary parts of a unitary whole.

II Boethius based his first commentary on the Isagoge on the Latin translation of Marius Victorinus.10 But he was not satisfied with what he read: Victorinus paraphrases, and thus misinterprets, Porphyry’s account of the varieties of genera (in Isag1 34.12–35.6); again, ‘it seems that Victorinus has made a mistake’ in his account of species (ibid, 64.8–13); again, one passage is ‘very difficult — but rather because of the obscurity of Victorinus’ translation than because of what Porphyry says’, for either Victorinus used a bad Greek text or else he translated ‘I
º ª
’ as though it were ‘¼º ª
’ (ibid, 94.11–95.17). Victorinus’ translation has survived only in the sentences Boethius chose to quote from it; but it is clear that Boethius’ strictures were justified, and that he was right to retranslate the Isagoge before writing a second commentary upon it. As for Aristotle’s logical texts, Boethius claims originality: Hardly anyone has undertaken a continuous course of translation, let alone of commentary — except that Vettius Praetextatus has put the Prior and Posterior Analytics into Latin, not by translating Aristotle but by rendering Themistius — as anyone who reads both will easily see. [76] Albinus too is said to have written on the same subjects; but although I know the books on geometry which he produced, I have not managed to find any books on logic despite a long and careful search. Thus if he said nothing, I shall repair the omission; while if he did write something, I too, by imitating the study of a learned man, shall deserve the same praise. (in Int 2 3.5–4.9)* 10 See in Isag1 4.10–14; in Isag2 347.24–26; cf Cassiodorus, inst II iii 18. The fragments of Victorinus’ translation are published in Aristoteles Latinus i 6–7, and also in P. Hadot, Marius Victorinus (Paris, 1971), pp.367–380. See also Cassiodorus, inst II iii 1 for a general reference to Latin translations of Aristotle’s logic. * non facile quisquam vel transferendi vel etiam commentandi continuam sumpserit seriem — nisi quod Vettius Praetextatus priores postremosque analyticos non vertendo Aristotelem Latino sermoni tradidit sed transferendo Themistium, quod qui utrosque legit facile intellegit. Albinus quoque de isdem rebus scripsisse perhibetur, cuius ego geometricos quidem libros editos scio, de dialectica vero diu multumque quaesitos reperire non valui. sive igitur ille omnino tacuit nos praetermissa dicemus, sive aliquid scripsit nos quoque docti viri imitati studium in eadem laude versabimur.

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We have no reason to disbelieve Boethius: if he was not the first to put the Organon into Latin, at any rate a conscientious search could discover no precursor.11 Boethius took immense pains over his translations. Two versions of the Categories and two of the Prior Analytics have survived; and it is plausible to suppose that in the case of each treatise the translation went through more than one edition. Detailed comparison of the surviving twins reveals the meticulous care with which Boethius sought to capture the sense of the original Greek.12 Occasionally the commentaries give us a glimpse of the translator at work. Thus Boethius notes that here Aristotle uses a novel and admirable turn of phrase: quod complectitur. I spent much time trying to produce a translation within the bounds of Latinity, and that is the best I could do. But in truth it is expressed more clearly in the Greek, where it runs: a b e
æØ. (in Int 2 70.20 –71.1)

Boethius was not the first Roman philosopher to complain of patrii sermonis egestas. Again, Boethius translates a phrase from the de Interpretatione by ‘etenim hominis ratio, si non aut est aut erit ... ’. The Greek has no word answering to ‘ratio’; and Boethius explains at length why he introduced the word into his Latin version. Aristotle’s Greek text does not run as we have rendered it, but rather thus: ‘etenim hominis, si non aut est aut erit ... ’ — the philosopher leaving it to be understood that he is talking about the ratio, i.e. the definition, of man, for which the Greek term is º ª . Since he has just been talking about sentences, for which the Greek is again º ª , and now wants to talk about the ratio, i.e. the definition, of man ... , he makes use of the common word and refers back to º ª  which he has just been discussing, intending the word now in the sense not of oratio but of ratio. That explanation should satisfy those Greek experts who may perhaps find fault with my translation, and it should explain why I have added something not found in the original: I added the word with a view to the easier understanding of the Latin; for when we are talking 11 Cassiodorus, inst II iii 18 purports to give a survey of Latin logicians: the text survives in two very different versions — see e.g. Hadot, Victorinus, pp.105–115; J. Barnes, ‘Les cate´gories et les Cate´gories’, in O. Bruun and L. Corti (eds), Les Cate´gories et leur Histoire (Paris, 2005), pp.11–80, on pp.64–67 [English version above, pp.187–265]. 12 The introductions to the relevant volumes of Aristoteles Latinus give comprehensive information about the style and nature of Boethius’ translations; see also L. Minio-Paluello, ‘Les traductions et les commentaires aristote´liciens de Boe`ce’, Studia Patristica 2, 1957, 358–365 [= his Opuscula (Amsterdam, 1972), pp.328–335].

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about oratio, our minds cannot turn to ratio unless that word is explicitly added. (in Int 1 72.23–73.13)* [77]

All translation is difficult; and there are peculiar difficulties — experto credite — in translating Aristotle’s logic. Boethius rightly set himself to produce a literal version of the Greek: every nuance and every implication of the original had to be preserved, at whatever cost in loss of elegance or style. Boethius’ Latin is rough and rugged: syntax is strained; ugly technicalities are introduced; neologism and artifice are sometimes called upon. The result is not charming, but it is faithful; and Boethius’ Latin could observe the subtle turns, as well as the general direction, of Aristotle’s thought. Boethius was fully conscious of the shortcomings of his Latin style: I fear that I shall suffer the accusation usually levelled against a faithful interpreter; for I have rendered my text word for word. My reason for doing so is that in works where knowledge is being sought, what must be expressed is not the elegance of limpid prose but the unvarnished truth. Thus I shall seem to have achieved something if I have managed to put these works of philosophy into Latin with complete and pure fidelity of translation, so that the reader has nothing further to seek in the Greek originals. (in Isag 2 135.6–13)**

The Latin must be so close to the Greek that were the Greek text lost none of Aristotle’s thought would be lost with it: if fidelity produces inelegance, so be it — elegance matters less than truth. Some decades ago, the Clarendon Press inaugurated a series of translations of Aristotle designed to be of service to the Greekless philosopher: the Clarendon Aristotle had the same depressing motivation as the Boethius Aristotle; and the Clarendon translations have most of the virtues and the vices of Boethius’ translations. The goal of the two enterprises is no doubt * Aristotelis Graecus textus non habet ita ut nos supra posuimus sed hoc modo: etenim hominis, si non aut est aut erit aut fuit et caetera, subintellegendum relinquente philosopho quod de ratione diceret, id est definitione quam Graeci º ª
dicunt. sed cum supra de oratione tractasset, quae apud illos eodem modo º ª  vocatur, dum de hominis ratione, id est definitione, vellet dicere ... , communione vocabuli usus ad º ª
de quo superius tractabat rettulit ut non orationem intellegeremus sed potius rationem. de qua re illis nunc satisfacimus si qui Graecae orationis periti nos forte culpabunt cur quod illic non fuit nostrae translationi adiecerimus. nos enim ad faciliorem intellectum Latinae orationi famulantes hoc adposuimus quia de oratione loquentibus intellectus ad rationem nisi id esset adiectum transferri non poterat. ** vereor ne subierim fidi interpretis culpam cum verbum verbo expressum comparatumque reddiderim. cuius incepti ratio est quod in his scriptis in quibus rerum cognitio quaeritur, non luculentae orationis lepos sed incorrupta veritas exprimenda est. quocirca multum profecisse videor si philosophiae libris Latina oratione compositis per integerrimae translationis sinceritatem nihil in Graecorum litteris amplius desideretur.

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unattainable: translation, however faithful, will omit something present in the original, and import something absent from the original. But the goal can be approached; and if it is better to read Aristotle in translation than not to read Aristotle at all, then such an approach is to be admired. Boethius’ service to Aristotle is one which we, alas, are peculiarly able to appreciate.

III However carefully translated it may be, the Organon is a perplexing work: Aristotle’s style is craggy and abrupt, his arguments condensed and elusive; for his treatises were in all probability something like lecture-notes, and in any event not [78] works written up for general publication. So Aristotle needs a commentary: time and again, Boethius remarks upon the difficulties which Aristotle’s readers have to overcome. ‘He muddles his meaning by a confusing brevity, and he hides it in clouds of obscurity’ (in Int 2 99.25–27) — brevitas and obscuritas are features of Aristotle’ style on which all his commentators harp. Those features impose a double task on the commentator: he must be a philological guide, explaining what in Aristotle’s text is cryptic or crabbed; and he must be a philosophical exegete, analysing Aristotle’s arguments and teasing out the implications of his thought. Boethius was conscious of those twin duties; and he once thought to fulfil them by producing twin commentaries. At the beginning of his first commentary on the de Interpretatione he explains his purpose: This book is ascribed signal importance among the Peripatetic school; for in it Aristotle carefully examines the nature of simple propositions. But its path is rough and obstructed; and, being filled with subtle arguments, it does not give easy access to the understanding. For that reason I have devoted a double commentary to the elucidation of the book: the present treatment deals only with matters where Aristotle’s brief and obscure statements impede the simple understanding of his argument; a second volume will supply what is required for a more profound and pointed consideration. (in Int1 31.1–32.3)* * magna quidem huius libri apud Peripateticam sectam probatur auctoritas (hic namque Aristoteles simplicium propositionum naturam diligenter examinat); sed eius series scruposa impeditur semita et subtilibus pressa sententiis aditum intellegentiae facilem non relinquit. quocirca nos libri huius enodationem duplici commentatione supplevimus et quantum simplices quidem intellectus sententiarum oratio brevis obscuraque complectitur, tantum hac huius operis tractatione digessimus. quod vero altius acumen considerationis exposcit secundae series editionis expediet.

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Together, the two commentaries run to more than seven hundred pages: Aristotle’s text is barely thirty pages long. Boethius may have planned double commentaries on each part of the Organon; but he stresses the peculiar difficulty and importance of the de Interpretatione, and he perhaps thought that that work demanded special treatment. At all events, he is not known for sure to have written or projected twin commentaries on the other books of the Organon;13 and the two commentaries on Porphyry’s Isagoge are not strictly comparable to the two on the de Interpretatione.14 However that may be, Boethius certainly planned a sober and comprehensive series of commentaries. His earliest essay in the genre, the first commentary on the Isagoge, is cast in dialogue form and makes some small gesture towards literary style. But the dialogue is not a suitable form for learned commentary; and Boethius’ treatment of it is frigid. The later works are all written without literary embellishments: Boethius toils through the text paragraph by paragraph, line by line, word by word; his language is plain, clear, [79] workmanlike; he leaves nothing unexplained and he explains most things, sergeant-major fashion, three times over. The result is detailed and helpful commentary: it is not, and it was not intended to be, prose for pleasure. Boethius laboured long at his task. At the end of the commentary on the de Interpretatione he remarks that ‘the burden of this lengthy book should not discourage men from reading; it — for it did not stop me from writing it’ (in Int 2 422.5–6). For ‘this sixth book completes the long commentary which I have put together with great labour and expense of time. For I have collected into one book the opinions of many scholars, and I have sweated continuously over my commentary for a space of almost two years’ (ibid, 421.2–6). Boethius emphasizes his debt to earlier scholars. For his work on Cicero’s Topics he had before him the commentary by Marius Victorinus, and he 13 At in Cat 160A the text refers to ‘another commentary which I have proposed to write for the more learned on these same Categories’; but the passage is a later interpolation (see de Rijk, ‘Chronology’, pp.133–134). For all that, it is possible that Boethius did write a second commentary on the Categories; and indeed Pierre Hadot claims to have discovered a fragment of it: ‘Un fragment du commentaire perdu de Boe`ce sur les Cate´gories d’Aristote dans le Codex Bernensis 363’, Archives d’histoire doctrinale et litte´raire du Moyen Aˆge 26, 1959, 11–27 [¼ Plotin, Porphyre — ´etudes ne´oplatoniciennes (Paris, 1999), pp.383–410]. 14 For Boethius probably did not have in Isag 2 in mind when he wrote in Isag 1: at any rate, in Isag 1 13.126–132.2 (quoted above, p.74) suggests that his plan after writing in Isag 1 was to proceed to the Organon.

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spends some time in listing its inadequacies and in explaining why a new commentary is required (in Cic Top 270.16–271.17). For the Isagoge and the Organon Boethius had no Latin precursors;15 but Greek scholars had for centuries been producing learned commentaries on Aristotle’s works, and it is those men to whom he refers when he speaks of ‘collecting into one book the opinions of many scholars’. Indeed, Boethius’ commentaries largely consist of exposition and assessment of the views of his Greek predecessors; and much of the exposition is paraphrase or even direct translation — ‘I have prepared my commentary by translating into Latin Porphyry in particular but also others’ (in Int 2 7.5–7).* Modern scholars have discussed the question of Boethius’ sources. A superficial inspection might suggest that Boethius read widely in the writings of Aspasius, Alexander, Porphyry, Syrianus, Themistius and the rest, excerpting what he found most pertinent or worthy of record. Closer scrutiny reveals that much of Boethius’ learning is borrowed: his knowledge of scholars earlier than Porphyry is derived entirely from Porphyry’s own citations of his predecessors; and Boethius frequently follows the custom — not entirely unknown to modern scholars — of citing his sources at second hand. After all, do we not know from in Int 2 250.20–23 that Boethius possessed a manuscript of the de Interpretatione which contained abundant and ‘extremely obscure’ marginal comments or scholia? Is it not evident that what survives of Boethius’ work on the Prior Analytics is no more than a translation of such learned marginalia? Should we not suppose [80] that Boethius’ commentaries are nothing more than a cento of such translated scholia? So the ‘two years’ sweat’ on the de Interpretatione was not devoted to the perusal and collation of other men’s volumes; rather, it was spent in the decipherment and translation of a host of obscure notes scribbled in the margins of a single codex. If that theory is true, it presents Boethius’ scholarship in an unflattering light; and it raises fundamental questions about his own philosophical attitudes and aspirations. For example, when he refers to ‘us Peripatetics’, is he expressing his own adherence to Aristotelian doctrine, or merely translating the allegiance of his Greek source? When he presents a grandiose project 15 See in Int 2 3.5–4.9 (quoted above, p.[76]). Cassiodorus, inst II iii 18 ascribes a commentary on the Categories to Victorinus; but he is probably mistaken. (Victorinus’ commentary on Cicero’s Topics has not survived: fragments in Hadot, Victorinus, pp.313–321; his commentary on Cicero’s de Inventione is printed in C. Halm, Rhetores Latini Minores (Leipzig, 1863), pp.152–304). * cuius expositionem nos scilicet quam maxime a Porphyrio quamquam etiam a ceteris transferentes Latina oratione digessimus.

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for commenting upon the whole of Aristotle’s writings, is he announcing his own ambitions, or merely reporting the dead project of some old Greek scholar? How much about Boethius himself do we really learn from the commentaries? But the theory is less than compelling.16 That Boethius did sometimes translate scholia is true enough — the surviving notes on the Prior Analytics document the practice. But the difference between those short and inconsequential jottings and the polished commentary on the de Interpretatione shows that Boethius’ work cannot have been limited to a mechanical rendering of Greek scholia — and the manuscript equipped with extremely obscure notes is a phantom raised by a misreading of Boethius’ Latin.* The finished commentaries reveal on every page a thinking and organizing mind; and we know from the case of Cicero’s Topics that Boethius was well able to compose a commentary on his own. The ‘I’ and ‘we’ of Boethius’ texts certainly refer sometimes to Boethius himself — once, for example, he explicitly lays claim to originality: ‘that interpretation has, so far as I yet know, been proposed neither by Porphyry nor by any other commentator’ (in Int 2 121.25–26).** And I confess that I find it hard to conceive of a man of Boethius’ intellectual attainments translating a Greek ‘I’ or ‘we’ and not thinking that he might thereby be taken to advert to himself. Certainly, Boethius’ commentaries are largely derivative; certainly, they are often translation or paraphrase: that much Boethius himself openly proclaims — even in his commentaries he is still a translator of Greek 16 The theory is presented in detail by J. Shiel, ‘Boethius’ commentaries on Aristotle’, Mediaeval and Renaissance Studies 4, 1958, 217–244 [¼ R. Sorabji (ed), Aristotle Transformed (London, 1990), pp.349–372] (see also id, ‘Boethius and Eudemus’, Vivarium 12, 1974, 14–17); it is supported by Minio-Paluello, ‘Les traductions’, and by de Rijk, ‘Chronology’. For dissent, see C.J. de Vogel, ‘Boethiana I’, Vivarium 9, 1971, 49–66; E. Stump, ‘Boethius’ works on the Topics’, Vivarium 12, 1974, 77–93; S. Ebbesen, ‘Boethius as an Aristotelian scholar’, in J. Wiesner (ed), Aristoteles: Werke und Wirkung II (Berlin, 1987), pp.286–311 [¼ Sorabji, Aristotle Transformed, pp.373–391]; id, ‘The Aristotelian commentator’, in J. Marenbom (ed), The Cambridge Companion to Boethius (Cambridge, 2009), pp.34–55. * The text in question is this: est quidem libri huius ... obscura orationis series obscurissimis adiecta sententiis ... (in Int 2 250.20–23). The Latin does not mean ‘A manuscript of this book has an obscure course of argument with highly obscure notes added to it’: Boethius is referring to the de Interpretatione itself, not to a manuscript of the work; the orationis series is not the course of the argument but the sequence of Greek sentences; and the sententiae are not notes written in the margins by readers or scholars but the thoughts expressed by Aristotle. In short, Boethius means that in Int we find highly obscure thoughts expressed in obscure language. (That is a curious judgement; for surely Int is far clearer both in thought and in expression than most of Aristotle’s works. But it was the judgement of Boethius — and of Porphyry before him.) ** hanc expositionem (quod adhuc sciam) neque Porphyrius nec ullus alius commentatorum vidit.

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wisdom. But within those limits I incline to ascribe some originality to Boethius: he was out to present Greek logic to a Latin audience; he knew what that audience would require; and both the general tenor of the commentaries and some of the detailed annotation were planned by Boethius himself for his own readers. [81]

IV Two commentaries on the de Interpretatione were not enough: After these two commentaries on this book, I am producing a sort of handbook, in which I shall in several cases — indeed in almost all cases — make use of Aristotle’s own words, except that where he is brief and obscure I shall make some additions to clarify the course of his argument; thus I shall adopt a style as it were midway between the brevity of the text and the diffuseness of the commentary, abridging what is said diffusely and expanding what is written most concisely. (in Int 2 251.8–15)*

Boethius is not proposing a third commentary on Aristotle; rather, he is describing the style he adopts in what I have called his treatises. I too have decided to construct a sort of bridge to these highly obscure matters, setting things out in a middling fashion: whatever has been said briefly, I shall expand and make more intelligible; whatever Aristotle, in his usual manner, has confused by changing nouns or verbs, I shall present in ordinary terminology, thereby aiding the understanding; whatever he merely touches upon by way of allusion (he is writing for the learned), I shall set out, after the manner of an introduction, in an extended treatment. (syll cat 793CD)17

The treatises, taken together, were to present a Latin introduction to Peripatetic logic. * huius enim libri post has geminas commentationes quoddam breviarium facimus ita ut in quibusdam et fere in omnibus Aristotelis ipsius verbis utamur, tantum quod ille brevitate dixit obscure nos aliquibus additis dilucidiorem seriem adiectione faciamus ut quasi inter textus brevitatem commentationisque diffusionem medius ingrediatur stilus diffuse dicta colligens et angustissime scripta diffundens. 17 statui ego quoque in res obscurissimas aliquem quodam modo pontem ponere mediocriter unumquidque delibans ita ut si quid brevius dictum sit id nos dilatatione ad intelligentiam porrigamus, si quid suo more Aristoteles nominum verborumque mutatione turbavit nos intelligentiae servientes ad consuetum vocabulum reducamus, si quid vero ut ad doctos scribens summa tantum tangens designatione monstravit nos id introductionis modo aliqua in eas res tractatione disposita perquiramus. — cf int syll cat 761C; div 877A. But note that the commentary on the Categories also adopts a medius stilus : in Cat 159A.

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Boethius was not the first Roman logician: that honour goes to Varro.18 A little tract On Interpretation circulated under the name of Apuleius;19 Book IV of Martianus Capella’s Marriage of Philology and Mercury gives a potted Latin logic. Marius Victorinus wrote at length on hypothetical syllogisms — Cassiodorus counsels that ‘if anyone wants to gain a full understanding of the figures and moods of the syllogism, and of the difference between simple and complex syllogisms, he should read Aristotle from among the Greeks and Marius Victorinus from among the Latins’.20 But Boethius did not draw on Latin models: in his treatises, as in his commentaries, the Greeks were his primary sources. The breviarium was to be overtly derivative; and the work on categorical syllogisms was composed ‘by following Aristotle for the most part, and borrowing some things from Theophrastus and from Porphyry’ (syll cat 829D).* For hypothetical syllogistic Boethius had no source in Aristotle’s writings; but his treatment depends, indirectly, upon the treatises of Theophrastus and Eudemus (hyp syll I i 3).** On division is likewise derivative; and a main task of the [82] books On topical differences is to expound and combine the rival approaches to ‘topics’ of Cicero and of Themistius (top diff 1173C).21 Boethius divides his subject into two branches. The whole science of reasoning, which the old Peripatetics called logic, is divided into two parts, one of discovering, the other of judging. The part which purifies and 18 See e.g. Cicero, Acad iii 9; Cassiodorus, inst II iii 2. 19 cf Cassiodorus, inst II iii 12, 18. The attribution to Apuleius is contested, most scholars being sceptical. (But the best discussion of the work — M.K. Sullivan, Apuleian Logic (Amsterdam, 1967) — pleads on pp.9–14 in favour of the ascription. — On pp.209–227 Sullivan argues (to my mind unconvincingly) that Boethius read and used the work.) 20 expositio Psalmorum vii 6; see also inst II iii 13, 18. On Victorinus’ work, see Hadot, Victorinus, pp.144–163 (with the fragments collected on pp.323–327). Note that Capella and Victorinus presented a Stoic version of hypothetical syllogistic — had Boethius been acquainted with their work, he would not have used it; for he was concerned only with Peripatetic logic. A short tract by Victorinus On Definitions is still extant: text in Hadot, Victorinus, pp.329–362. At inst II iii 13 Cassiodorus refers to a comprehensive treatment of logic by one Tullius Marcellus: nothing else is known of the man, who may or may not have worked before Boethius. * Aristotelem plurimum sequens et aliqua de Theophrasto vel Porphyrio mutuatus ... ** And see S. Bobzien, ‘Wholly hypothetical syllogisms’, Phronesis 45, 2000, 87–137, on pp.111–115; ead, ‘A Greek parallel to Boethius’ de hypotheticis syllogismis’, Mnemosyne 55, 2002, 286–300. The Greek parallel is a short scholium on hypothetical syllogisms appended to a manuscript of the Analytics; the several and striking similarities between this text and parts of Boethius’ hyp syll strongly suggest that they have a common source — which may have been Boethius’ chief source. 21 For a survey of Boethus’ logical notions, see e.g. W.C. and M. Kneale, The Development of Logic (Oxford, 1962), pp.189–198.

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instructs the judgement is called analytics by them, and we may name it deconstruction. The part which aids competence in discovering is called topics by the Greeks, and commonplaces by us. (top diff 1173B)*

Topics is the subject of On topical differences. Following Cicero, Boethius defines a    or locus as a ‘seat of judgement’; and he explains that that is a ‘maximal’ proposition — a principle of argument which cannot itself be proved but which can be used for the generation of proofs (top diff 1185A). In truth, Boethius’ bipartition of logic, which he adopts from Cicero, is not particularly apt: topics deals with arguments which are informally valid (arguments, that is, which are not valid solely in virtue of their logical form); and although that study contains much of great interest, it is no more a ‘logic of discovery’ than analytics is. Analytics in turn divides into two, and the division rests upon a division of propositions into the simple and the complex: roughly speaking, a proposition is simple if it does not contain two or more propositions as parts; a proposition is complex if it does contain two or more propositions as parts.22 Thus ‘It is day’ is simple, ‘If it is day, it is light’ is complex. All simple propositions, according to Boethius, are ‘categorical’ or predicative; that is to say, they consist of a subject and a predicate.23 And categorical syllogistic, the first part of analytics, is the theory of arguments all of whose premisses are simple categorical propositions. Boethius’ account of categorical syllogistic is thoroughly Peripatetic: its main points of difference from Aristotle’s classic treatment in the Prior Analytics are that it includes a detailed consideration of negative terms24 and that it omits any discussion of modal syllogisms. The second part of analytics is the theory of the hypothetical syllogism. The theory is badly named: it deals with arguments some of whose premisses are complex propositions; and although hypothetical or conditional propositions are, from a logical point of view, the most important type of complex proposition, not all complex propositions are hypothetical — and Boethius’ logic uses conjunctions and disjunctions as well as conditionals. * omnis ratio disserendi quam logicen Peripatetici veteres appellaverunt in duas distribuitur partes, unam inveniendi alteram iudicandi. et ea quidem pars quae iudicium purgat atque instruit ab illis analytice vocata est, a nobis potest resolutoria nuncupari. ea vero quae inveniendi facultatem ministrat a Graecis topice a nobis localis dicitur. 22 ‘It is not day’ (or: ‘It is not the case that it is day’) counts as simple: it contains ‘it is day’ as a proper part, but it does not contain a plurality of propositions as proper parts. 23 What of ‘It is day’, or ‘dies est ’? Well, according to Boethius, the name ‘dies ’ is the subject and the verb ‘est ’ is predicated of it: si talis sit propositio quae solo nomine constet et verbo, veluti cum dicimus dies est, tunc dies subiicitur, est verbum sine dubio praedicatur (in Cic Top 353.18–20). 24 On which, see A.N. Prior, Formal Logic (Oxford, 19622), pp.126–134.

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Hypothetical logic was not developed by Aristotle; but after the [83] work of Theophrastus and Eudemus it became a standard part of Peripatetic studies. The Stoics developed a logical system which was hypothetical in Boethius’ sense and which came to be seen as a rival to Peripatetic analytics. Boethius knew Stoic logic, but he did not think to expound it.25 Indeed, he is generally dismissive of Stoic views: when his sources discuss Stoic doctrine, he often decides to pass it by — either because it would obscure the course of the argument (in Int 2 71.13–18) or because it ‘is not familiar to Latin ears’ (ibid, 201.2–6). We may regret the omission; but Boethius’ decision was, in its context, a sensible one. To the modern reader, On hypothetical syllogisms is perhaps the most interesting of Boethius’ logical treatises, both on historical and on philosophical grounds.26 From an historical point of view, it is a major source of information about a relatively ill-documented part of Peripatetic logic; philosophically speaking, it is difficult, perplexing; and stimulating. Boethius’ account of hypothetical arguments is highly elaborate; and it is based upon a puzzling view of the nature of hypothetical propositions. That puzzle is best approached by considering Boethius’ account of negative conditionals. Some hypothetical propositions are affirmative, others negative. Here I am speaking of those which, being posited in a relation of consequence, are said to be conditional. These are affirmative, as when we say: if A is, B is; if A is not, B is. Negative: if A is, B is not; if A is not, B is not. For you must look at the consequent in order to judge if a conditional is affirmative or negative. (hyp syll I ix 7)*

Take a conditional proposition of the form: (1) If P, then Q Boethius holds that the contradictory negation of (1) is: (2) If P, then not-Q Thus in effect he assimilates (2) to: (3) It is not the case that (if P, then Q). 25 But see in Cic Top 352.29–359.25. 26 On the whole subject, see K. Du¨rr, The Propositional Logic of Boethius (Amsterdam, 1951); L. Obertello, A.M.Severino Boezio: de hypotheticis syllogismis, Logicalia 1 (Brescia, 1969), pp.67–154. * sunt enim hypotheticae propositiones aliae quidem affirmativae aliae negativae. sed de his nunc loquor quae in consequentia positae in conexione esse dicuntur. affirmativae quidem ut cum dicimus: si est A, est B; si A non est, B est. negativae vero: si A est, B non est; si non est A, non est B. ad sequentem enim propositionem respiciendum est ut an affirmativa vel negativa sit propositio iudicetur.

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And that assimilation underlies and determines the form of his hypothetical syllogistic.* Now in standard modern logic, (2) and (3) are sharply distinguished: whenever (3) is true, (2) is true; but (2) may be true when (3) is false. In other words, (1) and (2) may be true together, so that they do not form a contradictory pair. Modern logic disagrees with Boethius at a fundamental level. It would be hasty to conclude that either Boethius or his modern successors must be mistaken. Modern logic, in its standard form, so defines the conditional that (1) and (2) may be true together. Had [84] Boethius adhered to that modern definition, he would have been simply mistaken in his account of negative conditionals. But there is no reason to believe that Boethius did adhere to the modern definition: on the contrary, we know that ancient logicians — like their modern counterparts — discussed at length the question of the truth-conditions of hypothetical propositions; the modern definition was familiar to them, but the major logicians, both Stoic and Peripatetic, preferred different analyses. And although our modern logical handbooks all adhere, for technical reasons, to the standard modern definition which turns conditionals into so-called ‘material implications’, modern * The remarks in this paragraph are ‘entirely incorrect’, according to C.J. Martin, ‘The logical textbooks and their influence’, in Marenbom, Companion, pp.56–84, on p.76. They are incorrect because ‘Boethius has no notion of propositional negation’. Rather, he ‘characterizes negation only for categorical propositions and insists that the negative particle must always apply to the predicate’ (p.63, referring to in Int 2 48.26–49.23). So ‘no sense can be made of in terms of propositional negation’ (p.80). See also id, ‘Boethius and the logic of negation’, Phronesis 36, 1991, 277–304; and (on the other side) M. Nasti de Vincentis, ‘Boethiana: la logica stoica nelle testimonianze di Boezio — nuovi strumenti di ricerca’, Elenchos 27, 2006, 377–407, id, ‘Dalla tesi di Aristotele alla tesi di Boezio: una tesi per l’implicazione crisippea?’, in M. Alessandrelli and M. Nasti de Vincentis (eds), La logica nel pensiero antico (Naples, 2009), pp.165–247. — It is true that in in Int 2 Boethius characterizes negation for categorical propositions (he is there explaining something in Aristotle’s Int). But he does not insist that the negative particle applies to the predicate — at least, he distinguishes (as Aristotle does) between ‘S is not P’ and ‘S is not-P’, the negative particle modifying the predicate in the latter but not in the former schema. And although he does not, so far as I know, anywhere offer an entirely general characterization of negation, he recognizes that a compound proposition may be negated — e.g. in Cic Top 358.35–38: negationem quippe affirmatio omnis evertit, vel cum connexae propositionis ex negationibus iunctae secundae parti negatio detrahituir totaque propositio denegatur ... For example: non si lux non est dies est. (Take the sentence ‘si lux non est, dies non est ’, remove the negation from the consequent, and negate the conditional as a whole.) And he does ‘assimilate’ (2) to (3) — or perhaps better, he takes (2) and (3) to be equivalent. The problem is not, I think, with his notion of negation. Rather, as I suggest below, it is a question whether there is any coherent notion of conditional propositions which will validate the equivalence.

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philosophers are by no means unanimous in their views on the correct analysis of the little word ‘if ’. Thus Boethius’ hypothetical syllogistic still presents a challenge to its philosophical interpreters: is there a coherent account of the truth-conditions of hypothetical propositions which will support Boethius’ contention that (1) and (2) are contradictories, and which may serve to provide a firm foundation for Peripatetic logic? I do not know the answer to that question; but I believe that the question is worth the consideration of contemporary students of logic.*

V What, then, was Boethius’ contribution to the study of logic? First, Boethius was not an original logician: he did not pretend to be. He saw himself as a translator, conveying Greek wisdom to a Greekless world: the insights which his works contain are not his own, and his knowledge is tralaticious. From time to time we can, I believe, hear Boethius’ own voice; and some at least of the disposition and organization of his material originated in his own head. But those touches of personality are relatively rare and relatively unimportant: the summa logicae which Boethius determined to present was traditional Peripatetic logic; and it is an error to speak of a Boethian logic. Secondly, it must be admitted that today we owe little to Boethius’ immense labours. He strove to transmit Aristotle to the West; but our present knowledge of Aristotle depends hardly at all on his strivings. Aristotle’s texts, and the texts of his Greek commentators, have survived in their original Greek: we can study Peripatetic logic, as Boethius himself did, in the original sources. Had all Boethius’ [85] logical writings been lost, the modern student of logic would have little to bewail, apart perhaps from the treatment of hypothetical syllogistic. It is rather within the context of his own dark times that Boethius’ service to logic must be sought. Greek learning was increasingly inaccessible, and the * The question is addressed by Nasti de Vicentis, ‘Dalla tesi di Aristotele’, pp.167–190. His answer, pp.182–183, is this: ‘If P, then Q’ is true, a` la Boethius, if and only if either (i) ‘P’ and ‘Q’ are both contingent and ‘Necessarily (P  Q)’ is true or else (ii) ‘P’ and ‘Q’ are not both contingent and ‘Necessarily (P  Q)’ is true. Whatever the formal merits of that suggestion may be, it is difficult to believe that anyone could offer it as an account of the sense of conditional sentences.

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Latin world was rude. By his sole efforts Boethius ensured that the study of Aristotle’s Organon, and with it the discipline of logic, was not altogether eclipsed in the West. Boethius’ labours gave logic half a millennium of life: what logician could say as much as that for his work? what logician could desire to say more?

27 Syllogistic in the anon Heiberg* The anon Heiberg is a short text in five parts or chapters: Logic, Arithmetic, Music, Geometry, Astronomy. The parts are of unequal size, the first being by far the longest.1 The edition prepared by Heiberg and published posthumously in 1929 is based on seven MSS, the earliest of which is dated to 1040. Heiberg describes a further fifteen MSS. I do not know if any more have since been discovered. Although Heiberg’s was the first critical edition of the text, the work was not previously unknown: chapter I had been published in 1600 and ascribed to Gregory;2 chapters II–V had been published in 1533, and again in 1556, under the name of Michael Psellus.3 The ascription to Psellus can hardly be correct, for chronological reasons. Heiberg rejects the ascription to Gregory, apparently because the work is left anonymous in the oldest MSS. But perhaps the author was the monk Gregory Aneponymus.4 As for the date, the astronomical chapter of the work gives 6516 as ‘the present year’ (V 8 [108.14], 9 [109.9–10]), and the Byzantine year 6516 ran from 1 September 1007 to 31 August 1008 in the Julian calendar. The same chapter also establishes some correlations between the Byzantine and the Egyptian calendars, and these indicate a period between 1 September and 14 December 1007.5 * First published in K. Ierodiakonou (ed), Byzantine Philosophy and its ancient sources (Oxford, 2002), pp.97–137. 1 In Heiberg’s edition (J.L. Heiberg (ed), Anonymi logica et quadrivium cum scholiis antiquis, Det Kgl. Danske Videnskabernes Selskab., Historisk-filologiske Meddelelser, XV 1, (Copenhagen, 1929)), Logic occupies some 50 pages, Arithmetic 15, Music 7, Geometry 30, Astronomy 18. — References to the anonymus will be given by chapter-, section-, page-, and line-numbers in Heiberg’s edition. 2 The ascription is found in two late MSS: Heiberg, Anonymi, p.XV. 3 I take this information from Heiberg, Anonymi, p.XIX. 4 So L. Benakis, ‘Commentaries and commentators on the logical works of Aristotle in Byzantium’, in R. Claussen and R. Daube-Schackat (eds), Gedankenzeichen: Festschrift fu¨r Klaus Oehler (Tu¨bingen, 1988), pp.3–12, on p.5. 5 I lift all this from C.M. Taisbak, ‘The date of anonymus Heiberg, Anonymi logica et quadrivium’, Cahiers du Moyen-Aˆge Grec et Latin 39, 1981, 97–102.

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Hence if the five chapters of the work form a unitary composition, the date is fixed. Each chapter of the work has its own title (each title is an iambic trimeter); but no MS offers a title for the work as a whole. Is the piece a conjunction of five independent essays? Several MSS contain only a selection of the chapters, which clearly had some independent circulation. Again, some [98] minor differences of style may be observed. For example, Chapter IV contains ten references to early authorities — six of them to Euclid —, whereas in the other chapters references are sparse.6 On the other hand, the first section of Chapter II explicitly announces a discussion of all four parts of the quadrivium, so that the last four chapters at any rate appear to have been conceived of as a unitary whole. Chapter I does not introduce itself as the first of five discussions, nor do I find any clear reference in II–V to a preceding account of logic;7 but in I 12, and again in I 67 (the last section of the chapter), the four sciences of the quadrivium are mentioned and logic is said to be the instrument for their discovery. On the whole, then, it seems reasonable to think that the five essays were written as parts of a single treatise.8 The treatise is unoriginal.9 I have not tried to elicit its sources — about which its author is elegantly silent.10 But there are numerous parallels to be found in the earlier literature, and for the chapter on logic it is plain — and unremarkable — that the author is writing in the Peripatetic tradition: most

6 In chapter I Aristotle is named four times (and ‘the Stoics’ once); in II, the Pythagoreans; in III, Plato; in V, Ptolemy (twice); in IV we find Archimedes (§ 51), Euclid (§§ 10, 18, 29 [twice], 30, 39), Plato (§§ 21, 33), Theo (§ 22 — of Alexandria, the commentator on Ptolemy); and note the epigram in § 26. 7 The first sentence of II 1 begins thus: ºº
  Ø ŒÆd æd H
æø
ÆŁÅÆØŒH
... ØƺÆE
[50.26–27] You might take ‘ŒÆ’ to mean ‘also’, and hence to imply that chapter II had been preceded by something else — a chapter on logic, say. But that is at best a veiled hint, not a clear reference. 8 See, with further argument, S. Ebbesen, Commentators and Commentaries on Aristotle’s Sophistici Elenchi, Corpus latinum commentariorum in Aristotelem graecorum 7 (Leiden, 1981), I pp.262–265. 9 Several of the symposiasts at Thessaloniki, where a version of this chapter was presented, spoke as though Byzantine philosophy must be original if it is to be worthy of praise — or even of study. Originality is the rarest of philosophical commodities. It is also an over-rated virtue: a thinker who strives to understand, to conserve, and to transmit the philosophy of the past is engaged in no humdrum or unmeritorious occupation. At any rate, most of my fellow symposiasts had the same reason as I have for hoping that that is true. 10 The references listed in n.6 do not imply that the author used those texts as his own sources of information.

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of his ideas surely derive from the commentaries on the Organon, and I guess that he often copies closely.11 The chapter on logic, to which the following pages restrict themselves, carries the title: ı
ØŒe

ƪÆ B çغ  çÆ. It seems as though logic were identical with philosophy, as though ‘logic’ and ‘philosophy’ were synonyms.12 But the first section addresses itself to ‘those who are seeking the instrument of philosophy [e B çغ  çÆ ... ZæªÆ

]’ (I 1 [1.5]); and the last section informs the reader that he now possesses a summary account ‘of the whole instrumental philosophy [B ‹ºÅ OæªÆ
ØŒB çغ  çÆ]’ (I 67 [50.12–13]). So the ‘çغ  çÆ’ of the title is presumably short for ‘instrumental philosophy’; and instrumental philosophy [99] is the philosophical study of the instrument of the sciences — in other words, it is logic. For logic is conceived of as a tool or instrument. The text affirms roundly that ‘all sciences were discovered by the ancients’ by means of logic (I 67 [50.16–17]). And it adds that while those who have set out unversed in logic may indeed have arrived at ‘experience [EæÆ]’, they have certainly not attained ‘knowledge [KØÅ]’ (50.18). Only the trained logician, ‘with the unwavering and necessitating guides of the syllogisms, is able to track down every science and art’ (50.21–23). It would be unfair to ask the author to explain or justify those large and agreeable claims — he is, and he surely takes himself to be, parroting a commonplace.13 The plan of the chapter is equally traditional. When you learn to read, you start with letters, move up to syllables, and finally reach whole expressions. So, when you learn logic, you start with the ten categories, move up to ‘matters concerning interpretation’, and finally reach the figures of the syllogism (I 1; cf 25 [18.4–7]). In other words, you study the matter of Aristotle’s Categories, of his de Interpretatione, and of his Prior Analytics. The programme announced in the opening section is carried out in §§ 2–48: first, a discussion of the categories — prefaced by an account of the Porphyrean quinque voces (§§ 2–20); then, material deriving from de Int (§§ 21–24); and finally, the syllogistic (§§ 25–48). The programme is done, but there is a 11 See in general K. Praechter, review of Heiberg, Anonymi, Byzantinische Zeitschrift, 31, 1931, 82–90; and for the source of I 59, see id, ‘Michael von Ephesos und Psellos’, Byzantinische Zeitschrift 31, 1931, 1–12 (on pp.2–6); Ebbesen, Commentators, I pp.269, 274–279. 12 Note also I 39 (at 32.8 and 32.17 ‘çغ  çÆ’ refers specifically to logic), and I 48 (at 39.8 ‹ºÅ çغ  çÆ is logic). So too in a ninth-century biography of St John Psichaites: Ebbesen, Commentators, I p.257. 13 For the commonplace, see e.g. T.-S. Lee, Die griechische Tradition der aristotelisehen Syllogistik in der Spa¨tantike, Hypomnemata 79 (Go¨ttingen, 1984), pp.44–54.

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supplement: just as there are tares among the wheat,14 so there are fallacies among the syllogisms — and ‘expert philosophers must know the types of paralogisms so that they will not stumble into falsity instead of truth’ (I 49 [39.21–23]).15 There follows a long account of fallacies and sophisms, based ultimately on Aristotle’s Sophistici Elenchi (§§ 49–63). And the chapter is rounded off by a summary description of the different types of syllogism — probative, dialectical, rhetorical, sophistical, poetical (§§ 64–67).16 Of the six books of Aristotle’s Organon, three form the background to the items promised in the programme, and a fourth lies behind the supplementary matter. The work contains no hint of the Topics — perhaps because the Topics deals with dialectical syllogisms and our text sees itself as a preparation for scientific study.17 But equally, the work contains no hint of the Posterior Analytics — the Aristotelian treatise which deals expressly with scientific syllogisms and in which, on the traditional interpretation, Aristotle shows how logic serves as the instrument of the sciences. To be sure, our text [100] makes a passing reference to probative syllogisms; but its characterization of them is cursory and inadequate, and it betrays no acquaintance with Aristotle’s subtle account.18 Why is APst thus cold-shouldered? ‘Ignorance, Madam, pure ignorance’?19 It would be false to suggest that the chapter offers rich treasures to the logician, or even to the historian of logic.20 Its intellectual pretentions are modest. To be sure, it purports to give the pious reader all he needs to know about the subject; but it presupposes no anterior knowledge, and it rarely engages in any deep or difficult matter. Occasionally an I æÆ is discussed — e.g. I 2; sometimes differences in opinion are noted — e.g. I 13; and there is 14 Matthew, xiii 24–30: already applied to philosophy by Clement, strom VI viii 67.2. 15 See Ebbesen, Commentators, I pp.88–89; III pp.116–117. 16 On these five types, which are found earlier in Elias, see Praechter, review, pp.87–89; Ebbesen, Commentators, I pp.102–105. 17 One of the scholia printed by Heiberg lists the contents of the Topics (134.19–135.6); and most of the scholia attached to chapter I refer to matters discussed in the Topics and have no visible connection to our treatise. 18 ‘Syllogisms put together from true premisses are themselves true and are called probative [I ،، ]’: I 64 [48.2–4]; contrast e.g. Psellus, Philosophica minora xiii 35–42; John Italos, dialectica 2. But the inadequate definition is not idiosyncratic: see e.g. — much earlier — Clement, strom VIII iii 6.2–4. 19 Ebbesen, Commentators, I p.264 (seconded by Benakis, ‘Commentaries’, p.6), says that the neglect of Top and APst ‘was hardly remarkable in the 11th century’; and he supplies parallels. Note that John Italos was well acquainted with Top: dialectica 4–12. 20 I do not know how well the work sold: Benakis, ‘Commentaries’, p.8, thinks that Blemmydes probably made use of it. (See below, n.64.)

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one long and detailed exegesis of an Aristotelian definition — at I 59.21 But for the most part, the chapter is purely expository in style and elementary in scope. I here discuss six issues, of unequal magnitude. All are drawn from the syllogistic sections of the chapter. The first four concern what might be termed the range of the syllogistic; the fifth centres about proofs of nonconcludency; and the sixth occupies itself with what later mediaeval logicians called the bridge of asses.

Undetermined syllogisms A contemporary presentation of Aristotle’s categorical syllogistic is likely to explain that a categorical syllogism consists of three categorical propositions, and that a categorical proposition links two terms in a certain quality and a certain quantity. There are two qualities: a term may be either affirmed or denied of a term. There are two quantities: a term may be predicated either universally or particularly of a term. There are thus four types of categorical proposition: universal affirmative, universal negative, particular affirmative, particular negative.22 I shall represent such propositional forms by way of schematic letters23 and standard abbreviations, thus: [101] AaB, AeB, AiB, AoB — ‘A holds of every B’, ‘A holds of no B’, ‘A holds of some B’, ‘A does not hold of some B’.24 Our text is more generous. It asserts that Aristotle built his syllogistic about not a tetrad but a hexad of types of proposition;25 for in addition to the four types which I have just enumerated, there are two more, ‘the undetermined [Iæ Ø æØ ] affirmative and the undetermined negative’ (I 28 [20.11– 14]). A proposition is undetermined if it lacks a determinator or

21 Taken from a commentary on Soph EI 167a21: parallels in Ebbesen, Commentators, I p.172 n.2. 22 That is the roughest of characterizations; but the refinements which a serious exposition of the syllogistic would require may here be left aside. 23 In its exposition of the syllogistic, our text does not use schematic letters (but see below, p.[131]): like most ancient accounts of logic, it prefers metalogical description. The use of letters has certain familiar advantages; and for the moment it will be harmless; but see below, n.69. 24 In the Peripatetic style, the predicate is presented before the subject (see Apuleius, int xiii [212.4–10] — here and elsewhere I write ‘Apuleius’ rather than ‘[Apuleius]’ for convenience rather than from conviction). — Note that ‘A does not hold of some B’ is to be construed as ‘Of some B, A does not hold’. 25 I return to this assertion below, p.[112].

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æ Ø æØ , if it lacks a sign of quantity.26 As an example of an undetermined affirmative we are offered: Men walk [¼
Łæø  æØÆE] and for an undetermined negative: Men do not walk [¼
Łæø  P æØÆE]27 (I 24 [17.1–5]). I introduce the formulae AuB and AyB to represent such propositional forms. Categorical syllogistic, as our text develops it, will thus be more bulky than the standard contemporary version; and our text finds types of syllogism unrecognized in contemporary accounts.28 [102] For the text adds two moods each to the first two Aristotelian figures, and four moods to the third. The third and fourth moods of the first figure — Darii and Ferio — may be presented schematically as follows: AaB, BiC:: AiC AeB, BiC:: AoC Our text subjoins a fifth and a sixth mood, to wit: AaB, BuC:: AuC AeB, BuC:: AyC I dub these moods Daruu and Feruy. The extra moods in the second figure are Festuny and Barycy: BeA, BuC:: AyC BaA, ByC:: AyC And in the third figure we meet Datusu, Dusamu, Ferusyn and Bycardy: 26 The æ Ø æØ  are introduced in I 21, where there are said to be two of them, the universal and the particular (13.26–28); at I 22 [15.11–12], it is said that there are affirmations and negations ‘both without determinators and with determinators’. Singular propositions (‘Socrates walks’), although they do not carry determinators, do not count as undetermined: an undetermined proposition is one which might but does not sport a determinator. In I 24, at the end of the enumeration of the different types of proposition (on which see below, p.[112]), our author remarks that he has not included singular propositions ‘which Aristotle does not use in his exposition of the syllogisms, since he constructs the syllogisms from what is universal and eternal’ (17.24–27) — a commonplace (e.g. Philoponus, in APr 12.22–23), which goes back ultimately to Aristotle, APr A 43a40–43. 27 The Greek sentences are not barbarisms — hence I use the English plural to translate them. ‘Man walks’ is strained English. ‘Horse sleeps’ is babu. 28 i.e. contemporary versions of Aristotle’s assertoric syllogistic: categorical syllogistic had a long history, and different logicians discovered different numbers of moods.

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AaB, CuB:: AuC AuB, CaB:: AuC AeB, CyB:: AyC AyB, CaB:: AyC Why consider the additional moods to be valid? Although the treatise offers no formal proof, its description of Daruu provides a broad hint: Fifth is the combination which deduces an undetermined affirmative conclusion from a universal affirmative major and an undetermined affirmative minor. The terms are those of the third combination: Animal to every man Man in white (this is the undetermined item) Therefore: man in animal29 [103] This is equivalent to ‘to some’; for the undetermined propositions are equivalent to particulars. (I 30 [22.3–9])30

Thus we are invited to accept the two equivalences: AuB , AiB and AyB , AoB. Whence it is easy to see that Daruu is a valid mood: its validity follows directly from the validity of Darii and the equivalence between ‘AuB’ and ‘AiB’. The same holds for all the extra moods. But then is not our text a niggard? It does not, for example, mention Daraptu — 29 In our text, examples of a, e, i, and o propositions are regularly expressed by verbless sentences of the form e ` Æ
d [ P
d, Ø
Ø, P Æ
d] ´ You would expect undetermined examples to be expressed thus: e ` [ P] fiH ´ In fact we get e ` [ PŒ] K
´ It is tempting to connect this use of ‘K
’ with Porphyry’s thesis that affirmations and negations signify aliquid alicui inesse or non inesse (see Boethius, in Int 2 122.7–15 — Boethius connects the thesis with the 
Ø
Ø r
ÆØ of Cat 1a20–b9: in Int 2 68.4–69.22; and in fact it is already found in Apuleius, int iii [191.1–6]); but it is difficult to make anything out of that. 30   › KŒ Ç
 ŒÆŁ º ı ŒÆŪ æØŒB ŒÆd Kº
 Iæ Ø æØ ı ŒÆŪ æØŒB Iæ Ø æØ
ŒÆŪ æØŒe
ı
ªø
ıæÆÆ· ‹æ Ø ƒ  F æ ı æ  ı· e ªaæ ÇfiH
Æ
d I
Łæ ı, › ¼
Łæø  K
ºıŒfiH ( F ªaæ e ¼
ı æ Ø æØ F), e ÇfiH
¼æÆ K
ºıŒfiH: N ı
ÆE b  F fiH Ø
Ø ºıŒfiH· a ªaæ Iæ Ø æØÆ  E æØŒ E N ı
ÆE: — cf I 36 [28.13–14]: ‘the undetermined propositions are equivalent to the particulars’; I 32 [25.13–14]: ‘we said that the undetermined items are taken as [ºÆ
ŁÆØ I
] particulars’. See also I 59 [44.13–17], with Ebbesen, Commentators, I pp.197–199.

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AaB, CaB:: AuC — which, given the equivalences, follows directly from Darapti. It does not mention Dariu or Darui, or Feriy or Feruo, or ... In short, its system appears to be radically incomplete. Hence when the text explicitly claims to have given an exhaustive account of the contents of each figure,31 this seems to be an error. An explanation for these apparent omissions might be sought in I 33. There, after the exposition of the valid moods, the text propounds the socalled peiorem rules. (peiorem semper conclusio sequitur partem.) You must know that it is common to the concludent combinations32 of the three figures that the conclusion follows the worse of the premisses ... A particular is worse than a universal, a negative than an affirmative, and an undetermined than a determined. (26.5–9)

Hence, in particular, if one of the premisses is assumed in undetermined form, the conclusion will follow undetermined. (26.23–24)*

Now in Darui — AaB, BuC:: AiC — the conclusion is determined and the second premiss undetermined. The peiorem rule is violated — and Darui is therefore not valid. If our text [104] implicitly rejects Darui and its fellows, that is not the result of oversight: rather, the text explicitly adopts a rule which outlaws such moods. But if the peiorem rule outlaws Darui, it does not outlaw Dariu — AaB, BiC:: AuC — for here the conclusion is ‘worse’ than each premiss. Then why omit Dariu? Perhaps our author implicitly strengthens the peiorem rule so that it requires the conclusion to be neither better nor worse than the worse of the premisses? Such a strengthened rule will outlaw Dariu; and many formulations of the peiorem

31 See I 30 [22.13–14]; 31 [23.19]; 32 [25.14–15]. 32 ıºº ªØØŒ d æ  Ø: (i) the text uses ‘æ  ’ for the traditional ‘ıÇıªÆ’, and I translate it accordingly; (ii) a combination is ıºº ªØØŒ  if it yields a conclusion of the form ‘AxC’ — I use ‘concludent’ for ‘ıºº ªØØŒ ’ and ‘non-concludent’ for ‘Iıºº ªØ ’. * E b N
ÆØ ‹Ø Œ Ø
e
b
H
ıºº ªØØŒH
æ ø
H
æØH
åÅø
e fiB åæ
Ø H
æ ø
ŁÆØ e ıæÆÆ ... Ø b B b
ŒÆŁ º ı åæø
æØŒ, B b ŒÆŪ æØŒB æÅØŒ, B b æ ØøæØ
Å Iæ Ø æØ : ... Iæ Ø æ ı b ØA æ ºÅçŁÅ Iæ Ø æØ
łÆØ e ıæÆÆ:

Syllogistic in the anon Heiberg

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rule — including the formulation in our text — appear to propose it.33 But it cannot be right; for it will also outlaw Darapti.34 Then recall the fact that our text ignores the subaltern moods — moods such as Barbari, AaB, BaC:: AiC, which may be derived from a canonical mood by applying one of the rules of subalternation35 to its conclusion. These moods, we happen to know, were added to the syllogistic by Aristo of Alexandria; but standard ancient accounts do not mention them, and Apuleius, who does, rejects them as ‘utterly stupid’ (int xiii [213.9]). Now, given the peiorem rule of our text, Dariu and its fellows might be considered to be special types of subaltern mood; and the fact that the text does not mention Dariu is of a piece with the fact that it does not mention Barbari. But this seems to increase rather than decrease the difficulty. Perhaps Barbari is ‘utterly stupid’; but it is assuredly valid. Why reject it? Well, our text does not explicitly reject Barbari; and although it pretends to give a complete treatment of the syllogistic figures, it does not explicitly claim to have listed all the valid moods: it explicitly claims to have listed all the concludent combinations. The combination for Barbari is not overlooked: it is the same as the combination for Barbara. And although the text does not expressly indicate that this combination will yield ‘AiC’ as well as ‘AaC’, neither does it expressly deny the entailment; for it does not explicitly claim to have listed every conclusion which may be inferred from a given combination. What holds for Barbari holds equally for Dariu: its combination is listed (it is the combination for Darii); and nothing in the text expressly states that Dariu is not a valid mood. So perhaps Dariu is implicitly accepted? No. In I 27, having computed the number of concludent combinations, the text observes that ‘the syllogisms in abstraction from perceptible matter [i.e. the valid moods] are so many and no more’ (20.2–4); that is to say, here at least the text implicitly supposes that each concludent combination [105] answers to precisely one valid mood. The combination ‘AaB, BiC’ certainly answers to Darii: it does not, therefore, answer to Dariu. Unless we dismiss the remark in I 27 as a passing negligence, we must conclude that our text implicitly outlaws Dariu (and also the subaltern moods). 33 See e.g. Alexander, in APr 51.31–32: ‘It seems that the conclusion is always similar to the worse of the items assumed in the premisses, both in quantity and in quality’. 34 As well as other, less celebrated, moods: Baralipton, Fapesmo, ... 35 i.e. AaB:: AiB, and AeB:: AoB (see Aristotle, Top B 109a3–6).

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However that may be, we must revisit Darui. Our text implicitly rejects Darui, on the basis of the peiorem rule. But the rule — the pertinent part of the rule — is false. A universal proposition is better than a particular in this sense: from ‘AaB’ or ‘AeB’ you may infer ‘AiB’ or ‘AoB’, but not vice versa. Our text insists that undetermined propositions are equivalent to particular propositions: from ‘AiB’ or ‘AoB’ you may infer ‘AuB’ or ‘AyB’ and also vice versa. Undetermined propositions are not worse than particulars: they are no better either — they are much the same. Perhaps they are worse in some other fashion? After all, negatives are worse than affirmatives; but that cannot be because ‘AaB’ entails ‘AeB’ but not vice versa. There is another canon of goodness operating here — and so also, perhaps, in the case of the undetermined items. Well, no doubt we could discover or invent a criterion according to which the undetermined is worse than the particular. But no such discovery or invention will do any good: given the equivalences, then Dariu is valid — and that’s an end on it. I conclude that, in the matter of undetermined syllogisms, our text is logically inept.36 Undetermined moods had been considered by every Peripatetic logician since Aristotle. Aristotle introduces undetermined propositions at the beginning of the Prior Analytics.37 And at A 26a28–30, after expounding Darii and Ferio, he remarks: Similarly if BC is undetermined, being affirmative — for there will be the same syllogism whether it is taken as undetermined or as particular.*

Undetermined propositions do not reappear in the exposition of the valid moods in A 4–6;38 but in A 7 we find a general claim: 36 The same ineptitude recurs in Blemmydes: at epit log xxix 917AC, he remarks that Aristotle subscribed to both the pertinent equivalences; but he adds that although the u–i equivalence is evidently true, the y–o equivalence is not: y-propositions are sometimes equivalent to o-propositions but more often equivalent to e-propositions. When he develops categorical syllogistic in xxxi–xxxiv, he constructs it around the four standard propositions (and allows only the 14 canonical moods: xxxii 944B). But at the end of the exposition, he announces that thus far he has dealt with syllogisms of which the premisses are determined: as for those with undetermined premisses, what has already been said will serve — providing the reader bears in mind the relevant peiorem rules, on which Blemmydes takes the same view as our text (xxxiv 961A). No reader will be able to elaborate the undetermined moods on the basis of Blemmydes’ remarks. 37 A 24a16–20: his term ‘IØ æØ ’ was later enlarged to ‘Iæ Ø æØ ’. * › ø b ŒÆd N IØ æØ
YÅ e ´ˆ, ŒÆŪ æØŒe
Z
· › ªaæ ÆPe ÆØ ıºº ªØe IØ æ ı  ŒÆd K
æØ ºÅçŁ
 : 38 But they are sometimes noticed in connexion with non-concludent combinations: 26a30–32, b21–25; 27b36–39; 29a8–10.

Syllogistic in the anon Heiberg

693

it is evident that if an undetermined item is posited instead of an affirmative particular, it will produce the same syllogism in all the figures. (29a27–29)*

Each of the two passages I have just quoted is puzzling. [106] In A 7 Aristotle mentions only affirmative undetermined propositions,39 and he speaks only of undetermined premises. Thus you would take him to be giving the accolade to Darui, Feruo, Festuno, Dusamis, Datusi, and Feruson — and by implication to be rejecting Daruu, Dariu, ... , Feruy, Feriy, ... and all the rest. Yet it is desperately difficult to conjure up a justification for such a view. As for 26a28–30, it is not clear to me whether the word ‘similarly’ invites us to consider one mood or two — a mood similar to Ferio, or moods similar to Darii and to Ferio. The former I find an easier construal of the Greek; but most commentators opt for the latter.40 Nor is it clear whether we should think of Feruo (and Darui ) or of Feruy (and Daruu). If, in the expression ‘the same syllogism’, the word ‘ıºº ªØ ’ means ‘conclusion’, then Feruo (and Darui ) are presumably intended. On the other hand, if ‘ıºº ªØ ’ means ‘syllogism’, then A 4 claims that Feruo (or Feruy) is the same mood as Ferio; and A 7 claims that Darui and its congeners are the same as Darii and its congeners. It may reasonably be said that there is a lacuna — or at least a vagueness — in Aristotle’s treatment of the categorical moods. Theophrastus, we should expect, will have tried to fill the gap — that was his general modus operandi. And in fact it is clear that he said something on the subject of undetermined moods; more particularly, that he explicitly admitted at least one undetermined mood to the first figure. Only one short text on the matter survives, and that text is wretchedly corrupt.41 But whatever we do with it, Theophrastus was certainly prepared to acknowledge undetermined moods as superadditions to the canonical moods. * Bº
b ŒÆd ‹Ø e IØ æØ
I
d  F ŒÆŪ æØŒ F  F K
æØ ØŁ

e
ÆPe
 ØØ ıºº ªØe
K
–ÆØ  E åÆØ
: 39 Alexander pertinently asks why he did not add ‘and negative’ at 29a28; but he returns no satisfactory answer (in APr 111.13–27). 40 e.g. Alexander, in APr 61.1–3; Philoponus, in APr 79.6–9. 41 Apuleius, int xiii [212.12–213.5] ¼ 92 in W.W. Fortenbaugh, P.M. Huby, R.W. Sharples, and D. Gutas (eds), Theophrastus of Ephesus: sources for his life, writings, thought and influence, Philosophia Antiqua, 54 (Leiden, 1994); see P.M. Huby, Theophrastus of Eresus: commentary II — Logic, Philosophia Antiqua 103 (Leiden, 2007), pp.61–63 — Pace J. Barnes, S. Bobzien, K. Flannery, and K. Ierodiakonou, Alexander of Aphrodisias: On Aristotle Prior Analytics 1. 1–7 (London, 1991), p.136 n.157, this text has nothing to do with the five moods which Theophrastus added to the first figure (on which, see Alexander, in APr 69.27–70.20, and other texts in Fortenbaugh et al., Theophrastus, 91A–91E).

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Many later logicians followed Theophrastus’ lead. But there were some dissenters — thus according to Apuleius, the undetermined moods are otiose, since the undetermined is taken for a particular, and the same moods will come about as from particulars. (int xiii [212.15–213.5])42

And some logicians havered.43 [107] The issue depends on the status of the two equivalences, AiB , AuB and AoB , AyB. Most, but not all, ancient logicians took both equivalences to be true; and they ascribed the two truths to Aristotle.44 The ascription is not without textual support;45 and if it goes beyond what Aristotle’s words explicitly 42 hoc supervacaneum est tradere cum infinita pro particulari accipiatur et idem futuri sint modi qui sunt ex particularibus. — With ‘pro particulari accepi ’ compare ‘ºÆ
ŁÆØ I
d æØŒH
’ (above, n.29). 43 Undetermined moods are implicitly rejected by e.g. Galen (inst log ii 4: if you predicate A of B and B is a general term, then ‘it must be determined [ØøæŁÆØ] whether it is said of all or of some’; xi 2: there are only 16 combinations, although there are several equivalent expressions for them); and Boethius, syll cat 813C. They are implicitly accepted by e.g. the Ammonian scholia (see Ammonius, in APr IX 34: there are 36 combinations — so also Philoponus, in APr 68.30–34); and explicitly accepted by e.g. Philoponus (the first figure contains six valid moods [in APr 79.4–9], the second six [94.32–95.7], and the third ten [110.8–11]); and they are later expressly noted by Blemmydes, epit log xxxiv 961A (see above, n.36). Alexander is ambivalent: at in APr 51.24–25, he remarks, neutrally, that ‘if we count in the combinations of undetermined propositions’, then we shall get more concludent pairings; at 61.1–3 (commenting on APr A 26a28–30) he says that with undetermined premisses we get deductions ‘similar to [‹ Ø ]’ — and hence, by implication, not identical with — Darii and Ferio; and at 94.18–20 and 112.1–2 he implies that the undetermined moods are identical with their particular counterparts. 44 e.g. Alexander, in APr 30.29–31; 62.22–24; Apuleius, int iii [190.21–22]; v [196.5–8]; xiii [213.1]; Martianus Capella, IV 396; Boethius, int syll cat 776C; syll cat 802C; Ammonius, in Int 116.7–8; [Ammonius], in APr 70.20–22; 71.3–4; Philoponus, in APr 79.4-5; 110.10–11, 27; 203.6–8; 222.14; 228.10; 277.12–13; 323.3–4; 349.9–10 (but at 42.31–33 Philoponus states that undetermined propositions, as Aristotle has remarked in Int, I
ƺ ª FØ ... j ÆE ŒÆŁ º ı j ÆE æØŒÆE). But note the long discussion in Ammonius, in Int 111.10–120.12: some had contended that ‘AoB’ and ‘AyB’ are not equivalent, appealing both to theoretical considerations and to facts of Greek usage (cf e.g. Boethius, in Int 2 152.12–161.18; anon, in Int 45.12–46.5 Tara´n; 87.2–14). I note that C.W.A. Whitaker, Aristotle’s de Interpretatione: contradiction and dialectic (Oxford, 1996), pp.86–92, argues that, at least in de Int, Aristotle accepted neither equivalence. (It is plain that if AuB then AiB and that if AyB then AoB: it is the reverse implications which are contested.) 45 The interpretation is based not only on APr A 26a28–30 and 29a27–29, but also on Int 17b29–37. There Aristotle states that it is possible that sentences of the form ‘AuB’ and ‘AyB’ should be true at the same time; he admits that this may seem odd, since ‘AyB’ appears to mean that AeB; but in point of fact — or so he claims — ‘AyB’ does not mean the same as ‘AeB’ nor is it even the case that AeB , AyB.

Syllogistic in the anon Heiberg

695

supply, it is, I suppose, the most plausible way of squeezing a precise thesis out of Aristotle’s various remarks.46 If the equivalences are not true, then evidently there may in principle be further moods to add to the canonical fourteen. Whether or not there are in fact further moods to be added will depend on the sense which is assigned to the undetermined sentences. If the equivalences are true, then — as I have already observed — Daruu, Darui and Dariu and the rest are all of them valid moods; but the truth of the equivalences does [108] not in itself establish whether these moods must be added to the canonical fourteen. Suppose that the equivalences are grounded on synonymies, that undetermined sentences are synonymous with their particular counterparts. ‘Men walk’, for example, is short-hand for ‘Some men walk’; and in general, between ‘AiB’ and ‘AuB’, while there may be some difference of nuance or of colour, there is no difference of sense. In that case Daruu, Darui, and Dariu are not three additional moods, to be annexed to Darii: they are all one mood, and the mood is Darii. The validity of Daruu and the rest does not mean that the syllogistic of Aristotle must be enlarged; for Aristotle has already mentioned Daruu — he has mentioned Darii, and Darii is identical with Daruu. Suppose — as Theophrastus perhaps supposed — that the undetermined propositions are equivalent to their particular counterparts, but that undetermined sentences are not synonymous with their particular counterparts: then Daruu and the rest are plausibly taken to be additional moods.47 In this way the distinction between synonymy and the weaker relation of expressing equivalent propositions is fundamental to the dispute over the status of undetermined moods. Yet no ancient text ever makes the Plainly, those remarks do not entail the two equivalences. But they are most satisfactorily explained on the hypothesis that in fact Aristotle did accept the two equivalences. 46 Why not propose that Aristotle accepted AiB , AuB, but rejected AoB , AyB, as some later logicians did (above, n.44)? Well, he certainly did not accept AeB , AyB (above, n.45); and when he refers to y-propositions in his proofs of non-concludence (above, n.37), he implicitly treats them as equivalent to o-propositions. 47 Suppose that the expressions E and E* each formulate a syllogism, and that they differ from one another in that where E contains the sentence S, E* contains the sentence S*. (1) If S and S* are synonymous, then E expresses the same syllogism as E* — thus, almost explicitly, our text (I 59 [44.21–45.5], on ‘begging the question’; cf the scholium at 139.12–13). (2) If S and S* are not synonymous but express propositions which are logically equivalent to one another, then E and E* express different syllogisms.

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distinction plain, or offers a clear and unambiguous gloss on ‘N ı
ÆE
’. Ammonius, for example, ascribes the equivalences to Aristotle: first he uses the phrase ‘c
ÆPc

ÆØ
åØ
’, which he apparently glosses in terms of having the same truth-value (in Int 110.24–25; cf 114.22–23); a page later he affirms that, according to Aristotle, ‘AiB’ and ‘AuB’ ‘say [çŁªªŁÆØ]’ or ‘signify [ÅÆ
Ø
] the same thing’ (111.10–15). The undetermined moods are an intriguing ripple on the surface of categorical syllogistic; but it must be confessed that an ancient logician who wished to replace the Aristotelian tetrad by a hexad might rather have considered other non-standard types of determined proposition.48

Singular syllogisms Tacked on to the end of the discussion of the third figure comes the following short and perplexing paragraph: [109] Syllogisms consisting wholly of singulars, about which not even Aristotle said anything, resemble universal syllogisms: just as the latter embrace all the subject kind, so the former embrace the whole person. e.g. Levi of Jacob Jacob of Isaac Isaac of Abraham Therefore: Levi of Abraham (Hence the noble Paul says: And as I may so say, Levi also, who receiveth tithes, payed tithes in Abraham [Hebrews vii 9].) Similarly, the negative syllogisms consisting of singulars are compared to the negative universals. (I 32 [25.26–26.4])*

48 Perhaps most obviously, in view of Aristotle’s interest in ‘what holds for the most part’, they might have considered propositions of the form ‘A holds of most Bs’: such items were indeed discussed in the context of modal logic; but so far as I am aware, no ancient logician ever thought of treating them as a type of non-modal determined proposition. — It might also be wondered why Aristotle ever paid any attention to undetermined propositions; and one possible answer might be that ‘for the most part’ truths are typically formulated as undetermined propositions: the sentence ‘Men go grey’ (and its Greek counterpart) will in many contexts naturally be taken to express the thought that men for the most part go grey. * ƒ b KŒ H
ŒÆŁ ŒÆÆ Ø ‹º ı ıºº ªØ d æd z
Pb æØ ºÅ ØºÆ  E ŒÆŁ º ı ıºº ªØ E æ  ŒÆØ
, ‰ KŒE
Ø e A
 Œ

r   oø ŒÆd y Ø e ‹º
æغÆ

 æ ø
x
› ¸ıd  F ÆŒ, › ÆŒg  F ÆŒ, › ÆaŒ  F æÆ, › ¸ıd ¼æÆ  F æÆ: Ø çÅØ
› ŁØ  —ÆFº  ŒÆd ‰   NE
Øa æÆa ŒÆd ¸ıd › ŒÆ ºÆ
ø
ŒøÆØ: › ø ŒÆd ƒ KŒ H
ŒÆŁ ŒÆÆ æÅØŒ d  E ŒÆŁ º ı æÅØŒ E Ææƺº
ÆØ:

Syllogistic in the anon Heiberg

697

The only thing which is clear in that paragraph is the remark about Aristotle: he did not mention purely singular syllogisms — no doubt because, as our text has already reported (I 24 [17.24–27]), he did not use singular propositions at all in his syllogistic. It seems improbable that our author is himself responsible for the invention of wholly singular syllogisms; but I can recall no close parallel to the paragraph in any ancient logic text. By way of comment I offer three guesses, none of which is very satisfactory. The first two guesses start from the comparison which the text draws between singulars and universals. Although our author speaks explicitly of singular syllogisms and universal syllogisms, it is easy to swallow the suggestion that there is an underlying comparison between singular propositions and universal propositions. Just as ‘All men are mortal’ ascribes something, namely mortality, to the whole ensemble of men (and not just to one or two of its component parts), so ‘Socrates is mortal’ ascribes something, namely mortality, to the whole of Socrates (and not just to one or two of his component parts). Just as ‘No men are mortal’ denies mortality of the whole human ensemble, so ‘Socrates is not mortal’ denies mortality to the whole individual. In general, there is a parallel between ‘AaB’ and ‘Fx’ and between ‘AeB’ and ‘not-Fx’. The parallel is rough; and there is no call to make it more precise by invoking notions taken from set theory or mereology. The first guess now recalls that for centuries a stock example of a syllogism in Barbara was this:49 All men are mortal Socrates is a man Therefore: Socrates is mortal That syllogism does not — or does not evidently — possess the canonical form of Barbara, [110] AaB, BaC:: AaC; but it does possess the form AaB, Bx:: Ax. And you might call that form quasi-Barbara. Quasi-Celarent will look like this: AeB, Bx:: not-Ax And there are several other quasi-moods, among them quasi-Darapti: Ax, Cx:: AiC 49 It is the illustrative syllogism in e.g. John Italos, dialectica 15 (but Italos does not say that it is in Barbara).

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Hence — the first guess — it is such quasi-moods which underlie our text. The guess has two advantages: it gives sense to the comparison between singulars and universals; and it presents us with moods, with (as our text calls them) ‘syllogisms in abstraction from perceptible matter’ (I 27 [20.2–3]). Its disadvantages are equally evident: it does not fit the illustrative example; and the quasi-moods are not properly described as wholly singular — each contains a non-singular proposition. The second guess is free from the second of those disadvantages. Contemporary logic offers us any number of wholly singular inferences — for example, the schema: Fx, Gx:: Fx & Gx In general, take any valid schema in propositional logic, replace the Ps and the Qs by an ‘Fx’ and a ‘Gx’, and you have a wholly singular inference schema. Perhaps such things lie behind our text? Well, they are moods, and they are wholly singular moods. But they suffer from at least one disadvantage of their own: all such schemata will contain complex propositions (‘hypothetical’ propositions, in the ancient jargon); and it seems certain that in our text wholly singular syllogisms need not contain — and probable that they may not contain — complex propositions as components. The third guess forgets the parallel between singular and universal propositions and instead fastens its attention on the illustrative example. It is expressed with less than perfect limpidity. I suppose that the telegraphic ‘Levi of Jacob’ means ‘Levi is of the house of Jacob’; and in any event it must express some relation between Levi and Jacob. Thus the text offers an example of what Galen called relational syllogisms.50 For the example has the form: xRy, yRz, zRw:: xRw. You might reasonably analyse that as a polysyllogism, taking it to be the copulation of two arguments of the form: [111] xRy, yRz:: xRz. And a negative singular syllogism? Consider the example: Caesar not of Ptolemy Ptolemy of Cleopatra Therefore: Caesar not of Cleopatra And then the general formula: not-xRy, yRz:: not-xRz. 50 On which, see J. Barnes, ‘ ‘‘A third sort of syllogism’’: Galen and the logic of relations’, in R.W. Sharples (ed), Modern Thinkers and Ancient Thinkers (London, 1993), pp.172–194; R.J. Hankinson, ‘Galen and the logic of relations’, in L. Schrenk (ed), Aristotle and Later Antiquity

Syllogistic in the anon Heiberg

699

Such relational syllogisms may now be compared to universal syllogisms not in virtue of any parallel between singular and universal propositions, but rather for the following reason: just as the validity of Barbara and of Celarent depends on the logical properties of the term-connexion marked by ‘a’ and ‘e’, so the validity of the two argument forms I have given depends on the logical properties of the relation marked by ‘R’. (The affirmative argument is valid inasmuch as ‘R’ marks a transitive relation; the negative argument is valid inasmuch as the relation is also symmetrical.51) So the third guess finds Galen’s relational syllogisms behind our text. It may be objected that the two schemata which I have given are not formally valid, and that, according to the third guess, the text does not concern itself with moods but rather with ‘concrete’ arguments. Perhaps that is so52 — but exactly the same can be said of Galen’s examples. It may also be objected that our text does not explicitly talk of relations or of a æ  Ø, and that Galen does not talk of wholly singular syllogisms. That is a serious objection. Nonetheless, the third guess is the best that I can do. I am too timid to speculate that relational syllogisms found their way into Christian texts thanks to the Theodotian heretics who used Galen’s logic in their biblical exegesis.53

Two million more moods Near the beginning of its formal development of the syllogistic our text makes the following declaration: [112] (Washington DC, 1994), pp.57–75; J. Barnes, ‘Proofs and syllogisms in Galen’, in J. Barnes and J. Jonanna (eds), Galien et la philosophie, Entretiens Hardt 49 (Vandoeuvres, 2003), pp.1–29 [reprinted in volume III]. 51 A simple proof: 1 2 3 3 1, 3 1, 3 1, 2

(1) (2) (3) (4) (5) (6) (7)

xRy not-yRz xRz zRx zRy yRz not-zRx

premiss premiss hypothesis 3, symmetry 1,4, transitivity 5, symmetry 1,2,3, reductio

52 But the notion of ‘formal’ validity is notoriously hard to capture: see J. Barnes, ‘Logical form and logical matter’, in A. Alberti (ed.), Logica mente e persona (Florence, 1990), pp.7–109 [reprinted above, pp.43–146]. 53 On the Theodotians, see Eusebius, HE V xxviii 13–14; cf R. Walzer, Galen on Jews and Christians (Oxford, 1949), pp.75–86; J. Barnes, ‘Galen, Christians, logic’, in T.P. Wiseman (ed), Classics in Progress: essays on ancient Greece and Rome (Oxford, 2002), pp.399–418 [reprinted above, pp.1–27].

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Such being the number of the syllogisms,54 Aristotle, for the sake of simplicity, takes up a single hexad of propositions — the one consisting of two unquantified propositions and four quantified ones, with definite names — and illustrates the syllogisms by way of these, supposing that by way of them the others too will be made clear. (I 28 [20.11–15])*

There is a comparable passage at the end of the discussion of syllogistic: If to these combinations you join those from the other hexads — not only those depending on subject and predicate but also those compounded from a third item co-predicated — and if you attach and count in those with modes and their mixtures, and if you are ready to put together those thousands of syllogisms ... (I 48 [39.1–7])**

then you will have brought your study of syllogisms to its completion. In I 24 our text computed the total number of types of categorical proposition. There is the basic hexad in which all the terms are simple names and verbs (‘Men walk’); then there are propositions with indefinite names (‘Not-men walk’); then those in which there is a third item copredicated — these being simple (‘Men are just’), or metathetic (‘Men are not-just’), or privative (‘Men are unjust’). In addition, categorical propositions of any of these varieties may carry a modal operator (‘Necessarily... ’, ‘Possibly... ’, ... ); and finally, every proposition must bear one of three tenses. The various permutations which these possibilities allow yield in all 576 types of categorical proposition.55 Next, I 26–27 computes the total number of combinations: 576  576 ¼ 331,776 (18.27–28) — a figure which must be multiplied by 12 to take care of the modalities,56 and then by 3 for the 54 Here, as often, ‘ıºº ªØ ’ means ‘syllogism in abstraction from perceptible matter’ or ‘mood’. *   ø
b  ø
Z
ø
› æØ ºÅ Æ Æ
æ ø
ŒÆa e ±º æ
I ºø
c
KΠ b
H
Iæ Ø æø
, æø
b H
æ ØøæØ
ø
K
侯
fiø fiH O
ÆØ, Kd  ø
 f ıºº ªØ f  تÆÇØ ‰ Øa  ø
ήd H
º ØH
ź ı
ø
: ** oø Œi
 f Ie ÆH
H
ø
P H
K  ί
ı 

ŒÆd ŒÆŪ æı
ı Iººa ŒÆd H
KŒ æØ ı æ ŒÆŪ æ ı
ı   Ø KØı
łfi Å, Œi
 f a æ ø
ήd B K
FŁ
ø KØı
æÆ   Ø ı
ÆæØŁfi Å, Œi
a ıæØÆ KŒ
Æ H
ıºº ªØH
KØı
ƪƪE
KŁºfi Å ... 55 Syrianus did not get past 144 (see Boethius, in Int 2 321.20–323.13), while Ammonius managed to arrive at the figure of 3,024 (in Int 219.19–21). Our text confesses that it omits certain further complications: 17.21–28. 56 19.7: the modalities are already catered for in the 576 types of proposition: I suppose — the text is not clear on the point — that modality comes into the picture twice, first with reference to the modal status, of the ‘matter’ of the proposition (thus e.g. ‘2 þ 2 ¼ 4’ has a necessary matter), and secondly, with reference to the form of the proposition (thus e.g. ‘Necessarily 2 þ 2 ¼ 4’ has a necessary form): see e.g. Alexander, in APr 27.1–5; Ammonius, in Int 88.18–28; Philoponus, in APr 43.18–44.1; John Italos, dialectica §§ 25, 31.

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figures. The result is 11,943,936 combinations (19.16–17), of which 2,433,552 are concludent.57 According to our text, Aristotle’s syllogistic, as he presents it in the Prior Analytics, concerns itself with a mere six of the 576 types of proposition, and with a mere 108 of the 12 million combinations. Aristotle therefore elaborates only a minute fragment of categorical syllogistic. The suggestion that Aristotle restricts himself, ‘for the sake of simplicity’, to six types of proposition is surprising — on several counts. First, our text plainly implies that Aristotle did not discuss modal syllogisms in APr. And [113] that is bizarre. It is not in the least odd that our text does not discuss modal syllogistic — such an arcanum has no place in an elementary text.58 The oddity lies in the implication that Aristotle was mum on the subject. For no one who had read the Analytics — or who had seen any ancient commentary on the work — could conceivably have thought that Aristotle had said nothing about modal syllogistic. It appears to follow that the author of our text had not read either Aristotle’s work or any commentary on it — a consequence which is awkward. I have no explanation worth recording. Secondly, the text plainly implies that an extension of the syllogistic to cover all 576 types of proposition is a simple enough task — or so at least I understand the remark that ‘the others too will be made clear’ by way of the basic syllogisms. Again, no one familiar with the Analytics, or with the commentatorial tradition, could have thought such a thing. Aristotle’s account of modal syllogisms is notoriously difficult, and evidently it does not depend on a simple transposition from the non-modal to the modal. The commentators show how the Peripatetic tradition was in a state of perplexity. Thirdly, our text plainly implies that the syllogistic expounded by Aristotle in APr — and taken over by itself in I 30–33 — concerns only those combinations each of whose propositions consists of a simple name and a simple verb (plus determinators). ‘Every man runs’ but not ‘Every man is an animal’, nor ‘Some man is unjust’, nor ‘No non-man is just’, nor ‘No nonman laughs’, ... That is patently false. Not only does Aristotle explicitly remark, in the later parts of APr, that the component propositions of syllogisms may have any degree of complexity,59 but the illustrative examples 57 19.20–21 — but the total must be modified in some unspecified ways to account for the vagaries of certain modal combinations. 58 But the text does say something about the modalities, and in particular about modal conversion: I 22 [15.12–14], 36 [28.21–29.4]. 59 See esp APr A 36–38.

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in the formal exposition of the syllogistic are rarely of the simple ‘noun plus verb’ structure. Rather, they usually contain, at least implicitly, a copula or ‘third item co-predicated’. The same is true of our text itself. Not one of its illustrative examples contains a verb. The example of a syllogism in Barbara — typical for all the subsequent examples — is this: Substance to every animal Animal to every man Therefore: substance to every man60 True, the example is expressed in telegraphese rather than in Greek, and there is nothing in it which answers to the copula. Nonetheless, the jargon expressions correspond to Greek sentences in which a third item is co-predicated: they do not correspond to Greek sentences of the structure ‘noun plus verb’. Here it appears that the author of our text has not merely not read [114] his Aristotle — he has not looked at the text which he is in the course of writing. How, in any event, might you think that Aristotle’s syllogistic would need an extension in order to accommodate propositions outside the basic hexad? In order to accommodate, say, the proposition ‘Every man is unjust’? Here an exciting answer suggests itself: propositions of this sort have logical properties which are not shared by all universal affirmative propositions. For example, from ‘Every man is unjust’ we may infer ‘No man is just’; and in general, from ‘AaB’ we may infer ‘AeB’.61 That formal inference is not recognized in basic syllogistic. An extension of syllogistic might come to display it — and might therefore open the way to some extra moods. Thus an extended syllogistic might acknowledge the validity of, say: AaB, BaC:: AeC which follows from Celarent together with the inference in question. That idea was to have a future, and perhaps it — or something like it — lies darkly behind our text. But nothing in basic syllogistic could be said to ‘make clear’ the validity of AaB, BaC:: AeC,

60 I 30 [21.22–23] — already at I 25 [18.11–12]; see above, n.29. 61 I use a double bar to indicate term-negation: ‘A’ is ‘non-A’. — The equivalence between ‘AaB’ and ‘AeB’ is noted by Psellus, Philosophica minora xv 1–14; earlier essays in the same field include Apuleius, int vi [198.7–17]; Boethius, int syll cat 785A; and the thing goes back ultimately to Aristotle, int 19b32–20a15.

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which depends on a rule beyond its ken. If our author did have such moods in mind, he failed to see — or contrived to hide — their relation to what he took to be the basic moods of the syllogistic.

Hypothetical moods They occupy I 38. There are precisely six of them. They are said to be ‘different from the syllogisms we have just described’ (30.16); but the first is ‘similar’ to a categorical mood. Our text does not trouble to explain what a hypothetical syllogism is.62 A curious sentence which announces that such things contain five distinct features63 clearly implies that every hypothetical syllogism contains a conditional proposition (31.26–32.2).64 [115] But that is true of only half the types of hypothetical syllogism which the text has just enumerated. Again, no explanation is offered of why there are only six kinds of hypothetical syllogism — and precisely those six kinds. There was no unanimity on the point in the Peripatetic tradition.65 62 Normally — and roughly — a hypothetical syllogism is a syllogism at least one of whose premisses is a hypothetical proposition; and a proposition is hypothetical if it is of the form ‘f(P1, P2, ... , Pn)’ — where each ‘Pi’ is a proposition and ‘f ’ is an n-placed sentential connector. 63 cf Boethius, hyp syll II i 1: ‘Some think that hypothetical syllogisms consist of five parts, others of three’; in his discussion of the controversy (§§ 1–6), Boethius refers to Cicero in rhetoricis (i.e. inv I xxxvii 67–xxxix 72; cf Marius Victorinus, in Cic rhet I ([pp.102–104]), and I suppose that the issue derives from the rhetorical tradition. 64 Each such syllogism is declared to contain an antecedent and a consequent — and hence, by implication, a conditional proposition. Unless our author thinks that disjunctions and conjunctions also divide into antecedents and consequents? Blemmydes, epit log xxxvi 973 bc, says that in the disjunctive proposition ‘ŒÆ j ¼æØ  KØ
j æØ ’ ‘ŒÆ’ is the antecedent and ‘j ¼æØ  KØ
j æØ ’ the consequent. 65 Alexander, for example, lists eight forms of hypothetical syllogism; but his extra hypothetical items concern such things as arguments based on ‘the more and the less’: in APr 389.31–390.9 [¼ Theophrastus, 111E, in Fortenbaugh et al., Theophrastus). Some later texts recognize seven types of hypothetical syllogism: Martianus Capella, IV 420; Marius Victorinus, apud Cassiodorus, inst II iii 13 [¼ Isidore, etym II xxviii 23–26]) — ultimately from Cicero, Top xiii 53–xiv 57 (cf Boethius, in Cic Top 353–359). See below, p.[118]. Others acknowledge six: the Ammonian scholia (apud Ammonius, in APr XI 1–36) — one ‘wholly hypothetical’ syllogism and five ‘mixed’ (but very different from what is to be found in our text); cf Philoponus, in APr 243.11–246.14. Some like five: [Ammonius], in APr 68.23–26 (corresponding, but not precisely, to items (1)–(5) below — wholly hypothetical syllogisms being noted separately at 67.29–30); Boethius (?), in APr 304.5–19 Minio-Paluello (for the authorship, see L. Minio-Paluello, ‘A Latin commentary (? translated by Boethius) on the Prior Analytics and its Greek sources’, Journal of Hellenic Studies 77, 1957, 93–102, on p.95; id, Aristoteles Latinus : iii 1–4 — Analytica Priora (Leiden, 1962), pp.lxxix–lxxxviii; J. Shiel, ‘A recent discovery: Boethius’ notes on the Prior Analytics ’, Vivarium 20, 1982, 128–141). Blemmydes, epit log xxxvi, recognizes the same six syllogisms as our author, to whom in this chapter he is very close. (But he has not simply copied our text, and I imagine that he and our author depend on a common source.)

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Modern scholarship tends to associate hypothetical syllogistic with the Stoics; but although the Stoics are mentioned in our text (31.28–29), it is only as the users of a variant terminology.66 Hypothetical syllogistic is not presented as a Stoic annexe to a Peripatetic system — and in fact Peripatetic logic, since the time of Theophrastus, had always incorporated a treatment of hypothetical syllogisms.67 The Peripatetics generally supposed that hypothetical syllogisms were in some fashion subordinate, or even reducible, to categorical syllogisms.68 The claim in our text that hypothetical syllogisms of the first type are ‘similar’ to categoricals perhaps hints at some sort of reduction. An obscure remark at the end of I 38 claims — traditionally and falsely — that the premisses of a hypothetical syllogism, when they are contested, are proved by way of categorical syllogisms;69 and that, too, may be taken to hint at a thesis of reduction or subordination. But there is nothing explicit on the subject in our text. The five hypothetical moods which are not similar to categoricals are closely related to the five kinds of unproved or ‘indemonstrable’ argument which formed the basis of classical Stoic logic. These kinds are sometimes presented by way of the following schemata: (1) If P, Q; P:: Q (2) If P, Q; Not-Q:: Not-P (3) Not-(both P and Q); P:: Not-Q [116] (4) Either P or Q; P:: Not-Q (5) Either P or Q; Not-P:: Q70 66 cf e.g. [Ammonius], in APr 68.4–14. 67 See J. Barnes, ‘Terms and sentences’, Proceedings of the British Academy 69, 1983, 279–326 [reprinted above, pp.433–478]; id, ‘Theophrastus and hypothetical syllogistic’, in J. Wiesner (ed), Aristoteles Werk und Wirkung — Paul Moraux gewidmet I (Berlin, 1985), pp.557–576 [reprinted above, pp.413–432]; M. Maro´th, Ibn Sina und die peripatetische ‘Aussagenlogik’ (Budapest, 1989); S. Bobzien, ‘Wholly hypothetical syllogisms’, Phronesis 45, 2000, 87–137; ead, ‘A Greek parallel to Boethius’ de hypotheticis syllogismis ’, Mnemosyne 55, 2002, 285–300. 68 The supposition is founded on Aristotle, APr A 23; see e.g. J. Barnes, ‘Proofs and the syllogistic figures’, in H.-C. Gu¨nther and A. Rengakos (eds), Beitra¨ge zur antiken Philosophie: Festschrift fu¨r Wolfgang Kullmann (Stuttgart, 1997), pp.153–166 [reprinted above, pp.364–381]; Maro´th, Ibn Sina, pp.74–81. 69 32.2–7: so too e.g. Alexander, in APr 262.32–263.25; Ammonius, in Int 3. 22–28; Philoponus, in APr 301.2–5. 70 The schematic versions are unhistorical, and in the case of (3)–(5) they are inaccurate: e.g. if the fourth indemonstrable is to be presented schematically rather than metalogically (see above, n.23), then it must be given by a pair of schemata: (4a) Either P or Q; P:: Not-Q (4b) Either P or Q; Q:: Not-P See S. Bobzien, ‘Stoic Syllogistic’, OSAP 14, 1996, 133–192, on pp. 134–141; J. Barnes, Truth, etc. (Oxford, 2007), pp.286–314.

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The first two of our author’s pentad are indeed completely stoical.71 The presentation of the other three is in one respect different inasmuch as it is explicitly allowed that the conjunction and the disjunctions which they contain may have more than two members (31.15, 18, 21).72 Thus instead of (4) we have a mood which may be described as follows: Given a disjunction (with any number of disjuncts) and also any one of the disjuncts, infer the conjunction of the negations of each of the other disjuncts. (See 31.17–21)

Schematically, and for the particular case of a triple disjunction, we might write: (4*) Either P or Q or R; P:: Not-Q and not-R.73 Disjunction in ancient logic is standardly taken to be ‘exclusive’; that is to say, a disjunction is true if and only if precisely one of its disjuncts is true. Hence (4*) is valid. There is thus no difficulty with the transformation of (4) into (4*) — or, more generally, with its extension to multiple disjunctions of any degree of complexity. For (5) the case is more complicated. The best generalization might be thought to be something like this: [117] Given a disjunction (with any number of disjuncts) and also the negation of at least one but not all of the disjuncts, infer the disjunction of the remaining disjuncts (or, if only one disjunct remains, the remaining disjunct). 71 But the name of (2) is unusual: ‘this is also called conversion with contradiction [f
I
ØŁØ I
Øæ ç] inasmuch as we convert from animal to man but contradictorily’ (31.6–8). The same name is found in [Ammonius], in APr 68.28, and in the Ammonian scholia, apud Ammonius, in APr XI 8–13 (‘it is called the second hypothetical and, Ææa  E
øæ Ø, conversion with contradiction’). Earlier ‘conversion with contradiction’ describes either the operation of contraposition, which takes us from ‘If P, then Q’ to ‘If not-Q, then not-P’, or else the contrapositive itself (e.g. Alexander, in APr 29.15–17; 46.6–8). And this presumably explains the origin of the unusual nomenclature; for in fact [Ammonius] offers us not (2) but rather (2*) If not-P, not-Q; Q:: P So too in Cicero, Top xiii 53, we find (2*) rather than (2); and also Martianus Capella, IV 420. Boethius, in Cic Top 356.5–14, gives (2); and in his comment on Cicero’s text he explains that (2*) is a special case of (2) (361.16–43). The Ammonian scholia give (2), and then offer (2*) as another example of the same mood. Marius Victorinus apparently offered (2): Cassiodorus, inst II iii 13 (cf Isidore, etym II xxviii 23). 72 So too e.g. Sextus, PH II 191; Galen, inst log vi 6; Augustine, c Acad III xiii 29; Philoponus, in APr 245.23–24, 31–35; Blemmydes, epit log xxxvi 976D–977B. 73 That is not exact, for the reason given in n.70 with reference to (4); and the same inexactitude will mark the following schemata. (And it is not at all easy to produce a perspicuous schematic representation of the generalization of (4).) If I nonetheless persist with schemata, that is because their disadvantages do not affect the points which I am concerned to bring out.

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Logical Matters

A schematic version, for the particular case of triple disjunctions, requires two schemata: (5*) Either P or Q or R; Not-P and not-Q:: R (5þ) Either P or Q or R; Not-P:: Either Q or R. Each of the schemata is valid. Our text (31.21–26) offers a generalization of (5*) and ignores (5þ). It has, to be sure, precedents for so proceeding;74 but from a logical point of view the procedure is arbitrary. The case of (3) is more serious. The generalization of (3) might be thought to look like this: Given the negation of a conjunction (with any number of conjuncts) and also at least one but not all of the conjuncts, infer the negation of the conjunction of the remaining conjuncts (or, if only one conjunct remains, the negation of the remaining conjunct). For triple conjunctions consider the pair of schemata: (3*) Not-(P and Q and R); P and Q:: Not-R (3þ) Not-(P and Q and R); P:: Not-(Q and R). Our text offers something different: The fourth mood is the one which, from a negated conjunction and the positing of one of the conjuncts, rejects the others; e.g. It is not the case that the same thing is a man and a horse and an ox. But it is a man. Therefore: it is not the others. (31.13–17)*

In other words, for triple conjunctions it suggests neither (3*) nor (3þ) but rather: (3%) Not-(P and Q and R); P:: Not-Q and not-R.75 And that is surely invalid. A conjunction is true if and only if each of conjuncts is true. Hence the negation of a conjunction is true if and only if at least one of its conjuncts is false. Hence a proposition of the form Not-(P and Q and R) [118] may be true when both ‘P’ and ‘Q’ are true. Hence from Not-(P and Q and R) together with ‘P’ we cannot validly infer ‘Not-Q’. 74 e.g. Philoponus, in APr 245.34–35; cf Galen, inst log vi 6. * Ææ  æ   › K I çÆØŒB ıº ŒB fiB ŁØ H
ıºÆŒ
ø

e a º Øa I
ÆØæH
x
Påd e ÆPe ŒÆd ¼
Łæø  KØ
ŒÆd ¥   ŒÆd  F, Iººa c
¼
Łæø  KØ
, PŒ ¼æÆ ŒÆd a º Ø. 75 To be sure, the example rather suggests a schema from predicate logic, to wit: (3P) (8x)¬ (Fx & Gx & Hx); Fa:: ¬ Ga & ¬ Ha Similarly with one of the two examples which illustrate (4*) and (5*). Are the examples merely careless? I doubt it — but the matter is too intricate to be broached here.

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The error is not peculiar to our author. In his Topics Cicero lists seven hypothetical moods.76 The first of the seven is (1) and the second is (2*); the fourth is (4), the fifth (5), the sixth (3). As for the third, it may be represented by (3C) Not-(P and not-Q); P:: Q.77 That is not identical with (3); but it is either a special case or else an immediate consequence of (3); and its presence in the list has, for that reason, been found odd.78 Finally, this is Cicero’s seventh mood: (7) Not-(P and Q); Not-P:: Q.79 The mood is invalid: if both ‘P’ and ‘Q’ are false, then Not-(P and Q) is true. Cicero does not explain why he takes (7) to be valid; but Boethius correctly observes that the mood may be accepted if ‘P’ and ‘Q’ are restricted to propositions which are jointly exclusive and mutually exhaustive. Hence it is tempting to guess that Cicero presupposed that a negated conjunction is true if and only if exactly one of its conjuncts is true;80 in other words, that he took [119] Not-(P and Q and R and ... ) to be equivalent to: Exactly one of: P, Q, R, ... 76 See above, n.65. 77 So at least Cicero’s example suggests; and so Martianus Capella, Marius Victorinus, and Boethius certainly understood the text. Cicero’s description of the inference, as the MSS present it, is this: When you negate certain conjuncts and assume one or several of them [ex eis unum aut plura sumpseris] so that what is left is rejected, that is called the third type of argument. (Top xiii 54) That is, I suppose: Given a negated conjunction (with any number of conjuncts) and also all but one of the conjuncts, infer the negation of the remaining conjunct. That does not fit the example: excision of ‘aut plura ’ clears up the difficulty (but see M. Frede, Die stoische Logik (Go¨ttingen, 1974), pp.160–161). 78 Boethius, in Cic Top 356.30–357.3, replaces (3C) by (3B) Not-(if P, not-Q); P:: Q — which (see 364.40–365.6) he seems to take to be the correct interpretation of Cicero’s text. Marius Victorinus retains (3C) but replaces (6) by something which is not formally valid: Cassiodorus, inst II iii 13 (cf Isidore, etym II xxviii 24). 79 So the MSS; and the text is protected by the parallels in Martianus Capella, IV 420, Marius Victorinus (Cassiodorus, inst II iii 13; cf Isidore, etym II xxviii 25), and Boethius, in Cic Top 359.17–22; see Frede, Stoische Logik, pp.161–167 (who also refers to Philoponus, in APr 246.5–16). 80 Note that he calls his third type of argument illa ex repugnantibus sententiis conclusio (Top xiv 56).

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Given such an equivalence, (7) is valid. Given such an equivalence — to return to our text — (3%) is valid. In our text, then, I suppose that (3%) is not a carelessness or casual error: rather, it derives from a tradition which took an unorthodox view of negated conjunctions, and which is represented for us by certain Latin logic texts. Perhaps the tradition itself depends on nothing more diverting than carelessness? I suspect not: rather, someone considered various ordinary sentences of the sort ‘You can’t have an entre´e and a dessert with this menu, you know’; and he decided that such negated conjunctions were true when exactly one of the conjuncts was true. Not an implausible decision — but discussion would lead to distant and deepish waters. The five Stoic indemonstrables do not constitute the sum of their hypothetical syllogistic. On the contrary, in calling the five moods ‘indemonstrable’ the Stoics suggest — what they also roundly affirm — that there are many other demonstrable syllogisms. (Indeed, infinitely many.) Why does our text limit itself to its versions of the five indemonstrables, suggesting that they (together with one further item) constitute the whole of hypothetical syllogistic? Perhaps our author thought it enough to list the moods of the indemonstrables: inasmuch as all other hypothetical moods can be derived from them, he has, in listing them, potentially encompassed all possible hypothetical moods. But in that case why did he not do the same thing with categoricals? Why, that is to say, did he not content himself with giving the indemonstrables of the first figure? (Or, come to that, Barbara and Celarent?) Categorical syllogistic recognizes compound inferences. For example, AaB, BaC, CaD:: AaD is a valid mood.81 But compound categoricals — as their name suggests — were construed as abbreviated strings of simple syllogisms. My example is an abbreviation of a pair of Barbaras, which you might write thus: AaB, BaC:: AaC, CaD:: AaD If a Peripatetic logician affirms that there are precisely n valid categorical moods, he means that there are n simple categorical moods: the compound [120] moods, infinite in number, do not count — they are not conceived of as additions to the logical repertoire. 81 For compound categorical syllogisms see the Ammonian scholia, apud Ammonius, in APr IX 41–X 28; [Ammonius], in APr 65.29–31; Blemmydes, epit log xxxi 933B. For compound hypotheticals: the Ammonian scholia, apud Ammonius, in APr Xl 37–XII 3.

Syllogistic in the anon Heiberg

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Perhaps the Peripatetics took a similar view with regard to the hypothetical syllogisms. There are n simple moods. Any other valid moods are compound. For example, If P, Q; Either R or P; Not-R:: Q is an abbreviated version of: Either R or P; Not-R:: P; If P, Q:: Q Hence the limitation to five hypotheticals. Or rather, to six — for there is also the first of the hypotheticals mentioned in our text, the one which is not a version of a Stoic indemonstrable but is ‘similar’ to a categorical. First, let us introduce the syllogism similar to the categoricals: If God is just, there are courts of justice in the hereafter If there are courts of justice in the hereafter, souls are immortal If God is just, souls therefore are immortal82 This appears in the first combination of the first figure of the categorical syllogisms, differing only in being hypothetical, as I have said. If the problem in question is negative, it will be established hypothetically either through the first figure or through the others. (30.20–28)*

The example is a case of what the Peripatetics called a ‘wholly hypothetical syllogism’.83 Wherein lies the similarity between such syllogisms and categorical syllogisms?84 Most presentations of wholly hypothetical syllogistic operate with telegraphic examples, of which the following is typical: If man, then animal If animal, then substance Therefore: if man, then substance85 82 Similar examples in Philoponus, in APr 243.25–32. * ŒÆd æH  b
›  E ŒÆŪ æØŒ E ‹ Ø  NƪŁø· N Łe ŒÆØ  Nd a KŒEŁ
ØŒÆØøæØÆ, N Nd a KŒEŁ
ØŒÆØøæØÆ IŁ
Æ Ø Æƒ łıåÆ, N › Łe ŒÆØ  IŁ
Æ Ø ¼æÆ Æ łıåÆ: y  b
s
K
fiH æfiø æ fiø  F æ ı åÆ  H
ŒÆŪ æØŒH
ıºº ªØH
I
ÆçÆ
ÆØ 
fiø fiH  ŁØŒfiH Øƺºø
‰ YæÅÆØ: N b æÅØŒe
YÅ e æ Œ

æ ºÅÆ, ŒÆd Øa  F æ ı åÆ  ŒÆd Øa H
º ØH
 ŁØŒH ŒÆÆŒıÆŁÆØ. 83 See Barnes, ‘Terms and sentences’; K. Ierodiakonou, ‘Rediscovering some Stoic arguments’, in P. Nicolacopoulos (ed), Greek Studies in the Philosophy and History of Science, Boston Studies the Philosophy of Science 121 (Dordrecht, 1990), pp.137–149 — she discusses our text on pp.140–141; Bobzien, ‘Wholly hypothetical syllogisms’. 84 [Ammonius], in APr 68.15–23, which also talks of such similarities, does not help. 85 e.g. Alexander, in APr 326.23–25 — see Barnes, ‘Terms and sentences’, pp.289–295); T. Ebert, Dialektiker und fru¨he Stoiker bei Sextus Empiricus, Hypomnemata 95 (Go¨ttingen, 1991), p.17 n.16.

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You might be prepared to accept the following schema as the pertinent logical form of the argument: If Fx, Gx; If Gx, Hx:: If Fx, Hx. And you might be tempted to say of the schema that it is nothing other than Barbara in hypothetical dress. For ‘If Fx, Gx’ is best construed universally, so that ‘If man, then animal’ amounts to ‘Anything is, if a man, then an animal’; [121] and that — according to some ancient logicians — is tantamount to the categorical sentence ‘Every man is an animal’.86 In general, ‘If Bx, Ax’ is equivalent to — if not synonymous with — ‘AaB’. Wholly hypothetical syllogisms — of this particular sort — are ‘similar to’ categorical syllogisms inasmuch as they are lightly disguised instances of the categorical mood Barbara. That conclusion is pleasingly close to the claim made in our text. But it cannot be correct. The example given in the text87 has the form If P, Q; If Q, R:: If P, R. It does not have the form If Fx, Gx; If Gx, Hx:: If Fx, Hx. Thus the alleged equivalence between ‘If Bx, Ax’ and ‘AaB’ cannot be the explanation of the similarity which our text claims to hold between wholly hypothetical syllogisms and categoricals. A second attempt to unearth the similarity calls on Theophrastus. Alexander reports that Theophrastus had examined wholly hypothetical syllogisms and that he had established certain analogies between conditional propositions and categorical propositions.88 Being a consequent or apodosis is analogous to being predicated, and being antecedent to being subject — for in a way it is subject for what is inferred from it. (Alexander, in APr 326.31–32)*

‘AaB’ sets down B and says A of it. ‘If P, Q’ sets down P and says Q on its basis. Aristotle had allowed himself the locution ‘A follows B’ as an expression of universal affirmative propositions:89 just as ‘AaB’ says that A follows B, so (and more obviously) ‘If P, Q’ says that Q follows P. The schema 86 See e.g. Galen, simp med temp XI 499; Boethius, hyp syll I i 6. 87 Compare the example in the Ammonian scholia, apud Ammonius, in APr XI 2–3; cf Boethius, hyp syll I iii 5. 88 in APr 325.31–328.7 (see Theophrastus, item 113B, in Fortenbaugh et al., Theophrastus; cf Philoponus, in APr 302.6–23 [¼ Theophrastus, 113C]; see Barnes, ‘Terms and sentences’. * I
º ª
ªaæ e b
ºªØ
ŒÆd ŁÆØ fiH ŒÆŪ æEŁÆØ, e b ¼æåŁÆØ fiH  ŒEŁÆØ  ŒØÆØ ªæ ø fiH KØçæ 
fiø ÆPfiH. 89 See below, p.[131].

Syllogistic in the anon Heiberg

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If P, Q; If Q, R:: If P, R is similar to Barbara AaB, BaC:: AaC inasmuch as ‘If P, Q’ is analogous to ‘BaC’, ‘If Q, R’ to ‘AaB’, and ‘If P, R’ to ‘AaC’. So Theophrastus; and it is reasonable to conclude that our author works in the Theophrastan tradition. Thus one sort of wholly hypothetical syllogism is similar to Barbara. A second sort is then described: ‘If the problem in question is negative, it will be established hypothetically either through the first figure or through the others’. What does it mean to say that ‘the problem in question is negative’? [122] A ‘problem [æ ºÅÆ]’ is, on Aristotle’s definition, a question of the form: Is it the case that P or not? And syllogisms were construed as answers to problems — that is to say, you solve the ‘problem’ by finding an appropriate syllogism the conclusion of which is either ‘P’ or ‘Not-P’.90 Hence the word ‘problem’ came to be used as a general designation for the conclusion of a syllogism. We might therefore imagine that the ‘problem’ in the illustrative example is: If God is just, souls therefore are immortal; and we might then guess that an example of a negative problem might be: It is not the case that if God is just, souls therefore are immortal. But it is evident that the ‘problem’ in the example is not the conditional proposition but rather its consequent, ‘Souls are immortal’. Note the position, of ‘¼æÆ’ in the last line: N › Łe ŒÆØ , IŁ
Æ Ø ¼æÆ Æƒ łıåÆØ (30.23). That clearly suggests that the ‘real’ conclusion of the argument — and hence the substance of the problem — is ‘Souls are immortal’. The underlying idea is this: the conclusion of a wholly hypothetical argument is not a conditional proposition — it is not ‘If P, R’. Rather, the conclusion is the consequent of the conditional proposition, ‘R’. The last line of the wholly hypothetical argument presents the conclusion, but presents it hypothetically. The argument is not taken to establish that if P, then R: it is taken to establish that R — on the hypothesis that P.91

90 For ‘æ ºÅÆ’, see also I 39 [32.12], below, p.[130]. 91 The same idea is found in Alexander: in APr 265.15–17; 326.12–17; cf Philoponus, in APr 243.32–36, 244.16–21; Boethius (?), in APr 320.7–16 [¼ Theophrastus, 113D]: Alexander et plurimus chorus philosophorum nec syllogismos huiusmodi contendunt: nil enim nisi consequentiam eos aiunt ostendere (320.14–16). See Barnes, ‘Terms and sentences’, pp.307–309.

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A negative problem will then be something of the form ‘Not-R’ for example: ‘Souls are not immortal’; and the conclusion — the last line — of a negative wholly hypothetical argument will therefore have the form If P, not-R Given that ‘If P, Q’ is analogous to ‘AaB’, presumably ‘If P, not-Q’ will be analogous to ‘AeB’. And corresponding to Celarent AeB, BaC:: AeC we shall find the wholly hypothetical schema: If P, Q; If Q, not-R:: If P, not-R. Two other categorical moods conclude to propositions of the form ‘AeC’ namely Cesare BeA, BaC:: AeC and Camestres BaA, BeC:: AeC [123] Corresponding to them we may invent the schemata If P, Q; If R, not-Q:: If P, not-R and If P, not-Q; If R, Q:: If P, not-R, each of which is valid. No doubt our text has those three negative schemata in mind. But it actually says that a negative problem ‘will be established hypothetically either through the first figure or through the others’;92 and ‘the others’ must refer to the second and the third figures. Yet no third-figure mood yields a universal negative conclusion. Our author has blundered — but it is perhaps no more than a careless slip. Our text explicitly takes wholly hypothetical syllogisms to constitute a single type of syllogism; yet Barbara, Celarent, Cesare, and Camestres are four distinct categorical moods: why not embrace four distinct wholly hypothetical moods? To be sure, the hypothetical companion of Celarent might be regarded as a special case of the hypothetical companion of Barbara; but the same is not true of the other two negative moods.93 More generally, our text 92 Theophrastus invented three hypothetical figures corresponding to the three categorical figures. Yet we should not be tempted to think that our text refers to the hypothetical figures: to change reference without warning and in the space of three lines would be unpardonable; and the text clearly supposes that affirmative problems can be proved only in the first figure — which is false of the hypothetical figures. 93 Blemmydes, epit log xxxvi 977D–979A (cf Philoponus, in APr 243.13–15), recognizes four types of wholly hypothetical mood, inasmuch as the conclusion of such a syllogism may have any of the four forms ‘If P, Q’, ‘If P, not-Q’, ‘If not-P, Q’, and ‘If not-P, not-Q’.

Syllogistic in the anon Heiberg

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offers no hint that wholly hypothetical syllogisms had once been elaborated in a systematic fashion.94

Non-concludent combinations Our text works with a hexad of categorical propositions, and it affirms that the six varieties of categorical proposition allow the construction of thirty-six combinations, thus: aa ae ai ao au ay ee ea ei eo eu ey ii ia ie io iu iy oo oa oe oi ou oy uu ua ue ui uo uy yy ya ye yi yo yu [124] The calculation presupposes that an ea pairing, say, is distinct from an ae pairing. The pairing which yields Cesare is {BeA, BaC}. The pairing which yields Camestres is {BaA, BeC}. And these two sets are supposedly distinct. Most, but not all, ancient accounts of the syllogistic took that line. It is not immediately evident how the two pairings were thought to be distinguished. That does not concern me here. But I venture to add that the orthodox line does not imply that combinations are ordered pairings: the pairing for Cesare is {BeA, BaC}, not . There is no such thing as ‘the first premiss’ of a syllogism.95 However that may be, our text informs us which combinations in each figure are concludent, and then affirms that all the rest are non-concludent. It offers no systematic proofs for the concludence of concludent combinations or for the non-concludence of non-concludent combinations. But it offers a sketch of the ways in which concludence may be proved, and it passes some

94 Contrast e.g. Boethius, hyp syll II ix 1–III vi 4. 95 See J. Barnes, Logic and the Imperial Stoa, Philosophia Antiqua 75 (Leiden, 1997), pp.121–125.

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remarks on the manner of proving non-concludence. I shall say something about the latter remarks — and first it is worth saying what a proof of nonconcludence ought to establish. To say that a combination is non-concludent is not to say that nothing can be deduced from it: trivially, from any combination an infinite number of propositions can be deduced. Rather, a combination is non-concludent if and only if it is not concludent; and a combination is concludent if and only if it entails a categorical proposition the two terms of which are identical with the two extreme terms of the combination. For example, a combination of the type ae in the first figure is concludent if and only if at least one of the following twelve schemata is a valid mood: (1) AaB, BeC:: AaC (2) AaB, BeC:: AeC (3) AaB, BeC:: AiC (4) AaB, BeC:: AoC (5) AaB, BeC:: AuC (6) AaB, BeC:: AyC [125] (7) AaB, BeC:: CaA (8) AaB, BeC:: CeA (9) AaB, BeC:: CiA (10) AaB, BeC:: CoA (11) AaB, BeC:: CuA (12) AaB, BeC:: CyA Consequently, the combination is non-concludent if and only if each of the twelve schemata is invalid. To prove non-concludence, then, we shall apparently need to produce no fewer than twelve distinct demonstrations, one for each schema. Aristotle made the task lighter for himself: in APr A 4–6 he restricts his attention to six of the twelve schemata; and he supposes that the first-figure combination ae is concludent if and only if at least one of schemata (1)–(6) is valid. Moreover, he saw that the task could be made lighter still. Given the equivalence between ‘AiB’ and ‘AuB’ and between ‘AoB’ and ‘AyB’, (5) is invalid if and only if (3) is invalid, and (6) is invalid if and only if (4) is invalid. And given the rules of subalternation, if (3) is invalid then (1) is invalid, and if (4) is invalid then (2) is invalid. Hence if we can show that (3) and (4) are invalid, the invalidity of all six schemata will have been demonstrated. How might the invalidity of, say, (3), be proved? In several ways. One of them — the way which Aristotle himself trod — relies on the production of

Syllogistic in the anon Heiberg

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counterexamples. If (3) is valid, then any triad of terms whatever has the following property: if, when the terms are substituted for ‘A’, ‘B’, and ‘C’ in the premisses of the mood, two truths result, then when the appropriate two terms are substituted for ‘A’ and ‘C’ in the conclusion of the mood, a truth results. Hence (3) is invalid if there is at least one triad of concrete terms — say ‘X’, ‘Y’, ‘Z’ — such that ‘XaY’ and ‘YeZ’ are both true and ‘XiZ’ is false; or equivalently, if there is at least one triad such that all of XaY, YeZ, XeZ are true. How might we show that there is such a triad? By producing one — for example, the triad ‘animal’, ‘man’, ‘inanimate’. The following three propositions are all true: Animal holds of every man Man holds of nothing inanimate Animal holds of nothing inanimate Hence not all concrete triads which make ‘AaB’ and ‘BeC’ true also make ‘AiC’ true. Hence (3) is not valid. The invalidity of (4) can be shown in the same way — say by means of the triad ‘substance’, ‘animal’, ‘inanimate’. [126] Hence — or so Aristotle concludes96 — the combination in question is non-concludent.97

96 Had he considered all twelve schemata, he would have come to a different conclusion; for schema (10) is a valid mood — it is the mood called Fapesmo. Here is a proof: 1 (1) AaB premiss 2 (2) BeC premiss 3 (3) not-CoA hypothesis 3 (4) CaA 3, square of opposition 1,3 (5) CaB 1,4 Barbara 1,3 (6) not-CoB 5, square of opposition 2 (7) CeB 2, conversion 2 (8) CoB 7, subalternation 1,2 (9) CoA 1, 2, 3, 6, 8 reductio 97 Here is Aristotle’s version of the proof: If the first follows each of the middle and the middle holds of none of the last, then there will not be a syllogism of the extremes; for nothing necessary results by virtue of the fact that this is so. That is to say, the combination {AaB, BeC} is non-concludent insofar as there is no valid mood of the form ‘AaB, BeC:: AxC’. For it is possible for the first to hold of each of the last and of none of it, so that neither the particular nor the universal is necessary.

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So much for what must be done, and for one way of doing it. Here is the passage in which our text remarks on proofs of non-concludence in the first figure: All the combinations apart from these are non-concludent. They are called nonconcludent because they infer to contrary and incompatible conclusions. So — to take as a single example the second combination of the first hexad in this first figure — Substance to every animal Animal to no inanimate Therefore: substance to every inanimate And again, for the same combination: Animal to every man Man to no inanimate Therefore: animal to no inanimate Observe how, for the same combination and the same quality and quantity, contrary conclusions have been inferred. (I 30 [22.13–22])98 [127]

Those remarks have some affinity with the Aristotelian method which I have just sketched; but they do not reproduce that method, and the method which they describe is doubly bizarre. First, the reason for denying that a

That is to say, possibly (AaB and BeC and AaC), so that ‘AaB, BeC:: AoC’ is not valid (and hence ‘AaB, BeC:: AeC’ is not valid either); and possibly (AaB and BeC and AeC), so that ‘AaB, BeC:: AiC’ is not valid (and hence ‘AaB, BeC:: AaC’ is not valid either). And if nothing is necessary, there will not be a syllogism by way of these items. Terms for holding of each: animal, man, horse. Of none: animal, man, stone. (APr A 26a2–9) That is Aristotle’s most elaborate exposition of a proof of non-concludence. It is nothing if not concise, and it has often been misunderstood. On Aristotle’s method, see G. Patzig, Aristotle’s Theory of the Syllogism (Dordrecht, 1968), pp.168–92; J. Lear, Aristotle and Logical Theory (Cambridge, 1980), pp.54–75; P. Thom, The Syllogism (Munich, 1981), pp.56–64. 98 ƒ b Ææa   ı 
 Nd
Iıºº ªØ Ø· Iıºº ªØ Ø b ºª
ÆØ Øa e K
Æ
Æ ŒÆd IØŒæØÆ ı
ªØ
ıæÆÆ, x
‰ Kd 
e  ªÆ   F ıæ ı æ  ı B æÅ   K
fiH ÆPfiH æfiø åÆØ PÆ Æ
d Çfifiø, e ÇfiH
P
d Iłåfiø, PÆ ¼æÆ Æ
d Iłåfiø: ŒÆd ºØ
Kd  F ÆP F æ  ı e ÇfiH
Æ
d I
Łæfiø, › ¼
Łæø  P
d Iłåfiø, e ÇfiH
¼æÆ P
d Iłåfiø: N f Kd  F ÆP F æ  ı ŒÆd B ÆPB  Ø Å   ŒÆd   Å  K
Æ
Æ ı
åŁÅÆ
ıæÆÆ. — cf I 31 [23.19–25], on the second figure, and I 32 [25.14–26], on the third. In the case of the second figure the text simply gives us two triads of true propositions and leaves us to decide what to make of them. In the case of the third figure there are two triads, and then the statement that, in the case of all the non-concludent combinations, an appropriate choice of terms will show that ‘they do not always infer to the same conclusions’. Note also the scholium (130.18–21 — virtually identical with Philoponus, in APr 34.7–10): ‘The word ‘Ø’ [in Aristotle’s definition of the syllogism] is taken for ‘‘the conclusion which is inferred ought to

Syllogistic in the anon Heiberg

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combination is concludent is precisely the fact that certain propositions of the form ‘AxC’ can be inferred from it. Secondly, the conclusions which our text invites us to draw quite evidently do not follow from the premisses which it offers us. It is worth citing a second passage. After a description of Darapti, AaB, CaB:: AiC we find this: Sometimes ‘to every’ is also concluded, the terms or the matter being responsible and not the combination nor the structure of the syllogism — for in that case ‘to every’ would always be inferred. e.g. Substance to every man Animal to every man Therefore: substance to every animal. (I 32 [24.1–5])*

The pseudo-mood Darapta — AaB, CaB:: AaC — is not valid. It is not valid because you cannot always infer a universal affirmative conclusion from premisses of that form. But sometimes a universal affirmative conclusion can be inferred; and in such cases it is the ‘matter’ of the particular concrete argument, or the particular concrete propositions which are its premisses, which account for the validity.99 The connexion between this passage and the proofs of non-concludence is plain;100 and the passage shares one of the oddities of the proofs — for it approves an argument which is evidently invalid. Given Substance to every man and Animal to every man, you may not infer Substance to every animal, even though this third proposition is also true. [128]

be a single determined item’’ — it is there to distinguish syllogisms from non-concludent combinations which conclude both to ‘‘to every’’ and also to ‘‘to no’’ ’. * ı
ªÆØ b
ªaæ ŒÆd e Æ
 KØ
‹ H
‹æø
ªØ

ø
ÆNø
Xª ı
B oºÅ ŒÆd P  F æ  ı Pb B  F ıºº ªØ F º ŒB· j ªaæ i
Id e Æ
d ı
ª x
PÆ Æ
d I
Łæfiø, e ÇfiH
Æ
d I
Łæfiø, PÆ ¼æÆ Æ
d Çfifiø: 99 On matter and form in ancient logic, see Barnes, ‘Logical form’, pp.39–65; K. Flannery, Ways into the Logic of Alexander of Aphrodisias, Philosophia Antiqua 62 (Leiden, 1995), pp.109–145. 100 The connexion is explicitly noted at 25.19–26.

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In order to prove the non-concludence of the first-figure combination in ae the text purports to produce a triad of concrete terms such that the concrete argument XaY, YeZ:: XaZ is valid; and a second concrete triad such that X*aY*, Y*eZ*:: X*eZ* is valid. Although the text fails to produce such triads, we may still ask why such things — were they to be found — should be thought to prove nonconcludence. The underlying idea is surely this: the first argument shows that arguments of the form (4) are not always valid, and the second argument shows that arguments of the form (3) are not always valid. Hence the schemata (4) and (3) are not valid moods. Hence the combination is non-concludent. Both Aristotle’s method and the method indicated by our text hunt for pairs of triads. But the methods differ in this respect: Aristotle requires triads of terms which make certain triads of propositions true; our text requires triads of terms which make certain arguments valid. Our text is not innovative. On the contrary, the method which it patronizes is found in Alexander, and then in most later Peripatetic texts which deal with non-concludence.101 It is, in short, the orthodox method of the late Peripatos102 — where it began life as an interpretation of Aristotle. It is a false interpretation of Aristotle. Moreover, it is a method which is invariably bungled in its application inasmuch as we are urged to accept arguments which in fact are invalid.103 Nonetheless, the method need not be considered as an interpretation of Aristotle (nor does our text offer it as such); and even if its applications are bungled, the method might itself be acceptable. At the heart of the method there lies a certain thesis, never explicit but clearly implicit in our texts. It is this: If propositions of the form P and Q sometimes entail a proposition of the form R, then the schema 101 See e.g. Alexander, in APr 52.22–24 (‘combinations which change and are reshaped along with their matter and have different and conflicting conclusions at different times are nonconcludent and unreliable’); cf 55.21–32, 57.3–4, 61.18–20; Philoponus, in APr 34.7–10, 75.3–7, 25–30, 76.6–20, 80.25–81.21; [Ammonius], in APr 48.40–49.6, 62.12–14 — see Patzig, Aristotle’s Theory, pp.171–172; Barnes, ‘Logical form’, pp.58–62; Barnes et al., Alexander, pp.12–14 (which the present pages amplify and correct); Flannery, Alexander, pp.136–142). 102 But perhaps not the only method. Thus Apuleius holds that a combination is non-concludent ‘because it can infer a falsity from truths’ (int xiv [215.6–7]; cf viii [203.5–6]). Or is Apuleius merely proposing the orthodox method in a confused manner? 103 The two points are connected: the applications are bungled because they use Aristotle’s triads, or triads closely modelled on them.

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P, Q:: Not-R is not a valid mood. [129] The thesis has a certain plausibility. But it is false. It is worth showing that it is false — and first it is worth showing that one seductive objection to it is itself false. The seductive objection suggests that the antecedent of the thesis can never be given a true instantiation; for it makes no sense to suppose that propositions of a given form might sometimes entail a certain form of proposition and sometimes not entail one. Entailment, after all, is an all or nothing affair: items do not ‘sometimes’ entail other items. The objection is mistaken. Consider again the schema AaB, BeC:: AeC. The schema is not a valid mood — that has already been demonstrated. But now take the concrete triad of terms ‘man’, ‘man’, and ‘stone’; and construct the argument: MaM, MeS:: MeS. That argument is an instance of the invalid schema. It is also — and trivially — a valid argument. (It is not a syllogism, you will say. True — it does not satisfy the conditions laid down by Aristotle in his definition of the syllogism. But no matter. The question is not: Is the argument an Aristotelian syllogism? But rather: Is the argument valid?) An invalid schema may have instances which are formally valid deductions; and the seductive objection is false.104 There is a true objection. As terms take ‘man’, ‘man’, and ‘Greek’. Consider the argument: MeM, MaG:: MaG That argument is evidently and trivially valid. Now the argument is an instance of the schema AeB, BaC:: AaC. Hence arguments which instantiate that schema are sometimes valid. But then, if we accept the thesis which lies at the heart of the late Peripatetic method, we shall be obliged to reject the schema AeB, BaC:: AoC — and a fortiori the schema AeB, BaC:: AeC. 104 The schema P,Q:: R is not a valid mood. Every valid syllogism is an instance of the schema ...

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But the first of those schemata is Celaront and the second Celarent. Thus the thesis at the heart of the orthodox method is false, and the method itself is to be rejected. [130]

The colophon of philosophy I 39–48 contains a continuous argument. It is the most technically sophisticated part of the treatise; it is presented as the summit or culmination — the Œ º ç
— of the study; and it purveys a ‘remarkable method’ which rests on ‘a genuinely profound and most scientific consideration’. It is evidently the most important part of the chapter in its author’s eyes. So that we may have a ready supply of premisses for any disputed problem which is put forward, a remarkable method has been discovered: by way of it we have a ready supply of premisses and thus can demonstrate by way of a conclusion the communality or the alienation of the terms in the problem. He hands this method down by way of a certain consideration ... (I 39 [32.10–15])*

‘He hands down’ — who does? Aristotle, although our text does not say so; and the ultimate source of the discussion is I 39–48 is APr A 27–28,105 where Aristotle explains ‘how we shall have a ready supply of syllogisms in relation to whatever may be posited’ (43a20–21).** That is to say, the colophon of philosophy is what the Middle Ages later pictured as the pons asinorum.106 The method or Ł   is apparently distinguished from the consideration or ŁæÅÆ; and at 32.8 the text announces: ‘This is the ŁæÅÆ’. Since there is nothing answering to a theorem in the following lines, I take the word ‘ŁæÅÆ’ in a relaxed sense — a certain heuristic method is to be based on certain logical considerations. It is difficult to say where the account of the ŁæÅÆ ends and the account of the method begins. Indeed, I incline to

* ‰ ªaæ i
P æ Å
æ ø
Æ
e Ø
 F
æ Ł
  IçØÅ ı
ı æ ºÆ  ŁÆıÆÆ Ø KæÅÆØ Ł   Ø w æ ø
P æ F
 H
K
fiH æ ºÆØ ‹æø
c
Œ Ø
ø
Æ
j c
Iºº æøØ
Øa ıæÆ  I Œ
ı
: ÆæÆøØ
s
c
 ØÆÅ
Ł 
Ø Ø
 ŁøæÆ  ... 105 Which Alexander, in APr 290.16–18, and Philoponus, in APr 270.10, 273.21, explicitly characterize as a Ł  . ** H ... P æ 
ÆP d æe e ØŁ

Id ıºº ªØH
... 106 The diagram — or at any rate, a diagram — was used by Alexander (in APr 301.10 — but it is not preserved in our MSS of the commentary), and by Philoponus (in APr 274.7 — with a diagram in the MSS); and it is found in many MSS of APr itself (Minio-Paluello, ‘Latin commentary’, p.97 n.7). See e.g. Thom, Syllogism, pp.73–75.

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think that there is no exposition of the method itself: we get the ŁæÅÆ and are left to deduce the method for ourselves. However that may be, the method must sound like a piece of hocus-pocus. How could any method help me to solve every problem, to prove every provable truth?107 To be sure, the method is less audacious than at first it appears to be. Every problem is said to be ‘contained in two terms’; and every solution to a problem consists of a syllogism, the conclusion of which is an appropriate proposition of the form ‘AxC’: Since each problem in dispute is contained in two terms, we need another term to mediate and either to connect the extremes to one another or else to separate and dissever them. (I 39 [32.18–21])*

[131] The question is, how do we find such a middle term? And the method answers the question. If the question is sensibly less daunting than its first expression suggested,108 it is nonetheless daunting enough — how could any method be devised to answer it? Surely each science will have its own methods? The ŁæÅÆ on which the method is based is complex; and the exposition in our elementary text is (or so I have found) more difficult to follow than Aristotle’s original version. We start with a problem, the terms of which will be designated ‘A’ and ‘E ’. (This is the first time in our text that schematic letters have been used: they are not explained.) And we construct — or discover — six sets of terms, ´ˆ˜ and ˘˙¨, three of them associated with A and three with E (I 39 [32.21–26]).109 For the middle term has three qualities in relation to each of the two extremes: either the middle is one of the terms which follows them, i.e. one of the more universal terms, or it is one of those which they follow, i.e. one of the more particular terms, or it one of the alien terms. (32.26–33.1)110 107 The method is presented as a method of proof: cf 32.14 (I Œ
ı
); APr A 43a38, b11 (cf 43a21–22: a æd ŒÆ
Iæå). But Aristotle’s method, in virtue of the division which he makes in the lists of terms (see below, p.[131]), will enable us to supply both demonstrative and non-demonstrative syllogisms: see 43b9–11; Philoponus, in APr 280.11–27. * Kd ªaæ ŒÆ
æ ºÅÆ N IçØÅØ
K
åŁb
ıd
‹æ Ø KæغÅÆØ, æ ı Ø
e ‹æ ı  ºÆ F
   ŁÆ ıØÇ
  a ¼ŒæÆ æe ¼ººÅºÆ Y ı
I ؜H
  ŒÆd ØÆŒæ

 : 108 Not, to be sure, in Aristotle’s view; for he has already purportedly shown that every proof must take such a form (APr A 23). See Barnes, ‘Proofs and the figures’. 109 cf APr A 44a11–17 — at 32.22 ‘› çغ  ç ’ designates Aristotle. 110 æE ªæ Ø
Æ  Ø ÅÆ æe Œæ
H
¼Œæø
›   åØ: j ªaæ H
 
ø
ÆP E KØ
›   Xª ı
H
ŒÆŁ ºØŒøæø
j H
x  
ÆØ Xª ı
H
æØŒøæø
j H
Iºº æø
: — At 32.28 I omit ‘K
’ before ‘ x ’: cf 33.3, 5, 14, 18, 25.

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B, ˆ, and ˜ terms associate with A; Z, H, and ¨ terms associate with E. X is a B term if it ‘follows’ or is ‘more universal than’ A. In Peripatetic jargon, ‘X follows Y’ normally means ‘XaY ’.111 But from ‘XaY ’ it does not follow that X is more universal than Y; for ‘XaY ’ is compatible with ‘YaX’, in which case the two terms are equally universal. X is more universal than Y if it holds of every Y and also of some non-Y. Hence X is a B term if XaA and also AoX. Similarly X is a Z term if XaE and EoX. If X is a ˆ term, it is ‘more particular’ than A; that is to say, X is a ˆ term if AaX and also XoA. And X is an H term if EaX and XoE. As for ‘alien’ terms, it emerges that X is a ˜ term if XeA and X is a ¨ term if XeE. It is evident that the three ‘qualities’ do not exhaust the relations in which the middle term may stand to the extremes. (Although the run of the text may suggest exhaustivity, there is no explicit claim to this effect — and the word ‘Ø
Æ’ at 32.26 perhaps insinuates non-exhaustivity.) Why, for example, not construct sets of terms such that XiA or XiE ? On this point our text is at one with Aristotle, who remarks that ‘we should not select terms which follow some, but rather those which follow all the object’ (APr A 43b11–12).112 Nonetheless, our text is at once more generous and more sparing than Aristotle. The touches of generosity are harmless;113 but the omission of [132] certain types of term which Aristotle includes is another matter — an elementary treatise may perhaps suppress the refinement which calls for sets of ‰ Kd e  º predicates (APr A 43b32–36); but it is strange — and potentially disastrous — to exclude co-extensive terms.114 111 See e.g, Aristotle, APr A 43b3, 44a13; Alexander, in APr 55.10–11, 294.1–2 (with reference to 43b3); see above, p.[121]. 112 E  KŒºªØ
c a  
Æ Ø
d Iºº ‹Æ ‹ºfiø fiH æªÆØ ÆØ: — Nor need we select terms such that AeX and EeX, for ‘the negative converts’ (APr A 43b5–6) — i.e. such terms are identical with ˜ terms and ¨ terms. 113 e.g. our text will require ‘substance’ to appear among the B terms for ‘animal’ and also among the B terms for ‘man’: according to Aristotle, if X is a B term for Y and YaZ, then X should not appear among the B terms for Z (APr A 43b22–26). 114 Aristotle explicitly requires us to list YØÆ (APr A 43b2–3, 26–29), which our text implicitly excludes. Here APr distinguishes between ›æØ , YØÆ, and ‹Æ ÆØ fiH æªÆØ (43b2–4), so that you might reasonably infer that, in this context at least, ‹Æ ÆØ are always taken to be ŒÆŁ ºØŒæÆ. Now when in A 28 the ŁæÅÆ is developed, Aristotle speaks exclusively of ‹Æ ÆØ: a reader might naturally suppose that ‹Æ ÆØ here are the same items as ‹Æ ÆØ at 43b2–4, and so he might conclude that the ŁæÅÆ applies only to ŒÆŁ ºØŒæÆ terms. Thus Alexander, in APr 306.24–307.7, takes APr A 44a38–b5 to restrict the sets of terms to ŒÆŁ ºØŒæÆ. Later, at 309.11–35, he rightly concludes that the sets will contain co-extensional terms as well as ŒÆŁ ºØŒæÆ (something he had already stated plainly enough at 295.1–3). Nonetheless, he still gives a certain preference to ŒÆŁ ºØŒæÆ inasmuch as, according to him, the method requires us to look first for ŒÆŁ ºØŒæÆ and to take in co-extensional terms only if no ŒÆŁ ºØŒæÆ are to be found. In sum: our text is mistaken when it excludes co-extensional terms.

Syllogistic in the anon Heiberg

723

Having constructed the six sets of terms, consider next those terms which are found both in one of the sets associated with A and in one of the sets associated with E.115 Our text gives the impression that, for any A and any E, there will always be at least one such term. In any event, the ŁæÅÆ implicitly limits itself to pairs of terms, A and E, for which that holds true.116 Any such common term must fall into one of nine classes: either it is both a B term and a Z term — either, as the text puts it, it is a BZ term —, or it is a ˆZ term, or a ˜Z, or a BH, or a ˆ˙, or a ˜H, or a B¨, or a ˆ¨, or a ˜¨. The text develops an illustrative example of a ˆH term; and it then goes through, in schematic fashion, each of the nine classes in the order in which I have listed them.117 The ŁæÅÆ is most easily presented by way of an example. Suppose that the problem is this: What is the connexion between pipe-smoking and affability, between being a pipe-smoker and being affable? In other words, for what x do we have it that PxA? We consult the pertinent sets of terms for P and A; and we find that the term ‘contented’ appears both as a B term and as an H term. What next? Well, in this particular case, you might well imagine the following response: ‘Since C is a B term, CaP and PoC, and since C is also an H term, [133] AaC and CoA. Now, by Barbara, we may infer that AaP (from ‘‘AaC’’ and ‘‘CaP’’); and then — if you insist — we may convert and assert that PiA.’ Now that is exactly what Aristotle does with BH terms.118 But it is not how the ŁæÅÆ proceeds in our text. Rather, we find this: But Aristotle’s text invites the mistake. Alexander narrowly avoids it. And Philoponus in effect warns against it: ‘It is clear that what follows something either extends further or is equal — animal, which extends further, follows man, and so does laughing, which is equal’ (in APr 273.30–33, on APr A 43b4). 115 cf APr A 43b42, 44a1, 6, 11. 116 So, explicitly, Alexander, in APr 294.21–22. 117 Aristotle goes through the classes first at APr ` 43b39–44a11, using metalogical descriptions, and then at 44a11–35, using schematic letters. In the metalogical treatment he mentions ˆZ, ˆH, ˜Z, B¨, and ˜H, which he uses to generate syllogisms in Barbara, Darapti, Celarent, Camestres, and Felapton. In the schematic treatment he lists the same five classes and moods, and adds to them BH and Baralipton. Later, at 44b25–37, he remarks that BZ, ˆ¨, and ˜¨ terms are ‘useless for making syllogisms’. Aristotle is interested in the production of (demonstrative) syllogisms: for each of the four types of categorical proposition, his procedure identifies (at least one) class of common term which will serve for its deduction. Our text — in the interest of a scientific hunt and discovery (I 39 [33.26–27]) — wants to ensure that every combination (and hence every concludent combination) has been considered. 118 ‘If B is the same as H, there will be a converted syllogism. For E will hold of every A — since B of A and E of B (it is the same as H ) — whereas A will not necessarily hold of every E but will necessarily hold of some since a universal affirmative predication converts to a particular’ (APr A 44a30–35).

724

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From BH terms there are generated sixteen non-concludent combinations in the first figure: with a particular affirmative major and a minor which is either particular affirmative or particular negative or undetermined affirmative or undetermined negative; or with a particular negative major and ... (I 43 [35.24–28])*

It would be tedious to quote the whole passage. The sum of it is this: A BH term generates — in the first figure: ii, io, iu, iy, oo, oi, ou, oy, uu, ui, uo, uy, yy, yi, yo, yu — all which are non-concludent; — in the second figure: ao, ay — both concludent; and ai, au — both non-concludent — in the third figure: ia, oa, ua, ya — all concludent. In all, then, a BH term generates twenty-four combinations, six of which are concludent. Similar accounts are given of the eight other classes. Taken together — what magic — they generate all 192 combinations. What is going on? Let us return to our example. The BH term ensures that CaP, PoC, AaC, and CoA. It also, according to our text, generates twenty-four combinations — among which the combination for Barbara is not to be found. First, why not Barbara? I suppose, with little confidence, that the answer is this: the ŁæÅÆ generates only those combinations which have a configuration appropriate to the problem. The problem — the conclusion to any pertinent syllogism — must have the form ‘PxA’. In the first figure, every combination appropriate to this problem must have the form Px1C, Cx2A. The combination AaC, CaP does not have that configuration. Hence the ŁæÅÆ does not generate it. (‘So much the worse for the ŁæÅÆ: the restriction which it places on the generation of combinations is wholly arbitrary; and although there is nothing thereby logically amiss with it, the arbitrariness makes it an implausible candidate for the founding of a useful method.’) However that may be, a BH term does not generate the combination for Barbara. But it does generate twenty-four other combinations — how? The * Ie b  F ´˙ ŒÆb K
fiH æHfiø åÆØ Iıºº ªØ Ø I Œ
ÆØ æ  Ø: › KŒ Ç
 æØŒB ŒÆŪ æØŒB ŒÆd Kº
 j æØŒB ŒÆŪ æØŒB j æØŒB æÅØŒB j Iæ Ø æ ı ŒÆŪ æØŒB j Iæ Ø æ ı æÅØŒB, ŒÆd › KŒ Ç
 æØŒB æÅØŒB ...

Syllogistic in the anon Heiberg

725

text says nothing on the matter; and it is not easy to devise a convincing answer. [134] It will seem plausible to think along the following lines. The definition of a BH term guarantees four propositions, which constitute what I shall call the ‘basic group’. In our case: CaP, PoC, AaC, CoA. The members of this group entail various other propositions by way of the conversion laws and the equivalences for unquantified propositions. Adding all the entailed propositions to the basic group, we arrive at the ‘extended group’, in our case: CaP, PiC, CiP, PuC, CuP, PoC, PyC, AaC, CiA, AiC, CuA, AuC, CoA, CyA, PiC, AiC Pair off the members of this extended group to form combinations in the various figures, and all the twenty-four combinations listed in the text are generated. That is satisfactory enough in itself. But it does not meet all the demands of the text. For the extended group generates more than the twenty-four desiderated combinations. For example, it generates PiC, AiC which is a non-concludent third-figure combination. According to our text, this combination is generated not by a BH term but rather by a BZ term (I 40 [34.11–13]). The procedure I have rehearsed may generate all the combinations listed — but it does not generate only those combinations. We need something more sophisticated. No simple procedure will do the trick. Here is one complex procedure. The key to it is this: although we start, as before, with the basic group, we construct three extended groups, not one — and the construction is done under certain restrictions. I start with the notion of a ‘serviceable’ proposition: a proposition is serviceable for a given figure if it may serve as a member of an appropriate combination in that figure. Next, consider, for each figure, the universal propositions in the basic group. (1) If both these propositions are serviceable, they alone form the extended group. (2) If one of the propositions is serviceable, then the extended group is formed from that proposition together with all the entailments of the other propositions in the basic group which are serviceable in tandem with the first proposition. (3) If neither of the propositions is serviceable, then the extended group consists of all the serviceable entailments of the universal members of the basic group together

726

Logical Matters

with the serviceable non-universal members of the basic group and their serviceable entailments. The basic group for the BH term C was CaP, PoC, AaC, CoA. [135] For the first figure, neither universal proposition is serviceable. Hence rule (3) applies and we generate the following extended group: PiC, PuC, PoC, PyC, CiA, CuA, CoA, CyA — which yields the sixteen listed combinations. For the second figure ‘CaP’ is serviceable; rule (2) applies; we get: CaP, CiA, CuA, CoA, CyA — and hence the four listed combinations. For the third figure ‘AaC’ is serviceable. Rule (2) gives AaC, PiC, PuC, PoC, PyC — hence, again, the listed combinations. The rules I have laid down are tortuous and arbitrary. I do not suppose that our author had thought them out — and I have not found them in any other ancient text. But at least the procedure I have sketched gives the desired results for BH terms; and I hope that it gives the desired results for the other eight classes of common term. But I am sure that it is possible to invent other complex procedures; and in all probability there are some which are superior to the one I have here set out. So much for the ŁæÅÆ. I am not sure why it should be called deep and scientific — unless those two words mean something like ‘contorted’. In any event, the ŁæÅÆ is presented as the basis for a method. The method will give us a ready supply of premisses for any problem (32.12–14); and the text also assures us that if we consider matters in this way, we shall discover all the combinations, both concludent and non-concludent, by the little — and not so little — method, and not one of all of them will be able to escape or run away from us. (34.3–6)*

The ŁæÅÆ purports to show that, for any problem, the nine classes of associated middle terms will yield all possible combinations. The method, then, is presumably to be described in something like the following way: ‘If you want to solve the problem ‘‘For what x is it the case that AxC?’’, then make the six sets, construct the nine classes, produce the groups, assemble the * I
ÆŁøæ F
 oø  f 
Æ I
ıæ 
æ  ı ıºº ªØØŒ   ŒÆd Iıºº ª ı K
ØŒæfiH  fiø ŒÆd P ØŒæfiH Ł ÆØ ŒÆd Pb
A H

ø
ØÆºÆŁE
j ØÆæA
ÆØ ı
ÆØ:

Syllogistic in the anon Heiberg

727

combinations, select the concludent combinations, and embrace the concludent combination which yields a syllogistic proof for the problem.’ I am not sure whether the method is offered as a sure-fire way of finding a proof, as the best possible way, or simply as one good way among others. It seems to me evident that it is not a good way — certainly not as good as Aristotle’s original way; but I shall limit myself to showing that it is not a sure-fire way. The value of the method depends on the nature of the sets of terms on which it draws. In order to guarantee a proof of a problem, the sets must be complete: every middle term of every type must be found among them. It is [136] wildly unreasonable to imagine that such complete sets are ever available.119 But even if the sets were complete, there would be no guarantee of a proof; for the three qualities which determine the construction of the classes are three among many, and the terms needed for a proof might exhibit one of the other sorts of quality. In particular, the sets contain no co-extensive terms; and yet, according to Aristotle, many proofs use counterpredicable terms. Finally, even if the sets of terms were extended to include all the possible qualities, the method would not guarantee that we hit on a proof: the most it could hope to guarantee is that we should hit upon at least one syllogism with true premisses.120 But a syllogism with true premisses is not thereby a proof.121 In short, the colophon of philosophy is a curious item. The ŁæÅÆ which it rehearses is serpentine and inexplicably arbitrary. The method which it trumpets is of no scientific value. Logic, in the Peripatetic tradition, purports to be the instrument of the sciences; in particular, its value is measured by its capacity to formulate scientific proofs. Notoriously, in Aristotle’s own writings there is a gap between the scientific pretensions and the logical content of the syllogistic. As the Peripatetic tradition developed, so the gap widened. 119 To be sure, each set, according to Aristotle (and doubtless according to our text), can have only a finite number of members (APst A 19–22). But there is no upper limit to the number of members of any set, and no way of ensuring that all have been discovered. Moreover, there is (according to our text) an infinite number of problems and hence of sets of terms (I 27 [20.4–10]). Alexander’s illustrative examples of sets list a certain number of concrete terms and then add ‘ŒÆd a  ØÆFÆ’ (in APr 301.21, 23, 31). 120 Aristotle’s sets of terms are differentiated into ŒÆŁ Æ and ŒÆa ıÅŒ  predicates (APr A 43b6–11 — cf 44a36–b5; Alexander, in APr 295.28–296.19); and the provenance of a middle term will thus indicate whether or not it is suitable material for a demonstrative syllogism. 121 But see above, p.[100].

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Index of Passages The index lists substantial references to the ancient texts: bold entries signal citation or discussion; and a prefixed asterisk marks textual comment. Against each work there is (usually) an English version of its abbreviated Latin title, an indication of the edition used, and an explanation of the style of reference. The indications use these symbols: BT Bibliotheca Teuberiana CIAG Commentaria in Aristotelem Graeca CMG Corpus Medicorum Graecorum GG Grammatici Graeci GL Grammatici Latini OCT Oxford Classical Texts PG Patrologia Graeca PL Patrologia Latina The explanations use these abbreviations: b book c column ch chapter l line p page s section sb subsection v volume w work Alcinous didask : Didascalicus; Whittaker (Paris, 1990); ch þ [p þ l (ed Hermann)] vi [158] 48 vi [159.4–7] 452, 469 vi [159.12–17] 452 vi [159.43–4] 217 Alexander of Aphrodisias fat : On Fate : Bruns CIAG suppt II ii; p þ l 207.5–21 499 n.2 209.31–210.1 499 n.2 in APr : Commentary on Aristotle’s Prior Analytics ; Wallis CIAG II i; p þ l 6.16–21 74 7.25 458 n.1 11.17 437 n.3

12.23–4 80 n.92 13.12–20 80 n.92 15.12 162 n.56 16.7–10 162 n.56 17.12 103 n.146 18.12–22 398 n.31 18.12–20.29 409 n.* 21.10–23.2 123 21.28–22.25 100–1, 127 n.212 21.31 100, 103 22.2–3 127 n.213 22.5–6 127 n.213 22.9–12 127 n.213 22.10–15 127 n.214 22.18–23 100 n.141, 103, 113 n.171, 127 n.213, 128 n.214 26.15–18 623

752 27.27 81 27.27–28.30 79, 637 28.13–16 82, 85 28.17–24 85 29.15–17 705 n.71 29.23–7 95, 458 n.5 30.21–6 82–3 35.6–9 83 38.6 627 n.20 44.27–8 162 n.56 45.14–46.16 95 46.5–6 95 46.6–8 705 n.61 51.24–5 694 n.43 51.31–2 691 n.33 52.22–4 718 n.101 53.28–54.2 83–84 54.21–9 156 n.28 55.21–6 92–3 61.1–3 693 n.40, 694 n.43 68.21–4 106–7, 116–17, 120 69.26–70.21 474 n.1, 693 n.41 71.3–4 116 71.4–5 125 n.200 81.3–82.1 90 n.113 84.12 98 n.135 84.12–19 105 n.153 94.18–20 694 n.43 97.27–30 664 111.13–27 693 n.39 112.1–2 694 n.43 119.22–8 633 n.39 123.28–128.16 86 n.104 147.18–19 627 n.20 149.4–7 627 n.20 164.23–165.8 45–6, 409 n.* 177.25–7 389–90 177.26–32 404 n.40 185.2–3 115 n.175 208.16–18 83 243.17–21 449 244.7 444 n.3 250.1–2 409 n.* 255.20–1 366 256.11–14 *369 n.10 262.28 104 n.144 262.32–264.6 422 263.7–11 440 n.3

Index of Passages 263.15–17 440 n.3 263.26–264.6 372 n.16, 421 264.7–14 422–3 264.14–17 422 and n.16, 501 n.4 265.5–10 440 n.3 265.13–17 94, 462, 711 n.91 265.19–23 378 n.18 265.30–1 424 269.5–8 125 n.201 270.10–28 638 n.48 272.33–5 135 n.229 274.19–24 390 and n.*, 409–10 278.10–11 390 n.* 278.12–14 409 284.10–17 390, 408–11 290.16–18 720 n.105 294.21–2 723 n.116 295.1–3 722 n.114 301.10 720 n.106 301.21 727 n.119 301.23 727 n.119 301.31 727 n.119 306.24–307.7 722 n.114 309.11–35 722 n.114 324.5–15 441 n.1 324.19–22 423–4 324.26–9 424 325.31–328.7 416, 440 n.1, *475–8, 710 n.88 326.8–12 425, 441–2 and n.2, 461–2 326.8–328.7 426 326.12–17 711 n.91 326.21–2 416, 463, 465 326.22–5 442–3, 446, 709 n.85 326.25–7 449 326.27–8 451 326.31–2 463, 467 n.2, 469 n.3, 710–11 326.37–327.1 453 327.7–8 454 and n.2 327.11–12 444, 454 327.12–13 453 327.17–18 454 327.20–1 464–5 and n.3 327.32–5 429, 458–9, 664 328.1–2 459–61 328.2–5 451 328.6 451 328.10–30 91 n.15

Index of Passages 329.20–1 627 n.20 329.30–330.5 638 n.48 330.29–30 448 n.3 344.7–346.6 99–101, *112–15, 144–6 344.9–13 87–8 344.13–27 114 344.14–15 99 344.15–18 124 n.198 344.19 129 344.23–6 124 n.198 344.27–31 88–9, 90–2 344.31–4 99 344.31–345.3 114, 124 n.198 345.1–2 129 345.3–5 135 345.3–12 121–3, 278–9 345.13–17 99, 104, 117 n.181 345.18–20 117 and n.191, 125 n.203 345.23–8 124 n.198, 136 n.232 345.28–9 99 345.28–346.4 114 345.32–5 124 n.198, 129 345.37–346.2 124 n.198 347.18–348.23 116 n.180 347.23–9 140 369.12–24 162 n.55 369.34–370.6 162 n.55 372.31–2 129 373.29–35 98–9 374.21–35 448 n.3 379.20–1 88 386.5–8 440 n.3 386.13–14 378 n.18 387.5–11 379, 440 n.3 387.27–388.12 379 388.12–17 440 n.3 388.17–20 379, 429 n.*, 440 n.3, 441 n.1 389.31–390.9 413, 438 n.3, 703 n.65 390.2–3 439 390.3–6 420–3 and *n.16 390.8–10 *425 n.* 390.9–19 104, 378 n.18, 462 392.23 95 n.123 397.2–4 468 n.2 397.25–398.15 425 397.27 425 398.15–17 425 n.19 398.31–390.9 405

753

402.1–405.16 401–4 402.3 173 n.4 402.5 173 n.5 402.8–12 175 n.10 402.9 173 n.5 402.12–19 175–6 and *n.9, 401 402.17 175 n.11 402.27 173 n.5 402.29–30 175 n.11, 403 402.33 175 n.11 402.36–404.31 401 402.37–403.2 176 403.5 175 n.11 403.6 175 n.11 403.10 173 n.5 403.11–14 175 n.11, 176, 401 403.14–18 177, 401 403.18–26 401 403.26–404.11 178 and *n.14, 401 403.26–34 179–81 403.34–404.4 181–5 and *nn.17 and 19 404.3–10 185–6 404.5–6 178 n.14 404.7–10 173 n.5, 183 404.12 175 n.11 404.14–15 175 n.11 404.28–9 175 n.11 404.34 178 n.14 405.13–14 178 n.14 405.15–16 173 and n.5 406.32–4 162 n.56 410.30–2 135 n.229 411.32–5 638 n.49 411.35–7 638 n.49 in Met : Commentary on Aristotle’s Metaphysics ; Hayduck CIAG I; p þ l 51.15 307 n.4 59.8 213 n.3 77.12 307 n.4 247.9–24 300 n.5 247.27–9 296 n.2 270.24–5 360 371.20–6 276–7 in Meteor : Commentary on Aristotle’s Meteorologica; Hayduck CIAG III ii; p þ l 223.27 306 n.2

754

Index of Passages

in Top: Commentary on Aristotle’s Topics ; Wallis CIAG II ii; p þ l 2.26–3.4 80–1 5.27–8 260 7.10–12 101 n.143 14.20–15.14 100–1 14.23–6 124 n.198 15.1–3 124 n.198 15.3–5 124 n.198, 134 15.3–14 115 n.174 15.7–10 124 n.198 37.32–3 325 39.2–7 325 39.16–17 326 n.i 58.8–11 308 n.2 319.22–3 263 411.15–412.9 333 412.1–2 335 n.6 412.7–9 337 n.10, 343 mixt : On Mixture ; Bruns CIAG suppt II ii; p þ l 216.7–12 400 On conversion 386 apud Boethius, in Int 2 40.30–41.11 589–90 [Alexander] in Met : Commentary on Aristotle’s Metaphysics ; Hayduck CIAG i; p þ l 645.36 103 n.146 in Soph El : Commentary on Aristotle’s Sophistical Refutations; Wallies CIAG I iii; p þ l 161.18–20 *555 n.46 Alexander of Lycopolis adv Man: Against the Manicheans; Brinckmann BT; ch i 238–9 al-Farabi de Int : Short treatise on Aristotle’s de Interpretatione ; Zimmermann (Oxford, 1981); p þ [p] 75–6 [242] 633 n.36 77 [243] 633 n.36 in Int : Commentary on Aristotle’s de Interpretatione ; Zimmermann (Oxford, 1981); p þ l þ [p]

18.18–21 [2–3] 636 n.44 53.1–12 [45] 414 n.2 163.8–15 [158] 637–638 163.16–23 [158] 632 n.34, 636 n.44 Ammonius in APr : Commentary on Aristotle’s Prior Analytics ; Wallies CIAG IV vi; p þ l 1.3–9 77 4.9–11 74 11.3 74 n.71 11.9–11 78 11.14–16 78 12.30–13.18 78 23.27–8 162 n.57 24.6–10 160 n.48 27.27–28.30 637 27.35–6 398–9 in Cat : Commentary on Aristotle’s Categories ; Busse CIAG IV iv; p þ l 13.20–5 191, 207 13.26–14.1 191 n.2 14.20 260 16.24–17.3 300 n.5 18.16 286 n.1 in Int : Commentary on Aristotle’s On Interpretation ; Busse CIAG IV v; p þ l 5.28–6.4 585 n.7 6.4–7.14 585 n.7 7.29–8.19 621 n.2 9.14–15 630 n.30 10.7 632 n.35 10.37 632 n.35 11.7–15.13 624 11.9–11 78 11.13 631 n.33 11.15–12.4 624 n.14 11.25–6 630 n.30 11.28–30 625 n.18 11.30–2 626 12.6–9 624–5 13.7–18 595 13.19–14.2 625 13.27–9 630 n.30 14.2–17 625–6 17.22–6 587–8 17.27–8 591 18.5–7 589 n.18 18.30–5 589 n.18

Index of Passages 27.4 632 n.35 38.1–33 633 n.36 42.30–43.20 388–9 43.9–12 591–2 68.20–7 625 n.18 70.4–10 621 n.3 73.19–33 407 n.48 87.12–13 621 n.3 88.4–91.3 622 n.8 88.17–23 76–7, 622 n.6 88.26–8 76–7 110.24–5 696 111.10–15 696 111.10–120.12 116 n.178, 694 n.44 113.13–15 74 159.24–160.32 622 n.8 160.10–14 148 n.7 160.14–16 621 n.3 165.8–16 162 n.57 166.2–5 160 n.46 171.1–6 190 n.51 176.17–177.18 169 n.76 181.30–1 622 n.6 207.28–208.8 169 n.76 208.3–8 162 n.57 214.7–8 621 214.11–24 621–2 214.25–9 79–8, 623–4, 626 214.25–219.23 622 and n.5 214.29–215.3 81, 82 n.96, 631, 636 215.3–7 632 n.34 215.7–8 81 n.93 215.22–3 630 215.29–216.29 632–6 216.19–21 635 n.42 216.31–217.34 631–2 218.8–10 621 n.3 219.19–21 700 n.55 225.16–28 626 n.19 230.8–13 631 n.31 263.22 160 n.45 272.24–5 74 in Isag : Commentary on Porphyry’s Isagoge ; Busse CIAG IV iii; p þ l 22.12–22 229 81.23 286 n.1 83.21 286 n.1

755

84.21 286 n.1 [Ammonius] documentum Ammonianum; Wallis CIAG IV vi; p þ l IX 23–4 50 n.15, 108 IX 34 694 n.43 XI 1–36 703 n.65 XI 2–3 441 n.1, 447–8 XI 8–13 705 n.71 XII 3 50 n.15, 108 XII 10–16 107–8 in APr: Commentary on Aristotle’s Prior Analytics; Wallis CIAG IV vi; p þ l 39.32 75 n.76 45.42–46.2 351 n.** 67.29–30 703 n.65 67.35 438 n.3 68.6 591 68.15–23 709 n.84 68.23–6 703 n.65 68.28 705 n.71 69.11–28 48 n.13 70.10–13 96 n.125, *109–10 70.11–15 132 70.12 75 n.72 70.13 110 n.162 70.14 131 70.20–2 115–17 anonymi Anecdoton Holderi; Usener (Bonn, 1877); p 4 667 Division of Speusippus 290 n.16 Florentine Logic ; PSI 1095 426 in EN : Commentary on Aristotle’s Nicomachean Ethics ; Heylbut CIAG XX; p þ l 140.6–12 552, *574 n.83 in Rhet : Commentary on Aristotle’s Rhetoric ; Rabe CIAG XXI 2; p þ l 109.31–2 204 in Tht : Commentary on Plato’s Theaetetus ; Bastianini and Sedley CPF III; c þ l LXVI 11–22 452 n.4 Logica et quadrivium; Heiberg (Copenhagen, 1929); b þ s þ [p þ l] I 1 685 I 2 686

756

Index of Passages

I 2–20 685 I 12 684 I 13 686 I 21 [13.26–8] 688 n.26 I 21–4 685 I 22 [15.11–12] 688 n.26 I 22 [15.12–14] 701 n.58 I 24 700 I 24 [17.1–5] 688 I 24 [17.21–8] 688 n.26, 697, 700 n.55 I 25 [18.11–12] 702 n.60 I 25–48 685 I 26 [18.27–8] 700 I 26 [19.7] 700 n.56 I 27 [19.16–17] 701 I 27 [19.20–1] 701 n.57 I 27 [20.2–3] 691, 698 I 27 [20.4–10] 727 n.119 I 28 [20.11–15] 687, 699–700 I 30 [21.22–3] 702 n.60 I 30 [22.3–9] 689 I 30 [22.13–14] 690 n.31 I 30 [22.13–22] 716–20 I 31 [23.19] 690 n.31 I 31 [23.19–25] 716 n.98 I 32 [24.1–5] 717 I 32 [25.13–14] 689 n.30 I 32 [25.14–15] 690 n.31 I 32 [25.14–26] 716 n.98, 717 n.100 I 32 [25.26–26.4] 696–9 I 33 [26.5–9] 690 I 33 [26.23–4] 690 I 36 [28.13–14] 689 n.30 I 36 [28.21–29.4] 701 n.58 I 38 [30.16] 703 I 38 [30.20–8] 709–12 I 38 [31.6–8] 705 n.71 I 38 [31.13–17] 706–8 I 38 [31.15] 705 I 38 [31.17–21] 705 I 38 [31.21–6] 706 I 38 [31.26–32.2] 703 I 38 [31.28–9] 704 I 38 [32.2–7] 704 n.69 I 39 [32.8] 685 n.12, 720 I 39 [32.10–15] 720, 721 n.107, 726 I 39 [32.17] 685 n.12 I 39 [32.18–33.1] 721–2

I 39 [32.28] *721 n.110 I 39 [33.26–7] 723 n.117 I 40 [34.3–6] 726 I 40 [34.11–13] 725 I 43 [35.24–8] 723–5 I 48 [39.1–7] 700 I 48 [39.8] 685 n.12 I 49 [39.21–3] 686 I 49–63 686 I 59 687 I 59 [44.21–45.5] 695 n.47 I 64 [48.2–4] 686 n.18 I 64–67 686 I 67 684 I 67 [50.12–13] 685 I 67 [50.16–18] 685 I 67 [50.21–3] 685 II 1 [50.26–7] 684 n.7 V 8 [108.14] 683 V 9 [109.9–10] 683 Paraphrasis Themistiana; Minio-Paluello (Bruges, 1961); ch þ [p þ l] xx [137.20–2] 247 lxx [149.1–2] 247 —æd ºø; PHamburg 128 586 n.9 Apollonius Dyscolus adv : On adverbs ; Schneider GG II i, p þ l 119.5–6 624, 636 120.6–122.34 80 n.90, 624 n.16 122.13–15 625 n.18 123.1–125.5 636 n.45 124.8–14 629 n.27 128.10–133.12 629–30 148.6–8 625 n.18 158.20 591 n.22 158.28 625 n.18 conj : On connectors ; Schneider GG II i; p þ l 213.7–10 517 213.11–15 517–18 214.1–5 518 214.8–10 523–4 215.14–221.15 407 n.47 216.11–16 514–16 216.16–218.19 519–27, 524 n.14, *534–5 217.1–2 524 n.14 218.20–7 516–19

Index of Passages pron : On pronouns ; Schneider GG II i; p þ l 59.1 591 n.22 synt: Syntax ; Uhlig GG II ii; b þ s þ [p þ l] I 73–9 [62.6–67.8] 522 n.13 I 107 [90.7–10] 523 II 51 [165.4] 521 n.12 II 70 [59.12–60.12] 522 II 71 [60.13–61.23] 522 III 5 [271.2–4] 522 III 9 [274.7–12] 522 Apuleius int: De interpretatione; Moreschini BT; ch þ [p þ l] i [189.3–4] 23 n.8 iii [191.1–6] 689 n.29 iv [192.1–7] 161 n.48 vi [198.7–17] 702 n.61 xii [209.9–210.11] 483–4 xii [209.14] 483 n.11 xiii [212.4–10] 156 n.28, 687 n.24 xiii [212.12–213.5] 693 n.41, 694 xiii [213.5–10] 415, 691 xiv [215.6–7] 718 n.102 [Archytas] ŒÆŁ º ª: On universals ; Thesleff (A˚bo, 1965); p þ l 30.18–31.5 222 Arethas in Cat : Commentary on Aristotle’s Categories; Share (Athens, 1994); p þ l 136.12–13 260 Aristocles apud Eusebius, PE XV ii 3 552 n.35 Aristotle p þ c þ l (ed Bekker) An: On the Soul; Ross OCT ` 402a15 316 ´ 418a11–12 327 APr : Prior Analytics ; Ross OCT ` 24a19–22 116

24b16–20 159, 366, 398, 692 n.37 24b20 123 25a17–19 471 25a20–2 471 25b14 349 25b16–25 348 25b22–4 161 and n.53 25b32–9 269–270 26a2–9 270–1, 716 n.97 26a8–9 92 26a28–30 692–3, 694 nn.43 and 44 26a30–2 692 n.38 26b2 464 n.4 26b15–16 471 n.1 26b21–5 692 n.38 26b34–6 90 n.113 27b36–9 692 n.38 29a8–10 692 n.38 29a27–9 692–3 and n.39, 694 n.44 29b1 440 n.3 30a15–32 85 n.104 32a29–33 350–1 32b4–7 349 32b16 348 32b20–2 349 40b17–22 364–5 and n.2 40b21 366 n.5 40b23–5 369 40b25–6 369 40b26–41a20 369–70 and n.12, 373–6 40b30–41a20 450 n.2 40b31–3 365 40b33–7 449 n.4 41a17 366 n.5 41a21–3 366 n.5, 370 n.12 41a21–41b1 371–3, 378–80 41a35–7 366 n.5 41a37–41b1 369, 372, 378 41b1–5 365 41b2 366 n.5, 370 42a1 390 42a1–4 410–11 43a20–21 720 43a38 721 n.107 43a40–4 688 n.26 43b2–4 464 n.4, 722 n.114 43b5–6 722 n.112 43b6–11 721 n.107, 727 n.120

757

758 43b11–12 441 n.1, 721 n.107, 722 43b22–6 722 n.113 43b26–9 722 n.114 43b32–6 347, 722 43b39–44a11 723 n.117 44a30–5 723 n.118 44a38-b5 722 n.114 44b13 441 n.1, 464 n.4 44b25–37 723 n.117 45b17 423 45b19 440 45b24 91 n.115 46b3–11 157 n.33 46b40 440 n.3 46b40–47a2 157 n.32 47a22–3 87–8, 113 47a28–30 446–7 47b20–36 157 47b29 325 n.* 47b35 325 n.* 47b40 325 n.* 48a40–49a5 157–8 49a25 162 n.55 50a16–18 376, 378, 440 n.3 50a20–8 377–9 50a29–30 376 50a30–2 377, 378 50a39–b3 376, 413, 416, 438–9 50b31–2 95 n.123 51b3–5 157 n.32 51b10–27 425 51b22–52a14 162 n.58 51b32 173 n.6 56b20 464 n.4 ´ 57a36-b16 448 n.2 57b1–2 428 n.21 62b29–32 369 70b7–14 323 70b18–20 323 APst : Posterior Analytics ; Ross OCT ` 71a15–16 307 n.1 73a7 314 73a16–18 316 74b5–12 316 78a10–13 316 79a18–21 168

Index of Passages 83a21–3 235 87b22–7 348 ´ 91a15–18 314, 319, 329 96a11–19 347 99a7–13 309–10 Cat : Categories ; Minio Paluello OCT 1a1 298, 301 n.3 1a1–2 285 1a2 *262, *293 n.1 1a2–6 305 1a4 262 1a6–7 286, 301 n.3 1a7 262 1a10 262 1a20–b9 689 n.29 1b23–4 *263 1b25–7 193, 258 2a10 263 2a11–14 221–2 2a19–21 264 2a35 263 2b5–6 263 2b37 263 3b7 297 n.1 3b10 264 3b17 307 n.1 3b20 264 5b12–25 555 n.46 6a30–2 264 11a15–16 258 11a35–7 261 n.* 11a38 273 11b1–8 193, 258 11b8–17 193–5, 258 12a2–4 263 12a9–11 263 13b27–33 172 14a26 265 EE : Eudemian Ethics ; Susemihl BT ˙ 1236a17 306 1236b25 306 EN: Nicomachean Ethics; Bywater OCT ` 1096a23–4 217 ´ 1109b20–2 552–3

Index of Passages ¯ 1120a30 305 GA : On the Generation of Animals; Drossaart Lulofs OCT ´ 734b25 305 ˜ 777a19–20 346 Int : On Interpretation; Minio-Paluello OCT 16a3–9 564–85, 587–90 16a10 587 16a14 587 16a15 159 n.43 16b6 153 n.22, 161 n.54 16b8 161 n.54 16b9 161 n.54 16b12 161 n.54 16b18 161 n.54 16b22–5 160 16b24 162 n.54 17a2–7 249 17a32–3 172 17a35–7 359 n.5 17a38–b1 154 17b6 159 n.43 17b29–37 694 n.44 17b37 172 19b13 160–2 19b14 161 n.54 19b19–22 160–2 19b24–5 161 and *n.51 19b32–20a15 702 n.61 20a3–6 164 20a13 161 n.54 20a20–3 468 n.2 21a34 621 21b9–10 164 21b27–8 160–1 22a13 631 n.31, 638 n.49 23a7 306 24b1–2 585 Met: Metaphysics ; Ross (Oxford, 1924) ˆ 1003a34 306 1003b26–9 161 n.54 1004a10–16 360 n.7 1005b11–12 358–63

759

1005b18–32 358–63 and *n.6 1005b26 360 1005b31 360 1006a4 359 1011b15–20 359–60 ˜ 1017a22–7 275–6 1022a14 307 n.2 1023a26 307 n.2 1025a31–2 316 ˘ 1035b1 305 1035b25 306  1054a16–17 161 and n.54 Meteor : Meteorologica ; Fobes (Cambridge MA, 1919) ˜ 389b31 305 PA: Parts of Animals; Peck (London, 1937) ` 643b4–7 309 Phys : Physics ; Ross OCT ´ 195a18–19 73 ˆ 207b9 310 H 248b7–9 305, 310 248b12–21 310 250a19–28 553 n.43 ¨ 253b14–26 553 and n.43 Poet : Poetics ; Kassel OCT 1457a17 161 n.54 1457a28 307 n.1 Rhet : Rhetoric ; Kassel (Berlin, 1976) ` 1374a12 161 n.54 ´ 1396a3 347 1402a15 347 1402b21 349 n.* 1402b28 348 1402b36 350 ˆ 1404b37–1405a2 310 1407b12–18 161 n.52

760

Index of Passages

Soph El : Sophistical Refutations ; Ross OCT 166b37–167a35 359 n.5 167a24 310 167b1–8 428 n.21 169b11 161 n.54 174b23–7 289 175a37 310 177b7–9 288–9 179a32–6 554–5 179b34–7 554–5 and n.46 181a22–9 428 n.21 182a18 307 n.1 182a21 307 n.1 182a30 307 n.1 183a37–b15 313 183b37–184a8 217 Top : Topics ; Brunschwig (Paris, 1967 and 2007) ` 100b21–3 342 n.13 101b17–18 317 101b19–25 317 101b22–3 326 n.i 102a5 341 102a18–19 313–14, 333 n.4 102a19–22 314 102a22–3 314–15, 324, 326 102a22–9 319–20 102a26 325 102a28–30 315 102b4–5 316 102b6–7 316 102b20–26 322 102b23 325 102b27–35 318 103a1–4 319 103a9–10 308 n.2 103a25–7 308 n.2 103b20–33 189–90, 196–7 103b27–9 197 105b19–21 396–7 106a21 306 107a39 309 107b16–17 308 ´ 108b34–109a26 324 109a3–6 471 n.1, 691 n.35 109a11–12 324

110b20 340 n.11 111a26–9 343 and n.14 112b5–9 348 113b15–26 468 n.2 115b11–15 324 ˆ 119a32–120b6 324 120a28–31 342 ˜ 120b11–12 313, 318 120b12–15 312 120b36–121a9 196 121b26–38 342 ¯ 128b16–17 320, 321–2 128b19 321 128b20 325 128b25 341 128b34–5 320–1 128b39–129a2 321 129a5 325 129a6–16 321 129a9 341 129a23 321 129a26 321 129a28 320 129a32–4 122 129b7–8 311, 341 129b30 310 129b30–3 341 130a5 311 130b3 307 n.1 131a1 311, 341 131a27–33 322 131a31–2 315 131b5–18 320, 321 131b12 325 131b17 325 131b19–25 315–16 131b32 321 131b38 318 132a18–138b33 338 132a22–6 318 132a27–b3 316 132a34–b7 318 132b8–18 318 132b18 341 132b19–21 327

Index of Passages 132b19–34 318, 327 132b21–4 327 132b24–8 327 132b35–133a11 317 133a12–23 315, 317, 321 134a18–25 316, 318 134a26–8 322 134a28–135a8 322–3, 343–4 134a29–33 323, 325–6, 344 and n.15 134b1–4 329, 344 and n.15 134b9 325 134b5–10 323 134b19 344 134b21 344 n.15 134b22–135a5 326 135a9–19 317, 329 136a5 334 136a29 334 136b33–5 334 136b33–137a7 333–4 137a1–7 334 137a8–20 330–45 137a8–10 *337–9 and n.10 137a10–12 332 137a16–18 *333, 336 137a17–18 332 and *n.i, *339–44, *345 137a21–b2 318 137b3 334 138a13 334 138a20 328 138a21 334 138b6 334 138b16 334 ˘ 139a31–2 318 139b3–4 318 139b4–5 313 139b21 306 140a19 190 n.54 140a33–b15 119 140b16–26 119 141a13 307 n.1 142a24–5 340 n.11 142b5 307 n.1 ˙ 152a39–b2 342 154b2 319 154b33–155a2 324

761

155a7–10 318 155a23–7 319 155a28–31 343 155a33 190 n.54 ¨ 162a19–23 86 n.108 174a8–9 307 n.1 175a37 310 177b7–9 288–9 174b23–7 289 Arnobius adv nat : Against the Nations ; Reifferscheid (Vienna, 1875); b þ s I 58 7, 16 Aspasius in EN: Commentary on Aristotle’s Nicomachean Ethics ; Heylbut CIAG XIX i; p þ l 56.27–57.7 552–3 56.32–4 551 n.31 57.2–7 574 n.83 Athenaeus Deipnosophists ; Kaibel BT; p þ s (ed Conti) 354C 552 n.35 Atticus apud Eusebius, PE XV iv 19 214 Augustine c Acad: Against the Academics; Green (Turnhout, 1970); b þ ch þ s III xiii 29 19 c Crescon: Against Cresconius; PL 43; b þ ch þ s I xvii 21 242 c Iul: Against Julianus; PL 44; ch þ s iii 7 19 iii 199 18 vi 18 19 conf : Confessions; Skutella BT; b þ ch þ s IV xvi 28–29 19, 205, 244 op imperf : Opus imperfectum; PL 45; ch þ s iii 31 19 n.44 retract: Recantations; Mutzenbecher (Turnhout, 1984); ch þ s i 5 19

762

Index of Passages

Aulus Gellius Attic Nights; Marshall OCT; b þ ch þ s I ii 4 556 n.49 XVIII ii 10 35 n.44 Blemmydes epit log: Epitome of Logic; PG 142; ch þ p þ s xxix 917AC 692 n.36 xxxii 944B 692 n.36 xxxiv 961A 692 n.36, 694 n.43 xxxvi 973BC 703 n.64 and n.65 xxxvi 977D-979A 712 n.93 Boethius hyp syll: On Hypothetical Syllogisms; Obertello (Brescia, 1969); b þ ch þ s I i 3 414, 415, 416–18, 439 n.3, 456–7, 677 I i 6 470, 710 n.86 I ii 2 470–1 I ii 4 561 n.65 I iii 4 423, 448 n.2, 501 n.4 I iii 5 448 n.2 I iii 6 524 I iii 7 448 n.2 I v 1 459 I viii 6–7 461 n.1 I ix 2–3 444–5, 461 n.1 I ix 7 679–81 I xii 5 416 II i 1 703 n.63 II ii 4 75 II ii 5 75 II iii 6 75 II iv 2 75 II iv 3 75 II ix 1–III vi 4 455 n.2 II ix 2 451 n.2 II ix 3 456 n.3 II ix 4–5 456 n.3 II ix 7 446 n.1 II x 7 75, 456 n.3 II xi 1 75, 456 n.3 II xi 4 446 n.1 III i 1 451 n.2 III ii 6 456 n.3 III iii 2 456 n.3 III iii 7 456 n.1 III iv 1 456 n.1

III iv 2 451 n.2 III iv 3 459 III iv 6 456 n.3 III vi 2 456 n.3 III vi 5 75 III ix 2–4 456 n.1 in Cat: Commentary on Aristotle’s Categories; PL 64; p þ s 159A 676 n.17 160A *673 n.13 201B 666–7 in Cic Top: Commentary on Cicero’s Topics; Orelli (Zurich, 1833); p þ l 270.16–271.17 674 272.4–26 668 n.7 327.11–19 75 n.73 353.18–20 678 n.25 356.5–14 705 n.71 356.30–357.3 707 n.78 358.35–8 680 n.* 359.17–22 707 n.79 360.25–8 75 n.73 361.16–24 705 n.71 364.40–365.6 707 n.78 in Int: Commentary on Aristotle’s On Interpretation; Meiser BT; p þ l first edition (in Int1) 31.1–32.3 672–3 72.23–73.13 670–1 second edition (in Int 2) 3.5–4.9 669–70, 674 n.15 7.5–7 674 12.3–16 416, 586 n.9 29.16–21 586 n.9 40.30–41.11 589–90 48.26–49.23 680 n.* 68.4–69.22 689 n.29 70.20–71.1 670 71.13–18 679 79.16–80.1 667 99.25–7 672 121.25–6 675 122.7–15 689 n.29 201.2–6 679 208.1–3 389 250.20–3 674–5 and n.* 251.8–15 676 264.8–14 160 n.44, 190 n.51

Index of Passages 264.24–265.28 162 n.57 272.14–17 190 n.51 272.28–273.2 190 n.51 321.20–323.13 700 n.55 377.4–14 628 n.23 379.12–380.11 629 n.26 380.12–382.8 629 n.24 382.16 633 n.36 397.6–22 628 n.23 421.2–6 673 422.5–6 673 in Isag: Commentary on Porphyry’s Isagoge; Brandt (Vienna, 1906); p þ l first edition (in Isag1) 4.10–14 669 n.10 14.8–25 667 n.6 34.12–35.6 669 64.8–13 669 94.11–95.17 669 131.26–132.2 667, 673 n.14 second edition (in Isag 2) 135.6–13 671 347.24–6 669 n.10 int syll cat: Introduction to Categorical Syllogisms; Tho¨rnqvist (Gothenburg, 2009); p þ l (ed PL 64) 785A 702 n.61 syll cat : On Categorical Syllogisms; Tho¨rnqvist (Gothenburg, 2008); p þ l (ed PL 64) 793CD 676 796D 260 n.48 813C 694 n.43 829D 677 top diff : Topical Differences; Nikitas (Athens, 1990); p þ l (ed PL 64) 829D 668 n.8 1173BC 677–8 1185A 678 1191A 668 n.8 1209C 668 n.8 1216D 668 n.8 Boethius (?) in APr : Commentary on Aristotle’s Prior Analytics; Minio-Paluello (Bruges, 1962); p þ l 304.5–19 703 n.65

763

320.14–16 711 n.91 Cassiodorus expositio Psalmorum; PL 70; ch þ s vii 6 677 n.21 inst: Institutions; Mynors (Oxford, 1937); b þ ch þ s II iii 1 669 n.10 II iii 2 677 n.18 II iii 12 677 n.19 II iii 13 677 n.21, 703 n.65, 705 n.71, 707 n.78 II iii 18 245–6, 670 n.11, 674 n.15, 677 n.19, 677 n.21 Variae; Mommsen (Berlin, 1894); ch þ s i 45 666 Chrysippus Logical Investigations; Marrone (Naples, 1997); c þ l (PHerc 307) I 15–26 506 IX 17–22 556 n.50, 563 n.68 IX 19–20 546 n.16 XII–XIII *486–98 apud Galen, PHP V 243 *595–600 V 345 595–600 Cicero Acad: Academica; Plasberg BT; s þ s ii 5 24, 26–7 iii 9 677 n.18 v 19 22 and n.3, 23, 24, 25 vi 22 22 n.3 vii 25 25–6 viii 30 23 nn.1 and 3 viii 30–3 *24–8, 32 n.37 xi 40–2 27, 34 n.42 ad Att: Letters to Atticus; Shackleton-Bailey (Cambridge, 1965–1970); b þ w þ s VII ii 1 102 n.144 XIII xxi 3 567 n.73, 568 n.77 div: On Divination; Giomini BT; b þ s þ s II i 4 23 n.10 II iv 11 546 n.18 II lxxii 150 559 n.62 fat : On Fate, Bayer (Munich, 1980); s þ s i 1 23 vi 12 542 n.10

764

Index of Passages

vii 14 510 viii 15 503 x 21 32 xvi 38 32 fin: On Ends; Tschiche BT; b þ s þ s II vi 17 23 n.11 II xiii 42 559 n.62 III xii 41 27 n.22 IV xviii 50 557 n.54, 567 n.74 Hort: Hortensius; Grilli (Milan, 1962) frag 26 546 n.18 leg: Laws; Powell OCT; b þ s þ s I xxiv 62 24 n.13 Luc: Lucullus; Plasberg BT; s þ s viii 26 26 n.20 xvi 49–50 548 n.21, 557 n.54, 567 n.74 xxviii 90-xxix 92 559 xxviii 91–2 26, 28–9, 563–5 xxviii 92-xxix 94 29–30 xxix 92–3 548, 571 n.80 xxix 93–4 565–8 xxix 95 29, 30–7 xxx 95–6 31, 33, *40–1 xxx 96–8 38–42 xxxvi 114 22 n.4, 23 xlii 131 559 n.62 xlvii 143 26 and n.18, 483 nd: On the Nature of the Gods; Ax BT; b þ s þ s I xvi 43 606 n.8 III xvii 43 559–60 orat : Orator ; Wilkins OCT; b þ s þ s II xxxviii 158 30 n.31 top: Topics; Reinhardt (Oxford, 2003); s þ s i 3 203–4 xiii 53 705 n.71 xiii 53-xiv 57 703 n.65 xiii 54 *707 n.77 xiv 56 707 n.80 Tusc: Tusculan Disputations; Pohlenz BT; b þ s þ s I vii 14 30 n.* Clement of Alexandria strom: Stromateis; Sta¨hlin and Fru¨chtel (Berlin, 19854); b þ s þ s þ sb

I viii 40.2 7 I viii 44.2 18, 243 I x 47.2 18, 243 II iv 16 606 n.8 V i 11.6 558 n.58 VI viii 67.2 686 n.14 VI x 80.5–81.1 18 VIII iii 8.2 97 n.131 VIII iii 13.1 591 Cornutus —æd ŒH
; POxy 3649 399 n.35 Democritus apud Proclus, in Crat xvi [7.3–6] 297 n.4 Demosthenes Speeches; Dilts OCT; w þ s vii 31 156 n.27 xviii 294 188 Dexippus in Cat: Commentary on Aristotle’s Categories; Busse CIAG IV ii; p þ l 5.16–25 212, 389 7.1–8.23 586 n.10 8.15–18 589 n.18 20.24–7 301 n.2 21.18–19 262 40.20–2 227–8 42.18–26 224 Didymus Commentaries; Cavini, CPF I 1* 265 Diogenes Laertius Lives of the Philosophers; Marcovich BT; b þ s I 18 481 n.* II 106 481 n.* II 108 550 II 109 552 n.35 II 111 550 n.28 II 113 481 n.6 IV 4 289 V 24 260 V 42–50 417 V 47 586 n.9 V 49 260, 397 V 59–60 416

Index of Passages VII 5 556 VII 41 250 VII 43 593 n.31 VII 45 47, 97–8 VII 51 592, 593 VII 55 596–7 VII 57 595 VII 63 593 n.30 VII 68 437 n.3 VII 71 500–1 VII 72 513–14 VII 75 499 VII 77 97 and n.129 VII 78 97, 98 VII 82 541–2 and *n.9 VII 187 550 n.28 VII 190 404, 499 VII 192 555 n.48 VII 194 499 n.2 VII 197 72 n.144, 392 n.21, 546 n.16, *556 n.49, 564 n.68 VII 201 72 n.144, 392 n.21, 396–8 X 33 605, 611–14 Diogenes of Babylon apud Galen, PHP V 242 596–600 [Dionysius Thrax] Art of Grammar; Uhlig GG I i; s þ [p þ l] 12 [24.3] 153 n.22 13 [46.4–5] 153 n.22 19 [72.3–86.1] 624 n.14 19 [78.1–3] 625 n.18 19 [85.2] 630 n.30 Elias in Cat: Commentary on Aristotle’s Categories; Busse CIAG XVIII i; p þ l 132.26 260 133.3 260 241.30 260 Epictetus diss: Dissertations; Schenkl BT; b þ ch þ s I i 1–6 28 n.26

765

I xvii 6–9 229–30 II xviii 18 556 n.49 Epicurus ad Hdt: Letter to Herodotus; von der Mu¨hll BT; s 37 604–5, 611–14 42 631 n.31 On Nature XXVIII; Sedley (Naples, 1973); fragment þ c þ l (PHerc 1479/1413) 6 I 5–13 614–15 Epiphanius pan: Panarion; Holl (Leipzig, 1933); v þ p III 351 9, 15 III 352 15 III 357 15 III 361 9 Euclid Elements: Stamatis BT; b þ s I i 43–4 Eudemus Wehrli (Basel, 1969) frag 13 351 n.** Eunomius apol: Apology; Vaggione (Oxford, 1987); s 22 9 Eusebius HE: History of the Church; Bardy (Paris, 1952–1958); b þ ch þ s V xxviii 13–14, 10–14, 699 n.53 PE : Preparation for the Gospel; Mras (Berlin, 1954 and 1956); b þ ch þ s I iii 5 19 XI v 5 242 XV ii 3 552 n.35 XV iv 19 214 Faustinus trin: On the Trinity; PL 13; s 12 9, 240 Fronto eloq: On Eloquence; van den Hout BT; s þ sb ii 13 556 n.51

766

Index of Passages

Galen v þ p (ed Ku¨hn) — save where noted aff dig: Passions of the Soul V 17–18 6 Against the First Unmoved Mover; Walzer (Oxford, 1949) frag 5 diff puls: On Kinds of Pulse VIII 578 4 VIII 579 4 VIII 580 236 VIII 624 238, 266 VIII 657 5 inst log: Introduction to Logic; Kalbfleisch BT; ch þ s ii 235–6 ii 4 694 n.43 iii 1 407, 423, 501 n.4 iii 3 420–1 iv 4 529–30 iv 4–6 *536 iv 6 532–3 vi 3–4 458 n.5 vii 2 415 viii 2 429–30 ix 3–8 527–30, 536–7 ix 9 528 xi 2 694 n.43 xiii 236 xiii 11–12 214–15 xiv 3–8 527–33, *536–7 xiv 5 531 xiv 6 529 xiv 7–8 531 xvi 1 50, 127, 135 and n.228, 277 xvi 5 *127 n.211 xvi 10 50 xvi–xix 100 n.142 xviii 8 126 n.207 xix 6 98 n.135, 109 lib prop : On his own Books; Boudon-Millot (Paris, 2007) XIX 16–17 540 n.6 XIX 39 46–7 XIX 42 212, *235 XIX 43 126 n.209 loc aff : On Affected Parts VIII 25 541, 546 n.16, 548

Med Exp: On Medical Experience ; Walzer (Oxford, 1947); ch þ s II 3 540 n.7 VI 5 573–4 and *n.82 VII 7 576 and *n.86 VII 8-VIII 1 538–9 IX 1 570–1 XV 6 571 XVI 1 548 XVI 2 546 n.16, 547 XVII 1–3 547 XVII 4 548 n.21 XVII 7 572 XVII 8 571 and n.80 XX 3 551 n.31 XX 6 571 XXI 1 571 meth med: On Therapeutic Method; Johnston and Horsley (Cambridge MA, 2011) X 148 266 On the Anatomy of Hippocrates ; Walzer (Oxford, 1949) frag 5 PHP : On the Doctrines of Hippocrates and Plato ; de Lacy CMG V iv 1.2 V 242 596–600 V 243 *595–600 V 345 595–600 V 502 504 n.6 praecogn: On Prognosis; Nutton CMG V viii 1 XIX 660 1 n.1 protr : Protrepticus ; Barigazzi CMG V i 1 I 8 11 simp med temp: On the Powers of Simple Medicines XI 499 466, 710 n.86 XI 500 458 n.5 subf emp: Outline of Empiricism; Deichgra¨ber (Berlin, 1965); p þ l (ed Bonnet) 38.12–17 539–40, 572 Synopsis of Plato; Walzer (Oxford, 1949) frag 5–6 us part : On the Use of Parts ; Helmreich BT III 904–6 5, 239 [Galen] hist phil: History of Philosophy ; Diels (Berlin, 1879)

Index of Passages XIX 230 481 XIX 235–6 479 ren affect: On Diseases of the Kidney XIX 679 6 n.9

Isidore of Pelusium ep: Letters; PG 78; b þ w IV 27 16

Gregory of Nazianzus orat : Speeches xxiii: Mossay (Paris, 1890); p þ s (ed PG) 1164D 8, 17 xxvii: Gallay (Paris, 1978); s 9 9, 239–40 xliii: Bernardi (Paris, 1992); s 23 17–18, 241

Isidore of Seville Etymologies; Lindsay OCT; b þ s þ sb III xxiii 1 26

Gregory of Nyssa an et res : On the Soul and Resurrection; Ramelli (Milan, 2007); p þ s (ed PG) 52B 8, 17 vit Mos: Life of Moses ; Musurillo (Leiden, 1964); ch þ s ii 115 17 Gregory the Thaumaturge ad Orig : To Origen; Crouzel (Paris, 1969); ch þ s vii 106–9 18, 244 [Hesychius] vit Arist : Life of Aristotle; Gigon (Berlin, 1987) [item 57] 260 Hippolytus ref haer : Refutation of All Heresies ; Marcovich (Berlin, 1986); b þ c þ s I xx 1 12 I xxi 1 13 VI xxiv 1–2 217 VII xxi 240 Horace Epistles ; Wickham þ Garrod OCT; b þ w þ l I vi 35 550 n.26 II i 36–49 550 Iamblichus in Nic : Commentary on Nicomachus’ Introduction to Arithmetic ; Klein BT; ch þ [p þ l] xii [11.5–9] 102 n.145

767

Jerome ep : Letters; Labourt (Paris, 1952); w þ s l 1 18, 242 lvii 12 16 cxxxiii 2 8 n.14 in Amos : Commentary on Amos ; PL 25; ch þ s þ sb Ii49 in Naum: Commentary on Nahum; PL 25; s þ sb ii 15 8 in Tit: Commentary on the Epistle to Titus ; PL 26; s iii 239 John Italos Dialectica ; Cereteli (Tbilisi, 1924); s 2 686 n.18 4–12 686 n.19 15 697 n.49 Julian c Gal: Against the Galileans; Masaracchia (Rome, 1990); p þ s (PG 76) 222A 242 ep : Letters ; Wright (Cambridge MA, 1913); w 46 9 n.16 Justinian dig: Digest; Mommsen (Berlin, 1869); b þ ch þ s I xvi 177 546 n.17 Lactantius div inst: Divine Institutions; Monat (Paris, 1986–2007); ch þ s I xvi 558 n.54 III xiii 7, 16

768

Index of Passages

Marius Victorinus in Cic rhet: Commentary on Cicero’s On Invention; Orelli (Zurich, 1833); ch þ s þ [p þ l] I 9 [183.32–3] 204 apud Cassiodorus, inst II iii 13 703 n.65, 707 n.79 Martianus Capella Wedding of Philology and Mercury; Willis BT; b þ s IV 329 3–4 IV 393–4 162 n.59 IV 420 703 n.65, 705 n.71, 707 n.79 New Testament Col: Letter to the Colossians ii 8 240 Hebrews vii 9 696 Mt: Gospel of Matthew v 38 6 and n.* xiii 24–30 686 n.14 I Tim: First Letter to Timothy vi 4 7 Old Testament Genesis XVIII 22–3 550 n.28 Olympiodorus in Cat: Commentary on Aristotle’s Categories; Busse CIAG XII i; p þ l 13.24–35 199–200 22.34 260 22.38–40 191 Origen c Cels: Against Celsus; Ko¨tschau (Berlin, 1899); b þ s II 27 10 VII 15 96 n.125 hom in Gen: Homily on Genesis; Baehrens (Leipzig, 1920); p þ l 28.14 15 in Rom: Commentary on Paul’s Letter to the Romans; Heither (Freiburg, 1993); b þ ch VI xiii 19 Persius Satires; Clausen OCT; w þ l VI 75–80 550

Philip of Megara apud Diogenes Laertius II 113 461 n.6 Philodemus de ira: On Anger; Indelli (Naples, 1988); c þ l (PHerc 182) XLV 1–6 605–606 sign: On Signs; de Lacy and de Lacy (Naples, 1978); c þ l (PHerc 1065) VII 26–38 504–5 XIX 12–19 575 n.84 XX 31-XXI 16 575 n.84 To his Colleagues; Angeli (Naples, 1988); frag þ l (PHerc 1005) 111.9–10 385, 614 n.13 Philoponus in APr : Commentary on Aristotles Prior Analytics; Wallies CIAG XIII ii; p þ l 9.6 74 25.3–4 160 n.48 34.7–10 716 n.98 36.5–13 100 n.142, 128 n.215 40.2–8 95 n.121 42.13–19 95 n.123 42.31–3 694 n.44 42.35–45.20 633 n.36 46.6–7 632 n.34, 633 n.36 51.2–4 75 68.30–4 694 n.43 75.17–20 75 75.25 75 75.28 75 79.4–9 693 n.40, 694 n.43 83.23–4 75 94.32–95.7 694 n.43 110.8–11 694 n.43 158.28–159.17 90 n.112 165.27–9 390 242.14–15 414, 438 n.3 242.18–21 404–5, 415, 417–18, 439 n.3 243.4 591 243.16–17 441–2 243.25–32 709 n.82 245.34–5 706 n.74 270.10 720 n.105 273.21 720 n.105 273.30–3 722 n.114

Index of Passages 274.7 720 n.106 280.11–27 721 n.107 302.6–23 440 n.1 302.9 442 302.12–15 462 n.1 302.15–22 451 302.20–3 444 n.2, *454 n.2 302.23–32 462 n.1 304.28–31 636 n.44 321.3–5 74–75, 135–6 321.7–8 128, 135–6 321.7–322.18 100 n.142 321.9 75 321.12–14 115 321.16 128 n.215 321.18–20 128 n.215 322.1–3 128 n.217 322.15 128 n.215 322.17–18 128 n.217 349.30 74–5 359.30–2 438 n.3 in Cat: Commentary on Aristotle’s Categories; Busse CIAG XIII i; p þ l 5.18–20 230 7.20–2 199, 415–16, 586 n.9 7.22–8 207–8, 387 Plato p þ s (ed Stephanus) Charmides; Burnet OCT 155A 156 n.27 Parmenides; Burnet OCT 137D 452 n.1 Republic; Slings OCT 408C 100 n.140 535B 186 n.27 Sophist; Robinson OCT 261D-262E 152 261E-262A 152 n.17 and 18 262A 153 n.22 262BC 152 n.18 262CD 152 nn.16 and 18, 153 262E 152 n.18 263A 153 Plotinus Enneads: Henry and Schwyzer OCT; b þ ch þ s I iii 5 74 n.71

769

VI i–iii 219–20 VI i 25 202 Plutarch p þ s (ed Stephanus) adv Col: Against Colotes; Westman BT 1119F 603 comm not: Common Notions; Westman BT 1084AC 558 n.57, 562 n.67 quaest plat: Platonic Questions; Hubert BT 1001B 160 n.48 Stoic rep: Stoic Contradictions; Westman BT 1034F 556 1035A 395–6 1036F 556 1039C 558 n.54 1045F-1046B 392–5 1084AC 546 n.16 fragments; Sandbach BT 215f 606 n.8, 611 Porphyry in Cat: Commentary on Aristotle’s Categories; Busse CIAG IV i; p þ l 56.8–15 216 56.18–31 259 56.28–9 226–7 59.17 290 59.17–34 298 59.20–2 211 60.22–34 296, 301 n.3 61.14 286 n.1, 311 62.34–64.22 297 n.1 68.12 286 n.1 68.15–18 262 69.1–2 295–6 69.12 296 n.3 86.21–2 399 n.34 86.22–4 204, 213 89.16–17 263 92.15–16 263 Isag: Isagoge; Busse CIAG IV i; p þ l 1.7.9 228–9 4.14–16 228 4.21–2 228 6.6–7 228 12.12–22 324

770

Index of Passages

12.20–1 322 13.3–5 254 v Plot: Life of Plotinus; Henry and Schwyzer OCT; ch þ l xxiv 9–11 231 apud Ammonius in Int 73.19–33 407 n.48 apud Simplicius in Cat 10.22–11.1 586 n.9 Priscian Institutions; Keil GL I–III; b þ s þ s [p þ l] praef 2–3 [2.7–9] 642 praef 4 [2.30–1] 642 II iii 14 [53.8–12] 642 II iv 15 [53.28–9] 646 II iv 18 [55.4–5] 639 II iv 21 [56.16–21] 644–6 II iv 21 [56.21–7] 639–40, 649 XI ii 6–7 [551.18–552.14] 644 n.4, 645 n.5 XIV i 2–3 [24.23–25.22] 649 XIV i 2 [25.1–5] 647 XIV ii 13 [31.16–20] 649 XIV ii 18 [34.23–35.3] 649 XVI i 1 [93.1–2] 640–2 XVI i 1 [93.2–8] 639–41 XVI i 1 [93.9–10] 639 XVI i 1 [93.11–12] 639 XVI i 2 [93.17–18] 652 XVI i 2 [93.20–2] 643 XVI i 2-ii 15 [93.13–104.13] 639 XVI i 3 [94.15–20] 641 XVI i 3 [94.22–5] 641 XVI i 5 [95.26–96.1] 643–4 XVI i 5 [96.13–16] 644 XVI i 6 [96.23–4] 654–8 XVI i 6 [97.4–5] 655 XVI i 6 [97.17–19] 650 XVI i 9 [99.3–4] 644 XVI ii 1 [100.5–10] 654–5 XVI ii 11–12 [100.15–101.8] 658 XVI ii 13 [102.12–19] 653–4 XVI ii 13 [102.20–6] 655 XVI ii 15 [103.16–23] 652–3 XVI ii 15 [103.23–5] 656 XVI ii 15 [104.5–6] 643 XVI ii 16 [104.14–105.14] 639

XVI ii 16 [105.4–6] 643 XVII i 4 [110.6–8] 652 XVII xv 95 [160.16–18] 645 XVII xxiii 171 [196.7–9] 652, 653 n.6 XVIII xxi 173 [287.8–10] 658 part: Partitions; Keil GL III; ch þ s þ [p þ l] i 26 [465.37–9] 640 iv 85 [478.15–16] 640 n.2 vi 125 [488.16–17] 640 n.2 vii 142 [492.32–3] 652 vii 142 [493.2–3] 640 n.2 Proclus in Crat: Commentary on Plato’s Cratylus; Pasquali BT; s þ [p þ l] xvi [7.3–6] 297 n.4 in Eucl: Commentary on Euclid’s Elements; Friedlein BT; p þ l 194.9–11 60–1 194.20–195.5 60–1 210.2–5 44 in Parm: Commentary on Plato’s Parmenides; Steel OCT; p þ l (ed Cousin) 1111.1–6 452 n.1 Psellus Philosophica minora; Duffy BT; w þ l xiii 35–42 686 n.18 xv 1–14 702 n.61 lii 1–5 204 Quintilian Institutions; Radermacher BT; b þ s þ sb III vi 23 203, 245 scholia on anonymus, Logica et quadrivium; Heiberg (Copenhagen, 1929); p þ l 130.18–21 716 n.98 134.19–135.6 686 n.17 on Dionysius Thrax; Hilgard GG I iii; p þ l 100.21–7 629 n.27 236.14 290 n.2 274.8 625 n.18 456.27–457.13 623 n.12 563.13–17 629 n.27 583.27 625 n.18 on Persius; Jahn (Leipzig, 1843) ad VI 80 [p.350] 548 n.21, 550 n.25

Index of Passages Seneca ben: On Benefits ; Haase BT; b þ s þ sb V xix 9 561 n.64 ep: Letters; Reynolds OCT; w þ s cxvii 11–12 481 n.6 Sextus Empiricus M: Against the Mathematicians; Mutschmann and Mau BT; b þ s I 57 606 n.8 I 68–9 546 n.16, 559 n.60 I 72 559 n.60 I 78 591 n.22 II 108–9 482 n.9 II 253 558 n.55 VII 11–12 602 VII 13 551 VII 267 604 n.7 VII 401–35 557 n.54 VII 416 557–8, 563–5 VII 417 567 VII 418–20 564–5 and n.70 VIII 13 586, 603 VIII 70 593 and n.31 VIII 80 594, 598–9 VIII 89–90 518 VIII 90 173 n.5 VIII 93 481 VIII 99 481 VIII 108 481 VIII 110–19 482–3 VIII 112 481, 483 VIII 112–29 482 VIII 118 481 VIII 119 481 VIII 145–50 519 n.11 VIII 244–56 480 VIII 258 602 VIII 265 483 VIII 302 97 VIII 303 97 n.129 VIII 331a 606 n.8 VIII 417 97 VIII 434 479 VIII 435 562 n.65 VIII 443 103 n.147 IX 139 504 n.6

771

IX 182 559 IX 184 545 n.15, 560 X 112–7 556 n.52 XI 21 606 n.8 XI 30 396 n.27 PH: Outlines of Pyrrhonism; Mutschmann BT; b þ s I 234 557 n.53 II 25 604 n.7 II 97–9 519 n.11 II 104–6 479 II 110–12 443 n.1, 483 II 131–2 525 II 135 97 II 137 97 and n.129 II 146 561–2 II 150 479, 562 II 167 449 n.4 II 186 525 II 189 515, 525–6 II 191 514–16 II 250 572 n.81 II 253 563, 568 n.77 Simplicius in Cael: Commentary on Aristotle’s On the Heavens; Heiberg CIAG VII; p þ l 237.2–4 409 552.31–553.4 443 n.1 in Cat : Commentary on Aristotle’s Categories; Kalbfleisch CIAG VIII; p þ l 1.3–4 210 1.8–9 210 1.17 290 1.18–2.2 213 2.3–8 220–1 2.15–16 218 4.4–11 226–7 10.2–4 582–3, 591 11.23 291 n.4 11.23–9 298 13.17 226 15.28 260 15.30 260 15.36–16.13 260 16.14 260 18.16–20 208

772

Index of Passages

22.26 295 22.31–3 300 n.5 25.7–9 286 n.1 25.11 298 25.18–26.2 298–9 29.5 291 n.4, 293 29.5–12 301 n.2 29.25 293 29.29–30.5 262 29.30 291 n.4 30.16–17 214, 301 36.8–11 295 36.8–31 294 36.25–31 294–6 36.28–30 291, 301 n.1 38.19–20 298, 299 38.19–39.2 289–93 38.24–6 300 38.26–39.2 300, 303 58.24–60.10 265 58.27–9 263 62.25–6 399 n.34 62.28 213 66.32–67.8 201–2 74.22–31 224–5 76.13–14 219 78.4–5 223 78.20 291 n.4 88.24–9 263 152.13 211 159.14 290 206.10–15 222–3 340.26–9 215 351.4–7 103 n.147 379.7–10 194, 260 382.7–10 194 387.18–22 390–1 389.22 391 in Phys: Commentary on Aristotle’s Physics; Diels CIAG IX and X; p þ l 1177.2–4 546 n.17 1177.4–9 553 n.42 1197.35–1199.5 553 Socrates HE: Church History; Hansen (Berlin, 1995); b þ s I59 II 35 9, 240

Sozomenus HE: Church History; Bidez and Hansen (Berlin, 1960); b þ s III 15 9 VI 26 9 Stephanus in Int: Commentary on Aristotle’s On Interpretation; Hayduck CIAG XVIII iii; p þ l 53.14–27 82 n.96, 636 n.44 53.24–54.2 633 n.36 Stobaeus ecl: Anthology; Wachsmuth and Hense (Berlin, 1884–1912); b þ ch þ s I xii 3 396 and *n.29 I xxviii 18 488 II ii 22 240 n.1 Suda Adler (Berlin, 1948–1935) s.v. ¯PŒºÅ 481 n.* s.v. ŒÆŪ æÅÆ 593 n.30 s.v. Þ   ºÅŁæÆ 552 n.35 s.v. øŒæÅ 481 n.* Tacitus dial: Dialogue; Furneaux OCT; s 16 550 n.24 Tatian adv Graec: Against the Greeks; Whittaker (Oxford, 1982); s 27 550 n.26 Tertullian an: On the Soul; Waszink (Amsterdam, 1947); s þ sb iii 1 8 n.14 c Hermog: Against Hermogenes; Kroymann (Vienna, 1906); ch þ s viii 3 8 n.14 praescr: On the Prescription of Heretics; Refoule´ (Turnhout, 1954); ch þ s vii 3–8 240 vii 6 8 xliii 1 8 test an: The Testimony of the Soul; Willems (Turnhout, 1954); ch þ s i17

Index of Passages [Tertullian] adv haer: Against all Heresies; Kroymann (Vienna 1906); s 6 8–9 Themistius orat: Speeches; Downey BT; w þ p þ s (ed Harduin) xxiii 285C 552 n.35 Reply to Maximus; Badawi (Paris, 19872); p 180–94 386, 664–5 184 457 n.* [Themistius] in APr: Paraphrase of Aristotle’s Prior Analytics; Wallies CIAG XXXIII iii; p þ l 121.20–123.8 100 n.142 Theodoretus cur: A Cure for Greek Diseases; Raeder BT; b þ s V 72 16–17 VIII 2 16 Theophrastus fragments: Fortenbaugh et al (Leiden, 1992) 72A 586 n.9 87A 468 n.2 91A 474 n.1 92 693 n.41 103C 351 n.**

773

111A 416–18, 439 n.3 111B 439 n.3 111C 414 n.2 111E 413, 439, 703 n.65 112B 441 n.3 112C 443 n.1 113B 440 n.1, 710 n.88 Ulpian apud Justinian, dig I xvi 177 546 n.17 Varro ling Lat: On the Latin Language; Kent (Cambridge MA, 1970); b þ s þ s VI vii 56 595 VIII iii 10 161 n.48 Vergil Aeneid; Mynors OCT; b þ l I 5 653 VII 1 652 XI 42 652 XII 931 655 Xenophon anab: Anabasis; Marchant OCT; b þ c þ s VII vii 32 156 n.27

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General Index The Greek alphabet precedes the Roman. Head-words must sometimes be construed autonymously. IØ æØ  116 [see also indeterminate propositions] IŒ º ıŁÆ 24, 52 n.20, 464 n.4, 526–7 [see also conditional] IŒ Ø
400 n.36 IŁ ø æÆ
Ø
108–9 [see also unmethodical arguments] I
ªØ
440 n.3, 458 n.1, 612 [see also reduction] I
ƪŒÆE
, vs ıºº ªØ  97–8 [see also necessity] I
ƺØ
440 n.3, 458 n.1 I
ŁØ 95 I
ØŒÆŪ æEŁÆØ 313–14 [see also properties] I
Øæ ç 663 f
I
ØŁØ 705 n.71 vs I
Ææ ç 458 n.5 [see also conversion] IøÆ 30–1 and n.33 [see also statables] IæÆ
  97 [see also inconcludency] I ØØ 26 n.20 ¼ æÆ 33, 541 n.8, 561 n.64 I
ƌ  97 [see also inconcludency]

N 443 and K 443 n.1 [see also conditional] r   72 [see also forms] NΠ 349 r
ÆØ 159–64, 275–7 þ participle 164 and n.64 [see also copula] Nƪøª 211 KŒº ª 441 n.1 K
689 n.29 K
å 
ø 626–7 and n.20 [see also modifiers] 
 
86–7, 342 and n.13, 638 ŁÆØ 464 n.4 KææÅÆ 624 and nn.15 and 18, 630 n.30 [see also adverbs] ÆEæ  415 n.4

E 629–30 ،،  369 and n.10, 378 n.18   160 n.48 [see also copula] ØÆØæØŒ  421 ØƺªŁÆØ 23 ØƺŒØŒ 22–3, 47 ØƺŒØŒ , vs ˜ØƺŒØŒ  480–2 and n.6 [see also dialectic] ØÇıª
 421 [see also disjunctive]

YØ  313, 317–18, 326–7 [see also properties] Y

ÆŁÆØ 129 n.218 Yø 379 -Å 546 n.18

ª
،
597

ıåÇØ
556 n.49, 564 n.69 [see also sorites] X Ø ... j ... 513, 532–3 [see also disjunctive] ŁæÅÆ 720–1

ŒÆŁ Æa ıÅŒ Æ 316 [see also properties] ŒÆ 593 ŒÆa  h
Æ 293, 297 n.1 ŒÆÆçÆØŒ  369 n.10

776

General Index

ŒÆŪ æE
156 n.27, 158, 188–9 ordinary use of 188 [see also predicates] ŒÆŪ æÅÆ 487–8 ŒÆŪ æÆ 188–9, 215–16 and ‘category’ 188–9, 256, 266 n.3 [see also categories] ŒÆŪ æØŒ  369 n.10, 437 nn.2 and 3, 621 n.3 [see also categorical] Œ
 614–15 ºŒ
487–8, 582 n.1, 591 and n.22 [see also sayables] º ªØŒ 22 [see also logic] º ªØŒ  499 n.2 º ª Ø 
ºÆ Ø 103 n.147, 449 n.4 [see also arguments] º ª  ¼ ratio/oratio 670–1 ¼ sentence? 646 Stoic definition of 97 in Top 325, 340–1 vs ºØ 78, 513 vs æ   96–7

ZæªÆ

230 [see also logic; Organon] PÆ 196–7, 245 [see also substance] ÆæƺÆ
Ø
290 n.16 Ææa ØŒæ
546 n.16 [see also sorites] æÆ
ØŒ  97, 108 ØŁÆ
 499 [see also plausibility]  ººÆåH ºªŁÆØ 306–7, 308 n.1  ºı
ıÆ 294 [see also polyonymy] æAªÆ 74, 77 ¼ ºŒ
488, 532–3, 599 in Top 325 æ ºÅÆ 711 æ ºÅłØ 606 [see also preconception] æ Ø æØ  687–8 and n.26 æ ŒÆŪ æEŁÆØ 160–2 æ ŒEŁÆØ 161 æ ºÅłØ 421 æ ÅÆ
Ø
161 n.54 ÞBÆ 152–3 and n.22

åÅ 24 vs IŒ º ıŁÆ 530 [see also conflict] Ł   720–1 ŁØ 468 n.2 ƺÆ
Ø
372 and n.16 ºÅłØ 421 

631–2
ÅÆ, vs
ÅØ 592 [see also thought] ƒ
æ Ø 102–3 and nn.144 and 147 [see also ancients; moderns] ƒ æd X 135 n.228, 558 n.55, 602 n.1 ›
ı  Aristotle’s usages 304–8, 308 n.1 and ›ø
ıÆ 311 [see also homonymy] Z
Æ 148, 152–3 and n.22, 166–7 in Top 325, 340–1 [see also names]

ıÇıªÆ 90 n.112, 428 ıºº ªØ  365–6, 693, 700 n.54 ıºº ªØØŒ  97–8 ı
ƌ،  97 ı
Æç 520 
  160 n.48 [see also copula] ı
å 420–1 ı
Å
 420, 499, 520 [see also conditional] ı

ı  291, 294–5 and ‘synonymous’ 286 n.3 [see also synonymy] øæÅ 546–7 and n.18 [see also sorites] øæ  546 n.18, 550 n.26 a æ  Ø 169–70 ÆP
ı  297 [see also tautonomy]

General Index -
649 n.30  KØ; 196–7    678 æ   ¼ modifier 79–80 and n.89, 82 n.97, 85, 621, 623–4 formal vs material 79–81 and n.94 modal 161 and universality 84–5 [see also modifiers] ¼ schema 96–7, 499 n.2 ¼ ıÇıªÆ 690 n.32 fiH ÆFÆ r
ÆØ 123, 138, 381 n.20 oºÅ 56, 72 and æAªÆ 74, 77 [see also matter] æåØ
156 n.27, 158, 343 and n.14 Ææå
ø 633 n.33 [see also actually]  ªæÆç 53, 524  ıºº ªØØŒ  98–9 and nn.135 and 136  Ø
614–15 çغ  çÆ 685 and n.12 åæ 629–30 -
ı  294 and n.4 [see also onymies] ‰ Kd e  º 346–52, 637–8 and n.49 [see also for the most part] Abelard, on wholly hypothetical arguments 455 n. 3 Academics, Old, and logic 27 accidents definition of 316 fallacy of 553–4 and n.46 per se 316 transference of 254 [see also substance] a
cervus 546 n.18, 550 n.26 [see also sorites] actually, a modifier? 632–6 and n.36 adcopulas 626–7 Adrastus, on Cat 208, 260 adsentences 80, 82 n.85, 658 [see also copula]

777

adverbs 80, 624–5 and n.18, 629–30 particular vs universal 84–5, 636 types of 625 [see also modifiers] Ae¨tius, a heretic and Aristotle 9, 240–1 life of 9 n.16 and logic 9, 15–16 his Syntagmation 9, 15 Alcinous and categories 217 and logic 48 and wholly hypothetical arguments 452, 460–1 Alcuin, on categories 247, 252 Alexander of Aphrodisias on actually 633 n.36 on arguments from a hypothesis 379 on Aristotle’s definition of syllogism 398 n.31 on conversion 83–3, 94–6, 458 n.5, 664–5 and copula 162, 276–7 on deictic arguments 369 n.10, 378 n.18 and Euclid’s arguments 45 n.5 on form and matter in logic 73–4, 88–9 on form and universality 83–4 on generation of the figures 457–8, 663–5 and n.** on hypothetical arguments 419–20, 423–6, 703 n.65 reduction of 440–1 and n.3 some infelicities 90–6, 127 n.14, 130, 133 and n.225, 143 and logical constants 87 on material validity 90–3 on meaning 589–90 his metatheorem 136 on mixed hypothetical arguments 440 n.3 on mixture 400 on modality 79–83 on the moderns 98, 101, 102–3, 105–6, 173n.4, 421 on modifiers 79–82, 85–7 on necessity vs syllogism 87–9 and n.110, 662–3 on negated conjunctions 421–3 on negation 172–4, 401–4

778

General Index

Alexander of Aphrodisias (cont.) on past tense 177 and peiorem rules 691 n.33 and pons asinorum 720 n.105, 722 n.114 on predicates and existence 180–4 on proofs of inconcludency 92–3, 718 and n.101 on proper names 179 n.15 on properties 337 n.10 on propositional identity 135 n.229 on schematic letters 83–4 on singular terms 119 n.187, 120 n.187 on ‘Socrates died’ 176–84 and Stoic themata 390, 408–11 on subsyllogistic arguments 98–9 and synthetic theorem 408–11 on Theophrastus 12–13, 199–200, 416, 419–20 on unmethodical arguments 99–101, 112–16 and n.175, 117 n.181, 120–3, 127 n.214, 129–31, 278–9 and utility of logic 45–6 on wholly hypothetical arguments 93–4, 139–40, 441–3, 448 n.3, 451 and n.1, 461–3 writings, chronology of 101 Alexander of Lycopolis, on Christianity 238–9 Alexander the Valentinian 9, 14 al-Farabi, and hypothetical arguments 414 n.3 Ammonius on actually 632–6 on adverbs 624–6, 630 n.30 on Aristotle’s definition of syllogism 398–9 and n.32 on categorical propositions 700 n.5 edition of Int 621 his in APr 661 on indeterminate propositions 116 n.178 on matter and form in logic 74, 76–9 on modifiers 79–80, 82, 621–7, 631–8 on perfect syllogisms 661 on unmethodical arguments 115–16 anachronism 584 analogical transference 224–5 ancients, the on analysis of syllogisms 483–4

in Chrysippus 391–2 and n.21, 385–97 [see also moderns] and 407–8 Andronicus on Cat 194, 259–60, 262 his edition of Aristotle 209–10 and Int 233, 585 n.7 his Organon 230–3 his Pinakes 206, 231, 233 and Ptolemy the Unknown 206, 231 anon Heiberg and Blemmydes 686 n.20, 692 n.32, 703 n.65 on categorical moods, how many? 699–703 on categorical propositions 700–1 date 683–4 doesn’t know Top 686 on hypothetical arguments 703–13 and indeterminate arguments 687–99 and indeterminate propositions 688 n.26, 689 and n.30 on modal propositions 700–1 and n.56 his notion of logic 685–7 and Organon 686 and n.17 his originality 684–5 and n.9 and peiorem rules 690–2 on pons asinorum 720–7 and proofs of inconcludency 716–18 and singular arguments 696–9 structure of 683–4 on wholly hypothetical arguments 709–13 anon in Tht, on wholly hypothetical arguments 452 n.4 Antiochus, and logic 28, 39 Apelles, a heretic 8–9 on Noah’s ark 14–15 Apollonius Cronus 556 Apollonius Dyscolus on adverbs 624, 629–30 and n.30, 636 and conditionals 520–2, 526–7 and n.* On Connectors 516 on disjunctions 518–23 and grammatical incoherence 522–3 on modifiers 629–30 and Posidonius 518 and Stoicism 517–18

General Index Apollonius of Perga, and Euclid’s axioms 60–1 and n.40, 66, 122 apologies, Christian 2 Apuleius (?) and analysis of arguments 483–4 on categories 234–5 and indeterminate moods 694 on logic 23 n.8 on proofs of inconcludency 718 n.102 Arcesilaus against Stoics 557–8 and Diodorus 557 and sorites 557–8 and n.54 Archigenes 4 Archytas [see pseudo-Archytas] Arethas 251–2 arguments conclusion always categorical 369–70, 373, 462 deictic 370–1 and formal rules 109–10 formal vs material 52–3 from a hypothesis and hypothetical arguments 438 n.1* not reducible to categoricals 376–7 not syllogisms 378–80 partly categorical 377–8 and reductio ad impossibile 371–2, 380–1 vs deictic 369 n.10 materially valid, outside scope of logic 110–11 proportional 425 prosleptic 50 n.15, 107–8, 421 n.* qualitative 423–4, 426 reduplicated 398–9 single-premissed 94, 103 n.147, 449 n.4 singular 696–9 subsyllogistic 98–9, 105 n.153 vs schemata 96–7 [see also categorical; hypothetical; relational; unmethodical] Aristo and categorical arguments 415, 452 and subaltern moods 691 Aristotle on arguments from a hypothesis 369, 371–3, 404, 413–14 and n.2, 424, 438–9

779

and ‘to be’ 159–64, 275–7 bishop of the Arians 240 and Christians 9–10, 12 and n.25, 240–1 and Chrysippus 393–4 his completeness thesis 364–73 confusions in 325–7 On Contraries 390–1 and n.16 criticized 103–8 definition of syllogism 381 n.20, 398–9 on definitions 329 on deictic arguments 369–71 doctrine of the mean 552–3 and Eubulides 552–3 and n.35 and fallacy of accident 553–5 and n.46 on ‘for the most part’ 346–52, 696 n.48 and grammar 152–4 and heretics 8–10, 12 and n.25, 240–1 and homonymy 285–6 on indeterminate propositions 116, 692–3, 694 nn.44 and 45, 696 n.48 on law of contradiction 358–63 and laws of thought 358, 474 n.1* and logic 2–3, 435 and matter of arguments 73 and meaning 584–5 and Millet Seed 553 and n.43 and modifiers 631, 636 and names 154 on necessity vs syllogism 87–8, 446–7, 662–3 and negation 162 n.58, 425 obscurity of 672 On Opposites 390–1 and n.16 and ordinary usage 326 and n.i and pons asinorum 722 and n.114, 723 and n.117, 727 and n.119 on primary substances 220–1 and proofs of inconcludency 270–1 and n.11, 714–15 and nn.96 and 97 and proper names 166 on properties 313–30 and qualitative arguments 424 and reductio ad impossibile 371–2 and singular propositions 324–6, 688 n.26 and sorites 552–4 and n.46 and Speusippus 288, 304 and Stoic logic 382–400

780

General Index

Aristotle (cont.) and synonymy 286–7 and synthetic theorem 410–11 his theory of meaning? 584–90 Top Book E, authenticity of 312–13, 322 n.iv origins of 312–13, 322, 324 text of 338–9, 341 works Andronicus’ edition 209–10 catalogues of 206–7, 386–7 fate of 385–7 known in Hellenistic period 385–8 read by early Stoics? 387–97 read by Epicurus 385–6 and n.6 read by Eubulides 386 read by Strato 385 and wholly hypothetical arguments 446–7 [see also Categories] Arius, a heretic 9 article, definite, 522 and n.13 as quotation marks 298–9, 307 and nn.1–2 Aspasius on Cat 212 and sorites 552–3, 574 n.83 assertibles [see statables] asses [see pons] Athenagoras 2 Athenodorus, a Stoic, on Cat 105, 213, 399, 403 Atticus, on Cat 214, 217 Augustine the Carthaginian Aristotle 18 and Cat 205, 244–5 enemies of 19 and logic 18–19 and n.42 Avicenna, on Cat 249 baldness [see sorites] Barbara 85–8, 140–3, 270, 364–6 and quasi-Barbara 697–8 [see also categorical] Basilides, and Aristotle 240 Begriffswort 147–8, 163–4 and n.61 [see also concept; Frege]

belief and assertion 359 n.*, 617 and n.17 and conditionals 354 and conjunctions 353–4 and disbelief 355–8 and disjunctions 354 and negation 357 Bible, the Holy 6–7 and n.8 emended 10 and n.19 and logic 242 bivalence, principle of arguments against 33–4 arguments for 32–3 counterexamples to? 31 the foundation of logic 29–31 Blemmydes on hypothetical arguments 703 nn.64 and 65 on indeterminate propositions 692 n.36 on wholly hypothetical arguments 712 n.93 Boethius and Cat 247–8 on categorical arguments 678 on categorical vs hypothetical propositions 470–1 his commentaries 248 and n.5, 672–6, 668 and n.8, 673 n.13 modus operandi in 674–6 and n.* sources of 674–6 and n.* on conditionals 443 n.1, 444–5, 448 n.3, 523–4, 679–81 and conjunctions 423 on Eudemus 416–17 his grand project 667–9 on hypothetical arguments 416–18, 678–81, 707–8 and n.78 reduction of 429–30 intellectual eminence of 666–7 and n.1 logic of discovery vs proof 677 logical works of 668 dating of 246–7, 668 n.9 originality 669–70, 673–4, 681 sources of 677 and n.** and Marius Victorinus 669, 673–4 on matter and form in logic 75 on modifiers 628 n.23, 629 n.26

General Index and negation 680 n.* and Porphyry 248 on propositions 678–9 schematic letters in 444–5 sources of 660–1 and Stoic logic 679 and theological predication 254 and Theophrastus 416–17, 457 n.*, 523–4, 677 on topics 677–8 his translations 246–8, 669–72, 667 n.4 on wholly hypothetical arguments 451–2, 455–7, 459 nn.3 and 1 first figure 455 n.1 modal 461 n.1 sources for 456–7 and n.2 Boethus and Cat 262–3 on categories 223, 298–9 and hypothetical arguments? 429–30, 452 and logic 230–1, 415 and onymies 289–93, 298–300 and physics 230 read by Simplicius? 290–1 and n.4 Brentano, his syllogistic 472 Buridan 52–3, 126 n.208, 282–3 Byzantine philosophy 250–2 Carneades against the Stoics 559 n.62 on sorites 557 n.54, 559–60 and n.63, 565–9 Carroll, L. 138 n.237 case, grammatical 591 and n.26 Cassiodorus text of Inst 245–6 on translations 667 n.4 catalogues, ancient of Aristotle 206–7 and n.1, 231–3, 386–7 of Chrysippus 391–2 and n.21, 395–6, 499 and n.2, 555–6 and n.49 categoria 188 categorical propositions and class relations 169 and n.74 and conditionals 463–4, 466–8, 470–1 how many? 700–1

781

simple? 419 and n.*, 437 and n.3, 438 n.*, 678 categorical arguments analogous to wholly hypotheticals 463–6 and categories 269–77 characterized 2–3, 49, 269 compound 708–9 criticized 103–8 figures of 90 n.2 their generation 457–8 and n.*, 663–5 a fourth figure? 662 indeterminate moods 688–96, 694 n.43 the logic of science 168, 364 modal difficulties with 35 and sciences 350–2 moods, how many? 694 n.43, 699–703 never two particular premisses 105–6, 116–17, 125 partly vs purely 366–7 reduced to Barbara and Celarent 364–6 and relations 168–9 and Stoics 398–9 and n.31 subaltern moods 691 [see also completeness] cate´gorie 188 Categories the antepraedicamenta 192–3 and APr 234 authenticity of 191–2, 207–8, 263–4 a bestseller 198, 238 and Byzantines 204, 250–2 in catalogues 206–7 and n.1 a collection of sophisms? 240–1 commentaries on 210–14 Arabic 249 by Peripatetics 212 by Platonists 213–14 after Porphyry 226–7 by Stoics 213 Syriac 249 deals with terms 234–5 a difficult work 227 and early Peripatetics 199–201 first part of Organon 230–4 in Hellenistic libraries 206–7 and Int 234

782

General Index

Categories (cont.) introductory 211, 227–8 the postpraedicamenta 194–5, 235 and pseudo-Archytas 194, 215, 218–19, 222 a schoolbook 228–9 structure of 192–5 text of 251–2, 261–3 incomplete? 195, 258–9 interpolations in? 193 title of 189, 191, 194, 207 n.1, 258, 259–64 translations of Arabic 248–9 Armenian 248 Latin 245–8 Syriac 248–9 two versions of? 207–8 categories, Aristotle’s theory of applies to perceptible items? 220–3 and APr 271–2 in APst 235 and arguments categorical 239, 249, 269–71 hypothetical 269 material 281–3 relational 277–81 classifies predicates 196–8, 215–16, 267–8, 271–2, 276 n.6, 298–9 controversial 211–12 criticisms of 219–21 dialectical? 259 and heretics 240–1 as highest genera 190 how many? 214–15 and logic 234–7, 249 the ‘minor’ categories 193–4, 258, 281 not applicable to intelligible items? 220–1, 223–4 order of 215 philosophically neutral? 217 and Platonism 216–23 in rhetorical tradition 203–6 and simple predicates 190, 271–2 and Stoics? 202–3, 212, 389 and study of Bible 243–4 and syllogisms 239, 249, 268–83 and theology 252–5 in Top 189–91 vs in Cat 196–8 [see also predicates]

categories, Stoic theory of 201–3 and Plotinus 202 a rival to Aristotle? 202–3, 203 n.*, 211–12, 389 categories, syntactic 624 n.17 causes, containing 598 n.39 Celsus, and Christians 4 and n.5, 7, 10 certainty 509–10 Christ, the Lord Jesus, a logician 242 Christianity, a simple philosophy 2, 238–9 Christians and Aristotle 8–10, 12 and n.25, 240–1 embrace logic 2, 17–19, 20–1, 240–4 ethics of 5–6 and Euclid 12 and n.24 and Galen 4–7, 11–12 and n.22 and proofs 3–4 reject logic 7–17, 239–40 and rhetoric 15–17, 242 and Stoic logic 13 and n.27 and Theophrastus 13–14 [see also heretics] Chrysaorius 229 Chrysippus on Academics 393 on Aristotle 391, 393–4 and bivalence 32 catalogue of his works 391–2, 395–6 and commands 488–94 and conditionals 38, 499–500, 503–4, 542 On Dialectic 391, 392–5 on dialectic 392–5 and the Liar 38–42 and logic 2–3, 13 Logical Investigations 486, 506, 563 n.68 text of 496–8 and modality 389–90 on negation 403–4 on plausible conditionals 499–511 on plurals 506 on sorites 555–8, 561 n.64, 563–70, 574 on speaking and thinking 595–600 his style in logic 431–2 works of 391–2 and n.21, 395–6, 485, 499 and n.2, 555–6 and nn.48 and 49 [see also Stoics]

General Index Cicero and Aristotle 27, 203–4 on bivalence 30–42 and Cat 209 on hypothetical arguments 707–8 and n.77 on Liar 34–42 on logic 22–42 ¼ Plato’s logic 27–8 6¼ Stoic logic 27 on sorites 29–30, 546 n.18, 548, 557 n.54, 568 n.77 his Top 203–4, 668 n.7 on tripartition of philosophy 22–3 Clement and logic 18–19, 243 on philosophy 2 Clitomachus 560 commands conjunctive 489–91 disjunctive 491–3 logic of 488–94 and predicates 489 and statables 489 commentaries, ancient 14 formalize arguments 14–15, 100 and n.40, 108 n.158, 452 n.1 imaginary debates in 172–3, 388–9, 398–9, 402 rarely original 171, 226, 285 n.7 [see also Categories] comparatives 411 n.5 completeness of categorical syllogistic arguments for 369–73 for deductions 364–6, 436–7 for proofs 364–5 versions of 366–8 compound propositions how defined 500–1 kinds of 531–2 either separate or connect 407–8, 422–3, 438, 529–31 concepts 396 incomplete (unsaturated) 147 and n.4, 155 conditional propositions analyses of 38, 443 and n.1, 447 n.1, 499 n.2, 500, 501 n.5, 526, 532, 542 n.11, 680–1 and n.*

783

in arguments 421 and categoricals 463–4, 466–8, 470–1 and conflict 524–7, 525 n.*, 529–30, 621 corresponding 42, 51–2, 97 Dialecticians on 482 dispute over 443, 482–3, 680 do not commute 526–7 natural 520–2 vs accidental 523–4 negated 468 n.1, 679–80 and negated conjunctions 499, 503–4, 542–3 not genuine propositions? 462–3 and n.4, 711 and n.91 plausible 499, 502–3, 506–7 conflict complete vs incomplete 529, 531–2 and conditionals 524–7, 525 n.*, 529–30, 621 and contradiction 516–18 multilateral 529 n.17 conjunctive propositions and belief 353–4 commute 526–7 defined 531–2, 650–1 negated in arguments 421–2, 527–9, 706–8 and conditionals 499–500, 503–4, 542–3 how recognized 528–9 not genuine propositions? 407–8, 421–3 and n.17 with more than two conjuncts 705–6 connectors abnegative 654–5 approbative 655 in arguments 13–14 causal 644 classification of 643–4 they connect expressions 640, 648 homogeneous items 644–5 nothing 651–4 parts of sentences 647–8 parts of speech 640, 644–7 including connectors? 645 sentences 648–51 thoughts 640, 648

784

General Index

connectors (cont.) and connectives 649 copulative 652–3 they co-signify 641 defined 639–42 and definition of compound propositions 500–1 dictiones 642 expletive 643, 651–4 functionally defined 639–40, 643–4 indeclinable 641 indicate force or order 641, 649 meaning of 650–1 a part of speech 639–40 preferential 644 and prepositions 647, 649 rational 655–8 in Stoic logic 649 consequentia defined 52 n.20 formalis vs materialis 52–3, 88–9, 282–3 logical form of 53 constants, logical and adsentences 82 n.95 enumerated 57 and n.36 and modifiers 637 pragmatically determined 63–5 relative to systems 64–5, 143 syntactically defined? 62–3, 433 n.1 topic neutral 62–3, 85, 87 contradiction defined 516–17 law of, a law of thought 358, 363 contraposition 449 n.4, 453, 458–9 and n.3 contraries definitions of 354–5 fall under the same science 340 n.11 conversion AI 95 and n.123, 273, 471 and contraposition 453, 458 and n.5, 705 n.71 of E-propositions 149, 552 n.35 not inferences? 94, 95 n.123, 449 n.4 and oppositions 95 and O-propositions 82–3, 552 n.35 rules of 94–6 and substitution 95 of terms vs propositions 95, 664–5

copula absurdity of? 150 additionally predicated 160–2, 621 ambiguous? 275–7 function of 148–9 and n.7 and identity 169 n.75 no semantic value? 169 n.76 one only 169 syntax of 154–5, 161–3 and n.60 terminology of 160 n.48 unnecessary? 155–9 and n.40 [see also adcopula] Cornutus 105, 403, 550 n.25 on Cat 204, 213, 399 and negation? 403 and Persius 550 n.25 counterpredication 313–14, 316 criterion of truth 24, 26, 28–9 Darapti 273 David the Invincible 248 declarare 189 deductions general form of 366–7, 371–2 partly vs purely categorical 367, 373–5, 377–8 [see also arguments] deficiency, logical 562–3 definitio 32 and n.37 definition 24, 32 and n.37, 329 vs delineation 53, 639–40 demonstratives, vs names 403–4 and n.40, 489, 492–3 de Morgan, Augustus on copula 169 n.75 on logical form 56, 66 Dexippus on Cat 212, 389 on the intelligible world 224 and Porphyry 221 diagrams, logical 720 n.106 dialectic despised 391, 394 and n.25 Stoic 394–5, vs logic 394 [see also logic] dialectica 23, 25–6 Dialecticians

General Index and analysis of arguments 483–4 on conditionals 482 inventors of sentence logic? 383, 479 and Megarics 481 n.* a School? 480–2 and n.* dialecticus 481 n.6, 482 dictio, simple 642 and n.3 Diodorus, a Dialectician 480–1 on conditionals 482 pupils of 556–7 and sorites 556 and n.51 Diogenes of Babylon, on speaking and thinking 596–600 Diogenes Laertius on Peripatetic philosophy 209 on Stoic logic 541–2 disbelief 355–8 contrary to belief 360–1 disjunctive propositions in arguments 15–16, 374–5, 407, 421, 705–6 and belief 353–4 commute 526–7 and conditionals 520–1 defined 447 n.1, 512–16, 532–3, 650 exclusive vs inclusive 407–8 and n.7, 514 n.4, 705 interrogative 515 and n.5 natural 518–24 always true 524–5 vs connection 407–8, 422–3 with more than two disjuncts 514–15, 705–6 disserere 23 and n.8 Eigenname 147–8 and n.5 [see also names] Empirical doctors on indeterminacy 573–8 and logic 571–8 on medicine 539–40 on reason vs experience 571–2 on sorites 539–40, 549–50, 559, 570–8 vs Dogmatists 539–41, 575 n.84 enim 656 enthymemes 124 n.197 Epictetus, on logic 28 n.26, 229–30 Epicureans

785

and logic 23–4, 26–7, 241 and metaphysics 607 n.10 reject sayables 602 theory of meaning 582, 586, 603–4 absurd? 607–9 admirable 609–10 and epistemology 611, 614–17, 619–20 meanings are preconceptions? 605–6, 614–19 meanings determined by preconceptions? 616–17 no intermediate items 603–4, 607 n.10 two theories? 610–11 traduced by their adversaries 606–7 [see also preconceptions] Epicurus and bivalence 39 knowledge of Aristotle 201, 614 n.13 Epiphanius 9, 15 equality defined 61, 66 and identity 122–3 a logical constant? 62, 111–12 equidem 655 essentia 245, 641 Eubulides against Aristotle 551–2 and n.35 on conversion 386 and paradoxes 550–3 and n.31 and philosophy 551–3 and sorites 550–3 Eucharist 254 Euclid and Christians 12 n.24 first theorem of 43–4 his Pseudaria 12 [see also Apollonius] Euclidean Argument 43–5 and n.2, 48–9 and Alexander 45 n.5 and Barbara 141–2 formally valid 59 [see also Truncated Argument] Eudemus of Rhodes his Cat ? 199–200 on Int 586 n.9 on logic 415–17 on meaning 586 n.9 Eudorus, on Cat 213, 222–3

786

General Index

Eunomius, and logic 9, 15, 239–40 Eusebius, and logic 19 excluded middle, exceptions to? 39 existence, a predicate 678 n.23 experiences 539–40 and nn.4 and 5, 685 and sorites 539–40 expressions complex but not sentential 646–7 significant 77–8 vs uses of expressions 643–4 fallacies of accident 553–5 and n.56 and matter and form 89 n.11 a typology of 562–3 focal meaning 225 forma, and formula 79 n.87 forms, logical of arguments 57–8 defined 70–1, 76–9 and fallacies 89 n.111 ¼ highest forms? 57, 67–8, 89 of propositions 54–7 plurality of 56, 373–4 terminology of 72–6 understood by ancients? 72–3 and nn.61 and 62 and universality 82–5 and validity 58–9, 68–9, 88–9, 138 vs matter 56–7 [see also matter] Forms, Platonic 222, 396 for the most part and indeterminate propositions 696 n.48 knowable 347 logic of 347–8 a modal operator? 349 ¼ possible? 349–52 ¼ natural? 346–7 and Plato 350 and pons asinorum 722 a quantifier? 348 semantics of 348–52 temporal interpretation of 349 vs chance 347 vs necessary 346–7 Frege no categories in 257 on concept and object 147–8 and n.5

on concepts 163 n.61 on generality 157 n.31, 464, 466, 467 n.3 on meaning 588 n.15 on multiple quantification 168 rejects subject/predicate analysis 149–50, 166–7 on relations 170 and sentence logic 435 and Stoic logic 435 n.1* the superiority of his logic 150 and n.13 on traditional grammar 151 n.15 future contingents 39, 389 Galen and the Bible 6–7 on categorical and hypothetical propositions 466–8 on categories 214–15, 235–7, 266–7, 272 on Christians 4–7, 11–12 and n.22 commentary on Cat 210–11, 235 on compound propositions 532–3 on conflict 529–32 and implication 530 on conjunctions 523, 530–1 criticizes Peripatetics 127, 135 criticizes Stoics 532 detests isms 235 and indeterminate moods 694 n.43 Introduction to Logic 1, 20–1, 235–6, 527 on Jews 4–5 known to Church Fathers? 11–12 and n.22 life and works 1–2 and n.1 On Medical Experience 539 and n.1 his metatheorem 126–8 on the moderns 102, 420–1 on negated conjunctions 527–9, 530–1 and Posidonius 126 n.207, 127 n.212 on proofs 1, 236, 531 on relational arguments 2–3, 20–1, 50–1, 277–9 and sorites 538–41, 547–8, 570–2 as textual critic 11 and Theodotians 11 on third indemonstrable 527–9 on unmethodical arguments 106–7, 126–7 on useless parts of logic 528, 531 and utility of logic 46–7 [see also relational arguments]

General Index Geach, P.T. on corruptions of logic 153, 169 n.74 on an incoherence of Aristotle’s 165 and n.64 on names 154 n.23 gods, vulnerable to sorites? 559–60 and n.63 grammar ancient definition of 559 n.60 traditional 150–3, 165–6 and n.66 Gregory of Nazianzus on Aristotle 8 on logic 9, 17–18, 239–41 Gregory of Nyssa, on logic 8, 17 heretics and Aristotle 8–10, 240–1 and Greek philosophy 8–9, 240 and logic 8–14, 14–17, 19 and n.42, 240–1 [see Christians] Herminus on Cat 211 on matter and form in logic 75 heteronomy 289–90 defined 296, 303 [see also onymies] Hippolytus on categories 217–18, 240 on heretics 8 history of philosophy, and biography 384–5 homonymy Aristotelian vs ‘Speusippan’ 284–8 defined 285, 287–8, 294 and derivative senses 306 and fallacy 288–9 and things said in several ways 306–7 varieties of 305–8 of words or things? 284–8 [see also onymies] hypothetical arguments ¼ arguments from a hypothesis? 438 n.1* characterized 2–3, 48–9, 116, 269 defined 418–19, 437–8, 703 n.62 elliptical versions of categoricals? 375–6 kinds of 703 and n.65 mixed analysis of 429–30 defined 420 figures of 427–9

787

modal? 461 n.1 not syllogisms? 440 n.3 perfect vs imperfect? 429 reduced to categorical arguments? 429 n.*, 468–3 varieties of 420–3 vs wholly hypothetical 48 n.13, 420, 441–2 not syllogisms? 377–81, 462–3 partly categorical? 377–8 and Peripatetics 404–5, 413–16 in Plato 452 n.1 proportional 425 qualitative 423–4, 426–7 reducible to categoricals? 376–7, 704 vs categorical arguments 419, 437–8 vs deictic arguments 369–70 [see also wholly hypothetical] hypothetical propositions defined 418–19, 437–8, 703 n.62 either disjunctive or conditional 407–8, 422–3, 438 identical with categoricals? 466–8 in Peripatetic logic 704 reducible to categoricals? 704 reduplicated 450 n.1 and relational arguments 698–9 and Stoic indemonstrables 704–8 types of 438 and n.2, 703 and n.65 how defined 438 n.2 vs categorical 419, 437–8, 438 n.*, 678–9 [see also conditional, conjunctive, disjunctive] Iamblichus, and [Archytas] 218 identity 66 and copula 169 n.75 a logical constant? 61–2, 64–5, 67, 122–3 numerical 309 n.2 ‘If P, then not-P’ never true? 524–7, 530, 679–81 ‘If P, then P’ always true 39–40 impressions apprehensive 557 and n.54 rational 592–4 incoherence grammatical 522–3 logical 562

788

General Index

inconcludency, proofs of 92–3, 270–1 and n.11, 274–5, 713–20 indemonstrables 38, 98, 405–8, 431, 704–5 and n.70 first 38–9 and Theophrastus 405–8 third 527–9 [see also Stoic logic] indeterminacy and alternative logics 577–8 and n.88 grades of 573–8 and third truth-value 577 n.87 indeterminate propositions in arguments 688–96, 693–4 and n.43 equivalent to particulars 116 and n.178, 688 n.26, 689 and n.30, 692 n.36, 694–6 and nn.44–6 and ‘for the most part’ 696 n.48 and relational arguments 698–9 and singulars 117–18, 166–7, 688 n.26 induction, mathematical 543 and n.13 inexplicabilia 33–4, 39, 561 n.64 itaque 658 Jerome and Galen 12 n.22 and logic 8–9, 16, 18, 239, 242 John of Damascus, on logic 243 Julian, and Ae¨tius 9 n.16 Justin, and philosophy 2, 238 Kant on categories 255–6 on propositional form 56 n.32 languages, artifical 512–13 Latin terminology 23–4 and n.8, 25–6 and nn.16 and 20 Leibniz, and term logic 435 Lenin, on categories 255 letters, dummy or schematic kinds of 55 and metalogical descriptions 687 n.23, 704 n.70, 723 n.117 not variables 99 n.139 in pons asinorum 721–2 sentential vs term 443–6 and universality 83–4

Liar, paradox of 34–42, 397 not concerned with lying 36 n.47 Little Labyrinth 10–12 and n.18 Locke, and meaning 588 n.15 locus 678 logic alternative 577–8 and n.88 and criterion of truth 24, 26, 28–9 defined 47 deontic 57 n.36, 638 of discovery vs proof 677–8 a disease 7–8 epistemic 86–7, 638 first part of philosophy 229–30 formal 72 and n.60 foundation of 29–31 fraternal 64–5 and n.50 and heretics 8–17, 19, 239–40 and inference 26 modal 85–6 and n.104 and paradoxes 25 part or instrument of philosophy? 22–3, 45–7 and n.7, 230, 252, 659, 685 parts of 2, 24–7, 230 topics vs analytics 677–8 of preference 64–5 and n.49, 71 and proof 24–5, 46–7 rejected 7–8, 239–41, 391 and n.18 and rhetoric 15–17, 23 and nn.8 and 10, 25, 242, 249–50 and sophisms 25 systematic 70–1 and theology 243–4, 252–5 a third sort? 2–3, 20–1, 50–1 two sorts of categorical vs hypothetical 2–3, 48–50, 269, 419 Peripatetic vs Stoic 427, 431–2, 435–6 of terms vs sentences 433–7, 473–4 collaborators or rivals? 434, 436, 474–5 [see also arguments; categorical; hypothetical; relational; unmethodical] logical constants [see constants] logical form [see forms] logical relations, two only? 407–8, 422–3, 438, 529–31

General Index logicians, Roman 677 Lucius, on Cat 213–14 Mansel, H.L., on categories 257 Marius Victorinus and Boethius 669, 673–4 commentary on Cat ? 204, 674 n.15 commentary on Cicero 673–4 on hypothetical arguments 677 and n.20 life and works 245–6 translation of Cat ? 245–7 translation of Isag 245, 669 Martianus Capella on categories 205–6 on logic 3–4 material implication 501 n.5, 542–3 matter of propositions 56–7 relational 56 vs form in logic 73–9 terminology of 72 n.62, 74–5, 77 [see also forms] mean, doctrine of, and sorites 552–3 meanings and convention 619–20 how to talk about them 583–4 and intention 600, 620 ¼ sayables (Stoics) 582, 590–601 ¼ things (Epicureans) 582, 586, 603–20 ¼ thoughts (Peripatetics) 582, 584–90, 600 ¼ affections in the soul? 587–8 general or particular? 588–90 and n.21 and truth-conditions 609–10 Mill, J.S., on categories 256 Millet Seed, paradox of 550–1 and n.30, 553 n.43 moderns, the and logical terminology 420–1 on onymies 291, 294 ¼ Stoics? 101–2, 103 n.147, 173 n.4, 294–5 on subsyllogistic arguments 98, 105 n.153 on unmethodical arguments 100 and n.142, 105–6 [see also ancients] modes [see modifiers]

789

modifiers actually 632–6 adcopulas? 626–7 adsentences? 80, 628–9 and n.27 adverbs? 79–81, 84–5, 624–6 and arguments 636–7 and copula 161 defined 623–4 how many? 637–8 induce generality 82–5, 636–7 innumerably many 631 and n.31, 636 n.34 logical 79–81 and n.94, 82 n.96 logical constants? 637 and negation 628 n.24, 635–6 vs modal status 81, 700 n.56 modus ponens 543–4 and n.* Moses, and Plato 5 nam, a connector? 655–8 names 166 and noun phrases 646–7 plural 122 n.192, 131 proper empty 179 n.15 and existence 176 n.12, 180–4 vs common 153–4, 166–7, 295 in traditional grammar 148–9 vs demonstratives 403–4 n.40, 489, 492–3 necessitas consequentiae vs consequentis 662 necessity and omnitemporality 321 vs syllogism 87–8 and n.110, 114, 116, 662–3 negation 437 n.3, 438 n.1, 622 n. 7, 629 n.27, 678, 680 n.*, 702 n.61 and existence 175–6 and modifiers 628–9 and n.24, 635–6 of predicate vs proposition 173 and n.5, 175 n.10, 425 of singular propositions 173, 175–6 of terms 162 n.58, 425, 468 and n.2, 678 two accounts of 172–43 [see also conjunctives] Nicostratus on Cat 213–14, 219 on onymies 293, 301

790

General Index

Ockham, on modifiers 628 Olympiodorus, on Cat 191, 199–200 ‘only’, a mode? 631–2 onymies Aristotelian vs ‘Speusippan’ 284–8 a division of names? 289–90 and n.2, 292–3, 300 not a division 301–4 not kinds of things 301 and n.3 ‘Speusippan’ in Aristotle? 308–11 and Aristotle’s translators 308 n.* of words vs things 284–8 oppositions 95 oratio and ratio 670–1 ¼ sentence? 646 Organon invention of Andronicus? 230–1 jerry-built 234–5, 237 long version of 249–50 name of 230 and Ptolemy the Unknown 231–5 structure of 230–1, 237, 267 Origen and Galen 12 n.22 and logic 18–19, 243–4 paradoxes 24, 550–1 and n.31 names of 546 and n.18 [see also Eubulides; Liar; Millet Seed] paraphrasis Themistiana 246–7 paronymy 296, 302 [see also onymies] parts of speech determined by function 639–40 dictiones 642 one expression with several functions 643–4 simple 642 uses of expressions vs expressions 643 vs parts of sentence 647–8 past tense, syntax of 177 Paul, St Galen’s nephew? 6 on logic 7, 19, 242 peiorem rules 690–2 Pelops, a doctor 541

Peripatetic logic programme in 436–7 style of 427, 431 Peter of Spain, on modifiers 627–8 Phanias his Cat 199–200 and Int 586 n.9 and logic 415–16 Philippus, a doctor 541 Philo of Megara, on conditionals 482, 501 n.5 Philodemus on induction 575 n.84 and plausibility 504–5 Philoponus on conversion 661 a duffer at logic 128, 661–2 on hypothetical arguments 417–18 and indeterminate propositions 694 n.44 on logical matter and form 74–5 misunderstands Ammonius 661 misunderstands Aristotle 661 on modifiers 636 n.44 and pons asinorum 720 n.105, 722 n.114 schematic letters in 444 on Theophrastus 417–18 on unmethodical arguments 115, 128, 135–6 on wholly hypothetical arguments 116, 442, 451, 454 n.2 philosophers, vs fishermen 8 and n.11 philosophy Christian 238–42 tripartite 22–3, 229, 395–7 order of parts 22–3, 229 and Plato 27 physiognomy 332 Plato his arguments formalized 14, 100 and n.140, 107, 108 n.158, 452 and n.1 and Fregean grammar 54, 152 and n.18, 153–4 hypothetical arguments in 452 n.1 and logic 27–8, 48 on names and verbs 153–4 and parts of philosophy 27–8, 396 and primary propositions 152–4

General Index Platonists on Cat 213–14 and categories 212, 216–19 plausibility 499, 502 n.* and certainty 509–10 and probability 504–5 Plautus, L. Sergius, and Cat 245 Plotinus on Aristotle’s categories 219–21, 253–4 on bare rules 74 n.71 on kinds of beings 223–4 on Stoic categories 202–3 plurals of plurals? 506 Plutarch on Chrysippus 392–5 on Epicurus and meaning 603, 607 Polemo, and dialectic 392, 394 polyonymy defined 294–6 and identity 309 n.2 ‘Speusippan’ 300 and n.* [see also onymies] pons asinorum 720–7 ‘the colophon of philosophy’ 720 as a method 726–7 and properties 722 and n.114 Porphyry on accidents 354 and [Archytas] 218 and Boethius 248 in Cat 220–1 defends categories 220–2 and Dexippus 221 Isagoge 228–9 on polyonymy 295–6 and predicates 216 and Simplicius 220–1, 291 n.4 and text of Cat 261–3 Posidonius on connectors 518, 523 and Galen 126 n.207, 127 n.212 and logic 399–400 on unmethodical arguments 110 and n.163 possibility, and for the most part 349–52 praedicare 189 preconceptions axiom-like? 612, 614 n.13

791

¼ beliefs 611–12 and epistemology 611–14 evident 612–13 and meaning 611, 614–19 ¼ meanings? 605–6 primary 613, 615 n.15 true 613 predicables 189 predicates Aristotle’s jargon 155–6 not barbarism 156 n.27 metalinguistic? 158–9 regimentational? 156–8 and n.32 compound 625 ¼ concepts/expressions/things? 215–16, 267 and n.6, 298–9 and n.3 and existence 180–4 interchangeable with subjects 165–6 many-placed 168–71, 279–80 nature of 215–16 negative, and existence 184–6 propositional 469–70 rejected by Frege 149–50 relational 277–81 simple 190, 216, 271–2 and n.12 soritical 29–30, 544–5 and nn.14 and 15, 548–9 in Stoicism 487, 489 theological 253–4 traditional vs modern 148–9, 279–81 and n.20, 325, 433–4 vague 71 vs predicative expressions 279–80, 325 premisses explain conclusion 120–3, 138 vs rules of inference 138–43 prepositions, and connectors 647, 649 priority, two kinds of 222 Priscian dislike of cement 644–5 Institutions 639 Greek examples in 642, 654–5 a general grammar 642–3 on prepositions 647 on sentences 646 [see also connectors]

792

General Index

Proclus against Apollonius 60–1 on Euclidean Argument 44–5 proofs 24, 686 proper sensibles 326–7 properties and accidents 316 asymmetrical 341 counterpredicated 91, 313–14 defined 313–15, 317, 319–21, 326, 333 n.4 and essence 317–19 generic 323 of individuals 325–7 irreflexive? 329–30 and knowledge 315–16, 341 natural 323 and necessity 314–16, 326–7 plurality of 327–9, 332 and pons asinorum 722 n.114 and quantification 324 quasi-properties 319–24 ‘now’ properteis 320 relative properties 319–20 sometimes properties 319–20 strong vs weak 317–19 prophets, and logic 242–3 propositions definite vs intermediate 403–4, 492–3 form and matter of 54–7 several forms and matters 56 individuation of 656–8 primary 147–9 and n.3 heterogeneous? 148, 153, 155, 164–5, 434 n.2 homogeneous? 148–9 quantified? 166–7 reduplicated 450 n.1 simple three types of 621–2 vs complex 678 with a modifier 621–3 [see also categorical; compound; conditional; conjunctive; hypothetical; indeterminate; singular] prosleptic arguments 50 n.15, 107–8 a third sort of argument? 108

prudence, properties of 330–45 Psellus 204–5 pseudo-Archytas, his Universals and Cat 194, 215, 218–19, 222 date of 218–19 held to be genuine 218 Ptolemy Philadelphus, and Cat 207–8, 387 Ptolemy the Unknown and Andronicus 206, 231 his catalogue 206, 231–3 and Int 232–3 his Organon 231–3 Pyrrhonists on sophisms 572 n.81 and sorites? 558 n.58 Pythagoreans, on categories 217–19 [see also pseudo-Archytas] quantification 159–60 Quintilian, and categories 203, 245 quoque, a connector? 652–4 reductio ad impossibile 371–2, 380–1 reduction and priority 440 n.3 by selection 440–1 and n.1, 461 varieties of 440 n.3, 483–4 why bother? 473–4 redundancy, logical 562 relational arguments and categories 277–8 and relations 169–70 and singular arguments 698–9 a third species of argument? 2–3, 20–1, 50–1 and unmethodicals 106–7 used by mathematicians 50 vs categorical 127 relations, a puzzle in antiquity 169–70 rhetoric, and logic 15–17, 23 and nn.8 and 10, 242, 249–50 sayables characterized 592–3 common errors about 591 complete vs incomplete 487–8, 594 definition of 592–4 and grammatical mood 488

General Index incorporeal 592, 594 n.33, 602 and speech-acts 488 and thinking 583, 590, 591–4 and n.32, 600–1 ¼ thoughts? 582–3, 592–600 6¼ thoughts 592 unsaid 598–9 varieties of 487–8, 513, 515, 594 [see also speaking; thoughts] schemata, vs arguments 96–7 sentences [see propositions] Sextus Empiricus on conflict and conditionals 525–6 does not mention categories 209 on Epicurus and meaning 602–3, 607 his modus operandi 480 PH prior to M ? 479–480 and n.3 on relations 169–70 on sayables 598–9 significant expressions 78, 169 n.76 Simplicius on analogical transference 224–5 and Boethus 290–1 and n.4 on commentaries on Cat 210–11, 226–7 on order of categories 215 and Porphyry 220–1, 291 n.4 on sayables 582–3 and n.2, 591 on Stoic categories 201–2 singular arguments 696–9 singular propositions in categorical arguments 118–20 and existence 175–6 and n.11, 184 indeterminate? 117–18, 166–7 and negation 173 and properties 324–6 and sorites 544 and universal propositions 697–8 wild 119 n.186 singular terms analysed 176 n.12, 324–5 eliminated 118–19 Socrates, and dialectic 392, 394 ‘Socrates died’ 176–86 sophisms and dialectic 25 and Pyrrhonists 572 n.81 [see also Liar; sorites]

793

sorites adding vs subtracting 548 and alternative logics 577–8 and n.88 and apprehensive impressions 557–8 and n.54 and baldness 551 n.31 and bivalence 29–30 and clarity 564–6, 569 and n.78 and conditionals 500, 542–3 and n.11 and the doctors 538–41, 549, 559 essentially paradoxical? 544 and experiences 539–40 and gods 559–60 and n.63 history of 549–60 and indeterminacy 573–78 interrogative form of 541, 547, 564 logical form of 542–4 and material implication 507–11, 542–3 and medicine 539–41 and negated conjunctions 507–11, 542–3 not in the least metaphysical 558 n.56 original form of 547–8 and philosophy 549–50 and predicates 29–30, 544–6 and nn.14 and 15, 548–9 resolutions of by Chrysippus 561 n.64, 563–70, 574 by Empirical doctors 570–8 radical vs conservative 561–2, 566–7 and n.74 and silence 564 and n.69, 565–6 and sceptics 29–30 self-refuting? 571 n.80 significance of 548–9 and singular terms 544 and Stoics 541–2, 549, 558–9 terminology 546–7 and n.18 texts on 578–81 and typology of fallacies 562–3 [see also Carneades] Sosigenes, on meaning 586 n.10 speaking and believing 369 n.*, 617 and n.17 caused by thinking 597–600 comes from the heart 597 defined 598–9 physiology of 597 and thinking 590–600, 617–18 and n.18

794

General Index

Speusippus and Aristotle 288, 304 his definitions of the onymies 294–6 equivalent to Aristotle’s 297 ‘Speusippan’? 298–304 not ‘Speusippan’ 296–7 texts on onymies 288–94 statables and commands 489 compound 513–14 defined 30–1 and n.33 definite vs intermediate 403–4, 492–3 types of 532–5 [see also propositions; sayables] Stephanus, on modifiers 82 n.97 Stoic logic arguments in concludent vs inconcludent 97 defined 97 reduplicated 398–9 and n.31 subsyllogistic 98–9, 105 n.153 syllogistic 97–8 vs schemata 96–7 and Christians? 13 defined 47, 250 evidence for 13 n.37, 485–6 and fallacies 561–2 formalistic 500–1, 512, 532 general character of 250, 431–2 history of 96 n.126, 399–400, 485–6 rivals Aristotle? 237 and sentential connectors 649 and Theophrastus 405–8, 430–2 and utility 47 [see also Dialecticians; indemonstrables; themata] Stoics on cases 591 n.26 on Cat 213, 295 n.4 and categorical arguments 398–9 and n.31 and categories? 201–3 on conditionals 447 n.1 on conflict and conditionals 516–17 on contraries 390–1 criticize Aristotle 202–3, 212, 388–90 on disjunctions 447 n.1, 513–16, 532 natural 523–4 and future contingents 389

and grammar 516–18 on meaning 582, 590–601 on mixture 400 on negation 172–3 and n.4, 401–4 and n.40 on prepositions and connectors 649 on proper names 176 n.12 and sorites 29–30, 541–2, 549, 558–9 on synonymy 294–5 on thought 592 on unmethodical arguments 108–11 and n.165 on validity 42, 97 [see also Chrysippus] Strato and logic 392, 394, 416 on meaning 586, 602 subalternation 471–2 laws of 471 n.1, 472 n.4, 474 n.1, 691 substances and accidents 192, 253–4 and essence 196–7, 253 perceptible 221–2 primary vs secondary 221–2 superfluity, grammatical 651–4 syllogisms Aristotle’s definition 381 n.20, 398–9 and conversions 94–6 ¼ deductions? 365–6 identity conditions for 135 n.229, 695 n.47 plurality of premisses 94 vs necessity 87–8 and n. 110, 114, 116, 662–3 [see also arguments; categorical; hypothetical; relational] synonymy defined 286–7, 296, 297 n.1 Stoic 294–5 [see also onymies] syntax, Peripatetic 78–9 synthetic theorem, and Stoic themata 390, 408–11 Tarski, Alfred, on logical constants 63–5 tautonymy 289–90 defined 296 [see also onymies] tense, and syntax 177 and n.5

General Index terms artificial 158 n.35, 469 n.1 empty 273 negative 468 n.2, 678, 702–3 propositional 469 singular 117–18, 119 n.187 Tertullian, and logic 8, 240 themata and synthetic theorem 390, 408–11 third 409 Themistius, on generation of categorical figures 664–5 Theodoretus, and syllogisms 16–17 Theodotus 10–14, 699 admires Galen 11–12 and Aristotle 12 syllogizes the Bible 10–14 tampers with the Holy Scriptures? 10 and n.19 and Theophrastus 12 theology and logic 243–4, 252–5 and predication 253–4 Theophrastus and arguments by analogy? 442 and n.2 and arguments from a hypothesis 379 and Boethius 456–7 his Cat ? 199–200 on categories 260 and Christians 12 on conditionals 443 n.1, 523–4 and disjunctions 407 on hypothetical arguments 12–13, 404–8, 439 writings on? 416–18, 439 and indeterminate moods 693, 695 on the Liar 397 and logic 12–13 on meaning 586 n.9 on mixed hypothetical arguments 427–30, 429 n.*, 463–8, 472–3 and modal logic 85 n.104, 351–2 his modus operandi 416 on qualitative arguments 426 and Stoic indemonstrables 405–8, 430–2 on wholly hypothetical arguments 425–6, 439–61, 464–5, 710, 712 n.92 therefore 59 n.38, 658

795

thoughts corporeal? 592 laws of 358–9, 363, 474 and n.1* and meanings 582, 587 particular vs general 588–90 and n.21 [see also meanings; sayables] Truncated Argument, the and Barbara 141–3 and categorical arguments 48–9 and Euclidean Argument 44–5, 111–12, 278–9 formally valid? 59–62, 65–6, 141–3 and hypothetical arguments 48 and relational arguments 50–1, 278–9 unmethodical? 111–12 truth a predicate 133–4 degrees of? 566 n.72 [see also criterion] ¨ berweg, F., on categories 257 U unmethodical arguments and amalgamated premiss 119–20, 129–31 and ‘associated’ syllogisms 52, 111–13, 123–6, 131–5 like categorical arguments? 104–7, 142 definition of 109–10 and n.165 examples of 99–101 formally valid? 120 and n.190 materially valid 109–11, 135–6 missing premisses 123–8 axioms? 125–7 outside scope of logic 110–11, 283 not enthymemes 124 n.197 not syllogisms 53, 104–5, 108–9 not valid? 115 n.175 relational? 106–7 some of them syllogistic? 117 n.181 varieties of 99–100, 114–15 validity ¼ concludency 97 defined 51–2 explained 68–9 formal defined 58–9 vs informal 52–3 and n.25, 87–9, 109, 114

796

General Index

validity (cont.) material 90–3, 281–3, 717–18 Stoic notion of 42, 97 and universality 82–5 Valla, L., and categories 255 Varro, and logic 25–7 verbs many-placed 168–71 and modifiers 634–5 and time 153 n.22, 633–5 vero 654 vis 641 wholly hypothetical arguments analogies with categorical arguments 463–6, 464 n.2, 709–13 and analogy 442 and n.2 defined 441–2 do not show anything 93–4, 448 n.3, 462–3 figures of 451–2, 719 n.92 generation of 457–8 no fourth figure 451 n.1 order of 451–2, 465–6 and n.* four interpretations of 443–9, 448 n.3, 710

general form of 448–50 history of 448 n.3 materially valid 116 metatheorems for 449–50, 454 modal? 461 n.1 not materially valid 93–4 not syllogisms 93–4, 139–40, 462–3 reduce to categoricals? 456–72 reduction of 458–9 simple vs compound 459–61 William of Moerbeke 248 Word, the 242 words, empty 614–15, 618–19 world, the real and Aristotle’s categories 220–1, 223–4 ¼ intelligible 220–2 how described? 223–6, 253–4 by analogical transference? 224–5 indescribable? 225–6 Zeno of Citium on concepts 396 and logic 27, 556–60 Zeno of Elea his Millet Seed 550–1, 553 and n.43 and sorites 550–51