Signs and Demonstrations from Aristotle to Radulphus Brito 9004543155, 9789004543157

Citation preview

Signs and Demonstrations from Aristotle to Radulphus Brito

Investigating Medieval Philosophy Managing Editor John Marenbon Editorial Board Margaret Cameron Thérèse Cory Nadja Germann Martin Lenz Charles H. Manekin Christopher J. Martin

volume 20

The titles published in this series are listed at brill.com/imp

Signs and Demonstrations from Aristotle to Radulphus Brito By

Costantino Marmo Francesco Bellucci

leiden | boston

The Library of Congress Cataloging-in-Publication Data is available online at https://catalog.loc.gov LC record available at https://lccn.loc.gov/2022060656

Typeface for the Latin, Greek, and Cyrillic scripts: “Brill”. See and download: brill.com/brill-typeface. issn 1879-9787 isbn 978-90-04-54315-7 (hardback) isbn 978-90-04-54697-4 (e-book) Copyright 2023 by Koninklijke Brill NV, Leiden, The Netherlands. Koninklijke Brill NV incorporates the imprints Brill, Brill Nijhoff, Brill Hotei, Brill Schöningh, Brill Fink, Brill mentis, Vandenhoeck & Ruprecht, Böhlau, V&R unipress and Wageningen Academic. All rights reserved. No part of this publication may be reproduced, translated, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without prior written permission from the publisher. Requests for re-use and/or translations must be addressed to Koninklijke Brill NV via brill.com or copyright.com. This book is printed on acid-free paper and produced in a sustainable manner.

Contents Acknowledgments ix Abbreviations x Introduction 1 1 Aristotle on Signs and Demonstrations 13 1 An Overview of APr B 23–26 14 2 The Official Doctrine of Signs 18 3 Interlude: The Figures 25 4 Syllogisms from Signs 30 5 Physiognomics 37 6 Demonstration 40 6.1 Demonstrations of the That and of the Why 42 6.2 Demonstrations καθ’αὑτό and Demonstrations κατὰ συμβεβηκός 50 6.3 Demonstration in Phys A 1 53 7 Signs versus Demonstrations 55 8 Logic, Semiotics, and Epistemology 64 9 Conclusion 66 2 The Greek Commentators 69 1 Alexander of Aphrodisias 70 2 Themistius 82 3 Philoponus 96 4 Philoponus and Simplicius on Physics A 1 113 5 Ps-Philoponus-1 In APr B 27 117 6 Ps-Philoponus-2 In APo B 123 7 Michael of Ephesus on the Sophistici Elenchi 129 8 Conclusion 131 3 D  emonstratio in the First Half of the Twelfth Century Before the Introduction of the logica nova 137 1 Demonstratio as a Rhetorical Genre 137 2 Demonstratio as Deixis 142 3 Demonstratio as Signification and Argumentation 148 4 Necessity of the Inference, Truth of the Conditional and Necessity of the Consequent: Brief History of an Example 156 5 Conclusion 171

vi

Contents

4 The First Influence of Aristotle’s logica nova on the Theories of Signs in the Second Half of the Twelfth Century 173 1 Inferences from Signs as Atypical Signs: A Glimpse from the Thirteenth Century 176 2 The Sign as an Effect that Infers its Cause: The Pseudo-Alexander and the Commentaries on the Sophistici Elenchi 177 3 Alan of Lille, Simon of Tournai, and the Cause as Sign 193 4 Conclusion 199 5 Demonstration through Signs in Thirteenth-Century Commentaries on the Posterior Analytics 201 1 Robert Grosseteste 202 2 Robert Kilwardby 216 3 Albert the Great: New Arabic and Latin Sources 226 3.1 Arabic Theories of Semiotic Demonstrations 230 3.2 Albert the Great on Signs 241 4 Thomas Aquinas and the Question Commentaries 252 4.1 Aquinas 252 4.2 Question Commentaries 259 5 Giles of Rome between Astrologers and Sailors 262 6 Conclusion 274 6 Thirteenth-Century Parisian Commentaries on the logica nova about Inferences from Signs 279 1 Signs in Commentaries on Prior Analytics B and in Other Texts 281 1.1 The Commentaries on Prior Analytics B 27 281 1.1.1 Robert Kilwardby on Enthymemes, Signs, and “Images” 284 1.1.2 Albert the Great on Inferential Signs 291 1.2 Giles of Rome’s Commentary on Rhetoric A 2 298 1.3 T  he Enthymeme ex signis et ycotibus in the Commentaries on Peter of Spain’s Tractatus V and in a Question on Enthymemes 304 1.4 Physiognomics as scientia de signis 310 2 The locus a communiter accidentibus and the Fallacy of the Consequent 319 2.1 Logic Textbooks and Commentaries between the End of the Twelfth and the First Half of the Thirteenth Centuries 320 2.2 Logic Textbooks and Commentaries from the Second Half of the Thirteenth Century 338 3 Conclusion 354

Contents 

vii

7 Thirteenth-Century Classifications of Signs 359 1  Scientiae de signis and Natural Signs in the Pseudo-Kilwardby’s Commentary on the Priscianus maior 359 2 Roger Bacon’s De signis: A New Definition and Classification of Signs 368 2.1 The Relational Nature of Signs and the Pivotal Role of the Interpreter 369 2.2 Bacon’s Sign Classification and Inferential Signs 373 2.3 T  he aestimativa: Intentional and Inferential Signs in Non-Human Animals 386 3 Conclusion 395 8 Conclusion 397 Appendix: Thirteenth-Century Unedited Texts on the Typology of Demonstrations and Sign-Inferences 401 A Radulphus Brito, Questiones super Posteriora Analytica I.68. 401 B Giles of Rome (Aegidius Romanus), Expositio super Rhetoricam Aristotelis, lectio 6, ad Rhet A 2 1357a22–29 404 C Magister Simon, Expositio super Tractatus Petri Hispani V 412 D Simon of Faversham, Questiones libri Priorum II.15 421 E Radulphus Brito(?), Questiones libri De physionomia, q. 1 424 F Anonymus Monacensis, Commentum super Sophisticos Elenchos 428 G Robertus Kilwardby(?), Expositio super libros Elenchorum 434 H Radulphus Brito, Questiones super Sophisticos Elenchos I.48 441

References 445 Index of Ancient and Medieval Names 471 Index of Modern Names 474 Index of Manuscripts 477

Acknowledgments Several scholars, colleagues, and friends have helped us in many different ways with this book. Pia Campeggiani, Carlotta Capuccino, and Camillo Neri assisted us with the translation of some passages from Themistius’ work. Paolo Leonardi read some chapters in a first draft version. Christina Thomsen Thörnqvist and Sten Ebbesen shared with us some digital copies of some manuscripts that we publish in the Appendix. Sten Ebbesen (again) shared with us his transcriptions of several Posterior Analytics commentaries of the second half of the thirteenth century. Pietro B. Rossi and Luigi Campi generously provided some textual anticipations of their edition of Kilwardby’s Commentary on the Posterior Analytics. Debora Cannone gave us her permission to read and quote some parts of her doctoral thesis on Kilwardby’s Commentary on the Posterior Analytics. Parwana Emamzadah read and gave useful suggestions about the working edition of a question from Radulphus Brito’s Commentary on the Sophistici Elenchi (we regret that we could not use her dissertation and edition of that work). Irène Rosier-Catach, Laurent Cesalli, Frédéric Goubier, and Alain de Libera provided us with an anticipation of their French translation of, and commentaries on, Roger Bacon’s De signis. Special thanks are due to Sten Ebbesen and Irène Rosier-Catach, who read the whole manuscript with care and offered useful comments, corrections, and suggestions. We also thank Brill’s anonymous readers for helpful criticism. This book is the result of collaborative work carried out by the two authors. While reciprocally contributing to each part of the book, Bellucci is the main author of Chapters 1 and 2, while Marmo is the main author of Chapters 3, 4, 6 and 7. Chapter 5 has been written together. The texts in the Appendix have been edited by Marmo. Bologna, June 2023 C.M. F.B.

Abbreviations AL CAG LM I LM II

PL SE#

Aristoteles Latinus Commentaria in Aristotelem Graeca Logica Modernorum. A Contribution to the History of Early Terminist Logic. Vol. I. Edited by Lambert M. de Rijk. Assen: van Gorcum, 1962. Logica Modernorum. A Contribution to the History of Early Terminist Logic. Vol. II.1: The Origin and Early Development of the Theory of Supposition. Vol. II.2: Texts and Indices. Edited by Lambert M. de Rijk. Assen: van Gorcum, 1967. Patrologiae Latinae Cursus Completus. Edited by Jacques P. Migne, Paris, 1844–1855. numeration of Sophistici Elenchi commentaries in Ebbesen (1993).

Introduction In the first book of the Posterior Analytics Aristotle draws a contrast between demonstrations, which proceed from the cause, and syllogisms through signs (οἱ διὰ σημείων συλλογισμοί), which do not proceed from the cause.1 An analogous contrast is drawn in a passage of the second book.2 At the same time, in the Prior Analytics, in the context of the “official” exposition of his doctrine of sign-arguments in chapter 27 of the second book, Aristotle defines a sign (σημεῖον) as a “demonstrative premise” (πρότασις ἀποδεικτική), i.e., as the premise of a demonstration.3 The question which thus naturally arises is whether or not there can be demonstrations from signs, i.e., “semiotic demonstrations,” according to Aristotle. The Posterior Analytics gives us the theory of “paradigmatic” demonstration. A paradigmatic demonstration is a variety of syllogism that differs from other varieties of syllogism by the following characters: its premises must be true, primitive, immediate, better known than, prior to, and causes of the conclusion.4 Arguments that do not satisfy all these conditions are discussed here and there in the Posterior Analytics, and sometimes they are also called “demonstrations.” Several commentators, both ancient and modern, have conceded that allowance should be made in Aristotelian theory and exegesis for different varieties not only of syllogisms, but also of demonstrations, i.e., for demonstrations less perfect than paradigmatic demonstrations. Assuming a positive answer to the first question, i.e., assuming that there may be semiotic demonstrations, the following further question arises too: what kind of demonstration is a semiotic demonstration? The problem of whether sign-arguments are demonstrations, and if yes, what kind of demonstration they are, is typically discussed in Posterior Analytics commentaries, especially in connection with the distinction drawn in chapter 13 of the first book between διότι-demonstrations (“demonstrations of the why”) and ὅτι-demonstrations (“demonstrations of the that”).5 We find discussions of this problem in Alexander of Aphrodisias (whose commentary on the Posterior Analytics is lost, but who addresses the question in some of the surviving commentaries), Themistius, and Philoponus. Building upon 1 Aristotle, APo A 6, 75a31–34. 2 Aristotle, APo B 17, 99a1–4. 3 Aristotle, APr B 27, 70a6–7. 4 Aristotle, APo A 2, 71b20–22. 5 Aristotle, APo A 13, 78a22–b34. © koninklijke brill nv, leiden, 2023 | doi:10.1163/9789004546974_002

2

Introduction

these late-ancient authors and on Arabic translations of Aristotle’s Posterior Analytics, the Arabic commentators took up the question again. There is evidence that al-Fārābī, Avicenna, and Averroes carefully studied the problem of the classification of demonstrations and that in their works semiotic demonstrations have a definite place. Through the Greek glosses translated into Latin and the Arabic intermediation the problem of the demonstratio signi passed to the Latin West: traces of the Greek-Arabic assimilation of the syllogism from signs of Prior Analytics B 27 with the ὅτι-demonstration of Posterior Analytics A 13 are detectable, even if never brought to central stage, in the thirteenth-century Latin commentaries by Robert Grosseteste, Robert Kilwardby, Albert the Great, Thomas Aquinas, and Giles of Rome. Traces of the Aristotelian notion of semiotic demonstration are also found outside the tradition of the Posterior Analytics. One natural place where to look is the ancient commentaries on the first book of the Physics. Here Aristotle says that the method of investigation must start from what is better known and clear for us and proceed to what is better known and clear by nature. The Greek commentators took this to be a reference to the ὅτι-demonstration of Posterior Analytics A 13 and interpreted it in terms of the theory of sign-arguments of Prior Analytics B 27. Another is the tradition of commentaries on the Prior Analytics itself. The only ancient commentary on the second book, published under the name of Philoponus, is spurious; the earliest Latin commentary that reaches up to Prior Analytics B 27 is Robert Kilwardby’s in the 1240s. It contains a sophisticated discussion of Aristotle’s doctrine of sign-inferences and an examination of the claim that a sign is a demonstrative premise. Through Kilwardby, this problem is transmitted to Latin Aristotelianism. Still another place where to look for a discussion of semiotic demonstrations is the tradition of the commentaries on the Sophistici Elenchi. Here Aristotle introduces the fallacy of the consequent and associates it with rhetorical demonstrations through signs. Both lateancient and medieval commentators take this association quite seriously, and some of them even make a further association with the sign-argument in the second figure of Prior Analytics B 27. Aristotle’s doctrine of semiotic demonstrations emerges also on the background of some eleventh-century works on rhetoric, in connection with thirteenth-century commentaries on Peter of Spain’s Summule, and in the classifications of signs of the pseudoKilwardby and Roger Bacon. The present work is an attempt to provide a comprehensive picture of the origins, motivations, implications, reception, transmission, interpretation, and development of the idea of semiotic demonstration in Western Aristotelianism. Each chapter reconstructs a part of this history, highlighting sources and lineages of influence from roughly the third through the thirteenth centuries.

Introduction

3

Like any work on the Aristotelian tradition, this book does not sail unchartered waters, but rather builds upon the work of a great number of scholars. Giovanni Manetti’s history of semiotics from Hippocrates to Augustine remains to date the most comprehensive overview over ancient semiotic thought.6 Chapter 1, on Aristotle, is in continual dialogue with a number of important studies, especially with Myles Burnyeat’s and James Allen’s sophisticated studies of the Aristotelian theory of sign-inferences,7 and with such eminent modern interpreters of the Posterior Analytics as Sir William D. Ross, Mario Mignucci, and Jonathan Barnes.8 Chapter 2 may be taken as a development and expansion of Donald Morrison’s pivotal analysis of the late-ancient doctrine of “tekmeriodic proof” in Philoponus and Simplicius.9 Our Latin Chapters (especially 4–7) are greatly indebted to the works of Sten Ebbesen on the development of logical and linguistic theory from late antiquity onwards. Other important works that have helped us in reconstructing the history that we tell in this book are duly acknowledged, discussed, and sometimes criticized at various junctures of our exposition. The narrative of this book opens, quite naturally, with Aristotle. Chapter 1 presents the essentials of Aristotle’s “official” presentation of the doctrine of sign-inference in Prior Analytics B 27 and in Rhetoric A 2, and connects this doctrine to the theory of demonstration expounded in the Posterior Analytics. We also examine some of Aristotle’s scattered remarks about signs in the physiognomic section of APr B 27, in the Sophistici Elenchi, and in On divination by dreams. The Chapter not only offers an overview of the Aristotelian materials that constitute the basis of subsequent commentaries and interpretations. We also seek to offer a plausible interpretation of them. One focus of this Chapter is on the syllogistic treatment of sign-inferences, for the analysis of signs and their typology that Aristotle offers in APr B 27 in terms of the syllogistic figures: there is one type of deductively valid semiotic syllogism in the first figure (called τεκμήριον) and two types of deductively invalid semiotic syllogisms in the second and third figure (called σημεῖα in the strict sense). A full understanding of Aristotle’s figure-oriented analysis of signs requires a detour into some crucial aspects of the syllogistic theory of APr A 4–6. The main focus however is on the relation between the doctrine of sign-inferences of APr B 27 and the contrast drawn in the Posterior Analytics between demonstration proper and syllogism through signs. As the reader will discover, these dimensions may be regarded as mutually explicatory: the “demonstrative” nature of 6 7 8 9

Manetti (1993); see also Manetti (2013). Burnyeat (1982); Allen (2001). Ross (1949); Mignucci (1975); Barnes (1993). Morrison (1997).

4

Introduction

sign-premises of APr B 27 is properly understood only by reference to a lower standard of demonstration, which emerges here and there in the Posterior Analytics. Conversely, the two references to sign-syllogisms in APo A 6 and APo B 17 can only be properly understood against the background of the syllogistic analysis contained in APr B 27. Aristotle’s contrast between signs and demonstrations inaugurated a discussion that was taken up and carried on in the Greek Aristotelian tradition, and this is the topic of Chapter 2. There can be little doubt that Alexander of Aphrodisias produced a commentary on the Posterior Analytics. Traces of it ended up in the anonymous commentary on the second book of the Posterior Analytics published by Maximilian Wallies in CAG 13.3. Here, as in his commentary on the Prior Analytics, Alexander answers our question whether there are demonstrations from signs by distinguishing a logical from an ontological sense in which one may say that in a syllogism the premises are “cause” of the conclusion: in one sense, they are the cause of the drawing of the conclusion (logical sense); in another sense, they are the cause of the fact stated in the conclusion (ontological sense). While in a proper demonstration the premises are “cause” in both senses, in a semiotic demonstration they are the cause in the first sense only. Some passages from Alexander’s commentary on the Prior Analytics and the Topics, in which examples of signs taken from APr B 27 are employed, corroborate that view. In his commentary on the Topics, Alexander distinguishes the demonstration in the strict sense (κυρίως), which is one from the cause to the effect, from the demonstration in a secondary sense (δευτέρως), which is one from the effect to the cause. Together with the distinction between the logical and the ontological sense of “cause,” this was destined to become the standard answer to the question whether and how there may be demonstrations from signs. Themistius and Philoponus depend on Alexander. Themistius explains the distinction of APo A 13 between διότι- and ὅτι-demonstrations by identifying semiotic syllogisms with ὅτι-demonstrations (this was implicitly suggested, though not explicitly made, by Alexander). He also uses the Alexandrian distinction between the two senses of “cause.” He carefully outlines the various possible relations that cause and effect can have in a demonstration, and also considers the case in which the demonstration goes from one effect to another effect of the same cause; this possibility had apparently been neglected by Aristotle and Alexander, but will re-emerge again in Arabic and Latin interpreters. Philoponus, who in turn probably depends also on Themistius’ paraphrase, discusses semiotic syllogisms at various junctures of his commentary on the first book of the Posterior Analytics (the commentary on the second book transmitted under his name is spurious). He adopts Alexander’s distinction between

Introduction

5

demonstration κυρίως and demonstration κατὰ δεύτερα μέτρα. As the reader will see, Philoponus’ main contribution to the debate about sign-inferences is his coinage of the expression τεκμηριώδης ἀπόδειξις. This expression, and the use that Philoponus makes of it, betrays an implicit reference to the distinction of APr B 27 between the deductively valid semiotic syllogism in the first figure (τεκμήριον) and the deductively invalid semiotic syllogisms in the second and third figure (σημεῖα in the strict sense). By qualifying the semiotic demonstration (or demonstration according to a secondary standard) as “tekmeriodic” Philoponus emphasizes that such a demonstration is a deductively valid syllogism (as any demonstration, in either the proper or the secondary sense, must be), and not an invalid syllogism, which he calls, following Aristotle, σημεῖον, and to which he refuses the title of ἀπόδειξις. Philoponus also provides a detailed and comprehensive taxonomy of demonstrations, including “tekmeriodic” demonstrations and various other kinds of διότι- and ὅτι-demonstrations. Chapter 2 also includes a discussion of the passage in Physics A 1 which Themistius, Philoponus, and Simplicius interpreted as a reference to sign-demonstrations; an examination of the scant comments that the anonymous author of a commentary on Prior Analytics B (Ps-Philoponus-1) made on APr B 27; a discussion of another pseudo-Philoponean commentary, on Posterior Analytics B (Ps-Philoponus-2); and a final annotation on the commentary on the Sophistici Elenchi by Michael of Ephesus (pseudo-Alexander), where the inferences associated with the fallacy of the consequent are called σημειώδεις ἀποδείξεις. With Chapter 3 we land on the Latin shores. This Chapter provides a general map of the uses of the term demonstratio in the Latin West before the rediscovery of the Posterior Analytics. The earliest occurrence of the term demonstratio in a somewhat technical sense is in rhetoric. The only rhetoric taught in the first half of the twelfth century is contained in two works, Cicero’s De inventione and the anonymous Rhetorica ad Herennium, also attributed to Cicero at that time. Here demonstratio has two principal meanings: (i) it translates the Greek ἐπίδειξις, which in Aristotle’s Rhetoric indicates the epideictic genre, as opposed to the deliberative (or political) and the legal (or forensic) genres; (ii) it has the logical meaning of “argumentation,” which is closer to the meaning that ἀπόδειξις has in logical Aristotelianism. The first section of Chapter 3 examines the former meaning in several rhetorical commentaries of the early twelfth century. In grammatical contexts we also find another distinct use of the term. Demonstratio is the term which, following Apollonius Dyscolus, Priscian uses to indicate what we now call the token-reflexivity of pronouns; in this sense, it is the Latin equivalent of the Greek grammatical term δεῖξις. The root is of course the same as the Greek ἀπόδειξις, “demonstration” in the logico-philosophical sense.

6

Introduction

The narrower, logical meaning of the term is investigated in the next section of this Chapter. In his Dialectica, Abelard sometimes uses the verb demonstrare as synonymous of significare (to mean, to signify); in other contexts, he uses demonstratio in the Ciceronian sense of “argumentation.” This sense constitutes a central element in Abelard’s theory of signification, within which the demonstrationes are regarded as inferential (or argumentative) signs, i.e., premises of an argumentation. Some other texts from the first half of the twelfth century which we examine also refer to this narrower meaning of demonstratio. In Cicero’s De inventione the example of necessary argumentation (or “demonstration” for the authors met in this Chapter) is the following conditional: “If she has borne a child, she has lain with a man” (si peperit, cum viro concubuit). This example has a double origin: in the Latin world it starts with Cicero’s De inventione, in the Greek world with Themistius and Philoponus. The last section of this Chapter contains a reconstruction of its story in the Latin world. Chapter 4 is about the second half of the twelfth century. The earliest appearance of some direct or indirect influence of the Greek commentators upon the Latin understanding of Aristotle’s theory of semiotic demonstrations is in three anonymous works that were composed between the third and the last quarter of the twelfth century: the Commentarium in Sophisticos Elenchos of the so-called “Anonymus Aurelianensis I,” the De paralogismis of the so-called “Anonymus Aurelianensis II,” and the Commentarium in Sophisticos Elenchos Aristotelis of the so-called “Anonymus Cantabrigiensis.” In these works the distinction of APo A 13 between a demonstration of the why (that proves the effect from the cause) and a demonstration of the that (that proves the cause from the effect) is illustrated by means of examples that ultimately derive from APr B 27 through the intermediation of the Greek commentators and of Cicero’s De inventione. Like in Alexander of Aphrodisias (who is explicitly referred to, although the actual source is most likely Philoponus) the demonstration from the cause is a demonstration in the strict sense, that from the effect a demonstration in a secondary sense. In the Anonymus Aurelianensis I the secondary type of demonstration also takes the name of indicium, “sign.” The relation between signs and demonstrations emerges with particular clarity in the commentaries on Soph El 5. Here Aristotle himself suggests the connection with demonstration, understood here as a demonstration from signs (ἡ κατὰ τῶν σημείων ἀπόδειξις, demonstratio secundum signa), also called “rhetorical demonstration” (ῥητορικὴ ἀπόδειξις, demonstratio rhetorica), which Michael of Ephesus called σημειώδης ἀπόδειξις. This is the occasion for the Anonymus Cantabrigiensis to offer a sketchy typology of sign-inferences whose examples come from Soph El 5 itself as well as from the Prior and the Posterior Analytics.

Introduction

7

In the second part of Chapter 4 we discuss two theologians of the second half of the twelfth century, Alan of Lille and Simon of Tournai, who like the authors of the commentaries on the Sophistici Elenchi distinguish the two types of science or demonstration (of the why and of the that), refer to a Greek commentator (“Alexander”), and associate the demonstration of the that with sign-inferences by the aid of those very same examples that occur in the Greek commentaries. In the case of Simon of Tournai, the discussion is cast in the framework of a general theory of the modes of signification. With Chapter 5 we return to the Posterior Analytics. While there is evidence of this work having been taught in the schools of the late twelfth century, yet there are no written commentaries prior to Robert Grosseteste’s, which was composed in the 1220s–1230s and which paved the way for a more regular teaching of the Posteriora Analytica in the curriculum of logic in Western universities. Grosseteste uses James of Venice’s translation and has access to the translation of (parts of) Philoponus’ commentary made by James. He also uses Themistius’ paraphrase, which Gerard of Cremona had translated from the Arabic and which was in circulation together with Gerard’s own translation of the Posterior Analytics. Grosseteste inaugurates an interpretive tradition in which semiotic demonstrations are somehow removed: in neither of the two passages (APo A 6, APo B 17) where Aristotle contrasts demonstration with sign-syllogisms does Grosseteste make any reference to signs. A symptom of such removal is his rendering of the occurrence of σημεῖον at APo B 17 as effectus rather than as signum. Unlike his Greek predecessors, in his comment on APo A 13 Grosseteste does not identify the demonstratio quia (Aristotle’s ὅτι-demonstration) with demonstration through signs: his taxonomy of ὅτι-demonstrations follows quite closely the Aristotelian text. The removal is not without exception: he does identify sign and effect, and thus demonstration from the sign and demonstration from the effect or quia, in a later passage of his commentary (II.2). The second Latin commentary on the Posterior Analytics that has reached us in complete form is that by Robert Kilwardby. While in the main he follows Grosseteste’s tendency to suppress any reference to sign-inferences, yet unlike Grosseteste in his comments on APo A 6 Kilwardby explicitly follows Themistius and Gerard’s translation in equating the “inseparable accidents” with “accidental signs,” an equation which in fact simply makes Aristotle’s own reference to sign-syllogisms in that context more explicit. The example from APr B 27 also comes from Themistius (via Gerard). Kilwardby also makes some sporadic use of the Alexandrian and Themistian distinction between the

8

Introduction

logical and ontological sense of “cause.” His comments on APo B 17 “restore” the signum that Grosseteste had hidden behind the term effectus and associates it with the medium probabile. Albert the Great’s paraphrase is not only dependent on Kilwardby, but also on the Arabic commentators, especially al-Fārābī and Avicenna. This gives us the occasion to take a little detour into the Arabic tradition of the Posterior Analytics. Al-Fārābī distinguishes three kinds of demonstration: demonstration of existence, demonstration of the cause, and absolute demonstration. Demonstration of existence is also called dalāʾil, “sign,” because in such demonstration the middle term is a sign of the conclusion. The tripartite division is grounded on the Alexandrian distinction between the logical and the ontological sense of “cause”: in the demonstration of existence the premises are cause in the logical sense only. The same distinction is found in Avicenna, who distinguishes two kinds of demonstrative syllogism: one is “through the cause,” the other is “of existence.” All demonstration is demonstrative “through the cause,” if with “cause” we intend the cause of assent or the cause of affirmation (logical cause). But only causal demonstrations are “through the cause” in the ontological sense. Avicenna further divides the demonstration of existence into two subspecies: a demonstration of existence which leads from effect to cause is called, in the manner of the Greek commentators and of al-Fārābī, an “indication” or “sign,” while a demonstration of existence that leads from an effect to another effect of the same cause is called “absolute demonstration of existence.” This latter is highly reminiscent of Themistius. Both the Alexandrian distinction between the logical and the ontological cause, and the Themistian idea of a demonstration from effect to effect are discussed at length in Averroes’ commentaries on the Posterior Analytics, where they are included in a more sophisticated taxonomy of demonstrations. Like al-Fārābī, Averroes distinguishes between demonstration simpliciter, which exhibits both the existence of the thing and its cause, demonstration causae tantum, which only exhibits its cause, and demonstration existentiae tantum, which only exhibits its existence. These three main species are further sub-divided into sub-species. Semiotic demonstrations also play an important role in Averroes’ commentary on Aristotle’s Physics and in the debate with Avicenna about the subject matter of metaphysics. Albert does not make much of his semiotically-oriented Arabic sources. He rather follows quite closely the path opened by Grosseteste and Kilwardby. Unlike his Latin predecessors, however, he associates quite explicitly the demonstratio quia with sign-inferences. Further, unlike Grosseteste and Kilwardby but like Alexander and Themistius, he explains APo B 17 by appealing to the Alexandrian distinction between the two senses of “cause.” These

Introduction

9

elements notwithstanding, the association between signs and demonstrations remains feeble in Albert’s work. Aquinas’s commentary, composed between 1271 and 1272 but circulating in Paris only around 1275, as well as the question commentaries produced in Paris at the end of the century, confirm the substantial disconnection between demonstratio quia and sign-inferences which characterizes the Latin reception of the Posterior Analytics, in opposition to the Greek-Arabic tradition which had straightforwardly assimilated the two notions. Giles of Rome’s literal commentary on the Posterior Analytics, the last of the thirteenth century, follows the interpretative thread of its predecessors. He makes some interesting use of the Alexandrian distinction between the two senses of “cause” in order to avoid the exclusion of the demonstratio quia, or at least of one of its species, from the realm of scientific demonstrations sanctioned by the requirements of APo A 2. But for him, as for earlier Latin commentators, effects are simply effects, not signs. Yet, some discussion of signs resurfaces in Giles’ two dubitationes about the second and last mention of signinferences in the Posterior Analytics (APo B 17), where again the Alexandrian distinction between the two senses of “cause” is appealed to. With some exceptions here and there, the Latin tradition of the Posterior Analytics removes sign-inferences from the realm of the theory of science. Sign-inferences emerge however in other areas, works, and authors of the logica nova in the thirteenth century. This is the topic of Chapter 6. We examine Kilwardby’s and Albert the Great’s commentaries on APr B 27, which contains Aristotle’s official theory of sign-inferences. Albert’s overall interpretation of this chapter is roughly the same as Kilwardby’s: the signum in its generic sense (Aristotle’s σημεῖον in the wide sense) comprises signs in all of the three figures; the signum in the proper sense (Aristotle’s σημεῖον in the strict sense, covering second- and third-figure sign-syllogisms) is called icos/ycos and is identified with the εἰκός-enthymeme that is discussed by Aristotle in the first part of the chapter. (This identification is found in the Ps-Philoponus-1, the only Greek commentary that we have that reaches up to APr B 27). The sign in the first figure is called prodigium (which was Boethius’ translation of τεκμήριον). Kilwardby also observes that since neither a prodigium nor a ycos can be the middle term of a proper demonstration, “demonstrative” in the sign definition of APr B 27 has to be taken in the sense that any sign vult esse (βούλεται εἶναι), i.e., aims at being a demonstration, but is not so. Both Kilwardby and Albert have a section on physiognomic signs, which we examine in some detail and connect to later work in physiognomics by Peter of Abano and Radulphus Brito. Another section of this Chapter is about the earliest commentary on Aristotle’s Rhetoric that we possess, composed by Giles of Rome between 1272

10

Introduction

and 1273. Giles’ interpretation of the typology of signs of Rhet A 2 is quite original and does not fit with Kilwardby’s and Albert’s reading of APr B 27. According to Giles, “signs” are only those in the first figure (prodigia) and those in the third, which latter have no specific name and are simply described as “non-necessary signs”; ycos for Giles is only the sign in the second figure. Giles thinks that this better explains what Aristotle says next, i.e., that “signs” behave either like the universal to the particular (first figure), or as the particular to the universal (third figure). We discuss the notion of enthymeme ex signis et ycotibus in the commentaries on Peter of Spain’s Summule (1230–1231), the most widespread and famous medieval textbook of logic. The Summule are commented on in Southern France in the 1250s or 1260s, and in Paris in the 1280s (and then in Bologna, upon the Parisian model, where it enters into the university statutes as textbook). We focus on an interpolation in the treatise devoted to the topics (loci). (Something about this interpolation was anticipated in Chapter 3.) Here, the anonymous interpolator uses Aristotle’s definition of enthymema as an inference which takes a likelihood or a sign as its only premise. We examine several commentaries on the Summule that take the interpolation into some account: the author of a commentary attributed to Simon of Faversham, whom we call “Master Simon,” and the Anonymous of Munich, perhaps to be identified with Radulphus Brito. The second part of Chapter 6 is about the commentaries on Boethius’ De differentiis topicis, those on Peter of Spain’s Summule (esp. the fifth and seventh tracts, about loci and fallacies, respectively), and those on Aristotle’s Sophistici Elenchi, which are thematically intertwined and reciprocally influenced. It is impossible to recapitulate the contents of the several works of which we give an account in this part; here we limit to an enumeration of them. Besides the Dialectica Monacensis (ca. 1290s–1320s), we consider both Parisian and Oxonian commentaries on Peter of Spain from the first half of the thirteenth century, especially with reference to the analyses and examples of locus a communiter accidentibus; an anonymous literal commentary on the Sophistici Elenchi from Munich; the commentary on the Sophistici Elenchi attributed to Robert Kilwardby; the commentary on Boethius’ De differentiis topicis by Nicholas of Paris (coeval with or slightly later than Kilwardby); the commentaries on Peter of Spain attributed to a not-better-specified Robertus Anglicus (ca. 1250s and 1260s); Albert the Great’s Liber Elenchorum; Giles of Rome’s commentary on the Sophistici Elenchi (ca. 1274); modistic commentaries on Peter of Spain of the second half of the thirteenth century; Radulphus Brito’s questions on Boethius’ De differentiis topicis (1280s or 1290s) and on the Sophistici Elenchi (probably late 1290s).

Introduction

11

Chapter 7 is about two thirteenth-century authors who elaborate a complete classification of signs: the pseudo-Kilwardby and Roger Bacon. The pseudo-Kilwardby, who commented on the first sixteen books of Priscian’s Institutiones grammaticae, elaborates a classification of signs in which different sources are mixed. He identifies a class of natural signs, but unlike in Bacon these are not regarded as species of inferential signs. All natural signs, according to him, follow the Aristotelian model of effects signifying their cause, so that either they are convertible with their cause or they are not. This subdivision of signs with respect to convertibility is highly reminiscent of similar subdivisions in Themistius and Philoponus, but also of thirteenth-century commentaries on the Posterior Analytics. These signs may belong to two different domains: the natural world (in genere naturae) and the moral world (in genere moris). In the first part of Bacon’s De signis, a fragment of his Opus maius, besides a discussion of the definition of sign that emphasizes its relational character, we find a complex classification of signs. This was resumed and then modified in 1292, just before Bacon’s death, in his Compendium studii theologiae. Among natural signs, Bacon distinguishes three kinds of signs: those working by inference, those functioning by resemblance, and those that are effects of some causes. While the third kind seems to be connected with the tradition of the Posterior Analytics, the other two kinds are illustrated with examples taken from various sources, which are analyzed in detail. Bacon further specifies that there is no difficulty in the fact that the relationship between effect and cause, and that between sign and meaning, are in the same objects: the first relationship connects two objects regardless of whether they are known, while the second relationship instead takes three elements into account, namely the sign, the signified thing, and the entity for whom the sign is produced (the recipient or interpreter). The sign is, according to thirteenth-century theories of relations, a twofold relationship (or a double dyadic relationship) between sign and object, on the one side, and between sign and knowing subject, on the other. As Bacon points out in the incipit of this fragment on signs, the second relationship is the essential one: if there is no recipient (or knowing subject), there is no signification at all. The Chapter also contains a discussion of the relation between Bacon’s classification of signs and the problem whether non-human animals can make inferences. As we argue in this last part of the book, Bacon’s doctrine of non-human animal intelligence is based on the Arabic model of Alhazen’s optical investigations. This sketch of the contents of this book is selective. In point of fact, the book is much richer than the foregoing synopsis suggests. It contains several historical and theoretical digressions and excurses on areas, topics, works, authors, and

12

Introduction

words that are strictly intertwined with the main thread and which contribute to shedding light on it. Another feature of this book is that it pays special attention to the examples, their structure, their genealogy, and the context of their occurrence, as we believe that the use of an example may sometimes tell us more about the sources and the influence of a work than the doctrines that work expounds. Most of the works that we examine in this book have been published, but few of them are unpublished. The Appendix collects a transcription of eight texts that we discuss in the book, especially in Chapter 6. The transcriptions and working editions have been made by Costantino Marmo from a single witness or, in some cases, by collating two or more witnesses.

CHAPTER 1

Aristotle on Signs and Demonstrations The story that we shall tell in the following Chapters is about the relationship, we might say the opposition, between the notions of “sign” and “demonstration” in the Aristotelian tradition. The birthplace of that opposition is in the Posterior Analytics. In the present Chapter, we shall examine the Aristotelian beginnings of our story. In order to understand the contrast between sign and demonstration, we first need to understand what a sign is according to Aristotle. The official exposition of Aristotle’s analysis of signs is in chapter 27 of the second book of the Prior Analytics. APr B 27 is itself the last of a series of five chapters (B 23–27) whose function is programmatically explained in APr B 23: now, it should be explained that not only dialectical and demonstrative syllogisms (οἱ διαλεκτικοὶ καὶ ἀποδεικτικοὶ συλλογισμοί) come about through the figures previously mentioned, but also rhetorical ones (ῥητορικοί), and absolutely any form of conviction (πίστις) whatever, arising from whatever discipline. For we have conviction about anything either through syllogism or from induction (ἢ διὰ συλλογισμοῦ ἢ ἐξ ἐπαγωγῆς).1 The present Chapter is organized as follows. As a preliminary to our analysis of APr B 27 (§§1.2–1.4), we shall briefly go through the four chapters that precede it (§1.1). Moreover, since the analysis of signs in APr B 27 is in terms of the syllogistic figures, our analysis of APr B 27 will be interluded by a discussion of the figures (§1.3). The following section (§1.5) is devoted to physiognomic inferences, which are the last topic touched upon by Aristotle in APr B 27 and which is almost an appendix to his analysis of signs. The sixth section (§1.6), then, introduces Aristotle’s theory of demonstration as it is expounded in the Posterior Analytics, and the seventh section (§1.7) examines the contrast, drawn in this work, between signs and demonstrations; this section also deals with two other places of the Aristotelian corpus (from the Sophistici Elenchi and the Parva naturalia) where some such contrast seems to come to the fore. The last section (§1.8), then, offers some concluding comments on the possibility of an epistemic interpretation of APr B 27 and its examples. 1 Aristotle, APr B 23, 68b11–14; transl. Smith, modified. © koninklijke brill nv, leiden, 2023 | doi:10.1163/9789004546974_003

14 1

chapter 1

An Overview of APr B 23–26

According to Aristotle, conviction (πίστις) is produced either by syllogism or by induction.2 A demonstrative syllogism or demonstration is a syllogism that produces knowledge, and its premises must therefore be true and be known to be true; demonstrations must also satisfy the further requirements specified in APo A 2.3 Dialectical and rhetorical syllogisms are syllogisms that produce conviction merely, and their premises need not be true but ἔνδοξοι, “reputable” or likely to be believed. The difference between dialectical and rhetorical syllogisms does not affect the matter of which they are made (ἔνδοξοι premises) nor their logical form, but the contexts in which they are used: dialectical syllogisms are used in philosophical contexts, rhetorical syllogisms in political and ethical contexts. The program announced in APr B 23 is brought to completion in the sequence of chapters B 23–27, devoted respectively to induction, example, abduction, objection, and enthymeme. “Induction,” ἐπαγωγή (B 23), is an argument proving the major term of the middle term by means of the minor,4 where “major,” “minor,” and “middle” are to be taken in reference to the syllogism in the first figure. Here is Aristotle’s example: (1) Syllogism Every animal without gall (B) is long-lived (A) Man, horse, and mule (C) are without gall (B) Therefore, man, horse, and mule (C) are long-lived (A). (2) Induction Man, horse, and mule (C) are long-lived (A) Man, horse, and mule (C) are without gall (B) Therefore, every animal without gall (B) is long-lived (A). Induction is the inversion of syllogism, for while syllogism connects the major term (A) with the minor (C) by means of the middle term (B), induction connects the major (A) with the middle (B) by means of the minor (C) (68b33–34). 2 Cf. Aristotle, APo A 18, 81a40; Eth Nic Ζ 3, 1139b24–30. At Top A, 105a10–19 the division into syllogism and induction is presented as a sub-division of dialectical arguments. 3 See infra, §1.6. 4 Aristotle, APr B 23, 68b16–17; cf. Ross (1949), 481.

Aristotle on Signs and Demonstrations

15

Aristotle sets a condition for the validity of induction: “If, then, C converts with B and the middle term does not reach beyond the extreme, then it is necessary for A to belong to B.”5 If B and C convert, (2) becomes the first-figure syllogism in (3), which is deductively valid: (3) Man, horse, and mule (C) are long-lived (A) Animals without gall (B) are man, horse, and mule (C) Therefore, every animal without gall (B) is long-lived (A). But of course this requires that man, horse, and mule are the only animal species without gall. In Part An IV, 676b28–32 species other than the three comprised under C are mentioned (deer, dolphin, camel) which are without gall, and this would seem to empirically invalidate the condition of convertibility. However, in APr B 23 Aristotle’s concerns are purely logical: the empirical falsity of the convertibility does not affect his logical point that if such terms are convertible, then induction is deductively valid. “Example,” παράδειγμα (B 24), is an argument in which “the < first > extreme is proved to belong to the middle by means of something similar to the third extreme.”6 In this definition, mention is made of four terms: what Aristotle has in mind is a combination of two arguments. The instance he offers is supposed to prove that the war of the Athenians against the Thebans is evil. To prove this he first has to arrive at the universal proposition that making war against neighbors is evil. This is itself the result of something very similar to induction. (4) The war of Thebans against Phocians (D) was evil (A) The war of Thebans against Phocians (D) was war against neighbors (B) Therefore, war against neighbors (B) is evil (A) (5) War against neighbors (B) is evil (A) The war of Athenians against Thebans (C) is war against neighbors (B) Therefore, the war of Athenians against Thebans (C) is evil (A)

5 Aristotle, APr B 23, 68b23–25; transl. Smith. 6 Aristotle, APr B 23, 68b38–39; transl. Smith.

16

chapter 1

In the Rhetoric Aristotle calls the example a “rhetorical induction,”7 making it correlative to the enthymeme, the “rhetorical syllogism.”8 Aristotle so explains the similarities and the differences between example and induction in APr B 24:9 It is evident, then, that an example is neither as a part to a whole nor as a whole to a part, but rather as a part to a part, when both are below the same thing but one of them is known. But it differs from induction in that induction proves the extreme to belong to the middle from all the individuals and does not connect the syllogism to the extreme, while example both does connect it and does not prove from them all.10 The example is neither from part to whole (as induction), nor from whole to part (as the standard first-figure syllogism), but from a part to another part having the same character—both the war of Thebans against Phocians and the war of Athenians against Thebans are wars between neighbors—and one of which is better known than the other—it is assumed that the war of Thebans against Phocians is better known than the war of Athenians against Thebans, so that the evil character of the former can be taken as an example of the evil character of the latter (another assumption is of course that what happened in the past is better known than what is still to happen). Aristotle also explains that the example differs from induction in two ways. First, while induction “moves from all the individuals” (e.g., from all the species of animals without gall), the example only moves from one single instance (e.g., from the single historical event of the war of Thebans against Phocians). The middle term of induction is a collection of individuals (i.e., species) that are collectively convertible with the genus to which they all belong, while the middle term of the example is a single individual object or event which is of course not convertible with its genus. Second, while induction “does not connect the syllogism to the extreme” (πρὸς τὸ ἄκρον οὐ συνῆπτε τὸν συλλογισμόν),11 the example does. With this it is probably meant that while induction does not 7 Aristotle, Rhet A 2, 1356b5–6. 8 See infra, §1.2. 9 A parallel explanation is given in the Rhetoric: the example “is reasoning neither from part to whole nor from whole to part but from part to part, like to like, when two things fall under the same genus but one is better known than the other” (Aristotle, Rhet A 2, 1357b26–30; transl. Kennedy). Unlike in APr B 24, here it is also excluded that the example is a relation of “one whole to another whole.” 10 Aristotle, APr B 24, 69a13–19; transl. Smith, modified. 11 Aristotle, APr B 24, 69a18; transl. Smith, modified.

Aristotle on Signs and Demonstrations

17

use the universal predication to which it concludes to conclude about a further extreme (i.e., a further individual falling under the subject of that universal predication), the example does precisely that. Thus, the example is a first-figure syllogism (5) whose major premise is reached by an argument which is like induction (4).12 That it is a first-figure syllogism amounts to saying that it “connects the syllogism to the extreme,” i.e., concludes about a particular; that its major premise is reached by an argument like an induction amounts to saying that like an induction this argument concludes to a universal proposition, but unlike induction it moves from a particular case and not from a collection of cases. We will see in what follows that the induction-like argument that forms the first part of an example actually qualifies as a sign-argument in the third figure.13 “Abduction,” ἀπαγωγή (B 25), is an argument in which “it is clear (δῆλον) that the first term belongs to the middle and unclear (ἄδηλον) that the middle belongs to the third, though nevertheless equally convincing (πιστόν) as the conclusion, or more so; or, next, if the middles between the last term and the middle are few.”14 Ἀπαγωγή has two sub-species, which are first described in general terms and then illustrated with examples. The first sub-species is a first-figure syllogism in which the major premise is known to be true (“clear”) while the minor premise is not known to be true but is equally or more “convincing” than the conclusion. The example is the following: (6) Science (B) is teachable (A) Justice (C) is a science (B) Therefore, justice (C) is teachable (A) If the minor premise (“Justice is a science”) is not less known than the conclusion (“Justice is teachable”), then the argument qualifies as ἀπαγωγή.15 The second sub-species of ἀπαγωγή is a first-figure syllogism in which the major premise is known to be true (“clear”), while the minor premise is not an “immediate” premise but requires a few middle terms to be established. The example is the following:

12 Cf. Marmo (1988), 21–25. 13 See infra, §1.4. 14 Aristotle, APr B 25, 69a20–23; transl. Smith. 15 Aristotle may have Plato’s Meno in mind, where Socrates argues that “if virtue is a kind of knowledge, it clearly would be taught” (87c).

18

chapter 1

(7) Any rectilinear figure (E) is capable of being squared (D) The circle (F) is a rectilinear figure (E) Therefore, the circle (F) is capable of being squared (D) Here the minor premise is not immediate, i.e., it can be established only by means of a middle term, which Aristotle specifies as the “lunes” (μήνισκοι, figures bounded by two arcs of circles). The reference is to Hippocrates of Chios’ attempt to square the circle by means of lunes.16 Ἔνστασις, “objection” (B 26), is defined “as a premise contrary to a premise.”17 Aristotle’s meaning is that objection consists in the construction of a syllogism whose conclusion disproves a proposition that may function as a premise of another syllogism. For example, the proposition that there exists a single science of contraries can be objected to in the first figure, as in (8), or in the third, as in (9): (8) There is no single science of opposites Contraries are opposites Therefore, there is no single science of contraries (9) Of the known and the unknown there is no single science Known and unknown are contraries Therefore, of some contraries there is no single science 2

The Official Doctrine of Signs

The program announced in APr B 23 is finally brought to completion with APr B 27, which contains Aristotle’s official analysis of signs. This chapter is about the enthymeme and, like the other chapters in the series, it opens with a definition

16

Cf. Ross (1949), 490–491. In the nineteenth century, Charles S. Peirce conjectured that the text of B 25 is corrupt, and that its proper restoration would show that Aristotle intended to present an argument having the form of a deductively invalid second-figure syllogism (the argument by which an explanatory hypothesis is made, which Peirce, following Aristotle’s Latin translator, calls “abduction”). See Peirce (1933–1958), VII, §249. The conjecture itself is not very plausible; see Florez (2014) and Bellucci (2019). 17 Aristotle, APr B 26, 69a37; transl. Smith.

Aristotle on Signs and Demonstrations

19

of its subject matter:18 an enthymeme is a syllogism from likelihoods and signs. In the Rhetoric the enthymeme is said to be the “rhetorical syllogism,” just as the example is the rhetorical induction.19 In what sense an enthymeme is a syllogism, as Aristotle says in APr B 27, and in what sense is it a rhetorical syllogism, as he specifies in the Rhetoric, it is now our task to determine. It is important to point out at this stage, because it will turn out to be useful in what follows, that συλλογισμός in Aristotle does not always mean the technical notion of “syllogism” that he expounds in APr A 4–6. The definition of συλλογισμός in the Prior Analytics runs like this: “syllogism is a discourse in which, certain things having been supposed, something different from the things supposed results of necessity because these things are so” (Συλλογισμὸς δέ ἐστι λόγος ἐν ᾧ τεθέντων τινῶν ἕτερόν τι τῶν κειμένων ἐξ ἀνάγκης συμβαίνει τῷ ταῦτα εἶναι).20 A virtually identical definition is found in the Topics: “a syllogism, then, is an argument in which certain things being supposed, something different from the suppositions results of necessity through them” (Ἔστι δὴ συλλογισμὸς λόγος ἐν ᾧ τεθέντων τινῶν ἕτερόν τι τῶν κειμένων ἐξ ἀνάγκης συμβαίνει διὰ τῶν κειμένων).21 This definition is satisfied by any deductive argument.22 It is the συλλογισμός so intended that is usually contrasted with induction. However, Aristotle’s technical analysis of syllogisms in the Prior Analytics has proved (A 28, 44b7–8) that every συλλογισμός qua deductive argument is valid in virtue of being of one of the three figures, i.e., in virtue of having the specific form of an Aristotelian syllogism (three terms, two premises and one conclusion in which the terms are connected by the syllogistic constants “belongs to all,” “belongs to some,” “belongs to none,” “does not belong to some”). We therefore have to confront with two notions:23 the wider notion of syllogism qua deductive argument, and the narrower notion of syllogism qua deductive argument cast in one of the three syllogistic figures. When Aristotle says that an enthymeme is a rhetorical syllogism, he is using συλλογισμός in its wider 18

Ross transposes the sentence Ἐνθύμημα δὲ ἐστὶ συλλογισμὸς ἐξ εἰκότων ἢ σημείων, from 70a10 to 70a3, so that B 27 begins just like each of B 23–26, i.e., with a summary definition of the subject matter of the chapter. Mignucci (1969) accepts Ross’ emendation. For objections to it, see Smith (1989), 226, and Burnyeat (1994), 9. 19 Cf. supra, §1.1. 20 Aristotle, APr A 1, 24b18–20; transl. Smith, modified. 21 Aristotle, Top A 1, 100a25–27; transl. Smith, modified. 22 Cf. Ross (1949), 291; Patzig (1968), 44–45; Mignucci (1969), 190; Barnes (1981), 22–25; Allen (2001), 21. For an argument to the effect that the definition does capture the technical notion of syllogism see Angioni (2019). 23 Cf. Barnes (1981), 22–23, where also the still wider notion of “inference” (sometimes expressed by Aristotle by τὸ ἀναγκαῖον, cf. APr A 32, 47a31–35) is added to the count.

20

chapter 1

sense. But since his method to determine whether a συλλογισμός is valid or not consists in the application of the technical apparatus of his syllogistic, we should not be surprised when he uses that apparatus and thus the technical notion of “syllogism” to determine which of the semiotic enthymemes are valid and which are not.24 Having pointed out the difficulties raised by Aristotle’s use of the term “syllogism,” let us now ask what it means that an enthymeme is a rhetorical syllogism. That the traditional definition of the enthymeme as an abbreviated or truncated syllogism was in neither Aristotle’s spirit nor letter has been persuasively shown by Myles Burnyeat.25 Both Alexander of Aphrodisias and the ps-Philoponus say that an enthymeme is a syllogism with one premise omitted.26 This, Burnyeat conjectures, was the doctrinal basis for the occurrence of the word ἀληθές at APr 70a10 in many editions of the Organon since the Aldine of 1495, an occurrence first stigmatized as a gloss by Pacius in 1597 and rarely occurring thereafter.27 The doctrine has certainly some basis in what Aristotle says later in the chapter (69b24–25) concerning sign-syllogisms, i.e., that when the missing premise is added the sign-inference becomes a syllogism. However, the fact that enthymemes may have one implicit premise is no part of their definition. The possible omission of one premise rather depends on the fact that enthymemes are arguments used in rhetorical contexts, where brevity is a virtue and where the audience can easily supply the implicit material.28 Omission of the premise is a character of the presentation of enthymemes to audiences, not of enthymemes as such.29 As Burnyeat explains, Aristotle “did not suppose that people ordinarily present their arguments in strict syllogistic form, but that the arguments they present are valid, i.e., their conclusion results necessarily from their premises, if and only if they can be recast in one or a combination of the formally valid syllogistic moods.”30 An enthymeme is thus a syllogism in the sense of being an argument whose validity (or, as we shall see, invalidity) can be determined once we have reconstructed it as a syllogism.

24 See infra, §1.4. 25 See Burnyeat (1994). 26 Alexander, In Top, ed. Wallies, CAG 2.2, 62.9–13; Ps-Philoponus, In APr, ed. Wallies, CAG 13.2, 33.10–23. 27 Burnyeat (1994), 6. 28 Cf. Aristotle, Rhet A 1, 1357a16–22. On the brevity of the enthymeme, see Piazza (2000), 145–151. 29 Cf. Allen (2001), 24. 30 Burnyeat (1994), 15.

Aristotle on Signs and Demonstrations

21

Enthymemes, qua rhetorical syllogisms, are not a “species” of the genus syllogism in the same sense in which dialectical and demonstrative syllogisms are. Let us pause for a moment to consider this issue. In Top A 1 Aristotle says that there are three species of syllogism: demonstrative (ἀποδεικτικοί), dialectical (διαλεκτικοί), and eristical (ἐριστικοί) syllogisms. In Soph El 2 he says that the syllogistic species are four: didactic (διδασκαλικοί), dialectical (διαλεκτικοί), examinatory (πειραστικοί), and eristical (ἐριστικοί). Since “didactic” in Soph El 2 amounts to “demonstrative,” the only difference between the taxonomy of Top A 1 and that of Soph El 2 is the addition of examinatory (πειραστικοί) syllogisms. In his commentary on the Prior Analytics, Alexander reduces Aristotle’s taxonomy to three: demonstrative, dialectical, and eristical, and this seems to have been standard peripatetic doctrine.31 Demonstrative syllogisms, i.e., demonstrations, are syllogisms that satisfy the requirements of APo A 2.32 Dialectical syllogisms, by contrast, are those which are drawn from what is reputable (ἔνδοξον).33 Aristotle explains that those things are true and primary which get their trustworthiness through themselves and not through other things, while those things are reputable which seem trustworthy to everyone, or to the majority, or to the wise men.34 Eristical syllogisms are either (a) deductively valid syllogisms which are drawn from premises that seem reputable but are not so, or (b) syllogisms that seem deductively valid which are drawn from premises that either seem or are reputable;35 (a) are genuine syllogisms, (b) are not. In APr B 23, as we have seen above, the list comprises dialectical (διαλεκτικοί), demonstrative (ἀποδεικτικοί), and rhetorical (ῥητορικοί) syllogisms. As we shall see in a moment, enthymemes come in two main species: an enthymeme is a syllogism from likelihoods or from signs. That there are two kinds of enthymemes, then, depends on the fact that enthymemes are defined through their sources, i.e., their premises. An enthymeme is a syllogism one of whose premises is a likelihood (εἰκός) or a sign (σημεῖον). The two forms of rhetorical syllogism, then, can be considered as the rhetorical counterpart of the “philosophical” syllogisms: to the εἰκός-enthymeme there corresponds the dialectical syllogism, and to the σημεῖον-enthymeme the demonstrative syllogism (even though the σημεῖον-enthymeme itself is further divisible into the necessary and the probable, as we shall see). There therefore exist both demonstrative 31 Alexander, In APr, ed. Wallies, CAG 2.1, 7.8–9, 49.6–7; cf. Barnes (2016), 138. 32 See infra, §1.6. 33 Aristotle, Top A 1, 100a30. 34 Aristotle, Top A 1, 100b18–24. 35 Aristotle, Top A 1, 100b24–26.

22

chapter 1

(necessary) and dialectical (reputable) rhetorical syllogisms, and this parallelism implies that rhetorical syllogisms should not constitute a species of the same rank as demonstrative and dialectical syllogisms. Rather, a rhetorical syllogism, i.e., an enthymeme, is not a species of syllogism, but a “syllogism of a kind,”36 i.e., a syllogism, either demonstrative or dialectical, that is used in rhetorical contexts, in which some of the features of full-fledged syllogisms may be missing but which is nonetheless capable of being reconstructed as a valid syllogism. Let us now see how. In APr B 27 εἰκός is defined as follows: A likelihood is an accepted premise (πρότασις ἔνδοξος); for what people know for the most part (ὡς ἐπὶ τὸ πολύ) happens or does not happen thus, or is or is not, this is a likelihood, for example, “people hate those they envy” or “people show affection for the ones they love.”37 An εἰκός-enthymeme is a syllogism from an ἔνδοξος premise, i.e., from a proposition that holds ὡς ἐπὶ τὸ πολύ. The expression ὡς ἐπὶ τὸ πολύ is often used in a technical sense by Aristotle: it indicates a category intermediate between what is necessary and always, and what is accidental and casual.38 The Rhetoric—in one of the passages which depend upon the Analytics39—offers the following definition of εἰκός: a probability (εἰκός) is what happens for the most part (ὡς ἐπὶ τὸ πολὺ γινόμενον), not in a simple sense, as some define it, but whatever, among things that can be other than they are, is so related to that in regard to which it is probable as a universal is related to a particular.40 This definition is closely related to that of APr B 27, but adds to it the important qualification that a likelihood is related to that to which it is a likelihood like the universal is related to the particular. This helps us determine in what manner an εἰκός-enthymeme can be constructed. Take Aristotle’s example in APr B 27: “people hate those they envy.” This is a (relational) universal proposition that expresses a ὡς ἐπὶ τὸ πολύ truth. If this proposition has to be the ἔνδοξος premise in an εἰκός-enthymeme, it has to be the major premise. Thus, 36 Cf. Burnyeat (1994), 15–17. 37 Aristotle, APr B 27, 70a3–6; transl. Smith. 38 Cf. Aristotle, APr Α 13, 32b4–13; Top Β 6, 112b1–12; Rhet B 25, 1402b35–37; cf. also Mignucci (1981) and Di Piazza (2011), 137–170. 39 See infra, footnote 83. 40 Aristotle, Rhet A 2, 1357a34–b1; transl. Kennedy.

Aristotle on Signs and Demonstrations

23

we may think of the εἰκός-enthymeme as a syllogism like the following, whose only limit is its being a relational syllogism and thus not wholly legitimate in the Aristotelian framework:41 (10)

People hate those they envy Hector envies Achilles Therefore, Hector hates Achilles.

The major premise expresses a likelihood: people usually hate those they envy, but there may be exceptions to this. The syllogism, however, is strictly deductive and therefore necessary. The ὡς ἐπὶ τὸ πολύ character belongs primarily to the major premise of the εἰκός-enthymeme, and from the premise it is transferred to the conclusion. In other words, the probabilitas antecedentis is transferred to the conclusion (probabilitas consequentis) by means of a necessary form of inference (necessitas consequentiae). There is nothing surprising in this: as Aristotle says in the Posterior Analytics, in a syllogism through necessary premises the conclusion is necessary too, whereas in a syllogism through premises that holds for the most part (ὡς ἐπὶ τὸ πολύ) the conclusion also holds for the most part.42 The necessary or probable character of premises and conclusion does not affect the necessary character of the inference in either case. In an εἰκός-enthymeme it is the minor premise that can usually be omitted. Thus (10) can be presented in a compressed form as (10a)

Hector hates Achilles, because people hate those they envy

which closely mirrors the presentation of sign-arguments in APr B 27. The general proposition that acts as major premise has to be expressed, because, as explained, it is its probability that is transferred to the conclusion. An opponent who wants to refute an εἰκός-enthymeme has to show that the conclusion is not likely because the major premise from which it is inferred is not likely; he does not oppose the truth of the minor premise, but the probabilistic character of the major.43 Though they can both function as premises in an enthymeme, likelihood and sign are not the same thing:

41

As is well known, Aristotle’s syllogistic does not allow relational inferences. But since both examples of ὡς ἐπὶ τὸ πολύ premises in APr B 27 are relational, we need to consider relational syllogisms. 42 Aristotle, APo A 30, 87b22–25. 43 Cf. Allen (2001), 25.

24

chapter 1

A sign, however, professes to be either a necessary or an accepted demonstrative premise (πρότασις ἀποδεικτικὴ ἢ ἀναγκαία ἢ ἔνδοξος). For whatever is such that if it is, a certain thing is, or if it happened earlier or later the thing in question would have happened, that is a sign of this thing’s happening or being.44 A sign “professes to be” (βούλεται εἶναι) a πρότασις ἀποδεικτική. Now, being a πρότασις ἀποδεικτική can mean nothing else than being the premise (πρότασις) of an ἀπόδειξις. Unlike the εἰκός-enthymeme, a σημεῖον is a premise in a syllogism that professes to be a demonstration. The phrase βούλεται εἶναι is crucial here. Bonitz observed: “saepe per βούλεται εἶναι significatur quo quid per naturam suam tendit, sive id assequitur quo tendit, sive non plene et perfecte assequitur.”45 A sign is not a demonstration, but professes to be so: it professes to demonstrate something. The qualification that a sign βούλεται εἶναι the premise of an ἀπόδειξις helps solving the apparent problem connected with Aristotle’s use of the adjective ἀποδεικτική in this context. For if a sign were the premise of an ἀπόδειξις, and if ἀπόδειξις were taken in the strong sense outlined at APo A 2, this would straightforwardly contrast with what APo A 6 says of syllogisms through signs, i.e., that they are not demonstrations.46 After all, a sign is the premise of one kind of enthymeme, and an enthymeme is a rhetorical syllogism, i.e., the syllogism used in rhetorical discourse to produce conviction, not a scientific syllogism (or ἀπόδειξις), i.e., the syllogism used to produce or impart scientific knowledge. Some have proposed that ἀποδεικτική and ἀπόδειξις are to be taken in a “relaxed” sense, “which can prescind not only from the standards of the APo notion of demonstrative proof from necessary premises, but also, when as here Aristotle is discussing rhetorical argument, from the standards of logical validity.”47 This problem will form one of the subjects of what follows, both in this and in later Chapters. For the moment, let us limit ourselves to preliminary considerations on the basis of APr B 27. Here, even if ἀποδεικτική is taken in the strong sense, no real tension with the strong sense of ἀπόδειξις arises, because a sign just βούλεται εἶναι the premise of an ἀπόδειξις, without necessarily being one. A sign professes to be a πρότασις ἀποδεικτική which can be either necessary (ἀναγκαία) or reputable (ἔνδοξος). Ross has suggested that the contrast at APr B 27, 70a7 between ἀναγκαία and ἔνδοξος corresponds to that between 44 Aristotle, APr B 27, 70a6–9; transl. Smith, modified. 45 Bonitz (1870), 140b41–43. 46 See infra, §1.7. 47 Burnyeat (1982), 198 n. 13; cf. also Mignucci (1969), 722.

Aristotle on Signs and Demonstrations

25

τεκμήριον and σημεῖον outlined in APr B 27 in terms of the syllogistic figures.48 However, as Allen notices, the difficulty for this view is that the distinction between ἀναγκαία and ἔνδοξος seems to refer to the modal status of the premises, while the distinction between τεκμήριον and σημεῖον in the strict sense refers to the deductive validity of the corresponding syllogism.49 If Allen is right, Ross and Burnyeat would be conflating the necessitas consequentiae (distinction between τεκμήριον and σημεῖον in the strict sense) with the necessitas antecedentis (distinction between ἀναγκαία and ἔνδοξος πρότασις). Evidence of the correctness of the Ross-Burnyeat interpretation comes however from the following passage from the Rhetoric: “I call necessary (ἀναγκαία) those from which a syllogism can be formed.”50 “Necessary” here should mean “syllogistically valid,” and as we shall see later in this Chapter it is precisely in this sense that the syllogistic reconstruction of sign-inferences allows to distinguish between necessary and reputable sign-inferences, i.e., between τεκμήρια and σημεῖα. A sign professes to be a πρότασις ἀποδεικτική either ἀναγκαία or ἔνδοξος which allows to infer that something is, that something has been, or that something will be. This temporal tripartition of the sign, absent in the Rhetoric, plays no special role in the analysis that follows, but will sporadically re-emerge in later commentators.51 Aristotle proposes an analysis of signs in terms of the syllogistic figures. Thus, in order to understand his analysis it is important that we understand how the three figures are distinguished in the first place. 3

Interlude: The Figures

The three syllogistic figures are distinguished according to the manner each displays a determinate arrangement of three terms (ὅροι), one of which is called the middle term (μέσον) and the others the extremes (ἄκρα), the major and the minor extreme. In APr A 4–6 Aristotle gives no definition of the three terms which is valid for all the figures, but gives definitions of them for each

48

Ross (1949, 500). So have argued Burnyeat (1982), 199, and Grimaldi (1972), 111–112. Burnyeat notes that this interpretive line goes back to the ps-Philophonus’ commentary on the Prior Analytics; cf. Ps-Philoponus, In APr, ed. Wallies, CAG 13.2, 481.7–9. We return to the ps-Philoponus in the next Chapter. 49 Allen (2001), 30. 50 Aristotle, Rhet Α 2, 1357b5–6; transl. Kennedy. 51 E.g., in the classification of signs of Roger Bacon, cf. infra, §7.2.1.

26

chapter 1

figure individually. Definitions of the middle term and of the extremes that are valid for all the figures are given later in the same work.52 In APr A 4 Aristotle defines the middle term of the first figure as “[the term] which both is itself in another and has another in it [and] is also middle in position (ὃ καὶ τῇ θέσει γίνεται μέσον)”;53 he defines the extremes as “both that which is itself in another and that which has another in it.”54 Slightly later in the same chapter, he adds that he calls “that extreme the major which the middle is in and that extreme the minor which is under the middle.”55 In the second figure (APr A 5) the definitions of middle, major, and minor terms are: “I call that term the middle which is predicated of both and call those of which this is predicated extremes; the major extreme is the one lying next to the middle, while the minor extreme is the one farther from the middle. The middle is placed outside the extremes and is first in position (πρῶτον δὲ τῇ θέσει).”56 In the third figure (APr A 6) the definitions are: “By the middle in it [i.e., in the third figure] I mean that term of which they are both predicated, and by extremes the things predicated: by major extreme I mean the one farther from the middle and by minor the one closer. The middle is placed outside the extremes and is last in position (ἔσχατον δὲ τῇ θέσει).”57 The upshot of these definitions is the following.58 In all the figures, the middle term is defined according to its predicative relations in the premises. Let us call these the “predicative” definitions. In the first figure, it is the predicate of one and the subject of the other;59 in the second, it is predicate in both 52

“The middle term must occur in both premises in all of the figures” (Aristotle, APr A 32, 47a39–40; transl. Smith); the negation of this sentence gives a definition of the extremes (cf. Patzig 1968, 108): the extremes are those terms that do not occur in both premises in all the figures. 53 Aristotle, APr A 4, 25b35–36; transl. Smith. 54 Aristotle, APr A 4, 25b36–37; transl. Smith. 55 Aristotle, APr A 4, 26a21–23; transl. Smith. 56 Aristotle, APr A 5, 26b36–39; transl. Smith. 57 Aristotle, APr A 6, 28a12–15; transl. Smith. 58 See the detailed discussion in Patzig (1968), 89–109, 118–127, and Mignucci (1969), 213–214, 229–230, 242. 59 According to Patzig (1968), 97–100, the predicative definitions of the first figure (APr A 4) are rather extensional definitions, for Aristotle is considering a paradigmatic case of firstmood of first-figure syllogism (Barbara) in which the middle term is contained extensionally in the major and the minor in the middle. Of course, such extensional definitions do not apply to moods of the first figure other than Barbara. In Celarent, for example, the major premise is a negative universal (No A is B), and this makes it impossible to say that the middle term (B) is contained extensionally in the major (A). According to Patzig, Aristotle realized this shortcoming and used purely “predicative” definitions for the second and the third figure. Against this it could be argued that Aristotle’s definitions in APr

Aristotle on Signs and Demonstrations

27

premises; in the third it is subject in both premises. The extremes are also “predicatively” defined: the major term of the first figure is the term which is predicated of the middle term, the minor the one of which the middle term is predicated. The predicative definitions of the extremes of the second and third figure, however, are unable to distinguish one extreme from the other: how is the major term of a second-figure syllogism to be distinguished from the minor, if both are subject of the middle term in the premises and so do not differ at all with regard to their predicative relations? And how is the major term of a third-figure syllogism to be distinguished from the minor, if both are predicated of the middle term in the premises? One classical proposal was to consider the predicative relation in the conclusion: the major term would be the predicate of the conclusion, the minor its subject.60 But this proposal does not fit with what Aristotle says of the extremes of the second and third figures, namely that in the second figure the major extreme is the one “lying next to the middle,” while the minor extreme is the one “farther from the middle,” and conversely, in the third figure the major extreme is the one “farther from the middle” and the minor the one “closer” to it. The predicative relation, either relative to the premises or to the conclusion, is unable to account for the difference between the two extremes in the second and third figure. The problem has to be connected with the further characterization of the middle term in the three figures which Aristotle gives in addition to its “predicative” definition: in the first figure, the middle term is middle in position, in the second it is placed outside the extremes and is first in position, in the third it is placed outside the extremes and is last in position. Let us call this the “positional” definition of the middle and of the extremes. One is tempted to interpret these positional definitions in terms of extension: the extension of the middle term of the first figure is intermediate between the greater extension of the major extreme (which therefore is predicated of it) and the lesser extension of the minor (of which therefore it is predicated). Likewise, the extension of the middle term of the second figure is greater than both the extension of the major extreme and the extension of the minor (of both of which it is therefore predicated), while the extension of the middle

60

A 4 are predicative precisely because he is considering the paradigmatic case of Barbara: the middle term is itself in the major and thus the major can be predicated of it, and it has the minor in it and thus can be predicated of the minor. Be that as it may, this point does not affect the fact that, as Patzig explains, besides the “predicative” definitions (or, if we accept Patzig’s point, “extensional” definitions in the first figure), Aristotle also gives “positional” definitions for all the figures. See below. Proponents of this solution are ps-Philoponus, In APr, ed. Wallies, CAG 13.2, 67.14–30, followed by Lukasiewicz (1957), 32.

28

chapter 1

term of the third figure is lesser than both the extension of the major extreme and the extension of the minor (both of which are therefore predicated of it). Accepting this interpretation of the positional definitions of the middle term would also explain the positional definitions of the extremes of the second and third figure: in the second figure the major extreme is “next to the middle” in the sense that it is immediately subordinate in extension to it (which has the greater extension), while the minor extreme is “farther from the middle” in the sense that it is subordinate in extension to both the major and the middle; conversely, in the third figure the major extreme is the one “farther from the middle” in the sense that it is superordinate in extension to it (which has the lesser extension), and the minor is the one “closer” to it in the sense that it is superordinate to both the major and the middle. Ross61 favors such an “extensional” interpretation and offers the diagram in Fig. 1 as an explication of it, where the length of the lines represents the relative extensions of the three terms. Thus, in the first figure the middle has the middle position, i.e., has an intermediate extension; in the second it is first in position, i.e., it has the greater extension; in the third it is last in position, i.e., it has the lesser extension.

Figure 1  Syllogistic figures according to Ross (1949)

That an “extensional” interpretation of the “positional” definitions given by Aristotle is impracticable was already recognized by Alexander of Aphrodisias and is criticized at length by Patzig.62 In the first-figure syllogism Celarent (“No B is A, all C is B, hence no C is A”) the major premise is a universal negative proposition. How could Aristotle’s positional definition of the middle term (“is also middle in position,” ὃ καὶ τῇ θέσει γίνεται μέσον) be taken to mean that the middle term, B, is less extended than the major, A, given that it makes no sense to speak of the relative extensions of B and A in the universal negative proposition “No B is A”? Likewise, in the second-figure syllogism Baroco (“All A is B, some C is not B, hence some C is not A”) the minor premise is a particular negative proposition. How could Aristotle’s positional definition of the middle term (“is first in position,” πρῶτον δὲ τῇ θέσει) be taken to mean that the middle 61 Ross (1949), 301–302. Ross follows Einarson (1936) here. 62 Alexander, In APr, ed. Wallies, CAG 2.1, 47.27–50.22; cf. supra, footnote 59.

Aristotle on Signs and Demonstrations

29

term, B, is more extended than the minor, C, given that it makes no sense to speak of the relative extensions of B and C in the particular negative proposition “Some C is not B”? Mutatis mutandis, the same line of reasoning applies to all the moods in all the figures in which premises other than universal affirmative propositions occur. A definition by relative extension is only possible if universal affirmative propositions are presupposed for all terms. “Middle in position,” “first in position,” and “last in position” must then be taken in another sense. The most plausible explanation of this sense has been advocated by Patzig: the three terms are defined by the order in a standard formulation of the syllogism. The standard formulation of the first figure is: “If A is predicated of every B and B of every C, it is necessary for A to be predicated of every C.”63 The standard formulation of the second figure is: “Let M be predicated of no N but of every X. Then [...] N belongs to no X.”64 The standard formulation of the third figure is: “When both P and R belong to every S, it results of necessity that P will belong to some R.”65 Disregarding the uses of different schematic letters in the three standard formulations we can assume a standard ordering of three terms along the lines of Ross’ diagrams displayed in Fig. 1 but without any indication of the relative extensions of the three terms (see Fig. 2):

Figure 2  Syllogistic figures according to Patzig (1968)

The three standard formulations then become (we only state the premises): i. “A is said of all B and B of all C”; ii. “A is said of no B and of all C”; iii. “A and B are said of all C.” In the first figure, the middle term B is middle in position; in the second, the middle term A is first in position; in the third, the middle term C is last in position.

63 Aristotle, APr A 4, 25b37–39; transl. Smith. 64 Aristotle, APr A 5, 27a5–8; transl. Smith. 65 Aristotle, APr A 6, 28a18–19; transl. Smith.

30 4

chapter 1

Syllogisms from Signs

We are now in the position to evaluate Aristotle’s analysis of signs in terms of the syllogistic figures. (In this part, we follow Aristotle and use the term “syllogism” in the technical sense specified above.66) Aristotle says: A sign may be taken in three ways, corresponding to the ways the middle term in the figures is taken: for it is taken either as in the first figure, or as in the middle, or as in the third. For instance, proving that a woman has given birth because she has milk is from the first figure, for the middle term is having milk (let A stand for giving birth, B having milk, C for a woman). But “The wise are good, for Pittakos was good” is through the last figure. A stands for good, B stands for the wise, C stands for Pittakos. So it is true to predicate both A and B of C, except that people do not state the latter premise because they know it, though they do take the former. And “She has given birth because she is pale” is intended to be through the middle figure: for since paleness follows having given birth and also follows this woman, people think it has been proved that she has given birth. A stands for pale, B stands for giving birth, C stands for a woman.67 In the form in which they are enunciated, the three sign-arguments that illustrate Aristotle’s analysis are made up of a claim backed by a reason, which logically speaking count as one-premise arguments. These are: (11) This woman has milk, therefore she has given birth (12) Pittakos was good, therefore the wise are good (13) She is pale, therefore she has given birth. With reference to the third-figure sign-syllogism Aristotle observes that “people do not state the latter premise [i.e., that C is B, or that Pittakos was wise] because they know it, though they do take the former.” As mentioned, later in the same chapter he explains in more general terms that “if one premise alone 66 Cf. supra, §1.2. 67 Aristotle, APr B 27, 70a11–24; transl. Smith, modified. We translate the verb κύειν with “giving birth.” For an explanation of the rationale of this choice, which has conceptual implications, see infra, §1.9.

Aristotle on Signs and Demonstrations

31

is stated, then, it is only a sign, but if the other premise is also taken in addition, it is a syllogism.”68 The validity or invalidity of the three kinds of signs depends on the manner they are reconstructed as syllogisms, and this in turn depends on the role the sign-premise plays in the syllogistic structure with respect to the premise supplied in the reconstruction. Signs differ according as middle terms differ across the three syllogistic figures. Aristotle is here considering what we have called the “predicative” definition of the middle term in APr A 4–6. In the first figure, the middle term is the predicate of one premise and the subject of the other. Thus, the one-premise argument in (11) is expandable into the first-figure syllogism (14) Women with milk have given birth This woman has milk Therefore, this woman has given birth by supplying the major premise “Women with milk have given birth.” When the major premise is supplied, the argument appears as a deductively valid first-figure syllogism. Aristotle calls it a τεκμήριον, i.e., evidence.69 The major premise is usually omitted, as in (11), because it is a proposition taken for granted and accepted by the audience to which the argument is addressed. When the major premise is supplied and the argument is reconstructed as a full syllogism, it can only be refuted by saying that the minor premise, the sign itself, does not hold. It cannot be refuted by saying that the major premise does not hold,70 as with εἰκός-enthymemes.71 A τεκμήριον is irrefutable (ἄλυτος) if true, i.e., if the minor premise is such. By contrast second- and third-figure sign-syllogisms are deductively invalid. By supplying the missing premise, (12) is recast as (15) and (13) is recast as (16): (15) Women who have given birth are pale This woman is pale Therefore, this woman has given birth

68 Aristotle, APr B 27, 69b24–25; transl. Smith. 69 In the Rhetoric, the etymological support that Aristotle provides for the name of the sign in the first figure is that τέκμαρ (proof) and πέρας (limit, conclusion) meant the same thing in the “old language” (Aristotle, Rhet A 2, 1357b9); cf. Grimaldi (1980a), 66. 70 Aristotle, Rhet B 25, 1403a13–16. 71 Cf. supra, §1.2.

32

chapter 1

(16) Pittakos was good Pittakos was wise Therefore, the wise are good. Second- and third-figure sign-syllogisms are refutable (λύσιμος) because their syllogistic reconstruction does not yield a valid syllogistic argument. The sign-syllogism in the third figure is refutable even if it is true, i.e., even if its conclusion is true (κἂν ἀληθὲς ᾖ τὸ συμπέρασμα), because in that figure only a particular conclusion can be drawn from two universal premises, not a universal conclusion as “professed” by the syllogism proposed (διὰ τὸ μὴ εἶναι καθόλου μηδὲ πρὸς τὸ πρᾶγμα τὸν συλλογισμόν).72 The sign-syllogism in the second figure is also refutable even if it (i.e., its conclusion) is true,73 because in that figure no conclusion at all can be drawn from two affirmative premises.74 Second- and third-figure arguments are called simply σημεῖα. In the last passage of his analysis of signs in APr B 27, Aristotle presents a terminological dilemma: Now, should signs be divided in this way, so that the sign which is a middle term is taken to be evidence (τεκμήριον) (for we say that what makes us know is evidence, and the middle is most like this)? Or should the ones from the extremes be called a sign and those from the middle term be called evidence (for that which is through the first figure is most accepted and most true)?75 At 70b4 the term σημεῖον occurs in the strict sense of “premise of a secondor third-figure syllogism.” But at 70b1, when Aristotle says “should signs be divided …,” it occurs in a wider sense, as it does at 70a3, and in that wider sense it includes both τεκμήρια and σημεῖα in the strict sense. Both the terms

72 Aristotle, APr B 27, 70a31–32. 73 Aristotle, Rhet A 2, 1357b20. 74 Aristotle, APr B 27, 70a34–36. 75 Aristotle, APr B 27, 70b1–6; transl. Smith.

Aristotle on Signs and Demonstrations

33

τεκμήριον and σημεῖον occur in earlier medical,76 historiographical,77 and rhetorical78 literature, but not with the difference in meaning that Aristotle gives them in the Prior Analytics.

76

77

78

In the Hippocratic corpus both τεκμήριον and σημεῖον are used in the sense of sign, symptom, or basis for diagnostic and prognostic reasoning (e.g., Hippocrates, Progn. 25.11–12); more often, a collection of σημεῖα is the basis for inferring (τεκμαίρεσθαι) a condition (e.g., Hippocrates, De arte, 12.2; Progn. 2.13; 17.46; 24.72–73; Prorrh. II.1 (220.9–11)); see Perilli (1991); Hankinson (1997), 1172–1177; Fausti (2008); Piazza and Di Piazza (2011). Diller (1932) was the first to argue that in the fifth century the two terms were used in different senses: τεκμήριον was used for a sign that corroborates a thesis already set forth, while σημεῖον was used for a sign that contributes to set forth a thesis. On the basis of Progn. 25.11–12, Perilli (1991), 164–165, argues on similar lines that τεκμήριον is a species of the generic σημεῖον, like in Aristotle. Hankinson (1997) sees no real difference between the two terms in the Hippocratic texts. Herodotus uses τεκμήριον in the general sense of “proof” (II, 13, 43, 58, 104) and τεκμαίρομαι in the sense of “drawing conclusions” (I, 57; II, 33), but he never uses σημεῖον in this sense; see Gaetano (2018) for an interesting study of Herodotus’ dependence on Homer for his use of τεκμαίρομαι. In Thucydides the occurrences of τεκμήριον and τεκμαίρομαι are even more evident, as are those of σημεῖον. Although attempts have been made (cf. e.g., Diller 1932) to argue that Thucydides means different things by τεκμήριον, σημεῖον and the related verbs, yet it seems that they invariably mean “proof,” “evidence,” “sign,” etc., with no discernible difference in the use he makes of them; see I, 1, 3, 6, 20, 21, 132; see also Hornblower (1987), 100–106; Hornblower (1997), 25; Manetti (2013), 31–36. According to Grimaldi (1980b, 397n12), there is no evidence in the Attic orators of a significant difference in meaning between τεκμήριον and σημεῖον. In the Rhetoric to Alexander, once attributed to Aristotle and probably coeval to the latter’s Rhetoric (Chiron 2011), the definition of σημεῖον is as follows: “One thing is a sign of another, not a chance event of a chance event, nor everything of everything, but what usually happens before another event, at the same time, or after it. Not only is what happens a sign of what happens, but it is also a sign of what does not happen, and similarly what does not happen is a sign of what is not, and also of what is. One sign creates belief, another knowledge, but the best creates knowledge, and the second best produces very persuasive opinion” (1430b30–38; transl. Mirhady). The analogy with Aristotle’s definition of σημεῖον in APr B 27 is evident. By contrast, τεκμήριον is defined as “whatever has been done in a way contrary to what the speech is about and those things with respect to which the speech is contrary to itself” (1430a14–16; transl. Mirhady). According to this definition, a τεκμήριον is the evidence of a contradiction between the opponent’s speech and acts, or within the speech itself, which contributes to calling into question the reliability of the opponent’s claims. The distance from Aristotle’s notion of τεκμήριον is evident (cf. Piazza and Di Piazza 2011, 14–15). Isocrates uses τεκμήριον in a sense fully compatible with the Rhetoric to Alexander (Noël 2011). A clear-cut distinction between τεκμήριον and σημεῖον occurs in a fragment attributed to Antiphon of Rhamnus: “concerning past events we need trust to σημεῖα, concerning future events to τεκμήρια” (Fr. 72), a distinction also found in Ammonius (Peri diaphorōn lexeōn, ed. Valck, 127; cf. Perilli 1991, 159). Hankinson (1997), 1177, observes however that Antiphon nowhere else seems to draw upon this distinction.

34

chapter 1

Aristotle calls the sign-syllogisms in the second and third figure “from the extremes” and that in the first figure “from the middle.” This nomenclature reflects neither the predicative nor the positional definitions of middle, major, and minor terms which he has given in A 4–6, but an extensional conception. His use of the letters “A” for the extensionally major term, “B” for the extensionally middle, and “C” for the extensionally minor in all the three figures of sign-syllogisms is a clear indication of this. In the first figure, the predicative middle term is “having milk.” Since all women who have milk have given birth, so that the major term is at least as extended as the middle,79 the predicative middle term is also intermediate in extension. The inference is therefore deductively valid. In the second figure, the middle term is “being pale.” All women who have given birth are pale, but not all women who are pale have given birth; so, the predicative middle term has the greater extension, and the inference is deductively invalid. In the third figure, the predicative middle term, being an individual term, has the lesser extension; the inference commits the fallacy of illicit minor and is therefore deductively invalid. Secondand third-figure sign-syllogisms are called “from the extremes” at 70b4 because they are drawn through predicative middle terms that are either the major in extension (second figure) or the minor in extension (third figure). First-figure sign-syllogisms are drawn through predicative middle terms that are also intermediate in extension, and this is the meaning of “middle term” at 70b1–4. After having explained why second- and third-figure sign-syllogisms are deductively invalid, Aristotle adds the remark that “the truth, then, can occur in all signs, but they have the differences stated (ἀληθὲς μὲν οὖν ἐν ἅπασιν ὑπάρξει τοῖς σημείοις, διαφορὰς δ᾿ ἔχουσι τὰς εἰρημένας).”80 This remark suggests that while first-figure sign-syllogisms are the only ones which are irrefutable, yet second- and third-figure sign-syllogisms are still of some value, especially in rhetorical contexts, despite their deductive deficiency. Burnyeat notes that Aristotle’s statement at 70b4–6 that first-figure sign is “the most reputable and the most true” (ἐνδοξότατον γὰρ καὶ μάλιστα ἀληθές) should have the scalar implicature that the second- and third-figure signs do in fact have some claim to reputability and truth.81 79

That this should be so is a logical requirement: the admission of lactating women who have not given birth clearly invalidates Aristotle’s first-figure sign-syllogism. Yet in the Historia animalium (522a2ff) Aristotle points out that some animals are known to produce milk without getting pregnant. The convertibility of middle and major term in a first-figure sign-syllogism seems to have been central for the commentators: we shall have occasion to return to this in the following Chapters. 80 Aristotle, APr B 27, 70a37–38; transl. Smith. 81 Burnyeat (1982), 197.

Aristotle on Signs and Demonstrations

35

In the Rhetoric, the terminological dilemma of APr B 27, 70b1–6 is resolved by accepting the first horn: the necessary, i.e., deductively valid σημεῖον is called a τεκμήριον, while non-necessary, i.e., deductively invalid σημεῖα do not have a specific name (ἀνώνυμον).82 The term σημεῖον here only occurs in the wider sense recorded at APr B 27, 70a3 and 70b1. But for this slight terminological variation, Aristotle’s analysis of signs in the Rhetoric substantially coincides with that of the Analytics, even though with somewhat different examples, with an important qualification and a more negative attitude towards deductively invalid sign-inferences.83 82 Aristotle, Rhet A 2, 1357b4–5. 83 Two sections of the Rhetoric in which sign arguments are discussed explicitly refer to the Analytics: A 2, 1357a22–1358a2 and B 25, 1402b13–1403a16. According to Solmsen (1929), these were later insertions in a work whose main bulk only know the dialectical logic of the Topics but not yet the syllogistic logic of the Prior Analytics. Solmsen’s argument has more recently been refined and reargued by Barnes (1981). Since the problem of the stratification of the Rhetoric falls outside the scope of the present work, we only briefly mention some relevant points of Solmsen’s argument. In Rhet A 2, immediately after the discussion of likelihoods and enthymemes that is parallel (and refers) to APr B 27, Aristotle unexpectedly presents a “major division” of enthymemes, which is said to correspond to a division of dialectical syllogisms: (i) there are enthymemes that belong to rhetoric itself and depend on τόποι that are common to different disciplines; (ii) other enthymemes are based on τόποι that are proper to special disciplines or arts; after a reference to the Topics, Aristotle concludes the passage by saying that the “major division” of enthymemes is thus between those that proceed from premises that are “species” (special τόποι) and those that proceed from premises that are τόποι (common τόποι) (Rhet A 2, 1358a1–35). According to Solmsen, this passage represents an early layer, composed at a time when Aristotle had not yet discovered the formal theory of the syllogism exposed in the Prior Analytics and when his logic still was the informal dialectic of the Topics based on τόποι. Evidence of the stratification of the Rhetoric also comes from the second book. In Rhet B 22 Aristotle assumes the “major division” of enthymemes of Rhet A 2 and in B 23 he enumerates twenty-eight genuine enthymemes, all based on τόποι. No mention is made of the distinction between εἰκός-enthymemes and σημεῖον-enthymemes of APr B 27 and the first part of Rhet A 2. Then in Rhet B 24 Aristotle enumerates apparent enthymemes, one of which (1401b9–14) is based on a τόπος which is a sign (σημεῖον); the examples are third- and second-figure sign-arguments. This implies that, contra APr B 27 and the first part of Rhet A 2, signs in the strict sense are not genuine enthymemes. All this points unmistakably to the fact that the Analytics-oriented passages of the Rhetoric are later insertions: after the full theory of the syllogism had been elaborated a syllogisticallyoriented description of enthymemes was inserted in a text that only knew the logic of the Topics and in which enthymemes were described and classified according to the τόποι they are based on; and further, this earlier layer was allowed to remain in the text along with the new material. On the stratification of the Rhetoric see Solmsen (1929), 13–31; Stocks (1933), 119–121; Grimaldi (1972), 18–52; Barnes (1981), 51–52 n. 55; Burnyeat (1994), 31–38. On Aristotle’s discovery of the syllogism see Ross (1939) and the reply in Solmsen (1941).

36

chapter 1

The sign-syllogism in the first figure, Aristotle says at Rhet A 2, 1357b4, is necessary (ἀναγκαῖον). His examples comprise the lactating woman of APr B 27 and the fever as a τεκμήριον of illness. He repeats what he says in the Analytics, i.e., that a τεκμήριον is the only sign-syllogism that is irrefutable if true. Second- and third-figure sign-syllogisms are further qualified. The third-figure sign “stands as the particular to the universal.”84 With this he evidently means that this kind of sign-argument invalidly infers a universal conclusion from a particular, indeed a singular, premise. The example is the same as that of APr B 27, but with Socrates instead of Pittakos. The second-figure sign “stands as the universal to the particular.”85 This means that in this kind of sign-argument the middle term is the most extended of the three terms, and thus a particular conclusion is invalidly inferred from a universal one, as we explained above. The example is new: from one’s breathing fast we can infer that one has a fever. This is refutable, says Aristotle, because one can breathe fast without having a fever (the middle term, breathing fast, has a wider extension than the major term, having a fever). Both second- and third-figure sign-syllogisms are refutable even in case they are true, which we know from the Analytics. In the Rhetoric Aristotle also adds that second- and third-figure sign-syllogisms are asyllogistic (ἀσυλλόγιστοι), while the first-figure sign-syllogism is necessary (ἀναγκαῖος) precisely because a syllogism can be derived from it. This additional qualification, which is absent in the Analytics, is interesting because it shows that the term συλλογισμός is being used here (as it usually is in APr B 27) in the strict sense of a deductively valid syllogism in one of the three figures. He has told us that enthymemes are rhetorical syllogisms, and with this he probably meant that they are deductive arguments used in rhetorical contexts. But since his method for determining the validity of a deductive argument consists in the application of the formal apparatus of his syllogistic, he has also shown that second- and third-figure sign-syllogisms are deductively invalid, i.e., are not reconstructable as valid second- and third figure syllogisms. But if second- and third-figure sign-syllogisms are ἀσυλλόγιστοι, are they enthymemes? In Rhet B 24, 1401b9–14 the sign-enthymeme (where “sign” is taken in the strict sense) is treated as one of the τόποι of the apparent enthymeme, that is, of an argument that (to use the APr B 27 phrase) βούλεται

84 Aristotle, Rhet A 2, 1357b11; transl. Kennedy. 85 Aristotle, Rhet A 2, 1357b17–18; transl. Kennedy.

Aristotle on Signs and Demonstrations

37

εἶναι an enthymeme but fails to be one.86 Aristotle’s examples are second- and third-figure sign-syllogisms: “Lovers benefit their cities because Harmodius and Aristogeiton killed the tyrant Hipparchus” can be roughly recast as a third-figure sign-syllogism on the model of Pittakos example of APr B 27: (17) Harmodius and Aristogeiton were lovers Harmodius and Aristogeiton benefited their city by killing Hipparchus Lovers benefit their cities The other example, “Dionysius is a thief, for he is wicked,” can be recast as a second-figure sign-syllogism: (18) Thieves are wicked Dionysius is wicked Therefore, Dionysius is a thief This is ἀσυλλόγιστος, Aristotle says, because the major premise cannot be converted. A similar negative attitude towards inferences that can be cast in the form of second-figure sign-syllogisms is manifested in the Sophistici Elenchi, as we shall see.87 5 Physiognomics We saw that not all enthymemes are based on signs. In like manner, not all sign-inferences are enthymemes.88 In the final section of APr B 27 Aristotle

86

The relation of this passage to the others that mention sign-enthymemes is of course problematic; see supra, footnote 83. 87 Cf. infra, §1.8. 88 Apart from its collocation in a chapter devoted to enthymemes, and therefore to signs, there seems to be no other ground for the claim (cf. Ross 1949, 501; Magli 1988, 52) that physiognomic inferences are enthymemes. It is safer to assume that physiognomics provides a further illustration of the applicability of the syllogistic technique, which somehow plays the role of an appendix to the program carried on in APr B 23–27; cf. Allen (2001), 13. We shall see in what follows (esp. infra, §6.1.4) that some commentators of the Prior Analytics would consider this physiognomic section to fall within the scope of the chapter on enthymemes, thereby assuming that physiognomic inferences are enthymematic.

38

chapter 1

offers a further illustration of the applicability of the syllogistic technique to inferences by considering physiognomics. He says that physiognomic inferences are possible if three conditions are met: i) body and soul are altered simultaneously (ἅμα μεταβάλλειν) by nature; ii) there is a one-to-one correspondence between bodily affections or signs and spiritual affections, i.e., there is a single sign of a single thing (ἓν ἑνὸς σημεῖον εἶναι); iii) the spiritual affection and the bodily affection or sign are both “proper” to a kind (ἴδιον ἑκάστου γένους πάθος καὶ σημεῖον).89 Aristotle suggests that the second part of condition (iii)—that a bodily affection or sign is “proper” to a kind of animals—derives from the first part of condition (iii) together with (i) when he adds: “for if there is some affection belonging peculiarly to an indivisible kind, as courage to lions, then there must also be some sign (for body and soul are assumed to be affected together with each other),”90 i.e., if body and soul are altered simultaneously, to a “proper” affection of the soul there will correspond a “proper” sign of it. Aristotle offers the following counter-example: “if the whole kind has two peculiar affections (as, for example, the lion is courageous and generous), then how can we tell which one of the signs that follow peculiarly is the sign of which affection?”91 If a kind K has two proper affections, A1 and A2, and two proper signs corresponding to them, S1 and S2, it is impossible to determine which is the sign of which. It would be different, Aristotle says, if a member of a kind distinct from K has A1 and S1. In that case, we could transfer the correspondence between S1 and A1 to the kind K: “if something is courageous but not generous and possesses a certain one of the two signs, then it is clear that this is also the sign of courage in the case of the lion.”92 As Ross observes, the whole idea of a physiognomics so construed is intelligible only on the assumption that Aristotle is discussing “the inferring of mental characteristics in men from the presence in them of physical characteristics which in some other kind or kinds of animal go constantly with those mental characteristics.”93 In order for this to be practicable, the sign has to be “proper” to one animal kind and not to humans. Aristotle says: “the sign is proper (ἴδιον) in this sense, that it is proper of the whole kind, but not that it is proper of one kind, as we usually say.”94 This explication of “proper” conflicts with the defini89 Aristotle, APr B 27, 70b7–14. 90 Aristotle, APr B 27, 70b14–16; transl. Smith. 91 Aristotle, APr B 27, 70b26–28; transl. Smith. 92 Aristotle, APr B 27, 70b30–32; transl. Smith. 93 Ross (1949), 501. 94 Aristotle, APr B 27, 70b18–20; transl. Smith.

Aristotle on Signs and Demonstrations

39

tion of “proper” given in the Topics: “A proper is what does not exhibit what it was to be for some subject but belongs only to it, i.e., it counterpredicates with it.”95 The predicate of being capable of becoming literate is a proper of men, because while this character does not exhibit the essence of man (a predicate that exhibits the essence of something and converts with it is a definition96), yet it is convertible with it: all men are capable of becoming literate, and anything capable of becoming literate is a man. The sense of “proper” explained at APr B 27, 70b18–20 does not coincide with the sense of this term in the Topics, and Aristotle’s specification of the non-coincidence in the phrase “not proper of one kind, as we usually say” is probably a reference to the sense of “proper” defined at Top A 5.97 Physiognomic inference is in the first figure: Now, recognizing natures is by means of a syllogism in the first figure in which the middle converts with the first extreme but reaches the third and does not convert with it. For example, courage is A, B stands for large extremities, C is lion. Now, B belongs to everything to which C belongs, but also to others. But A belongs to everything to which B belongs and to no others, but instead it converts (if it does not, then there will not be a single sign of a single thing).98 Aristotle has in mind the following syllogism in the first figure: (19) Courage (A) belongs to having large extremities (B) Having large extremities (B) belongs to the lion (C) Hence, courage (A) belongs to the lion (C) Aristotle notes that while the major premise is convertible, the minor premise is not. The major premise is convertible (all courageous beings have large extremities, and all those with large extremities are courageous) because of condition (ii), i.e., that there is a single sign of a single thing. The minor premise does not convert because of the sense of “proper” that Aristotle has specified: if the minor premise were convertible, i.e., if not only all lions had large extremities, but if also all those with large extremities were lions, then we would be unable to transfer the one-to-one correspondence stated in the

95 Aristotle, Top A 5, 102a18–19; transl. Smith, modified. 96 Cf. Aristotle, Top A 8, 103b9–11. 97 Cf. Barnes (1970), 146. 98 Aristotle, APr B 27, 70b32–38; transl. Smith, modified.

40

chapter 1

major premise to men: it is because what is proper to lions is also found in another kind (though not in every member of that kind) that it is possible to infer of a man that has large extremities that he is courageous. This is done, again, by means of another first-figure physiognomic syllogism: (19*)

Courage (A) belongs to having large extremities (B) Having large extremities (B) belongs to this man (C) Hence, courage (A) belongs to this man (C)

6 Demonstration The Posterior Analytics are devoted to ἐπιστήμη, i.e., scientific knowledge. Scientific knowledge is knowledge through demonstration (ἀπόδειξις), and a demonstration is a kind of syllogism (συλλογισμός τις99). Not all syllogisms are demonstrations, but all demonstrations are syllogisms. A demonstration is a scientific syllogism (συλλογισμòς ἐπιστημονικός100), i.e., a syllogism used to produce (or to impart101) scientific knowledge. In order to qualify as a demonstration the premises of a syllogism must satisfy six requirements: they must be (i) true, (ii) primitive, (iii) immediate, (iv) better known than, (v) prior to, and (vi) causes of the conclusion. Premises satisfying these six requirements are said to be appropriate to what is demonstrated through them.102 The premises of a demonstration must be true (i) because they must be known, and it is impossible to know something that is not true.103 They must further be primitive (ii) and immediate (iii) in the sense of being indemonstrable.104 99 Aristotle, APr A 4, 25b30. 100 Aristotle, APo A 2, 71b18. 101 According to Barnes (1969), the theory of demonstrative science presented in the Posterior Analytics was not meant to describe how scientists do, or ought to, acquire knowledge. It was meant to describe how teachers should impart knowledge. Burnyeat (1981), 115–120, has further observed that if the aim of the Posterior Analytics is, as Barnes thinks, pedagogical, then we should admit that it deals with teaching as the imparting of “understanding” (ἐπιστήμη, the highly sophisticated notion of knowledge discussed in that work, which can also be called “scientific knowledge”), rather than as the imparting of “knowledge” (γνῶσις, the ordinary notion of knowledge). More recently, Bronstein has argued that demonstration is an instrument of both teaching and discovery: students of a science are taught and learn by demonstration, but demonstration is also a source of new scientific knowledge for experts; see Bronstein (2016), esp. chapters 2, 4, and 11. 102 Aristotle, APo A 2, 71b21–23. 103 Aristotle, APo A 2, 71b25–26 104 Aristotle, APo A 2, 71b28–29.

Aristotle on Signs and Demonstrations

41

Of immediate and primitive premises there is no demonstration, and thus no demonstrative scientific knowledge, but only νοῦς.105 Demonstrative premises must also be better known than (iv), and prior to (v), the conclusion. At APo A 2, 71b33–72a4 Aristotle explains that things can be said to be better known (γνωριμώτερα) and prior (πρότερα) in two senses: things are better known and prior in relation to us when they are closer to perception; they are better known and prior absolutely or by nature when they are farther from perception. In which of the two senses, then, the premises must be better known than and prior to the conclusion? The answer comes from the sixth requirement, i.e., that the premises of demonstration must be causes (αἴτια) of the conclusion:106 since to know scientifically is to know by means of the cause, and since causes are prior and better known by nature than their effects, the premises of demonstration must be better known than and prior to the conclusion by nature and not for us. Traditionally, these six requirements have been divided in two groups of three: (i), (ii), and (iii) are “absolute” requirements, i.e., requirements that the premises of a demonstration must satisfy in themselves, while (iv), (v) and (vi) are “relative” requirements, i.e., requirements to be satisfied relatively to the conclusion.107 The absolute requirements have generally appeared too stringent. The traditional way of “relaxing” a bit the absolute requirements is to concede that the premises of a demonstration must either be propositions satisfying (i), (ii), (iii) or else be propositions demonstrated from (i), (ii), and (iii). This is indeed Aristotle’s definition of demonstration in the Topics: a syllogism is demonstrative if it “is from things which either are themselves true and primary or have attained the starting-point of knowledge about themselves through some primary and true premises.”108 The sixth requirement is the most important for our present purpose. At APo A 13 Aristotle distinguishes between scientific knowledge “of the that” and scientific knowledge “of the why.” Since scientific knowledge is knowledge by demonstration, and a demonstration is a scientific syllogism, the two kinds of scientific knowledge correspond to two kinds of scientific syllogisms, the “syllogism of the that” (συλλογισμὸς τοῦ ὅτι) and the “syllogism of the why” (συλλογισμὸς τοῦ διότι).

105

Cf. Aristotle, APo B 19, 100b6–17. Νοῦς can be translated as “intuition,” “intuitive reason” (Ross), “intellezione” (Mignucci), “intuitive knowledge” (Biondi 2004). 106 Aristotle, APo A 2, 71b31–32. 107 Cf. Mignucci (1975), 22–23; Barnes (1993), 93. 108 Aristotle, Top A 1, 100a27­–29; transl. Smith. Cf. also APo A 10, 76b10. Barnes (1981), 26, argues that all six requirements should be so relaxed.

42

chapter 1

6.1 Demonstrations of the That and of the Why APo A 13 is a complex chapter, and since it is central in substantially every later interpretation of Aristotle’s theory of demonstration, an analysis of it is indispensable. The chapter is divided into two main parts, for knowledge of the that and knowledge of the why differ in two ways, first within the same science and secondly within distinct sciences. The sequence 78a23–78b34 is about the difference within the same science, the sequence 78b34–79a16 is about the difference within distinct sciences. Our analysis is limited to the former sequence. We divide this portion of the chapter in five sections (i–v). The difference between that- and why-knowledge within the same science is itself twofold: in a way (i), knowledge of the that and knowledge of the why differ if the syllogism is not from immediates (μὴ δι᾽ ἀμέσων);109 in another (ii), if the syllogism is from immediates (δι᾽ ἀμέσων).110 There follow some examples and additional explanations: (iii) converting middle and major term, with two astronomical examples;111 (iv) non-converting middle and major term, with no example;112 (v) an example of a syllogism in the second figure that qualifies as a demonstration of the that, with an allusion to an argument by Anacharsis about Scythia having the same form.113 The two examples in (iii) clearly illustrate (ii); but it is far from clear whether the examples in (v) illustrate (i) and how (iv) is related to (i).114 Here is the passage containing sections (i), (ii), and (iii): Knowing scientifically (ἐπίστασθαι) the fact and the reason why differ, first in the same science—and in two ways. In one way, [(i)] if the syllogism does not proceed through immediates: in this case the primary cause is not assumed, but the scientific knowledge (ἐπιστήμη) of the reason why occurs in virtue of the primary cause. In a second way [(ii)], if, although the syllogism does proceed through immediates, it proceeds not through the cause but through the better known of the converting terms. For there is no reason why of the counterpredicated terms that which is the non-cause should not sometimes be better known, so that the demonstration will proceed through this term. [(iii)] E.g., a demonstration that 109 Aristotle, APo A 13, 78a23–26. 110 Aristotle, APo A 13, 78a26–28. 111 Aristotle, APo A 13, 78a30–78b11. 112 Aristotle, APo A 13, 78b11–13. 113 Aristotle, APo A 13, 78b14–31. 114 Ross (1949), 553–554, and Mignucci (2007), 195–198, think that neither (iv) nor (v) illustrate (i) but are distinct cases of the difference between that- and why-knowledge. Barnes (1993, 155) supposes that sections (iv) and (v) further explain (i), but admits the supposition is not without difficulties.

Aristotle on Signs and Demonstrations

43

the planets are near, through their not twinkling. Let C be the planets, B not twinkling, A being near. It is true to say B of C: the planets do not twinkle. And also to say A of B: what does not twinkle is near. [...] Thus it is necessary that A holds of C, and it has been demonstrated that the planets are near. Now this syllogism gives not the reason why but the fact: it is not because the planets do not twinkle that they are near— rather, because they are near they do not twinkle. It is also possible to prove the latter through the former, and then the demonstration will give the reason why. E.g., let C be the planets, B being near, A not twinkling. B holds of C and A of B: hence A holds of C. The syllogism gives the reason why, since the primitive cause has been assumed. Again, consider the way in which they prove that the moon is spherical through its waxing: if what waxes in this way is spherical, and the moon waxes, it is clear that it is spherical. In this way the syllogism gives the fact, whereas if the middle term is posited the other way about the syllogism gives the reason why. (It is not because of its waxing that the moon is spherical: rather, because it is spherical it waxes in this way. Moon, C; spherical, B; waxing, A.)115 Let us start from the relation between sections (iii) and (ii). Aristotle assumes a case in which two convertible terms (“counterpredicated terms,” ἀντικατηγορούμενα) are related as cause (τὸ αἴτιον) and effect (in the passage: the “non-cause,” τὸ μὴ αἴτιον), and in which the effect is better known (γνωριμώτερον) than the cause. (It has to be noted that, according to the distinction of APo A 2, a cause is less known for us but is better known in itself, and an effect is better known for us but less known in itself.) Suppose that, in an astronomical context, the fact that something is near is the cause of its not twinkling, and that cause and effect are convertible terms: that which is near does not twinkle and that which does not twinkle is near. At the same time, the effect is, as usually, better known than the cause. Given these assumptions, consider the following syllogism: (20) That which does not twinkle is near Planets do not twinkle Hence, planets are near

115 Aristotle, APo A 13, 78a22–78b11; transl. Barnes, modified.

44

chapter 1

Here, the cause (“being near”) is inferred from the effect (“not twinkling”). The syllogism that infers the cause, or the less known, from the effect, or the better known, is a “syllogism of the that.” But since cause and effect are convertible terms, another syllogism is possible: (21) That which is near does not twinkle Planets are near Hence, planets do not twinkle Here, the effect (“not twinkling”) is inferred from the cause (“being near”). The syllogism that infers the effect, or the better known, from the cause, or the less known, is a “syllogism of the why.” In a demonstration τοῦ διότι something better known for us is inferred from something better known in itself, while, conversely, in a demonstration τοῦ ὅτι something better known in itself is inferred from something better known to us. The second example,116 about the sphericity of the moon inferred from its waxing (that-demonstration) or its waxing inferred from its sphericity (why-demonstration), illustrates the very same point. Sections (ii)–(iii) contain an exposition of the “paradigmatic” distinction between that- and why-demonstrations. We say “paradigmatic” because it is the clearest, the most popular, and the most commonly commented upon. Yet it already points to some of the difficulties of the remaining sections of the first part of APo A 13. For the distinction is introduced by saying that both these syllogisms are δι᾽ ἀμέσων, “from immediates.” If “from immediate” is taken to mean “from immediate premises,” then it is hard to see how “immediate” could straightforwardly be taken in the sense of APo A 2, i.e., as meaning “indemonstrable.” For the minor premise of (20) is in fact demonstrable; it is demonstrated in (21), where it occurs as the conclusion of a why-demonstration. Thus, it is hard to believe that “immediate” here means the same as it does in APo A 2, where “to be ‘immediate’ (amesos) is to lack a middle term.”117 To make some advance, let us consider section (i), where Aristotle presents the first of the two cases announced at 78a23, i.e., the case in which the syllogism is not from immediates (μὴ δι᾽ ἀμέσων). Taking sections (iv) and (v) as clarifications and illustrations of (i) may suggest a solution. For in (iv) Aristotle says: “where the middle terms do not convert and the non-cause is better

116 Aristotle, APo A 13, 78b4–11. 117 Barnes (1993), 94. Cf. Zuppolini (2021). Zuppolini solves the problem by distinguishing that-immedacy from why-immediacy. Our solution is different.

Aristotle on Signs and Demonstrations

45

known, the fact is proved but not the reason why.”118 It is clear that the case of non-converting cause and effect is opposed to the case of converting cause and effect introduced in section (ii) and illustrated in section (iii). Let us consider again section (ii): “In a second way [(ii)], if, [(iia)] although the syllogism does proceed through immediates, [(iib)] it proceeds not through the cause but through the better known of the converting terms.” In the first place, it appears that the subject-matter is the that-demonstration, implicitly contrasted with its corresponding why-demonstration. In the second place, section (ii) is composed of two sub-sections: section (iia) says that the argument is from immediates; section (iib) says that it is from one of two convertible terms. Reading section (i) along with section (iv) gives a parallel result: “In one way, [(i)] if the syllogism does not proceed through immediates […] [and] [(iv)] the middle terms do not convert and the non-cause is better known, the fact is proved but not the reason why.” Here again the subject-matter is a that-demonstration, implicitly contrasted with an impossible why-demonstration. Here, too, section (i) (parallel to section (iia)) says that the argument is not from immediates, and section (iv) (parallel to section (iib)) says that it is from one of two non-convertible terms. The close parallelism between the internal structure of section (ii) and the combination of sections (i) and (iv), together with the fact that just like section (ii) is illustrated by the examples in section (iii), so section (i) cum (iv) may be taken to be illustrated by the examples in section (v), suggests the following conjecture: δι᾽ ἀμέσων in this context means “from convertible terms” and μὴ δι᾽ ἀμέσων means “from non-convertible terms.”119 Our interpretation of APo A 13, however, does not depend on this strong assumption. It depends on the weaker assumption that the cases under consideration in the first part of APo A 13 are indeed two, one of which involves converting terms and the other non-converting terms, and that sections (ii) and (iii) introduce and illustrate the first case (converting terms) while section (i) together with sections (iv) and (v) introduce and illustrate the second case (non-converting terms). This, as we shall see in the following Chapters, is roughly the manner in which the first part of APo A 13 has been interpreted by both late-ancient and medieval commentators of the Posterior Analytics. 118 Aristotle, APo A 13, 78b11–13; transl. Barnes, modified. 119 Ferejohn (2013), 74–76, offers an extensional interpretation of the immediacy requirement in APo A 13, but his interpretation covers both what he calls “primitive proper inclusion” (i.e., “S is P” is “immediate” if there is no term extensionally intermediate between P and S) and co-extensiveness, while our conjecture only allow “immediate” terms to be co-extensive; the example in section (v) may involve Ferejohn’s primitive proper inclusion, and thus be “immediate” in his sense. That the (primary and most appropriate) cause must be convertible with the effect is persuasively shown by Angioni (2018).

46

chapter 1

We thus come to the second case, that involving non-converting terms. Here are sections (iv) and (v): [(iv)] Where the middle terms do not convert and the non-cause term is better known, the fact is proved but not the reason why. [(v)] Again, consider cases in which the middle term has outside position. Here too the demonstration gives the fact and not the reason why; for the cause is not stated. E.g. why do walls not breathe? Because they are not animals. If this were the cause of their not breathing, then being an animal would have to be the cause of breathing: i.e., if the negation is the cause of something’s not holding, then the affirmation is the cause of its holding […] But in the example set out above, the condition I have just stated is not satisfied—for not every animal breathes. A syllogism giving a cause of this type comes about in the middle figure. E.g. let A be animal, B breathing, C wall. A holds of every B (for everything which breathes is an animal), but of no C: hence B too holds of no C—therefore walls do not breathe. Causes of this sort resemble extravagant statements (i.e. when you argue by setting the middle term too far away)—e.g. Anacharsis’ argument that there are no flute-girls among the Scyths since there are no vines.120 Section (iv) contemplates a case involving two non-converting terms (one of which is better known than the other: this qualification matches with the parallel qualification in section (iii) concerning converting terms), but offers no examples of it. Section (v), then, presents an example involving non-converting terms (plus an allusion to Anacharsis’ argument, which follows the same pattern). Section (v), introduced by the adverb ἔτι (“again,” “moreover”), is said to be about a case in which “the middle has outside position.” That this expression has not to be taken as a reference to the second figure was already suggested by Philoponus, who claimed to be following Alexander in this.121 The example that follows is indeed a second-figure argument; but Aristotle’s explanation at 78b24 that “a syllogism giving a cause of this type comes about in the middle figure” is no repetition of something already stated. As the example shows, “the middle has outside position” may easily refer to the fact that the middle term has a greater extension than the major. This is perfectly coherent with our extensional interpretation of the whole chapter, and immediately

120 Aristotle, APo A 13, 78b11–31; transl. Barnes, modified. 121 Cf. Philoponus, In APo, ed. Wallies, CAG 13.3, 174.4–177.15; Barnes (1993), 157; Angioni (2018), 174.

Aristotle on Signs and Demonstrations

47

connects section (v) to section (iv), which indeed announces a case involving non-converting terms but offers no examples of it. Before proceeding to clarify further the relation between section (iv) and section (v), let us review the example contained in the latter section. It is the following second-figure syllogism: (22) Everything that breathes (B) is an animal (A) No wall (C) is an animal (A) No wall (C) breathes (B) The argument is a deductively valid syllogism in Camestres. The middle term, “animal,” has greater extension than the major (in the predicative sense), “breathes,” because there are animals that do not breathe (e.g., fish and insects122) but no breathing things that are not animal. Now, Aristotle asks, can we take the wall’s not being an animal as the cause of its not breathing? If this were the case, he answers, it should also be the case that its being an animal is the cause of its breathing. But since there are non-breathing animals, being an animal cannot be the cause of breathing, and thus not being an animal cannot be the cause of not breathing. Since the middle term does not express the cause of the major term (or of the major’s being predicated of the minor), the argument is not “of the why” and is “of the that” instead. It is important to notice that the rule according to which “if the negation is the cause of something’s not holding, then the affirmation is the cause of its holding” amounts to the rule that the “primary cause” (τὸ πρῶτον αἴτιον) of something must be co-extensive with that of which it is the cause. Of course, one may speak of “a cause” of something that is not coextensive with it. But if anything has to be the primary cause of something else, the two things are to be co-extensive. The syllogism of the why of sections (ii) and (iii) does in fact involve such a co-extensive cause.123 If something has some causal connection with something else (its effect) without being co-extensive with it, the argument that proves the effect from that non-primary cause is a demonstration of the that, not of the why. In order for the argument in section (v) to become a syllogism of the why, one should take a middle term that is co-extensive with the major and which would furnish the primary cause of it; an example comes from Themistius:

122 123

Cf. Aristotle, Part An IV.13, 697a21; IV.5, 678b1; cf. also Philoponus, In APo, ed. Wallies, CAG 13.3, 174.29–30. See Angioni (2018) on the coextensiveness of the primary cause and for a detailed and convincing analysis of the second-figure argument in APo A 13.

48

chapter 1

having lungs is the primary cause of breathing (and thus not having lungs is the primary cause of not breathing), so that if “having lungs” is taken instead of “being an animal” in (22), the argument becomes a syllogism of the why.124 Two issues remain to be addressed. The first issue is why Aristotle resorts to a syllogism in Camestres in making his point in section (v). For if we take the phrase “the middle has outside position” as a reference to the extension of the (non-primary) cause, then the argument is in the second figure only accidentally.125 The second issue is what the role of the epistemic characterization of the effect is in section (iv); for in the example in section (v) it is hard to see in what sense the effect (“not breathing”) can be “better known” than the non-primary cause (“not being an animal”). The two issues are connected. The two sections under consideration, section (iv) and section (v), do in fact involve non-converting terms; but both the second-figure example in section (v) and the epistemic characterization of the effect in section (iv) become explainable only on the supposition that section (iv) alludes (without illustrating it) to an argument in which a more extended cause (and thus, a non-primary one) is inferred from the effect (for the effect is better known than the non-primary cause), while section (v) illustrates an argument in which an effect is inferred from a more extended cause (and thus, a non-primary one). Consider the following argument, suggested by Themistius in his explication of section (iv):126 (23) Whoever gives birth has had sexual intercourse with a man This woman has given birth Hence, this woman has had intercourse with a man The fact that a woman has given birth is generally better known than her having had intercourse with a man, which latter may be taken as the cause of it. Not, however, as the primary cause, because the terms do not convert: not all intercourses have that effect (the cause is non-primary as it has a greater extension than the effect). So (23) perfectly illustrates the case under consideration in section (iv). Now consider the following inversion of it: (24) Whoever gives birth has had sexual intercourse with a man This woman has not had intercourse with a man Hence, this woman has not given birth 124 Themistius, In APo, ed. Wallies, CAG 5.1, 28.3–7; cf. infra, §2.2. 125 Cf. Barnes (1993), 157. 126 Cf. infra, §2.2. The example is also used by Philoponus and is found in several later works; cf. infra, §§2.3, 3.4

Aristotle on Signs and Demonstrations

49

Here the negation of the non-primary cause is inferred from the negation of the effect. The example is perfectly parallel to the non-breathing wall of section (v). Both (23) and (24) are deductively valid, and both involve a cause that is more extended than the effect (thus both are μὴ δι᾽ ἀμέσων, “not from immediates,” if our conjecture is accepted). But while (23) infers the non-primary cause from the effect, (24) infers the negation of the effect from the negation of the non-primary cause. In other words, if deductive validity has to be preserved, the inference from a non-primary cause must be in the second figure, i.e., can only negatively infer the effect from the non-primary cause , while the inference of a non-primary cause can be in the first figure. Our analysis of the first part of APo A 13 thus involves, as the Latin tradition of the Posterior Analytics would explicitly recognize,127 a fourfold typology of demonstrations: when cause and effect convert, (1a) the demonstration is of the why if the effect is inferred from the (primary) cause, and (1b) the demonstration is of the that if the (primary) cause is inferred from the effect; when the cause is more extended than the effect, (2a) the demonstration is of the that if the (non-primary) cause is inferred from the effect, and (2b) is also of the that if the negation of the effect is inferred from the negation of the (non-primary) cause. The case of an effect more extended than the cause (should we say, then, a “non-primary” effect?) is not discussed by Aristotle, and with some justification. From an effect that is more extended than the cause no deductively valid inference to the cause can be made, and indeed only an invalid inference in the second-figure can be made (like the second-figure sign-syllogism of APr B 27 and the fallacy of the consequent of Soph El 5). As Philoponus would recognize, in this case only a demonstration from the cause to the effect is deductively valid.128 But Aristotle implicitly refuses to call such an inference a “demonstration of the why.” Do all the three type of syllogisms τοῦ ὅτι of APo A 13 qualify as demonstrations? Both the syllogism inferring the cause from the effect (1b) and the syllogism inferring the negation of the effect from the negation of the non-primary cause (2b), explicitly receive the title of ἀπόδειξις (1b at 78a30, 2b at 78b14); the

127

As we shall see in what follows, an explicitly “extensional” interpretation of APo A 13 was advocated by Albert the Great, Aquinas, and Giles of Rome in their commentaries on the Posterior Analytics. The fourfold typology that results from it is also found in Grosseteste and Kilwardby; see infra, Chapter 5. 128 Cf. infra, §2.3.

50

chapter 1

syllogism inferring the non-primary cause from the effect (2a) is not explicitly called an ἀπόδειξις, but at 78b13 Aristotle says that in that case the that is “proved” (δείκνυται). The problem is not merely terminological: if an argument qualifies as an ἀπόδειξις only in case it satisfies the six requirements of APo A 2, then the syllogisms of the that of APo A 13 are not entitled to that qualification, for at least the causal requirement fails in all of them.129 Barnes thinks that in calling the “syllogism of the that” an ἀπόδειξις Aristotle is “countenancing a weaker sense of ‘understand’ [which is Barnes’ translation for ἐπίστασθαι] than his official one.”130 Lloyd considers the ἀπόδειξις obtained by a “syllogism of the that” as indicating a relaxation of the ultra-strict conditions set out in APo A 2.131 Mignucci observes that the role of the demonstration τοῦ ὅτι in the overall economy of APo A 13 is to show how a demonstration τοῦ ὅτι of the first type (1b) might serve to the construction of a demonstration τοῦ διότι, especially by providing premises to the latter: thus, the demonstration τοῦ ὅτι that infers that planets are near from their not twinkling is subservient to the corresponding demonstration τοῦ διότι because it provides material, i.e., adequate premises, for the latter.132 But by thus making the demonstration τοῦ ὅτι subordinate to the demonstration τοῦ διότι, Mignucci implicitly accepts Barnes’ idea that the demonstration τοῦ ὅτι is a demonstration only in a weak sense, while demonstrations in the strong sense (the sense outlined in APo A 2) can only be a demonstration τοῦ διότι. We shall see in what follows that some such distinction between a strong and a weak sense of ἀπόδειξις may have some role to play in the Aristotelian theory of semiotic inferences. 6.2 Demonstrations καθ’αὑτό and Demonstrations κατὰ συμβεβηκός Chapter 4 of the Posterior Analytics adds further requirements to demonstration, which we have to examine because they seem to be involved in both of Aristotle’s mentions of sign-inferences in that work. At APo A 4, 73a34–b16 Aristotle distinguishes four senses in which something can hold or be predicated of something else καθ’αυτό (“in itself”). In the first sense, A holds of B καθ’αὑτό if A is predicated ἐν τῷ τί ἐστι, “in the what-it-is,” of B, that is, if A is

129

130 131 132

That the inference of the negation of the effect from the negation of the non-primary cause (2b) should not satisfy the requirements of APo A 2 is not immediately evident. But it can be gathered from APo A 14, 79a27, where it is said that scientific knowledge is affirmative; cf. also APo A 25, 86b30–39 about privative demonstrations. Barnes (1993), 155. Lloyd (1989), 377. Mignucci (1975), 301–302.

Aristotle on Signs and Demonstrations

51

contained in the definition of B.133 Thus, “animal” holds καθ’ αὑτό of “man” because it is contained in the definition of “man” (man is a rational animal). Aristotle’s geometrical examples of APo A 4 satisfy this requirement: “line” holds of “triangle” καθ’αὑτό because it is contained in the definition of the latter (a triangle is a figure bounded by three straight lines); “point” holds of “line” καθ’αὑτό because it is contained in the definition of the latter (a line is a flowing point134). In the second sense, A holds of B καθ’αὑτό if B is contained in the definition of A. No definition of “straight” and “curve” could fail to include “line,” as no definition of “even” and “odd” could fail to include “number”; in this sense, “straight” and “curve” hold of “line” καθ’αὑτό (in the second sense), and “odd” and “even” hold of “number” καθ’αὑτό (in the second sense). As Aristotle’s mathematical examples unmistakably show, typically a differentia holds καθ’αὑτό (in the second sense) of its genus.135

133

134 135

In the Topics the notion of “being predicated in the what-it-is” is explained as follows: “those sorts of things are ‘predicated in the what-it-is’ (ἐν τῷ τί ἐστι κατηγορούμενον) which it would be appropriate to give as answers when asked what the thing in question is (τί ἐστι), as it is appropriate in the case of a man, when asked what it is, to say that it is an animal” (Aristotle, Top A 5, 102a32–35; transl. Smith). The genus primarily and eminently is predicated ἐν τῷ τί ἐστι of the species; thus, “animal” is predicated ἐν τῷ τί ἐστι of “man.” But the difference too is predicated ἐν τῷ τί ἐστι of the species (Top Θ 5, 154a28). Genus and difference form together the definition (ὁρισμός), or discourse that says the τί ἦν εἶναι or “essence” of the thing defined (154a32). To be predicated ἐν τῷ τί ἐστι of something is to be part of its definition. This definition is non-Aristotelian; it is proposed by Philoponus (In APo, ed. Wallies, CAG 13.3, 60.24). On the problem raised by Aristotle’s geometrical examples in APo A 4 see Mignucci (1975), 59–60; Barnes (1993), 112–113. But that the definition of the differentia must mention the genus does not yet show that καθ’αὑτό predication in the second sense always concerns differentiae predicated of a genus; cf. Barnes (1993), 114. Granger (1981) persuasively argues that a differentia is a type of what Aristotle in other places calls καθ’αὑτό accidents (Aristotle, APo A 7, 75b1, A 22, 83b19–20; Met Δ 30, 1025a30–31), i.e., is a καθ’αὑτό accident of the genus. It is far from clear how καθ’αὑτό accidents should fit within the typology of καθ’αὑτό predications of APo A 4. A case could however be made for the view that at least some καθ’αὑτό accidents are καθ’αὑτό predications in the second sense of APo A 4. For at APo A 4 the examples of καθ’αὑτό predications in the second sense are clearly examples of differentiae of a genus (straight and curve with respect to the line, even and odd with respect to the number). And since, as Granger has argued, a differentia is a type of καθ’αὑτό accident, it follows that at least some καθ’αὑτό accidents (namely, those that are differentiae) are καθ’αὑτό predications in the second sense. The identification of καθ’αὑτό predication in the second sense and καθ’αὑτό accidents is suggested by Mignucci (1975), 79.

52

chapter 1

In the third sense, A holds of B καθ’αὑτό if B is said of A in virtue of what A is, and not in virtue of A’s being something else. An example from A 22 is helpful here. When I say that “the log is white,” “white” holds of “log” καθ’αὑτό because it is by being log that the log is white; on the contrary, when I say that “the white thing is a log,” “log” does not hold of “white” καθ’αὑτό, because it is not by being white, but by being something else, that the white is log. In the fourth sense, A holds of B καθ’αὑτό if A and B are two events that occur together and one is the cause of the occurrence of the other. Thus, if there was lightning while I was walking it was not because of my walking that there was lightning. But if I die while being sacrificed, I die because of the sacrifice. This second case counts as a καθ’αὑτό predication in the fourth sense. Lucas Angioni has persuasively argued that the expression καθ᾿αὑτό is often used in opposition to the expression κατὰ συμβεβηκός.136 What does not hold καθ᾿αὑτό in either of the four senses explained in APo A 4 holds κατὰ συμβεβηκός or accidentally. As we shall see in the next section, some such opposition is actually at work in the two passages of the Posterior Analytics that mention signs. Before considering those two passages, it is helpful to say something more about the opposition in question.137 The expressions καθ᾿αὑτό and κατὰ συμβεβηκός may be used to characterize a predicative relation, i.e., the relation between subject and predicate in a proposition. The sense of συμβεβηκός as “contingent attribute” belongs to this predicative dimension of the opposition (without exhausting the opposition, however). But these expressions can also be used to characterize the manner in which the middle term of the demonstration performs its causal or explanatory role with respect to the predication expressed in the conclusion of the demonstration. In their first use, καθ᾿αὑτό and κατὰ συμβεβηκός characterize the dyadic relation between subject and predicate in a proposition; in their second use, they characterize the triadic relation between major, middle, and minor in a (demonstrative) syllogism. In this second, triadic use the expression καθ᾿αὑτό is an attribute of ἀπόδειξις or some cognate of it: “ἀπόδειξις καθ᾿αὑτὸ […] ἐστί”;138 “καθ᾿αὑτὸ ἀποδέδεικται.”139 With respect to this second use of them, the expressions καθ᾿αὑτό and κατὰ συμβεβηκός should be taken to mark the opposition between a proper demonstration and an improper demonstration. A conclusion is demonstrated καθ᾿αὑτό when the middle term introduces the “appropriate” cause of the fact expressed in the conclusion. By contrast, a conclusion is demonstrated κατὰ 136 See Angioni (2016), Angioni (2020). 137 We follow Angioni (2016). 138 Aristotle, APo A 4, 74a1–2. 139 Aristotle, APo B 17, 99a2.

Aristotle on Signs and Demonstrations

53

συμβεβηκός when the middle term does not introduce the cause, or introduces an inappropriate cause, of the fact expressed in the conclusion. Two things are to be noticed here. First, an appropriate cause must convert with that of which it is the cause; this much is implied by Aristotle’s discussion of the cause-effect relationship in APo A 13, where it is clear that a “primary” cause is co-extensive with the effect, and this is a condition that has to be satisfied if anything has to be a cause in this sense. But co-extensiveness is only a logical, extensional requirement. It is a necessary but not sufficient condition for being the appropriate cause. Of course, it is tempting to simply identify καθ᾿αὑτό demonstrations with why-demonstrations and κατὰ συμβεβηκός demonstrations with that-demonstrations; but nothing in Aristotle’s text guarantees that the identification is correct. As we shall see in what follows and as it has been already anticipated, the whole tradition of Posterior Analytics commentaries assumes some distinction between proper and improper demonstrations, onto which the why/that distinction is usually projected. But that also the καθ᾿αὑτό/ κατὰ συμβεβηκός distinction is to be projected onto the why/that distinction no commentator seems to have claimed. Secondly, it is important to notice that that something is demonstrated κατὰ συμβεβηκός does not mean that the deductive validity of the argument is compromised. Quite the contrary, something may be concluded κατὰ συμβεβηκός while being a perfectly true conclusion of a perfectly valid deductive argument. 6.3 Demonstration in Phys A 1 One more observation is in order. The “strong” notion of demonstration that Aristotle expounds in the Posterior Analytics, and especially in APo A 2, seems to be in tension with what Aristotle says in a famous passage from the ouverture of the Physics about the method of natural science. In Physics A 1, Aristotle says that we have scientific knowledge when we know the principles and the causes of something.140 This is in agreement with APo A 2, where it is said that we have scientific knowledge when we know the cause why something is, that it is its cause, and that it cannot be otherwise.141 However, as we know in APo A 2 Aristotle also says that things can be said to be better known and prior for us or by nature, and we noticed that the causal requirement, according to which the premises of demonstration must be cause of the conclusion, entails that the premises must by nature be better known than and prior to the conclusion.142 Now, in Physics A 1 Aristotle says that the method of investigation 140 Aristotle, Phys A 1, 184a10–16. 141 Aristotle, APo A 2, 71b9–12. 142 Aristotle, APo A 2, 71b33–72a4.

54

chapter 1

must start from what is better known and clear for us and proceed from these to what is better known and clear by nature.143 This idea is clearly in tension with the doctrine of APo A 2. The tension between Phys A 1 and APo A 2 did not pass unnoticed. For example, in his commentary on the Physics, Philoponus observes that it was “a matter of debate […] why Aristotle says [in the Physics] that universals are posterior in nature and less clear, but to us prior and clearer, given that elsewhere he suggests the opposite.”144 Ross notices the same tension and suggests a conciliatory interpretation: “Aristotle is there [in APo A 2] stating the nature of scientific proof. Here [in Phys A 1], on the other hand, he is describing the method of attaining knowledge of the ἀρχαὶ […] This is the very reverse of scientific proof.”145 Demonstration would go from the cause (better known by nature) to the effect (better known for us), while the method of knowing principles would go from the effect (better known for us) to the cause (better known by nature).146 The analogy with the why/that distinction of APo A 13 stands out. Be that as it may, it is certain that the ancient and medieval commentators of the Physics have interpreted the passage from Physics A 1 like Ross has, i.e., as containing an opaque reference to a lower kind of demonstration, and 143 Aristotle, Phys A 1, 184a16–18. Similar descriptions of a method from what is better known to us are found in other places, too. In the Nicomachean Ethics the method presented in Phys A 1 and in that context limited to the science of nature is extended to politics, where one proceeds from what is better known to us to what is better known by nature. The two proceedings are here termed argument “from the principles” (which are better known in nature) and argument “to the principles” (i.e., from the principled, better known to us) (Eth Nic A 2, 1095b2–4). In the De Anima a similar claim concerns the investigation about the soul: here one also starts from what is confused but more apparent and proceed to what is clearer and better known by reason (De Anima B 2, 413a11–13). In the Metaphysics, the description of method of Phys A 1 is extended to all knowledge (Met Z 3, 1029b3–12). 144 Philoponus, In Phys, ed. Vitelli, CAG 16, 10.23–25, transl. Osborne. 145 Ross (1936), 456–457. 146 Another solution takes what Aristotle says at Phys A 1, 184a23–25, that one starts from generals to particulars, or from the whole to its elements, to refer to the preceding description (184a16–18) of the method of investigation as proceeding from what is better known and clear for us to what is better known and clear by nature. An effect is in no obvious sense a whole whose elements correspond to its cause; nor is it a general with respect to a particular cause; Aristotle is therefore not thinking of the demonstration of the cause from the effect; and if he is not, then the relation of Phys A 1 to APo A 2 is less problematic than it appeared; see Ross (1936), 457. Bolton (1995) argues that the description of method in Phys A 1 is fully compatible with the method of getting to the first principles of science discussed in APo B 8 and APo B 19. Dutmer (2020) argues that what is better known to us in Phys A 1 is what Aristotle goes on to consider in Phys A 2—that nature exists and that natural things change—and that these are indeed the starting points from which we get to the principles and the causes.

Aristotle on Signs and Demonstrations

55

some have even construed the method of knowing principles of which Aristotle speaks in that chapter as a sign-inference from effects to causes, as we shall see in the next Chapters. 7 Signs versus Demonstrations We should now be in the position of fulfilling the promise made at beginning of this Chapter, i.e., of providing an elucidation of the two passages of the Posterior Analytics in which demonstration is contrasted with sign-inference. Two other places will be considered at the end of this section which shed further light on this contrast. It has first to be noted that in the context of the Analytics, Aristotle does not generally deal with demonstrations with singular terms, though he sometimes does deal with sui generis singulars as the moon, the sun, etc.147 At APo A 6 Aristotle contrasts proper demonstrations with improper demonstrations (sign-syllogisms), and these latter do include singular terms. A first, obvious way of contrasting demonstration proper and demonstration from signs is therefore at Aristotle’s disposal. But the contrast that Aristotle draws has nothing to do with the singularity of terms. It rather concerns the nexus between cause and effect in a causal demonstration. Here is the first passage in which demonstration is contrasted with sign-syllogisms: Since in each kind whatever holds of something in itself (καθ᾿αὑτά) and as such holds of it from necessity, it is clear that scientific demonstrations are concerned with what holds of things in themselves (καθ᾿αὑτά) and that they proceed from such items. For what is incidental is not necessary (συμβεβηκότα οὐκ ἀναγκαῖα), so that you do not necessarily know why the conclusion holds (οὐκ ἀνάγκη τὸ συμπέρασμα εἰδέναι διότι ὑπάρχει). Not even if it is the case always but not in itself, as for example in syllogisms through signs (οὐδ᾿ εἰ ἀεὶ εἴη, μὴ καθ᾿αὑτὸ δέ, οἷον οἱ διὰ σημείων συλλογισμοί). For you will not understand in itself (καθ᾿αὑτό) something that holds in itself (καθ᾿αὑτό), nor will you understand why it holds. (To understand why is to understand by way of the cause). Therefore, the middle term must hold of the third term, and the first of the middle, because of itself.148 147 Cf. Morrison (1997), 12. 148 Aristotle, APo A 6, 75a28–37; transl. Barnes, modified.

56

chapter 1

This passage involves several difficulties. One of these is that Aristotle seems to be equating “holding καθ᾿αὑτό” and “being necessary.”149 Of course, the necessitas consequentiae is not in question here: in order to qualify as a demonstration a syllogism has to be deductively valid. Quite another thing is to say that in order to qualify as a demonstration a syllogism has to have necessarily true premises and necessarily true conclusions (necessitas consequentis et antecedentis). This seems to be a too stringent requirement even for Aristotelian demonstrations. It is safer to assume that “being necessary” (ἀναγκαῖον) here, as in some other contexts, means “being the required middle term that expresses the cause of the fact expressed in the conclusion.”150 On the assumption that “holding καθ᾿αὑτό” and “being necessary” are not equal the purpose of the passage becomes more acceptable: Aristotle wants to argue that scientific demonstrations are concerned with what holds of things in themselves and that they proceed from such items, i.e., are concerned with καθ᾿αὑτό predications (in the conclusion) and proceed from καθ᾿αὑτό predications (in the premises). This is repeated at the end of the passage (which is also the end of APo A 6): the middle term must hold of the third term because of itself (δι᾿αὑτό), and the first must hold of the middle in the same manner. Another problem is that Aristotle seems to be using the expression “καθ᾿αὑτό” both as a characterization of the predicative relation expressed in the premises and conclusion of a demonstration, and as a characterization of the syllogistic relation between premises and conclusion in a demonstration. This latter problem confirms that we should distinguish, with Angioni, a dyadic and a triadic sense of the opposition between “καθ᾿αὑτό” and “κατὰ συμβεβηκός.” Both senses seem to be present in the sentence “you will not understand in itself (καθ᾿αὑτὸ ἐπίστήσεται) something that holds in itself (καθ᾿αὑτό)”: to understand καθ᾿αὑτό something is to have a καθ᾿αὑτό demonstration of it, i.e., a demonstration in which the middle term introduces the appropriate cause of the fact expressed in the conclusion. It is not clear, however, whether premises expressing καθ᾿αὑτό predications (dyadic sense) are sufficient for a conclusion, which itself may be a καθ᾿αὑτό predication, to be said to have been demonstrated καθ᾿αὑτό (triadic sense). However, it is clear that the opposition between a καθ᾿αὑτό and a κατὰ συμβεβηκός demonstration forms the backdrop for the whole passage, and the reference to the συλλογισμοὶ διὰ σημείων has to be interpreted with that contrast in mind. In a sign-syllogism, the major premise does not express a καθ᾿αὑτό predication (in the dyadic sense). The predicate may hold of the subject always, but if it does not hold καθ᾿αὑτό it only holds κατὰ συμβεβηκός. 149 150

Cf. Barnes (1993), 139–140; against this see Angioni (2016). Cf. Angioni (2014) and (2016).

Aristotle on Signs and Demonstrations

57

Some commentators151 take the accidents of 75a31 to be “inseparable accidents”: an inseparable accident “is the case always but not in itself” (ἀεὶ εἴη, μὴ καθ᾿αὑτό). Having milk is an inseparable accident of having given birth, but is not a καθ᾿αὑτό predicate of it. If we further accept—and it is by no means clear that we should do so—that premises expressing καθ᾿αὑτό predications (dyadic sense) are sufficient for a conclusion to be demonstrated καθ᾿αὑτό (triadic sense), then it also follows that in a sign-syllogism the conclusion is not demonstrated καθ᾿αὑτό (triadic sense). Now, we saw that a conclusion is demonstrated καθ᾿αὑτό when the middle term introduces the appropriate cause of the fact expressed in the conclusion. Then, in a sign-syllogism the middle term is not the cause of the fact expressed in the conclusion: the syllogism that we can construct with “having milk” as middle term is deductively valid, but the conclusion is not demonstrated καθ᾿αὑτό (in the triadic sense), but only κατὰ συμβεβηκός. A sign-syllogism is deductively valid because its premises contain a predication that is “always” true; but that predication is not καθ᾿αὑτό, and thus the conclusion is not demonstrated καθ᾿αὑτό in the sense specified. According to APo A 6, a sign-syllogism qualifies as a κατὰ συμβεβηκός demonstration. If this interpretation is correct, then the term σημεῖον at 75a33 is used in the wide sense registered at APr A 27, 70b1, the sense that includes both τεκμήρια (first-figure sign-syllogisms) and σημεῖα in the strict sense (secondand third-figure sign-syllogisms). For a σημεῖον in the strict sense (70b4) not only fails to qualify as a καθ᾿αὑτό demonstration; it also fails to qualify as a valid deduction at all: second- and third-figure signs are deductively invalid; they lack necessitas consequentiae. Therefore, when Aristotle in the passage in question contrasts proper demonstrations with the συλλογισμοὶ διὰ σημείων, he cannot have the strict sense of σημεῖον in mind. Moreover, for the very same reason, in that context he should have talked of τεκμήρια, not of σημεῖα (although in the wide sense), and should have rather contrasted demonstrations with the συλλογισμοὶ διὰ τεκμηρίων. In a first-figure sign-syllogism, the major premise predicates an inseparable accident of a subject, which “is the case always but not in itself” (ἀεὶ εἴη, μὴ καθ᾿αὑτό). A τεκμήριον shows something but only κατὰ συμβεβηκός, because it does not move from a καθ᾿αὑτό predication. As we shall see in the next Chapter, Philoponus seems to have been the first to realize this point, because in his commentary on the first book of the Posterior Analytics he prefers to contrast demonstration proper with what he calls τεκμηριώδης ἀπόδειξις, “tekmeriodic” demonstration. A tekmeriodic demonstration is a 151 See infra, §5.2.

58

chapter 1

demonstration τοῦ ὅτι which, though necessary (i.e., deductively valid), yet fails to demonstrate through an appropriate cause. In the terminology of APo A 6, is not a καθ᾿αὑτό demonstration but only a κατὰ συμβεβηκός demonstration. As mentioned above, Aristotle nowhere suggests that κατὰ συμβεβηκός demonstrations are somehow associated with that-demonstrations. The association is made by the commentators. What Aristotle does suggest is that a sign-­inference demonstrates something, but only κατὰ συμβεβηκός. The second passage from the Posterior Analytics in which sign-inferences are mentioned requires a different analysis: Can it or can it not be the case that the cause (αἵτιον) of some feature is not the same for every item but different for different items? If the conclusions have been demonstrated in themselves (καθ’αὑτὸ ἀποδέδεικται), and not in virtue of a sign or an accident (μὴ κατὰ σημεῖον ἢ συμβεβηκός), then perhaps it is not possible, for the middle term is the account (λόγος) of the extreme. But if they have not been demonstrated in this way, perhaps they can be different.152 As in the passage from APo A 6, proper καθ᾿αὑτό demonstrations are contrasted with improper demonstrations. Unlike in that passage, however, the improper demonstration is said to be through a middle that is a sign or an accident (κατὰ σημεῖον ἢ συμβεβηκός). Such assimilation of signs and accidents reinforces our interpretation of the passage in APo A 6 as being founded upon the opposition between καθ᾿αὑτό and κατὰ συμβεβηκός demonstrations, where sign-syllogisms belong to the latter pole of the opposition. The central question of APo B 17 is whether or not the cause of an attribute is the same for different things. With “different things” Aristotle means “different things belonging to one kind,” as will soon become apparent. Aristotle notices that a causal relationship involves three terms: the cause (τὸ αἴτιον), that of which it is the cause (τὸ οὗ αἴτιον), and that for which it is the cause (τὸ ᾧ αἴτιον).153 These correspond to the three terms of a typical syllogistic demonstration: that of which it is the cause (τὸ οὗ αἴτιον) is the major term (A), that for which it is the cause (τὸ ᾧ αἴτιον) is the minor term (C), and the cause (τὸ αἴτιον) is the middle term (B). The central question of the chapter, then, is whether the cause (τὸ αἴτιον) of the belonging of an attribute (τὸ οὗ αἴτιον) is the same for distinct things (τὸ ᾧ αἴτιον) or whether it is different for each. Aristotle’s initial answer to this question is that if the conclusion is 152 Aristotle, APo B 17, 99a1–4; transl. Barnes, modified 153 Aristotle, APo B 17, 99a17–18.

Aristotle on Signs and Demonstrations

59

demonstrated καθ᾿αὑτό, then the cause (τὸ αἴτιον) of the belonging of an attribute (τὸ οὗ αἴτιον) must be the same for different things (τὸ ᾧ αἴτιον), while if the conclusion is not demonstrated καθ᾿αὑτό, then it is possible that the cause (τὸ αἴτιον) of the belonging of an attribute (τὸ οὗ αἴτιον) is different for different things (τὸ ᾧ αἴτιον). It is clear that it is the triadic, not the dyadic sense of καθ᾿αὑτό that is at play here. Aristotle imagines a situation in which to each of the things of which an attributed is predicated in the conclusion of a demonstration there corresponds a distinct cause. Thus, if D and E are both A, it may be the case that the cause of D’s being A is B, while the cause of E’s being A is C. He then argues that this is possible only if D and E are not the same in form, i.e., do not belong to the same species. To show this, he proposes to investigate how the three terms “follow reciprocally” (παρακολουθεῖν ἀλλήλοις) in a demonstration, i.e., how the three terms are related to one another extensionally. Suppose that that of which something is the cause (τὸ οὗ αἴτιον), A, is more extended than the different things for which it is the cause (τὸ ᾧ αἴτιον), D and E, but that, taking D and E collectively, A is coextensive with them. (The cause’s equal or greater extension with respect to the attribute or effect, τὸ οὗ αἴτιον, is a distinct question.) For example, both vine (D) and fig (E) shed their leaves (A); shedding leaves (A) is more extended than either vine (D) or fig (E) taken separately, but is coextensive with them taken collectively.154 Now the question is, is the cause of the vine’s and the fig’s shedding their leaves the same for both, or different? Aristotle believes that the cause of their shedding their leaves can be unique if fig and vine are treated as members of a common kind or species, “that all are such and such,”155 e.g., that they are broad-leaved trees. Call the species to which vine and fig belong F. Then, a more appropriate demonstration of their shedding their leaves is available: broad-leaved trees (F) shed their leaves (A) because the sap solidifies at the connection of the seed (B). In syllogistic form: (25) Solidification of sap (B) holds of all broad-leaved trees (F) Shedding leaves (A) holds of solidification of sap (B) Therefore, shedding leaves (A) holds of all broad-leaved trees (F) Such a demonstration as (25) is possible only if E and D, fig and vine, are of the same form, i.e., belong to one species, F. If this is not the case, then different causes, i.e., different middle terms, can be found that explain the predication 154 Aristotle, APo B 17, 99a23–25. 155 Aristotle, APo B 17, 99a27.

60

chapter 1

expressed in the conclusion. For example, both quadrupeds (D) and birds (E) are long-lived (A); is the cause of their longevity the same for both, or different? Quadrupeds and birds are different in form, i.e., are not of the same ­species; their longevity is thus to be explained by reference to different causes: the cause of longevity for quadrupeds is their not having bile, while for birds it is their being dry.156 Aristotle’s conclusion, reached at the end of the chapter after a complex and admittedly obscure argumentation, is therefore that “it is possible for there to be several causes of the same feature—but not for items of the same form.”157 In Barnes’ words, the idea is that “there cannot be different explanations [i.e., causes] of the same attribute for different individuals of the same species; but there can be different explanations [i.e., causes] of the same attribute for ­different types of thing.”158 If this is what Aristotle has in mind in the whole of APo B 17, what is the role of the reference to signs in the ouverture of the chapter? Aristotle says that if the demonstration is not κατὰ σημεῖον ἢ συμβεβηκός, then the cause of an attribute must be unique for different items; this implies that if on the contrary the cause is different for each item, then the demonstration is κατὰ σημεῖον ἢ συμβεβηκός. Suppose we are confronted with the following syllogism: (26) Broad-leaved trees shed their leaves The fig is a broad-leaved tree Therefore, the fig sheds its leaves Here, the major and the middle term convert (all broad-leaved trees shed their leaves and all trees that shed their leaves are broad-leaved), but the middle is not the cause of the major. As Aristotle has argued, the cause of shedding leaves is a further middle term, the solidification of the sap at the connection of the seed, which is true of all the members of the species to which the fig belongs. In a sense, this is a sign-argument: being a broad-leaved tree may be taken to be the “better known” of two convertible terms, from which the other term can be inferred through a deductively valid syllogism of the that of the first type (1b). In the terms of APr B 27, we would have a τεκμήριον: having broad leaves is the necessary sign of shedding leaves, but not the cause of it.

156 Aristotle, APo B 17, 99b15–17. 157 Aristotle, APo B 17, 99b4–5. 158 Barnes (1993), 255.

Aristotle on Signs and Demonstrations

61

In the terms of APo A 6, that broad-leaved trees shed their leaves “is the case always but not in itself” (ἀεὶ εἴη, μὴ καθ᾿αὑτό). It should be remarked that having broad leaves is no “accident” of the fig in the sense of a contingent predicate. The “accidentality” is rather a triadic character of the demonstration: since the conclusion is not demonstrated through the appropriate cause, the demonstration is not καθ’αὑτό; it is κατὰ σημεῖον ἢ συμβεβηκός. In this perspective, only in proper (i.e., causal) demonstrations the conclusion can be said to be demonstrated καθ’αὑτό. In demonstrations other than proper ones the conclusion is demonstrated κατὰ συμβεβηκός: sign-­ syllogisms are of this latter kind. Hence, if we are to make sense of Aristotle’s contrast between demonstration and sign in the two passages from the Posterior Analytics under examination, we have to recognize that in both passages a proper, καθ’αὑτό demonstration (in the triadic sense) is contrasted with an improper, κατὰ συμβεβηκός ­demonstration. Sign-syllogisms qualify as κατὰ συμβεβηκός demonstrations because they do not infer an effect from its appropriate cause, but the cause from the effect. In both cases, what Aristotle has in mind is a deductively valid syllogism that corresponds to the first-figure sign-syllogism or τεκμήριον (Philoponus’ τεκμηριώδης ἀπόδειξις). In neither the passage in APo A 6 nor in that in APo B 17 does Aristotle associate such κατὰ συμβεβηκός demonstration with the first species of syllogism of the that of APo A 13 (1b). Such association is, however, quite natural, and will be explicitly made by later commentators.159 Two other places are relevant for the determination of the Aristotelian opposition between sign and demonstration. One is the following passage from the Sophistici Elenchi: In rhetorical arguments proofs from signs (κατὰ τὸ σημεῖον ἀποδείξεις) are founded on consequents (ἐκ τῶν ἐπομένων); for, when men wish to prove that a man is an adulterer, they seize upon the consequent of that ­character, namely, that the man dresses himself elaborately or is seen wandering around at night—facts that are true of many people, while the accusation is not true.160

159

The interpretation of APo B 17, 99a1–4 offered in Bellucci (2018) ignores some of the difficulties pointed out here. That interpretation is substantially equivalent to that given by Alexander of Aphrodisias and Themistius (cf. infra, §§2.2, 2.3) as well as by some medieval commentators of the Posterior Analytics (cf. infra, Chapter 5). 160 Aristotle, Soph El 5, 167b8–12; transl. Forster, modified.

62

chapter 1

The “demonstration from a sign” is a species of the fallacy of the consequent. Aristotle explains that this fallacy derives from thinking that “the consequence converts” (ἀντιστρέφειν τὴν ἀκολούθησιν).161 The “consequence” (ἀκολούθησις) mentioned here should be construed as an implication of two characters or events which may be expressed by distinct but equivalent sentences, for example by an affirmative categorical proposition (“Every A is B”), or by a conditional proposition (“If A then B”). The fallacy thus comes from thinking that in the categorical proposition subject and predicate can be transposed (“Every B is A”) or, equivalently, that in the conditional proposition protasis (antecedent) and apodosis (consequent) can be transposed (“If B then A”). There is no evidence that Aristotle himself would express the “consequence” as a conditional proposition, as all of his examples are cast in terms of categorical propositions. We should follow his usage, and will accordingly take τὸ ἐπόμενον to indicate not the apodosis of a conditional proposition, but the predicate of a categorical proposition, bearing in mind that the conditional formulation is perfectly equivalent to the categorical.162 The fallacy of the consequent derives from taking as minor premise of an argument a proposition whose predicate is the “consequent,” i.e., the predicate of the major premise: Every A is B C is B Therefore, C is A This argument is invalid because it is asyllogistic: no syllogism is valid in the second figure with affirmative premises. It would be valid if the major premise were convertible, because it would become a valid first-figure syllogism; and this is the reason why Aristotle insists that this fallacy results from thinking that the “consequence” expressed in the major premise is convertible. Aristotle offers three groups of examples of the fallacy of the consequent, one of which is the κατὰ τὸ σημεῖον ἀπόδειξις.163 The example of this group is problematic in that Aristotle offers two “consequents” of being an adulterer: smartly dressing and wandering about at night. For a correct interpretation of the example, these should be taken to constitute two parallel consequents in

161 Aristotle, Soph El 5, 167b1–2. 162 See Schreiber (2003), 130–139. 163 The other two are the fallacy deriving from perception (examples of yellow gall and of wet ground) and the fallacy in syllogistic arguments (example of Melissus’ argument for the infinity of the world).

Aristotle on Signs and Demonstrations

63

two parallel and distinct examples, and not as the two disjuncts of a disjunctive consequent in one and the same example.164 (27a) All adulterers are nighttime wanderers This man wanders about at night Hence, this man is an adulterer (27b) All adulterers dress smartly This man is smartly dressed Hence, this man is an adulterer Wandering about at night and smartly dressing are “signs” of adultery, but only fallible signs, because the inference they allow is deductively invalid. Once it is syllogistically reconstructed the inference appears as a second-figure invalid syllogism. It would be valid if the major premise were convertible, for in that case we would have a valid first-figure syllogism in Barbara. In the expression κατὰ τὸ σημεῖον ἀπόδειξις, σημεῖον has therefore to be taken in the strict sense of APr B 27, 70b4, while ἀπόδειξις is only used in an improper sense, for on Aristotelian principles no ἀπόδειξις can fail to be deductively valid. A second-figure sign-syllogism is thus an instance of the fallacy of the consequent; it βούλεται εἶναι an ἀπόδειξις but is not one, for it falls short of deductive validity. Soph El 5 does not mention causal relationships, but on the basis of the preceding discussion it is possible to frame the semiotic example of fallacy of the consequent in causal terms. In some cases, the cause of someone’s fancy dressing or night wandering is that he is an adulterer; while in some other cases the cause may be different. In extensional terms, here we have an effect that is more extended than its cause; when this happens, the inference of the cause from the effect is always a fallacy and results in a deductively invalid second-figure syllogism. (This is the case that Aristotle does not consider in APo A 13, precisely because it yields a deductively invalid argument.) If the effect is then called a “sign” of the cause, the syllogism is a sign-syllogism and corresponds to the deductively invalid sign-syllogism in the second figure that Aristotle analyzes in APr B 27. Another relevant place is the following passage from On divination by dreams: Now dreams must be either causes (αἴτια) or signs (σημεῖα) of events which occur, or else coincidences (συμπτώματα); either all or some of 164 Later commentators take Aristotle’s adulterer example to involve a disjunctive consequent. See infra, Chapter 6.

64

chapter 1

these, or one only. I use the word “cause” in the sense in which the moon is the cause of an eclipse of the sun, or fatigue is the cause of fever; the fact that a star comes into view I call a “sign” of the eclipse, and the roughness of the tongue a “sign” of fever; but the fact that someone is walking when the sun is eclipsed is a coincidence. For this is neither a sign nor a cause of the eclipse, any more than the eclipse is a cause or a sign of a man’s walking.165 The interposition of the moon is the cause of the eclipse of the sun, while the fact that stars come into view is an effect and a sign of the same thing. In like manner, fatigue is the cause of fever, while the roughness of the tongue is an effect and a sign of it. No mention is made in this passage of the inferential relationship between cause and sign of the cause, but the preceding discussion authorizes the following inferential interpretation. The inferential interpretation depends on whether cause and effect in these examples are taken to be convertible or not. If the cause is taken to be convertible with the effect (the appearance of a star with the eclipse, the roughness of the tongue with fever), then the sign is in both cases a τεκμήριον, and the argument that can be constructed upon it a deductively valid that-demonstration of the first kind (1b). If, on the contrary, the effect is not convertible with the cause (all cases of eclipse are cases of appearance of a star but not vice versa; all cases of fever are cases of roughness of the tongue but not vice versa), then the sign is in both cases a σημεῖον in the strict sense, and the argument which can be constructed upon it a deductively invalid syllogism and no demonstration at all. We should now be in a good position to determine in what senses it is ­possible to say, as Aristotle does at APr A 27, that a sign is (or more precisely, professes to be) a πρότασις ἀποδεικτικὴ. Before that, few other observations about sign-inferences are in order. 8

Logic, Semiotics, and Epistemology

According to Sextus Empiricus, for the Stoics a sign is the antecedent in a sound conditional that is revelatory of the consequent.166 It is not sufficient that the conditional be sound, nor that the antecedent be true. The antecedent must also reveal the consequent, i.e., knowing the truth of the antecedent (or sign) must lead us to know the truth of the consequent (or thing signified). 165 Aristotle, De div, 462b29–463a2; transl. Hett. 166 Sextus Empiricus, Adv Math VIII.245.

Aristotle on Signs and Demonstrations

65

A sign signifies something non-evident (ἄδηλον).167 Stoic σημεῖα have a decidedly epistemic character.168 In our reconstruction of the semiotic doctrine of APr B 27 we have purposely said nothing about the possibility of an epistemic interpretation of Aristotle’s doctrine. We have done so because Aristotle himself seems strangely silent on this point. As Burnyeat has pointed out, Aristotle’s account of signs in APr B 27 makes no use of epistemic notions: the only epistemic characterization that he offers concerns the major premise of the third-figure sign-syllogism about Pittakos, which is omitted because it is common knowledge; but he nowhere characterizes in an epistemic manner the sign-premise itself, saying for example that it is better known or more easily perceived than the conclusion. As Burnyeat put it, “for all he says to the contrary, pregnancy could be a sign of lactation.”169 It is time to fulfill a promise made earlier concerning the milk example of APr B 27.170 We translated the verb κύειν (usually rendered with “being pregnant”) with “giving birth.” We did so on the basis of its reception and interpretation by Greek commentators, especially Alexander of Aphrodisias and Philoponus,171 and Latin translators, especially Boethius (who used the verb parĕre172). This translation also matches with Rhet A 2, 1357b15–16, where the form used is τέτοκεν. Now, both “being pregnant” and “having borne a child” are biologically plausible: Aristotle typically calls γάλα both the milk and the colostrum,173 and in Gen An Δ, 776a15–b4, he explains that milk (i.e., colostrum) is produced in the woman’s breast by the seventh month of pregnancy. Yet, the translation of κύειν as “giving birth” provides an interpretation of the example that is epistemically more plausible. Let us imagine a woman in her seventh month of pregnancy visiting a doctor who for some reason is ignorant of her status. Her breast has started to leak a clear fluid called colostrum and her baby-belly pouch is of the size of a basketball. Which of the two “signs” is more “evident” to the doctor? Does the doctor need to check for the presence of colostrum or be informed thereof in order to safely infer that the woman is 167 168

Sextus Empiricus, Adv Math VIII.143. On Stoic semiotics see Burnyeat (1982), 206–238; Manetti (1993), 97–110; Allen (2001), 147–193. 169 Burnyeat (1982), 206. By contrast, Ross (1949), 500, says that Aristotle’s definition of “sign” at 70a8–10 “states a connexion between a relatively easily perceived characteristic and a less easily perceived one simultaneous, previous, or subsequent to it.” 170 Cf. supra, §1.4. 171 Cf. infra, §§2.1, 2.3. 172 Cf. AL III.1, 137. 173 Cf. Burnyeat (1982), 204 n. 30.

66

chapter 1

pregnant? Is it not the size of the baby-belly the natural candidate for being a sign of pregnancy? But now let us imagine a mother who has been breast-­ feeding her child for some months. All other signs of the previous pregnancy are gone, but she has a copious quantity of milk in her breast. In this case, the milk can become the sign of the past events of delivery and birth. However, if κύειν is translated with “giving birth” in the milk example, it should also be so translated in the paleness example. Here we have the complication that paleness is typically a visible feature of pregnant women at several stages of pregnancy, i.e., even at those stages in which no more evident sign of it can be gained. In this context, paleness can very well be a sign of pregnancy, even in the epistemic sense: a visible mark is the apparent sign of a hidden cause. “Being pregnant” would therefore be a perfectly appropriate translation for κύειν in that context, perhaps even a better translation than “giving birth,” for paleness is a more typical (though not convertible) sign of pregnancy than it is of having given birth. We face a dilemma. Either we admit that Aristotle was guilty of a semantic inconsistency in his use of κύειν, which means “giving birth” in the milk example and “being pregnant” in the paleness example, or—if we think that he wanted κύειν to maintain a constant semantic value across the whole ­chapter—we have to admit that his examples are not equivalently plausible from an epistemic point of view. Accepting the first alternative would save the epistemic plausibility of Aristotle’s analysis of signs, for in both contexts the sign is not only more evident than, but precisely the more evident or more typical ­manifestation, of a hidden cause. By contrast, accepting the second alternative would save the parallelism between the two examples but would undermine the epistemic plausibility of his analysis. (No such dilemma arises with the Rhetoric, where only the milk example occurs, with τίκτειν instead of κύειν.) Notwithstanding his silence about the epistemic status of the “sign” in APr B 27, the commentators interpreted Aristotle’s milk example so that the milk in a woman’s breast is an epistemically relevant sign of her having borne a child (not of her being pregnant). This idea was built, as we now shall see, upon their systematic interpretation of the first kind of “demonstration of the that” of APo A 13 as a sign-syllogism, an interpretation which was favored by Aristotle’s own explicit contrast between demonstration and sign-inference in APo A 6 and B 17. 9 Conclusion Aristotle’s Prior Analytics contain his theory of the syllogism and his Posterior Analytics contain his theory of the demonstrative syllogism, i.e., demonstration

Aristotle on Signs and Demonstrations

67

(ἀπόδειξις). At the end of the Prior Analytics (B 23–27) Aristotle shows how his syllogistic can be used to evaluate a variety of forms of arguments, among which sign-arguments (B 27). His analysis is in terms of the syllogistic figures, and distinguishes first-figure sign-syllogisms, which are deductively valid (a sign-argument of this type is labeled τεκμήριον, “proof” or “evidence”), from second- and third-figure sign-syllogisms, which are deductively invalid and yet (it appears) not completely devoid of any value (a sign-argument of these types is labeled σημεῖον in the strict sense). A sign in the wide sense (covering both τεκμήρια and σημεῖα in the strict sense) is defined a πρότασις ἀποδεικτική. Given that in two places of the Posterior Analytics (A 6 and B 17) demonstrations seem to be opposed to sign-syllogisms, the question that the sign definition in APr B 27 poses is: Can a sign be a demonstration? As far as Aristotle is concerned, our conclusion is the following. As both ancient and modern commentators have proposed, we need to recognize a strong and weak sense of ἀπόδειξις. In the strong sense, an ἀπόδειξις is a syllogism that fulfills the causal requirement of APo A 2, and which therefore infers the effect from its cause. A conclusion obtained by such ἀπόδειξις can be said to have been demonstrated καθ’αὑτό (APo A 6). In the weak sense, an ἀπόδειξις is a syllogism which, when cause and effect are convertible, infers the cause from the effect. Given convertibility, an ἀπόδειξις in the weak sense is still a deductively valid argument, and can be identified with the first type of demonstrations τοῦ ὅτι of APo A 13 (1b). A conclusion obtained by such ἀπόδειξις can be said to have been demonstrated κατὰ συμβεβηκός (APo A 6)— even if Aristotle nowhere says anything that unmistakably suggests that the projection of the καθ’αὑτό / κατὰ συμβεβηκός distinction onto the why/that distinction is legitimate. Moreover, since an effect is, at least sometimes, a sign of its cause, an ἀπόδειξις in the weak sense can also be identified with the sign-inferences examined in APr B 27. In two passages of the Posterior Analytics, demonstration in the weak sense is opposed to demonstration in the strong sense and is identified with sign-inferences (διὰ σημείων συλλογισμοί in APo A 6, demonstration κατὰ σημεῖον in APo B 17). But since it is a deductively valid sign-­ inference, the sign that functions as πρότασις ἀποδεικτική cannot correspond to the σημεῖον in the strict sense; it must rather correspond to the τεκμήριον, so that, as Philoponus clearly perceived, it would have been more appropriate if at APo A 6, 75a33–34 Aristotle had talked of διὰ τεκμηρίων συλλογισμοί.174 174

Of course, it may well be that at the time of the composition of APo A 6 Aristotle had not yet drawn the distinction, officially presented at APr B 27, between τεκμήριον and σημεῖον in the strict sense. But this is a genetic argument which we decided not to address. See supra, footnote 83.

68

chapter 1

When cause and effect are not convertible, the inference of the cause from the effect is possible only if the cause is more extended than the effect; in this case the syllogism can only be of the that (that-demonstrations of types 2a and 2b). Aristotle never says that such that-demonstrations are sign-­inferences. If, by contrast, the effect is more extended than the cause, the inference of a ­possible cause from the effect is always invalid. Arguments of this form are the second- and third-figure sign-syllogisms of APr B 27, the apparent enthymeme of Rhet B 24 and the apparent argument from the consequent κατὰ τὸ σημεῖον of Soph El 5, 167b9. These cannot be considered as ἀποδείξεις, not even in the weak sense. Rather, an argument of this sort is only improperly called an ἀπόδειξις, for a deductively invalid argument cannot be an ἀπόδειξις at all. An ἀπόδειξις κατὰ τὸ σημεῖον in the sense of Soph El 5, 167b9 is, despite its name, a demonstration in neither the strong nor the weak sense. Unlike in the Stoics’ sign theory, Aristotle’s analysis of signs in APr B 27 makes no use of epistemic notions. Some epistemic interpretation of that theory would be available if the relation between sign and thing signified were explicitly construed as a causal relation. In APo A 13 Aristotle is clear that from the “better known,” the effect, the “less known,” the cause, can be inferred, and this inference qualifies as a demonstration of the that (of type 1b if convertibility is in place, of type 2a if cause and effect do not convert). In the two passages in APo A 6 and B 17 some association between the demonstration of the that (of type 1b) and sign-inferences is implicitly made. Yet, apart from this implicit association nothing in Aristotle’s theory of sign-inferences seems to legitimate an epistemic interpretation of APr B 27. Such epistemic interpretation will in fact be advanced by his commentators, beginning with Alexander of Aphrodisias, precisely on the basis of the identification of the first kind of demonstration of the that of APo A 13 with the sign-inference of APr B 27.175 It is this explicit identification that allows projecting the epistemic relation between cause and effect of APo A 13 onto the non-epistemic relation between sign and signified thing of APr B 27. 175 Cf. infra, §2.1.

CHAPTER 2

The Greek Commentators Aristotle’s remarks on the relationship between signs and demonstrations were taken up and carried on by Aristotle’s Greek commentators. They made explicit what was implicit in Aristotle. They read certain passages in the Posterior Analytics, including the two passages where Aristotle explicitly contrasts demonstration with sign-inference, as implying a typology of demonstrations, and connected that typology to the theory (and to some extent also to the nomenclature) of signs of APr B 27. By so doing, they inaugurated an interpretative lineage whose effects are still detectable in thirteenth-century Latin Aristotelianism. Outside the tradition of the Posterior Analytics, the connection between signs and demonstrations also appears in the commentaries on the first book of the Physics. This Chapter is about the Greek reception and development of the Aristotelian notion of “semiotic demonstration.”1 It is divided as follows: the first section (§2.1) is on Alexander of Aphrodisias (fl. c. 200 CE); we examine some passages of his commentaries on the Prior Analytics and the Topics and connect them to those contained in an anonymous commentary on the Posterior Analytics that derives, in whole or in part, from Alexander. The second section (§2.2) is about Themistius (ca. 317–390 CE), whose paraphrase of the Posterior Analytics is the oldest complete companion to the work that we possess. The third section (§2.3) is on John Philoponus (ca. 490–570 CE), whose commentary on the first book of the Posterior Analytics has exerted a considerable influence, to which we return in later Chapters. The spurious commentary on the second book that has been transmitted under the name of Philoponus is quite Philoponean in spirit, and is discussed in the sixth section (§2.6). The fourth section (§2.4), then, examines some Greek commentaries on Physics A 1. The fifth section (§2.5) is on the spurious commentary on Prior Analytics B published by Wallies in CAG 13.2, whose author we refer to as Ps-Philoponus-1. The final section (§2.7) is on a passage in Michael of Ephesus’ commentary on the Sophistici Elenchi (early twelfth century) that may depend on the late-­ ancient tradition of the Posterior Analytics, and in particular on Philoponus.

1 Studies on the theory of sign-inferences in late-ancient Greek commentators of Aristotle are few; Morrison (1997) is a seminal contribution with a focus on the commentaries on the Physics; Dubouclez (2008), 140–150, says almost nothing about Alexander of Aphrodisias. © koninklijke brill nv, leiden, 2023 | doi:10.1163/9789004546974_004

70 1

chapter 2

Alexander of Aphrodisias

There can be little doubt that Alexander of Aphrodisias produced a commentary on the Posterior Analytics. In the commentaries that survive, Alexander himself refers several times to the Posterior Analytics, either quoting passages or referring to doctrines expounded in that work. Also, several manuscripts of the Posterior Analytics contain scholia explicitly attributed to Alexander,2 and it is likely that one or more copies of Alexander’s commentary, or at least some collection of excerpts based on it, were still available in Constantinople at the beginning of the twelfth century, because Eustratius of Nicaea seems to have used it while compiling his own commentary on the Posterior Analytics.3 ­Furthermore, Paul Moraux has persuasively shown that the anonymous commentary on the second book of the Posterior Analytics published by Max Wallies in CAG 13.3 is made out, at least in its greater part, of bits and pieces only slightly modified of Alexander’s lost commentary.4 In this section, we shall attempt a reconstruction of Alexander’s doctrine of sign-inferences on the basis of both the anonymous commentary in CAG 13.3 and of Alexander’s own commentaries on the Topics and the Prior Analytics. Let us begin with these latter. We have mentioned that in Topics A 1 Aristotle says that there are three species of syllogism: demonstrative, dialectical, and eristical. These are the species of syllogism that Alexander considers in turn. Here, we focus only on what he says about demonstrative syllogism. In Topics A 1 Aristotle says that a demonstration is a syllogism “from things which either are themselves true and primary or have attained the starting-point of knowledge about themselves through some primary and true premises.”5 Of the six requirements mentioned in APo A 2,6 here only the absolute requirement that the premises be true (i) and the relative requirement that they be prior to the conclusion (v) are mentioned. Also, as we noticed, in the Topics these requirements are “relaxed” in the sense that it is not necessary that the premises of a demonstration should satisfy (i) and (v); it is sufficient that they derive from premises that satisfy (i) and (v). Alexander comments as follows:

2 Moraux (1979), 7. 3 Moraux (1979), 6; Ebbesen (2015), 12. 4 Moraux (1979), 131–135; see also Ebbesen (2012), 363. It has to be noted that Moraux did not prove Alexandrian authorship for the whole commentary; cf. infra, footnote 26. 5 Aristotle, Top A 1, 100a27–30; transl. Smith. 6 See supra, §1.6.

The Greek Commentators

71

For not every syllogism from true is a demonstration in the strict sense, but it is if the things through which such a syllogism is proved, in addition to being true are also primary. For they will thus be giving the cause as well—and demonstration is the syllogism through what gives the cause—since what is primary gives the cause for what comes after. […] This is why someone who proves that the moon is eclipsed because it is screened by the earth offers a demonstrative proof, e.g. The moon is screened or obscured by the earth What is screened or obscured suffers an eclipse for what gives the cause of the eclipse is the screening. But if someone proves that the moon is screened by the earth because it is eclipsed, he does not offer a demonstration in the strict sense even though what he obtains is true, since he is not proving in the strict sense what is posterior and caused through what is primary and gives the cause, but what is prior through what is posterior: for the eclipse is posterior to the screening and results from it. In this way someone who proves “She has borne a child” by her lactating, is proving by what is posterior, since the milk is not the cause that she has borne a child, but her having borne a child is the cause that she is lactating. In any case someone who proves that she is lactating by her having borne a child offers a proof by what is a cause and primary. Similarly, someone who proves that a man has lungs by his being capable of breathing is syllogizing through what is true but not through what is primary, and therefore is not offering a demonstration. On the other hand, if he proves that the man is capable of breathing by his having lungs, then he offers a demonstration. Again, someone who proves that a living creature is endowed with sensation by its being sensitive is not practicing demonstration; however, if he proves that it is sensitive by its being endowed with sensation, then he has offered a demonstration. Now if demonstration is through things that are primary, one may further inquire what will be a syllogism which proceeds through what is true but posterior. Either this is a dialectical syllogism, since what is true in this way is assumed as being approved—for it is something approved that the woman who is lactating has borne a child, and that the body that is eclipsed is being obscured—or, whereas the former is a demonstration in the strict sense, the latter is also one in a secondary sense, as relating to us, since the things which are assumed are better known to us.7 7 Alexander, In Top, ed. Wallies, CAG 2.2, 16.1–30: “οὐ γὰρ πᾶς ὁ ἐξ ἀληθῶν συλλογισμὸς καὶ κυρίως ἀπόδειξις, ἀλλ’ εἰ πρὸς τῷ ἀληθῆ εἶναι τὰ δι’ ὧν ὁ τοιοῦτος δείκνυται συλλογισμός, καὶ πρῶτα εἴη. οὕτως γὰρ ἔσται καὶ αἴτια· ὁ γὰρ δι’ αἰτίων συλλογισμὸς ἀπόδειξις· τὰ γὰρ πρῶτα τῶν μετὰ ταῦτά

72

chapter 2

Alexander here seeks to explain Aristotle’s claim that the premises of a demonstration should satisfy (i) and (v), i.e., be true and primary, or should be themselves derivable from such premises. The explanation is by way of a contrast with a kind of syllogism that satisfies (i) but not (v). In what sense can a syllogism be from premises that are true but not primary? He explains that “what is primary gives the cause for what comes after” (τὰ γὰρ πρῶτα τῶν μετὰ ταῦτά ἐστιν αἴτια). Thus, a syllogism from premises that are true but not primary is a syllogism from premises that, while true, do not give the cause of “what comes after,” i.e., of the conclusion, while a demonstration is a syllogism from premises which are true and which in addition give the cause of the conclusion, because “demonstration is the syllogism through the cause” (ὁ γὰρ δι’ αἰτίων συλλογισμὸς ἀπόδειξις). At this point the astronomical example of APo B 16 (rather than that of APo A 13, the official treatment of the distinction between syllogism of the why and syllogism of the that8) is invoked. In that context, Aristotle says that the inference of the interposition of the earth from the eclipse of the moon is a demonstration of the that, while the inference of the eclipse of the moon from the interposition of the earth is a demonstration of the why.9 This argument has the form of the “prototypical” that-demonstration of APo A 13, that in which cause and effect convert (1b). Alexander’s use of the astronomical example of APo B 16 suggests that he thinks that while the Aristotelian demonstration of the why is an inference from true and primary (i.e., causal) premises, the Aristotelian demonstration of the that is an inference from true but non-primary (i.e., non-causal) premises. ἐστιν αἴτια. [...] διὰ τοῦτο ὁ μὲν δεικνὺς ὅτι ἐκλείπει ἡ σελήνη διὰ τὸ ἀντιφράττειν αὐτῇ τὴν γῆν ἀποδείκνυσιν· οἷον ἡ σελήνη ἀντιφράττεται ἢ ἐπισκοτεῖται ὑπὸ τῆς γῆς, τὸ ἀντιφραττόμενον ἢ ἐπισκοτούμενον ἐκλείπει· αἴτιον γὰρ τῆς ἐκλείψεως ἡ ἀντίφραξις. ἂν δέ τις τὸ ἀντιφράττειν τὴν γῆν τῇ σελήνῃ δεικνύῃ διὰ τοῦ ἐκλείπειν αὐτήν, οὐκέτι ἀποδείκνυσι κυρίως, καίτοι λαμβάνων ἀληθές· οὐ γὰρ διὰ πρώτου οὐδὲ δι’ αἰτίου δείκνυσι κυρίως τὸ ὕστερόν τε καὶ αἰτιατόν, ἀλλὰ διὰ τοῦ ὑστέρου τὸ πρῶτον· ὕστερον γὰρ ἡ ἔκλειψις τῆς ἀντιφράξεως καὶ δι’ ἐκείνην γινομένη. οὕτως δείκνυσι δι’ ὑστέρου ὁ δεικνὺς τὸ ‘αὕτη τέτοκε’ διὰ τοῦ γάλα ἔχειν· οὐ γὰρ τὸ γάλα αἴτιον τοῦ τετοκέναι, ἀλλὰ τὸ τετοκέναι τοῦ γάλα ἔχειν· ὁ γοῦν διὰ τοῦ τετοκέναι δεικνὺς τὸ γάλα ἔχειν δι’ αἰτίου τε καὶ πρώτου δείκνυσιν. ὁμοίως καὶ ὁ δεικνὺς ὅτι ὁ ἄνθρωπος πνεύμονα ἔχει διὰ τοῦ ἀναπνευστικὸν αὐτὸν εἶναι δι’ ἀληθοῦς μὲν συλλογίζεται, οὐ μὴν διὰ πρώτου· διὸ οὐδὲ ἀποδείκνυσιν. ἂν δὲ ἔμπαλιν διὰ τοῦ πνεύμονα ἔχειν αὐτὸν δείξῃ ὅτι ἐστὶν ἀναπνευστικόν, ἀποδείκνυσιν ἤδη. ἀλλὰ καὶ ὁ τὸ ζῷον δεικνὺς ὅτι αἴσθησιν ἔχει διὰ τοῦ αἰσθητικοῦ οὐκ ἀποδείκνυσιν· ἂν μέντοι διὰ τοῦ αἴσθησιν ἔχειν δείξῃ ὅτι καὶ αἰσθητικόν, ἀπέδειξεν. ἐπιζητήσειε δ’ ἂν τις, εἰ ἡ ἀπόδειξις διὰ πρώτων, ὁ δι’ ἀληθῶν μὲν ὑστέρων δὲ συλλογισμὸς τίς ἂν εἴη. ἢ καὶ οὗτος διαλεκτικός· τὰ γὰρ οὕτως ἀληθῆ ὡς ἔνδοξα λαμβάνεται· ἔνδοξον γὰρ τό τε τὴν γάλα ἔχουσαν τετοκέναι καὶ τὸ ἐκλεῖπον ἐπισκοτεῖσθαι. ἢ κυρίως μὲν ἐκεῖνος ἀπόδειξις, δευτέρως δὲ καὶ οὗτος· ὡς γὰρ πρὸς ἡμᾶς, ἐπεὶ ἡμῖν γνωριμώτερα τὰ λαμβανόμενα.” Transl. Van Ophuijsen. 8 Cf. supra, §1.6.1 9 Aristotle, APo B 16, 98b18–22.

The Greek Commentators

73

Alexander’s second example comes directly from APr B 27, the official treatment of sign-inferences, where it illustrates Aristotle’s sign-syllogism in the first figure, or τεκμήριον:10 the argument that shows that a woman is lactating because she has borne a child shows what is posterior (lactating) from what is primary (i.e., causal) (having borne a child), while the argument that shows that she has borne a child because she is lactating shows what is primary (i.e., causal) from what is posterior. Alexander’s third and fourth examples may have some basis in ­Aristotle’s biology and psychology, respectively. Since having lungs is the cause of ­breathing,11 the argument that shows that a man breathes because he has lungs shows what is posterior (breathing) from what is primary (i.e., causal) (having lungs), while the argument that shows that man has lungs because he breathes shows what is primary (i.e., causal) from what is posterior. The example ­indirectly points to the second-figure argument of APo A 13, where “being an animal” is the non-primary (i.e., non-convertible) cause of “breathing”; “having lungs” is, by contrast, the primary (i.e., convertible) cause of breathing. The last example has the same structure: since the sensitive faculty is the cause of sensation (as implied in the De Anima), the argument that shows that an animal has sensation because it has a sensitive faculty goes from what is primary (i.e., causal) to what is posterior, while the argument that shows that an animal has a sensitive faculty because it has sensation goes from what is posterior to what is primary (i.e., causal). If then a demonstration is an argument satisfying both (i) and (v), i.e., is an argument whose premises are both true and primary or are themselves derivable from true and primary premises, what kind of argument is the one that satisfies (i) but not (v)? Alexander offers two answers. The first answer is that such an argument is a dialectical syllogism. A dialectical syllogism is one whose premises are ἔνδοξοι, “reputable” or likely to be believed. In Topics A 1 Aristotle contrasts the things which are true and primary, which get their trustworthiness through themselves and not through other things, with the things that are “reputable,” which seem trustworthy to everyone, or to the majority, or to wise men.12 Since the two sorts of things contrasted here are respectively the premises of demonstrative and dialectical syllogism, Alexander’s natural supposition is that when the premises of an argument satisfy neither (i) nor (v), the argument must be a dialectical syllogism. This solution is unsatisfactory, however. In the examples of “non-demonstrative” arguments that he has 10 Cf. supra, §1.4. 11 Aristotle, De respiratione 9, 417b26–29. 12 Aristotle, Top A 1, 100b18–24.

74

chapter 2

so far contrasted with proper demonstrations, the minor premise is true but not primary (i.e., not causal). Yet, the reason for regarding them as dialectical that Alexander offers does not concern the minor but the major premise. Alexander says “what is true in this way is assumed as being approved—for it is something approved that the woman who is lactating has borne a child, and that the body that is eclipsed is being obscured.” It is the major premise here that counts as ἔνδοξος, not the minor; the character of the minor is not under discussion. Alexander’s second solution seems preferable. He says that while an argument satisfying both (i) and (v) is a demonstration in the strict sense (κυρίως), an argument satisfying (i) but not (v) is not a demonstration in the strict sense (οὐκέτι ἀποδείκνυσι κυρίως). It is nonetheless a demonstration and not a dialectical syllogism; only, it is a demonstration in a “secondary sense” (δευτέρως). As we will show with abundant evidence, this move is difficult to underestimate: the idea that a deductive argument from non-primary (i.e., non-causal) premises constitutes a demonstration in a secondary sense inaugurates a paradigm of Aristotelian exegesis that reaches up to the thirteenth century. The contrast between demonstration and syllogism through signs, which as we have just seen is implicit in Alexander’s commentary on the Topics, becomes explicit in his commentary on the Prior Analytics. The context in which the contrast occurs is Aristotle’s definition of the syllogism.13 A syllogism is a discourse in which, certain things having been supposed, something different from the things supposed results of necessity inasmuch as they are the case (τῷ ταῦτα εἶναι). By “inasmuch as they are the case,” I mean “resulting through them” (διὰ ταῦτα συμβαίνειν), and by “resulting through them” I mean “needing no further term from outside in order for the necessity to come about.”14 In a syllogism the conclusion results necessarily from the premises “inasmuch as they are the case” (τῷ ταῦτα εἶναι). Aristotle explains the expression τῷ ταῦτα εἶναι as meaning that the conclusion “results through them” (διὰ ταῦτα συμβαίνειν), and this latter is explained in turn as meaning that the conclusion “results through them alone,” i.e., without the need of further assumptions. Alexander wants to explain why the second explanation is added to the first. The reason, he says, is that the first explanation (“resulting through them” as an explanation of “inasmuch as they are the case”) could be taken as implying 13 Cf. supra, §1.2. 14 Aristotle, APr A 1, 24b18–22; transl. Smith, modified.

The Greek Commentators

75

that the premises are always (i.e., in any kind of syllogism whatever) causes of the conclusion. This is not what Aristotle has in mind, and this is the reason for the second explanation. In order to show that the causal interpretation of “resulting through them” is not what Aristotle has in mind Alexander makes a distinction between two senses in which the premises may be said to be causes of the conclusion. As to why he added “inasmuch as they are the case” to the definition of the syllogism, he himself explained this when he said: “By ‘inasmuch as they are the case’ I mean that ‘it comes about because of them’.” This itself might still seem less than plain. For “because of them” betokens a cause, and yet there can be syllogisms which do not proceed by way of causes— for example, syllogisms by way of signs which prove what is primary from what is posterior. This feature—viz. being syllogized by way of causes— is a proper characteristic of demonstrations. For although the premises must indeed be causes of the conclusion if there is to be a syllogism, what is meant by the premises need not always be causes of what is meant by the conclusion. (For you can also syllogize what is prior by way of what is posterior—proving that she has given birth from the fact that she is lactating, or that there was a fire from the ashes—and in general, syllogisms by way of signs are of this sort: for the posterior is not cause of the prior). This is why he also explained “it comes about because of them,” by saying that they “need no external term for the generation of the necessity,” i.e., that the terms laid down are sufficient in themselves for the conclusion.15 In a general sense, in syllogisms of any kind the conclusion comes about “because of” the premises. In the Metaphysics Aristotle says that the premises are “causes” (αἴτια) of the conclusion in the sense of “that from which” (τὸ ἐξ 15 Alexander, In APr, ed. Wallies, CAG 2.1, 21.10–24: “Τὸ δὲ τῷ ταῦτα εἶναι τίνος χάριν τῷ τοῦ συλλογισμοῦ ὅρῳ προσέθηκεν, αὐτὸς ἐξηγήσατο εἰπὼν λέγω δὲ τῷ ταῦτα εἶναι τὸ διὰ ταῦτα συμβαίνειν, ὃ καὶ αὐτὸ ἔτι δοκοῦν ἀσάφειάν τινα ἔχειν (τὸ γὰρ διὰ ταῦτα αἰτίας ἐστὶ δηλωτικόν· δύναται δὲ καὶ μὴ δι’ αἰτίων συλλογισμὸς γίνεσθαι, ὡς ὁ διὰ σημείων ἐκ τῶν ὑστέρων τὰ πρῶτα δεικνύς· τῆς γὰρ ἀποδείξεως ἴδιον τοῦτο, τοῦτ’ ἔστι τὸ δι’ αἰτίων συλλογίζεσθαι· δεῖ μὲν γὰρ αἰτίας τοῦ συμπεράσματος τὰς προτάσεις εἶναι, εἰ συλλογισμὸς ἔσται, οὐ μέντοι δεῖ πάντως τὰ ὑπὸ τῶν προτάσεων δηλούμενα αἴτια εἶναι τοῦ πράγματος τοῦ δηλουμένου ὑπὸ τοῦ συμπεράσματος · δύναται γάρ τις καὶ δι’ ὑστέρων τὸ πρότερον συλλογίσασθαι, ὡς ὁ ἐκ τοῦ γάλα ἔχειν τὸ τετοκέναι δεικνὺς καὶ διὰ τῆς τέφρας τὸ πῦρ, καὶ ὅλως οἱ διὰ σημείων συλλογισμοὶ τοιοῦτοι· οὐ γὰρ τὸ ὕστερον τοῦ προτέρου αἴτιον) διὰ τοῦτο καὶ τὸ διὰ ταῦτα συμβαίνειν ἐξηγήσατο εἰπὼν τὸ μηδενὸς ἔξωθεν ὅρου προσδεῖν πρὸς τὸ γενέσθαι τὸ ἀναγκαῖον, τοῦτ᾿ ἔστι τὸ αὐτάρκεις εἶναι τοὺς κειμένους ὅρους πρὸς τὸ συμπέρασμα.” Transl. Barnes et al., modified.

76

chapter 2

οὗ) the conclusion is obtained.16 In this general sense, the premises are better characterized as the logical cause of the conclusion, i.e., the cause of the drawing of the conclusion (αἰτίας τοῦ συμπεράσματος). In another sense, however, only in those special syllogisms which are demonstrations the premises are cause of the conclusion in the sense that they are the ontological cause of the conclusion, i.e., of the fact expressed in the conclusion (αἴτια εἶναι τοῦ πράγματος τοῦ δηλουμένου ὑπὸ τοῦ συμπεράσματος). This distinction is crucial and will form the basis of subsequent interpretations, as we shall see. Without some such distinction, Alexander suggests, it would be impossible to explain how a sign-syllogism, which proceeds from what is posterior and caused to what is primary and causes, and in which the premises are not, therefore, ontological causes of the conclusion, could qualify as a syllogism at all. His examples are, again, quite instructive. The first example is the lactating woman of APr B 27. This is a τεκμήριον in which the fact expressed in the minor premise (having milk) is not the cause of the fact expressed in the conclusion (having borne a child); the premises are thus in no sense the ontological cause of the conclusion; it is the fact expressed in the conclusion that is the cause of the fact expressed in the minor premise. Yet, the minor premise is that from which the conclusion is drawn, and thus is the cause of the conclusion in the logical sense. The second example is not Aristotelian and may have Stoic origins: when I infer the (past) presence of fire from the (actual) presence of the ash, I infer the cause (fire) from the effect (ash). The premises cannot contain the ontological cause of the conclusion; they are only the logical cause of it. As Alexander sees it, Aristotle’s second explanation (at 24b21–22) is intended precisely not to exclude non-demonstrative syllogisms from his definition of the syllogism, an exclusion that could be misleadingly suggested by the first explanation (at 24b20–21): in all syllogisms the premises are logical causes of the conclusion, but only in demonstrations they contain, in addition, the ontological cause of the fact expressed in the conclusion.17 The two passages from Alexander’s commentaries suggest a number of things, and when read together they imply even more. In the first place, the juxtaposition of the example of the lactating woman of APr B 27 and the example of the eclipse of APo B 16 in the passage from the commentary on Top A 1 suggests that Alexander regards Aristotle’s τεκμήριον as a that-syllogism of the first type (1b): both are deductively valid first-figure syllogisms which, to use the description of APo A 13, do not proceed from the cause but from the better known of two convertible terms. The identification projects the epistemic 16 Aristotle, Met Δ 2, 1013b21. 17 Cf. Gili (2011), 103.

The Greek Commentators

77

dimension of the that/why distinction of APo A 13 onto the analysis of signs of APr B 27. Both the τεκμήριον of APr B 27 and the that-syllogism of APo A 13 may be said to be “demonstrative” to some extent: the τεκμήριον is one of three forms of πρότασις ἀποδεικτική, and the that-syllogism is also called ἀπόδειξις, even if it does not satisfy the requirement set forth at APo A 2 as to the causal status of its premises. In this passage from the commentary on Top A 1, Alexander implicitly (i.e., by means of the examples that he uses) offers a solution: both the τεκμήριον of APr B 27 and the that-syllogism of the first type (1b) of APo A 13 are demonstrations in a secondary sense (δευτέρως), and as such they may be contrasted with demonstrations in the proper sense (κυρίως). The passage from the commentary on APr A 1 adds to this that sign-­ syllogisms in general are arguments in which the premises are the logical cause of the c­ onclusion without being the ontological cause of the fact expressed in the ­conclusion. The generic reference to sign-syllogisms (οἱ διὰ σημείων συλλογισμοί) should not mislead us into thinking that Alexander is here ­making room for deductively invalid sign-syllogisms: his use of the term σημεῖον in this generic sense is comparable to Aristotle’s use of that term in APo A 6 and APo B 17.18 Together, the two passages imply that both deductively valid sign-syllogisms and that-syllogisms of the first type (1b) are demonstrations in a secondary sense, i.e., are arguments in which a cause is inferred from an effect that is convertible with it (and in such convertibility resides its deductive validity); they also imply that in demonstrations in this secondary sense the premises are the logical cause of the conclusion but not the ontological cause of the thing or fact expressed in the conclusion. Aristotle never explicitly says that a syllogism through signs can be considered as a syllogism of the that, even though in the two parallel passages in APo A 6 and APo B 17 he comes very near to suggest some such identification. Alexander makes the identification quite evident (even if not explicitly), and by so doing inaugurates an exegetical pattern that would become quite popular among Greek and Arabic commentators of the Posterior Analytics. As mentioned, according to Paul Moraux the anonymous commentary on the second book of the Posterior Analytics published by Wallies in CAG 13.3 derives, at least in its greater part, from Alexander’s lost commentary. Since only the commentary on the second book survives, we shall content ourselves with examining what the Anonymous (i.e., Alexander) says about the chapter

18 Cf. supra, §1.7.

78

chapter 2

that contains the second and last mention of sign-inferences in the Posterior Analytics, namely APo B 17. In commenting on, 99a1–4 the Anonymous says: Having shown that it is not possible that the same belongs to the same through multiple causes (for the universal holds primarily and holds for one cause: through that to this, through this to each of those to this) now cites as an example, if the same belongs to many through several causes, he seeks how it works and whether it is possible. For example, if it is shown that animal belongs to man through a middle term, and to eagle through a different middle term: of the belonging of the animal to those to which it belongs there seem to be different causes; to some flying, to other walking, to still others swimming. Solving this and showing the duplicity of the cause (for not always the cause of the conclusion is also the cause of the thing) showing this says that, if we have demonstrated in itself, that is if the demonstration is produced through the cause, which is the cause of the thing, it is necessary that the same cause is assumed of all the things of which the same is demonstrated. Of this provides the reason, already shown, saying the definition of the extreme which is the predicate and which belongs to many is through which the demonstration is carried out, and this is the middle term: in fact, this cause belongs to many in a somehow general and identical way. If we could not demonstrate through the cause, but through a sign or assuming a middle that is an accident, it is possible to demonstrate that the same thing belongs to one through the other.19

19 Anonymous, In APo, ed. Wallies, CAG 13.3, 593.4–22: “Δείξας ὅτι τὸ αὐτὸ τῷ αὐτῷ οὐχ οἷόν τε διὰ πλειόνων ὑπάρχειν αἰτίων (τὸ γὰρ καθόλου ᾧ πρώτῳ ὑπάρχει, δι᾿ ἑνὸς αἰτίου ὑπάρχει· δι᾿ οὗ δὲ τούτῳ, διὰ τούτου καὶ ἑκάστῳ τῶν ὑπὸ τοῦτο) νῦν ὃ παρέθετο παράδειγμα, πρὸς τὸ δύνασθαι τὸ αὐτὸ πλείοσί τισιν ὑπάρχειν διὰ διαφόρων αἰτίων ζητεῖ πῶς ἔχει καὶ εἰ οἷόν τε τοῦτο. οἷον εἰ τὸ ζῷον δι᾿ ἄλλου μὲν μέσου ἀνθρώπῳ, δι᾿ ἄλλου δ᾿ ἀετῷ δείκνυται ὑπάρχον· τοῦ γὰρ τὸ ζῷον ὑπάρχειν οἷς ὑπάρχει δόξει πλείω εἶναι τὰ αἴτια· τοῖς μὲν γὰρ τὸ πτηνόν, τοῖς δὲ τὸ πεζόν, τοῖς δὲ τὸ ἔνυδρον. λύων δὴ τοῦτο καὶ τὸ διττὸν τοῦ αἰτίου ἐνδεικνύμενος (οὐ γὰρ πάντως τὸ τοῦ συμπεράσματος αἴτιον καὶ τοῦ πράγματός ἐστιν αἴτιον) τοῦτο δὴ δεικνὺς λέγει ὅτι, εἰ μὲν καθ᾿αὑτὸ ἀποδέδεικται, τουτέστιν εἰ διὰ τοῦ αἰτίου, ὃ τοῦ πράγματός ἐστιν αἴτιον, ἡ δεῖξις εἴη γινομένη, τὸ αὐτὸ αἴτιον ἀνάγκη ἐπὶ πάντων λαμβάνεσθαι οἷς δείκνυται τὸ αὐτὸ ὑπάρχον. οὗ τὴν αἰτίαν παρέθετο, ἣν ἔδειξεν ἤδη, εἰπὼν ‘ὁρισμὸς γὰρ τοῦ ἄκρου ἐστὶ τοῦ κατηγορουμένου καὶ τοῖς πλείοσιν ὑπάρχοντος ἡ αἰτία δι᾿ ἧς δείκνυται, καὶ οὗτος ὁ μέσος ὅρος᾿· ἡ γὰρ τοιαύτη αἰτία κατὰ κοινόν τι καὶ ταὐτὸν τοῖς πλείοσιν ὑπάρχει. εἰ δὲ μὴ εἴη ἀποδεικνύμενον διὰ τοῦ αἰτίου ἀλλὰ διὰ σημείου ἢ διὰ συμβεβηκότος μέσου λαμβανομένου, ἐνδέχεται ἄλλῳ δι᾿ἄλλου τὸ αὐτὸ ὑπάρχον δείκνυσθαι.” When not otherwise specified, translations are our own.

The Greek Commentators

79

As we saw,20 the central question of APo B 17 is whether there may be different causes of an attribute belonging to different things. Aristotle’s initial answer is that if the demonstration is καθ᾿αὑτό, it is not possible and the cause must be unique, while if the demonstration is not καθ᾿ αὑτό but κατὰ σημεῖον ἢ συμβεβηκός, then it is possible, and the cause may not be unique. If the demonstration is καθ᾿αὑτό, the cause must be unique even in case of “different things,” for these must be supposed to belong to the same species and the demonstration of the attribute to be relative to such common species. This is the Anonymous’ explanation: the universal (the attribute whose cause is sought) holds for one cause; through that cause it belongs to this (the common species); through this it belongs to each of those that belong to this (the different things belonging to the species). In recalling Aristotle’s answer, the Anonymous makes a distinction that is very much the same as we find in Alexander’s commentary on APr A 1. He observes that not always being “the cause of the conclusion” (τὸ τοῦ συμπεράσματος αἴτιον) in a syllogism is the same as being “the cause of the thing” (τὸ τοῦ πράγματος αἴτιον); that is, not always the middle term by which a syllogism is produced, and which thus may be considered the logical cause of the conclusion, is also the cause of the fact expressed in the conclusion, i.e., the ontological cause of it.21 When this happens, the Anonymous says, we have not only a syllogism, but a proper or causal demonstration. The Anonymous is clear that a καθ᾿αὑτό demonstration is a demonstration through an ontological cause, and explains Aristotle’s reference to signs by means of the opposition between the logical and the ontological cause: in a syllogism through a sign, the cause is only logical, and thus the demonstration is not καθ᾿αὑτό. The Anonymous also offers a cursory interpretation of the difference between “sign” and “accident” that seems to be based on the triadic “consecution” of major, minor, and middle term of which Aristotle speaks at B 17, 99a17–21: The sign always follows the thing, the accident can also from outside.22 This seems to suggest that while a sign is a middle term that is coextensive with “the thing” (the major extreme), the accident can be more extended than it (“is from outside”). A τεκμήριον is coextensive with the thing that it proves (having milk is coextensive with having borne a child); but an accident can be 20 Cf. supra, §1.7. 21 The same contrast is drawn slightly later, at CAG 13.3, 594.18–19. 22 Anonymous, In APo, ed. Wallies, CAG 13.3, 593.25–26: “Τὸ μεν σημεῖον ἀεί τῷ πράγματι παρακολουθεῖ· τὸ δὲ συμβεβηκὸς δύναται καὶ ἔξωθεν .”

80

chapter 2

more extended than that. This distinction is not Aristotelian, but contributes to the idea that a syllogism through a sign in this sense is a deductively valid argument (for major and middle term are coextensive) which fails to conclude by means of the cause. Another passage from the anonymous commentary confirms this picture: Having shown that more extended than that of which it is predicated23 it is not impossible that, in a syllogism through more than one cause and middle, something is brought together which belongs to different in form, adds that it is possible that there are several causes of the same thing, but not for things which are the same in form: through one cause the substance to animal and through another to the stone. This is possible as concerns the causes of the conclusion in the syllogism, of which is now speaking. says indeed “if the syllogism is produced through accidents or sign.” That as concerns the demonstration and the syllogism through the cause it is not possible has been shown. The same cause was in fact the definition of the predicate, which , also for things which differ in form, is the same cause of the belonging of the genus to them. And in fact the animal belongs demonstratively to the horse and to the man through the capacity of sensation.24 Animal and stone are different in form (i.e., do not belong to the same genus), and thus the cause of their both being substances is different. Horse and human being, by contrast, are the same in form (i.e., they belong to some common genus), and thus the cause of their being animals is the same (the capacity of sensation). These examples have the same structure of the two typical cases envisioned by Aristotle in APo B 17:25 fig and vine are the same in form 23

Cf. Barnes (1993), 117: “The verb kategorein sometimes means ‘to apply a predicate to’ (e.g., Aristotle, APr A 32, 47b1; perhaps APo A 22, 83b1), so that ta kategoroumena are the items to which predicates are applied.” 24 Anonymous, In APo, ed. Wallies. CAG 13.3, 597.21–598.2: “Δείξας, ὅτι ἐπὶ πλέον λεγομένου τοῦ κατηγορουμένου οὐκ ἀδύνατον ἐν συλλογισμῷ διὰ πλειόνων αἰτίων τε καὶ μέσων συνάγεσθαι τὸ αὐτὸ τοῖς διαφόροις κατ’εἶδος ὑπάρχον, ἐπιφέρει ὅτι ἐνδέχεται τοῦ αὐτοῦ αἴτια πλείω εἶναι, ἀλλ’οὐ τοῖς αὐτοῖς τῷ εἴδει· δι’ἄλλου γὰρ αἰτίου ἡ οὐσία ζῴῳ καὶ δι’ἄλλου λίθῳ. τοῦτο δ’ἐπὶ μὲν τῶν ἐν συλλογισμῷ αἰτίων τοῦ συμπεράσματος, ἐφ’ ὧν νῦν ποιεῖται τὸν λόγον, οἷόν τε· εἶπε γὰρ ‘ἂν διὰ συμβεβηκότων καὶ σημείων ὁ συλλογισμὸς γένηται’. ἐπὶ δὲ τῶν ἀποδείξεων καὶ τῶν δι’ αἰτίου συλλογισμῶν οὐχ οἷόν τε ὂν ἐδείχθη· ἦν γὰρ τὸ τοιοῦτον αἴτιον ὁρισμὸς τοῦ κατηγορουμένου, ὃς καὶ τοῖς κατ’ εἶδος διαφέρουσιν ὁ αὐτὸς αἴτιος τοῦ τὸ γένος αὐτοῖς ὑπάρχειν· καὶ γὰρ ἵππῳ καὶ ἀνθρώπῳ τὸ ζῷον διὰ τοῦ αἰσθητικοῦ ἀποδεικτικῶς.” 25 Cf. supra, §1.7.

The Greek Commentators

81

because they are broad-leaved trees, and the cause of their being deciduous qua broad-leaved trees is the same (the coagulation of the sap at the connection of the seed); quadrupeds and birds are not the same in form and the cause of longevity is different for each (quadrupeds are long-lived because they do not have bile, birds are so because they are dry). The Anonymous observes that when Aristotle says that in some cases the causes can be multiple, he is talking of the “logical cause” of the conclusion, and that this is what Aristotle has in mind is shown, according to the Anonymous, by Aristotle’s mention of semiotic syllogisms. When, by contrast, Aristotle says that no multiplicity of causes is possible, according to the Anonymous he is talking of the “ontological cause” of the fact expressed in the conclusion. It was the purpose of APo B 17 to provide an argument to this effect. If we accept that the commentary on the Posterior Analytics contained in the anonymous commentary in CAG 13.3 derives from Alexander’s lost commentary,26 it is possible to conclude that the contrast between demonstration proper and demonstration through signs was actually taken up and commented upon by the Aphrodisiensis in connection with APo B 17, 99a1–4 and 99b4 (the Anonymous’ commentary on the first book is missing). The ­distinction between the two senses in which the premises are “causes” of the conclusion which Alexander discusses in his commentary on the Prior A ­ nalytics—the logical and the ontological sense—is also at the center of these passages from the anonymous commentary. As the Anonymous puts it in the commentary on APo B 17 99a1–4, “not always the cause of the conclusion is also the cause of the thing,”27 i.e., (in the terms of Alexander’s commentary on APr A 1, 24b18–22) “what is meant by the premises need not always be explanatory of what is meant by the conclusion.”28 Syllogisms through signs are precisely those syllogisms in which the premises are logical causes of the conclusion without being ontological causes of the fact expressed in the conclusion. As we shall see, this idea was quite influential in the tradition of interpretations of the Posterior Analytics.

26

Besides Moraux’s argument for the Alexandrian authorship of the commentary as a whole, the attribution of the scholia ad 99a1 and ad 99b4 to Alexander is independently justified by the fact that in them a distinction is used (that between “being the cause of the conclusion” and “being the cause of the thing”) which we have seen is an authentically Alexandrian distinction. 27 Anonymous, In APo, ed. Wallies, CAG 13.3, 593.12–13. 28 Alexander, In APr, ed. Wallies, CAG 2.1, 21.18.

82

chapter 2

2 Themistius Since the anonymous commentary in CAG 13.3 is on the second book only, the paraphrase of Themistius has to be considered as the oldest complete companion to the Posterior Analytics to have reached us. Alexander of Aphrodisias is cited only once in Themistius’ paraphrase,29 yet its dependence on Alexander’s lost commentary on the Posterior Analytics is quite likely.30 One symptom of that dependence is that at various junctures of his paraphrase Themistius makes use of the crucial distinction between the logical and the ontological sense of “being the cause of the conclusion” that we find both in Alexander’s commentary on the Prior Analytics and in the anonymous commentary containing excerpts from Alexander. In commenting on APo A 2 Themistius says: Demonstration is the scientific syllogism; then, if it is necessary to the syllogism that the premises are causes of the conclusions, to the one who intends to know is expedient also to apprehend the cause of the thing, and it is necessary that both run together in demonstration: that is, the propositions have to be not only cause of the conclusion but also of the thing that is proved. Thus, for instance the cause of the conclusion of the fire having burnt its leaving the ash behind, but this is not the of the thing: for the ash is not cause of the fire, but rather the fire of that.31 In a demonstration the premises are not only the logical cause of the conclusion, but also the ontological cause of the thing expressed in the conclusion. Themistius’ example is the inference of the presence of fire from the presence of ash: the presence of ash is the cause of the conclusion about a past burning fire, but could not be the cause of fire itself. This is precisely Alexander’s 29 Themistius, In APo, ed. Wallies, CAG 5.1, 20.15. 30 See Moraux (1979), 4–5. The dependence of Themistius’ paraphrase on Alexander is conjectured on the basis of the Alexandrian commentaries on the Prior Analytics and the Topics, but not on the basis of the Anonymous on the Posterior Analytics, by Borgo (2009), 188–192. 31 Themistius, In APo, ed. Wallies, CAG 5.1, 5.17–24: “ἀπόδειξις γάρ ἐστι συλλογισμὸς ἐπιστημονικός, ὥστε εἴπερ τῷ συλλογισμῷ μὲν δεῖ τὰς προτάσεις αἰτίας εἶναι τοῦ συμπεράσματος, τῷ δ’ἐπίστασθαι οἰομένῳ προσήκει γινώσκειν καὶ τὴν αἰτίαν τοῦ πράγματος, καὶ ἄμφω δεῖ συνδραμεῖν ἐπὶ τῆς ἀποδείξεως καὶ τὰ λήμματα μὴ τῆς ἐπιφορᾶς εἶναι μόνον ἀλλὰ καὶ τοῦ πράγματος αἴτια τοῦ δεικνυμένου. ὡς μὲν γὰρ συμπεράσματος αἴτιον τοῦ πῦρ ἐνταῦθα κεκαῦσθαι τὸ τὴν τέφραν ὑπολελεῖφθαι, ὡς [τοῦ] πράγματος δ’ οὐκέτι· οὐ γὰρ ἡ τέφρα τοῦ πυρὸς αἰτία, ἀλλὰ τὸ πῦρ μᾶλλον ἐκείνης.”

The Greek Commentators

83

example in his commentary on Aristotle’s definition of the syllogism in APr A 1.32 The passages in which Themistius makes use of this Alexandrian idea are several: With regard to proper demonstration, the that and the why are shown together, if indeed it was said correctly regarding demonstration the middle term is cause not only of the conclusion but also of the thing.33 These are objects of demonstration, and in these the middle term is cause of the conclusion and of the thing.34 For the eclipse of the moon is not the cause of the interposition of the earth, but the middle term is equally cause of the syllogism and of the conclusion, of the thing not at all.35 The inference of the eclipse (effect) from the interposition (cause) shows not only that the moon is eclipsed, but also why it is eclipsed. Both the that and the why are shown in a proper demonstration, and according to Themistius this holds whenever the premises contain both the logical cause of the conclusion and the ontological cause of the thing expressed in the conclusion. Like Alexander, Themistius brings sign-inferences within the realm of the theory of demonstration. The first reference to sign-inferences to be found in this work is in the discussion of APo A 2, where Aristotle defines the scientific syllogism or demonstration. Themistius compares the scientific syllogism to distinct kinds of un-scientific syllogisms: The scientific syllogism differs above all from the remaining in this respect. For in the other cases the true is shown through the false, as often by rhetoricians, and that which is prior through that which is posterior, as in the syllogisms through signs, and through true, but just not appropriate, as if the physician were 32 Cf. supra, §2.1. 33 Themistius, In APo, ed. Wallies, CAG 5.1, 43.27–29: “ἐπὶ γὰρ τῆς κυρίως ἀποδείξεως τοῦ ὅτι καὶ τὸ διότι συναναφαίνεται, εἴπερ ὀρθῶς ἐλέγετο ἐπὶ τῆς ἀποδείξεως τὸ μέσον αἴτιον εἶναι μὴ τοῦ συμπεράσματος μόνον ἀλλὰ καὶ τοῦ πράγματος.” 34 Themistius, In APo, ed. Wallies, CAG 5.1, 50.21–22: “ταῦτα γὰρ τὰ ἀποδεικτά, καὶ ἄλλο ἐπὶ τούτων τὸ μέσον τε καὶ τὸ αἴτιον τοῦ συμπεράσματος καὶ τοῦ πράγματος.” 35 Themistius, In APo, ed. Wallies, CAG 5.1, 60.25–27: “οὐ γάρ ἐστιν αἴτιον τοῦ τὴν γῆν ἐν μέσῳ εἶναι τὸ τὴν σελήνην ἐκλείπειν, ἀλλὰ μέσον τοῦ συλλογισμοῦ καὶ τοῦ συμπεράσματος ἴσως αἴτιον, τοῦ πράγματος δὲ οὐδαμῶς.”

84

chapter 2

to prove that the circular wound is the most difficult to heal because this figure contains a larger area than the others. For this demonstration is that of a geometer, not of a physician.36 At APo A 2, 71b21–23 Aristotle claims that in order for a syllogism to qualify as a demonstration its premises must satisfy six requirements, and that premises satisfying the six requirements are appropriate to what is demonstrated through them.37 In this passage Themistius is considering two of the six requirements, the first (premises must be true) and the fifth (premises must be prior, πρότερον, to the conclusion), and takes the “appropriateness” of 71b23 to constitute a third requirement. Then, he offers examples of syllogisms that fall short of satisfying his three requirements. A syllogism whose premises are not true is an eristical syllogism. A syllogism whose premises are true but not appropriate to the conclusion seems to form no determinate species; Themistius limits himself to an illustration of it (a geometrical premise is inappropriate to a medical conclusion).38 A syllogism whose premises are posterior to the conclusion is a syllogism through signs, for in such syllogisms that which is prior is proven through that which is posterior. No further explanation of this claim is provided in this context, but the idea is presumably that in a sign-­ syllogism the cause (what is prior) is proven from the effect (what is posterior). We know from the previous Chapter that Aristotle’s first mention of sign-inferences in the Posterior Analytics is in APo A 6. Here Aristotle draws a contrast between attributes that hold (i.e., are shown to hold) “always but not in themselves” (ἀεὶ εἴη, μὴ καθ᾿αὑτό) and those that hold (i.e., are shown to hold) “in themselves” (καθ᾿αὑτό), and says that οἱ διὰ σημείων συλλογισμοί are to be classed with the former. Themistius makes the following comment on that passage: It should rather be considered those that hold in themselves of each genus about which we make demonstrations; from those and about those are the demonstrative syllogisms. Otherwise, accidents are not necessary, not only 36 Themistius, In APo, ed. Wallies, CAG 5.1, 6.20–26: “ὁ γὰρ ἐπιστημονικὸς συλλογισμὸς τούτῳ μάλιστα τῶν λοιπῶν διενήνοχεν· ἐν μὲν γὰρ τοῖς ἄλλοις δείκνυται καὶ διὰ ψευδῶν τὸ ἀληθές, ὡς παρὰ τοῖς ῥήτορσι πολλάκις, καὶ δι’ὑστέρων τὸ πρότερον, ὥσπερ οἱ διὰ σημείων συλλογισμοί, καὶ δι’ἀληθῶν μὲν οὐκ οἰκείων δέ, ὥσπερ εἴ τις ἰατρὸς τὰ περιφερῆ τῶν τραυμάτων δυσιατότερα ἀποδεικνύοι, διότι τὸ σχῆμα πολυχωρητότερον τῶν λοιπῶν· γεωμέτρου γὰρ ἡ ἀπόδειξις, οὐκ ἰατροῦ.” 37 Cf. supra, §1.6. 38 Cf. Aristotle, APo A 13, 79a15–16.

The Greek Commentators

85

the things that can hold and not hold , but also those that always hold together , but not in themselves. Since also the syllogisms through signs take middle terms that always hold together with the thing; indeed “having milk” always holds of “having given birth,” and “smoke” of “fire”; and yet we are not entitled to call those demonstrative in the strict sense, because what is prior is syllogized through what is posterior.39 Themistius’ interpretation is quite the same as the one we have offered of this passage.40 In a sign-syllogism, the middle term “is the case always but not in itself.” But something that is not καθ᾿αὑτό cannot form the premise of a demonstration καθ᾿αὑτό, i.e., the middle term does not contain or express the appropriate cause of the fact expressed in the conclusion. Themistius uses both the example of τεκμήριον of APr B 27 (the lactating woman) and the example of the smoke as sign of fire. (Alexander uses the example of the ash as sign of fire in his comment on the Prior Analytics;41 as we have just seen, this example is also used by Themistius to illustrate the distinction between the logical and the ontological cause, cf. supra; a related example of smoke and fire is discussed in the comment on APo A 13, and one analogous involving both ash and carbon are used to explicate APo B 17; see infra.) Themistius also says that such inferences that proceed through something that “is the case always but not in itself” are not to be called demonstrations in the proper sense (κυρίως) because they infer what is primary (the cause) from what is secondary (the effect) and not the other way around as demonstrations proper do. It is no hazardous speculation to maintain that Alexander is also the source of the notion of “­demonstration κυρίως” that Themistius is employing here. Themistius’ most exhaustive discussion of sign-inferences occurs in the context of his commentary on APo A 13, the official presentation of the distinction between why-syllogisms and that-syllogisms. We have seen in the previous Chapter that according to APo A 13 that-syllogisms differ from why-syllogisms both across sciences and within the same science, and that within the same 39 Themistius, In APo, ed. Wallies, CAG 5.1, 17.15–23: “μᾶλλον δὲ ἐπισκεπτέον ὅσα καθ᾽αὑτὰ ὑπάρχει περὶ ἕκαστον γένος ὑπὲρ ὧν ποιούμεθα τὰς ἀποδείξεις· ἐκ γὰρ τῶν τοιούτων καὶ περὶ τῶν τοιούτων εἰσὶν οἱ κατ’ἐπιστήμην συλλογισμοί. τὰ δ’ἄλλως συμβεβηκότα οὐκ ἀναγκαῖα, οὐ μόνον δὲ τὰ ἐνδεχόμενα καὶ μὴ ὑπάρχειν, ἀλλὰ καὶ ὅσα ἀεὶ συνυπάρχει, μὴ καθ’αὑτὰ δέ. ἐπεὶ καὶ οἱ διὰ σημείων συλλογισμοὶ λαμβάνουσι μὲν τοὺς μέσους ἀεὶ τῷ πράγματι συνυπάρχοντας· ἀεὶ γὰρ τὸ γάλα ἔχειν ὑπάρχει τῷ τετοκέναι, καὶ ὁ καπνὸς τῷ πυρί· ἀλλ’ ὅμως οὐδὲ τούτους κυρίως ἀποδεικτικοὺς εἴποιμεν ἄν, ὅτι δι’ὑστέρων τὸ πρότερον συλλογίζονται.” 40 Cf. supra, §1.7. 41 Cf. supra, §2.1.

86

chapter 2

science there is again a twofold distinction, according as to whether the syllogism does not proceed from immediates (μὴ δι᾽ ἀμέσων) or whether it does proceed from immediates (δι᾽ ἀμέσων). We conjectured that the expression δι᾽ ἀμέσων may be interpreted extensionally, i.e., as referring to convertibility (and thus μὴ δι᾽ ἀμέσων to non-convertibility); our extensional interpretation of the first part of APo A 13 had the following result. When cause and effect convert and the syllogism is “from immediates” (in our division of the passage, it is the case introduced in section (ii) and illustrated in section (iii)), the demonstration is of the why if the effect is inferred from the (primary, i.e., convertible) cause (1a) and is of the that if the (primary, i.e., convertible) cause is inferred from the effect (1b); this latter is the “prototypical” demonstration of the that. When the cause is more extended than the effect and the syllogism is “not from immediates” (the case introduced in section (i) and further discussed and illustrated in sections (iv) and (v)), the demonstration is of the that if the (non-primary, i.e., non-convertible) cause is inferred from the effect (2a) and is also of the that if the negation of the effect is inferred from the negation of the (non-primary, i.e., non-convertible) cause (2b). The case of an effect more extended than the cause is not discussed by Aristotle. Themistius opens his discussion of APo A 13 with a reference to both the Alexandrian distinction between the logical and the ontological sense of “cause” and the Alexandrian notion of demonstration κυρίως: Knowing scientifically through the cause is said in two ways, one when it is through some middle term; for any middle term is the cause of the inferring of the conclusion; another when it is through the cause of the thing to be proven. Therefore, according to the first sense any syllogism is through the cause; for any is through some middle term. According to the second , however, not any is through the cause of the thing, but only that which we have called demonstrative in the proper sense; although also the other is called demonstrative, when it meets at least the other that we have defined. Thus, let us call “syllogism of the why” that through the cause of the thing, “ of the that” any through the middle term and the true through the true. Thus, it happens both in the same science sometime that one sometimes knows the that and sometimes the why, and that in one science one knows the that and in a distinct the why.42 42 Themistius, In APo, ed. Wallies, CAG 5.1, 27.9–19: “Τὸ δ’ ἐπίστασθαι δι’ αἰτίου λέγεται διχῶς, ἓν μὲν ὅτι διὰ μέσου τινός· πᾶν γὰρ μέσον αἴτιον τῆς συναγωγῆς τοῦ συμπεράσματος· ἓν δὲ

The Greek Commentators

87

In a why-syllogism, the premises are the cause of the conclusion in the ­ontological sense: τοῦ πράγματος αἰτία, “cause of the thing” that is demonstrated in the conclusion. In a that-syllogism, by contrast, the premises are the cause of the conclusion only in the logical sense: διὰ μέσου τινός, “through some middle term,” i.e., not through a middle term that is also the cause of the conclusion in the ontological sense; in this second sense, the middle term is only the cause of the drawing of the conclusion (αἴτιον τῆς συναγωγῆς τοῦ συμπεράσματος). The difference between why-demonstrations and that-demonstrations is both in the same and in different sciences. Thus, let us first speak about how in the same science. One way is this. Since the cause of the thing must belong in itself and proximately to that of which it is the cause, the one that syllogizes through a mediate syllogizes the that, the other that through an immediate for the most part the why.43 Following Aristotle, Themistius begins with the that/why contrast within the same science, and offers his interpretation of the first way in which this difference occurs, i.e., the case announced in section (i) of APo A 13. The basic idea is that the inference of an effect from a non-proximate cause is a that-­demonstration, the inference of an effect from a proximate cause a why-demonstration. Some examples follow which show that with regard to the first difference announced in section (i) Themistius is not thinking in terms of convertibility (as we conjectured Aristotle does in APo A 13). Thus, if we prove that southern stars set sooner than northern stars because they are farther from the north pole we have a that-demonstration because being far from the north is the non-proximate cause of setting sooner; but if we prove that southern stars set sooner than northern stars because they have a smaller arc above the earth than below the earth, this counts as a why-demonstration διὰ τῆς τοῦ πράγματος αἰτίας τοῦ δεικνυμένου. κατὰ μὲν οὖν τὸ πρῶτον σημαινόμενον ἅπας συλλογισμὸς δι’ αἰτίου· καὶ γὰρ ἅπας διὰ μέσου τινός. κατὰ τὸ δεύτερον δὲ οὐχ ἅπας ἀλλ’ ὁ διὰ τῆς αἰτίας τοὐ πράγματος· τοιοῦτος δὲ μόνος ὃν κυρίως ἀποδεικτικὸν ἐλέγομεν· ἐπεὶ λέγεται καὶ ὁ ἕτερος ἀποδεικτικός, ὅταν ἔχῃ τἄλλα γοῦν ὅσα διωρίσαμεν. λεγέσθω τοίνυν τοῦ μὲν διότι συλλογισμὸς ὁ διὰ τῆς αἰτίας τοῦ πράγματος, τοῦ δ’ ὅτι πᾶς ὁ διὰ μέσου καὶ δι’ ἀληθῶν ἀληθής. ἔστι μὲν οὖν καὶ κατὰ τὴν αὐτὴν ἐπιστήμην ποτὲ μὲν τὸ διότι ἐπίστασθαι ποτὲ δὲ τὸ ὅτι, ἔστι δὲ καὶ καθ’ ἑτέραν μὲν τὸ ὅτι καθ’ ἑτέραν δὲ τὸ διότι.” 43 Themistius, In APo, ed. Wallies, CAG 5.1, 27.20–23: “Πρῶτον μὲν οὖν εἴπωμεν πῶς κατὰ τὴν αὐτὴν ἐπιστήμην. εἷς μὲν οὖν τρόπος οὗτός ἐστιν· ἐπειδὴ γὰρ τὸ τοῦ πράγματος αἴτιον καθ’ αὑτὸ δεῖ ὑπάρχειν καὶ προσεχῶς οὗ ἐστιν αἴτιον, ὁ μὲν δι’ ἐμμέσων συλλογιζόμενος τὸ ὅτι συλλογίζεται, ὁ δὲ δι’ ἀμέσων ὡς ἐπὶ τὸ πολὺ τὸ διότι.”

88

chapter 2

because having a smaller arc above the earth than below it is the proximate cause of setting sooner.44 The two syllogisms that Themistius has in mind are the following: (28a, that-demonstration) What is farther from the north pole (non-proximate cause) sets sooner than the northern ones (effect) Southern stars (subject) are farther from the northern pole (non-­ proximate cause) Hence, southern stars (subject) set sooner than northern ones (effect) (28b, why-demonstration) What has a smaller arc above the earth than below (proximate cause) sets sooner than the northern ones (effect) Southern stars (subject) having a smaller arc above the earth than below (proximate cause) Hence, southern stars (subject) set sooner than northern ones (effect) Both (28a) and (28b) are first-figure syllogisms. It is a condition of the truth of the major premise in both that its subject (middle term) be not more extended than its predicate (major term in the predicative sense). If this is so, then ­neither (28a) nor (28b) can be assimilated to the case considered by Aristotle in sections (iv) and (v) of APo A 13, where he explicitly says that he is considering a middle term that is more extended than the major. We noticed that when the middle term is more extended than the major, a that-syllogism from the effect to the cause is possible in the first figure (it is what Aristotle alludes to in section (iv)), while a that-syllogism from the cause to the effect is only possible in the second figure, i.e., is only possible in the form of an inference of the negation of the effect from the negation of the cause (like in the second-­ figure argument of section (v)). Themistius is not thinking in extensional terms here; for him, a cause that belongs καθ’ αὑτὸ καὶ προσεχῶς to the effect is not convertible with that effect; for him δι’ ἀμέσων is not related to convertibility. His two causes, the proximate and the non-proximate, are in the same extensional relation to the effect, and must not be more extended than it if the truth of the major premise has to be preserved. The example that follows has the same form as the one concerning southern stars: thus, if we prove that the soul is immortal because it is a self-mover, the 44 Themistius, In APo, ed. Wallies, CAG 5.1, 28.24–28.

The Greek Commentators

89

cause is not proximate and the argument is a that-demonstration; if by contrast the same thing is proved on the basis of its being a principle of life, the cause is proximate and the argument a why-demonstration.45 By contrast, the third example, clearly inspired by the non-breathing wall of APo A 13, is explicitly extensional: [...] that plants do not breathe, because they are not animals, through a mediate , that < plants do not breathe > because they have no lungs, through an immediate . For not being an animal is not the proximate cause of not breathing (for if it were, also being an animal would be the proximate cause of breathing; and yet there are many animals that do not breath, like insects), but the primary cause of not breathing is not having lungs; thus animal has been taken as a cause at some distance, and in addition externally and not immediately predicated of breathing, but by means of having lungs, not being an animal is an exceding predicate. […] And the syllogisms concerning such causes are in the second figure, I mean those from a distant which I have just mentioned; for since animal is predicated of anything that breathes, and of no plant, plants do not breathe.46 The example is the same as Aristotle’s, with plants as the minor term. Themistius seems to be saying that in this case (as in the following example concerning Scythia having the same form) the middle term is not just a cause that belongs non-proximately (προσεχῶς) to the effect, as in the preceding two examples; in this case the middle term (“not animal”) is “at some distance” (πόρρωθεν): this means, he proceeds to explain, that the middle is “externally” (ἔξω) and “not immediately” (οὐκ ἀμέσως) predicated of the major term (“not breathing”); ἔξω is precisely the expression used by Aristotle at APo A 13, 78b13 in his introduction of section (v). Themistius seems to realize that when the middle term is more extended than the major, the argument from the middle term (the cause) to the major (effect) can only be in the second figure, i.e., from the negation of 45 Themistius, In APo, ed. Wallies, CAG 5.1, 28.29–31. 46 Themistius, In APo, ed. Wallies, CAG 5.1, 27.31–28.13: “ὁ μὲν τὰ φυτὰ μὴ ἀναπνεῖν, ὅτι μὴ ζῷα, δι’ ἐμμέσων, ὁ δὲ ὅτι μὴ πνεύμονα ἔχει, δι’ ἀμέσων· οὐ γὰρ τὸ μὴ εἶναι ζῷον προσεχὲς αἴτιον τοῦ μὴ ἀναπνεῖν (ἦν γὰρ ἂν καὶ τὸ εἶναι ζῷον τοῦ ἀναπνεῖν αἴτιον προσεχῶς· πολλὰ δὲ ζῷα μέν, οὐκ ἀναπνεῖ δέ, ὡς τὰ ἔντομα), ἀλλὰ πρῶτον αἴτιον τοῦ μὴ ἀναπνεῖν τὸ μὴ πνεύμονα ἔχειν· τὸ ζῷον οὖν πόρρωθεν εἴληπται αἴτιον, ἔξω πάλιν καὶ οὐκ ἀμέσως κατηγορούμενον τοῦ ἀναπνεῖν ἀλλὰ διὰ μέσου τοῦ πνεύμονα ἔχειν, τὸ δὲ μὴ εἶναι ζῷον ὑπερβολή. […] γίνονται δὲ καὶ ἐν τῷ δευτέρῳ σχήματι τῆς τοιαύτης αἰτίας συλλογισμοί, λέγω δὲ [οἱ] τῆς πόρρωθεν, ὥσπερ οἱ νῦν εἰρημένοι· ἐπεὶ γὰρ τὸ ζῷον κατὰ μὲν τοῦ ἀναπνεῖν παντός, κατὰ φυτοῦ δὲ οὐδενός, τὰ φυτὰ οὐκ ἀναπνεῖ.”

90

chapter 2

the former to the negation of the latter. Themistius thus connects section (v) to section (i) as follows: not all syllogisms from a non-proximate cause (“not from immediates”) are in the second figure, but only those in which the middle term is more extended than the major. If this reconstruction is correct, Themistius does not read section (i) as involving some extenstional qualification of a cause that is more extended than the effect; and he does not connect the extensional qualifications introduced in section (iv) with the difference between that- and why-syllogisms announced in section (i) at APo A 13, 78a23 (“not from immediates”); section (iv) is rather read by him along with sections (ii) and (iii), as a further division of the case announced in section (ii) (“from immediates”). With regard to section (i), he seems to think that a non-immediate cause may be non-immediate both in the sense of being not-proximate but not necessarily more extended than the effect (examples of southern stars and immortal souls) and in the sense of being extensionally “external,” i.e., more extended than the effect (example of non-breathing plants). So his interpretation of the case announced in section (i) (“not from immediates”) is only partially extensional; it is so only with regard to the second-figure syllogism of section (v), which indeed is unexplicable other than extensionally. On the contrary, Themistius’ interpretation of the second difference between that- and why-syllogisms, the difference announced in section (ii) and illustrated in section (iii) (“from immediates”), is fully extensional: In another way when both are through immediates, but one is through the cause and the other through the sign. For the one the possession of milk through having given birth proves the why, while the one having given birth through the possession of milk the that; and the one the waxing of the moon through its being spherical the why, while the one its being ­spherical through its waxing the that. Often it certainly happens that cause and sign convert with one another and either is proved through the other, the that through the sign, the why through the other, through the former as far as better known than the conclusion, through the latter as far as the cause of the thing.47 47 Themistius, In APo, ed. Wallies, CAG 5.1, 28.15–23: “ἕτερος δὲ τρόπος, ὅταν δι᾽ ἀμέσων μὲν ἄμφω, άλλ’ ὁ μὲν διὰ τῆς αἰτίας ὁ δὲ διὰ τοῦ σημείου· ὁ μὲν γὰρ διὰ τοῦ τετοκέναι τὸ γάλα ἔχειν ἀποδείκνυσι τὸ διότι, ὁ δὲ διὰ τοῦ γάλα ἔχειν τό τετοκέναι τὸ ὅτι· καὶ ὁ μὲν τὰς αὐξήσεις τῆς σελήνης διὰ τοῦ σφαιροειδοῦς τὸ διότι, ὁ δὲ τὸ σφαιροειδὲς διὰ τῶν αὐξήσεων τὸ ὅτι. πολλάκις

The Greek Commentators

91

There is no indication that Themistius is interpreting δι᾽ ἀμέσων as a reference to convertibility; he simply follows Aristotle’s analysis of converting causes and effects in sections (ii) and (iii) of APo A 13. The example of the waxing of the moon which allows to infer its being spherical, comes from APo A 13, where it illustrates the prototypical that-syllogism (1b). The example of the lactating woman, by contrast, comes from APr B 27, and is there characterized by Aristotle as an irrefutable or deductively valid sign-argument or an enthymeme based on a τεκμήριον. Again, Alexander may well be the source for the association of the τεκμήριον of APr B 27 with the prototypical that-syllogism (1b) of APo A 13 that Themistius makes in commenting on this passage. Themistius then examines the case in which cause and effect do not convert. He says: Often the signs and the causes of the same things do not convert. If smoke, inevitably fire. If fire, not inevitably smoke. And if has given birth, has had intercourse with a man. If has had intercourse with a man, it is not inevitable that she has given birth. In such cases there is demonstration of the that, while the of the why is missing, for it is possible to demonstrate the cause through the sign, but not the sign through the cause.48 A cause may be more extended than the effect. In this case, either one infers the cause from the effect, as in (23) of Chapter 1, or the negation of the effect from the negation of the cause, as in (22) and (24) of Chapter 1. Both are that-­ demonstrations (of types 2a and 2b, respectively). Themistius interprets the extensional qualifications introduced in section (iv) (“cause more extended than the effect”) as a further division of the case announced in section (ii) (“from immediates”), and not, as we did, as a specification of the case announced in section (i) (“not from immediates”). Therefore, he considers only the positive inference of the cause from the effect (2a) because he has already treated of the negative inference of the effect from the cause, i.e., of the second-figure μὲν οὖν συμβαίνει καὶ ἀντιστρέφειν ἀλλήλοις τὸ αἴτιον καὶ τὸ σημεῖον καὶ ἄμφω δείκνυσθαι δι’ἀλλήλων, διὰ τοῦ σημείου μὲν ὡς τὸ ὅτι, διὰ θατέρου δὲ ὡς τὸ διότι, δι’ οὗ μὲν ὡς γνωριμωτέρου τοῦ συμπεράσματος, δι’ οὗ δὲ ὡς αἰτίου τοῦ πράγματος.” 48 Themistius, In APo, ed. Wallies, CAG 5.1, 28.23–28: “πολλάκις δὲ οὐκ ἀντιστρέφει τὰ σημεῖα τοῖς αἰτίοις αὐτών· εἰ μὲν γὰρ καπνός, πάντως καὶ πῦρ· εἰ δὲ πῦρ, οὐ πάντως καπνός· καὶ εἰ μὲν τέτοκεν, ἀνδρὶ πεπλησίακεν· εἰ δὲ πεπλησίακεν, οὐ πάντως τέτοκεν. ἐπὶ δὴ τῶν τοιούτων ἡ μὲν τοῦ ὅτι δεῖξις ἔστιν, ἡ δὲ τοῦ διότι ἐκλείπει· διὰ μὲν γὰρ τοῦ σημείου τὸ αἴτιον ἔστιν ἀποδεῖξαι, διὰ δὲ τοῦ αἰτίου τὸ σημεῖον οὐκέτι.”

92

chapter 2

argument of section (v), under the first mode of the why/that distinction (“not from immediates”); since he has already considered that case, his treatment of section (iv) is completely disconnected from it. The second example that he makes is the one that we have proposed in Chapter 1 to illustrate sections (iv) and (v). Indeed, it was so chosen precisely because it comes from this passage in Themistius’ paraphrase. Themistius is explicit in considering the effect as a sign of the cause. Having given birth and having had intercourse with a man do not convert: the intercourse is the cause of giving birth, but not all occurrences of the cause are accompanied by an occurrence of its sign. If from the fact that a woman has given birth we infer that she has had intercourse with a man, the syllogism is of the that (of type 2a), because the cause (intercourse with a man) is inferred from a sign of it (giving birth). But there cannot be a syllogism of the why in the first figure, because the cause is more extended than its sign (not all intercourses have that effect). If Themistius had connected sections (iv) and (v) of APo A 13 as we have done, he would have added that while it is impossible to demonstrate the sign through the cause (positively, or in the first figure), it is possible to demonstrate the absence of the sign from the absence of the cause (negatively, or in the second figure). (The first example is the relation between fire and smoke, to which we return below.) Sign-inferences are possible for Themistius in both the case illustrated in section (ii) and (iii) and in the case introduced in section (iv) (which he does not connect to section (i) or (v)). The first kind of sign-inference occurs when cause and sign convert, and the sign-inference that results has the form of a that-demonstration of type 1b. The second is when cause and effect do not convert and the cause has a wider extension than the effect; the sign-inference that results has the form of a that-demonstration of type 2a. In either case, the effect is associated with the sign because it is better known than the cause. That-demonstrations of kind 2b are not epistemically characterized; indeed there is no plausible epistemic characterization of the inference of the ­negation of the effect from the negation of the cause. This is perhaps the reason why Themistius disconnects section (v) from sections (ii), (iii), and (iv), and only provides an epistemic and semiotically oriented interpretation of the latter. We mentioned that the case of an effect more extended than its cause is not even mentioned by Aristotle, because in that case no deductively valid inference from the effect to the cause would be possible. Neither does Themistius consider such a case; but he does consider the case of converting effects of the same cause:

The Greek Commentators

93

And just as not all the causes and effects convert, so not all the terms that convert are causes and effects. It is indeed possible that several signs of one and the same cause convert with one another, for example the signs of fever which both tracheitis and this kind of heat. While these things indicate each other, according to neither is there a syllogism of the why but according to both of the that.49 It may happen that two or more effects follow from one and the same cause, and that these effects convert with one another. The example offered is that of the infection of the trachea and the heat of the body, which are both effects of fever and which convert (all cases of tracheitis are cases of heat of the body and vice versa). Both tracheitis and corporal heat are effects, and thus signs, of fever. Inferring the fever from either of its effects or signs counts as a valid syllogism of the that.50 But are converting effects also signs of each other? ­Themistius says that either of two (or more) converting effects δείκνυται the other, not that either is a σημεῖον of the other. However, a case can be made for the view that converting effects “indicate” in the sense of being each the sign of the other. Both tracheitis and corporal heat may be better known than their cause (fever), and thus they are able to function as signs of it. But it may also be the case that in certain circumstances either is better known than the other: we may be able to measure corporal heat but unable to detect tracheitis. In this case, since the effects convert, one can be said to indicate or be a sign of the other. We would thus have a syllogism of the that or τεκμήριον from either effect to the cause when the converting effects are equally known, and from either effect to the other effect when one is better known than the other. Be that as it may, Themistius is the only one among the commentators of the ­Posterior Analytics to have explicitly considered the inferential behavior of distinct effects 49 Themistius, In APo, ed. Wallies, CAG 5.1, 28.28–29.3: “ὥσπερ οὖν οὐδὲ πάντα τὰ αἴτιά τε καὶ αἰτιατὰ ἀντιστρέφει, οὕτως οὐδὲ πάντα τὰ ἀντιστρέφοντα αἴτιά τέ ἐστι καὶ αἰτιατά· δυνατὸν γὰρ τοῦ αὐτοῦ αἰτίου πλείω σημεῖα πρὸς ἄλληλα ἀντιστρέφειν, οἷον τοῦ πυρέττειν σημεῖα ἥ τε ταραχὴ τῆς ἀρτηρίας καὶ ἡ τοιάδε θερμότης. δείκνυται μὲν οὖν δι’ ἀλλήλων καὶ τὰ τοιαῦτα, κατ’οὐδέτερον δὲ ὁ τοῦ διότι συλλογισμός, ἀλλὰ κατ’ἀμφότερα ὁ τοῦ ὅτι.” 50 The example is not Aristotelian. In the Sophistici Elenchi the inference from a man’s being hot to his being in a fever is an instance of the fallacy of the consequent (Soph El 5, 167b19–20). In the Rhetoric fever is a necessary sign (τεκμήριον) of illness (Rhet A 2, 1357b15–16), and hard breath a refutable sign (σημεῖον in the strict sense) of fever (1357b18–21). In the first example the fever is the sign, in the other the cause revealed by the sign. Themistius’ example may derive from medical literature. The expression ταραχὴ τῆς ἀρτηρίας is here rendered with “tracheitis,” a bacterial infection of the windpipe resulting in severe cough, breathing difficulty and usually associated with high temperature.

94

chapter 2

of one and the same cause. The topic seems to have escaped the attention of later interpreters.51 The second part of APo A 13 is devoted to the that/why contrast in distinct sciences. When of two distinct sciences one is subordinated to the other, the superordinated science provides knowledge of the why, the subordinated science knowledge of the that.52 Since Themistius has identified two of the three types of that-demonstration of the first part of APo A 13 with sign-inferences, it is natural for him to make this identification whenever knowledge of the that is at stake. So e.g., in his commentary on APo A 27, 87a31–33, where Aristotle says that a science can be more rigorous than another if the former shows both the that and the why, while the latter only shows the that without the why, Themistius explicitly associates the science that shows the that without the why with the demonstration through signs: A science is more rigorous than and prior to another in different ways. In one way, when the one shows the that from the why, the other only the that without the why; it is clear that one of this sort demonstrates not through the primary causes but through secondary and through signs.53 The effect is secondary and the cause is primary; the science that shows both the that and the why shows that the effect is and why it is, while the ­science that shows only the that without the why only shows that the cause exists (for the effect is not the why of the cause), and thus shows what is ­primary through what is secondary, the cause through an effect or sign of it. It has emerged from our analysis of Themistius’ commentary on APo A 13 that like Alexander, Themistius identifies the prototypical that-demonstration of that chapter (1b) with the syllogism from signs, both implicitly by means of the examples, and explicitly: the identification is based on two Alexandrian ideas, i.e., the distinction between the logical and the ontological sense in which the premises of an argument may be said to be causes of the conclusion, and the distinction between a “proper demonstration” (in which the effect is inferred from the cause) and a demonstration in a “secondary sense” (in which 51 With two exceptions: Avicenna and Averroes; see infra, §5.3.1. 52 Aristotle, APo A 13, 79a2–3, 11–13. 53 Themistius, In APo, ed. Wallies, CAG 5.1, 37.8–11: “Ἀκριβεστέρα δὲ ἐπιστήμη ἐπιστήμης καὶ προτέρα κατὰ πλείονας τρόπους. καθ’ ἕνα μέν, ἐὰν ἐκ τοῦ διότι τὸ ὅτι δεικνύῃ, ἡ δὲ μόνον τὸ ὅτι χωρὶς τοῦ διότι· ἡ γὰρ τοιαύτη δῆλον ὅτι οὐ διὰ τῶν πρώτων αἰτίων ἀλλὰ διὰ τῶν ὑστέρων καὶ τῶν σημείων ἀποδείκνυσι.”

The Greek Commentators

95

the cause is inferred from the effect). In addition, he also identifies the second type of that-demonstration of APo A 13 (2a), in which a more extended cause is inferred from one effect of it, with sign-syllogisms. There is no evidence that Alexander ever made this latter identification, but nothing excludes it, either. With regard to APo B 17, which as we know contains the second and last mention of sign-inferences in that work, Themistius offers the following interpretation: It is not possible that of the same thing the middle and the cause be multiple, if the proof is through an accident or through a sign. For example, why do the trees shed their leaves? Because they shrivel up or because they lose their color. Or the fire has burnt? Because it has left carbon or because ash. But it was said many times that this is not a demonstration, nor are these things causes of the thing, but of the conclusion only.54 As we saw in the previous section, this is roughly the interpretation that we find in the anonymous commentary containing portions of Alexander’s lost commentary: according to the Anonymous, when in APo B 17 Aristotle says that sometimes the causes can be multiple, he is talking of the “logical cause” of the conclusion, and that this is what Aristotle has in mind is shown, according to the Anonymous, by Aristotle’s mention of semiotic syllogisms; when, by contrast, Aristotle says that no multiplicity of causes is possible, according to the Anonymous he is talking of the “ontological cause” of the fact expressed in the conclusion. Themistius’ interpretation is very similar, but he seems to further distinguish between the case in which something is inferred διὰ συμβεβηκότος from the case in which it is inferred διὰ σημείου. So, when a tree sheds its leaves it may happen that it also shrivels up or loses its color; if the shedding of leaves is inferred from either, these count as accidents from which something is inferred, and thus as logical causes of the inferred conclusion, by no means as the ontological cause of it. The same applies to the fire example: if the past presence of fire is inferred from the actual presence of carbon or ash, these count as signs of fire and may be taken as the logical cause of the inferred conclusion, but not as its ontological cause. In either case, Themistius’ point 54 Themistius, In APo, ed. Wallies, CAG 5.1, 61.6–11: “Πλείω δὲ ταὐτοῦ μέσα τε καὶ αἴτια εἶναι οὐχ οἷόν τε, εἰ μὴ ἄρα διὰ συμβεβηκότος ἡ δεῖξις ἢ διὰ σημείου προΐοι· οἷον διὰ τί τὰ δένδρα φυλλορροεῖ; διότι ῥυτιδοῦται ἢ διότι λευκαίνεται· ἢ τὸ πῦρ κέκαυται; διότι ἄνθρακες ὑπολείπονται ἢ διότι τέφρα. ἀλλ’ εἴρηται πολλάκις ὅτι οὐδὲ ἀπόδειξις τὸ τοιοῦτον οὐδὲ αἴτια τοῦ πράγματος τὰ τοιαῦτα, ἀλλὰ τοῦ συμπεράσματος μόνον.”

96

chapter 2

is that when the cause of something appears to be multiple, “cause” has to be taken in the logical sense. Fire, as a cause, may have smoke, carbon, and ash as effects or signs of it. What is the relation between these four ingredients of burning, extensionally speaking? The example of fire and ash is already in Alexander, and Themistius himself uses it in explaining the notion of logical cause. Alexander seems to consider fire and ash to be convertible, and so does Themistius. Moreover, in commenting on section (iv) of APo A 13 Themistius follows Aristotle and considers only the case in which the cause has wider extension than the effect; the first of his examples is smoke, which is an effect and a sign of fire, but an effect that is less extended than the cause (“If there is smoke, there is inevitably fire. If there is fire, there is not inevitably smoke”). Finally, in his comments on APo B 17 Themistius seems to think of carbon and ash as signs from which a deductively valid inference can be made to the past presence of fire as their cause, but it is not clear whether the converse inference of either or both carbon and ash from the actual presence of fire would count as a deductively valid inference from cause to effect. If it does, then we are again in the paradigmatic case of full convertibility between causes and (multiple) effects. If it does not, then the case is rather that of section (iv) of APo A 13, in which we have a cause that is more extended than its effect: not all cases of fire are also cases of either carbon or ash. Be that as it may, even though his interpretation of the first part of APo A 13 is not wholly extensional, Themistius may be said to have built upon Aristotle’s extensional typology of that-demonstrations in that chapter and to have (partially) turned it into an extensional typology of sign-inferences, for he ­recognizes at least two distinct sign-inferences in APo A 13 (1b and 2a), and perhaps he also sees a third, of which Aristotle says nothing, in the inference of an effect from another effect of the same cause. As we shall see in what follows, his ideas will be subject of further development and refinement in the Greek, Arabic, and Latin traditions of the Posterior Analytics. Themistius’ immediate follower in this tradition is, of course, John Philoponus. 3 Philoponus In his commentary on the first55 book of the Posterior Analytics, Philoponus declares that he is reporting the teachings of his master Ammonius (440–523 55

The commentary on the second book published in CAG 13.3 was deemed to be spurious already by Wallies. We discuss this work infra, §2.6.

The Greek Commentators

97

CE). While Alexander is criticized at various places in Philoponus’ commentary,56 it is probable that he never had Alexander’s commentary in his hands, and that in criticizing Alexander he was in fact relying on Ammonius.57 The same could apply to another prima facie obvious source for Philoponus, namely Themistius’ paraphrase;58 but the fact that on at least one occasion59 Philoponus invokes Themistius against Ammonius’ interpretation of APo A 13, 78b28–34 might suggest that he knew the former’s work independently of the latter. Like Alexander and Themistius, Philoponus makes some important associations between sign-inferences and scientific demonstrations. His first mention of sign-inferences is in his commentary on the beginning of APo A 2, which contains Aristotle’s definition of scientific knowledge. Aristotle says: “We think we understand something simpliciter (and not in the sophistical way, incidentally) when we think we know of the cause because of which the object holds that it is its cause, and also that it is not possible for it to be otherwise.”60 Philoponus explains that the contrast between proper knowledge and sophistical knowledge that is made in this passage should not mislead us into thinking that all non-demonstrative knowledge is sophistical. On the contrary, there is a sort of knowledge that is not properly demonstrative and yet is not sophistical: clearly there are other syllogisms, in between sophistical ones and scientific ones, that establish truths on the basis of likely , but in neither the demonstrative nor the sophistical way. For example, people who say “such and such a person is a dandy, so he is an adulterer” or “such and such a person wanders around during the night, so he is a thief” or “the woman has milk, so she has given birth.” These are plausible signs (πιθανὰ τεκμήρια), but they are certainly not the causes of the conclusion (αἴτια τοῦ συμπεράσματος). For it is possible for someone to be a dandy but not an adulterer or to be wandering around at night but not a thief, and to have milk but not to have given birth.61 56

He is mentioned in Philoponus, In APo, ed. Wallies, CAG 13.3, 4.1; 41.2; 62.2, 11–14; 111.20– 112.1; 122.11; 126.3; 139.9; 159.18; 160.8–13; 174.4–10; 181.11–13; 196.9. 57 Cf. Moraux (1979), 5; McKirahan (2008), 2. 58 Cited in Philoponus, In APo, ed. Wallies, CAG 13.3, 48.8; 70.8–10; 138.5–6; 177.27–28. 59 Philoponus, In APo, ed. Wallies, CAG 13.3, 177.19–178.14. 60 Aristotle, APo A 2, 71b9–12; transl. Barnes, modified. 61 Philoponus, In APo, ed. Wallies, CAG 13.3, 21.8–15: “εἰσὶ γὰρ δῆλον ὅτι καὶ ἄλλοι συλλογισμοὶ μεταξὺ τῶν τε σοφιστικῶν καὶ τῶν ἐπιστημονικῶν, ἀληθῆ μὲν καὶ ἐξ εἰκότων κατασκευάζοντες, οὐ μὴν τὸν ἀποδεικτικὸν τρόπον οὔτε τὸν σοφιστικόν, οἷον ὡς οἱ λέγοντες ῾ὁ δεῖνα καλλωπιστής, μοιχὸς ἄρα᾿· ῾ὁ δεῖνα νύκτωρ πλανᾶται, κλέπτης ἄρα᾿· ῾ἡ γυνὴ γάλα ἔχει, τέτοκεν ἄρα᾿· ταῦτα γὰρ πιθανὰ μὲν τεκμήρια, οὐ πάντως δ᾿ αἴτια τοῦ συμπεράσματος· δυνατὸν γὰρ καὶ καλλωπιστὴν

98

chapter 2

Philoponus’ idea is clear enough: sign-inferences are not demonstrative and yet are not sophistical. Yet the passage is puzzling for at least three reasons. The first is purely terminological. The first two examples that Philoponus adduces (the adulterer and the thief) are from Soph El 5, where they illustrate the semiotic variety of the fallacy of the consequent, which we have argued can be construed as deductively invalid sign-syllogism in the second figure. Actually, in Soph El 5 both fancy dressing and wandering about at night are taken to be signs (in the strict sense) of being an adulterer, while here the example is split: fancy dressing is a sign of being an adulterer, while wandering about at night is a sign of being a thief. It is in this split form that the example will return in later authors, as we shall see.62 Aristotle calls such arguments κατὰ τὸ σημεῖον ἀποδείξεις,63 and in APr B 27 and in the Rhetoric he reserves the term τεκμήριον for deductively valid sign-syllogisms in the first figure.64 Now, Philoponus is surely aware of this terminological distinction (as we shall see in a moment), but decides to call these invalid sign-inferences τεκμήρια rather than σημεῖα. The qualification πιθανά may perhaps be taken as indicating a weaker sense of τεκμήριον, but the problem remains that these arguments, as Philoponus himself certainly recognizes, are based on σημεῖα and not on τεκμήρια. The second reason why the passage is puzzling is both terminological and substantive. The third example that Philoponus uses, the lactating woman, is Aristotle’s example of deductively valid sign-syllogism in the first figure or τεκμήριον. Yet, Philoponus does not treat it as a deductively valid argument: he thinks that having milk is a sign (σημεῖον in the strict sense) of having given birth, but not a τεκμήριον of it, for it is possible for a woman to have milk without having given birth. As mentioned, in the Historia animalium Aristotle points out that some animals are known to produce milk without getting ­pregnant and a fortiori without giving birth.65 The syllogism that results in this case is, according to Philoponus, deductively invalid, and therefore qualifies, just like the two examples from Soph El 5, as a deductively invalid sign-syllogism in the second figure, and like them it should be called a σημεῖον, not a τεκμήριον. The third reason why the passage is puzzling is that of his three examples of invalid sign-inferences Philoponus says that they (i.e., their premises) are not the “causes of the conclusion” (αἴτια τοῦ συμπεράσματος). We know that this εἶναί τιvα, μὴ μοιχὸν δέ, καὶ νύκτωρ πλανώμενον, μὴ κλέπτην δέ, καὶ γάλα ἔχειν, μὴ τετοκέναι δέ.” Transl. McKirahan, modified. 62 Cf. infra, §§2.7, 6.2. 63 Cf. supra, §1.7. 64 Cf. supra, §§1.2, 1.4. 65 Aristotle, Historia animalium, 522a2ff; cf. supra, footnote Chapter 1, footnote 79

The Greek Commentators

99

expression stems from APo A 2 and that both Alexander and Themistius distinguish two senses of it: in one sense, the premises are causes of the conclusion in that they are the basis from which the conclusion can be (validly) inferred; in this sense the premises are the logical cause of the conclusion. In another sense, the premises are causes of the conclusion in that they express the element that is the cause of the fact expressed in the conclusion; in this sense, the premises are the ontological cause of the conclusion. Now, Philoponus seems to be aware of this distinction, for in a later passage he says that the phrase “necessarily follows” has two meanings: it means “either that the conclusion certainly follows if are posited [logical cause], or that in addition the cause of the conclusion is observed in the middle term [ontological cause].”66 Though he is probably aware of it, unlike Alexander and Themistius Philoponus never invokes this distinction in his discussions of sign-inferences. The only exception to this is the present passage. The question therefore is: what does it mean that in invalid sign-syllogisms like those of Soph El 5 and APr B 27 the premises are not the causes of the conclusion? They are certainly not the logical cause of the conclusion, because being the logical cause of the conclusion means, in the Alexandrian and Themistian sense, that the drawing of the conclusion is caused by the premises, i.e., that the conclusion can be validly inferred from the premises, and this is not the case with deductively invalid sign-syllogisms. On the other hand, in such arguments the premises are not the ontological cause of the conclusion (i.e., such arguments are not demonstrations), because the (probable) cause is inferred from its effect rather than the other way around. Yet, in this latter case either the claim or the examples are unhappy, because in all sign-inferences, including deductively valid ones, the premises are not the ontological cause of the conclusion. In invalid sign-inferences the premises are the cause of the conclusion in neither the logical nor the ontological sense. Which sense Philoponus meant remains undetermined. In any case, the Alexandrian and Themistian distinction between a logical and an ontological sense of the claim that the premises are causes of the conclusion appears to play no role in Philoponus’ explication of sign-inferences. When he in other places speaks of the “cause of the conclusion,” he has the ontological sense invariably in mind, and it is in opposition to the ontological causality of the premises in proper demonstrations that he speaks of “semiotic demonstrations.” With a few exceptions, one of which is the passage just considered—others will be discussed below—, Philoponus calls a deductively valid sign-syllogism 66 Philoponus, In APo, ed. Wallies, CAG 13.3, 96.18–20; transl. McKirahan.

100

chapter 2

in the first figure a τεκμήριον in the proper Aristotelian sense. For example, in commenting upon APo A 2, 71b22, where Aristotle says that the premises of a demonstration must be prior to and causes of the conclusion, Philoponus observes that “if we go backwards from the effect to the cause, such a thing is no longer a demonstration but a sign (τεκμήριον). For example, ‘the sun is eclipsed, that which is eclipsed is screened, therefore the sun is screened’.”67 We saw that in his commentary on Top A 1 Alexander juxtaposes the milk example of APr B 27 and the eclipse example of APo B 16, thus implicitly identifying Aristotle’s τεκμήρια with that-syllogisms of the first type (1b). The eclipse example of APo B 16 is explicitly considered by Philoponus not as a demonstration but as a “sign,” in which the premises are not the (ontological) cause of the conclusion but rather contain the effect from which the cause is inferred. According to Philoponus, a τεκμήριον is a demonstration, though not a demonstration in the strict sense: demonstration in the strict sense in fact should confirm things that are secondary and less clear on the basis of things that are primary, immediate, and better known. But since what is better known in nature is not in all cases better known to us too, it often happens that we construct our proofs of things that are prior on the basis of things that are posterior, on account of the fact, as I said, that the things that are prior are not better known to us. And this kind of proof is called from a sign and irrefutable. As a result it has received the name “demonstration” as well. For demonstration in the strict sense, as I said, is one that confirms things that are secondary on the basis of things that are prior, when being primary and known in nature and being better known to us coincide. But when this does not obtain, but we are compelled to confirm things that are prior on the basis of things that are posterior, this kind of proof is called from a sign, and because of the irrefutability of signs, it has been deemed worthy of the name “demonstration.”68

67 Philoponus, In APo, ed. Wallies, CAG 13.3, 26.13–15; transl. McKirahan. 68 Philoponus, In APo, ed. Wallies, CAG 13.3, 31.6–17: “ἡ μὲν γὰρ κυρίως ἀπόδειξις τῷ ὄντι ἐκ πρώτων καὶ ἀμέσων καὶ γνωριμωτέρων τὰ δεύτερα πιστοῦσθαι ὀφείλει καὶ ἀσαφέστερα· ἐπειδὴ δὲ οὐ πάντως τὸ τῇ φύσει γνωριμώτερον καὶ ἡμῖν ἐστι γνωριμώτερον, συμβαίνει πολλάκις ἐκ τῶν ὑστέρων ἡμᾶς τὰς πίστεις τῶν προτέρων ποιεῖσθαι διὰ τὸ μή, ὡς εἶπον, γνωριμώτερα ἡμῖν εἶναι τὰ πρότερα. καὶ καλεῖται τὸ τοιοῦτον εἶδος τῆς δείξεως τεκμηριῶδες καὶ ἄλυτον· ὅθεν καὶ τὸ ἀπόδειξις ὀνομάζεσθαι ἔσχεν. ἡ μὲν γὰρ κυρίως ἀπόδειξις, ὡς εἶπον, ἐστὶν ἐκ τῶν προτέρων πιστουμένη τὰ δεύτερα, ὅταν συνδράμῃ τὸ τῇ φύσει πρῶτον καὶ γνώριμον καὶ ἡμῖν εἶναι γνωριμώτερον· ὅταν δὲ τοῦτο μὴ παρῇ ἀλλ’ ἀναγκαζώμεθα ἐκ τῶν ὑστέρων τὰ πρότερα

The Greek Commentators

101

The adjective τεκμηριώδης is used by Aristotle in the Rhetoric: “proofs (τεκμήρια) and enthymemes from proofs (τεκμηριώδη ἐνθυμήματα) cannot be refuted on the basis that they are asyllogistic.”69 In that context, the adjective is used to express the contrast between syllogistic (i.e., deductively valid) and asyllogistic (i.e., deductively invalid) sign-syllogisms. Philoponus extends this use to demonstrations: a “tekmeriodic demonstration” is a demonstration from effect to cause. Already Alexander in his commentary on the Topics had distinguished the demonstration in the strict sense (κυρίως), which goes from the cause to the effect, from the demonstration in a secondary sense (δευτέρως), which goes from the effect to the cause.70 Philoponus echoes this distinction when he says that “since such signs or proofs (σημεῖα ἢ τεκμήρια) are irrefutable (ἄλυτα), this is why we call proofs based on them demonstrations, according to a secondary standard of demonstration (κατὰ δεύτερα μέτρα ἀποδείξεως).”71 A “tekmeriodic demonstration” (τεκμηριώδης ἀπόδειξις) is not a demonstration in the strict sense; but since it is irrefutable (deductively valid), it deserves the title of demonstration, though only κατὰ δεύτερα μέτρα.72 Philoponus’ use of the disjunction σημεῖα ἢ τεκμήρια at CAG 13.3, 32.6 should not mislead us into thinking that he overlooks the syllogistic distinction between σημεῖα and τεκμήρια. The qualification of both as irrefutable (ἄλυτα) is a first indication that he has deductively valid syllogisms in mind all along. His commentary on APo A 2, 72b25–8 is clear evidence that he was sensitive to the distinction between σημεῖα and τεκμήρια: establishing prior things through posterior things is not always necessary, except in cases where the posterior things are irrefutable signs, such as “since there is ash, fire was once here,” or “since the moon is illuminated in this way, it is spherical.” However, if from the fact that a woman is pale it is established that she has given birth, since the sign is refutable such would not be called a demonstration in any way. And in the case of irrefutable signs we will not say that such is demonstration in the strict sense, but that this whole thing is a demonstration from a sign, since it is necessary to establish effects from their

πιστοῦσθαι, τεκμηριῶδες τὸ τοιοῦτον εἶδος καλεῖται τῆς δείξεως. διὰ δὲ τὸ ἄλυτον τῶν τεκμηρίων ἠξιώθη τοῦ τῆς ἀποδείξεως ὀνόματος.” Transl. McKirahan. 69 Aristotle, Rhet B 25, 1403a10–12. 70 Cf. supra, §2.1. 71 Philoponus, In APo, ed. Wallies, CAG 13.3, 32.5–7; transl. McKirahan, modified. 72 Cf. also Philoponus, In APo, ed. Wallies, CAG 13.3, 50.5–8.

102

chapter 2

causes, which is a property of demonstration in the strict sense, and not causes from their effects.73 Fire and ash are cause and effect that convert (whenever there is fire there is ash, and whenever there is ash there was a fire). The syllogism that infers the effect from the cause qualifies as a demonstration proper; the syllogism that infers the cause from the effect is a syllogism through signs. But since cause and effect convert, this syllogism is irrefutable and deductively valid, and thus is, properly speaking, a syllogism from a τεκμήριον. Its character of irrefutability, Philoponus says, allows us to call it an ἀπόδειξις, though only κατὰ δεύτερα μέτρα; it can therefore also be called a τεκμηριώδης ἀπόδειξις. The same applies to the inference of the sphericity of the moon from its phases (one of the examples of syllogism of the that of APo A 13). By contrast, having given birth and paleness are cause and effect that do not convert: a woman who has borne a child is pale, but not all pale women have borne a child. In this case, the effect has a wider extension than the cause: all occurrences of the cause are occurrences of the effect, but not all occurrences of the effect are occurrences of the cause. Here, the syllogism that infers the cause from the effect is not a deductively valid syllogism, and therefore is no demonstration at all, either in its primary or in its secondary sense. Rather, it is an inference from a σημεῖον, and here σημεῖον has to be taken in the strict sense recorded at APr B 27, 70b4, i.e., as a deductively invalid or refutable sign (λύσιμον σημεῖον). The example chosen by Philoponus (the pale woman) comes directly from APr B 27, where it instantiates a deductively invalid sign-syllogism in the second figure, and behaves logically as the example of the lactating woman that as we have just seen he uses at CAG 13.3, 21.5 in the same manner (apparently neglecting that in APr B 27 that example instantiates a deductively valid sign-syllogism in the first figure). Philoponus’ comments on APo A 6, 75a31–33, the first of the two passages of the Posterior Analytics in which Aristotle himself contrasts demonstration with sign-inferences, requires a different terminological explanation. He says:

73 Philoponus, In APo, ed. Wallies, CAG 13.3, 49.5–14: “τὸ γὰρ ἐκ τῶν ὑστέρων τὰ πρότερα κατασκευάζειν οὐκ ἀεὶ ἀναγκαῖον, ἀλλ᾿ ἐν οἷς τὰ ὕστερα ἄλυτά ἐστι τεκμήρια, ὥσπερ τὸ τέφρας οὔσης πῦρ ἐνταῦθά ποτε εἶναι ἢ τὸ τοιῶσδε φωτιζομένης τῆς σελήνης σφαιρικὴν αὐτὴν εἶναι. εἰ μέντοι ἐκ τοῦ ὠχρὰν εἶναι τὴν γυναῖκα κατασκευάζοιτο ὅτι τέτοκε, λυτοῦ ὄντος τοῦ σημείου κατ᾿ οὐδένα τρόπον ἀπόδειξις ἂν τὸ τοιοῦτον λέγοιτο. καὶ ἐπὶ τῶν ἀλύτων δὲ τεκμηρίων οὐ κυρίως ἀπόδειξιν ἂν τὴν τοιαύτην φήσομεν ἀλλὰ τὸ ὅλον τοῦτο τεκμηριώδη ἀπόδειξιν, εἴπερ δεῖ ἐκ τῶν αἰτίων τὰ αἰτιατὰ κατασκευάζειν, ὅπερ τῆς κυρίως ἀποδείξεώς ἐστιν ἴδιον, καὶ οὐκ ἐκ τῶν αἰτιατῶν τὰ αἴτια.” Transl. McKirahan, modified.

The Greek Commentators

103

Because everything that does not belong per se belongs accidentally and things that belong accidentally can also not belong, therefore demonstration cannot be based on such things. For even if such accidents are never separated from their subjects, he says, unless they belong to them per se there will not be a demonstration based on them, for reasons that have been stated many times. As an example of this he gives syllogisms through signs, which infer causes from effects. For it is from the moon’s phases that we infer that it has a spherical body, and from smoke’s appearing that there is a fire.74 Again, the fact that here Philoponus calls the syllogism from the effect to the cause a διὰ σημείων συλλογισμός should not mislead us into thinking that he is ignoring the syllogistic distinction between σημεῖα in the strict sense and τεκμήρια. The examples adduced clearly indicate that he has in mind that-­ syllogisms which are deductively valid and which thus qualify as τεκμηριώδεις ἀποδείξεις. His use of σημεῖον in this passage has to be explained by the fact that he is indirectly reporting Aristotle’s own words in APo A 6, where Aristotle uses the term σημεῖον.75 An even more explicit instance of a report of Aristotle’s (and his commentators’) wording occurs in the passage to be presently considered. Philoponus’ most systematic discussion of sign-inferences is in his commentary on APo A 13. The substance of his interpretation of this chapter is the same as in Themistius. Like Themistius, Philoponus interprets section (i) of APo A 13 (“not from immediates”) as saying that when an argument infers an effect from a proximate cause it is a why-demonstration, when it infers an effect from a non-proximate cause it is a that-demonstration.76 Two of his examples are the same as Themistius’ first-figure arguments (southern stars and the immortal soul).77 Another is a variation of the eclipse example: if the moon’s eclipse is inferred from its being diametrically opposite the sun, this 74 Philoponus, In APo, ed. Wallies, CAG 13.3, 97.20–28: “Ὅτι ὅσα μὴ καθ᾿αὑτὸ ὑπάρχει, ταῦτα κατὰ συμβεβηκὸς ὑπάρχει· τὰ δὲ κατὰ συμβεβηκὸς ὑπάρχοντα ἐνδέχεται καὶ μὴ ὑπάρχειν· οὐκ ἄρα ἐκ τῶν τοιούτων ἂν γένοιτ᾿ἀπόδειξις. κἂν γὰρ μηδέποτε, φησί, χωρίζεται τὰ τοιαῦτα συμβεβηκότα τῶν ὑποκειμένων, μὴ καθ᾿αὑτὸ δὲ ὑπάρχῃ αὐτοῖς, οὐδ᾿οὕτως ἐξ αὐτῶν ἀπόδειξις ἔσται διὰ τὰ πολλάκις εἰρημένα. τούτου δὲ παράδειγμα τίθησι τοὺς διὰ σημείων συλλογισμούς, οἵτινες τὰ αἴτια ἐκ τῶν αἰτιατῶν συλλογίζονται· ἐκ γὰρ τῶν φωτισμῶν τῆς σελήνης τὸ σφαιροειδὲς ἔχειν αὐτὴν σῶμα συνάγομεν καὶ ἐκ τοῦ καπνὸν φαίνεσθαι τὸ πῦρ εἶναι.” Transl. McKirahan, modified. 75 Cf. supra, §1.7. 76 Philoponus, In APo, ed. Wallies, CAG 13.3, 166.22–167.3. 77 Philoponus, In APo, ed. Wallies, CAG 13.3, 167.3–18.

104

chapter 2

is a that-­demonstration because being diametrically opposite to the source of illumination is the non-proximate cause of the eclipse; if the inference is from the interposition of the earth, it is from a proximate cause and counts as a why-demonstration.78 Like Themistius, Philoponus interprets section (iv) of APo A 13 (“cause more extended than the effect”) as a further division of the case announced in ­section (ii). We return to this below. Moreover, like Themistius, Philoponus interprets section (v), about second-figure arguments, in connection with section (i). His discussion of the second-figure argument of section (v) is long and not perfectly transparent. He interprets the expression “the middle has outside position” not as a reference to the second figure (he claims to be following Alexander in this) but as a reference to the non-proximate or non-­immediate character of the middle term with respect to the major. For, he adds, this is precisely the first difference between that- and why-demonstrations.79 This shows that Philoponus takes section (v) and the second-figure argument in it as illustrating the case announced in section (i) (“not from immediates”). Yet, it is not clear whether he has an extensional interpretation of section (v) in mind. Unlike Themistius, he is not explicit in distinguishing this case of “non-­ immediateness” (which is extensional and in the second figure) from that from a remote cause (which is not extensional and in the first figure). His explanation of why Aristotle’s example is in the second figure is the following.80 He seems to be assuming that Aristotle wants to prove a negative conclusion (like “No wall breathes”). If the middle term has to be the cause of the major’s being predicated of the minor, its being negatively predicated of the minor has to be cause of the major’s being negatively predicated of the minor. Now, in the first figure a universal negative conclusion is possible only from a negative major premise (Celarent); i.e., in this figure the major’s being negatively predicated of the minor is caused not by the middle term’s being negatively predicated of the minor, as it should be if a proper causal relation were to be established, but by the major’s being negatively predicated of the middle term. In the second figure (Camestres), by contrast, the middle term is negatively predicated of the minor in one premise, and this can indeed be the cause of the major’s being negatively predicated of the minor in the conclusion. In other words, if the middle term (cause) has no connection with the major (effect), as it happens in Celarent (for the major premise says that “No M is P”), the former cannot be said to be the cause of the latter, not even negatively. 78 Philoponus, In APo, ed. Wallies, CAG 13.3, 167.22–168.7. 79 Philoponus, In APo, ed. Wallies, CAG 13.3, 174.3–12. 80 Philoponus, In APo, ed. Wallies, CAG 13.3, 176.16–177.15.

The Greek Commentators

105

As mentioned, Philoponus follows Themistius in interpreting section (iv) of APo A 13 (“cause more extended than the effect”) as a further division of the case announced in section (ii) (“from immediates”). Thus, he takes sections (ii) and (iii) as discussing converting cause and effect, and section (iv) as discussing non-converting cause and effect. Some causes and effects reciprocate and others do not. For example, if there is fire there must be ash as well, and if there is ash, there must be fire as well. Also in the case of the phases of the moon; if it is illuminated in the way it appears, it must be spherical too; and if it is spherical, it must be illuminated in that way. Now in cases where cause and effect reciprocate with one another, we frequently establish the cause on the basis of the effect because the effect is better known than the cause. For example, in proving that the moon is spherical on the basis of its phases – although the phases are not the cause of its being spherical, but rather that fact is of them . So this is called a syllogism of the “that,” since the sphericity of the moon is syllogized from its phases. Likewise “ash is here, where there is ash there was fire, therefore there was fire here.” But if we were to say “fire is here, where there is fire there must be ash as well, therefore there is ash here,” the ­syllogism is of the “why.” For the effect is syllogized from the cause. The former is of the “that,” since the cause is syllogized from the effect. And since such things are irrefutable (ἄλυτα), they are called signs (σημεῖα λέγεται) and this is a secondary kind of demonstration, or as a whole it is a demonstration from a sign (τεκμηριώδης ἀπόδειξις). This holds for things that reciprocate.81

81 Philoponus, In APo, ed. Wallies, CAG 13.3, 168.23–169.9: “τῶν αἰτίων καὶ αἰτιατῶν τὰ μὲν ἀντιστρέφουσι, τὰ δὲ οὐκ ἀντιστρέφουσιν. οἶον εἰ μὲν γὰρ πῦρ, πάντως καὶ τέφρα, καὶ εἰ τέφρα, πάντως καὶ πῦρ· καὶ ἐπὶ τῶν φωτισμῶν τῆς σελήνης· εἴτε γὰρ τοιῶσδε φωτίζεται ὥσπερ ἐμφανίζεται, πάντως καὶ σφαιροειδής ἐστιν, εἴτε σφαιροειδής ἐστι, πάντως καὶ τοιῶσδε φωτίζεται. ἐφ’ ὧν οὖν αντιστρέφουσι πρὸς ἄλληλα τὸ αἴτιον καὶ τὸ αἰτιατόν, πολλάκις διὰ τὸ γνωριμώτερον εἶναι τοῦ αἰτίου τὸ αἰτιατὸν ἐκ τοῦ αἰτιατοῦ κατασκευάζομεν τὸ αἴτιον, οἷον τὴν σελήνην σφαιροειδῆ δεικνύντες ἐκ τῶν φωτισμῶν· καίτοι οὐχ οἱ φωτισμοὶ τοῦ σφαιροειδῆ εἶναι αἴτιοι, αλλ’ ἐκεῖνο τούτων. λέγεται οὖν οὗτος τοῦ ὅτι συλλογισμός· τὸ γὰρ σφαιροειδὲς τῆς σελήνης ἐκ τῶν φωτισμάτων συλλογίζεται. ὁμοίως ‘τέφρα ἐνταῦθά ἐστιν· ὅπου δὲ τέφρα, ἐκεῖ πῦρ ἦν· ἐνταῦθα ἄρα πῦρ ἦν’. εἰ δὲ εἴποιμεν ‘πῦρ ἐνταῦθα· ὅπου δὲ πῦρ, ἐκεῖ πάντως καὶ τέφρα· ἐνταῦθα ἄρα τέφρα ἐστί’, τοῦ διότι ὁ συλλογισμός· ἐκ τοῦ αἰτίου γὰρ τὸ αἰτιατὸν συλλογίζεται. ἐκεῖνος δὲ τοῦ ὅτι· ἐκ τοῦ αἰτιατοῦ γὰρ τὸ αἴτιον συνελογίσατο. καὶ ἐπεὶ ἄλυτά ἐστι τὰ τοιαῦτα σημεῖα λέγεται, καὶ τοῦτο κατὰ τὰ δεύτερα ἀπόδειξις ἢ τὸ ὅλον τοῦτο τεκμηριώδης ἀπόδειξις. ἐπὶ μὲν οὖν τῶν αντιστρεφόντων οὕτως.” Transl. McKirahan, modified.

106

chapter 2

When the cause and the effect convert, the inference of the cause from the effect is a that-syllogism of type 1b. Both the astronomical example of APo A 13 and Alexander’s example of ash and fire are used here. Like in Themistius, this type of that-demonstration is semiotically qualified: since the convertibility of cause and effect guarantees the deductive validity of the inference, the effect is a τεκμήριον of its cause and the whole is a τεκμηριώδης ἀπόδειξις. It has to be noticed that Philoponus’ use of σημεῖα at CAG 13.3, 169.7 must again be taken as a report of Aristotle’s and his commentators’ wording: the premises of such inferences “are called” σημεῖα, but since these inferences are irrefutable, their premises are more precisely to be called τεκμήρια. Like Alexander and Themistius, Philoponus considers this kind of demonstration, which he calls a τεκμηριώδης ἀπόδειξις, not as a demonstration in the strict sense, but as a demonstration in a secondary sense (κατὰ τὰ δεύτερα ἀπόδειξις). Philoponus next considers the case of non-converting cause and effect. This is the case discussed by Aristotle in section (iv) of APo A 13 (and, if our ­reconstruction is correct, also in section (v); but Philoponus, like Themistius, disconnects section (v) from section (iv)). Aristotle and Themistius ­limited their concerns to the case in which the cause has a wider extension than the effect, for when the effect has a wider extension than the cause no that-­ demonstration is possible (on pain of deductive invalidity). Philoponus, by contrast, considers both options: But it often happens that when the cause occurs it is necessary for the effect to occur too, but not that when the effect occurs the cause must occur as well, and vice versa, that when the effect occurs the cause must too, but not the cause the effect must too. An example of the former: if a woman has given birth she must be pale, but the fact of having given birth does not always follow from the fact of being pale, for there can be several causes of the same thing: fear, illness and other things. Likewise, if someone has just walked a lot, he is tired, but it is not the case that if someone is tired he has also just walked a lot. For it is possible to be tired from doing a lot of work. And clearly in these cases the syllogism will be of the why and not just of the that, since the syllogism always proceeds through the causes establishing the effect on the basis of them. But it is not possible to prove the cause from the effect since they do not reciprocate. […] An example of the latter, namely where the cause is a consequence of the effect but the effect is not necessarily of the cause as well: if a woman has given birth, she has had intercourse with a man. But this cannot reciprocate—that if a woman has had intercourse with a man she has also given birth. Also,

The Greek Commentators

107

if there are fruits, there must have been rain, but if there has been rain there will not necessarily be fruits as well. In these cases the syllogism is only of the that and never of the why.82 Philoponus first considers an effect that is more extended than the cause. His first example (the pale woman) comes directly from APr B 27, where it illustrates the deductively invalid sign-syllogism in the second figure. A woman who has given birth is pale, but not all pale women have given birth. We saw above that at CAG 13.3, 49.8–10 Philoponus uses this example for an argument from a refutable sign or σημεῖον in the strict sense, and we shall see below that the very same example is used for the same purpose in his commentary on the De Anima. In the present passage, however, no reference is made to the semiotic nature of such a syllogism. The second example (the tired man) is not Aristotelian, but is susceptible of the same analysis. When the effect is more extended than the cause, the syllogism can only be of the why, and never of the that, for in fact the syllogism of the that that results is a deductively invalid argument. Later (at CAG 173.1–20) Philoponus explains why Aristotle does not treat of this case: a cause less extended than the effect is not strictly and unqualifiedly (μηδὲ κυρίως ἁπλῶς) the cause of that effect, but only accidentally; since cause and effect are relatives, it is not possible for the effect to occur without the occurrence of the cause. In the pallor example, the problem is homonymy: the particular pallor due to giving birth is coextensive with its cause, and is said homonymously with other pallors due to other causes. The converse case of a cause more extended than the effect is considered in turn. This is the case announced in section (iv) of APo A 13. One of the examples chosen by Philoponus for this case is the one discussed by Themistius at CAG 5.1, 28.24–25, and might come directly from that work. It is the example 82 Philoponus, In APo, ed. Wallies, CAG 13.3, 169.9–27: “πολλάκις δὲ τοῦ μὲν αἰτίου ὄντος ἀνάγκη καὶ τὸ αἰτιατὸν εἶναι, οὐ πάντως δὲ τοῦ αἰτιατοῦ ὄντος καὶ τὸ αἴτιον· καὶ ἔμπαλιν τοῦ μὲν αἰτιατοῦ ὄντος πάντως καὶ τὸ αἴτιον, οὐ πάντως δὲ τοῦ αἰτίου καὶ τὸ αἰτιατὸν. οἷον τοῦ μὲν προτέρου· εἰ μὲν γὰρ τέτοκεν ἡ γυνή, πάντως καὶ ὠχρά ἐστιν· οὐ πάντως δὲ τῷ ὠχρὰν εἶναι ἀκολουθεῖ τὸ τετοκέναι· ἐνδέχεται γὰρ τοῦ αὐτοῦ πλείονα αἴτια εἶναι, καὶ φόβον καὶ νόσον καὶ ἕτερα. ὁμοίως, εἰ πολλὰ βεβάδικε, κέκμηκεν· οὐ μήν, εἰ κέκμηκεν, ἤδη καὶ πολλὰ βεβάδικε· δυνατὸν γὰρ καὶ ἐκ πλείονος ἐργασίας κεκμηκέναι. καὶ δῆλον ὅτι ἐπὶ τούτων τοῦ μὲν διότι συλλογισμός ἔσται, τοῦ δὲ ὅτι οὐκέτι· ἀεὶ μὲν γὰρ διὰ τῆς αἰτίας πρόεισιν ἐπὶ τούτων ὁ συλλογισμὸς κατασκευάζων τὸ αἰτιατὸν· οὐ δύναται δὲ ἐκ τοῦ αἰτιατοῦ δεῖξαι τὸ αἴτιον διὰ τὸ μὴ ἀντιστρέφειν. […] τοῦ δὲ δευτέρου παράδειγμα, λέγω δὴ τοῦ τῷ μὲν αἰτιατῷ τὸ αἴτιον ἕπεσθαι, μὴ πάντως δὲ καὶ τῷ αἰτίῳ τὸ αἰτιατόν· οἷον εἰ τέτοκεν ἡ γυνή, πεπλησίακεν ἀνδρί· οὐκέτι δὲ καὶ ἀντιστρέψαι δυνατόν, ὅτι εἰ πεπλησίακεν ἡ γυνή ἀνδρί, καὶ τέτοκε. καὶ καρπῶν μὲν ὄντων πάντως ὑετὸς γέγονεν· ὑετοῦ δὲ γενομένου οὐ πάντως καὶ καρποὶ ἔσονται. καὶ ἐπὶ τῶν τοιούτων μόνου τοῦ ὅτι γίνεται συλλογισμός, οὐδαμῶς δὲ τοῦ διότι.” Transl. McKirahan, modified.

108

chapter 2

that we have ourselves used in Chapter 1 to illustrate this case. A woman who has given birth has had intercourse with a man, but not all intercourses with men cause women to give birth. Note that here having given birth is the effect (of having had intercourse with a man), and not, as in the example of the pale woman from APr B 27, the cause (of paleness). Themistius had said that in such cases there is demonstration of the cause through the sign, but not demonstration of the sign through the cause. As Philoponus explains, in this case the syllogism can only be of the that (from effect to cause) and never of the why (from cause to effect). The that-syllogism that results is of the type 2a. Like in the parallel consideration of the converse case (effect more extended than the cause), here Philoponus says nothing about the semiotic nature of such inferences.83 There is a passage from Philoponus’ commentary on APo A 6 that, he says, anticipates the results of his more detailed analysis of APo A 13.84 In fact, this earlier passage offers a typology of demonstrations that is fully, although only implicitly, extensional, and which is therefore not wholly compatible with that presented in the analysis of APo A 13. Here Philoponus says that both a ­that- and a why-demonstration can be through either mediate or immediate ­premises. Let us start with that-demonstrations. If the lunar eclipse (considered as cause) is inferred from the fact that the moon is not casting shadows 83

According to Morrison (1997), Philoponus’ doctrine of tekmeriodic proof differs from Aristotle’s in two ways: first, because unlike Aristotle, Philoponus considers induction as a kind of tekmeriodic proof; secondly, because unlike Aristotle, Philoponus does not recognize that some sign-inferences are deductively invalid. We find both these claims to be inaccurate. As to induction, nowhere in his commentary on the Posterior Analytics does Philoponus associate induction with sign-inferences. He says that induction has to do with the perception of particulars (CAG 13.3, 17.12–14; 18.10–11; 214.16-17; 216.1, 15–16), that by induction we establish universals on the basis of particulars, i.e., prior things on the basis of posterior things (49.20–24), and that by induction we learn axioms and postulates (215.7–8). But these claims entail in no obvious way that induction is a kind of sign-­ inference. Sign-inferences are inferences from what is posterior to what is prior. But not all inferences from the posterior to the prior are inferences from effect to the cause, and thus sign-inferences. Morrison’s straightforward equation of the two (“Philoponus’ account counts any form of reasoning from posteriors to priors, or from effect to cause, as a tekmeriodic proof,” 1997, 10) conflates two things that are kept distinct by Philoponus, and finds no justification in the text. As to the second alleged difference between Philoponus and Aristotle, we have seen above that, at CAG 13.3, 49.5–14, Philoponus clearly distinguishes the syllogism from an irrefutable sign (ἄλυτα τεκμήρια, 49.6–7) from the syllogism from a refutable sign (λυτόν σημεῖον, 49.9–10). Only the former merits the title of demonstration, even though in a secondary sense: the former is a τεκμηριώδης ἀπόδειξις, while the latter is an inference from a σημεῖον, which being deductively invalid is no demonstration at all. 84 Philoponus, In APo, ed. Wallies, CAG 13.3, 92.9–93.3.

The Greek Commentators

109

(­considered as effect), this is from “mediate” premises, for “not casting shadows” is not sufficient for establishing the conclusion that the moon is eclipsed; the moon may not be casting shadows because it is under the horizon. Philoponus is evidently thinking of an effect that is more extended than the cause, precisely as in the example of the pale woman from APr B 27. If the effect is adequately restricted, for example by saying that the moon is not casting shadows while it is full, this becomes the adequate, “immediate” middle term of an “immediate” that-demonstration, because the cause (eclipse) is inferred from an effect that converts with it. The same applies to why-­demonstrations. If the lunar eclipse (considered this time as effect) is inferred from the fact that the moon is diametrically opposite the sun (considered as cause), this is from “mediate” premises, for “being diametrically opposite the sun” is not sufficient for establishing the conclusion that the moon is eclipsed; the moon may be diametrically opposite the sun without being occulted by the earth. Again, here the cause (“being diametrically opposite the sun”) is more extended than the effect, and thus has to be adequately restricted. If it is adequately restricted, for example by saying that the moon is diametrically opposite the sun while being occulted by the earth, this becomes the adequate, “immediate” middle term of an “immediate” why-demonstration, because the effect (the eclipse) is inferred from a cause that converts with it. In other words, Philoponus is here taking “immediate” and “mediate” to mean “convertible” and “non-convertible,” respectively, and he is taking a that-demonstration to be the inference of the cause from the effect and a why-demonstration to be the inference of the effect from the cause. That this analysis of the that/why distinction is only partially compatible both with APo A 13 and with Philoponus’ later analysis of that chapter should be evident: neither Themistius nor Philoponus give to “immediate” in section (i) of APo A 13 the extensional sense that seems to be in question here. Further, no why-demonstration is “from mediates” (in either the extensional or the non-extensional sense) in either APo A 13 or Themistius’ and Philoponus’ commentaries on it. This last point is fully appreciated by Philoponus in his analysis of APo A 13: “syllogism of the ‘why’ necessarily through immediates. Still, those that through immediates are not necessarily of the ‘why’.”85 In the passage under consideration ad APo A 6 Philoponus says precisely the opposite: syllogisms of the why can proceed either through immediates or through mediates.

85 Philoponus, In APo, ed. Wallies, CAG 13.3, 168.17–18.

110

chapter 2

The typology that Philoponus offers in connection with APo A 6 is compatible with, and indeed it matches perfectly, the typology that Philoponus offers in connection with his interpretation of sections (ii), (iii), and (iv) of APo A 13, as we have reconstructed it above. From converting cause and effect arise both a why-syllogism and a that-syllogism (of type 1b); these correspond to the why-syllogism from an immediate cause and the that-syllogism from an immediate effect, respectively. From non-converting cause and effect arise either a why-syllogism (from a less extended cause) or a that-syllogism (from a less extended effect, of type 2a); these correspond to the why-syllogism from a mediate cause and to the that-syllogism from a mediate effect, respectively. This fourfold typology is not the same as Aristotle’s in APo A 13. Let us call “Aristotelian” the typology of APo A 13 and “Philoponean” the typology that Philoponus provides in his commentary on APo A 6 and which he then extrapolates from sections (ii), (iii) and (iv) of APo A 13. The two differ as follows. The Aristotelian typology is based on two extensional cases: converting cause and effect (arguments of types 1a and 1b) and cause more extended than the effect (arguments of types 2a and 2b); effects more extended than their causes are excluded. By contrast, the Philoponean typology is based on three extensional cases: converting cause and effect (corresponding to arguments of types 1a and 1b in the Aristotelian typology), cause more extended than the effect (corresponding to argument of type 2a in the Aristotelian typology), and effect more extended than the cause (no corresponding argument in the Aristotelian typology). As we shall see in Chapter 5, both the Aristotelian and the Philoponean typologies are to be found in the Latin commentaries on the ­Posterior Analytics. Let us now go back to sign-inferences. Notwithstanding the terminological (and to some extent conceptual) oscillations that we have reported, in his discussion of demonstrations Philoponus makes a terminological manoeuvre that makes perfect sense. Both Alexander and Themistius bring to the fore the contrast between sign and demonstration which was only hinted at in Aristotle’s Posterior Analytics, and both explicitly give a semiotic characterization of the prototypical that-syllogism of APo A 13 (1b); Themistius does it also for the that-syllogism of type (2a). Yet, Philoponus seems to have been the first to perceive that a that-syllogism of type 1b, though not causal, is a deductively valid syllogism, and thus merits the status of irrefutable sign or τεκμήριον. Accordingly, he is the first to use the terminology of APr B 27 to distinguish between deductively valid, i.e., “tekmeriodic” demonstrations, and deductively invalid sign-inferences which do not deserve the dignity of demonstration at all. With his theory of “tekmeriodic proof” Philoponus gives to Aristotle’s scattered remarks on the relationship between sign and demonstration a precise

The Greek Commentators

111

terminological systematization, which will be mostly completely ignored by subsequent commentators on the Posterior Analytics. Philoponus’ use of the doctrine of tekmeriodic proofs is not limited to his commentary on APo A. Besides his commentary on Physics A 1, which we consider in the next section, the doctrine also emerges in his commentaries on the Meteorologica and the De Anima. In the Meteorologica Aristotle says that “the sun which appears to be the hottest of the heavenly bodies is bright rather than fiery in appearance.”86 Philoponus interprets this as a sign-argument: Aristotle “seems to infer (τεκμαίρεσθαι) the temperatures of bodies from their colors,”87 but this is not true: there are red bodies that are hot (blood) and red bodies that are cold (roses), and the same is true of white, black, and violet bodies. Also, the sun appears yellow, not white. And, Philoponus adds, “even had it been of white colour, this is not a proof (τεκμήριον) of its not being of fire,”88 for the color of fire is relative to the subject matter. This manner of speaking89 generally follows the Aristotelian usage in the Meteorologica. For example, in another passage Aristotle says: “We may regard as a proof (τεκμήριον) that their [the comets’] constitution is fiery the fact that their appearance in any number signifies the coming of wind and drought.”90 These passages from the Meteorologica and Philoponus’ commentary testify to a certain use of the term τεκμήριον in the proper sense of “necessary sign,” but are certainly not part of Aristotle’s or his commentators’ theory of sign-inferences. There is a passage of Philoponus’s commentary on the De Anima that confirms that he was perfectly aware of the terminological distinction introduced by Aristotle in APr B 27 and that his use of the term τεκμήριον in his commentary on the Posterior Analytics is a conscious reference to the necessary character of the syllogism constructed on it. At the beginning of the first book Aristotle asks whether the method for the investigation of the soul should be the same for everything of which one inquires about the essence, just as there is one method for the demonstration of proper attributes (τῶν κατὰ συμβεβηκὸς ἰδίων ἀπόδειξις).91 The first part of Philoponus’ discussion of this passage is quite confusing.92 He seeks to show that κατὰ συμβεβηκός in 86 Aristotle, Meteor A 3, 341a36–38; transl. Lee. 87 Philoponus, In Meteor, ed. Hayduck, CAG 14.1, 47.12; Kupreva’s translation of this passage is: “he seems to be using the colours of bodies as evidence for their temperatures.” 88 Philoponus, In Meteor, ed. Hayduck, CAG 14.1, 47.20–21; transl. Kupreeva. 89 Cf. also Philoponus, In Meteor, ed. Hayduck, CAG 14.1, 49.29–30, 100.5, 102.34, 110.34, 111.21, 118.22. 90 Aristotle, Meteor A 7, 344b19–21; transl. Lee. 91 Aristotle, De Anima A, 402a16. 92 Philoponus, In De Anima, ed. Hayduck, CAG 15, 29.4–30.1.

112

chapter 2

this passage has not to be taken in the standard sense of συμβεβηκός, but as somewhat equivalent to καθ’αὑτό, as “what accompanies beings necessarily,”93 and refers the reader to what Aristotle says in APo A 6, i.e., that demonstration is concerned with καθ’αὑτό attributes.94 Indeed, Philoponus continues, ­demonstration ­cannot be of the accidental (standard sense of συμβεβηκός). A demonstration is proper (κυρίως ἀπόδειξις) if it proves the things caused by means of their causes.95 There are, however, other kinds of demonstrations: There is also a form of demonstration called tekmeriodic (τεκμηριώδης λεγομένη ἀπόδειξις), which proves the causes on the basis of the things caused, as Aristotle practices himself in the On the Heavens, where he uses the illumination of the moon as a demonstration that it is spherical. Yet what ought to be demonstrated was, conversely, that it is spherical and that for that reason it was illuminated in that way. We use this way of demonstration when what is caused is clearer to us than the cause, as is the case with the moon: the thing caused, the illumination, is clearer to us than the cause, the fact that it is spherical. […] A similar tekmeriodic (τεκμηριώδης) demonstration we call “if there is smoke here, there is fire too.” For smoke is a proof (τεκμήριον) of fire. A proof is an irrefutable sign (τεκμήριον δέ ἐστι τὸ ἄλυτον σημεῖον), as smoke is of fire, just as the moon being illuminated in a particular way of its being spherical. What is refutable is not called a proof, but a sign (τὸ δὲ λυτὸν οὐ τεκμήριον, ἀλλὰ σημεῖον λέγεται); that is, when what is caused is not in all circumstances accompanied by the cause, as in the following: she is pale, because she has given birth; for being pale is not always accompanied by having given birth. It is refutable, and therefore it is not a proof but a sign (οὐ τεκμήριον ἀλλὰ σημεῖον), just as standing near a freshly slaughtered body is a sign (σημεῖον) of having killed it.96 93 Philoponus, In De Anima, ed. Hayduck, CAG 15, 29.7–8; transl. van der Eijk. 94 Aristotle, APo A 6, 75a28–37; cf. supra, §1.6. 95 Philoponus, In De Anima, ed. Hayduck, CAG 15, 30.12–13. 96 Philoponus, In De Anima, ed. Hayduck, CAG 15, 30.20–31.22: “ἔστι δὲ καὶ ἡ τεκμηριώδης λεγομένη ἀπόδειξις, ἡ ἐκ τῶν αἰτιατῶν τὰ αἴτια πιστουμένη, ὥσπερ αὐτὸς ἐν τῇ Περὶ οὐρανοῦ ἐποίησεν ἐκ τῶν φωτισμῶν τῆς σελήνης ἀποδείξας ὅτι σφαιρική ἐστι. καίτοι τὸ προσῆκον ἦν ἀνάπαλιν δεικνύναι, ὅτι σφαιρική, διὰ τοῦτο καὶ οὕτω φωτίζεται. ταύτῃ οὖν κεχρήμεθα τῇ δείξει, ὅτε τὸ αἰτιατὸν πρὸς ἡμᾶς σαφέστερόν ἐστι τοῦ αἰτίου, ὥσπερ καὶ ἐπὶ τῆς σελήνης ἔχει· τὸ γὰρ αἰτιατὸν ὁ φωτισμὸς σαφέστερος ἡμῖν ἐστι τοῦ αἰτίου, λέγω δὴ τοῦ σφαιροειδῆ αὐτὴν εἶναι. [...] τὴν δὲ τοιαύτην δεῖξιν τεκμηριώδη λέγομεν ‘εἰ καπνὸς ἐνταῦθα, καὶ πῦρ ἄρα’· τεκμήριον γὰρ τοῦ πυρὸς ὁ καπνός. τεκμήριον δέ ἐστι τὸ ἄλυτον σημεῖον, ὡς τοὐ πυρὸς ὁ καπνός, ὡς τοῦ σφαιρικὴν εἶναι τὴν σελήνην τὸ οὕτω φωτίζεσθαι. τὸ δὲ λυτὸν οὐ τεκμήριον, ἀλλὰ σημεῖον λέγεται· τοῦτο δέ ἐστιν, ὅταν μὴ πάντως ἕπηται τῷ αἰτιατῷ τὸ αἴτιον, οἷον ὠχρά, ἐπειδὴ τέτοκεν· οὐ πάντως γὰρ τῇ

The Greek Commentators

113

The example of the illumination of the moon as basis for inferring its sphericity is the example that in APo A 13 illustrates the prototypical syllogism of the that (type 1b), but Aristotle presents a similar argument from the shape of illumination to the sphericity of the celestial body in the De Caelo.97 Philoponus refers to this work probably as evidence that Aristotle not only theorized tekmeriodic demonstrations, but also practicized them in his scientific works. Just like Philoponus’ commentary on APo Α 2 discussed above, this passage is remarkable for the terminological elucidations it contains. A τεκμήριον, as Aristotle has taught, is irrefutable if its premises are true. When Philoponus at CAG 15, 31.16–17 says that a τεκμήριον is an ἄλυτον σημεῖον, he is using σημεῖον in the wide sense of APr B 27, 70a3 and 70b1, in which sense it includes both τεκμήρια and σημεῖα in the strict sense. Besides the illumination of the moon, the other example of τεκμήριον and of τεκμηριώδης ἀπόδειξις is the usual one concerning smoke as sign of fire, already used by Themistius and Philoponus himself in his commentary on the Posterior Analytics. However, when at CAG 15, 31.18 he says that τὸ δὲ λυτὸν οὐ τεκμήριον, ἀλλὰ σημεῖον λέγεται, he is resorting to the strict sense of σημεῖον registered at APr B 27, 70b4, where it refers to second- and third-figure sign-syllogisms. Such signs are refutable even if their premises and conclusions are true. Philoponus gives two examples of such a σημεῖον in the strict sense. One is the pale woman of APr B 27, already used in his commentary on the Posterior Analytics. The other example appears not to be of Aristotelian origin, but can be explicated along the same lines as the example of the pale woman: standing near to a recently killed man is a probable sign of being responsible for the murder, but in no way necessitates this conclusion. In both cases, the inference is a second-figure invalid syllogism, and as such deserves to be called a σημεῖον in the strict sense. Notwithstanding the oscillations that we have noticed, then, that Philoponus was perfectly aware of the terminological distinction that Aristotle makes in APr B 27 is also confirmed by this passage from his commentary on the De Anima. 4

Philoponus and Simplicius on Physics A 1

We know from the first Chapter that the “strong” notion of demonstration d­ iscussed by Aristotle in APo A 2 is in tension with the doctrine set forth in a passage in the ouverture of the Physics, where Aristotle says that the method of ὠχρότητι ἕπεται τὸ τετοκέναι. λυτὸν οὖν τοῦτο καὶ οὐ τεκμήριον ἀλλὰ σημεῖον, ὡς τὸ παρεστάναι νεοσφαγεῖ σώματι τοῦ πεφονευκέναι σημεῖον.” Transl. van der Eijk, modified. 97 Aristotle, De Caelo, 291b19–25.

114

chapter 2

investigation must start from what is better known and clear to us and proceed to what is better known and clear by nature.98 We anticipated that ancient commentators on the Physics have interpreted that passage as containing a reference to a lower kind of demonstration, and that some construed the method of knowing principles mentioned in that passage as a sign-inference from effects to causes. This line of interpretation seems to have begun with Themistius: If demonstration is based on what is prior but we always inquired into the things that are prior, then our wish will be to discover principles for the principles. Priority, then, is twofold both as related to us and as related to nature. So what is prior in relation to us is what is better known to us and what we might more easily grasp (e.g., words and syllables as prior to letters), while the things that are simpler in substance are prior in relation to nature (e.g., letters as prior to words). And the process is reversed: we analyse from compounds to things that are simpler but prior in relation to nature, whereas nature devises compounds from simple things. So when we produce (i) an account of compounds, we will demonstrate from things that are prior by nature, but when we produce (ii) an account of principles, it is from things that are prior in relation to us. And while (i) is demonstration in its primary sense, (ii), even if not so in a primary sense, still suffices for us.99 Since demonstration is from principles, then if one wishes to inquire into principles demonstratively, one would be forced into a vicious circle. Circularity is avoided, according to Themistius, if we follow APo A 2 in distinguishing two senses of “priority.” Going from things that are prior for us to things that are prior by nature (the principles) is not a proper demonstration, but only a demonstration “for us,” a demonstration in a secondary sense. As is evident, this solution echoes Alexander’s comment on Top A 1, where the syllogism that 98 Aristotle, Phys A 1, 184a16–18. 99 Themistius, In Phys, ed. Schenkl, CAG 5.2, 1.12–2.3: “εἴ γε ἡ μὲν ἀπόδειξις ἐκ προτέρων, εἰ δὲ τὰ πρότερα ἐπιζητοίημεν, ἀρχὰς τῶν ἀρχῶν εὑρεῖν βουλησόμεθα; τὸ πρότερον οὖν διχῶς· καὶ πρὸς ἡμᾶς καὶ πρὸς τὴν φύσιν. πρὸς ἡμᾶς μὲν οὖν πρότερον τὸ γνωριμώτερον ἡμῖν καὶ ὃ ῥᾷον ἄν καταλάβοιμεν, οἷον τὰ ὀνόματα καὶ αἱ συλλαβαὶ τῶν γραμμάτων· πρὸς δὲ τὴν φύσιν πρότερα τὰ κατὰ τὴν οὐσίαν ἁπλούστερα, οἷον τὰ γράμματα τῶν ὀνομάτων, ἀνάπαλιν δὲ ἡ πορεία· ἡμεῖς μὲν γὰρ ἀπὸ τῶν συνθέτων ἐπὶ τὰ ἁπλούστερα πρὸς δὲ τὴν φύσιν πρότερα ἀναλύομεν, ἡ φύσις δὲ ἐκ τῶν ἁπλῶν τὰ σύνθετα μηχανᾶται. ὅταν μὲν οὖν περὶ τῶν συγκειμένων ποιώμεθα λόγον, ἐκ τῶν φύσει προτέρων αὐτὸ ἀποδείξομεν· ὅταν δὲ περί τῶν ἀρχῶν, ἐκ τῶν πρὸς ἡμᾶς προτέρων. καὶ ἔστιν ἐκείνη μὲν ἡ κυρίως ἀπόδειξις, αὕτη δὲ εἰ καὶ μὴ κυρίως, ἀλλὰ ἡμῖν ἱκανῶς.” Transl. Todd, modified.

The Greek Commentators

115

proceeds from things that are true but posterior is qualified as a demonstration “in a secondary sense, as relating to us.”100 Alexander’s idea of a demonstration “in a secondary sense” would become part and parcel of subsequent exegesis not only of the Posterior Analytics, but also of Physics A 1.101 In commenting on the same passage, Philoponus says: We need to be aware that Aristotle himself said, in the Posterior Analytics, that there are two ways of acquiring scientific knowledge, (a) the demonstrative method, and (b) the didactic method, and that these are in opposition to each other. For the demonstrative method demonstrates secondary things from things that are first and more fundamental in nature, while the didactic method, although it is also a demonstrative approach, demonstrates things that are prior from things that are posterior in nature, according to a second standard of demonstration; this approach he also calls “evidential” [i.e., tekmeriodic]. For example, if someone, on seeing smoke, were to say that there was a fire there: he has argued for what is prior from what is in nature posterior.102 It is difficult to determine what passage of the Posterior Analytics Philoponus refers to here, in which he thinks he finds the distinction between the demonstrative and the didactic method.103 Perhaps the distinction that Philoponus has in mind is that of APo A 13 between two types of demonstrations: precisely the distinction between why- and that-demonstrations which in his own commentary on the Posterior Analytics is the foundation of his notion of tekmeriodic proof. The example of fire and ash points unequivocally to that 100 Alexander, In Top, ed. Wallies, CAG 2.2, 16.29–30; cf. supra, §2.1. 101 Themistius on the Physics may well be dependent on Alexander’s lost commentary on the same work; see Todd (2012), 1. 102 Philoponus, In Phys, ed. Vitelli, CAG 16, 9.11–19: “ἰστέον οὖν ὅτι αὐτὸς εἶπεν ἐν τῇ Ἀποδεικτικῇ, ὅτι δύο τρόποι εἰσὶ τῆς ἐπιστημονικῆς γνώσεως, πρῶτος μὲν ὁ ἀποδεικτικός, δεύτερος δὲ ὁ διδασκαλικός, οὗτοι δὲ ἀντιπεπονθότως ἔχουσι πρὸς ἀλλήλους. ὁ μὲν γὰρ ἀποδεικτικὸς ἐκ τῶν πρώτων τῇ φύσει καὶ ἀρχικωτέρων ἀποδείκνυσι τὰ δεύτερα, ὁ δὲ διδασκαλικός, ἀποδεικτικός τις ὢν καὶ αὐτός, κατὰ δεύτερα μέτρα ἀποδείξεως ἐκ τῶν ὑστέρων τῇ φύσει τὰ πρότερα ἀποδείκνυσιν, ὃν καὶ τεκμηριώδη καλεῖ. οἷον εἴ τις ἰδὼν καπνὸν εἴποι πῦρ εἶναι ἐνταῦθα· ἐκ γὰρ τοῦ τῇ φύσει ὑστέρου τὸ πρότερον κατεσκεύασε.” Transl. Osborne, modified. 103 Cerami (2015), 321, argues that Philoponus might be referring to the distinction of APo A 1 between the deductive and the inductive method; Osborne (2006), 109 n. 39, points to both APo A 1 and Top A 12, where Aristotle presents his distinction between syllogism and induction. Neither place, however, has anything that really fits with what Philoponus says here. Moreover, in Soph El 2 “didactic” amounts to “demonstrative” rather than being opposed to it.

116

chapter 2

distinction: the demonstration of the that goes from what is posterior in itself but prior for us to what is prior in itself and posterior for us. Such a method constitutes a demonstration κατὰ δεύτερα μέτρα and is called τεκμηριώδης, for the very same reasons we have outlined with regard to Philoponus’ commentary on the Posterior Analytics. A similar analysis is found in Simplicius: The better known are taken either as principles and causes of that which is proved, as happens in demonstrations in the strict sense […] as when the cosmos to be good on the basis of the demiurge’s being good […] or as following necessarily from that which is proved, and concluding them [i.e., the better known premises] on the basis of that. The better known are assumed this latter way, as when god to be good on the basis of the cosmos being good and ordered, because this is more at our disposal in perception; […] the latter is more like a syllogism from sign (τεκμηριώδης), not demonstrative. And assumed for this kind of conviction are not principles of that which is proved, for they follow them rather than guide them, but the former kind of proof are principles, because they are better known and clearer and on the basis of them comes the conviction of that which is proved.104 While the idea is the same as we find in Philoponus, the example seems to be new in this context. It may refer to a passage in the Metaphysics: it is not that the world’s demiurge is good because the order of the world is good, but the order is good because the demiurge is.105 Thus, the syllogism that infers that the demiurge is good because the world’s order is good is a syllogism from the effect to the cause. Such a syllogism does not qualify as a demonstration in the proper sense, but only as a tekmeriodic demonstration. Principles and causes 104 Simplicius, In Phys, ed. Diels, CAG 9, 15.15–29: “τὰ δὲ γνωριμώτερα ἢ ὡς ἀρχαὶ καὶ αἴτια τῶν ἀποδεικνυμένων παραλαμβάνονται, ὅπερ ἐν ταῖς κυρίως ἀποδείξεσι συμβαίνει [...] ὡς ὅταν τὸ καλὸν εἶναι τὸν κόσμον ἐκ τοῦ τὸν δημιουργὸν ἀγαθὸν εἶναι συλλογιζώμεθα [..], ἢ ὡς ἀκολουθοῦντα ἐξ ἀνάγκης τοῖς ἀποδεικνυμένοις καὶ διὰ τοῦτο συνεισάγοντα αὐτά. οὕτω παραλαμβάνεται τὰ γνωριμώτερα (ὡς ὅταν τὸν θεὸν ἀγαθὸν δεικνύωμεν ἐκ τοῦ τὸν κόσμον καλὸν εἶναι καὶ τεταγμένον, προχειροτέρου τούτου κατ’ αἴσθησιν ἡμῖν ὄντος [...]) καὶ ἔστιν οὗτος τεκμηριώδης μᾶλλον ἀλλ’ οὐκ ἀποδεικτικὸς ὁ τοῦ συλλογισμοῦ τρόπος. καὶ τὰ πρὸς τὴν τοιαύτην πίστιν παραλαμβανόμενα τοῦ μὲν ἀποδεικνυμένου οὐκ εἰσὶν ἀρχαί (ἕπονται γὰρ αὐτῷ μᾶλλον ἤπερ προηγοῦνται), τῆς δὲ τοιαύτης ἀποδείξεως ἀρχαί, διότι γνωριμώτερά ἐστι καὶ προφανέστερα καὶ ἀπ’αὐτῶν ἡ πίστις γίνεται τοὐ ἀποδεικνυμένου.” Transl. in Tuominen (2007), 149, modified. 105 Aristotle, Met Λ, 1075a13–15.

The Greek Commentators

117

are better known in themselves, the things that follow (ἕπονται) from them are better known to us. In a tekmeriodic syllogism the premises do not contain the principles, but that which follows and is proved by means of the principles. Slightly later this is repeated: “It is clear that the knowledge of the principles is tekmeriodic, but not demonstrative.”106 In the attempt to resolve the tension between Physics A 1 and Posterior Analytics A 2, the ancient commentators interpreted Phys A 1 184a16–18 as a reference to a method of inquiry that does not qualify as a proper demonstration but only as a demonstration “in a secondary sense” or “according to a secondary standard.” Unlike in his commentary on the Posterior Analytics, Themistius does not mention sign-syllogisms in this context, and limits himself to ­speaking of a demonstration which, though not “proper,” is “sufficient to us,” which is a clear echo of Alexander, In Top A 1. Philoponus and Simplicius are explicit in associating the secondary standard of demonstration of which Aristotle is allegedly speaking in Phys A 1 with syllogisms from effect to cause or sign-syllogisms, which, just like in Philoponus’ commentary on the Posterior Analytics, are called “tekmeriodic demonstrations.”107 5 Ps-Philoponus-1 In APr B 27 In 1905 Max Wallies published two Greek commentaries on the two books of the Prior Analytics (CAG 13.2). That on Prior Analytics A was authored by Philoponus, and Wallies thought the commentary on Prior Analytics B to be from a distinct author. According to James Shiel, there is nothing in this commentary on Prior Analytics B that suggests that it is not ancient in content.108 According to Sten Ebbesen, by contrast, the commentary is a Byzantine collection of scholia. Moreover, Ebbesen thinks that “there is strong evidence that, while Philoponus’ and Alexander’s commentaries on APr. I were extant in Byzantine times, no ancient commentary on APr. II had been preserved.”109 Lorenzo Minio-Paluello found a considerable number of scholia translated or adapted from the Greek in the principal manuscript containing Boethius’ translation of the Prior Analytics—the manuscript of the Recensio ­Florentina. 106 Simplicius, In Phys, ed. Diels, CAG 9, 18.28–29: “δῆλον ὅτι τεκμηριώδης ἐστὶν ἡ γνῶσις ἡ περὶ τῶν ἀρχῶν ἀλλ’ οὐκ ἀποδεικτική.” 107 Morrison (1997) was probably the first to point to the doctrine of tekmeriodic proof in the Physics commentaries of Philoponus and Simplicius. On Morrison’s reading see supra, footnote 83 108 Shiel (1990). 109 Ebbesen (2008a), 178.

118

chapter 2

Minio-Paluello argued that the translator of these scholia was Boethius himself. According to Ebbesen, the scholia are excerpts from a more extensive work that perhaps was a full commentary on both books of the Prior Analytics, which Ebbesen calls “Commentum Graecum.”110 The so-called “Anonymus Aurelianensis III” (the anonymous author of the first Latin commentary on the Prior Analytics, dating to the years 1160–1180)111 was familiar with the Commentum Graecum.112 It has also to be noted that the Florentine scholia on Prior Analytics B have many cases of verbatim agreement with the Greek commentary on Prior Analytics B published by Wallies in CAG 13.2.113 We return to the Florentine scholia in Chapter 6. In what follows, we shall refer to the author of this commentary as Ps-Philoponus-1. We know from the first Chapter114 that APr B 27 is about enthymemes, that enthymemes are rhetorical syllogisms, and that they are of two kinds, those whose premise is a likelihood (εἰκός) and those whose premise is a sign (σημεῖον). An εἰκός-enthymeme is from an ἔνδοξος premise, i.e., from a proposition that holds “for the most part” (ὡς ἐπὶ τὸ πολύ). Ps-Philoponus-1 limits himself to repeat and paraphrase what Aristotle says about εἰκός-enthymemes at APr B 27, 70a3–7, but offers an original interpretation of Aristotle’s typology of sign-enthymemes: Since orators also demonstrate through enthymemes, and the enthymeme through eikota and signs, for this reason treats preliminarily of eikota and signs. And says at once the difference (so that through the difference we know everything) that the eikos is a reputable premise; therefore, those who demonstrate from eikos take one premise. That is said eikos which either is or is not for the most part; for example, for the most part the envied hate the envious, or for the most part the lovers love the beloved; indeed, the story says as much, that a certain lover killed the beloved. The sign divides into tekmerion and the homonymous sign. The homonymous sign is the same as the eikos. The tekmerion is formed with certainty in the first figure, and if it is true, it is irrefutable.115 110 Ebbesen (1981), 174ff. 111 Cf. Ebbesen (1981), 176; Thomsen Thörnquist (2014), 2; see infra, §4.2. 112 See Thomsen Thörnqvist (2014). 113 See Minio-Paluello (1972), and AL III.1–4. 114 Cf. supra, §§1.2, 1.4. 115 Ps-Philoponus-1, In APr, ed. Wallies, CAG 13.2, 480.20–481.3: “ἐπειδή οἱ ῥήτορες καὶ δι’ἐνθυμήματος ἀποδεικνύουσι, τὸ δὲ ἐνθύμημα διὰ εἰκότος καὶ σημείου, τούτου χάριν προδιαλαμβάνει περὶ τοῦ εἰκότος καὶ σημείου. καὶ λέγει εὐθέως τὴν διαφοράν, ἵνα διὰ τῆς διαφορᾶς γνῶμεν ἕκαστον, ὅτι τὸ εἰκός ἐστι πρότασις ἔνδοξος· ὥστε μίαν πρότασιν λαμβάνουσιν

The Greek Commentators

119

Signs in the wide sense of APr B 27, 70a3 and 70b1 divide into τεκμήρια and σημεῖα in the strict sense of 70b4. At Rhet A 2, 1357b4–5 the σημεῖον in the strict sense is said to have no name (ἀνώνυμον). Ps-Philoponus-1 here says that the σημεῖον ἀνώνυμον is rather ὁμώνυμον with the genus, i.e., with the σημεῖον in the wider sense. In addition, he identifies the σημεῖον ὁμώνυμον with the εἰκός. The reason for the identification has something to do with Aristotle’s contrast, at APr B 27, 70a7, between the necessary and the reputable character of the premises of a sign-enthymeme. Ps-Philoponus-1 so comments: Those who demonstrate from the sign demonstrate through one premise. The sign is a demonstrative premise, either necessary through the tekmerion, or reputable through the eikos. The sign is divided in two, the eikos and the tekmerion. We understand the sign in three ways: either it takes place while the fact is happening, like the fact of saying “if there is smoke, there is fire,” or the sign is after the fact, like the existence of ash signifies that a fire has taken place, or the fact takes place later and the sign first, like the fact of having milk of the woman who is going to give birth within two days.116 We saw117 that the contrast at APo B 27, 70a7 between ἀναγκαία and ἔνδοξος should be referred to the contrast between deductively valid τεκμήρια and deductively invalid (and thus, only “reputable”) σημεῖα. Yet, at 70a4 it is the εἰκός-enthymemes that is associated with an ἔνδοξος premise. We know that to have an ἔνδοξος premise (as εἰκός-enthymemes typically have) is not the οἱ ἐκ τοῦ εἰκότος ἀποδεικνύντες. ἐκεῖνο δὲ εἰκὸς λέγουσιν ὅ ὡς ἐπὶ τὸ πολὺ ἢ ἔστιν ἢ οὐκ ἔστιν· οἷον ὡς ἐπὶ τὸ πολὺ μισοῦσιν οἱ φθονούμενοι τοὺς φθονοῦντας, ἢ ὡς ἐπὶ τὸ πολὺ φιλοῦσιν οἱ ἐρῶντες τοὺς ἐρωμένους· φέρεται γάρ τις ἱστορία τοιαύτη, ὅτι ἐρῶν τις τὴν ἐρωμένην ἐφόνευσεν. τὸ δὲ σημεῖον διαιρεῖ εἰς τεκμήριον καὶ ὁμώνυμον σημεῖον. τὸ ὁμώνυμον δὲ σημεῖον ταὐτόν ἐστι τῷ εἰκότι. τὸ δὲ τεκμήριον μετὰ ἀσφαλείας γίνεται ἐν πρώτῳ σχήματι, καὶ εἰ ἀληθές ἐστιν, ἄλυτον γίνεται.” 116 Ps-Philoponus-1, In APr, ed. Wallies, CAG 13.2, 481.6–12: “καὶ οἱ ἀποδεικνῦντες ἐκ τοῦ σημείου διὰ μιᾶς προτάσεως ἀποδεικνύουσιν· πρότασις γάρ ἀποδεικτικὴ τὸ σημεῖον, ἢ ἀναγκαία διὰ τὸ τεκμήριον, ἢ ἔν̣δοξος διὰ τὸ εἰκός· Τὸ γὰρ σημεῖον εἰς δύο διαιρεῖται, εἰς εἰκὸς καὶ τεκμήριον. Τὸ δὲ σημεῖον τριχῶς νοοῦμεν· ἢ γάρ ἐστιν ὄντος τοῦ πράγματος, οἷον ἅμα τὸ πρᾶγμα καὶ σημεῖον, ὡς τὸ ‘καπνὸς εἰ ἔστι, πῦρ ἔστιν’· ἢ μετὰ τὸ πρᾶγμα τὸ σημεῖον, οἷον τὸ τέφραν εἶναι σημαίνει ὅτι πῦρ ἤδη γέγονεν· ἢ ὕστερον γέγονε τὸ πρᾶγμα, πρῶτον δὲ τὸ σημεῖον, ὡς τὸ γάλα ἔχειν τὴν μετὰ δύο ἡμέρας μέλλουσαν τίκτειν.” Transl. in Celli (2018), 107, modified. Cf. the passage in the Florentine scholia: AL III.4, 369: (ad 70a8) “Idem est hoc ac si diceret: Signum dicitur tripliciter: aut enim cum re est, ut fumus ignis est; aut post rem, ut incendium post ignem; aut ante rem, ut, si lac habet, post biduum futura parere.” 117 Cf. supra, §1.2.

120

chapter 2

same as to be ἔνδοξος in the manner of concluding (as second- and third-figure σημεῖα-enthymemes may be said to be). But this slight difference in the application of the qualification ἔνδοξος may have escaped our commentator, who on the basis of the fact that both arguments are said to be ἔνδοξοι may have found it reasonable to straightforwardly identify εἰκός-enthymemes with secondand third-figure σημεῖα-enthymemes, and all the more so because second- and third-figure σημεῖα-enthymemes receive no specific name in Aristotle’s treatise. All this shows that Ps-Philoponus-1 is well aware of both the wide and strict sense that the term σημεῖον has in APr B 27. As a comment on Aristotle’s ­terminological dilemma at APr B 27, 70b1–6, he writes: makes the difference among signs, that the sign divides into the tekmerion and the homonymous sign. For it is called tekmerion that sign which makes us know.118 Σημεῖα in the wide sense divide into σημεῖα in the strict sense (homonymous with the genus) and τεκμήρια. Τεκμήρια are sign-arguments from the middle, σημεῖα in the strict sense are sign-arguments from the extremes. We noticed119 that in APr B 27 the nomenclature of “middle” and “extremes” reflects neither the predicative nor the positional definitions of middle, major, and minor terms which Aristotle gives in APr A 4–6, but an extensional conception. His use of the letters “A” for the extensionally major term, “B” for the extensionally middle, and “C” for the extensionally minor in all the three figures of sign-syllogism should leave no doubt about it. Ps-Philoponus-1, however, interprets APr B 27, 70b1–6 predicatively rather than extensionally: Now he calls “middle” the first figure because the middle term is in this position along a straight line and is the subject of one and is predicated of the other. Or those from the extremes. He calls “extreme” the second and the third , because have the middle term as predicate in the one and as subject in the other; this we have to call a sign. That from the middle, or the “first figure,” tekmerion.120 118 Ps-Philoponus-1, In APr, ed. Wallies, CAG 13.2, 483.12–14: “Διαίρεσιν τοῦ σημείου ποιεῖται, ὅτι τὸ σημεῖον εἰς τεκμήριον διαιρεῖται καὶ ὁμώνυμον σημεῖον. λέγουσι δὲ ἐκεῖνο εἶναι τεκμήριον τὸ τὸ εἰδέναι ποιοῦν σημεῖον.” 119 Cf. supra, §1.4. 120 Ps-Philoponus-1, In APr, ed. Wallies, CAG 13.2, 483.16–21: “Μέσον νῦν λέγει τὸ πρῶτον σχῆμα διὰ τὸ τὸν μέσον ὅρον ἐνταῦθα κατ’εὐθεῖαν εἶναι καὶ τῷ μὲν ὑποκεῖσθαι τοῦ δὲ κατηγορεῖσθαι. Ἢ tὰ μὲν ἐκ τῶν ἄκρων. ἄκρα λέγει τὸ δεύτερον καὶ τὸ τρίτον, ὅτι ἔχουσι τὸν μέσον ὅρον τὸ μὲν κατηγορούμενον τὸ δὲ ὑποκείμενον· ὃ ὀφείλομεν λέγειν σημεῖον. Τὸ δὲ ἐκ τοῦ μέσου, ἀντὶ τοῦ

The Greek Commentators

121

The interpretation of the syllogistic nomenclature is predicative: the middle is that which is predicate in one premise and subject in the other in the first figure, the extremes are those that are either the subject (third figure) or the predicate (second figure) in both premises. The formulation τὸν μέσον ὅρον ἐνταῦθα κατ’εὐθεῖαν εἶναι also suggests a positional qualification. In any case, the predicative interpretation of the Aristotelian, extensional definitions is harmless, because in affirmative universal (or, for that matter, singular) propositions the predicative interpretation corresponds to the extensional: that which is predicatively intermediate is also extensionally intermediate (besides being, as Ps-Philoponus-1 observes, positionally middle), that which is always predicate is extensionally the major, that which is always subject is extensionally the minor term.121 Aristotle’s tripartite illustration at APr B 27, 70a8–10 of the temporal relationships between sign and that which the sign signifies is enriched by Ps-Philoponus-1 with examples. First, the sign and the thing signified may be simultaneous; an example of this is smoke as sign of fire. Second, the sign may follow temporally the thing signified; an example of this is ash as sign of fire; both examples have a long tradition in Posterior Analytics commentaries, as we noticed at various junctures in the present Chapter. Third, the sign may precede temporally the thing signified. This time the example is the lactating woman from APr B 27. In this context the presence of milk in the breast is taken as a prognostic sign of imminent delivery, not as a sign of having already delivered (as in the Rhetoric), nor as a sign of being pregnant (as sometimes κύειν of APr B 27 is translated).122 As we know, in APr B 27, 70a31–36 Aristotle explains that second- and third-figure sign-syllogisms are refutable (λύσιμοι) because their syllogistic reconstruction does not yield a valid syllogistic argument. Third-figure sign-syllogisms are refutable even if true, i.e., even if the conclusion is true, because in that figure only a particular conclusion can be drawn from two universal premises. Second-figure sign-syllogisms are also refutable even if the conclusion is true, because in that figure no conclusion at all can be drawn from two affirmative premises. Ps-Philoponus-1 considers the three examples

‘πρώτου σχήματος’, τεκμήριον.” Cf. the passage in the Florentine scholia: AL III.4, 370: (ad 70b3) “Medium hic dicit primam figuram, eo quod medium terminum positione habeat medium; extremitates vero secundam et tertiam, eo quod habeant medium terminum, haec quidem praedicatum, illa vero subiectum, et non positione medium, sed sursum vel deorsum.” 121 Cf. Mignucci (1969), 724. 122 Cf. supra, §1.8

122

chapter 2

of sign-arguments used by Aristotle, and explains the invalidity of those in the second and third figure very much as Aristotle does: That which is proved through the first figure cannot be destroyed, but remains irrefutable; the sign is a tekmerion, if it is true. That through the last can be destroyed. Through what? Through does not syllogize a universal . This is refutable, unless it syllogizes a particular . That through the middle can always be destroyed; for in the second from two affirmatives a syllogism with a syllogistic connection was never seen.123 The sign-syllogism in the third figure is invalid because it concludes universally, while in that figure only particular conclusions are possible from universal premises; the one in the second figure is invalid because in that figure no conclusion at all is possible from two affirmative premises. The difference, only adumbrated in APr B 27, is that while in the second figure a sign can always be destroyed (ἀεὶ ἀνασκευάζεται), i.e., is always λύσιμος, in the third it can be destroyed, i.e., is λύσιμος only if a universal conclusion is drawn, but not if a particular conclusion is drawn: in the first , the proof is true, the syllogism is always irrefutable, in the second always asyllogistic, in the third sometimes, because always particular.124 “Asyllogistic” here means “incapable of yielding whatever conclusion”: such is the sign-argument in the second figure. But the argument in the third figure is not, in this sense, “asyllogistic,” because it can yield a valid particular conclusion, even if not the universal conclusion it professes to yield. What is the role of the examples that Aristotle provides, then, if the ­arguments they exemplify are invalid? Ps-Philoponus-1 thinks they are just “examples.” About the Pittakos example, “it is evident that is said for the sake of example (ὅτι παραδείγματος χάριν εἴρηται), because in truth in the first figure we infer 123 Ps-Philoponus-1, In APr, ed. Wallies, CAG 13.2, 482.19–24: “Οὐκ ἀνασκευάζεται ὁ διὰ τοῦ πρώτου σχήματος δεικνύμενος, ἀλλὰ ἄλυτος μένει· τεκμήριον γὰρ γίνεται τὸ σημεῖον, ἐὰν ᾖ ἀληθές. ὁ δὲ διὰ τοῦ ἐσκάτου ἀνασκευάζεται. διὰ τί; διὰ τὸ μὴ καθόλου αὐτὸν συλλογίζεσθαι· λύσιμος δέ, ἐὰν τὸ μερικὸν συλλογίζηται. ὁ δὲ διὰ τοῦ μέσου ἀεὶ ἀνασκευάζεται· ἐκ γὰρ δύο καταφατικῶν οὐδέποτε ἐν δευτέρῳ ὤφθη συλλογιστικῆς συζυγίας συλλογισμός.” 124 Ps-Philoponus-1, In APr, ed. Wallies, CAG 13.2, 483.8–10: “ἐν πρώτῳ ἀεί, ἀληθὲς ἡ δεῖξις, ἄλυτος ὁ συλλογισμός, ἐν δευτέρῳ δὲ ἀεί ἀσυλλόγιστος, ἐν τρίτῳ δὲ ποτέ, ὅτι ἀεί μερικά.”

The Greek Commentators

123

from two universal affirmatives, but not in the third.”125 About the pale woman, “ is said for the sake of example (εἴρηται χάριν παραδείγματος), since in truth in the second figure the connection from two affirmatives is asyllogistic.”126 Second- and third-figure sign-arguments are invalid. The examples that instantiate them are to be taken, Ps-Philoponus-1 seems to suggest, as just that, as good examples of invalid forms. It should not be inferred that the forms that they instantiate are valid. 6 Ps-Philoponus-2 In APo B A commentary on the second book of the Posterior Analytics that has been transmitted under the name of Philoponus has been published in CAG 13.3. Sten Ebbesen has observed that the attribution, maintained in the CAG edition, was “doubtless due to pressure from the general editor, Hermann Diels, who repeatedly forced Maximilian Wallies, an excellent scholar, to leave untenable attributions found in the Aldine editions untouched.”127 In the introduction, Wallies argues against the attribution of this work to Philoponus on the basis of four reasons: (1) the commentary on Posterior Analytics A is much more expansive than that on Posterior Analytics B; (2) the commentary on Posterior Analytics A mentions both Alexander of Aphrodisias and Ammonius, that on Posterior Analytics B mentions neither; (3) the transmission of the two commentaries is different, as only later codices with the commentary on Posterior Analytics A also have the commentary on Posterior Analytics B, while earlier codices combine the commentary on Posterior Analytics A with the anonymous commentary in CAG 13.3, which Moraux has shown to derive from Alexander.128 To Wallies’s arguments Owen Goldin adds a stylometric consideration: the word ἤγουν (“that is”) has a much higher frequency in the commentary on Posterior Analytics B than in that on Posterior Analytics A, and this strongly suggests that the two commentaries are not by the same author.129 The same stylistic consideration has brought Ebbesen to attribute the commentary on Posterior Analytics B to Leo Magentinus, a Byzantine philosopher who lived in the thirteenth century.130 125 Ps-Philoponus-1, In APr, ed. Wallies, CAG 13.2, 481.28–29. 126 Ps-Philoponus-1, In APr, ed. Wallies, CAG 13.2, 482.10–12. 127 Ebbesen (2012), 363. 128 CAG 13.3, v–vi; cf. supra, §2.1. 129 Goldin (2009), 2. 130 Ebbesen (2012), 363.

124

chapter 2

However, Goldin also argues that the attribution to Philoponus is not groundless: “even if stylistic considerations tell against Philoponus as author in our sense of the term, the details and even the wording of much of the commentary may in fact derive from a lost commentary of Philoponus (or the lectures of Ammonius, his source).”131 The bases of Goldin’s argument are both stylometric and of doctrine. Goldin further observes that unlike the commentary on Posterior Analytics A, that on Posterior Analytics B “never cites Alexander, and presents some interpretations radically different from those of Alexander.”132 As we shall see, as far as the contrast between demonstration and sign-inference is concerned, the commentary on Posterior Analytics B uses the distinction, which originates with Alexander, between the two senses in which the premises may be said to be causes of the conclusion. Also, it draws the very same contrast as Alexander, Themistius, and Philoponus draw between a demonstration in the strict sense (κυρίως ἀπόδειξις) and a demonstration in a secondary sense (κατὰ δεύτερα μέτρα), and associates the latter with sign-inferences: a demonstration in a secondary sense is a τεκμηριώδης ἀπόδειξις or τεκμηριώδης συλλογισμός. Finally, the examples used to illustrate Aristotle’s demonstration κατὰ σημεῖον ἢ συμβεβηκός of APo B 17 are roughly the same as we find in ­Themistius. Since Themistius’ paraphrase, Philoponus on Posterior Analytics A, and excerpts from Alexander’s commentary were still available in the twelfth century, it may very well have been the case that aB ­ yzantine author used those sources in the compilation of a “new” commentary on ­Posterior Analytics B. Goldin’s hypothesis that the commentary in question derives from Philoponus or from Ammonius’ school is not more explicative than Ebbesen’s hypothesis that its author is a Byzantine philosopher that has those sources at his disposal. We shall leave the question undecided and shall call the author of this treatise by the name of Ps-Philoponus-2 (to distinguish him from the author of the spurious commentary on Prior Analytics B in CAG 13.2). According to Ps-Philoponus-2, in the first book of APo Aristotle taught that for the other syllogisms the middle term is the cause of the conclusion, but not of the fact as well, while in the demonstrative syllogism the ­middle term is the cause of both the conclusion and the fact.133 131 Goldin (2009), 3. 132 Goldin (2009), 3. 133 Ps-Philoponus-2, In APo, ed. Wallies, CAG 13.3, 334.5–7: “ἐν μὲν τοῖς ἄλλοις συλλογισμοῖς ὁ μέσος αἴτιος ἦν τοῦ συμπεράσματος, οὐ μὴν δὲ καὶ τοῦ πράγματος, ἐν δὲ τῷ ἀποδεικτικῷ συλλογισμῷ ὁ μέσος αἴτιός ἐστι καὶ τοῦ συμπεράσματος καὶ τοῦ πράγματος.” Transl. Goldin.

The Greek Commentators

125

As we know, in APo A 2 Aristotle claims that the premises of a demonstration have to be causes of the conclusion. His commentators, beginning with Alexander, distinguish two senses of this claim, and this is precisely what Ps-Philoponus-2 says in this passage: in a demonstrative syllogism the p ­ remises are both the logical and the ontological cause of the conclusion, in nondemonstrative syllogisms they are the logical cause only. The first reference to sign-inferences occurs later. In APo B 12 Aristotle considers the temporal relation between cause and effect. The main point of the first part of the chapter134 is that if cause and effect are simultaneous, this holds not only of the present but also of the past and the future; so, if the cause of the present eclipse is the present interposition of the earth, in like manner the cause of the past eclipse was the past interposition, and that of the future eclipse the future interposition. Ps-Philoponus-2 takes this to have something to do with convertibility: there is a necessary entailment between the cause and the effect, from whichever one might begin, whether from the cause or from the effect, for they convert with each other. For if water has solidified on account of the disappearance of heat, ice too must have come to be, and if ice came to be, there must have been a disappearance of heat when the water solidified. However, even if there is a necessary entailment between the cause and the effect (from whichever one might begin, whether from the cause or from the effect), there is nonetheless this distinction in the cases. For if when the cause is posited the effect will follow, there is demonstration in the strict sense, because demonstration comes from things that are prior and are causes. But if, when the effect is posited the cause will follow, there is a tekmeriodic demonstration. For the syllogism proceeded from posterior . Such a demonstration which is based on posterior premises meets standards of a lower order than those of demonstration, since it falls short of being a demonstration.135 134 Aristotle, APo A 12, 95a10–24. 135 Ps-Philoponus-2, In APo, ed. Wallies, CAG 13.3, 386.22–387.2: “ἐξ ἀνάγκης γίνεται ἡ ἀκολούθησις τοῦ τε αἰτίου καὶ τοῦ αἰτιατοῦ, ὅθεν ἄν τις ἄρξηται, ἤγουν εἴτε ἀπὸ τοῦ αἰτίου εἴτε ἀπὸ τοῦ αἰτιατοῦ· ἀντιστρέφουσι γὰρ πρὸς ἄλληλα. εἰ γὰρ τὸ ὕδωρ πέπηγε δι᾿ἔκλειψιν τοῦ θερμοῦ, ἀνάγκη καὶ κρύσταλλον γενέσθαι, καὶ εἰ κρύσταλλος γέγονεν, ἀνάγκη καὶ ἔκλειψιν θερμοῦ γενέσθαι πηχθέντος τοῦ ὕδατος. πλὴν εἰ καὶ ἐξ ἀνάγκης ἡ ἀκολούθησις τοῦ αἰτίου καὶ τοῦ αἰτιατοῦ γίνεται, ὅθεν ἄν τις ἄρξηται, εἴτε ἀπὸ τοῦ αἰτίου εἴτε ἀπὸ τοῦ αἰτιατοῦ, ἀλλ᾿οὖν διαφορά ἐστιν ἐν αὐτοῖς αὕτη· εἰ μὲν γὰρ τοῦ αἰτίου τεθέντος ἕψεται τὸ αἰτιατόν, ἔστι κυρίως ἀπόδειξις, διότι καὶ ἡ ἀπόδειξις ἐκ προτέρων καὶ αἰτίων γίνεται· εἰ δὲ τοῦ αἰτιατοῦ τεθέντος ἕψεται τὸ αἴτιον, γίνεται τεκμηριώδης ἀπόδειξις. ἐκ γὰρ τῶν ὑστέρων ὁ συλλογισμὸς προέβη· ἡ δὲ τοιαύτη

126

chapter 2

In this context Ps-Philoponus-2 considers only the case of converting causes and effects, the case discussed in sections (ii) and (iii) of APo A 13. His analysis is recognizably the same as that of Alexander, Themistius, and Philoponus: when the effect is inferred from the cause, the inference is a κυρίως ἀπόδειξις; when the cause is inferred from the effect, the inference is a τεκμηριώδης ἀπόδειξις and an ἀπόδειξις only in a secondary sense or according to a secondary standard. The same distinction is invoked in the comment on APo B 16, which contains a reiteration of the why/that distinction of APo A 13. Aristotle says that even when cause and effect convert there can be no reciprocal demonstration, because the cause is prior to the effect; thus, the demonstration through the cause is of the why, that through the effect is of the that.136 Ps-Philoponus-2 comments as follows: if the cause and the effect are of the same time, and one does not temporally precede the other (for you think about the cause, that the earth is in the middle, and the effect too, that the moon is eclipsed, is brought [to mind] at the same time), but to be sure the cause precedes the effect by nature and in one’s conceptualization and in definition. For we first conceive of that the earth is in the middle, and then later [the fact] that the moon is eclipsed. But nature too first knows the cause and then accordingly the effect. And since the cause precedes the effect, if a syllogism that the moon is eclipsed or that the trees shed their leaves should come about through a middle term that is the cause, for example, the earth’s being in the middle or the moisture congealing, it is a demonstration in the strict sense. For it is based on causes and things that are prior. But if the syllogism proceeds through a middle term which is the effect, it is not a demonstration but a tekmeriodic syllogism. For we infer what is prior on the basis of what is posterior […] Reciprocal proof is nothing strange, but when the syllogism is through the cause, it is a demonstration in the strict sense, when it is through the effect, as middle term, it is not a demonstration in the strict sense but is a tekmeriodic syllogism.137 ἀπόδειξις ἡ ἐκ τῶν ὑστέρων δεύτερα μέτρα φέρει ἀποδείξεως ὡς ταύτης ἐκπίπτουσα.” Transl. Goldin, modified. 136 Aristotle, APo B 16, 98b16–24. 137 Ps-Philoponus-2, In APo, ed. Wallies, CAG 13.3, 424.1–24: “εἰ γὰρ καὶ τὸ αἴτιον καὶ τὸ αἰτιατὸν ὁμόχρονά εἰσι καὶ κατὰ τὸν χρόνον θάτερον θατέρου οὐ προηγεῖται (ἅμα γὰρ ἐπινοεῖς τὸ αἴτιον, τὸ ἐν μέσῳ εἶναι τὴν γῆν, καὶ εὐθὺς συνεισάγεται καὶ τὸ αἰτιατόν, ἤγουν τὸ ἐκλείπειν τὴν σελήνην), ἀλλ’ οὖν τῇ φύσει καὶ τῇ ἐπινοίᾳ καὶ τῷ λόγῳ τὸ αἴτιον προηγεῖται τοῦ αἰτιατοῦ. καὶ γὰρ ἡμεῖς πρῶτον ἐπινοοῦμεν τὸ ἐν μέσῳ εἶναι τὴν γῆν, εἶθ’ὕστερον τὸ ἐκλείπειν τὴν σελήνην· ἀλλὰ καὶ

The Greek Commentators

127

As in the previous passage, here Ps-Philoponus-2 construes the convertibility of cause and effect—which is Aristotle’s assumption in APo B 16—in temporal terms: cause and effect are ὁμόχρονα. Their simultaneity, he says, does not prevent the cause from being prior to the effect by nature, in thought, and in the definition. We know that it is Aristotelian doctrine that the cause is by nature better known than and prior to the effect, while the effect is better known than and prior to the cause for us. It is also Aristotelian doctrine that the cause enters into the definition of the effect while the reverse is not true (for example, the interposition of the earth enters into the definition of the eclipse, but the eclipse does not into the definition of the interposition). Ps-Philoponus-2 also says that the cause is prior to its effect τῇ ἐπινοίᾳ, in thought, because even if they occur simultaneously, yet we first conceive the cause and then its effect. Having explained how it is possible that of two converting terms one is prior to the other, Ps-Philoponus-2 is ready to use the traditional distinction to explain in what sense there is and in what sense there is not reciprocal demonstration. Taking demonstration in its proper sense (κυρίως ἀπόδειξις), there is no reciprocal demonstration because the only proper demonstration is the demonstration of the why, in which the effect is inferred from the cause. But once allowance is made for a secondary standard of demonstration, the τεκμηριώδης συλλογισμός, we may say that there is reciprocal demonstration in the sense that the cause is demonstrated “tekmeriodically” from the effect, precisely as in Aristotle’s demonstration of the that (of type 1b). Ps-Philoponus-2’s use of the verb τεκμαίρομαι is meaningful. He adds ἐκ τοῦ ὑστέρου γὰρ τὸ πρῶτον τεκμαιρόμεθα as an explanation of the qualification τεκμηριώδης: that second standard of demonstration, by which causes are inferred from effects, has that name because it is constituted by the cognitive action of τεκμαίρεσθαι. It is not impossible that the addition was intended as a clarification of an obscure term (τεκμηριώδης) by means of a more common verb (τεκμαίρομαι). Ps-Philoponus-2’s comment on APo B 17, containing the second mention of sign-inferences in the Posterior Analytics, is very close to Themistius’:

ἡ φύσις πρῶτον γινώσκει τὸ αἴτιον, εἶθ’οὕτω τὸ αἰτιατόν. καὶ ἐπεὶ προηγεῖται τὸ αἴτιον τοῦ αἰτιατοῦ, εἰ μὲν ὁ συλλογισμὸς γέγηται, ὅτι ἐκλείπει ἡ σελήνη ἢ ὅτι φυλλορροεῖ τὰ δένδρα, διὰ μέσου τοῦ αἰτίου, ἤγουν τοῦ ἐν μέσῳ εἶναι τὴν γῆν ἢ τοῦ τὸ ὑγρὸν πήγνυσθαι, γίνεται κυρίως ἀπόδειξις· αὕτη γὰρ ἐξ αἰτίων καὶ προτέρων γίνεται. εἰ δὲ ὁ συλλογισμὸς προβῇ διὰ μέσου τοῦ αἰτιατοῦ, ἀπόδειξις οὐκ ἔστι τοῦτο ἀλλὰ τεκμηριώδης συλλογισμός· ἐκ τοῦ ὑστέρου γὰρ τὸ πρῶτον τεκμαιρόμεθα. [...] οὐδὲν ἄτοπον τὸ δι’ἀλλήλων δείκνυσθαι, ἀλλ’ὅτε μὲν ὁ συλλογισμὸς διὰ τοῦ αἰτίου γίνεται, ἀπόδειξίς ἐστι κυρίως, ὅτε δὲ διὰ μέσου τοῦ αἰτιατοῦ, ἀπόδειξις κυρίως οὐκ ἔστιν ἀλλὰ τεκμηριώδης συλλογισμός.” Transl. Goldin, modified.

128

chapter 2

if the per se cause is given, the cause, too, can be some one thing. He says that the per se cause is the definition of the effect, and the definition of each thing is one. For precisely this reason the per se cause of even the lunar eclipse is one: the blocking of the earth. But if the cause that is given is by way of a sign or is an accident, there can be many causes of the same thing. For example, ashes and smoke are signs of fire. In this case I will also prove that there is fire by taking as middle term either ashes or smoke. Let this be an example of the accidental. Trees shed their leaves, because their leaves become shriveled or lose their colour. Or that a human being is a rational animal, because he is capable of laughter and flatnailed.138 It will be recalled that in this chapter Aristotle asks whether there can be different causes of the same attribute (i.e., effect) for different things (i.e., different subjects), and that his initial answer is that if the demonstration is καθ᾿αὑτό, this is impossible, while if the demonstration is κατὰ σημεῖον ἢ συμβεβηκός it is possible that the causes be multiple.139 It will also be recalled that, in discussing this passage, Themistius distinguishes between the case in which something is inferred διὰ συμβεβηκότος from the case in which it is inferred διὰ σημείου. His example of the “sign” is the inference of the past presence of fire from the actual presence of carbon or ash, which count as multiple signs of fire and thus of multiple logical causes of the inferred conclusion. The example of “accident” is the inference that a tree sheds its leaves from the facts that it also shrivels up or loses its color; both count as accidents of shedding leaves and as multiple logical causes of the conclusion. In both cases, Themistius’ point is that when the cause of something appears to be multiple, “cause” has to be taken in the logical sense.140 Ps-Philoponus-2 says very much the same thing, and his examples are also very much the same. He distinguishes, like Themistius, the two cases alluded to by Aristotle, that κατὰ σημεῖον and that κατὰ συμβεβηκός. His example of the 138 Ps-Philoponus-2, In APo, CAG 13.3, 426.10–20: “εἰ καθ’αὑτὸ ἀποδοθῇ τὸ αἴτιον, ἐνδέχεται εἶναι ἕν τι. καὶ φησὶν ὡς τὸ καθ’ αὑτὸ αἴτιον ὁρισμός ἐστι τοῦ αἰτιατοῦ, ὁ δὲ ὁρισμὸς ἑκάστου πράγματος εἷς ἐστι. καὶ διὰ τοῦτο καὶ τῆς σεληνιακῆς ἐκλείψεως τὸ καθ’αὑτὸ αἴτιον ἕν ἐστιν, ἡ ἀντίφραξις τῆς γῆς. εἰ δὲ τὸ ἀποδοθὲν αἴτιον κατὰ σημεῖόν ἐστιν ἣ συμβεβηκός, ἐνδέχεται πολλὰ αἴτια εἶναι τοῦ αὐτοῦ. οἷον τοῦ πυρὸς σημεῖά εἰσιν ὁ καπνὸς καὶ ἡ τέφρα· καὶ δείξω ἐνταῦθα πῦρ εἶναι λαβὼν μέσον ὅρον ἢ τὴν τέφραν ἢ τὸν καπνόν. τοῦ δὲ κατὰ συμβεβηκὸς παράδειγμα ἔστω τοῦτο· τὰ δένδρα φυλλορροεῖ, διότι ῥυτιδοῦται τὰ φύλλα αὐτῶν ἣ λευκαίνονται. ἢ ὅτι ὁ ἄνθρωπος λογικὸν ζῷόν ἐστι, διότι γελαστικὸν πλατυώνυχον.” Transl. Goldin. 139 Cf. supra, §1.7. 140 Cf. supra, §2.2.

The Greek Commentators

129

former is the same as in Themistius, with ash and smoke (rather than carbon) as signs of fire. His examples of the latter are two: one is precisely Themistius’ example, i.e., shriveling and losing color as accidents of shedding leaves; the other is new in this context: capacity of laughing and having flat nails as accidents of man. In both cases, just like Themistius, Ps-Philoponus-2 suggests that when the causes of an attribute appear to be multiple, the demonstration is “from a sign” or “from an accident,” which are causes only in the logical but not in the ontological sense: the ontological cause of an attribute is unique, but the same attribute can be proved to belong to something through multiple middle terms, i.e., multiple logical causes. It should also be pointed out that the distinction between the κατὰ σημεῖον and the κατὰ συμβεβηκός demonstrations of APo B 17 that we find in both ­Themistius and Ps-Philoponus-2 may have Alexander as its ultimate source: we saw141 that the Anonymous in CAG 13.3 says that “the sign always follows the thing, the accident can also from outside.”142 This, we noticed, may be taken to mean that while a sign is coextensive with its cause, an accident can have a wider extension. Carbon, ash, and smoke may indeed be taken to be coextensive with fire (whenever there is fire, there will be carbon, ash, and smoke, and vice versa), and shriveling and losing color may be taken as more extended than shedding leaves (there may be cases of shriveling and losing color that are not cases of shedding leaves); Ps-Philoponus-2’s last example does not perfectly fit with this analysis: being flatnailed is more extended than man, but the capacity of laughing is notoriously a property of man, not an accident of it (the proper, in the Porphyrean sense, has the same extension as that of which is a proper, the accident may also be more extended).143 But for this last example, however, it is safe to assume that Ps-Philoponus-2 depends on Themistius, who in turn depends on Alexander. 7

Michael of Ephesus on the Sophistici Elenchi

Since it is no demonstration at all, Philoponus should not, and in fact does not, call the syllogism from a refutable sign in the strict sense a “semiotic demonstration” (in analogy with the syllogism from a necessary sign, which 141 Cf. supra, §2.1. 142 Anonymous, In APo, ed. Wallies, CAG 13.3, 593.25–26. 143 According to Alexander, In Top, ed. Wallies, CAG 2.2, 45.23–24, being flatnailed and ­capable of laughing are both proper of man; see also Philoponus, In APo, ed. Wallies, CAG 13.3, 223.10–24.

130

chapter 2

is called by him a “tekmeriodic demonstration”). But someone else used this expression. In his commentary on the Sophistici Elenchi by Michael of Ephesus (pseudo-Alexander)144 the semiotic inferences associated with the fallacy of the consequent are called σημειώδεις ἀποδείξεις: Moreover, also in rhetorical syllogisms semiotic demonstrations are produced from the consequents. For fancy dressing is a sign of the adulterer and wandering about at night of the thief (indeed fancy dressing follows the adulterer, and wandering about at night the thief), for this reason the rhetorical demonstrations are produced from the consequents. In order to show that is an adulterer, one takes the consequent that he dresses fancily, and in order to prove a thief that he wanders about at night. The confutation is that “many have these but not the predicate.” calls “predicate” adultery attribute of fancy dressing, and being thief of wandering about at night, not in the sense that they are true predicates ( has said indeed that they do not necessarily convert), but in the sense that they are taken as predicates by the sophists.145 An inference from the consequent to its antecedent is deductively invalid. Michael observes that the proof of deductive invalidity is in Aristotle’s explanation that one can have the one characteristic (the sign: fancy dressing, wandering about at night) without necessarily having the other (the cause of the sign: being an adulterer, being a thief); that is to say, the effect or consequent has a wider extension than its alleged cause or antecedent. We saw that this is an extensional relationship between cause and effect that Aristotle does not take into account in his typology of that-demonstrations in APo A 13, because 144 145

Ebbesen (1981), I, 268–285, has shown that the pseudo-Alexandrian text published by Wallies in CAG 2.3 was in fact produced by Michel of Ephesus (twelfth century) on the basis of older sources; cf. also Ebbesen (1979), viii–xii. [Michael of Ephesus], In Soph El, ed. Wallies, CAG 2.3, 48.27–49.3: “οὐ μὴν ἀλλὰ καὶ ἐν τοῖς ῥητορικοῖς συλλογισμοῖς αἱ σημειώδεις ἀποδείξεις ἐκ τῶν ἑπομένων γίνονται. ἐπειδὴ γὰρ σημεῖον τοῦ μοιχοῦ τὸ καλλωπίζεσθαί ἐστι καὶ τοῦ κλέπτου τὸ νυκτὸς πλανᾶσθαι (ἕπεται γὰρ καὶ τῷ μοιχῷ τὸ καλλωπίζεσθαι καὶ τῷ κλέπτῃ τὸ νυκτοπορεῖν), διὰ τοῦτο αἱ ῥητορικαὶ ἀποδείξεις ἐκ τῶν ἑπομένων γίνονται· ὁ γὰρ βουλόμενος δεῖξαι ὅτι μοιχός ἐστι, τὸ ἑπόμενον ἔλαβεν, ὅτι καλλωπιστής, καὶ ὁ τὸν κλέπτην ἐλέγξαι βουλόμενος ὅτι νύκτωρ πλανᾶται. τὸ δὲ πολλοῖς μὲν ταῦτα ὑπάρχει, τὸ δὲ κατηγορούμενον οὐχ ὑπάρχει λύσις ἐστί. κατηγορούμενον δὲ λέγει τὴν μὲν μοιχείαν κατηγορίαν τοῦ καλλωπίζεσθαι, τοῦ δὲ νυκτὸς βαδίζειν τὸ κλέπτειν, οὐχ ὡς ἀληθῶς κατηγορουμένων (εἴρηται γὰρ ὡς οὐκ ἀνάγκη ἀντιστρέφειν), ἀλλ’ὡς ὑπὸ τῶν σοφιστῶν ὡς κατηγορουμένων λαμβανομένων.”

The Greek Commentators

131

no inference from the effect to the cause would be possible in this case; only Philoponus explicitly considers this case while dealing with APo A 13, but does not associate this invalid inference with invalid sign-inferences. In the present passage from Michael of Ephesus, the example of Soph El 5 appears in the same split from as in Philoponus’ commentary on APo A 2146: in Aristotle both fancy dressing and wandering about at night are signs of being an adulterer; here only the former is a sign of adultery, while the latter is a sign of theft. In both cases, the inference from a consequent (the effect or sign) to one of its possible antecedents (its possible causes) is a fallacy. At Soph El 5 167b9 such fallacies are called κατὰ τὸ σημεῖον ἀποδείξεις.147 Michael renders this expression by means of an adjectival qualification: σημειώδης. Such an adjective is perfectly parallel to Philoponus’ τεκμηριώδης. Is Philoponus one of the sources of Michael? Could the adjective σημειώδης have been chosen to characterize rhetorical proofs so as to echo the adjective τεκμηριώδης that Philoponus used to characterize scientific (though noncausal) proofs? As Ebbesen has shown, there are two versions of Michael’s ­commentary, an early one (‟Ps-Alexander 2”) and a final and expanded one (‟PsAlexander 1”); the latter is the one edited by Wallies in CAG 2.3.148 A c­ omparison of the two versions149 reveals that the passage quoted above is present in the second but not in the first. Even if the passage was actually inspired by Philoponus, it was Michael who shaped the adjective, which then entered the expanded version of his commentary. Ebbesen thinks it more plausible to take Michael’s σημειώδης as just a rendering of Aristotle’s κατὰ τὸ σημεῖον. It is undeniable, however, that the adjectival contrast between σημειώδης and τεκμηριώδης remains a suggestive parallel, which in addition does full justice to the terminological distinction introduced by Aristotle in APr B 27. 8 Conclusion The question of the status of sign-syllogisms within the Aristotelian theory of science was raised, and the terms in which it was to be treated for several centuries were clearly formulated, by Alexander of Aphrodisias. Alexander is the 146 Cf. supra, §2.3. 147 Cf. supra, §1.7. 148 Ebbesen (1981). 149 See Ebbesen (2018), in a reply to our preliminary study of tekmeriodic demonstrations in the Greek tradition of the Posterior Analytics (Bellucci and Marmo 2018).

132

chapter 2

ultimate source of the idea that the syllogism of the that of APo A 13, and especially its prototypical variety (type 1b), can be identified with the first-figure sign-syllogism of APr B 27. This identification (that-syllogism = sign-syllogism = demonstration of a lower kind) is made both implicitly and explicitly, and has three important consequences. (i) In the first place, it projects the epistemic dimension of the that/why distinction onto the theory of signs. We noticed that Aristotle is remarkably silent on the epistemic status of the sign-premise of his sign-syllogisms. Now, if the better known of the convertible terms of APo A 13 (the effect) is identified with the sign from which the less known term (the cause) is inferred, then the theory of sign-inferences becomes ipso facto interpretable in epistemic terms: of sign (lactation) and signified thing (giving birth), it is the former that is better known and which makes us know something less known than it; the reverse inference would be blocked by the epistemic asymmetry of sign and signified thing (giving birth cannot become the sign of lactation150). As we saw in this Chapter, this element is a stable component of the Greek tradition of the P­ osterior Analytics. (ii) In the second place, Alexander’s identification implies that the first-figure sign-syllogism of APr B 27 and the syllogism of the that of APo A 13 may be said to be “demonstrative” to some extent: the τεκμήριον is one of three forms of πρότασις ἀποδεικτική, and the syllogism of the that is also called ἀπόδειξις, even if it does not satisfy the strict requirements of APo A 2. It is a demonstration in a secondary sense (δευτέρως), and as such it may be contrasted with demonstration in the proper sense (κυρίως). While some distinction between a strong and proper, and a weak and secondary sense of ἀπόδειξις is adumbrated in various places of the Posterior Analytics (one of these being APo A 13 itself), it is Alexander that explicitly makes this distinction. This element, too, is a quite stable component of the Greek tradition of the Posterior Analytics. (iii) In the third place, Alexander’s identification involves a “split” of the Aristotelian notion of “cause.” In APo A 2 Aristotle claims that in a demonstration the premises must be the cause of the conclusion. Now, in a demonstration in the secondary sense it is the conclusion that contains the cause of the premises. Alexander solves this difficulty by distinguishing two senses in which the premises are causes of the conclusion: in one sense, the premises 150

With at least the possible exception of the so-called “prognostic signs,” which are causes that are sign of their effects. These fall under the category of signs that signify something future, a category explicitly discussed by Roger Bacon; cf. infra, § 7.2.2.

The Greek Commentators

133

are the cause of the thing expressed in the conclusion (ontological sense of “cause”); in another sense, they are the cause of the inferring of the conclusion (logical sense of “cause”). In a proper demonstration the premises are the cause of the conclusion in both the logical and the ontological sense, while in a demonstration in the secondary sense they are the cause of the conclusion only in the logical sense. This idea was also quite influential in the tradition of the Posterior Analytics. It is also found, together with the distinction between demonstration in the strict sense and demonstration in the secondary sense, in the commentary on the second book of the Posterior Analytics that was transmitted under the name of Philoponus and which is very Philoponean in spirit (we labeled its author Ps-Philoponus-2 to distinguish him from the unknown author of a commentary on the second book of the Prior Analytics, whom we have labeled Ps-Philoponus-1). Like Alexander, Themistius identifies both the syllogism of the that from a convertible effect (type 1b) and that from a non-convertible effect (type 2a) with the sign-syllogism, both implicitly, by means of the examples, and explicitly; he distinguishes proper demonstration (in which the effect is inferred from the cause) from demonstration in a secondary sense, which is ­instantiated by sign-syllogisms. Moreover, at various junctures of his paraphrase Themistius also invokes the crucial distinction between the logical and ontological sense of “being the cause of the conclusion” that we find in Alexander. Alexander (at least for what we know of his commentary on the Posterior Analtyics) has no special typology of secondary demonstrations; he only considers the case of converting cause and effect (the paradigmatic syllogism of the that of APo A 13, of type 1b, which has a corresponding syllogism of the why). Themistius, by contrast, so interprets the first part of APo A 13 as to separate the non-­extensional distinction between that- and why-demonstrations when the inference is “not from immediates” (section (i) of APo A 13, which Themistius connects to the second-figure argument in section (v)) from the extensional typology of that-demonstrations when the inference is “from immediates” (sections (ii) and (iii) of APo A 13, which Themistius connects to section (iv)). The latter, extensional component of his analysis yields a tripartite extensional typology: converting cause and effect (that-syllogism of type 1b); non-converting cause and effect (where the cause is more extended than the effect: that-syllogism of type 2a); converting effects of the same cause. This last case is peculiarly Themistean; with the exception of Avicenna and Averroes, no other commentator of the Posterior Analytics seems to have taken this case (which was not contemplated by Aristotle) into account. While the first two (that-syllogisms of types 1b and 2a) are explicitly associated with sign-inferences, the third is

134

chapter 2

not, at least not explicitly; from either effect another co-extensive effect can be proved, but the proof is not a semiotic one. Like Alexander and Themistius, Philoponus identifies the that-syllogism of type 1b with the sign-syllogism, both implicitly and explicitly; he distinguishes proper demonstration from demonstration in a secondary sense, which latter is instantiated by that-syllogisms and thus also by sign-syllogisms. He seems to have made no special use of the distinction between the logical and the ontological sense of “being the cause of the conclusion” that we find in Alexander and Themistius. Unlike Themistius, he gives no semiotic characterization of the that-syllogism of type 2a. Unlike his predecessors, Philoponus gives to the tripartite conceptual identification of syllogism of the that, sign-syllogism, and secondary demonstration a precise terminological determination: a syllogism of the that, though not causal, is a deductively valid syllogism; if then it is identified with the sign-syllogism, it has to be identified with the deductively valid kind of sign-syllogism, i.e., with what Aristotle in APr B 27 calls a τεκμήριον. A secondary demonstration is therefore more adequately called a τεκμηριώδης ἀπόδειξις, a “tekmeriodic” demonstration. By so doing Philoponus gives to Aristotle’s remarks on the relationship between sign and demonstration a precise terminological systematization and coherence, one which, however, will be almost completely ignored by later commentators of the Posterior Analytics. Philoponus’ interpretation of APo A 13 is very much the same as Themistius’. Like Themistius, he interprets section (i) of APo A 13 non-extensionally, and like Themistius he connects section (i) to section (v). He also has an extensional typology of demonstrations, but one that does not coincide with Aristotle’s and Themistius’ (the “Aristotelian” typology). While Aristotle and Themistius consider two cases (converting cause and effect, and a cause more extended than the effect), Philoponus considers converting cause and effect (which give rise to both why-demonstrations of type 1a and to that-demonstrations of type 1b) and two varieties of non-converting cause and effect, i.e., both a cause more extended than the effect (where only a that-demonstration of type 2a is possible) and an effect more extended than the cause (where only a why-demonstration is possible). This is what we have called the “Philoponean” typology. Both the Aristotelian and the Philoponean typologies are fourfold; but while the Aristotelian typology has two arguments for a cause more extended than the effect and none for the effect more extended than the cause, the Philoponean has one for each. In Philoponus’ commentary on APo A 13, neither a cause inferred from a less extended effect nor an effect inferred from a less extended cause is regarded as a case of sign-inference. The typologies of demonstration in Aristotle and in the three main Greek commentaries on the Posterior Analytics are illustrated in Fig. 3.

The Greek Commentators

135

Figure 3 Typologies of demonstration in APo and APo Greek commentaries

In the ouverture of the Physics Aristotle had said that the method of investigation goes from what is better known to us to what is better known by nature. This is of course in tension with APo A 2, where it is one of the requirements of scientific demonstration that it goes from what is better known by nature to what is better known to us. In the attempt to resolve this tension, the ancient commentators interpreted Phys A 1 with the aid of the notion of demonstration “in a secondary sense” which we find in the tradition of the commentaries on the Posterior Analytics. In commenting on Phys A 1 Themistius speaks of a demonstration which, though not “proper,” is “sufficient to us.” Philoponus and Simplicius are explicit in identifying the secondary demonstration of which Aristotle is allegedly speaking in Phys A 1 to syllogisms from effect to cause or sign-syllogisms, which both commentators call “tekmeriodic demonstrations,” a clear echo of Philoponus’ commentary on the Posterior Analytics. The three consequences of Alexander’s seminal identification of the syllogism of the that of APo A 13 with the sign-syllogism of APr B 27—(i) projection of the epistemic dimension of the that/why distinction onto the doctrine of sign-inferences; (ii) distinction of proper demonstration from secondary demonstration; (iii) distinction of two senses in which the premises of a syllogism may be the cause of the conclusion—form the bulk of the Greek interpretation of the opposition between sign and demonstration that surfaces in various Aristotelian places and which Aristotle never explicitly tackles. It will also constitute a solid piece of doctrine and a point of departure for medieval Aristotelians, both within and outside the tradition of the Posterior Analytics.

CHAPTER 3

Demonstratio in the First Half of the Twelfth Century Before the Introduction of the logica nova

The rediscovery of the Posterior Analytics places the notion of demonstration at the very heart of the theory of scientific knowledge. Before that rediscovery, the Latin term demonstratio was already in use in various areas of philosophy, including rhetoric, grammar, logic, and theology. In the present Chapter we provide an outline of these uses, we review the sources other than Aristotle from which the different meanings of demonstratio derive, and we examine texts and authors that have used this term in its various meanings. On the basis of this recognition, in the next Chapters we shall consider the introduction of the so-called logica nova in the philosophical, theological, and semiotic panorama from the second half of the twelfth century. 1

Demonstratio as a Rhetorical Genre

The earliest occurrence of a technical use of the term demonstratio is in rhetoric. As Aristotle’s Rhetoric was translated into Latin only at the end of the 1260s, twelfth-century rhetoric was substantially based on Cicero’s De inventione and the anonymous Rhetorica ad Herennium. In these works the term is found with at least two rather distinct meanings.1 For Cicero, demonstratio is in the first place one of the three genres of oratory, besides deliberatio and iudicium:2 the term here translates into Latin the Greek ἐπίδειξις which in Aristotle’s Rhetoric indicates precisely the epideictic (or occasional) genre, in contrast to the deliberative (or political) and the legal (or forensic) genres. In the second place, Cicero uses the term demonstratio in the sense of “argumentation”;3 this is the 1 The author of the Rhetorica ad Herennium uses demonstratio also in a third sense: as a type of discourse (or conversational tone: sermo), the Explicative, alongside with dignitas (the Dignified), narratio (the Narrative), and iocatio (the Facetious): demonstratio, in this sense, is a discourse or conversational tone that “in a calm voice explains how something could or could not have been brought to pass” [ quae docet quomodo quid fieri potuerit aut non potuerit.] Ad Her. III.14.23, ed. Calboli, 261; transl. Caplan. 2 Cicero, De inv. I.9.12–10.13. 3 Cicero, De inv. I.29.44. © koninklijke brill nv, leiden, 2023 | doi:10.1163/9789004546974_005

138

chapter 3

sense that we examine later in the present Chapter.4 Let us first see how the commentaries on the two rhetorics (both were attributed to Cicero during the Middle Ages) have dealt with the first sense of the term. In De inventione I.8 Cicero treats of the types of constitutio. A constitutio (or status) is the determination of a legal cause or issue, and can be fourfold:5 (i) coniecturalis, when the dispute is about a fact and the plea is supported by conjectures or inferences (an sit? “Has a certain act taken place?”); (ii) diffinitiva, when the dispute is about a definition or classification of the fact (quid sit? “Is the act a murder?”); (iii) generalis or qualitatis, when the nature of the act is examined and the controversy concerns the value of the act and its qualification (qualis sit? “Was the murder justified?”); (iv) translativa, when the problem concerns the competence of the court or the correct attribution to the office, and so on. The commentaries on the De inventione and the Rhetorica ad Herennium composed between the end of the eleventh and the end of the twelfth centuries6 came progressively to a theory of the relationship between the genres of rhetorical discourse (deliberative, legal and epideictic) and the types of constitutio, giving birth to what has been called a “platonizing rhetoric.”7 The problem is first raised in the commentary of magister Menegaldus8 at the end of the eleventh century: According to master Menegaldus [...] [the rhetorical cases] differ by genus, implying that one case is treated as a lawsuit, another as political speech, and they differ by form, that is according to the status or issues (constitutiones). For these three genera that by themselves are almost formless (quasi informia) receive their respective forms in the different status or issues, and accordingly they intend to reach different ends, and they differ formally. For the lawsuit is shaped formally when it according

4 See infra, §3.3. If not otherwise indicated, translations from Latin are ours. 5 See Murphy (1974), 11. 6 For an overview of the medieval fortune of and the commentaries on Ciceronian rhetoric, see Ward (1995); for an overview of the reception of classical rhetoric in early Middle Ages, see De Filippis (2022). 7 Cf. Caiazzo (2011), 339; Fredborg (2015), 58. 8 Specialists have debated whether this magister Menegaldus might be Manegoldus of Lautenbach, author of some anti-imperial pamphlets during the investiture controversy. The question has not been settled; for further information see Caiazzo (2011); Fredborg (2015), 47 n. 6; Bognini (2015). We return to this issue below to show that some of the arguments in favour of the identification are not very solid (see infra, §3.4).

Demonstratio in the First Half of the 12th Century

139

to a specific status intends to reach the end of justice (or injustice), which is not the case in the other genres [viz. political or epideictic speeches].9 In order to clarify the meaning of the words attributed to master Menegaldus one has to observe that the determination of the kind of speech takes place through the application of oratory techniques to particular cases, in which the speaker tries to determine whether a certain act, fact, or decision is just or unjust (legal), whether it is useful or harmful (political), or whether it is honourable or not (epideictic). A discourse can be classified in one genre or in another according to its end (iustitia, utilitas and honestas), which according to Menegaldus plays a role similar to that of a natural form. While Menegaldus holds that the three genres are to be considered “almost formless” (quasi informia), thereby preventing an excessively realistic interpretation of the terms “form” and “genus” as applied to rhetorical discourses, his student William (probably) of Champeaux, by relying on a decidedly realist interpretation of Porphyry’s universals, takes the three genres of discourse as authentic res universales and makes constitutiones (or status) the species of these genres: The different rhetorical issues or status (constitutiones) cannot be merged into one, but a political case, which is a universal thing, may be subsumed by and specified as a conjectural handling of the case to make such a case, and, again, the same universal thing, that is a political case, may be subsumed and specified into a matter of definition of the case in order to make a different speech [...]. Accordingly, the same universal thing may be diversified because of the different status (constitutiones), but one status does not become specified into another status to make a speech, nor

9 William of Champeaux(?), In De inventione II.37.110, ms. York, Minster Library, XVI.M.7, 41bisvb: “Secundum magistrum Menegaldum, sic differunt GENERE quia aliud genus est iudiciale, aliud deliberativum, et FORMA i.e., constitutionibus. Illa enim tria quasi informia formantur in constitutionibus et ita ad suos fines tendunt et sic differunt forma. Iudicialis enim forma est cum in aliqua constitutione tendit ad iustum vel iniustum quod numquam alia faciunt.” Transl. in Fredborg (2015), 61. Cf. also Fredborg (1976), 31. Cf. Menegaldus, In Ciceronis Rhetorica glose, ed. Bognini, 228.12: “intelleget eas causas dissidere a se tum ‘genere,’ id est generali proprietate (quia iudicialis causa numquam erit deliberativa in hoc, quod est iudicialis, neque deliberativa erit iudicialis, neque demonstrativa), tum ‘forma,’ id est specificatione, ut ita dicam: aliter enim coniecturalis specificat deliberativam, aliter demonstrativam, aliter iudicialem, quia secundum diversos fines alio modo in omnibus tribus accipitur et in ceteris similiter.” See also In Cic. Rhet. I.7.9, and I.9.12, ed. Bognini, 37.13 and 41.2, also quoted in Fredborg (2015), 58–59 nn. 33, 35.

140

chapter 3

will one status accept several status and go together to make a collection of different individual speeches.10 What is crucial for William is the orator’s intention to “form” a certain object (fact or person): if the speaker intends to talk about it with praise or reproach, or intends to discuss its usefulness or righteousness, then his speech is “informed” and qualified as epideictic, political, or legal.11 A classic example is the following: “It is necessary to specify that either Verres in person, according to whether one speaks in his praise or reproach, or his action—that is the theft—, according to what is shown as laudable or vituperable, or even the proposition ‘Verres has made a theft,’ according to whether one speaks in praise or reproach of what is signified by these words, may be called ‘epideictic’ (demonstrativum).”12 The same can be said of the legal and the political genres: the person, the fact or their description do not fall by themselves into any of the three status or issues; it is the intention of the speaker which gives them a rhetorical “form.” “But how can an intention or thought give shape to real things?” asks William. The answer makes appeal to a simile: just as when one looks at a wall the latter receives a form from being seen, so when one thinks of something, this something—no matter how far it is—is “informed” by the thought. In a similar way, we can say that we give shape to a thing through the

10

11

12

William of Champeaux(?), In De inv. I.10.13, ms. York, Minster Library, XVI.M.7, 9vb: “Itaque diverse constitutiones non possunt se pati in eodem inferiori, sed deliberatio res universalis bene suscipit coniecturalem constitutionem ad eandem causam faciendam, et item eadem res universalis, scilicet deliberatio, suscipit definitivam ad aliam causam faciendam, […]. Itaque eadem res suscipit omnes constitutiones, sed una constitutio non suscipit aliam constitutionem ad unam causam faciendam nec una plures ad plures causas individuales faciendas.” Transl. in Fredborg (2015), 62. Cf. Fredborg (2009), 146–147 n. 31. Cf. Fredborg (1976), 33.27–34.4: “Sciendum itaque quod hoc ponit demonstrativum quod agendum est de illo negotio ad laudem alicuius vel vituperationem. Verbi gratia: furtum Verris, postquam inde aliquis intendit agere secundum Boethium eius est materia secundum vero Tullium non donec intendat aliquis inde agere /69ra/ et loqui ad laudem alicuius vel vituperationem quod ponit demonstrativum, sive ut ostendat utile vel inutile, honestum vel inhonestum quod ponit deliberativum, iustum vel iniustum quod significat iudiciale.” (ms. York, Minster Lib., XVI.M.7, 68vb-69ra). Fredborg (1976), 34.11–18: “Visa autem horum nominum significatione, quid unum quodque eorum nominat inspiciamus. Et est sciendum quod Verres ipse potest vocari demonstrativum secundum quod de eo agitur ad laudem et vituperationem, vel ipsa eius actio i.e., furtum secundum quod hoc ostenditur laudabile vel vituperabile, aut etiam propositio ista ‘Verres fecit furtum’ secundum quod agit de rebus significatis a vocibus istis vel ad laudem vel vituperationem. Eisdem rebus attribuitur et nomen deliberativum et iudiciale, sive Verri sive actioni sive orationi, quae inde agit.” (ms. York, Minster Lib., XVI.M.7, 69ra).

Demonstratio in the First Half of the 12th Century

141

deliberative, epideictic, or legal genre, namely when we talk about it through the properties that are signified by these words.13 Around 1139, Thierry of Chartres, commenting on the two rhetorics attributed to Cicero, tries to reconcile their terminological and conceptual differences.14 As far as we are concerned here, his commentary takes a decisive step back from William’s realism regarding the relationship between rhetorical genres and the status or issues (constitutiones), specifying that the parallelism between their relationship and that between a genus and its species is only a metaphor, and should not be taken literally.15 He then distinguishes three types of rhetorical genres and claims that each takes the name from its own end: from the determination of what is just (iustum) derives the legal genre (rhetorica iudicialis), from the determination of what is honest (honestum) the epideictic genre (rhetorica demonstrativa), and from the determination of what is useful (utile) the deliberative genre (rhetorica deliberativa).16 In general, Thierry rarely uses the term demonstration—basically he does so only when citing from Cicero17—, not adding much to what was said by his predecessors.18

13

14 15

16 17 18

Fredborg (1976), 34.19–25: “Quod autem cogitatione aliquis informet rem extrinsecam videtur impossibile, sed non est. Sicut enim parietem eminus positum informo mea visione, quia dum video eum ago in eum videndo et ipse probatur dum videtur, sic etiam dum cogito aliquam rem et ipsa a me cogitatur et ita rem informo quae eminus posita est mea cogitatione. Similiter itaque neminem laedat si informamus rem aliquam demonstratione et deliberatione et iudiciali, i.e., proprietatibus quae per haec vocabula significantur. Similiter itaque neminem laedat si informamus rem aliquam demonstratione et deliberatione et iudiciali, i.e., proprietatibus quae per haec vocabula significantur.” (ms. York, Minster Lib., XVI.M.7, 69ra). See Fredborg (1988). Thierry of Chartres, Commentarius super libros De inventione, ed. Fredborg, 54.9–20: “Species autem artis rhetoricae sunt genera causarum. Genera vero causarum sunt qualitates causarum generales secundum ipsarum fines. Nam fines causarum sunt, ut superius dictum est, aut iustum aut honestum aut utile. Inde igitur omnes causae qualitatem hanc recipiunt, quod aut iudiciales aut demonstrativae aut deliberativae dicuntur. Generales vero ideo dicuntur huiusmodi qualitates causarum, quoniam unuquodque istorum generum omnes constitutiones continet. Bene autem dicuntur genera causarum quoniam ex qualitatibus praedictorum finium omnes causae gignuntur. Species vero artis rhetoricae dicuntur genera causarum non quod rhetorica de ipsis praedicetur, sed hac similitudine quod omnes partes rhetoricae in singulis causarum generibus exercentur, sicut genus totum singulis speciebus inest.” Ibid. Cf. e.g., Thierry of Chartres, Commentarius super libros De inventione, ed. Fredborg, 86.43, 50. The commentary on the De inventione by his young disciple, Peter Helias (ante 1139), does not seem to add much in this respect; cf. Fredborg (1974), 36; Fredborg (2009).

142 2

chapter 3

Demonstratio as Deixis

Demonstratio is the term which, following his Greek model,19 Priscian (sixth century) uses to indicate a typical feature of (personal) pronouns, namely their ability to refer to the person speaking or mentioned in a speech (i.e., δεῖξις). According to Priscian’s definition, the pronoun is that part of speech which is used instead of the proper name of a thing or person, and which takes the character of that thing or person.20 The difference between first- and second-person pronouns on the one hand, and the third-person pronoun on the other—explains Priscian with an explicit mention of Apollonius—is that first- and second-person pronouns always refer to a definite person in praesentia, while “it is not without reason that Apollonius speaks of an indefinite (or uncertain) person as referred to by those of third person,”21 since these always require the addition of a name in order to render their reference definite. The (definite or indefinite) reference that is common to all personal pronouns is called demonstratio. Third-person pronouns add to demonstratio a further property: that of relatio or anaphora, namely the reference to something that has been previously introduced in a speech or discourse. (This also explains why third-person pronouns leave the (grammatical) gender and number undetermined.22) The difference between demonstratio and relatio is framed in terms of first and secondary knowledge: The difference between deixis (demonstratio) and anaphora (relatio) is that the former shows a first knowledge [of the person] in response to a question, such as “who did it?” [and one answers] “I [did]”; the latter instead introduces a secondary knowledge: “he” [i.e.] “[the one] of whom I have already spoken.”23 19

Apollonius Dyscolus, Περὶ συντάξεως (De la construction), II.6, ed. Lallot, I, 148. See also Merlin Defanti (2020), part II. 20 Priscian, Institutionum grammaticarum libri XII.1, ed. Hertz, I, 577.2–3: “Pronomen est pars orationis, quae pro nomine proprio uniuscuiusque accipitur personasque finitas recipit.” 21 Priscian, Inst. gram. XII.3, ed. Hertz, I, 577.22–578.1: “unde non irrationabiliter tertias ­personas infinitas Apollonius dicit.” See also Merlin Defanti (2020), 142–143, about ­Apollonius. 22 Priscian, Inst. gram. XII.3, ed. Hertz, I, 578; cf. also XVII.14, ed. Hertz, II, 117.1–2. See also Merlin Defanti (2020), 146–147, about Apollonius. 23 Priscian, Inst. gram. XII.5, ed. Hertz, I, 579.15–17: “Interest autem inter demonstrationem et relationem hoc, quod demonstratio interrogationi reddita primam cognitionem ­ostendit—“quis fecit?” “ego”—, relatio vero secundam cognitionem significat: “is,” “de quo iam dixi.”

Demonstratio in the First Half of the 12th Century

143

Since the ninth century, the text of Priscian begins to be commented on in the schools instead of or alongside the Ars maior by Aelius Donatus,24 but it is only between the end of the eleventh and the beginning of the twelfth centuries that we have the first continuous and complete commentaries: the so-called Glosulae and the Notae Dunelmenses. Both works have often been associated with the name of William of Champeaux and the School of Laon. A recent study,25 introducing the edition of the Notae Dunelmenses, attributes the layers II and IV of this work to William. And it is in Notae Dunelmenses II26 that William of Champeaux takes up Priscian’s idea that first- and second-person pronouns have a certain and definite meaning through reference (per demonstrationem), while third-person pronouns, having an indefinite and uncertain meaning, specify it either through deixis (per demonstrationem) or through anaphora (per relationem). Unlike what happens with the pronouns, third-person verbs (which like third-person pronouns have an indefinite meaning) have no way of specifying or correcting that meaning through deixis or anaphora.27 In Notae Dunelmenses IV William explains in what sense third-person pronouns, unlike first- and second-person pronouns, have an indefinite reference. It could be objected that there are innumerable individuals who can be referred to by “I” and “you”: in fact, any human individual can be indicated by first- and second-person pronouns; therefore first- and second-person pronouns can, just like third-person pronouns, have an indefinite reference. As William explains, someone replies to this objection that while this is true from one point of view, from another point of view (alio respectu) first-­person pronouns have a well-defined reference when, for example, a first-person pronoun refers to the person presently speaking of him/herself in a deictic way (demonstrative). Mutatis mutandis, this also applies to second-person pronouns. According to others (with whom William also agrees), the demonstratio, however realized at the linguistic level, is always associated with a deictic gesture, either by pointing a finger towards an object or by nodding: There are in fact those who intend that the deixis (demonstratio), as a property of pronouns, cannot occur in any other way than this: that 24 25 26 27

See the commentary and glosses by Sedulius Scotus (In Donati artem maiorem; In Priscianum; In Eutychem, ed. Lofstedt) and John Scotus (Eriugena) in Luhtala (2000). Grondeux and Rosier-Catach (2018). William of Champeaux, Notae Dunelmenses II ad V.48, ed. Grondeux and Rosier-Catach, 173.5–6. William of Champeaux, Notae Dunelmenses II, ed. Grondeux and Rosier-Catach, 127. 328–330; cfr. ad VIII.100, 448.6, ed. Grondeux and Rosier-Catach, 176.1628–1632.

144

chapter 3

when a pronoun is uttered, we must use a finger or an equivalent nod as a pointer. This implies therefore that the deixis should not be considered as a mere property of the phonic expression of the pronoun, but rather as a property that is founded precisely on the one who performs it (in ipso demonstrante), in such a way that the pronoun should never be uttered without a deictic gesture.28 Deixis, from this point of view, is not only a property of pronouns but also an act of the speakers that is accomplished only in virtue of their contribution. This aspect is underlined by a subsequent glossator.29 This same author also claims that the distinction made by Priscian between pronouns which perform a deixis for the eyes (ante oculos) and those which perform it only for the intellect (ad intellectum)30 does not make much sense, because the latter is common to any word that signifies ad placitum, unlike demonstrative pronouns which—as William said—always need some accompanying gesture.31 In the early decades of the twelfth century, the teaching of grammar based on Priscian consolidates further. William of Conches devotes to it as many 28

William of Champeaux, Notae Dunelmenses IV, ad XVII.7, 111.23–24, ed. Grondeux and Rosier-Catach, 429.112–118: “Sunt enim qui uelint intelligere nihil aliud esse demonstrationem pronomini accidere nisi quod fieri debeat demonstratio uel digito uel aliquo tali nutu quando pronomen illud profertur. Demonstratio itaque illa non ideo dicitur accidere pronomini quod fundetur in uoce pronominali, immo in ipso demonstrante sed ideo quod nunquam debet sine illa demonstratione proferri.” 29 Cf. Anonymous, Notae Dunelmenses V, ad XVII.64, 146.22, ed. Grondeux and Rosier-Catach, 500.2657–2671: “Et hoc plane possumus notare aliam demonstrationem quam illa quae est in uoce hoc facere. Illa enim quae est in uoce nihil aliud est quam significatio ipsius uocis demonstratiua, id est proprietas illa quae est in uoce secundum quam ita inuenta est quod ita significet substantiam quod etiam demonstret et significet circa substantiam accidentia quae uideri possunt. Sed haec uox pronominis non magis per se potest facere quam ‘Socrates’ uel aliquod aliud nomen per se. Vnde uidendum est quam demonstrationem hoc faciat. Et dicendum hoc facere demonstrationem loquentis personae uel per digitum uel per aliquem nutum demonstrantis personam quam per prolatum pronomen significare intendit. Et concedit M.G. hoc fere. Dicit uocem pronominalem demonstrationem facere non tamen prorsus per se, sed auxilio innuentis personae etc.” Cf. also Grondeux and Rosier (2018), 34 and 474–475, with reference to William’s position. 30 Priscian, Inst. gram. XVII.190, ed. Hertz, II, 202.13–14. 31 Anonymous, Notae Dunelmenses V, ad XVII.57, 142.17–18, ed. Grondeux and Rosier-Catach, 494.2441–2447: “Quomodo dicit pronomina demonstrationem facere ad intellectum, cum in hoc non differre uideantur a nominibus et quibuslibet uocibus ad placitum significantibus. Omnes enim demonstrare uidentur sua significata intellectui, praesertim cum pronomina demonstratiua in demonstratione facienda semper uideantur indigere aliquo nutu corporis, ut innuitione digiti uel aliquo tali etc.” We return below to the identification of demonstratio ad intellectum and ad placitum signification.

Demonstratio in the First Half of the 12th Century

145

as three versions of his own Glosses: one is composed quite early (probably during his teaching in Chartres in the 1120s),32 a radical revision of it at various points is made late in his life (towards 1154),33 and finally there is a third version, which differs from the preceding two.34 William of Conches permanently links the demonstratio to the presence and visibility of the referents of firstand second-person pronouns, and seems to suggest that there is an improper use of third-person pronouns (or the corresponding verbs) when they designate (or take as subjects) things that are absent or invisible in themselves.35 This double use of the pronoun can be explained by means of the distinction between demonstrativa ad oculos and ad intellectum that William presents in his commentary on book XVII of Priscian’s Institutiones (which was called De constructione): Once the treatise on relative pronouns has been completed, we return to the demonstratives to show some of their properties. says that some demonstratives are aimed at the eye and some others at the intellect. The deixis of the first type is that which always refers to present things which can be perceived with the eyes; the demonstratives

32 33

34 35

Redaction A of William’s commentary is witnessed by the ms. Firenze, Bibl. Medicea Laurenziana, S. Marco 310, 1ra–82vb; cf. Jeauneau (1960); Fredborg (1981). Redaction B is preserved in the ms. P = Paris, BNF, lat. 15130, 1ra–137va (digital copy now accessible on Gallica: https://gallica.bnf.fr/ark:/12148/btv1b90767223.r=15130?rk=42918;4); cf. Jeauneau (1960); Fredborg (1981). Reilly (1993), 29, questions a late datation of this redaction which, already in the 1140s, would have been accessible to Peter Helias. Redaction C of William’s commentary is in the ms. Oxford, Bodleian Lib., Laud. lat. 67, 15ra–19va (incomplete); cf. Jeauneau (1960); Fredborg (1981). William of Conches, Glose super Priscianum, red. B, P 78ra–b: “QUERITUR TAMEN CUR PRIMA [XII.1, 577.14]. Dixerat unum pronomen tantum esse prime persone, unum solum secunde et multa tertie persone. Facit hanc questionem non propter se, scilicet ut solvat eam. Et hec est summa solutionis, quod prima persona semper presens demonstratur et visibile; est similiter et secunda: unde ex presenti demonstratione et ita quod sunt visibiles unum solum pronomen sufficit in prima persona et unum solum in secunda. Nam quia per illa semper demonstrantur res presentes et visibiles, et ex presenti demonstratione hoc pronomen ‘ego’ diffinite potest significare omnes loquentes de se, ‘tu’ omnes illos ad quos sermo dirigitur, quod non fieret si prima et secunda persona essent absentes et invisibiles, ut animus, pietas invisibilia sunt etc. que pronomina tertie persone demonstrantur. Et hec est causa quare singula pronomina sufficiant in prima et secunda persona; sed quia in tertia persona iste VI principales diversitates quidem(?) demonstrantur, quidem relatiue significatur, quidem modo est presens, modo absens, et presens quidem modo est prope positum (-to/a P), modo longe positum (-to/a P) // et preter hec modo visibile, modo invisibile est, tot diversitates sint et tertia non possent una et eadem voce omnes certificari.”

146

chapter 3

of the second type are (those) through which we refer to things that cannot be seen or, visible, are absent.36 It should be possible to refer to objects that are not visible in themselves (as is the case in Priscian, when one says “hec pietas” or “hic animus”), but an observation added to the text just quoted shows that the connection between demonstratio and present perceivable objects is stronger and probably more appropriate: And notice that some are demonstrative only for the eyes, but there are no that are demonstrative only for the intellect: none is such that through it one does not sometimes refer to things present and perceptible with the eyes.37 Peter Helias, author of a Summa super Priscianum (probably composed in the 1140s) that will have an enormous influence on the following developments of grammatical thought, is in his turn deeply indebted to previous commentators.38 As for the pronoun, he follows both the Glosule and William of Conches, addressing the question of why first- and second-person pronouns have only one instance (considering only their nominative cases), while third-­person pronouns have different instances. The solution that he suggests ­follows the path of his predecessors, with a small difference: Peter specifies that the ­presence of the referents is not necessarily real, but can also be—so to speak— “­intentional” (or intended). It is necessary to know that in first- and second-person pronouns the same deixis is performed as it would be performed by a multiplicity of phonic expressions. Since first- and second-person pronouns always signify a present thing or they designate it as if it were present, and their reference 36

37

38

William of Conches, Glose super Priscianum, red. B, ms. P 104vb: “Finito tractatu de relativis pronominibus, revertitur ad demonstrativa ut quasdam eorum proprietates ostendat. Dicit ergo quod quedam sunt demonstrativa ad oculum, quedam ad intellectum. Demonstrativum est ad oculum illud quod semper demonstrat res presentes que possunt oculis percipi; demonstrativum est ad intellectum quo demonstratur res que non potest videri vel (et, cod.) visibilis et absens.” William of Conches, Glose super Priscianum, red. B, ms. P 104vb–105ra: “Et attende quod // quedam sunt demonstrativa tantum oculorum, non tamen aliqua sunt tantum demonstrativa intellectus: nullum enim est quo non demonstretur aliquando res presens oculis subiecta.” See Fredborg (1973); Reilly (1993), 21–30.

Demonstratio in the First Half of the 12th Century

147

is certain and definite so that they do not need a variety of phonic expressions .39 As William of Conches had already argued, the variety of third-person ­pronouns allows the signification of objects that can be present or absent, ­visible or invisible, placed near or far (with respect to the speaker). Peter Helias echoes the same idea in commenting on the books on syntax: since the pronoun “you,” in the case of figurative uses, such as apostrophe, can also indicate absent people, therefore, what we have said above is false, that “I” and “you” are always demonstrative for the eyes. So, should be understood in this way: “you” is demonstrative for the eyes or as if it were (quasi) for the eyes. It always designates something as if it were present (quasi presentem).40 Peter Helias repeats that demonstratio is typical of first- and second-person pronouns, but not always of third-person pronouns (which often have only relatio or both relatio and demonstratio): this is why demonstratio and relatio are not mentioned by Priscian among the accidental properties (accidentia) of the pronoun.41 While discussing the syntax of the pronoun in his commentary on book XVII of Priscian’s Institutiones, he defines the demonstratio pronominalis in opposition to the nominal one: “The deixis by the pronouns is a certain reference to the thing for the eyes or the intellect.”42 That of names, on the other hand, is uncertain, such as that of talis or tantum (which, being adjectives, are types of names): demonstratio of first- and second-person pronouns is only for the eyes; that of hic (third-person pronoun) is both for the eyes and the intellect (oculorum et intellectuum): 39

40

41 42

Peter Helias, Summa super Priscianum, ed. Reilly, II, 629.78–83: “sciendum est quod in prima et secunda pronominum persona idem operatur demonstratio quod vocum operaretur multitudo. Quoniam ergo pronomina prime et secunde persone demonstrative semper significant et rem presentem vel ut presentem semper designant, adeo certa et diffinita est eorum demonstratio ut diversitate vocum non egeant.” Peter Helias, Summa super Priscianum, ed. Reilly, II, 959.29–32: “Falsum est ergo quod superius diximus ‘ego’ et ‘tu’ semper esse demonstrativa oculorum. Ideo sic intelligatur. ‘Tu’ semper est demonstrativum oculorum vel quasi oculorum. Semper enim rem quasi presentem designat.” Peter Helias, Summa super Priscianum, ed. Reilly, II, 627, 954. Peter Helias, Summa super Priscianum, ed. Reilly, II, 955.28–29: “Pronominalis demonstratio est vel oculis vel intellectu rei proposite certa demonstratio.”

148

chapter 3

When a deixis is aimed at the intellect either it is performed because of the incorporeal nature of the thing, as in “this honor of piety,” “this soul,” or because of the absence of the thing, as when I say of someone absent “that made me this,” and in this case we are dealing with a deixis for the intellect.43 Finally, Peter Helias underlines the difference between the person of the pronoun and that of the verb. The latter, unlike the former, is confused and does not signify the person through demonstratio or relatio: the verb scribit for example does not concern Servius more than Virgil or anyone else; for this reason, the third-person singular pronoun has six forms (voces), or “six different properties, so that there is no confusion.”44 3

Demonstratio as Signification and Argumentation

As we saw in the previous section, the anonymous Notae Dunelmenses V called into question the distinction proposed by Priscian between a demonstratio ad oculos (actually, ante oculos45) and a demonstratio ad intellectum with an argument that brought the latter back to the normal signification of the words, established by the original impositor nominum: In what sense does Priscian say that pronouns make a deixis for the intellect, if in this respect they do not seem to differ from names and other words that signify by convention?46 The ambiguity of the verb demonstrare (and of the corresponding noun demonstratio) emerges with even greater clarity in Abelard’s logical writings, especially

43

Peter Helias, Summa super Priscianum, ed. Reilly, II, 955.32–35: “Quando autem fit demonstratio ad intellectum aut fit propter rei incorporeitatem, ut ‘hic pietatis honos,’ ‘hic a­ nimus,’ aut fit propter rei absenciam, ut si dicam de absente aliquo, ‘Hic fecit michi hoc,’ et est ad intellectum demonstratio.” 44 Peter Helias, Summa super Priscianum, ed. Reilly, II, 957.66–67: “sex diversas eius proprietates ut nulla ibi sit confusio.” 45 Anonymous, Notae Dunelmenses V, ad XVII.57, 142.18. 46 Anonymus, Notae Dunelmenses V, ad XVII.57, 142.17–18, ed. Grondeux and Rosier-­Catach, 494.2441–2447: “Quomodo dicit pronomina demonstrationem facere ad intellectum, cum in hoc non differre uideantur a nominibus et quibuslibet uocibus ad placitum ­significantibus.”

Demonstratio in the First Half of the 12th Century

149

in his Dialectica (years 1110−1115).47 Here Abelard often uses demonstrare and significare interchangeably, maybe just for variety’s sake. For instance: What in fact Aristotle said in the chapter on substance that some human beings are more clearly signified (demonstrari) by the name “human-being” (homo) than by the name “animal,” he also taught that some human beings are meant (significari) by both .48 It is interesting, however, that the meaning of demonstratio as argumentatio, probably derived from Cicero,49 emerges in the Dialectica in the very same context in which, after discussing the Aristotelian categories and the nature of the things they signify, Abelard examines the different modes of signification (modi significandi)50 and builds what can be considered a general semiotics in nuce. The premise—which as we will see in Chapter 4 will also be assumed by Simon of Tournai in the second half of the twelfth century—is that meaning is a character of both words and things:51

47 48

On Abelard’s life and works, see Marenbon (1997), 7–35. Peter Abelard, Dialectica, ed. de Rijk, 113.31–32: “Quod enim in Substantia Aristoteles dixit [Cat. 2b8–10] aliquem hominem manifestius demonstrari per nomen ‘hominis’ quam per nomen ‘animalis,’ aliquem etiam hominem ab utroque significari docuit.” The passages in which the verb demonstrare (or the noun demonstratio) is used synonymically with significare/designare/repraesentare (or significatio) are countless; see for instance: Dial. 80.15–16 (demonstrare / designare); 92.4 (“vocabulum… rei essentiae demonstratio ”); 99.35–36 (“demonstrationem vel repraesentationem”); 112 (modi significandi: see below); 113.31–32 (demonstrari / significari); 119.12 and 14 (demonstratio rerum); 120.10 and 13 (demonstratio / significatio, 14 and 18); 126.11 and 25 (demonstrare / significare); 128.13–14 (demonstrare / designare); 147.35–36 (demonstratio / significatio); 334.28 and 32 (= significare); 335.12 (= significare); 590.9 and 597.31 (“maior est definitionis demonstratio quam nominis”). 49 Cicero, De inv. I.29.44: “Omnis autem argumentatio, quae ex iis locis, quos commemoravimus, sumetur, aut probabilis aut necessaria debebit esse. Etenim, ut breviter describamus, argumentatio videtur esse inventum aliquo ex genere rem aliquam aut probabiliter ostendens aut necessarie demonstrans. Necessarie demonstrantur ea, quae aliter ac dicuntur nec fieri nec probari possunt, hoc modo: ‘si peperit, cum viro concubuit.’ Hoc genus ­argumentandi, quod in necessaria demonstratione versatur, maxime tractatur in dicendo aut per complexionem aut per enumerationem aut per simplicem ­conclusionem.” (emphasis ours). 50 The expression modi significandi, in this context, has no technical meaning, as it will acquire in both twelfth- and thirteenth-century grammar; cf. Marmo (2010), ch. 5. 51 Cf. also Peter Abelard, Glossae super Perì Hermeneias II.10, eds. Jakobi and Strub, 71. Cf. also LM II.1, 190; Marenbon (1997), 182.

150

chapter 3

Signifying is not just proper to phonic expressions (vocum), but also to things (rerum). The written letters themselves, once they are seen, represent phonic elements. This is why in De interpretatione [16a4] says: “Even what is written of what is in the phonic expression” is a sign (nota), i.e., is significant. Often some things are also signified by other things because of their similarity, as in the case of the statue of Achilles representing Achilles himself. Now, we mean something through signs (per signa), and consequently these things are properly said to signify because, similarly to the phonic expressions, they have been established for this purpose, i.e., to fulfil the task of meaning (officium significandi), as in the cases just seen. However, we often go from one thing to another, not following any act of institution that makes something meaningful, but rather following a custom (consuetudo) or some relationship (habitudo) that links two things.52 The last type of signification occurs, for instance, when we are used to seeing two objects or events that are regularly associated: if one of them is present or occurs, we immediately recall the other to the mind. Let us assume that we are used to always seeing a man and his son together: if the father is seen alone, the idea of his son, even if he is not currently visible, is immediately recalled to the mind.53 The signification of things therefore takes place according to at least three models: i) signification by convention or institution (the written letters are signs ad placitum of the phonic elements); ii) representation by resemblance (the statue of Achilles signifies Achilles himself); iii) inference based on custom or on some real, objective, and mind-independent relationship, existing between the sign and the thing signified. Beside the signification of things, Abelard specifies that phonic expressions (voces) can signify in multiple ways: a) by imposition: as for the word “human-being” (homo) which signifies the rational mortal animal, to which 52

53

Peter Abelard, Dial. ed. de Rijk, 111.13–23: “Est autem significare non solum uocum, sed etiam rerum. Litterae enim ipsae quae scribuntur, oculis subiectae uocalia nobis elementa repraesentant. Unde et in Periermenias dicitur: ‘et ea quae scribuntur eorum quae sunt in uoce,’ sunt scilicet notae, id est significatiua. Saepe etiam ex similitudine res quaedam ex aliis significantur, ut achillea statua ipsum Achillem repraesenta[n]t. Nunc etiam per signa aliquid innuimus et hae quidem rerum proprie significare dicuntur quae ad hoc institutae sunt, sicut et uoces, ut significandi officium teneant, quemadmodum suprapositae. Saepe tamen ex aliis rebus in alias incidamus, non secundum institutionem aliquam significandi, sed magis secundum consuetudinem uel aliquam earum ad se ­habitudinem.” Peter Abelard, Dial. ed. de Rijk, 111.23–26.

Demonstratio in the First Half of the 12th Century

151

that name was imposed; b) through determination (per determinationem), whereby “rational” or “human-being,” although they name some substances, also determine their quality (rationality); in the same way, adjectives, like “white,” name a substance (the substratum) and represent the quality inhering in the substance (ut quale); c) through generation (per generationem), as when a concept is generated in the soul of the listener through a sound emitted by a speaker; d) through exclusion (per remotionem), as in the case of a negated name (nomen infinitum) that somehow signifies the thing signified by the unnegated name (nomen finitum): “non-human-being” (non-homo) names a thing that is not a human being, but also somehow recalls a human being.54 Finally, there are two other types of signification of phonic expressions which Abelard calls demonstrationes, probably in the sense of Cicero’s De inventione, i.e., in the sense of the inferential relation between a sign and what it signifies. e) The first of them is based on a relation of either inherence or concomitance (secundum adhaerentiam uel comitationem) involving an accidental property and its own substrate, as when we say that the name “Socrates” also means the accidental properties of the individual so named, or when we say that the barking of a dog indicates its wrath, as the two always go together.55 In neither case the inferential relationship is made explicit by Abelard. Yet it is a plausible interpretation: if I hear the name “Socrates” and recall the man’s qualities, I can infer that he is bald, has a belly, is married to Xanthippe, and so on; if I hear the barking of a dog, I can infer that there is an angry dog; in 54

55

Peter Abelard, Dial. ed. de Rijk, 111.27–112.12: “Vocum quoque significatio, de qua intendimus, pluribus modis accipitur. Alia namque fit per impositionem, ut ‘hominis’ uocabulum animal rationale mortale, cui nomen datum est per impositionem, significat, alia uero per determinationem, ut ‘rationale’ uel ‘homo,’ cum subiectas nominant substantias, circa ipsas quoque rationalitatem determinant; unde in Praedicamentis Aristoteles: ‘genus, inquit, et species qualitatem circa substantiam determinant,’ [Cat. 3b19-20] cui scilicet secundum id quod qualitate formatur, sunt imposita atque eam ut qualem demonstrant; alia autem per generationem, ueluti cum intellectus per uocem prolatam uel animo audientis constituitur ac per ipsam in mente ipsius generatur; unde et in Periermenias dicitur: ‘constituit enim qui dicit, intellectum’; alia quoque per remotionem, ut res quoque finiti nominis ab infinito uocabulo quodammodo significari dicitur; unde etiam idem in Eodem dixisse creditur: ‘unum enim significat infinitum quodammodo,’ id est rem sui finiti perimendo. Quod enim uocabulum in eo rem subiectam nominat, quod homo non est, quamdam de homine ipso notationem facit, ut non-homo.” The two cases seem to be very different, because “Socrates” signifies by convention, while the barking of the dog signifies by nature. However, in the first case what is signified is not what the name has been imposed to (i.e., a man named Socrates), but rather what (necessarily though variably) accompanies it (i.e., his accidental features). This might imply that for Abelard this type of signification is an example of natural signification, just as connotation is for Roger Bacon in the thirteenth century (see infra, §7.2).

152

chapter 3

both cases I recall previous experiences of accidental features (Y) of an object X—such as Socrates’ baldness or a dog’s anger—and can build a conditional of the type: “if X, then Y.” f) The second (and last) type is based on a temporal relationship between objects or events which can be concomitant or consequent upon one another (secundum comitationem ac quamdam consecutionem): when someone tells me that I am the father of Hector, in some way he is indicating (innuerit) that Hector is my son.56 At the end of his short overview, Abelard adds a note suggesting that his list is not exhaustive: “And perhaps other ways of signification will emerge.”57 We summarize Abelard’s division of the ways of signification in the following Table: Table 1  Abelard’s division of the ways of signification

Significatio rerum

Examples

(per impositionem) ex similitudine secundum consuetudinem uel aliquam habitudinem

letters / vocal elements statue of Achilles / Achilles father / son

Significatio vocum

Examples

per impositionem per determinationem per generationem per remotionem secundum adhaerentiam uel comitationem secundum comitationem ac quamdam consecutionem

“human being” / rational and mortal animal “rational” / rationality in human beings phonic expression / concept “non-human being” / human being “Socrates” / his accidental proprerties; barking / anger (of a dog) “Y father of X” / “X son of Y”

56

57

Peter Abelard, Dial. ed. de Rijk, 112.13–20: “Est quoque quaedam etiam secundum adhaerentiam vel comitationem demonstratio, ut Socratis nomen ipsius quoque accidentia quodammodo demonstrare dicitur, vel latratus canis ipsius iram, qui numquam nisi ab irato proferri cognoscitur. Alia vero demonstratio fit secundum comitationem ac quamdam consecutionem, ut qui me illius patrem esse dixerit, et illum quoque filium meum esse innuerit.” Peter Abelard, Dial. ed. de Rijk, 112.21: “Et alii fortasse significandi modi apparebunt.”

Demonstratio in the First Half of the 12th Century

153

Some comments regarding this classification are in order: 1. the imposition, i.e., the act of original institution of the sign, lies at the origin of the significations of both words and some of the things: in his Glossae super Perì Hermeneias58 Abelard refers to the example of the ­circulus vini, a barrel circle or a circle made out of vine branches that was used as a tavern sign; it will become a classic example in later (theological, logical, and grammatical) literature;59 2. in the same context the latratus canis is taken as a natural sign of anger, or rather a sign instituted by nature or by God, but not by human beings;60 3. between the two general types of significatio (rerum and vocum) there is some other overlapping, as for example between the last species of both (secundum consuetudinem uel aliquam habitudinem and secundum comitationem ac quamdam consecutionem): it is possible to infer from “X is the father of Y” that “Y is a son of X,” but it can also happen to simply see a man and infer on the basis of a known relationship (such as fatherhood) between him and another individual that there is someone who is his son. In both cases it is possible to express the relationship in a conditional: “If this man is a father, then he has a son”; 4. the modes of signification of phonic expressions are ordered according to their respective degree of immediacy in the sign-signified thing relationship; 5. signification through determination61 is resumed later in the Dialectica with regard to the double signification of derived terms (nomina sumpta) (i.e., the concrete terms deriving from their respective abstract terms), which principally signify a form and secondarily signify the substratum to which the form inheres: the signification of derived names (sumpta) is twofold: one is the main one which concerns the form; the other is the secondary one, which concerns the informed . Thus “white” is said to mean 58 Glossae super Perì Herm. II.10, ed. Jacobi and Strub, 71. 59 See Rosier-Catach (2019). 60 Cfr. Glossae super Perì Herm. II.11, ed. Jacobi and Strub, 72. On the latratus canis see Eco et al. (1985), and Eco et al. (1989) for a slightly shorter English version. 61 Marenbon (1997, 182 n. 19) implicitly assumes an equivalence between signification through determination (per determinationem) and signification through representation (per repraesentationem), also used in the Glosulae on Priscian between the end of eleventh and the beginning of twelfth century (cf. Grondeux and Rosier-Catach 2018, 188), according to which every name has a signification per impositionem (to the substance in Priscian’s definition of the name) and a signification per repraesentationem (to the quality in Priscian’s definition).

154

chapter 3

in the first place the whiteness that it determines about the body, and secondly its substratum which is the object of nomination.62 6.

As it emerges from these texts, Abelard uses the term demonstratio only with regard to the two modes secundum adherentiam uel comitationem and secundum comitationem ac consecutionem, and this could be interpreted as an indication that between signs and meanings in these cases there is a relation of inference.

This last point is confirmed by the occurrence of the example of father and son in the Glosse super Porphirium, where Abelard uses the verb demonstrare again.63 This also suggests that in some contexts the meaning of demonstratio in the sense of argumentation is not simply occasional,64 but is operative and functional to the construction of a complex theory of signification, within which the demonstrationes are regarded as inferences from signs assumed as premises of an argumentation. Other texts from the first half of the twelfth century also refer to this narrower meaning of demonstratio. For instance, the author of a commentary on the Aeneid (attributed to Bernardus Silvestris) illustrates the meaning of integumentum as follows: Integumentum is the kind of demonstratio that brings with it the understanding of truth under the guise of a fabulous narration, and therefore it is also called involucrum.65 62

63

64

65

Peter Abelard, Dial. ed. de Rijk, 596.5–9: “duplex enim horum nominum quae sumpta sunt, significatio dicitur, altera uero principalis, quae est de forma, altera uero secundaria, quae est de formato. Sic enim ‘album’ et albedinem, quam circa corpus subiectum determinat, primo loco significare dicitur et secundo ipsius subiectum quod nominat.” Peter Abelard, Glosse super Porphirium, ed. Geyer, 41.26–31: “Plura namque ita simul cognosci possunt, ut tamen unius notitia per alterum consistat. Ut si alicui patrem ignoranti vel filium, demonstrarem utrumque per alterum dicens patrem esse, qui refertur ad filium, filium qui ad patrem, simul utrumque per alterum certifico, dum hunc ad filium se habere et illum rursus ad istum ostendo, alioquin nulla fieret relativorum cognitio.” Peter Abelard, Glosse super Porphirium, ed. Geyer, 5.4–5: “demonstrationes, id est argumentationes”; 7.15: “omnes argumentationes, quae similiter a Porphyrio demonstrationes appellantur”; Logica Nostrorum, Glossulae super Porphyrium, ed. Geyer, 511.22–23 e 28–29: “demonstrationes, idest/scilicet argumentationes.” Cf. also Glossae sup. Porph., ed. Geyer, 176.26ss., where Abelard uses the verb demonstrare in a complex argumentation showing the similarity between the nature of the voice and the waves produced in a water basin by throwing a stone in it (“ad naturam vocis demonstrandam convenientem similitudinem inducere de lapillo proiecto in aqua”). Bernardus Silvestris(?), Super sex libros Eneidos Virgilii, ed. Jones 1977, 3: “Integumentum vero est genus demostrationis sub fabulosa narratione veritatis involvens intellectum,

Demonstratio in the First Half of the 12th Century

155

Or in the definition of symbol proposed by Hugh of Saint Victor in his commentary on the Celestial Hierarchy by the ps.-Dionysius: Symbol is the collection of visible forms as demonstratio of the invisible ones.66 The symbol in this context is opposed to anagogy, that is to the pure and open (scriptural) narrative67 or, as he says elsewhere,68 to theophany, i.e., the direct divine revelation which does not involve inferential processes passing from the visible to the invisible or from the known to the unknown.69 It is interesting to observe that in Hugh’s definition of the symbol the term collatio appears as the genus of the definitum. The term simbolum (which is a transparent loan from the Greek σύμβολον) has two possible sources: (a) the definitions of the Nicene-Constantinopolitan creed, also called “symbol”;70 (b) the definition of imago in the Rhetorica ad Herennium: “Imago est formae cum forma cum

66

67

68

69 70

unde etiam dicitur involucrum.” Quoted in Mann (2001), 314, and previously in Jeauneau (1957), 130. Hugh of St. Victor, Super Hierarchiam Dionisii, II.1, ed. Poirel, 423.278–279: “Simbolum est collatio formarum uisibilium ad inuisibilium demonstrationem.” Cf. Super Hierarchiam Dionisii, VIII.8, ed. Poirel, 616.261–264: “In eo enim quod alius angelus dixit, alius audiuit, alius doctrinam protulit, alius suscepit, simbolum factum est, hoc est demonstratio sive argumentum, quod diuina perfectio per priores et superiores ad sequentes et inferiores partecipanda procedit.” Cf. Marmo (2006); Poirel (2013), who also points to the fact that the term symbolum is sometimes explained with other terms, such as figura, simulachrum, species and so on (397–398, 402 n. 15). Hugh of St. Victor, Super Hierarchiam Dionisii, II.1, ed. Poirel, 423.279–424.290: “anagoge autem ascensio siue eleuatio mentis est ad superna contemplanda. Notat autem hic duplicem modum reuelationis diuinae quae theologorum et prophetarum mentibus infusa est, per uisiones et demonstrationes quas Greci ‘theophanias’ appellant, id est diuinas apparitiones, quoniam aliquando per signa sensibilibus similia inuisibilia demonstrata sunt, aliquando per solam anagogen, id est mentis ascensum in superna pura contemplata. Ex his uero duobus generibus uisionum, duo quoque descriptionum genera in sacro Eloquio sunt formata: unum quo formis et figuris et similitudinibus rerum occultarum ueritas adumbratur, aliud quo nude et pure sicut est absque integumento exprimitur.” Hugh of St. Victor, Super Hierarchiam Dionisii, VII.7, ed. Poirel, 581, where he repeats that in the case of theophany there are no symbols involved, not even intelligible symbols (which, from Hugh’s point of view, are simply nonsense): “Foris enim in sensibilibus, ubi materialia signa sunt, simbola sunt; intus autem in intellectualibus, ubi signa non sunt sed ueritas, simbola non sunt.” (581.399–402). Cf. Hugh of St. Victor, Super Hierarchiam Dionisii, II.1, ed. Poirel, 446.963–965: “descripsit supercaelestes intellectus, id est inuisibiles spiritus qui nobis incogniti erant, sensibilibus imaginibus, ut per nota incognita disceremus.” Cfr. Rufinus of Aquileia, Commentarius in Symbolum Apostolorum, 21, ed. Simonetti, 134: “Symbolum enim Graece et indicium dici potest et conlatio, hoc est quod plures in unum conferunt.” Cf. also Marmo (2006), 141–144, and Poirel (2013), 401, for other witnesses.

156

chapter 3

quadam similitudine conlatio”71 (at that time, as mentioned, this work was attributed to Cicero, together with his De inventione).72 A complete account of Hugh of Saint Victor’s use of the term demonstratio might fill many pages.73 Our purpose here was merely to show what the meaning of the term was on the eve of the introduction of the new Latin translations of Aristotle’s logica nova, and of his Posterior Analytics in particular. Before moving to the logicians and theologians of the second half of the century in the next Chapter, we shall have a look at the way some of the authors that we have met in this Chapter understood the distinction, within a demonstratio in the logical sense, between the necessity of inference and the necessity of the conclusion. We shall address this issue by following the story of the reception of the following example: si peperit, cum viro concubuit. 4 Necessity of the Inference, Truth of the Conditional and Necessity of the Consequent: Brief History of an Example The example of necessary argumentation found in Cicero’s De inventione is the following conditional proposition: “If she has borne a child, she has lain with a man” (si peperit, cum viro concubuit), which we have met in Themistius and Philoponus.74 In the Latin world it has an interesting story, which is the topic of the present section. In the following Chapter, then, we shall see how the Greek and Latin traditions that make use of this example would meet in the general theory of signification of Simon of Tournai. The example in question is also found in late antiquity commentaries on the De inventione, such as those of Marius Victorinus (mid-fourth century) and Grillius (maybe first half of the fifth),75 and is accompanied by glosses of the 71 72

Ad Her. IV.49.62, ed. Calboli, 370. Concerning the use of the expression argumentum necessarium in Thierry of Chartres’ commentary on the De inv., Margareta Fredborg (1971), 29, says: “That the ­terminology is rare and maybe later abandoned, might only be an indication of the rise of new ­problems with the introduction of the rest of the Organon in the middle of the Twelfth century.” In this context he never uses the term demonstratio but makes use of the verb demonstrare in order to define the argumentum necessarium… (De inv. 149.89–92). 73 Poirel (2013), 406, gives an etymological explanation of the term demonstratio which should explain the meaning of symbolum and its action of un/veiling what is hidden under sensible appearances. On this point, however, Hugh does not seem very consistent, given all the quasi-synonyms of symbolum he proposes (402 n. 15). 74 See supra, §§2.2, 2.3. 75 See Jakobi (2005), 5, who points to the fact that since late-ancient witnesses of the ­reception of this commentary are missing a more precise datation is not possible. On

Demonstratio in the First Half of the 12th Century

157

following tenor. Commenting on the example of De inv. I.29.44, Marius Victorinus explains that the Christian point of view may differ from common sense: But what is necessary is as powerful between human beings as is valid according to human opinion; on the other hand, according to the opinion of Christians this is not a necessary argumentation: “if she has borne a child, she has lain with a man,” and even this: “if he was born, then he will die.” In fact, for them it is clear that someone was born without a man, and that but is not dead. Consequently, a necessary argument is one that some people are ready to accept in virtue of their own opinion [...] And so we believe it is a necessary argument the one with which the speaker easily persuades other people.76 Victorinus probably wrote this gloss before his conversion (355 CE), since a certain distance from Christian beliefs is apparent.77 This passage, however, can be seen as an anticipation of the position that will be supported, appealing to Christian Truth and not to mere opinion, first by Peter Damian78 and then by Manegold of Lautenbach,79 to whom we return shortly. Grillius, commenting on De inv. I.9.12, explains the type of argumentation that the conditional proposition can yield: The major premise (propositio) is what you propose, such as “if she has borne a child, she has lain with a man”; “but she has borne a child”; the conclusion “therefore she has lain with a man.” Here, therefore, the major premise (propositio) and the minor premise (assumptio) are explicit. But this argument works in different

76

77 78 79

Victorinus and Grillius, see also De Filippis (2022), 151–164 and 195–204. Marius Victorinus, Explanationes in Ciceronis Rhetoricam I.29, ed. Ippolito, 137.64–138.70, 75–77: “Sed tantum inter homines potest necessarium quantum secundum opinionem humanam valet; alioqui secundum Christianorum opinionem non est necessarium ­argumentum ‘si peperit, cum viro concubuit,’ neque hoc rursus, ‘si natus est, morietur.’ Nam apud eos manifestum est sine viro natum et non mortuum. Ergo necessarium argumentum illud est quod iam opinione persuasum est. [...] Itaque necessarium argumentum teneamus illud quod facile populo persuadet orator.” Quoted in Caiazzo (2011), 342 n. 89; correction proposed by Riesenweber (2015), II, 184. Cf. Riesenweber (2015), I, 12. A humanist hand added in the margin of a ms.: Nondum eras christianus, Victorine (cf. also I, 123). Peter Damian, De divina omnipotentia 12, ed. Cantin, 444; cf. Die Briefe des Petrus Damiani, ed. Reindel, III, n. 119, 366 (PL 145, col. 611). Manegold of Lautenbach, Liber contra Wolfelmum 14, ed. Hartmann, 75–76.

158

chapter 3

ways if we want to conclude affirmatively or negatively. [...] In fact, if we want to conclude in the affirmative, then we assume as minor premise the first part of the proposition “she has borne a child,” and the second part as conclusion “she has lain with a man.” If you want to conclude negatively, the argument is reversed: the second part will be taken as minor premise, and the first as conclusion; in fact, if it is said “she has not borne a child’ and it will be added by way of conclusion “therefore she has not lain with a man,” it ends negatively but in a wrong way. A woman can indeed very well have lain with a man and not borne a child.80 Let’s try to understand what Grillius is saying here. First of all, he assumes the conditional to be the major premise (propositio) of an argument, the antecedent of the conditional to be the minor premise (assumptio), and the consequent the conclusion. Such an argument has the form of the first Stoic indemonstrable or modus ponendo ponens: If p then q; but p; therefore, q. In this case, a valid affirmative conclusion is correctly drawn.81 In order to provide an equally valid, but negative, conclusion—suggests Grillius, implicitly recalling the second Stoic indemonstrable or modus tollendo tollens—it is necessary to invert the parts of the argument, assuming as a minor premise the

80 Grillius, Commentum in Ciceronis Rhetorica I.12, ed. Jakobi, 61.125–62.129, 62.143–150: “Propositio est, quod proponis, ut puta: ‘Si peperit, cum viro concubuit’; ‘peperit autem’; conclusio: ‘Igitur cum viro concubuit.’ Hic ergo et propositio et assumptio manifesta est. Sed hic categoricus aliter in confirmatione, aliter in infirmatione. […] Si confirmare vult, primam partem propositionis dat assumptioni: ‘Peperit autem’; secundam conclusioni: ‘Cum viro igitur concubuit.’ Si quis autem hoc infirmare vult, convertit thema, secundam partem propositionis dabit assumptioni, primam conclusioni; nam si dixerit ‘non peperit’ et subiecerit ‘igitur nec cum viro concubuit,’ vitiose infirmavit. Potest enim cum viro concumbere et non parere.” Also quoted in Caiazzo (2011), 342–343 n. 90. The addition “” (or something similar) appears to be required by what follows. Boethius, De hyp. syll., II.1.1, ed. Orbetello, 254 (“omnis syllogismus ex propositionibus texitur, prima uel propositio, uel sumptum uocatur; secunda uero dicitur assumptio, his quae infertur, conclusio nuncupatur”) and Isidore of Seville, Etymologiarum libri XX, 9.2 (on syllogisms) use the same terminology. 81 Grillius calls this inference invictus syllogismus (Commentum in Ciceronis Rhetorica I.12, ed. Jakobi, 62.139)

Demonstratio in the First Half of the 12th Century

159

negation of the consequent (secundam partem propositionis dabit assumptioni) and as a conclusion the negation of the antecedent (primam conclusioni): If p then q; but not q; therefore, not p. Both the negation of antecedent and consequent and their inversion is necessary if the argument is to be deductively valid. If, by contrast, one only negates antecedent and consequent without also inverting them, the argument is invalid: If p then q; but not p; therefore, not q. The example si peperit illustrates Grillius’ point: given the conditional “If she has borne a child, she has lain with a man,” the inference of the consequent (“she has lain with a man”) from the antecedent (“she has borne a child”) is valid, as is the inference of the negation of the antecedent (“she has not borne a child”) from the negation of the consequent (“she has not lain with a man”); but the inference of the negation of the consequent (“she has not lain with a man”) from the negation of the antecedent (“she has not borne a child”) is invalid: A woman can indeed very well have lain with a man and not borne a child.82 In the fifth century, Martianus Capella mentions this example as a supplement to the text of Cicero’s Topica, in book V of his De nuptiis, as an instance of locus a consequentibus, so that “if this fact has followed (another), then that other must have come first” (ut, si hoc secutum est, illud praecesserit).83 In the sixth century, Boethius mentions it in at least three occasions. First, in his commentary on Cicero’s Topica, like Martianus; the example is, however, part of a comparison between conditional and categorical (or predicative) propositions, a topic that is also discussed in his treatise on hypothetical syllogisms: In some cases, the predicative proposition does not differ from the conditional one, except in the way it is uttered; if in fact someone said so: 82 83

As we shall see below (§6.2), in thirteenth-century commentaries on the Sophistici ­Elenchi this fallacious argument will be discussed under the “fallacy of the consequent.” Martianus Capella, De nuptiis V.491.

160

chapter 3

“human being is animal” [predicative proposition: homo est animal], and then, again, he uttered: “if there is a human being, there is an animal” [conditional proposition: si homo est, animal est], these propositions would be different for the way of expressing what they mean, which does not appear to be different.84 In the first the predicate term is said of another term (the subject), and this is its most proper characteristic (vis); the conditional proposition is not only constituted by two predicative propositions, but also poses a condition:85 In these propositions that are called “conditionals” there is not the same way of predicating, and it is not the case that something is said of ­something else, but it is said that something happens, if something else happened, like when we say: “If she has borne a child, then she has lain with a man.” Here it is not said that having borne a child is having lain with a man, but what is proposed here is only that having borne a child could not have happened if had not had sexual intercourse with man.86 The commentary on Cicero’s Topica only adds that, while all predicative ­propositions (like “A human being is an animal”) can be transformed into conditionals (“If there is a human being, there is an animal”), the opposite is not true: “Who has borne a child has lain with a man” and “If she has borne a child, then she has lain with a man” are not equivalent, because the latter poses a condition: if what is asserted by the antecedent has occurred (having borne a child), then what is said in the consequent necessarily follows.87 Earlier in 84 Boethius, De hypotheticis syllogismis I.1.6, ed. Orbetello, 208: “Videtur enim in aliquibus propositionibus nihil differre praedicativa propositio a conditionali, nisi tantum quidem orationis modo; uelut 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 uero non videntur significasse diversam.” 85 Boethius, De hypotheticis syllogismis I.1.6, ed. Orbetello, 208. 86 Boethius, De hypotheticis syllogismis I.2.1, ed. Orbetello, 210: “At in his propositionibus quae conditionales dicuntur non est idem praedicationis modus; neque enim omnino alterum de altero praedicatur, sed id tantum dicitur esse alterum, si alterum fuerit, veluti cum dicimus: ‘Si peperit, cum viro concubuit.’ Non enim tunc dicitur ipsum peperisse id esse quod est cum viro concumbere, sed id tantum proponitur quod partus numquam esse potuisset nisi fuisset cum viro concubitus.” 87 Boethius, In Ciceronis Topica IV, ad Top. 53, ed. Clavis Patrum Latinorum (CLP) 888, 351 = PL 64, col. 1128D-1129A: “Omnis namque praedicatiua propositio in conditionalem uerti potest, hoc modo: omnis homo animal est, praedicatiua est; haec facile uertitur in

Demonstratio in the First Half of the 12th Century

161

the same commentary, while dealing with Cicero’s non-logical but temporal use of the terms antecedens and consequens in his classification of the loci, Boethius had specified that for antecedens we always mean the first proposition of a conditional (“protasis”) and for consequens the second one (“apodosis”), even if, as in the example in question, what is signified by the antecedent (the birth) temporally follows what is said in the consequent.88 In his De differentiis topicis, finally, Boethius uses the example in question to explain the difference between a conditional proposition and the argumentation that concludes with the consequent of the conditional, assuming its antecedent as premise. Here again, he says that sometimes what is said by the antecedent is contemporary with what is said by the consequent, sometimes it comes before and sometimes after: often these vary so that what comes after constitutes the antecedent in the proposition, as ­having borne a child (peperisse) comes after having had a sexual relationship (concubuisse). However, if she has borne a child, in any case she has lain with a man, and being what is precedent and expressed in the first conditionalem ita, si homo est, animal est. Non uero omnis conditionalis in praedicatiuam uerti potest, uelut haec: si peperit, cum uiro concubuit. Nemo enim dicere potest ipsum peperisse, id esse quod cum uiro concumbere, quo modo dicimus hominem, id esse quod animal sit. Alia enim ratio est in his propositionibus quae ita dicuntur, quae peperit, cum uiro concubuit. Haec enim similis est ei quae dicit, si peperit, cum uiro concubuit sed praedicatiua propositio id esse subiectum dicit, quod fuerit praedicatum. Conditionalis uero id ponit, ut si id quod antecedens fuerit necessario comitetur quod subsequitur. Cum uero praedicatiua est propositio, si ea uertatur in conditionalem, alia nimirum redditur propositio.” The necessity Boethius talks about here is what he calls necessitas consequentiae in De hyp. syll. I.9.4, ed. Orbetello, 250: “Necessitas vero hypotheticae propositionis, et ratio earum propositionum ex quibus iunguntur inter se conexiones, consequentiam quaerit, ut cum dico: ‘si Socrates sedet, et vivit’ neque sedere eum, neque vivere necesse est, sed, si sedet, vivere necesse est. Item cum dicimus: ‘si sol movetur, necessario veniet ad occasum’ tantumdem significat quantum, si sol movetur, veniet ad occasum. Necessitas enim propositionis in consequentiae immutabilitate consistit. Item cum dicimus: ‘si possibile est legi librum, possibile est ad versum tertium perveniri’, rursus necessitas consequentiae conservata est; nam si possibile est legi librum, necesse est etiam id esse possibile, ut ad versum tertium perveniatur.” When Boethius talks about the necessity of the conclusion, he uses the expression necessitas conclusionis (cf. De hyp. syll. III.2.1, ed. Orbetello, 326; III.3.1, 332; III.4.7, 344). 88 Boethius, In Ciceronis Topica II, ad Top. 19, ed. CPL 888, 303 = PL 64, col. 1075C: “Antecedentia sunt, quibus positis, aliud necessario consequatur, licet illud quod antecedit, minus sit atque posterius. Minus quidem, ut si homo est, animal est; homo enim minus est animali, et tamen posito homine, consequitur ut animal sit. Posterius uero, ut si peperit, cum uiro concubuit; posterius enim est peperisse quam cum uiro concubuisse.”

162

chapter 3

place , the second one must be understood. Sometimes instead happen at the same time, as “If the sun has risen, it is day”; sometimes the antecedent comes before, and the consequent comes after, as “If he is arrogant, he is heinous”; someone in fact becomes heinous because of his arrogant behaviour. From the antecedent an argument is formed in this way: “If she has borne a child, she has lain with a man”; I assume the antecedent “but she has borne a child”; I conclude with the consequent “therefore she has lain with a man.” From the consequent I thus assume what follows “but she has not lain with a man,” I conclude with the antecedent “therefore she has not borne a child.” 89 The distinction between a logical and a temporal or causal meaning of antecedens and consequens will be central in Simon of Tournai’s classification of the modes of signification.90 Here, even more than in the commentary on Cicero’s Topica, Boethius tries to replace the common-sense temporal interpretation of the terms (adopted by Cicero) with the logical interpretation and, like in Grillius’ commentary (which Boethius probably did not know, though), he considers the two Stoic indemonstrables (modus ponens and modus tollens) and shows what their role is in the construction of valid argumentations. Leaping a few centuries forward, in the eleventh century we find the same example cited again by two famous anti-dialecticians. The first is Peter Damian (1007–1072), a monk, pupil and follower of St. Romuald, who was trained in the liberal arts before devoting himself to monastic life. He writes an ­epistle De divina omnipotentia (ca. 1167), in which he criticizes the application of the techniques of dialectic to theological questions. Here, he also presents the example as a topos of dialectical dispute that is completely destroyed by the

89 Boethius, De differentiis topicis III.3.24–26, CPL 54 = PL 64 1198C–D: “saepe ista ita variantur, ut id quod posterius est tempore antecedens esse videatur in propositione (ut ‘peperisse’ posterius est quam ‘concubuisse’; tamen, ‘si peperit, modis omnibus cum viro concubuit’), et ut illo praecedente et prius posito illud necesse est intellegatur. Aliquoties vero simul sunt, ut: ‘si sol ortus est, dies est’; aliquoties prius est quod praecedit, posterius quod consequitur, ut: ‘si arrogans est, odiosus est’; ex arrogantia enim quisque fit odiosus. Ex antecedente igitur ita sumitur argumentum: ‘si peperit, cum viro concubuit’; sumo quod antecedit: ‘at peperit’; concludo quod consequitur: ‘cum viro igitur concubuit.’ A consequentibus ita; sumo quod consequitur: ‘at non concubuit cum viro’; concludo quod antecedit: ‘non igitur peperit.’ Cf. Grillius, Comm. in Cic. Rhet. I.12, quoted above. 90 Cf. infra, §4.3.

Demonstratio in the First Half of the 12th Century

163

mystery of human redemption and is therefore no longer usable as an invincible argumentation: It is evident that this alternative—about which we ask ourselves—is whether one could believe that something could have been and not been at the same time; to be and not to be; to exist in the future and not to exist in the future, and this alternative for no reason can match the nature of existing things; but it is relevant only for verbal battles, which deal with the consequences of discourse and reasoning. Consequently, it is undoubtedly to be believed that God is capable of everything, whether he acts or does not act. [...] And from this it derives that the divine power often wrecks the mighty syllogisms of the dialecticians and their astuteness; and it baffles what in their judgment appears necessary and inevitable, together with the arguments of all philosophers. Listen to this syllogism: “If wood burns, it is certainly consumed; but it burns, therefore it is consumed.” But here Moses sees the burning bush and it is not consumed. [...] What do all these produce, I say, if not baffling the miserable meanings of the wise of this world and reveal to the mortals the glory of the divine power against the normal order of nature? Let the dialecticians—or rather, as they are believed to be, these heretics—come and realize ; let them come, I say, with their word analyses, waving their questions as with the sound of trumpets, proposing, assuming and concluding what seems to them inevitable, and saying: “If she has borne a child, she has lain with a man; but she has borne a child, therefore she has lain .” Did not this seem an impenetrable argument, before the mystery of human redemption? A mystery, however, has been accomplished, and the reasoning has failed. And yet God has the power to impregnate a virgin without making her lose virginity (ante ruinam), as well as to restore her virginity after she has lost it (post ruinam).91 91

Peter Damian, De divina omnipotentia 12, ed. Cantin, 442.3–10, 15–20, 444.35–49; ed. Reindel, 365.12–17, 21–25, 366.11–367.2 = PL 145, col. 610C–611B: “Manifestum est igitur alternitatem istam, de qua quaeritur, scilicet, utrum possit credi aliquid fuisse simul et non fuisse; esse, et non esse; futurum esse et futurum non esse, naturis existentium rerum nulla posse ratione congruere; ad solas autem verborum pugnas, quae de disserendi ac ratiocinandi fiunt consequentiis pertinere. Quamobrem indubitabili fide credendum est, omnia Deum posse, sive faciat, sive non faciat. […] Hinc est, quod sepe divina virtus armatos dialecticorum sylogismos, eorumque versutias destruit; et quae apud eos necessaria iam atque inevitabilia iudicantur, omnium philosophorum argumenta confundit. Audi sylogismum: Si lignum ardet, profecto uritur; sed ardet, ergo et uritur. Sed

164

chapter 3

The dialectical expertise of Peter Damian, which was refined during his study of the liberal arts, is evidenced by his terminological precision: the dialecticians are proponentes (the major premise: if p then q), assumentes (the minor premise: p), concludentes (the conclusion: q) in a necessary way. Peter’s criticism concerns the truth or the necessity of the conclusion, however, not the necessity of the inference: what is no longer valid after the virginal birth of the Savior is the causal connection expressed by the major premise (which is not true of the case of Jesus’ birth). As Toivo Holopainen has pointed out, the monk’s opposition is not so much against dialectic in itself, as against the applicability of some of its traditional examples (derived, moreover, from how things happen in the course of natural events—naturae consuetudo).92 Indeed, as Anselm of Canterbury would do in his Cur Deus homo?,93 Peter Damian also seems to distinguish two types of possibilities: the one which Anselm calls “precedent” (praecedens), which does not affect divine omnipotence and which dialecticians can continue to apply correctly when they claim that “If a thing exists, as long as it exists, it is necessary that it exists” (and so on for all verb tenses);94 the one which Anselm calls “following (sequens) necessity,” which is exemplified several times in the quoted passage (also in the omitted parts), and is not applicable to theological questions, in the sense that it does not affect divine omnipotence.95

92 93 94

95

ecce Moyses videt rubum ardere, et non comburi. […] Quid, inquam, haec omnia sunt, nisi frivola sapientum huius mundi sensa confundere, et contra naturae consuetudinem divinae virtutis gloriam mortalibus revelare? Veniant dialectici, sive potius, ut putantur, heretici, ipsi viderint; veniant, inquam, verba trutinantes, quaestiones suas buccis concrepantibus ventilantes, proponentes, assumentes, et ut illis videtur inevitabilia concludentes, ac dicant: Si peperit, concubuit: sed peperit, ergo concubuit. Nunquid hoc ante redemptionis humanae mysterium non videbatur inexpugnabilis roboris argumentum? Sed factum est sacramentum, et solutum est argumentum. Et quidem poterat Deus, et foetare virginem ante ruinam, et reparare virginem post ruinam.” Halopainen (1996), 20–21. Anselm of Canterbury, Cur Deus homo? 2.17, ed. Schmitt, II, 125; cf. Holopainen (1996), 28–29. Cfr. Peter Damian, De div. omnip. 14, ed. Cantin, 460.30–37; ed. Reindel, 373.14–20 = PL 145, col. 615B: “sciantque impossibilitatem istam in ipsa rerum esse natura, et verborum ex arte procedentium consequentia, non ad virtutem pertinere divinam, nichilque supernae maiestatis evadere posse potentiam, ut dicatur iuxta solius naturae ordinem verborumque conditionem, si est aliquid, quamdiu est, non potest non esse, et si fuit, non potest non fuisse, et si futurum est, non potest non futurum esse.” Also quoted in Holopainen (1996), 26 n. 65. As Holopainen (1996), 22–43, argues, for Peter Damian the principle of contradiction and—as the discussion of the example in question shows—the laws of logic (such as

Demonstratio in the First Half of the 12th Century

165

On the same wavelength, Manegold of Lautenbach, in his Liber contra W ­ olfelmum, also argues that the eternal generation of the Son from the Father and the incarnation of the Word are two extraordinary events that challenge the foundations of philosophy: Therefore, each of the two nativities is wondrous; the arguments of human invention fail in either case. The first, on account of the unity of the Trinity, reaches beyond the understanding of angels and human beings; the second, on account of the unusual manner of His birth, is outside the realm of philosophical reasoning altogether. For they proposed, according to an invariable consequence, “If she gave birth, she must have had intercourse with a man.” However, a strong boy was born [Is. 9.6], angelic in wisdom, a philosopher of chastity, who canceled the aforementioned logical proposition by means of His honorable birth from one who was always a virgin, since He was born from a mother who did not know man [Luke 1.34] and who, therefore, could by no means be said to have had intercourse with a man.96 In this case the reference to dialecticians is absent (in fact he criticizes philosophers in general, and Platonists in particular)97 as well as the use of a specific logical terminology. The central point that Manegold shares with Peter Damian remains: the case of the virginal birth puts into question the truth of the

96

97

modus ponens) hold true, so that in conclusion “he can be characterized as an antidialectician to a mild degree” (Halopainen 1996, 43). Manegold of Lautenbach, Liber contra Wolfelmum 14, ed. Hartmann, 75–76 = PL 155, 163A–B: “Utraque igitur nativitas ammirabilis est. In utraque humane inventionis argumenta deficiunt. Prima enim propter unitatem Trinitatis, angelorum et hominum supergreditur intellectum; secunda propter insolitum nascendi modum tocius philosophice rationis evacuat firmamentum. Constanti namque consequencia proponebant: Si peperit, cum viro concubuit. Verum natus est puer fortis, angelus consilii, philosophus castitatis, et per venerandam de perpetua virgine nativitatem predictam propositionem cassavit, cum de matre natus sit quae virum non cognovit, et ideo nulla ratione cum viro concubuit.” Transl. Ziomkowski. On Manegold’s attitude towards rhetoric and dialectic, see also ­Hartmann (1997). In Manegold’s work, neither logicians nor dialecticians are mentioned, while no criticism is spared to the philosophers and the uselessness of naturalistic-philosophical research and Platonic cosmology (cf. Lib. contra Wolf. 8, ed. Hartmann, 58–61 = PL 155, col. 157B-C), that he knows from Plato’s Timaeus and from Macrobius’ Commentary to Scipio’s Dream (Lib. contra Wolf. 2, ed. Hartmann, 47–48 = PL 155, col. 153C–154A), and to the poetarum turba who followed them, seducing many innocent and simple souls with their allegorical discourses which embellish and hide indecent obscenities (obscena et turpia quibusdam involucris adornarunt) (Lib. contra Wolf. 9, ed. Hartmann, 62–63 = PL 155, col. 158B–C).

166

chapter 3

proposition, and the link between a cause and its own effect, in the normal natural order, which is considered constant and unchangeable by philosophers. That Menegaldus, who commented on Cicero’s De inventione, might be identified with Manegold of Lautenbach has been conjectured and debated by various scholars.98 In particular, Irene Caiazzo has proposed two parallels between Manegold’s Liber contra Wolfelmum and Menegaldus’ commentary on the De Inventione.99 In the first parallel, Caiazzo examines a passage from Manegold’s work in which he questions the applicability of the traditional definition of “human being” (homo) as rational and mortal animal to Christ,100 and a passage from Menegaldus’ commentary in which, illustrating a sort of “Porphyrian tree” proposed by Cicero, according to which natura is distinct in animalis and inanimalis, the former in turn is divided into mortal and divine.101 Menegaldus says about this passage that Cicero is not concerned with further subdividing divine nature, since the divine sphere is no part of his own competence (ad nos) and is outside the scope of rhetoric (ad hanc artem), unless it is introduced by some author speaking about it (nisi forte aliquando propter auctoritatem inducatur).102 This would normally be interpreted as the definition of a boundary between disciplines: rhetoric does not deal with theological issues, if not occasionally (and, incidentally, neither does Menegaldus, as commentator of Cicero’s rhetoric). From what Menegaldus says “it could be deduced that magister Menegaldus is not favorable to the application of the arts of language to theological questions,”103 and this position would match Manegold’s criticisms. As a confirmation of this interpretation, Caiazzo observes that Menegaldus here does nothing but follow Marius Victorinus, one of the most frequently quoted sources of Menegaldus’ commentary. Furthermore, in another passage of his commentary where he discusses necessary arguments, Victorinus talks about the immortality of Christ. From here, and only from here, Caiazzo draws the conclusion that “this does not prevent us from conceiving that magister Menegaldus, reader of Marius Victorinus, has remained in the grip of his views of youth and has retained his distrust of the application

98 See supra, footnote 8 99 Caiazzo (2011), 340–342. The two have the same name, but we prefer to keep them distinct by name as well. 100 Manegold, Lib. contra Wolf. 22, ed. Hartmann, 96–97 = PL 155, col. 171B. 101 Cicero, De inv. I.24.35. 102 Menegaldus, In Cic. Rhet. I.24.35, ed. Bognini, 74.2: “Ac si dicat: natura alia animalis, alia inanimalis; animalis alia mortalis, alia divina; divina nihil ad nos et ad hanc artem, nisi forte aliquando propter auctoritatem inducatur.” 103 Caiazzo (2011), 340.

Demonstratio in the First Half of the 12th Century

167

of ‘human arts’ to divine things even after becoming a fiery polemicist.”104 The hypothesis that the two authors are in fact the same is based on an alleged lack of confidence in the application of human arts to divine things that seems to have a weak basis: to say that logic, grammar, or rhetoric do not deal with God is not the same as being hostile to their application in areas other than the usual ones. Menegaldus, following Victorinus, actually admits occasional theological digressions; his attitude is not a generalized distrust. The second parallel where the example in question occurs is even less supportive of the identification. In commenting on the passage in which Cicero discusses the example, Menegaldus says: Those things are proved necessarily. Once shown the d­ escriptions of what is probable and what is necessary according to the value of the words, now he also wants to show the other descriptions of the same notions according to their own value and not according to the words. And having to say “those things are proved necessarily that cannot be proved in a way different from the way they are said,” he supplies the cause where he says: “they cannot happen otherwise.” From the fact that something cannot happen otherwise, in fact, derives that this cannot be proved otherwise, not that one cannot prove them with other words, but that one cannot prove them unless what is said is clear, and that is, if it is clear that she has not lain with a man, it cannot be proved that she has borne a child (si constet non concubuisse cum viro, non potest probari peperisse), and this with regard to the nature and so on. This type of argumentation is used for necessary proof. the definition of what a necessary argumentation is, and he divides it, and since it cannot be subdivided according to the nature of things, he divides it according to the way it is expressed.105 104 Caiazzo (2011), 341. 105 Menegaldus, In Cic. Rhet. I.29.44, ed. Bognini, 99.9–11: “Necessario demonstratur. Ostensis descriptionibus probabilis et necessarii secundum vim vocabulorum, vult ostendere et alias descriptiones eorundem secundum vim ipsorum et non secundum vocabulum. Et cum debuit dicere ‘necessarie demonstrantur que aliter, quam dicuntur, probari non possunt,’ premittit causam ubi dicit ‘aliter non possunt fieri’; namque ex hoc, quod aliter non possunt fieri, est hoc, quod aliter non possunt probari, non quod aliis verbis non possint probari, sed non possunt probari, nisi illud constet quod dicitur, id est: si constet non concubuisse cum viro, non potest probari peperisse, et hoc quantum ad naturam, et ­cetera. Hoc genus argumentandi quod in necessaria demonstratione versatur. Diffinito quid sit necessarium argumentum, dividit illud; et quid non potest illud dividere secundum naturam rei, quia necessitas non variatur, dividit illud secundum formam dicendi, id est tractandi.” Quoted in Caiazzo (2011), 341.

168

chapter 3

What is Menegaldus saying here? He seems to be considering an argument of the form of the modus tollens in which minor premise (antecedent of the conditional) and conclusion (consequent of the conditional) are formulated in epistemic terms (constare means “to be known, clear, evident,” and also probari is a verb of knowledge): If she has borne a child, she has lain with a man But it is clear that she has not lain with a man, Therefore, it cannot be proved that she has borne a child At the basis of this reasoning is the idea—clearly formulated by both Grillius and Boethius—that, given a conditional (si peperit, cum viro concubuit), we can both infer the consequent (cum viro concubuit) from the antecedent (peperit), and the negation of the antecedent (non peperit) from the negation of the consequent (cum viro non concubuit). But the epistemic outlook of Menegaldus’ argument complicates things. A charitable interpretation of it is the following: if one assumes that a certain woman had not lain with a man (because one doesn’t know the opposite), one can only prove the proposition “This woman has not borne a child,” and therefore one cannot prove its negation (“This woman has borne a child,” peperisse). That is, if one assumes the negation of the consequent, the negation of the antecedent can be inferred. A less charitable interpretation is that Menegaldus is here misled by a scope ambiguity concerning negation: it is not the same thing to say that it can be proved that she has not borne a child (potest probari non peperisse) and that it cannot be proved that she has borne a child (non potest probari peperisse); the former, but not the latter, follows from the premises “If she has borne a child, she has lain with a man. But it is clear that she has not lain with a man.” Be that as it may, Menegaldus’ commentary on Cicero’s De inv. I.29.44, although unusual and perhaps even surprising, is not to be read as a criticism of the conditional si peperit, cum viro concubuit. Furthermore, in this text there is no mention of the miracle of virginal birth and no consequence is drawn as to the universal applicability of the conditional in question or the necessity of the conclusion. Consequently, pace Caiazzo, this passage can neither be put in parallel with that of Manegold (see above), nor can it be interpreted by any means as the imposition of a limit to the applicability of the arts of language to theological questions. In the first half of the twelfth century, we still find the example in the writings of Peter Abelard, with whom we end this story. Its first mention can be read in his Dialectica, where he explicitly refers to Boethius’ De hypotheticis

Demonstratio in the First Half of the 12th Century

169

syllogismis as a direct source and auctoritas supporting the thesis that the truth of the conditional proposition is equivalent to its necessity: We argue that the truth of a hypothetical proposition consists in its necessity both in virtue of the reference to the authors (ex auctoritate) and of some reasoning (ex ratione). Boethius, in the first book of his treatise On the hypothetical syllogisms, clarifying the meaning of the hypothetical proposition, says this: “when we say: ‘If she has borne a child, then she has lain with a man’ […] what is proposed here is only that having borne a child could not have happened if had not had a sexual relationship with a man.” Whoever affirms that something cannot exist if another is absent, certainly says that the existence of the former necessarily requires the presence of the latter.106 And he quotes another passage from the same work, concerning the proposition “If [something] is a human being, then it is an animal,” in which Boethius emphasizes how “if there is something which is called ‘human being’ (homo), then there is necessarily something that is called ‘animal’.” Abelard concludes that here the focus is not on the necessity of the consequent, but on the necessity of the inference (consecutionis): this means that when we say that a conditional is true, that is, necessary (such as si homo est, animal est), we do not hold the consequent (which is a categorical proposition) to be necessary, or that “‘animal’ is necessarily inherent in what is a human being” (ut animal necessario inesse ei qui fuerit homo). Abelard—following Boethius—argues that, when we take the conditional “If Hugh is a human being, then Hugh is an animal” as a major premise of a hypothetical syllogism, and assume the antecedent as a minor premise, the conclusion (= consequent categorical proposition) follows necessarily; but it cannot be said that the conclusion in itself is also a necessary or necessarily true proposition. This is confirmed a little further on: As regards the value of the conditional (vis conditionis) and the meaning of the inference (sensus consecutionis), all the consequences propose a necessary inference, both those that are composed of necessary propositions, and those that are not.107 And he concludes by quoting again Boethius: “when we say that ‘If the sun moves, it necessarily goes towards the west,’ this means the same thing as ‘If the sun moves, it goes towards the west’.”108 Abelard finally quotes again the example in two of his Theologiae, as one of the many cases in which the rules of philosophy and dialectic clash with the unattainability and ineffability of the divine mysteries. We quote from his Theologia Christiana: Perhaps due to the healing of the blind man is not broken the known rule of the philosophers in which Aristotle says: “One can change from the disposition to privation, but from privation to the disposition this is impossible: just as those who are blind do not return to see” and so on? And maybe does not also the virginal birth destroy the proposition that is often presented as an example of necessary conditional or argumentation: “If she has borne a child, she has lain with a man”? Is it not clear from this what the Apostle says: “Has not God made foolish the wisdom of the world”?109 What differentiates Abelard’s approach from Peter Damian’s and Manegold of Lautenbach’s criticisms of dialecticians and philosophers is the proposal of a method through which we can recognize the peculiarity of theological discourse, which can be learned from the Scriptures and the writings of the Fathers: in his perspective, we should put aside what we, as human beings, can do with our language which was instituted to speak about our sensible world and communicate to others what we think and understand, making room 107 Abelard, Dial. ed. de Rijk, 273.11–14: “Quantum enim ad vim conditionis et ad sensum consecutionis pertinet, omnes consequentiae necessariam proponunt[ur] inferentiam, tam illae videlicet quae necessariae propositiones habent quam illae quae non habent.” 108 Abelard, Dial. ed. de Rijk, 273.25–26. 109 Abelard, Theologia Christiana III.128–129, ed. Buytaert, 243.1551–1559: “Numquid enim illuminatione caeci nota illa philosophorum regula infringitur qua ab Aristotele dictum est: ‘Ab habitu quidem in priuationem fit mutatio, a priuatione uero in habitum impossibile est: neque enim caecus factus rursus uidet’ etc.? Numquid et Virginis partus omnino illi praeiudicat propositioni quae frequenter a philosophis in exemplum necessariae ­consequentiae seu argumentationis affertur: ‘Si peperit, cum uiro concubuit’? Vt hinc quoque appareat quod ait Apostolus: Nonne stultam fecit Deus sapientiam huius mundi?” Cf. Theologia Scholarium II.87–88, ed. Buytaert and Mews, 450–451.1314–1323.

Demonstratio in the First Half of the 12th Century

171

for metaphors, enigmatic speeches, and similes that allow us to enjoy something of the ineffable divine majesty “conjecturing rather than understanding” (­suspicando potius quam intelligendo). As we will show in the last part of the next Chapter,110 this and other examples emerge again in the writings of some theologians of the second half of the twelfth century, which also testify to the first entry of Aristotle’s logica nova into the Latin world and its first influence on the philosophical and theological debate. 5 Conclusion Before the rediscovery of the theory of demonstration of the Posterior Analytics in the thirteenth century, the term demonstratio was in use in several distinct senses in philosophical, logical, grammatical, and rhetorical literature. In this literature the term has a least three senses. In the first place, in rhetoric demonstratio is the epideictic or occasional genre of oratory, along with deliberatio (deliberative or political) and iudicium (legal or forensic). This sense, deriving from Cicero’s De inventione, is found in the commentaries on this work by magister Menegaldus (late eleventh century), by Menegaldus’s student William of Champeaux (early twelfth century), and by Thierry of Chartres (first half of the twelfth century). In the second place, demonstratio also has a grammatical sense: it is Priscian’s translation of the Greek δεῖξις, and indicates the ability of personal pronouns to refer to the actors of communication (speaker, listener, or other person referred to); it contrasts with relatio, which only third-person pronouns have, and is the reference to something previously introduced in discourse (anaphora). Eleventh- and twelfth-century commentaries on Priscian—including the Glosulae and the Notae Dunelmenses of William of Champeaux (end of the eleventh, beginning of the twelfth century), the Glosses of William of Conches (three versions composed in the first half of the twelfth century), as well as the Summa super Priscianum of Peter Helias (1140s)—discuss the distinction and use demonstratio in the Priscianian sense of “deixis.” In the third place, demonstratio means “argumentation”; this logical or inferential sense of the term derives from Cicero’s De inventione and is the sense that more closely match the meaning that ἀπόδειξις has in Aristotle.

110 Cf. infra §4.3.

172

chapter 3

The ambiguity of demonstrare and demonstratio emerges with peculiar evidence in Abelard. In his Dialectica the verbs demonstrare and significare are used as synonyms and almost interchangeably. Yet in the context of the exposition of the “modes of signification” (or classification of signs) demonstratio means the mode of signification of phonic expressions that is based on inherence and concomitance, or on temporal concomitance and consequence, between sign and thing signified. In both cases, demonstratio is here to be taken in the logical sense deriving from Cicero’s De inventione, as inference or argumentation, i.e., as the inferential relation between sign and thing signified. It is this logical sense that remains the prevailing one after the discovery of Aristotle’s logica nova.

CHAPTER 4

The First Influence of Aristotle’s logica nova on the Theories of Signs in the Second Half of the Twelfth Century Already in the second half of the twelfth century, well before the works of the so-called logica nova (Aristotle’s Topics, Sophistici Elenchi, Prior and Posterior Analytics) made their entrance as basic teaching texts in the universities and in the studia of the mendicant orders, the idea that it is possible to draw inferences from signs is already an integral part of the discussions about signs in sacramental theology and in what can be considered the first medieval general semiotics: the first distinctio of Simon of Tournai’s Institutiones in sacram paginam (ca. 1160). The examples of sign-inferences used in these contexts are quite interesting, because in some cases they refer to glosses of Greek origin to the works of Aristotle’s logica nova, which were handed down in the margins of the Aristotelian texts and then translated along with them. The situation changes completely in the second half of the thirteenth century, when the logica nova becomes the object of specific commentaries at the Faculty of Arts in Paris and Oxford. At this time, the idea that some signs function by i­ nference and not only by substitution is definitively taken for granted and finds ­application in the two main classifications of signs of the 1260s, those of the pseudo-­Kilwardby and of Roger Bacon. These latter are the topics of Chapter 7. In the present Chapter we examine the antecedents by which these works have been influenced and we indicate the connections with the d­ octrines presented in the previous Chapters. Before entering into the details of the works, it is expedient to provide a picture of how the nova logica, together with some of the Greek commentaries, was transmitted to the Latin West. Here we refer to Sten Ebbesen’s fundamental research in this field. (As we will not deal with Aristotle’s Topics, this work will remain out of the picture).1 The Prior Analytics, translated by Boethius in the early sixth century and afterwards completely forgotten, appeared again 1 We follow Ebbesen (1981a) on late-ancient and medieval commentaries on the Sophistici Elenchi; Ebbesen (1981b) on the first medieval commentary on the Prior Analytics; Ebbesen (1990c) on the fortune of Greek commentaries and glosses on Aristotle’s logical books; Ebbesen (1993) for an overview of the medieval logical commentaries (with a list of commentaries on the Sophistici Elenchi); Ebbesen (2004) on the Posterior Analytics in the twelfth © koninklijke brill nv, leiden, 2023 | doi:10.1163/9789004546974_006

174

chapter 4

around the second quarter of the twelfth century in two versions.2 Abelard shows a superficial knowledge of this work and his pupil Otto of Freising seems to have been the first who brought a copy of it to Germany. Other witnesses, such as Thierry of Chartres and John of Salisbury, show that by the middle of the twelfth century the book was in circulation but had not yet become the object of thorough study; as John of Salisbury says in his Metalogicon, “we do not need the book itself so much. For whatever is contained there is presented in an easier and more reliable manner elsewhere, though nowhere in a truer or more forceful manner.”3 Only towards the end of the century some commentators on Aristotle’s Sophistici Elenchi, such as the so-called “Anonymus Parisiensis,” the “Anonymus Aurelianensis I,” the “Anonymus Aurelianensis II,” and the “Anonymus Cantabrigiensis,”4 show a direct acquaintance with the Prior Analytics. The first extant commentary, by another “Anonymus Aurelianensis” (III), stems back to the same period and might be identical with Anonymus Aurelianensis I.5 For our purposes, it is a pity that this commentary is incomplete, missing the last part of book A and, in particular, the whole book B. And yet it shows that other previous commentaries on the same book were circulating at that time, together with glosses coming from a Greek commentary by a contemporary of Philoponus or a Byzantine compilation dating from the sixth century (maybe translated by James of Venice, or, as Minio Paluello suggested, by Boethius), that Ebbesen called Commentum Graecum.6 The Posterior Analytics had a more complex story. It is not clear whether Boethius made any translation of it, and there is evidence of at least three (other) twelfth-century Latin translations, two directly from the Greek and one from an Arabic translation. Again, John of Salisbury shows a superficial

2 3

4 5 6

century; Ebbesen (2010) on the commentaries on the Prior Analytics in the thirteenth century; and Ebbesen (2015) on the commentaries on the Posterior Analytics in the thirteenth century. See Minio-Paluello (1962). John of Salisbury, Metalogicon IV.2, ed. Hall and Keats-Rohan, 141: “[iste] liber non eatenus necessarius est. Quicquid enim continet, alibi facilius et fidelius traditur. Sed certe verius aut fortius numquam.” Quoted and translated in Ebbesen (2010), 97 and n. 6. The alternative was offered by Boethius’ De syllogismo categorico and by Apuleius’ Peri hermeneias; cf. also Thomsen Thörnqvist (2010), 25. More on these texts below. Ebbesen (1981b), 7; cf. Thomsen Thörnqvist (2010), 28. Ebbesen (1981b), 8; cf. Thomsen Thörnqvist (2010), 28. On this commentary, see also MinioPaluello (1957) (who conjectures a Boethian attribution) and Ebbesen (1981b) (who calls Minio-Paluello’s conjecture into question). For a thorough analysis of the dependence of Anonymus Aurelianensis III on Greek sources, see Thomsen Thörnqvist (2010).

The First Influence of Aristotle’s logica nova

175

knowledge of the work, while one of the translators, a man called “Ioannes,” so describes the state of the art around the middle of the twelfth century: I know that the book contains many fruits of knowledge. I am equally sure that acquaintance with it is not widespread among the Latins of our generation, for Boethius’ translation is not to be found complete among us, and what is available of it is obscured by corruption. James’ translation, on the other hand, is known to the masters of France, as is the same James’ translation of a commentary, but they do by their silence bear witness that James’ version is wrapped up in the shadows of obscurity, and do not dare to teach the book.7 Given that Boethius’ translation (if any) was not (completely) available, James of Venice offered a translation of his own together with that of some Greek commentaries on the work. His efforts, however, proved useless: because of the obscurity of James’ translation, the French masters did not dare to lecture on it. This should explain why another translator, John himself, decided to make a new translation (actually, it was a revision of James’). John’s work, however, was probably considered not so crucial an improvement as to replace James’: as a matter of fact, James’ translation would remain the most widespread; it was often read together with Gerard of Cremona’s translation from the Arabic. In what follows we examine some of the glosses that were quoted and discussed in the commentaries on the Sophistici Elenchi: in the twelfth century, some of these glosses contain echoes of the Posterior Analytics.8 As we shall see in the next Chapter, the first extant commentary on the Posterior Analytics is that of Robert Grosseteste, composed around 1230. The Sophistici Elenchi were certainly the most successful among the books of the logica nova, and soon became part of the logic curriculum. Commentaries and compendia started to be written in the first half of the twelfth century (but the very first ones have been lost) and kept being written during the following centuries.9 Like for 7 Minio-Paluello (1968), XLIV: “[…] cognoscebam librum illum multas in se scientie fructus continere, et certum erat notitiam eius nostris temporibus Latinis non patere. Nam translatio Boetii apud nos integra non invenitur, et id ipsum quod de ea reperitur vitio corruptionis obfuscatur. Translationem vero Iacobi obscuritatis tenebris involvi silentio suo perhibent Francie magistri, qui, quamvis illam translationem et commentarios ab eodem Iacobo translatas habeant, tamen notitiam illius libri non audent profiteri.” Translated in Ebbesen (2004), 71. 8 See Ebbesen (2004). 9 See Ebbesen (1993), 148–173 (appendix), for a list of Latin commentaries on the Sophistici Elenchi and treatises on fallacies from 1125 to 1300.

176

chapter 4

the Prior Analytics and the Topics, in the case of the Sophistici Elenchi Boethius’ translation became again available in the 1120s and attracted the attention of various masters, who either integrated the theory of fallacies into their treatises on fallacies or composed literal commentaries on it. Here we focus on the first traces in the twelfth century of the influence of the Greek interpretation of the Aristotelian “demonstration of the that,” according to which, as we saw in Chapter 2, this kind of demonstration is associated with the semiotic inference of a cause from its effect, in both the logical (§4.2) and the theological domains (§4.3). Before analysing these traces, we anticipate the discussion of a thirteenth-century passage which is an interpolation in the text of the most widespread and famous medieval manual of logic, Peter of Spain’s so-called Summulae logicales (§4.1) The anticipation will contribute to a better understanding of the novelty introduced in semiotic theories and classifications by the explicit consideration of a species of inferential signs. 1 Inferences from Signs as Atypical Signs: A Glimpse from the Thirteenth Century The interpolation in question is in the treatise devoted to the topics (de locis) of Peter’s treatise.10 Here, the anonymous interpolator quotes Aristotle’s definition of enthymema as an inference which has a likelihood or a sign as its only premise: Aristotle has thus defined the enthymeme: the enthymeme is formed starting from what is likely (ycos) and from signs; what is likely means the same as “probable proposition”; the sign, instead, according to the sense in which it is understood here, is the same thing as “demonstrative proposition which is either necessary or probable,” and this happens when we infer .11 The novelty of this notion of sign is emphasized by the anonymous interpolator with the parenthetical note “secundum quod hic sumitur” and emerges from a comparison with the current definitions of the sign. These definitions, based 10 11

We return to this interpolated texts infra, §6.1.3. Petrus Hispanus, Tract. V.30, ed. de Rijk, 57, app: “Aristotiles sic diffinit entimema: ­Entimema est ex ycotibus et signis; ycos autem idem est quod propositio probabilis; ­signum autem, secundum quod hic sumitur, idem est quod propositio demonstrativa vel necessaria vel probabilis et hoc est inferendo.” (emphasis ours).

The First Influence of Aristotle’s logica nova

177

as they were on Augustine’s definition (despite the criticisms to which such definition was subjected in theological contexts),12 emphasized its sensible nature (praeter speciem quam ingerit sensibus), its ontological features (a sign is a thing, res, which is distinct from its referent) and its cognitive import (facit in cogitationem venire), without delving into how it signifies, that is, whether the sign signifies by substitution, inference, or similarity. The first reception of the Aristotelian and late-ancient theories of signs induces twelfth-century philosophers and theologians to focus exactly on the manner in which a sign signifies and to classify inferential signs together with other types of signs. We return below13 to the texts of the first half of the thirteenth century and to the meaning of terms such as enthymema and icos, which Peter of Spain mentions along with signa in the passage just quoted. 2 The Sign as an Effect that Infers its Cause: The Pseudo-Alexander and the Commentaries on the Sophistici Elenchi We saw in the second Chapter that Aristotle’s Greek commentators, on the basis of the idea that the demonstration of the why (ἀπόδειξις τοῦ διότι) is a syllogism that moves from the cause (κατὰ τὸν αἴτιον), were happy to identify those demonstrations of the that (ἀπόδειξις τοῦ ὄτι) that move from the effect (i.e., types 1b and 2a), with sign-syllogisms, because, generally speaking, an effect is a sign of its cause. We also saw in the first Chapter that in the Posterior Analytics Aristotle himself had implicitly laid the basis for such identification. Some ancient commentators also connected the typology of signs of APr B 27 with the difference between that- and why-demonstrations and with the examples of fallacy of the consequent examined in Soph El 5, where Aristotle refers to the use of demonstrations by signs (κατὰ τὸ σημεῖον ἀποδείξεις) in rhetorical discourses. We also saw in the second Chapter that the ouverture of the Physics, where Aristotle says that the method of investigation must start from what is better known and clear to us, and proceed to what is better known and clear by nature, was interpreted by the Greek commentators by means of an appeal to that-demonstrations and sign-arguments. 12

On Augustine’s definition and on a quite widespread definition, which was ascribed to many authors (Aristotle, Cicero, Augustine, Isidore of Seville and others) and was criticized by Bacon (“Signum est quod se ipsum demonstrat sensui et aliquid derelinquit intellectui”), see Rosier (1994); Rosier-Catach (2004); Marmo (2010), chs. 1, 4, and 10; infra, §7.2.1. On Augustine’s semiotics see the recent Gramigna (2020). 13 See infra, §6.2.1.

178

chapter 4

It is no coincidence, therefore, that the first references to the two types of demonstration are found in two commentaries on the Sophistici Elenchi and in a treatise on paralogisms. These are three anonymous works: the Commentarium in Sophisticos Elenchos and the De paralogismis, respectively by the “Anonymus Aurelianensis I” and “Anonymus Aurelianensis II” (so called from the place where the only manuscript that preserves their texts is kept, the Bibliothèque Municipale d’Orléans, cod. 283),14 and the Commentarium in Sophisticos Elenchos Aristotelis by the so-called “Anonymus Cantabrigiensis.”15 These three works are probably of French authorship and can be dated between the third and last quarter of the twelfth century.16 Since they are quite similar, we will examine them in parallel, focusing on what is most relevant for our purposes.17 The influence that the Greek commentaries on Aristotle’s Organon exerted upon the anonymous author of one of the first literal commentaries on the Sophistici Elenchi leaps to the eye even by only considering the high number of explicit references to an unspecified “Alexander” who reportedly commented on both the Elenchi and the Posterior Analytics. These references are also found in other slightly later or contemporary commentaries,18 but they are completely absent (although implicit in several cases) in the Summa Sophisticorum Elencorum, which is presumably a little earlier.19 As Ebbesen has shown in numerous publications from the 1970s to 2019, the quotations ascribed to “Alexander” are most likely glosses taken from both John Philoponus’ commentary on the Posterior Analytics and from glosses on the Sophistici Elenchi 14 15 16 17

18

19

Edited in Ebbesen (1979b) and (1976), respectively; they are respectively labelled as SE13, and SE14 (see Ebbesen 1993, 152–153). The name of the Bibliothèque Municipale d’Orléans has changed recently into Médiathèque d’Orléans. Edited in Ebbesen (2019) (= SE15; see Ebbesen 1993, 153). Cf. Ebbesen (2019), 12, 15–16. The Anonymus Cantabrigiensis’ work, in its final shape, is actually dated just after 1204, but probably reflects earlier courses (Ebbesen 2019, 16–17). In what follows, parallel passages from the Glose in Aristotilis Sophisticos Elenchos, in LM I, app. A, 187–255 (probably among the first glosses that comment on Aristotle’s text, probably written in France around the middle of the century, see de Rijk 1962, 83–88 = SE5, cf. Ebbesen 1993, 150), from the Summa Sophisticorum Elencorum, in LM I, app. B, 257–457 (probably composed in the third quarter of the twelfth century by a pupil of Alberic of Paris, cf. de Rijk 1962, 88–89; Ebbesen 2019, 12 = SE6; cf. Ebbesen 1993, 150–151) and from other related works published by de Rijk and Ebbesen, will be referred to. Like the Compendium Sophisticorum Elenchorum by the Anonymus Parisiensis (ed. Ebbesen and Iwakuma and, in the Uppsala version, Ebbesen 1996 = SE8; cf. Ebbesen 1993, 151): this commentary, however fragmentary, has confirmed that the source of the numerous citations and references to Alexander is the commentary on the Sophistici Elenchi by Michael of Ephesus (Ebbesen 1996, 255–257, 283). Cf. Ebbesen (2019), 12, for an overview of the dating of commentaries on the Sophistici Elenchi and other works inspired by it from the second half of the twelfth century.

The First Influence of Aristotle’s logica nova

179

translated by Jacob of Venice, and taken from the commentary by Michael of Ephesus,20 and from the commentary on the Sophistici Elenchi that Jacob himself reportedly composed (both were lost by the end of the century).21 These materials, translated or composed in the 1120s or 1130s, were in circulation in the second half of the century in French schools of logic and then disappeared at the turn of the thirteenth century.22 The three works mentioned above—the Commentarium in Sophisticos Elenchos by the Anonymus Aurelianensis I, the De paralogismis by the Anonymus Aurelianensis II, and the Commentarium in Sophisticos Elenchos Aristotelis by the Anonymus Cantabrigiensis—contain a discussion of the notions of scientia, ars and demonstratio. The discussion is unequally long and articulated in the three works, but it is here that the distinction that interests us emerges.23 Like the Greek commentators on Aristotle’s logic, the three anonymous commentators claim that the ultimate goal of logic and its culmination is the science of demonstration (viz. the Posterior Analytics). In this regard, the Anonymus Aurelianensis II quotes “Alexander” in support: Alexander thus describes the demonstrative discipline: “Demonstration is the aim of the whole of logical art, and for it Aristotle has handed down to us all the other treatises on logic.”24 This observation is part of the distinction of three senses of the word demonstratio that the two Anonymi Aurelianenses have in common. In a first sense, demonstratio is the science of demonstration (demonstrativa disciplina or 20 See supra, §2.7. 21 Block (2008) presents an argument against the existence of James’ commentary, without convincing Ebbesen (cf. 2015, 15 n. 3). 22 Cf. Ebbesen (1976), 9–10; Ebbesen (1979); Ebbesen (1981); Ebbesen (1990a) Ebbesen (1990b); Ebbesen (2008); Ebbesen (2018); Ebbesen (2019). The several thirteenth-century authors who still mention “Alexander” probably do it secondhand. 23 Cf. Ebbesen (1976), 98–107; Ebbesen (1979b), XXVIII. 24 Anonymus Aurelianensis II, ed. Ebbesen, 37.10–12; 38.8–10: “Hanc—sc. demonstrativa disciplina—autem ita describit Alexander: ‘demonstratio est finis totius artis logicae, et per ipsam ceteras logicas nobis tradidit Aristoteles’.” Cf. Philoponus, In APo, ed. Wallies, CAG 13.3, 1.5–7: “Τοῦτο τέλος ἐστὶ τῆς λογικῆς πραγματείας, φημὶ δὴ ὁ λόγος περὶ ἀποδείξεως· τὰ γὰρ ἄλλα λογικὰ συγγράμματα διὰ τῆς ἀπόδειξιν ἡμῖν παρέδωκεν ὁ Ἀριστοτέλης”; CAG 13.3, 2.23: “τέλος τῆς λογικῆς (πάσης add. Ra) πραγματείας ἡ ἀπόδειξις.” Cf. Ebbesen (1976), app. 92; Ebbesen (2008), 188. Cf. also Anonymus Aurelianensis I, ed. Ebbesen, 43 (who refers it to the work of the demonstrator). On the role of the science of demonstration also depends the position of the Posterior Analytics in the order to be followed in teaching the works of Aristotle’s Organon; cf. Anonymus Aurelianensis I, ed. Ebbesen, 8–9, 42; Anonymus Cantabrigiensis, ed. Ebbesen, 53–54.

180

chapter 4

scientia demonstrandi); in a second sense, it is the work of the demonstrator (opus or negotium demonstratoris); in a third sense, it is the instrument of demonstration, viz. the demonstrative syllogism (demonstrativus syllogismus).25 Precisely because of the latter sense, the three authors examine the definition of syllogism proposed by Aristotle in Soph El 126 and make a comparison with the definitions proposed by Aristotle in other works.27 In so doing they distinguish the necessity of the inference deriving from the disposition of the terms in the premises (necessitas complexionis) from the necessity of the premises or the things signified by them (necessitas propositionum or rerum). The clearest in this sense is the Anonymous of Cambridge, according to whom syllogistic necessity is threefold:28 since the necessity is threefold, one that derives from the relationship between the terms, another from the relationship between the premises, and a third considered only according to the arrangement of terms and premises, to understand what necessity we are talking about in this passage, he (viz. Aristotle) adds “through what has been put,” i.e., “by the necessity through which the terms and premises arranged according to mood and figure operate.”29 25

The Anonymus Cantabrigiensis recognizes only the last two senses: the actus demonstrantis (which coincides with the syllogism in general) and the demonstrative syllogism (ed. Ebbesen, 82), distinguished precisely as a general sense and a more specific one. Other authors of the same period (and the same Anonymus Cantabrigiensis, ed. Ebbesen, 111–113, passim) also use demonstratio in the (grammatical) sense of δείξις (on which see supra, §3.2); cf. Summa Soph El, 392 , 396, 409. 26 Aristotle, Soph El 1, 164b27–165a2; AL 5.17–18: nam syllogismus quidem ex quibusdam positis est ut dicatur diversum quid ex necessitate ab his quae sunt. Cf. Anonymus Cantabrigiensis, ed. Ebbesen, 64, who probably uses the translation that Dod attributes to Jacob of Venice and which has the variant aliud aliquid. 27 Cf. Aristotle, APr A 1, 24b18–20; Top A 1, 100a25–27 and supra, §1.2. Both Anonymus Aurelianensis I, ed. Ebbesen, 23, and Anonymus Cantabrigiensis, ed. Ebbesen, 64, wonder why the genus oratio is not made explicit. 28 Anonymus Aurelianensis I, ed. Ebbesen, 14, 22, 24, and Anonymus Aurelianensis II, ed. Ebbesen, 25–26, distinguish only two types of necessity, that of the thing or things (which should correspond to the first type of necessity and perhaps also to the second of the Anonymus Cantabrigiensis), and that of the complexio, which consists precisely in the arrangement according to the mood and figure of premises and terms of the syllogism; cf. Anonymus, Tractatus de dissimilitudine argumentorum, in LM I, 471 (= SE7, cf. Ebbesen 1993, 151), where the complexional arguments are distinguished from the local ones: the former receive their inferential efficacy by the mere arrangement of the terms, the latter by the relationship between the terms in a sentence. 29 Anonymus Cantabrigiensis, ed. Ebbesen, 64: “cum sit triplex necessitas, necessitas sc. proveniens ex habitudine terminorum, item alia proveniens ex habitudine propositionum,

The First Influence of Aristotle’s logica nova

181

We saw in the first Chapter that in the definition of the syllogism in APr A 1 Aristotle explains the expression τῷ ταῦτα εἶναι as meaning that the conclusion of the syllogism “results through them,” which in turn is explained as meaning that the conclusion “results through them alone,” i.e., without the need of further assumptions. We also saw in the second Chapter that in his commentary Alexander explains Aristotle’s qualifications by saying that in the syllogism simpliciter that is defined here the premises are logical causes but not necessarily ontological causes of the conclusion, as is the case in demonstrative syllogisms. The explanation of Aristotle’s first qualification (τῷ ταῦτα εἶναι = per ea quae posita sunt) that we find in the Anonymous of Cambridge is different. He explains that the qualification is added in order to indicate that the necessity in question is neither the first (concerning terms) nor the second (concerning propositions), but the third (deriving from the complexio of terms and propositions, i.e., the figures and moods).30 Yet the “necessity” of an argument should not be straightforwardly identified with its “syllogistic complexio.” The reason of this, according to the Anonymous, is precisely that there may be arguments that are necessary but whose necessity is not derived from its having the right syllogistic complexio.31 The Anonymous then argues that to each item of Aristotle’s definition of the syllogism there corresponds a differentia which distinguishes the syllogism simpliciter from other species of arguments and from some species of fallacy.32 Building on the discussion about the definition of the syllogism, our authors focus on the definitions of the demonstratio in its instrumental sense. The definition attributed to Alexander assumes that the syllogism is indeed the genus

30

31

32

item tertia secundum solam terminorum et propositionum dispositionem considerata, ad determinandum de qua necessitate hic loquitur, subdit ‘per ea quae posita sunt,’ quasi dicat ‘ex necessitate qua propositiones et termini in modo et figura dispositi operantur.’” Figure and moods are the form of syllogism, as opposed to the terms and premises that make up the matter. The Anonymus Cantabrigiensis includes the conclusion of the syllogism in the matter. Cf. Anonymus Aurelianensis II, ed. Ebbesen, 16–17; (less explicitly) Anonymus Aurelianensis I, ed. Ebbesen, 14, 23; Anonymus Cantabrigiensis, ed. Ebbesen, 63–64 (where the idea that the conclusion is also to be considered a form, as the two Anonymi Aurelianenses claim, is criticized); see Brumberg-Chaumont (2017) for more on this. The induction of Anonymus Cantabrigiensis, ed. Ebbesen, 65, is a case in point: omne rationale est substantia; omne irrationale est substantia; ergo omne animal est substantia; cf. Anonymus Aurelianensis II, ed. Ebbesen, 25. It is necessary but not syllogistic. The converse case is also mentioned (Anonymus Cantabrigiensis, ed. Ebbesen, 64) of a syllogistic argument that is not necessary. See Brumberg-Chaumont (2017), 203. For the Anonymus Aurelianensis II, ed. Ebbesen, 25 enthymeme and example are different from syllogism because they only posit one premise. See Brumberg-Chaumont (2017).

182

chapter 4

of demonstratio: “demonstratio est syllogismus faciens scire ex per se credibilibus et certis rationibus receptus.”33 The Anonymus Aurelianensis I, following “Alexander,” explains what knowing (scire) means and what is the difference between scientia, fides and opinio. “Knowing,” therefore, according to what Alexander says, “is knowing that the thing exists in the way it exists and for what causes and knowing that it cannot exist otherwise.”34 He also adds that knowledge acquired by common people (rusticana cognitio) —which does not derive from the causes, but rather depends on sensitive perception—should rather be called “opinion,” and proposes a ranking between the various types of knowledge: at the lower level there is opinio (as existimatio proveniens ex coniecturis), at the second level we find fides (as credulitas ex certis causis non proveniens), and at the peak there is scientia (as demonstrativus habitus rerum semper aut frequenter eodem modo se habentibus).35 In the other two works, although they share the discussion about the difference between sapientia (as an understanding of the principles) and scientia (as an understanding of what follows or is ruled by these principles),36 there is no trace of anything similar. As we shall see below, a similar ranking is to be found in 33

34

35

36

Anonymus Aurelianensis I, ed. Ebbesen, 45; Anonymus Cantabrigiensis, ed. Ebbesen, 82; cf. Philoponus, In APo, CAG 13.3, 3.1–2: “ἁπόδειξις τοίνυν ἐστὶ συλλογισμὸς έπιστημονικὸς ἐξ αὐτοπίστων καὶ ὁμολογουμένων λόγων λαμβανόμενος”; cf. Ebbesen (1976), 90, 94; Ebbesen (2008), 191; in its shorter form, Anonymus Aurelianensis II, ed. Ebbesen, 28.2–3 (syll. faciens scire). Anonymus Aurelianensis I, ed. Ebbesen, 45: “‘Scire,’ ergo, ut ait Alexander, ‘est rem cognoscere sic se habere ut se habet et ex quibus causis et quod aliter se habere non possit’.” Anonymus Cantabrigiensis, ed. Ebbesen, 82, does not attribute this definition to any auctoritas, while Anonymus Aurelianensis II, ed. Ebbesen, 28.4–6, claims to take it from Aristotle. Earlier the Anonymus Aurelianensis I, ed. Ebbesen, 33, had also attributed the definition to Aristotle; in fact it corresponds to Aristotle, APo A 2, 71b9–12. As Ebbesen (1976), 99–100, points out, it is likely that “Alexander” is the common source of all these passages. Anonymus Aurelianensis I, ed. Ebbesen, 45; cf. Anonymus Aurelianensis II, ed. Ebbesen, 30. Ebbesen (1976), 100–101, claims that the quotation (which recalls Aristotle, Eth Nic E 3, 1139b31) derives in part from “Alexander”’s commentary (aka Michael of Ephesus) on the Sophistici Elenchi ([Michael of Ephesus], In Soph El, ed. Wallies, CAG 2.3, 17.9), in part from Aristotle, Met Κ 8, 1065a4–5 and APo A 30, 87b19–22, for the clause relating to what happens mostly (ὠς ἐπὶ τὸ πολύ). Cf. Anonymus Aurelianensis I, ed. Ebbesen, 32–35; Anonymus Aurelianensis II, ed. Ebbesen, 31; Anonymus Cantabrigiensis, ed. Ebbesen, 74–75; Cf. Summa Soph El, 266 (cf. Ebbesen 1976, 101–103, about the sources of these definitions).

The First Influence of Aristotle’s logica nova

183

Simon of Tournai’s Institutiones in sacram paginam.37 The Anonymus Aurelianensis I comments, in the typical style of literal expositions, on each clause of the definition of scientia and says, among other things, that it is appropriate to distinguish between the science of immutable things (de rebus semper... eodem modo se habentibus) and the science of regular phenomena (de rebus… frequenter eodem modo se habentibus). The first type of science is like the one that can be had of the human being (homo), or of its property (risibile), as such, or of universals that maintain their permanence over time; the second type, on the other hand, is like medical knowledge, which is concerned with diseases and symptoms (de aegritudine et eius signo) that normally occur together (comitantur), but not always: In fact, the necessity of this type of concomitance remains stable unless a change of nature might occur. In fact, the nature of things whose knowledge the physician pursues, although rarely, is not always together with the natural order.38 A similar distinction is made by the Anonymus Aurelianensis II in his treatise on paralogisms, where he distinguishes the necessity of what is immutable (n. immutabilitatis) from the necessity dictated by custom (n. consuetudinis), precisely commenting on the same clause of the definition of scientia discussed by the Anonymus Aurelianensis I: When he [scil. Aristotle] says “what always presents itself in the same way” one understands the science of what is immutable, when he says “more frequently” the science of necessity dictated by custom is denoted. This way sometimes authoritative writers, and especially philosophers, habitually call “necessary” whatever they saw always happen in the same way, although it could have happened otherwise, as in the case “if has milk, she has lain with a man”: although this may not have happened, since however it seemed to happen constantly, they called it “necessary.”39 37 38 39

Cf. Simon of Tournai, Institutiones in sacram paginam, ed. Siri, 435; see infra, §4.2. Anonymus Aurelianensis I, ed. Ebbesen, 47: “Huiusmodi enim comitantiae necessitas immobilis manet nisi insueta fiat quandoque naturae mutatio. Nam naturae rerum quas exequetur physicus, etsi raro , non tamen semper naturalem comitantur ordinem.” Anonymus Aurelianensis II, ed. Ebbesen, 30: “Per hoc quod dicit ‘semper eodem modo sic se habentibus’ intelligitur scientia immutabilitatis, per ‘frequentius’ scientia necessitatis consuetudinis denotatur. Sic enim quandoque auctores et maxime philosophi consueverunt necesse appellare, sc. quicquid eodem modo semper videbant contingere, quamvis

184

chapter 4

The last example is rather interesting because it connects with the series of examples discussed in the previous Chapter from the rhetorical tradition, with the variant that the antecedent of the conditional proposition is not “giving birth to a child” but “having milk (in the breasts),” which perhaps represents a reference to both the example of τεκμήριον of APr B 27 and Cicero’s classic example of necessary argument.40 Here the author seems to allude to a (short) chain of inferences or compound conditional in which the intermediate step is tacit: si habet lac, [peperit, et si peperit,] cum viro concubuit, where the consequent of the first conditional and the antecedent of the second are omitted.41 There is no explicit element linking the precautionary clause to theological concerns,42 even though these cannot be excluded. On the basis of the explanations given by the various authors regarding necessity, it is possible to finally clarify the definition of demonstration given by Aristotle in the Posterior Analytics: Demonstration is described by Aristotle in these terms: “demonstration begins from what is first and true or from that from which, through what is first and true in this respect, knowledge starts.”43 The definition is actually from Top A 1, 100a27–29, where, as we mentioned, Aristotle offers a more “relaxed” version of the strict characterization of demonstrations in APo A 2.44 Then, the Anonymus Aurelianensis II explains that there are two species of demonstrative syllogism, one propter quid, and posset \non/ \ita/ contingere, ut si habet lac, cum viro concubuit: quamvis enim posset non contingere, quia tamen semper sic videbant contingere, appellabant necesse.” Cf. Anonymus Cantabrigiensis, ed. Ebbesen, 82: “Scientia enim est demonstrativus [rei] habitus rerum semper vel frequentius similiter se habentium. ‘Habitus demonstrativus’, i.e., demonstrationem comparatus; ‘rerum semper similiter se habentium’ quantum ad mathematicas disciplinas, in quibus doctrinae veritas immutabilis est; “aut frequentius” —hoc totale ad physicam, cuius documenta plerumque fallit medicorum experientia.” 40 Cicero, De inv. I.29.44. 41 The same example is quoted by Anonymus Cantabrigiensis, ed. Ebbesen, 188 (“Omnis mulier quae lac habet cum viro concubuit”). See infra, §6.2, for a very similar example in the Summa Soph El. 42 Cf. supra, §3.4. 43 Anonymus Aurelianensis II, ed. Ebbesen, 32: “Demonstratio igitur ab Aristotele sic describitur: ‘demonstratio est ex primis et veris vel ex talibus quae per prima et vera \eius/ quae circa ipsa sit cognitionis sumunt exordium’.” 44 Anonymus Aurelianensis I, ed. Ebbesen, 51, quotes the same passage (with some variations), clarifying that it is taken from Aristotle’s Topics, but he links it to the definition of syllogism (probably, the demonstrative one): “Quod volens innuere Aristoteles sic describit syllogismum in Topicis (tamen alii volunt quod describat negotium): ‘Demonstratio est

The First Influence of Aristotle’s logica nova

185

the other quoniam (or quia or enim, which “mean the same thing”), and says that the demonstrative propter quid syllogism is described by “Alexander” in these terms: The demonstrative syllogism is made up of primary, true, immediate, ­better-known premises and proximate causes of the conclusion.45 “Alexander”’s definition of propter quid demonstrations is based on the six requirements of APo A 2,46 of which only five are mentioned (“primitiveness” is missing). Each clause of the description is commented on in turn. Demonstrative premises must be true, and this distinguishes demonstrative from dialectical syllogisms (which can have false premises). They must, furthermore, be immediate and primary. The difference between “Alexander”’s two requirements seems to be the following: propositions are “mediate” if they have an origin through which they can be proved (habent exordium per quod possunt probari); the example that follows shows that immediateness has something to do with sense perception: the proposition ignis est calidus is immediate because it is true in virtue of sense perception, though it can also derive inferentially from other propositions; in this sense, it is not primary, for a primary proposition is one that does not derive from other propositions and from which other propositions derive. Later, the Anonymous explains that “Alexander”’s sense of “primary” is not the same as Aristotle’s: for “Alexander” a primary proposition is one that is true in virtue of sense perception, while for Aristotle it is one that cannot be demonstrated. This is confusing: for he has just explained that “immediate” means “true by sense perception,” while now it is “primary” that is so explained. Also, by so doing the two requirements are conflated, as both now refer to indemonstrability.47 Moreover, demonstrative premises must be better known than the conclusion. The example that follows is not fully transparent: si de aequalibus aequalia demas, aequalia sunt quae remanent. The idea seems to be that in this argument the premise is not better known than the conclusion, as it should be quando ex primis et veris vel ex talibus quae per prima et vera suae cognitionis sumpserunt initium fit syllogismus’.” 45 Anonymus Aurelianensis II, ed. Ebbesen, 32: “demonstrativus syllogismus est ex primis et veris et immediatis et notioribus et proximis causis conclusionis.” 46 Cf. supra, §1.6. 47 We saw (supra, §1.6) that in APo A 2, both “primitive” and “immediate” means “indemonstrable” (71b28–29), while in the Anonymous’ “Alexandrian” account, since primitiveness is missing, it is “primary” and “immediate” that mean “indemonstrable” (but only if “­primary” is taken in the Aristotelian and not in this “Alexandrian” sense).

186

chapter 4

in a demonstration. The last requirement is in fact twofold: the premises must not only be causes of the conclusion; they must be proximate causes of the conclusion. No example is offered, but the reference is certainly to Aristotle’s notion of πρῶτον αἴτιον; a non-proximate cause is remote.48 The Anonymous thus follows “Alexander” and takes the “strict” requirements of APo A 2 to characterize propter quid syllogisms. Then, the difference between propter quid and quoniam syllogisms is put in the terms of APo A 13: This way Alexander describes the syllogism of the why, and with this description he suggests that the syllogism of the why occurs wherever the cause proves its effect. The syllogism of the that instead is said to occur wherever the effect proves its cause.49 The reference is probably to the case, examined in sections (ii) and (iii) of APo A 13, in which cause and effect convert and the inference of the effect from the cause is a why-demonstration while the inference of the cause from the effect is a that-demonstration (the “prototypical” that-demonstration of type 1b).50 The Anonymous also observes that one could read somewhere (alicubi) that a syllogism from the effect is no demonstration: this should be interpreted, following “Alexander” (and Aristotle), as meaning that a that-syllogism is a syllogism that is not “simply demonstrative” (demonstrativus simpliciter), as the why-syllogisms. The allusion (alicubi) could well be to the Summa Sophisticorum Elenchorum. Here we read: The effect is demonstrated from the cause, but the cause is not from the effect. Again. We have a demonstration in medicine this way: “If it has lungs, it breathes; but it has lungs; therefore, it breathes,” and it is a demonstration because the lung is the cause of the breathing.

48 49

Anonymus Aurelianensis II, ed. Ebbesen, 32–33. Anonymus Aurelianensis II, ed. Ebbesen, 33: “Sic ergo describitur ab Alexandro syllogismus propter quid, et hac descriptione syllogismus propter quid innuitur esse ubi causa probat effectum. Syllogismus vero quoniam dicitur esse ubicumque effectus probat causam.” 50 Cf. supra, §1.6.1. According to the Anonymus Aurelianensis II, the description of the demonstrative syllogism in the Topics (quoted above) points precisely to this distinction: its first part (ex primis et veris) refers to why-demonstrations, the second part (vel ex talibus quae per prima et vera \ eius / quae circa ipsa sit cognitionis sumunt exordium) to that-demonstrations. Cf. Anonymus Aurelianensis II, ed. Ebbesen, 33–34.

The First Influence of Aristotle’s logica nova

187

But if you say: “If it breathes, then it has lungs; but it breathes; therefore, it has lungs,” there is only a good argument, but not a demonstration.51 The example is an adaptation of the second-figure argument of section (v) of APo A 13.52 There, a “non-proximate” and non-convertible cause was taken (“being an animal”) and from the negation of it the negation of the effect (“not breathing”) was inferred. Here, by contrast, a “proximate” and convertible cause of breathing is taken (“having lungs”), and its occurrence is inferred from the occurrence of the effect (“breathing”). The anonymous author of the Summa also uses the astronomical example of APo B 16: “If the earth opposes the moon, then the moon has an eclipse” (si terra obicitur lune, ergo luna patitur defectum), which again, when reversed, produces a good argument, but not a demonstration. The author appears to know Aristotle’s Posterior Analytics and perhaps also “Alexander”’s commentary on it, with which, however, he evidently does not agree.53 A third example is the lactating woman of APr B 27, even though the link with that chapter may be indirect and may have been mediated by Greek glosses.54 Here, the demonstration starts from the recent conception which causes (and therefore proves) the presence of milk in a woman’s breast: again, if reversed this argument produces a good argument but not a demonstration: lac habet, igitur concepit ex proximo (she has milk, therefore she has just conceived). In all these cases, and notwithstanding the source of the examples used, the author has in mind the prototypical that-demonstration (type 1b) of APo A 13. The Anonymus Aurelianensis I introduces the distinction between two types of demonstration with an overt appeal to “Alexander”: According to this variety of immediate two species of demonstrations are to be distinguished, namely the first criterion and 51

Summa Soph El, 270–271: “De causa ad effectum fit demonstratio, sed de effectu ad causam non. Item. Fit demonstratio in fisica sic: ‘si pulmonem habet, respirat; sed habet pulmonem; ergo respirat,’ demonstratio est, quia pulmo est causa respirandi et anelandi. Si vero dicatur sic: ‘si respirat, pulmonem habet; sed respirat; igitur habet pulmonem,’ bona est argumentatio, sed non est demonstratio.” 52 Cf. supra, §1.6.1. 53 Although, as Ebbesen (1981) has shown, both the author of the Summa and that of the Glose sup. Soph El know the glosses or commentary attributed to “Alexander,” they never mention them explicitly. 54 Regarding a similar example cited by the Anonymus Cantabrigiensis, ed. Ebbesen, 188 (see supra, footnote 41) Ebbesen refers to Philoponus’ τεκμηριώδης δεῖξις; see supra, §2.2. See also the Ps-Philoponus-1, In APr, ed. Wallies, CAG 13.2, 481.6–12, quoted above, §2.5.

188

chapter 4

the second criterion [...] Alexander calls the first criterion “demonstrative syllogism,” and in order to distinguish it from the dialectical one he adds “demonstrative.” The first is therefore said when the cause proves the effect, as when the definition the species, or the species its property; the second instead when the opposite happens. The first derives its priority from the dignity of the term that lies at the basis of the proof with respect to the term that plays a similar role in the second: the cause is in fact the basis of the proof in the first case, the effect in the second; and the cause is by nature prior to the effect.55 The type of that-demonstration that the Anonymus Aurelianensis I has in mind is, again, the prototypical inference of a cause from an effect that is convertible with it (type 1b). It must be so, for only with converting terms both the inference of the cause and the inference of the effect are allowed. A why-demonstration is a demonstrationis primum metrum, a that-demonstration a demonstrationis secundum metrum. Although as we know Alexander of ­Aphrodisias is in all probability at the origin of the distinction between a demonstration in the proper sense (κυρίως) which proceeds from the cause, and a demonstration in a secondary sense which proceeds from the effect,56 the direct source of the Anonymus Aurelianensis I is more likely Philoponus, who in his commentary on the Posterior Analytics presents the distinction in exactly the same terms.57 As said above, it has been hypothesized that Jacob of Venice, translating the Sophistici Elenchi, also collected and translated several scholia taken from Philoponus’ commentary, inspired by Alexander of Aphrodisias (both commentaries on the Sophistici Elenchi are now lost, however) or that he quoted materials used by his contemporary Michael of Ephesus, who had also collected scholia from Philoponus. There is another clue that points towards Philoponus: a little further on the Anonymus Aurelianensis I says that this secondary type of demonstration is more properly called indicium:

55

Anonymus Aurelianensis I, ed. Ebbesen, 42: “Secundum has vero immediatarum v­arietates distinguuntur duae demonstrationis species, scilicet primum metrum, et secundum metrum […]. Metrum itaque appellat Alexander syllogismum demonstrativum, quem ut separet a dialectico adiungit ‘demonstrationis.’ Primum autem dicitur quando causa effectum probat, ut si definitio speciem, species proprium; secundum vero quando sit econverso. Suam autem prioritatem contrahit primum a dignitate termini probantis in respectu illius termini qui probans est in secundo: causa enim est probans in primo, effectus in secundo; causa vero prior est effectu naturaliter.” 56 Cf. supra, §2.1. 57 Cf. supra, §2.3.

The First Influence of Aristotle’s logica nova

189

And again: the second criterion from Aristotle is called “syllogism of the that” or “clue” [...]. “Clue” is said as far as the effect either indicates that the cause is concomitant, as when the presence of the sun signifies the day, or indicates that is past, such as when the scar signifies that there has been a wound.58 Both the examples are of probable Stoic origins,59 but they are here employed to illustrate a case in which cause and effect convert; the inference of the cause from the effect is thus a that-demonstration of type 1b, the only one that Philoponus qualifies as τεκμηριώδης, i.e., as a “demonstration based on a τεκμήριον,” linking it to the first-figure sign-syllogism of APr B 27.60 The term indicium, used by the Anonymus Aurealianensis I to qualify the syllogism of the that, might be the Latin translation of τεκμήριον. The Anonymus Cantabrigiensis does not refer to “Alexander” in his ­exposition of the that/why distinction,61 but like his anonymous colleagues he nevertheless offers some interesting examples while discussing the fallacy secundum consequens. The discussion begins with a complex distinction between different senses of the term consequens which introduces the three modes of the fallacy. (i) In a first sense, consequens is a predicate that is said of a subject as a consequence of the fact that another predicate is said of the same subject and whose negation with respect to a subject follows the negation of another predicate with respect to the same subject: in this sense, animal can be called consequens of homo, because if homo is predicated of something, also animal is predicated of the same subject, and if animal is denied of a subject also homo is denied of the same (as suggested below, consequens in this case is synonymous with totum universale). (ii) In a second sense, one thing is said to be consequens of another if it is its cause (i.e., consequens is a synonym of causa): thus, Aristotle claims that sadness is consequens of anger, because sadness is the cause of anger.62 (iii) In a third sense, consequens is what comes after something else in temporal terms or according to nature, just as every effect is 58

Anonymus Aurelianensis I, ed. Ebbesen, 52: “Item secundum metrum ab Aristotele dicitur ‘syllogismus quia’ vel ‘indicium’ […]. ‘Indicium’ vero eo dicitur quod effectus ­indicat vel causam comitari se, ut diem praesentia solis, vel indicat praecessisse, ut cicatrix ­vulnus adfuisse.” 59 “If it is day, it is light” is a recurrent Stoic example of true conditional proposition, but given the epistemic constraints in Stoic sign theory, not of sign; cf. Sextus Empiricus, Adv Math VIII.251; the scar is a sign of the past wound in Sextus Empiricus, Adv Math VIII.254. 60 Cf. supra, §2.3. 61 Anonymus Cantabrigiensis, ed. Ebbesen, 83. 62 Aristotle, Top Δ 5, 125b28–34.

190

chapter 4

consequens (both temporally and according to nature) with respect to its cause. (iv) In a fourth sense, the proposition that is inferred from or follows another proposition can be called consequens. (v) In a fifth sense, it is consequens what is added to something else (and this also includes the signs, as we shall see).63 According to these senses of consequens, the Anonymous distinguishes four modes of the fallacy which depend on the omission of one of the following relationships between consequens and antecedens: (a) if the universal part64 of something is affirmed, then the universal whole is affirmed, but not vice versa; or if the universal whole of something is denied, then the part of the same is also denied, but not vice versa; (b) if the effect is affirmed, then the cause is affirmed, but not vice versa; (c) if the cause is denied, then the effect is denied, but not vice versa; (d) if a proposition is antecedent to another, the denial of the antecedent is inferred from the denial of the consequent.65 All these relationships can be summarized by the following two principles (maximae): “If the antecedent is affirmed, the consequent is affirmed too” 63

64

65

Anonymus Cantabrigiensis, ed. Ebbesen, 183–184. Anonymus Aurelianensis I, ed. Ebbesen, 134, more expeditiously, distinguishes only three senses: the proposition that follows another proposition (= iv), the predicable (= i), the meaning of the proposition (which corresponds to none of the senses of the Anonymus Cantabrigiensis). By implicitly rejecting all these senses, Anonymus Aurelianensis I holds that in this place Aristotle means by consequens “quod aliud in eadem veritate semper vel frequenter comitatur” (ibidem). Anonymus Aurelianensis II, ed. Ebbesen, 81, does not distinguish different meanings of consequens and simply affirms that we have a fallacia secundum consequens “quando aliquid praedicatur de aliquo vel subicitur alicui, et putamus converti.” Cf. Summa Soph El, 287 and 389. The Fallacie Parvipontane II.10 propose a threefold meaning of consequens: “Consequens adeo large hic sumitur ut omne id consequens dicatur quod sequitur ad aliquid vel ratione consecutionis vel ratione predicationis vel ratione comitantie. Sequitur enim aliquid ad aliud ratione predicationis ut genus ad speciem; similiter et proprium. Sequitur aliquid ad aliud ratione consecutionis, ut in naturalibus ypoteticis, ubi etiam genus ad speciem plerumque sequi ostenditur accidens ad subiectum. Consequitur aliquid ad aliud ratione comitantie, ut mador terre pluviam. Eorum autem que sequuntur ­comitantie ratione, quedam consequuntur semper sua antecedentia, ut terre mador pluviam, partum pallor, fumus ignem, cedere cruor; alia non semper ut esse adulterum ad eum esse errabundum de nocte, vel ad aliquem esse comptum capillos, eum esse adulterum.” (LM I, 603). By “universal part” here the Anonymous means what will later be called “subjective part” (pars subiectiva), that is what a universal, understood as a whole inclusive of what is subordinate to him, is predicated of: in this sense “human being,” “ox,” “horse,” etc. are universal or subjective parts of “animal.” This way we interpret a passage which is far from clear: “si aliqua positio antecedit aliam, dividens antecedentis sequitur ad dividentem inferentis” (Anonymus Cantabrigiensis, ed. Ebbesen, 184), taking divisio in the sense in which Aristotle talks of διαίρεσις (as opposite to σύνθησις) in Aristotle, De int 1, 16a12, 14; 3, 16b24.

The First Influence of Aristotle’s logica nova

191

(posito antecedente ponitur consequens) (corresponding to the modus ponens); and “If the consequent is denied, the antecedent is denied” (destructo consequenti destruitur antecedens) (corresponding to the modus tollens). Finally, the Anonymous specifies that among the adiuncta (case v) we can also consider the relationship between sign and meaning, although between them there is never a temporal succession (nulla potest attendi consequentia), but rather a frequent concomitance (sed quaedam frequens comitantia). Four modes of this fallacy can thus be specified: A. when the part-whole relationship between predicate and subject (= i) is disregarded, as in the following cases: “Every human being is an animal; Brunellus is an animal; therefore, Brunellus is a human being” or “Every human being is an animal; Brunellus is not a human being; therefore, Brunellus is not an animal”; B. when the inference relationships between cause and effect (= ii and iii) are disregarded, as in the following cases: “If there is battle, then there is victory” (pugna est, ergo victoria est) or “There is no victory, therefore there is no battle” (victoria non est, ergo pugna non est); C. when the laws of inference between propositions are not observed (quando non servatur lex consequendi inter propositiones) (= iv) (further divisions are neglected here for the sake of brevity); D. when one considers signs that do not always accompany what they are added to (= v), as in the following cases (which closely concern our theme): “Someone goes around at night, therefore he is an adulterer” or “Someone has dust in his shoes, therefore he walked.” In these cases, there is deception because the adulterer usually goes around at night and this property is added to it as a sign; likewise having dust in one’s shoes is a sign of having walked, but it is not necessary for everything to which the sign is assigned, that also what it is a sign of be assigned, rather the opposite is given, namely that the necessity of inference occurs from what something is a sign of to the sign itself. 66

66

Anonymus Cantabrigiensis, ed. Ebbesen, 186: “‘Iste est errabundus de nocte, ergo iste est adulter’ vel ‘Iste habet pulverem in calceis, ergo iter fecit.’ Inde autem fit deceptio quia solet adulter errare de nocte et habet illud adiunctum ut signum; similiter habere pulverem in calceis signum est itineris, sed non necessarium ut cuicumque conveniat signum ei conveniat id cuius est signum, immo potius videtur econverso quod ab eo cuius est aliquod signum si consequentiae necessitas ad signum.” The first example comes from Aristotle, Soph El 5, 167b9–12, the second from Cicero, De inv. I.30.47.

192

chapter 4

The last two modes of this fallacy (as the Anonymous seems to suggest when he resumes the literal commentary on Aristotle’s text) partially overlap with the two types suggested in the Sophistici Elenchi: the one based on sensation and the one based on discourse. Here the Anonymous follows Aristotle, who first treats of the fallacy deriving from the opinion that the substance of an object is of a certain type, because of its color (i.e., the opinion that something is honey, if it is of a reddish yellow color, rubeum) or that something happened, because some other event that usually accompanies it occurred (i.e., that it rained, because the earth is drenched).67 The second type of fallacy of the consequent is found both in rhetoric and dialectic according to Aristotle: in the first case when one shows that something exists because of what is added (and here are included the cases discussed above); in the second when the law of the conversion of inferences are not respected (and in this regard Aristotle discusses the paralogism by which Melissus of Samos sought to demonstrate the eternity of the world). The fallacies that occur in rhetoric are of particular interest to us. As we noticed,68 the text of the Sophistici Elenchi itself suggests the connection with demonstration, understood here as a demonstration from signs (ἡ κατὰ τῶν σημείων ἀπόδειξις, demonstratio secundum signa), also called “rhetorical demonstration” (demonstratio rhetorica), which Michael of Ephesus called σημειώδης ἀπόδειξις.69 As the Anonymus Cantabrigiensis says, in this case we are dealing with signs that indicate a past, present, or future event from which one can infer probable propositions, in rhetoric, such as “Whoever is elegant is adulterous” (Qui comptus adulter) or “Whoever does not take into account oaths is stingy” (Qui negligit iusiurandum avarus est); or one can infer necessary propositions, in physics and medicine, such as “Every star that does not sparkle is close” (Omnis stella quae scintillat prope est), which is the astronomical example of APo A 13, or “Every woman who has milk has lain with a man” (Omnis mulier quae lac habet cum viro concubuit), which is the “contracted” chain of inferences (from the milk to the intercourse via pregnancy and birth-giving) already used by the Anonymus Aurelianensis II. Unlike what happens in dialectics, in which the signified thing is necessarily accompanied 67

Anonymus Cantabrigiensis, ed. Ebbesen, 186: “Fit autem duobus modis deceptio secundum consequens, sensu sc. et oratione. Sensu ut cum videmus mel omne rub\e/um esse decipimur credentes quod omne rubeum comitetur necessario mel, et ita opinamur aliquod rubeum esse mel quod tamen non est mel. Similiter videntes terram madidam esse opinamur pluisse, quia pluviam solet comitari mador terrae.” Cf. also Anonymus Cantabrigiensis, ed. Ebbesen, 187. 68 Cf. supra, §1.7. 69 Cf. supra, §2.7.

The First Influence of Aristotle’s logica nova

193

by its sign (ubi sc. id cuius signum necessario comitatur signum), in rhetoric the use of signs as premises can produce fallacious arguments, since there is no necessary co-presence of the sign and what is signified (fallax signi et eius cuius est signum comitantia). After offering the adulterer examples of Soph El 5, the Anonymous re-states that in the case of arguments based on signs in order to have a correct inference one should go from what is signified (the cause) to its sign (the effect) rather than the other way around.70 3

Alan of Lille, Simon of Tournai, and the Cause as Sign

Two theologians of the second half of the twelfth century, Alan of Lille and Simon of Tournai, play a particular role in our story, as witnesses of the spreading of the logica nova and of the glosses attributed to “Alexander.” Both are probably part to the so-called “Porretan school,” that is, the pupils and followers of Gilbert of Poitiers,71 and compose the works that concern us here in the 1160s, in the same period in which Aristotle’s Sophistici Elenchi and Prior Analytics start to be commented on with the help of Greek glosses, which we have discussed in the previous section. Like the authors of the treatises on fallacies and the commentaries on the Sophistici Elenchi edited by Ebbesen, the two theologians distinguish the two types of science or demonstration (of the why and of the that) and refer to the same person as to their source: “Alexander.” Although less known than his more illustrious fellow countryman, Simon of Tournai is much more interesting from our point of view. In his Summa “Quoniam homines” (ca. 1160), in the context of a discussion about the definition of theophania,72 Alan of Lille distinguishes two types of demonstration:

70

71 72

Anonymus Cantabrigiensis, ed. Ebbesen, 188: “In rhetoricis enim ita est quod potius ab eo cuius est signum [quam] ad signum, quam econverso, est consequentia.” (We propose a slightly different emendation of the text, so as to make it more consistent with what is said at 186; Ebbesen proposes instead to expunge quam ad signum). Cf. Valente (2006), 18–19, 25–28; on Simon see Siri (2011), 3–36. Alan of Lille, Summa “Quoniam homines,” 144, ed. Glorieux, 282: “Theophania enim dicitur divina manifestatio, a ‘theos’ quod interpretatur Deus, et ‘phanes’ quod interpretatur apparitio. Theophania autem est ex consequentibus signis non ex substantificis geniis mentibus ab ymaginibus defecatis superessentialis et diffinitive originis simpla et reciproca manifestatio”; see also Alan of Lille, Expositio prosae de angelis, in Textes inédits, ed. D’Alverny, 203; Hierarchia Alani, in Textes inédits, ed. D’Alverny, 227–228; and Ralph of Longchamps’ commentary on Alan of Lille’s Anticlaudianus (in Minnis and Scott 1988, 162).

194

chapter 4

Our knowledge of things is of two types: sometimes we know the effect through the cause, as in the case in which the moon is placed between us and the sun, thus we know that the sun is undergoing an eclipse; we know the cause through the effect, as in the case in which the sun undergoes an eclipse, we know that the moon is interposing between us and the sun. As a result, sometimes the effect proves its cause, sometimes the cause proves its effect. This is why Alexander, in his commentary on the Sophistici Elenchi, said that one of the demonstrations is of the why and another of the that: and he calls “demonstration of the why” [the one we have] when the cause proves its effect, “demonstration of the that” [the one we have] when the effect proves its cause.73 Here, again, the reference is to the prototypical that-demonstration of APo A 13 (type 1b), in which a cause is inferred from an effect convertible with it. The standard example is the eclipse of APo B 16. Alan is very accurate in his reference to the source, the “Alexander” of the commentary on the Sophistici Elenchi (Michael of Ephesus), and places this reference within a brief digression about the types of knowledge that can be obtained from the effects. In what follows, Alan maintains that since the cause is not always necessarily known from its effects, sometimes we must rely on some signa consequentia that allow the inference of their cause only in a probable way: just as when I see some ash, I suppose that in that place there was a fire, or if I see dust on someone’s shoes, I suppose he’s been walking.74 Alan goes on to argue that, obviously, God cannot 73

74

Alan of Lille, Summa “Quoniam homines,” 144, ed. Glorieux, 282: “Duplex habetur de re cognitio: aliquando enim per causam habemus notitiam de effectu, ut si luna ponitur inter nos et solem, scimus solem pati eclipsim; per effectum habemus notitiam de causa, ut si sol patitur eclipsim scimus lunam interponi inter nos et solem. Unde aliquando effectus causam, aliquando causa probat effectum. Unde Alexander in commento super librum elencorum ait quod demonstrationum alia ‘ quid,’ alia ‘quoniam’; demonstrationem quid vocans quando causa probat effectum, demonstrationem quoniam quando effectus causam.” Alan of Lille, Summa “Quoniam homines,” 144, ed. Glorieux, 282: “Set non per effectum semper necessaria probatur causa, set aliquando sunt quedam signa consequentia ad rem ut probabiliter rem inferunt, non necessaria; ut si video hic cineres, coniecto fuisse hic ignem; si video pulverem in calceis eius, coniecto eum fuisse itinerarium.” The recurrence of Cicero’s example also in the commentary on the Sophistici Elenchi by the Anonymus Cantabrigiensis may raise the doubt that the previous distinction (that between two types of demonstration) does not derive from the Latin translation of “Alexander”’s lost glosses on the Sophistici Elenchi, but was attributed to such a commentary because it occurs in several commentaries on the Sophistici Elenchi and treatises on fallacies of the same period, where it is invariably connected to “Alexander.” This would imply, however, a dependence of Alan on one of those works, which cannot be proved and must remain a conjecture. The other example (the one about ash as sign of a previous fire) also

The First Influence of Aristotle’s logica nova

195

be known through the cause, but only from the effects, namely from the consequent signs or “from the effects that derive from their cause as following signs” (ex effectibus qui tamquam signa consequentia consecuntur ad causam).75 It seems quite clear that the meaning of consequens in this context coincides with that of an effect that follows its cause both by nature and temporally, which we have seen listed above as sense (iii) by the Anonymus Cantabrigiensis, and not with the one used in logical contexts, i.e., sense (iv) of the same list. Simon of Tournai in the distinctio 6 of his Institutiones in sacram paginam (ante 1170) reports the distinction, again attributed to “Alexander,” between demonstration or science of the why (propter quid) and demonstration or science of the that (quoniam) without referring to any particular work. The mention of this distinction is interesting for two reasons. In the first place, it is presented, like in the Anonymus Aurelianensis I, in the context of a comparison between opinio, fides and scientia, which leads to similar results (although the investigation proceeds from different definitions, as we shall see); in the second place, the distinction is part of a more complex semiotic framework, provided in distinctio 1 of the same work and referred to in distinctio 8 (where Simon discusses sacramental signs). Let us examine these texts in detail. As mentioned, in distinctio 6 the difference between the two types of demonstration—defined according to the criteria that we have seen (the first derives from the causes, the second from the consequent signs or effects) and with reference to “Alexander”76—is crucial for an examination of the relationship between opinion, faith and science. Opinion is defined in two ways: in a first sense it is defined as “knowledge of the thing that derives from causes that precede it only in a probable way (ex causis probabiliter precedentibus) and does not produce assent (citra assensionem, literally: below assent).” Only after having introduced “Alexander”’s distinction concerning science which produces assent, opinion is also defined as “knowledge that moves from signs that follow from it in a probable way (ex signis

75 76

appears in Alexander of Aphrodisias (In APr, ed. Wallies, CAG 2.1, 21.10–23; cf. supra, §2.1), Themistius (In APo, ed. Wallies, CAG 5.1, 5.17–24; 61.6–11; cf. supra, §2.2), Philoponus (In APo, ed. Wallies, CAG 13.3, 49.5–14; 168.24–169.8; cf. supra, §2.3), Ps-Philoponus-1 (In APr, ed. Wallies, CAG 13.2, 49.5–14; 168.24–169.8; 481.45-46; cf. supra, §2.5) and Ps-Philoponus-2 (In APo, ed. Oldin, CAG 13.3, 426.10–20; cf. supra, §2.6). Alan of Lille, Summa “Quoniam homines,” 144, ed. Glorieux, 282. Simon of Tournai, Institutiones in sacram paginam, d. VI.102, ed. Siri, 435: “Si uero perceptio ueritatis est cum assensione ex signis necessario consequentibus dicitur scientia, quod genus scientie dicitur ab Alexandro ‘demonstratio quoniam,’ sicut genus scientie ex causis necessario precedentibus dicitur demonstratio ‘propter quid’.”

196

chapter 4

probabiliter consequentibus) and does not produce assent (citra assensionem).”77 Science had been defined as “knowledge of the truth that moves from causes that precede it in a necessary way and that produces assent”78 and, thanks to “Alexander”’s distinction, also as “knowledge that produces assent moving from signs that follow in a necessary way.”79 Faith is defined here as “knowledge of the thing that produces assent and derives either from causes that precede it in a probable way or from signs that follow it in a probable way.”80 Faith, like in the Anonymus Aurelianensis I, has an intermediate position between opinion (which does not produce assent) and science (which produces assent to truths necessarily demonstrated either from causes or from signs/effects): like opinion it has the ability to infer its own conclusions in a probable way, but since it produces assent to the conclusions, faith is superior to opinion; like science, faith has the ability to produce assent, but it is inferior to science because it infers in a probable way and not necessarily.81 77

Simon of Tournai, Inst., d. VI.102, ed. Siri, 435: “Perceptio uero rei ex causis probabiliter precedentibus citra assensionem dicitur opinio. Ex signis quoque consequentibus percipitur dupliciter: uel ex signis necessario consequentibus uel probabiliter consequentibus. [then the distinction between demonstratio propter quid e quoniam follows, cf. preceding footnote] […]. Si uero citra assensionem sit perceptio ex signis probabiliter consequentibus, dicitur opinio. Si autem perceptio rei cum assensione sit ex causis probabiliter precedentibus uel ex signis probabiliter consequentibus, dicitur fides.” 78 It refers, among other things, to an Aristotelian definition of knowing as “causas rei nosse quare sic et aliter esse non possit,” supposedly taken from Aristotle’s Metaphysics, but very close to the commentaries on the Sophistici Elenchi cited in reference to the Posterior Analytics. Cf. Simon of Tournai, Inst., d. VI.102, ed. Siri, 434–435: “Perceptio ergo ueritatis ex causis necessario precedentibus cum assensione dicitur scientia. Scire enim est, ut ait Aristotiles in metaphisicis, causas rei nosse, quare sic sit et aliter esse non possit.” Before this text he mentioned geometry as an example of this kind of knowledge, where “precedentia necessarie cause sunt consequentium” (434). It is probably a reference to James’ translatio vetustissima (Met A 3, ed. Vuillemin-Diem, AL XXV.1, 11); cf. Siri (2011), 435, app. 79 The first one is obviously the science of the why, the second the science of the that. 80 Cf. supra, footnote 77 81 Simon of Tournai, Inst., d. VI.102, ed. Siri, 435: “Si autem perceptio rei cum assensione sit ex causis probabiliter precedentibus uel ex signis probabiliter consequentibus dicitur fides. Fides igitur media est inter opinionem et scientiam: est enim supra opinionem et citra scientiam. Cum enim opinio commune habeat cum fide, quod sit ex probabilibus, quia tamen opinio est sine assensione, fides uero cum assensione, dicitur opinio esse citra fidem et fides supra opinionem. Cum uero fides id habeat commune cum scientia, quod est cum assensione, tamen quia fides est ex probabilibus, scientia uero ex necessariis, ideo fides citra scientiam et scientia dicitur esse supra fidem.” Slightly earlier he had characterized medicine as a kind of knowledge that proceeds from probable causes (“ut in phisicis,” 434). Very subtly, Simon points out that some scientific conclusions can be matters of faith for someone: “Sed notandum quod alicui est aliquid scientia, quod alii est fides. Verbi gratia: doctus in geometricis, ut Euclides, scit lineam per equalia diuidi.

The First Influence of Aristotle’s logica nova

197

In distinctio 8 (devoted to the sacraments, a locus classicus for scholastic discussions on signs and signification82), Simon also presents the distinction between two types of natural sign: (i) those which are antecedents (i.e., the preceding causes) signifying their consequents (i.e., their effects) and (ii) those which are the consequents signifying their antecedents: Natural occur, for instance, when from the antecedent the consequent is signified, such as the impending rain moving from the morning red, or the antecedent from the consequent, like fire from smoke or ash.83 The example of smoke is of Stoic origins and was also used by Augustine to exemplify natural signs. The example of ash is also in Alan of Lille. Both smoke and ash are signs of fire in the Greek commentaries on the Posterior Analytics.84 Simon’s endeavour is also of interest for the following reasons. In distinctio 1 of the same work, the difference between scientia propter quid and scientia quoniam is implicitly inserted in a complex taxonomy of the modes of signification, which somehow recalls Abelard’s.85 Having distinguished the signification of words from the signification of things, alongside significations that work by substitution (pro re) Simon introduces two types of signification, one of which is explicitly inferential. As suggested by a marginal rubric in several manuscripts, these significations are valid not only in theology, but in all disciplines (in omni facultate).86 The signification of things is divided into two subtypes: signification in re and ex re. The first occurs when something that is Necessarias enim causas probationis preconcipit. Simplex uero aliquis expers geometrie, quia tamen hoc audit affirmare ab Euclide, lineam per equalia diuidi credit, quia notus in arte hoc asserit. Quod ergo a docto scitur a simplice creditur.” 82 Cf. Rosier-Catach (2004). 83 Simon of Tournai, Inst., d. VIII.3, ed. Siri, 515: “Naturalia sunt, ut quando per antecedens significatur consequens, ut rubore matutino imber futurus, uel per consequens antecedens, ut fumo uel cinere ignis.” Cf. Marmo (1997b); Siri (2011), 230. 84 Cf. supra, §§ 2.1, 2.2, 2.3. 85 See supra, §3.3. 86 Here we interpret facultas as a synonym of discipline (although Simon also uses the latter term to indicate the different areas of teaching). Up to that point of distinctio 1, Simon has dealt with the signification of things that finds application only in scriptural interpretation (significatio pro re), from here on he also deals with types of signification (in re and ex re) which, as the non-theological examples suggest, concern all disciplines and as Simon himself suggests at the end of the chapter: “Habent autem locum hec in secularibus d­ isciplinis, in quibus dictis modis, uel in re uel ex re, aliqua intelliguntur” (Simon of Tournai, Inst., d. I.4.2, ed. Siri, 282). However, see the precautions expressed by Siri (2011), 99–100 n. 35.

198

chapter 4

superior to a thing is understood in it (like the genus in one of its species, e.g., animal in homo)87 or something that is added to a thing is understood in it (like a property or an accident in a species, e.g., risibile in homo). Signification moving from things (ex re)—that is, the one that produces inferences—is in turn divided into two subtypes: one based on opposition relationships and one based on succession relationships. The first takes up three of the four types of opposition examined by Aristotle in Cat 10: one can understand (a) something from what is contrary to it (from white one can understand black or from right left, as they are contrary to each other);88 (b) a privation from its disposition (habitus) (from sight one can understand blindness, and vice versa); (c) a relative from its correlative (from father his son: an example that we have already met above in Abelard’s classification).89 The second is made explicit in these terms: Due to the succession relationship in a twofold way: either when the consequent is understood from the antecedent; or when the antecedent is understood from the consequent. The consequent from the antecedent: when the table is laid, this signifies that a meal is going to follow; the antecedent from the consequent: when the table is cleared, this signifies that the meal has been eaten. The consequent from the antecedent and the antecedent from the consequent can be understood in a twofold way: in a probable way, as in the examples just made, or in a necessary way, as from this antecedent “the sun tends to the west” it is understood to follow necessarily that the sun will set; and from this consequent “a woman has given birth” it is understood that it necessarily happened that she had intercourse with a man.90 87 88 89

90

Simon of Tournai, Inst., d. I.4.2, ed. Siri, 282. This subtype of signification produces a kind of knowledge that Simon calls subintellectus or innuitio (ibidem). This type of knowledge is called commemoratio: “cum enim sermo fit de dextera, simul ad memoriam reuocatur sinistra” (Simon of Tournai, Inst., d. I.4.2, ed. Siri, 282). Abelard also spoke of signification based on comitantia or consecutio; see supra, §3.3. Obviously, the fourth type of opposition examined by Aristotle, namely contradiction, is missing from the list: its elimination helps Simon to foster an interpretation of opposition which is ontological and cognitive, and not strictly speaking linguistic. Simon of Tournai, Inst., d. I.4.2, ed. Siri, 282: “Ratione consecutionis dupliciter: uel quando ex antecedenti intelligitur consequens, uel quando ex consequenti intelligitur antecedens. Ex antecedenti consequens, cum prius mensa ponitur comestio sequi significatur; ex consequenti antecedens, ut cum mensa tollitur comestio transacta significatur. Ex antecedenti autem consequens et ex consequenti antecedens intelligitur dupliciter: uerisimilis, ut in dictis exemplis, uel necessario, ut ex hoc antecedenti ‘sol tendit ad occasum’ intelligitur consequi necessario quia sol occidet; et ex hoc consequenti

The First Influence of Aristotle’s logica nova

199

Here we find some of the elements that will return in distinctio 6: the probable inference from either the antecedent or the consequent is called opinio or presumptio or coniectura; the necessary inference from either the antecedent or the consequent is called scientia and, as will be specified in distinctio 6, is divided into scientia or demonstratio propter quid (from the antecedent or the cause) and into scientia or demonstratio quoniam (from the consequent or the effect). In this context signs are not identified only with the effects, as suggested by the Greek commentators of Aristotle and by the first Latin commentators on the Sophistici Elenchi, but they also cover the causes, which thus become susceptible of a prognostic interpretation with respect to their own effects. The widening of the semantic spectrum of signification and signs effected by Simon of Tournai will have important consequences on the classifications of signs developed during the thirteenth century, as we shall see in due course.91 4 Conclusion In twelfth-century logical and theological works there are traces of the ­doctrine, which emerged and consolidated in the late-ancient Greek tradition of the Posterior Analytics, according to which the Aristotelian demonstration of the that is a semiotic inference of a cause from its effect, the effect being a sign of its cause. In the logical domain, the first traces of that doctrine are in some anonymous commentaries on the Sophistici Elenchi (the Commentarium in Sophisticos Elenchos of the Anonymus Aurelianensis I and the Commentarium in Sophisticos Elenchos Aristotelis of the Anonymus Cantabrigiensis) and in a treatise on paralogisms (the De paralogismis of the Anonymus Aurelianensis II). Since a demonstration is a syllogism that produces knowledge, the definition of syllogism (given by Aristotle in the Sophistici Elenchi) and of “knowing” (scire, as opposed to “opinion,” opinio, and “faith,” fides) are discussed in turn. It is in this context that the contrast between why- and that-demonstrations ‘aliqua peperit’ intelligitur necessario quia cum uiro concubuit.” A further mode of this kind of signification is the one that allows to understand something eternal moving from what is temporal as a consequent with respect to its antecedent; cf. Inst., d. I.4.2, ed. Siri, 283: “ut ex creaturis intelligitur creator… Hec autem intelligentia, cum ex creatis increatum, ex temporalibus intelligitur eternum, dicitur ‘anagoge’, ab ‘ana’ quod est sursum et ‘goge’ quod est ductio eo quod mens preconceptis creatis inferioribus sursum erigatur ad inuestigandum superiorem creatorem. Hoc genere ex consequenti intelligitur antecedens, neque enim ex antecedenti aliquo intelligi possit, quia omnia antecedit. Nihil enim superius supremo.” 91 See infra, Chapter 7.

200

chapter 4

typically emerges. Like in the Greek commentators, the former are demonstrations in the primary and proper sense, the latter only in a secondary and improper sense. The Anonymus Aurelianensis I explicitly associates the demonstration of the that with the indicium, the (deductively valid) sign of a concomitant cause. A typical place for a discussion of semiotic demonstrations is the chapter on the fallacy of the consequent, one of whose species are precisely the demonstrations from signs that are used in rhetoric. In his commentary, the Anonymous of Cambridge offers both rhetorical and medical examples, which respectively illustrate the inference of probable and necessary conclusions from signs. All of this, and many of the examples used by the three anonymous authors, betrays some knowledge and familiarity with the Greek tradition of the Posterior Analytics, which reaches the commentaries on the Sophistici Elenchi of the twelfth century in the form of glosses of Greek origin on the works of the logica nova. Similar traces of that doctrine are detectable in the theological domain, too. Alan of Lille, in his Summa “Quoniam homines” (about 1160), distinguishes two types of demonstration and links the second of these, the demonstration of the that or from the effect, to sign-inferences. Likewise, Simon of Tournai, in his Institutiones in sacram paginam (written before 1170), refers to the Aristotelian distinction between why- and that-demonstrations in the context of his general classification of signs. Not only does Simon distinguish among natural signs those in which an antecedent is a sign of a consequent and those in which a consequent is a sign of an antecedent; he also draws a parallel between these and the two species of demonstration, thus allowing for, so to speak, sign-demonstrations of the why (from cause to effect) and sign-demonstrations of the that (from effect to cause). Some of the examples used by Simon also echo the Greek tradition of the Posterior Analytics.

CHAPTER 5

Demonstration through Signs in Thirteenth-Century Commentaries on the Posterior Analytics Some of the works that we have mentioned in the previous Chapter had already disappeared at the beginning of the thirteenth century; among these, the commentary on the Sophistici Elenchi by James of Venice,1 the commentary or the glossae on the Posterior Analytics and the Sophistici Elenchi attributed to Alexander of Aphrodisias, and the so-called Commentum graecum on the Prior Analytics. Quotations from these works found in thirteenth-century commentaries on the logica nova are most often second-hand quotations, with the likely exception of Robert Grosseteste.2 Arabic commentaries and epitomes, also heavily influenced by the Greek tradition, progressively become an indispensible instrument for teaching Aristotle: Themistius’ paraphrase on the Posterior Analytics is transmitted to the Latin West in the translation from the Arabic of Gerard of Cremona and is already in use in the 1230s. Avicenna’s writings, especially the Libri naturales, become influential in psychological literature a bit earlier: John Blund’s Tractatus de anima (ante 1204) is probably the first to have used Avicenna’s Liber sextus de naturalibus, which as we shall see below,3 will contribute, together with other texts translated from the Arabic, to shape the debate about knowledge through signs. The Latin translations of the logica nova have been discussed at the beginning of Chapter 4. We should now say something about the commentaries. The Sophistici Elenchi are commented with continuity since the twelfth century.4 The first Posterior Analytics commentaries are from the 1230s and 1240s (Robert Grosseteste and Robert Kilwardby), while the first Prior Analytics commentary in the thirteenth century is with all probability that by Kilwardby (1240s). New introductions to logic are written in those and in the following years: Peter of Spain’s Tractatus, known as the Summulae logicales, are probably composed 1 We shall see (infra, §5.3) that James’ commentary on the Sophistici Elenchi might have been still available to Albert the Great around the middle of the century. 2 Cf. Rossi (1978); Ebbesen (2015), 17. Grosseteste’s commentary on the Posterior Analytics is discussed in §5.1. 3 See infra, §5.1. 4 See infra, Chapter 6. © koninklijke brill nv, leiden, 2023 | doi:10.1163/9789004546974_007

202

chapter 5

during the 1230s in Northern Spain;5 they first spread in South France and then in Paris and Italy.6 Next follow the Summa Lamberti by Lambert of Lagny (or Auxerre) (1240s) and the Summulae dialectices by Roger Bacon (1240s–1250s). Peter of Spain’s Tractatus are quite successful handbooks for the teaching of logic at the university; they become object of commentary quite soon (already in the 1240s) in Southern France and from the 1280s also in Paris (and then in Bologna after the Parisian model).7 Peter of Spain devotes one treatise to the loci (Tract. V) and one to the fallacies (Tract. VII): commentaries on both will contribute to the debates on signs and semiotic demonstrations. At the end of the 1260s two other Latin translations of Aristotle enter the picture: the Politics and especially the Rhetoric (while the Poetics remains poorly known and scarcely commented8): in the only literal commentary on the Rhetoric, that of Giles of Rome, one finds ideas and examples that connect it to the commentaries on the Posterior Analytics and the Sophistici Elenchi. The present Chapter is divided into five sections, each devoted to one of the five main commentators of the Posterior Analytics in the thirteenth century:9 Robert Grosseteste (§5.1), Robert Kilwardby (§5.2), Albert the Great (§5.3), Thomas Aquinas (§5.4), and Giles of Rome (§5.5). §5.3 also contains an overview of the Arabic doctrine of sign-inferences. 1

Robert Grosseteste

Unlike the Prior Analytics, which as we saw become object of commentary already at the end of the twelfth century, the Posterior Analytics were considered too difficult or too poorly translated to become the object of teaching and commentary. According to Roger Bacon, Edmond of Abingdon had been the first to comment on the Sophistici Elenchi at Oxford, while a no better-specified magister Hugo, whom Bacon had met and whose notes he read,10 had been the 5 6

Cf. de Rijk (1972). See also infra, Chapter 6, footnote 10. Cf. de Rijk (1968); de Rijk (1969); de Rijk (1970); Maierù (1992); Ebbesen and Rosier-Catach (2000); Ebbesen (2021). The Summulae logicales and the commentaries thereon are examined in Chapter 6. 7 See infra, §6.1.3. 8 Cf. Dahan (1980). 9 See Longeway (2005) for a general overview on medieval theories of demonstration. 10 “Etiam logicalia fuerunt tarde recepta et lecta. Nam Beatus Edmundus Cantuariensis Archiepiscopus primus legit Oxonie librum elencorum temporibus meis; et vidi magistrum Hugonem, qui primo legit librum posteriorum et verbum eius conspexi” (Compendium studii theologiae I.14, ed. Maloney, 46; cit. in Rossi (1981), 14–15 n. 17).

Demonstration through Signs in 13th-Century Commentaries

203

first to comment on the Posterior Analytics. While the dating of the teaching of Edmond of Abingdon (then Bishop of Canterbury) is between the end of the twelfth century and the 1230s, we possess no further information about Hugo and his teaching of the Posterior Analytics. Therefore, as justly observed by Pietro B. Rossi, one can only infer from Bacon’s testimony that “between the end of the twelfth and the beginning of the thirteenth century Oxford was sensible and open also to the new texts of logic.”11 It is in this context that Robert Grosseteste, magister at Oxford during the first decades of the thirteenth century, produces a full-scale commentary on the Posterior Analytics. Robert’s is the oldest Latin commentary on the Posterior Analytics that has reached us. It was probably composed slightly before 1230, “namely before the time when Averroes’ recently translated works begun to spread,”12 since there is no trace of Averroes in Robert’s commentary. ­René-­Antoine Gauthier dates it to the years 1229–1235.13 The commentary is peculiar, perhaps even unique in its kind. It is not a proper literal commentary (the translation used is that by James of Venice, translatio Iacobi); it condenses some parts and ignores others; the conclusions of each chapter are however regularly exposed and numbered.14 It is likely that Grosseteste had access to a copy of the translation of (parts of) Philoponus’ commentary made by James, as it is evidenced by a comparison of several passages in both commentaries.15 He also makes frequent use of Themistius’ paraphrase, which Gerard of Cremona had translated from the Arabic and which was in circulation together with Gerard’s own translation of the Posterior Analytics.16 Given Grosseteste’s sources, one would expect that he would develop or at least consider seriously the Greek understanding of the demonstratio quia as a sign-inference. This is not the case, however. What we find is rather a sort of removal of the semiotic nature of this kind of demonstration. Such removal begins with Grosseteste and would settle with subsequent commentators. Let us start by looking at the passages of the “canonical” interpretation of the demonstratio quia as a sign-inference. 11 12 13 14 15 16

Rossi (1981), 15. Cf. also Ebbesen (1977), 4–9, in connection with Grosseteste on the S­ ophistici Elenchi, to which we return below (infra, §6.2). Rossi (1981), 17. Gauthier (1989), 57*. See Ebbesen (1993), 143–144, where Robert’s commentary is described as a “Literal ­Commentary without Principles.” Cf. Rossi (1978); Ebbesen (1990c), 117–118; Ebbesen (2008c), 194–196; Ebbesen (2015), 17. Cf. Robert Grosseteste, Commentarius in Posteriorum Analyticorum libros, ed. Rossi, 409 (apparatus; works cited).

204

chapter 5

Robert offers no explicit comment on APo A 6, 75a31–34, which as we know contains the first mention of sign-inferences in the Posterior Analytics.17 Yet in I.6, corresponding to APo A 6, he offers a fourfold taxonomy of syllogisms which reflects and reinterprets, though it does not fully cohere with, the twofold distinction between why- and that-demonstration that Aristotle draws in APo A 13. It will be recalled that in that context Aristotle says that within the same science the distinction between “knowledge of the why” and “knowledge of the that” is twofold, according as to whether the syllogism is not from immediates (μὴ δι᾽ ἀμέσων) or whether it is from immediates (δι᾽ ἀμέσων) . Our conjecture, it will be recalled, was that the expression δι᾽ ἀμέσων has some extensional import: Aristotle may have used this expression to differentiate convertible (“immediate”) and non-convertible (“not immediate”) terms. In any case, we argued, our extensional interpretation of the first part of APo A 13 is independently plausible. The result of our analysis was a fourfold classification of demonstrations: when cause and effect convert and the syllogism is “from immediates” (the case introduced in section (ii) and illustrated in section (iii) of APo A 13), the demonstration is of the why if the effect is inferred from the (primary, i.e., convertible) cause (1a) and is of the that if the (primary, i.e., convertible) cause is inferred from the effect (1b); this latter is the “prototypical” demonstration of the that. When the cause is more extended than the effect and the syllogism is “not from immediates” (the case introduced in section (i) and further discussed and illustrated in sections (iv) and (v) of APo A 13), the demonstration is of the that if the (non-primary, i.e., non-convertible) cause is inferred from the effect (2a) and is also of the that if the negation of the effect is inferred from the negation of the (non-primary, i.e., non-convertible) cause (2b). The case of an effect more extended than the cause is not considered by Aristotle.18 It will also be recalled that in commenting on APo A 6 Philoponus offers a typology of demonstrations that differs from Aristotle’s and which is substantially the same as the one Philoponus provides, later in the commentary, in analyzing sections (ii), (iii) and (iv) of APo A 13. We called “Aristotelian” the typology of APo A 13 and “Philoponean” the typology of Philoponus’ commentary on APo A 6 and on the second part of APo A 13. The difference between the two is that the Aristotelian typology is based on two extensional cases (converting cause and effect, which gives rise to arguments of types 1a and 1b, and cause more extended than the effect, which gives rise to arguments of types 2a and 2b, while effects more extended than their causes are excluded), while the Philoponean typology is based on three extensional 17 Cf. supra, §1.7. 18 Cf. supra, §1.6.1.

Demonstration through Signs in 13th-Century Commentaries

205

cases (converting cause and effect, corresponding to arguments of types 1a and 1b in the Aristotelian typology, cause more extended than the effect, corresponding to argument of type 2a in the Aristotelian typology, and effect more extended than the cause, with no corresponding argument in the Aristotelian typology). The typology of demonstrations that Grosseteste provides in his commentary on APo A 6 is Philoponean. Like Philoponus, Grosseteste does not say explicitly that “mediate” and “immediate” are to be taken extensionally, but the examples that he makes, substantially identical to Philoponus’, can only be interpreted extensionally. It is worth quoting the passage from I.6 in full: it is necessary for the knower to have a syllogism from necessary , whether he knows the that through mediate or through immediate or whether he knows the why through mediate or through immediate . Both syllogisms can indeed be both mediate and immediate, although that is properly said syllogism of the why which demonstrates through an immediate cause, and not only that is said syllogism of the that which shows through the effect, but that which shows through a mediate cause. Yet if those that show through the effect are called syllogisms of the that and those that show through the cause are called syllogisms of the why, both show both through mediates and through immediates. The syllogism of the that from mediates is this: the moon casts no shadows; planets that cast no shadows are eclipsed; hence the moon is eclipsed. The syllogism of the that from immediates is this: when the moon is full it casts no shadows; when the moon is full and casts no shadows, it is eclipsed; hence, the moon is eclipsed. The syllogism of the why from mediates is this: the moon is in line with the sun; that which is in line with the sun is eclipsed; hence, the moon is eclipsed; The syllogism of the why from immediates is this: when the moon is in line with the sun the earth is interposed; when the earth is in line with the sun and the earth is interposed the moon is eclipsed; hence, the moon is eclipsed.19 19

Robert Grosseteste, Comm. in APo I.6, ed. Rossi, 133–134: “[…] oportet scientem habere sillogismum ex necessariis sive ipse sciat quia per mediata vel per inmediata, sive sciat propter quid per mediata vel per inmediata. Uterque enim sillogismus est tam mediatus quam inmediatus, licet proprie dicatur sillogismus propter quid qui demonstrat per causam inmediatam, et dicatur sillogismus quia non solum qui ostendit per effectum, sed qui ostendit per causam mediatam. Sed si dicatur sillogismus quia omnis qui ostendit per effectum et sillogismus propter quid omnis qui ostendit per causam, erit uterque tam ostendens per mediata quam per inmediata. Sillogismus quia mediatus est iste: luna

206

chapter 5

The examples are the very same as we find in Philoponus and are susceptible of the very same analysis.20 When the cause is convertible with the effect, the syllogism is “from immediates” or inmediatus; in this case, the cause or the effect that is the middle term in it is also said to be “immediate” (causa i­ nmediata, effectus inmediatus). When the cause is not convertible with the effect, the syllogism is “from mediates” or mediatus, and the cause or the effect that is the middle term in it is also said to be “mediate” (causa mediata, effectus mediatus). When the cause is more extended than the effect, the syllogism is quia mediatus (from the effect to the cause); in this case, no syllogism propter quid mediatus (from the cause to the effect) would be valid. When the effect is more extended than the cause, the syllogism is propter quid mediatus (from the cause to the effect); in this case, no syllogism quia mediatus (from the effect to the cause) would be valid. As it should be evident, besides its almost verbatim correspondence to Philoponus’ taxonomic passage ad APo A 6, it is the explicit consideration of a syllogism propter quid mediatus deriving from a more extended effect that renders Grosseteste’s typology Philoponean; none of the four arguments discussed by Aristotle in APo A 13 (1a, 1b, 2a, 2b) corresponds to Grosseteste’s syllogism propter quid mediatus. The only antecedent of Grosseteste’s syllogism propter quid mediatus is in Philoponus.21 In this passage Grosseteste offers two terminological alternatives: either the sillogismus propter quid is only that which proceeds from an immediate cause, and the sillogismus quia is anything that does not proceed from an immediate cause (whether from a mediate cause or from an effect, mediate or immediate); or the sillogismus propter quid is any syllogism proceeding from a cause and the sillogismus quia any syllogism proceeding from an effect, with the mediate/immediate distinction applying to both. A.C. Crombie thought that Grosseteste would accept the second alternative.22 Yet that Grosseteste’s position is rather to be identified with the first alternative (sillogismus propter quid is only the syllogismus propter quid inmediatus, i.e., that which proceeds from an immediate cause) is shown by Grosseteste’s examination of the

umbram non facit, planeta umbram non faciens deficit, ergo luna deficit. Sillogismus quia inmediatus est iste: plena luna cum sit, umbram non facit, non faciens umbram in plenilunio deficit, ergo luna deficit. Sillogismus propter quid mediatus est iste: luna secundum diametrum est cum sole, secundum autem diametrum cum sit deficit, luna igitur deficit. Sillogismus propter quid inmediatus: luna cum sit secundum diametrum a sole obicitur ei terra, ex obiectu autem deficit luna, ergo luna deficit.” 20 Cf. supra, §2.3. 21 Cf. Rossi (1978), 437–438. 22 Crombie (1953), 53.

Demonstration through Signs in 13th-Century Commentaries

207

“official” presentation of the contrast between demonstrations quia and propter quid, i.e., APo A 13. Here Robert limits the demonstration propter quid to that which proceeds through a proximate cause and calls anything a demonstration quia which does not proceed from a non-proximate cause: The science that is acquired through demonstration either is acquired through a proximate cause of the thing that is known or is acquired not through the proximate cause of the thing that is known. That which is acquired through the proximate cause is called “science of the why,” and this science is said to be such to the highest degree and most properly, and the demonstration through which this science is acquired is the demonstration at its highest degree. That which is not through a proximate cause is called “science of the that,” and this is said to be science in a secondary sense, and the demonstration through which this is acquired is said to be a demonstration in a secondary sense. […] since either the science of the that is acquired through that which is not a cause or is it acquired through a non-proximate cause.23 Given what we know of Grosseteste’s sources, there can be little doubt that the contrast here drawn between a “paramount” (maxime) demonstration and a demonstration “in a secondary sense” (dicta per posterius) is an echo of the contrast between κυρίως and δευτέρως demonstrations that we find in Alexander, Themistius, and Philoponus.24 There follows a discussion of sections (ii), (iii), (iv), and (v) of APo A 13 which adheres to Aristotle’s argumentation and examples quite closely.25 That causa proxima and causa remota in this context (I.12, ad APo A 13) have to be taken in the same sense as causa inmediata and causa mediata in I.6 (ad APo A 6), i.e., as referring to the co-extensiveness or 23

Robert Grosseteste, Comm. in APo I.12, ed. Rossi, 189: “Scientia itaque acquisita per demonstrationem aut est acquisita per proximam causam rei scite aut est acquisita non per proximam causam rei scite. Que autem est acquisita per proximam causam vocatur scientia propter quid, et hec est scientia maxime et propriissime dicta, et demonstratio qua hec scientia acquiritur est maxime demonstratio. Illa autem que non est per proximam causam dicitur scientia quia, et hec est scientia dicta per posterius, et demonstratio qua hec acquiritur est demonstratio dicta per posterius. […] quia scientia quia aut est acquisita per non causam aut est acquisita per non proximam causam.” 24 Cf. supra, §§2.1, 2.2, 2.3. 25 The passage contains an interesting optical explanation of why stars twinkle (Comm. in APo I.12, ed. Rossi, 190–192), also used by Kilwardby (cf. infra, §5.2).

208

chapter 5

non-coextensiveness of cause and effect, is shown by the use of these expressions in Grosseteste’s analysis of the second-figure argument of section (v) of APo A 13. Thus, when the cause is proximate to, i.e., co-extensive with, the effect, two arguments are possible, one propter quid (from cause to effect) and one quia (from effect to cause); these correspond to the syllogism propter quid inmediatus and the syllogism quia inmediatus of I.6, which in turn correspond to demonstrations of types 1a and 1b of APo A 13, respectively. The two astronomical examples of APo A 13 illustrate this first division. When the cause is non-proximate to, i.e., non-coextensive with, the effect, since the cause cannot be less extended than the effect, but at least as extended as that (cum causa non possit esse in minus quam causatum, sed in eque vel in plus),26 either the cause is inferred from the effect (as declared in section (iv) of APo A 13) or the negation of the effect is inferred (in the second figure) from the negation of the cause (as declared and illustrated in section (v) of APo A 13); these correspond to that-demonstrations of types 2a and 2b of APo A 13, respectively, and both also corresponds to the syllogism quia mediatus of I.6. Non-breathing walls illustrate the latter case (2b). It is evident that here the typology that Grosseteste has in mind is Aristotelian, not Philoponean: when he says scientia quia aut est acquisita per non causam aut est acquisita per non proximam causam, he does not explain, as he should have done if he had a Philoponean typology in mind, that the non causa (i.e., the effect) can be either proxima or non proxima. And the possibility of a non proxima non causa, i.e., of an effect that is more extended than the cause, is explicitly excluded when he says that causa non possit esse in minus quam causatum. He did consider this case in his commentary on APo A 6: it is the case in which a syllogism proper quid mediatus can be constructed in which the effect is inferred from a cause that is less extended than it; Philoponus’ and Grosseteste’s example of this argument is the inference of the lunar eclipse (considered as cause) from the fact that the moon is not casting shadows (considered as effect), in which “not casting shadows” is more extended than the cause (like in the paleness example of APr B 27). But in I.12 this kind of argument is not taken into account. Grosseteste’s fourfold typology in I.12 is Aristotelian, the one in I.6 Philoponean. Unlike Philoponus, Grosseteste makes no association in either I.6 or I.12 between demonstrations quia (of whatever type) and sign-inferences. The same is true of Robert’s comments on APo B 16, where Aristotle discusses the reciprocity of cause and effect: when there is such reciprocity, the inference of the effect through the cause is a demonstration propter quid, the inference of 26

Robert Grosseteste, Comm. in APo I.12, ed. Rossi, 193.

Demonstration through Signs in 13th-Century Commentaries

209

the cause through the effect a demonstration quia.27 The example is the lunar eclipse of APo B 16 itself, already used by Alexander and its Greek successors.28 No mention of signs or sign-inferences is made in this context. Grosseteste’s silence about the semiotic aspect of demonstrations quia is also manifest in his comments on the second and last passage of the Posterior Analytics containing a mention of sign-inferences: APo B 17, 99a1–4. It will be recalled that APo B 17 as a whole is devoted to the question whether there may be different causes of an attribute belonging to different things. Aristotle’s initial answer is that if the demonstration is καθ᾿αὑτό it is not possible and the cause must be unique, while if the demonstration is not καθ᾿αὑτό but κατὰ σημεῖον ἢ συμβεβηκός, then it is possible and the cause may not be unique.29 All Latin translations render Aristotle’s μὴ κατὰ σημεῖον ἢ συμβεβηκός at APo B 17, 99a3 as “non secundum signum aut accidens,”30 and we find a similar rendering into Latin in Gerard’s translation from the Arabic: “non secundum semitam signi et accidentis.”31 In II.5 Grosseteste departs from current translations and renders σημεῖον as “effectus” rather than as “signum”: After that [i.e., after the discussion about the mutual inferability of cause and effect] he returns to the second part of the question and inquires whether or not the cause of the same predicate with regard to all its subjects is not the same but multiple. And he answers: if the demonstration is per se and not through an effect or an accident, then it is not possible that the cause is the same, because the middle term either is absolutely the definition of the major extreme or because it is in its primary subject.32 27

Robert Grosseteste, Comm. in APo, II.5, ed. Rossi, 393 “Cum vere sint simul causa et causatum, dico, dubitabit aliquis si ex causato sequitur causa sicut ex causa sequitur causatum, velut ex terram esse in medio sequitur lunam deficere, quod si est, scilicet, conversio [convenientie] inter causam et causatum, tunc contingit utrumque demonstrari per reliquum, […] manifestum est quod altera demonstratio erit per causam et propter quid, reliqua vero per effectum et quia, sicut qui demonstrat de luna quod deficit per interpositionem terre, demonstrat per causam et propter quid; qui autem demonstrat interpositionem terre per defectum, demonstrat per effectum et quia.” The reading convenientie is a conjecture of the editor, because the manuscripts are indecipherable (conūe o conmē). The passage makes good sense even without it. 28 Cf. supra, §§2.1, 2.2, 2.3. 29 Cf. supra, §1.7. 30 Translatio Iacobi, AL IV.1–4, 101.15–16; translatio Ioannis, AL IV.1–4, 179.27–28. 31 Translatio Gerardi, AL IV.1–4, 277.15–16. 32 Robert Grosseteste, Comm. in APo, II.5, ed. Rossi, 394: “Post hoc redit ad hanc secundam partem questionis querens an contingat non eandem esse causam sed plures eiusdem predicati in omnibus subiectis aut non. Et respondet: si est demonstratio per se et non per effectum aut accidens, tunc non potest esse non eadem causa, quia medium est ratio

210

chapter 5

In one sense, the rendering of Aristotle’s σημεῖον at APo B 17, 99a3 as “effectus” rather than as “signum” is only possible on the basis of the idea that a demonstration from the effect to the cause can be identified with a d­ emonstration from a sign, which as we know characterizes the whole Greek tradition of the commentaries on the Posterior Analytics. Without such identification, the decision to turn the signum into an effectum is unconceivable. But at the same time, and for the very same reasons, Grosseteste’s lexical choice is a ­further indication of the obliteration of the semiotic dimension of demonstrations quia that characterizes his commentary. The obliteration is not complete, however. Besides the use of the term “­signum” in particular argumentations,33 there is an occurrence of it in the second book of Grosseteste’s commentary that suggests that after all for him an effect is a sign of its cause, as it certainly was for the Greek commentators. In II.2 Grosseteste devotes some pages to explain the XIII conclusio according to which “per quid est scimus si est simpliciter.” Here Aristotle’s famous example and argumentation about the lunar eclipse is used as an illustration.34 In the syllogism that infers that the moon is eclipsed because it is subject to the interposition of the earth, the effect (eclipse) is inferred from a cause co-­ extensive with it (interposition), and thus the argument qualifies as a demonstration propter quid. By contrast, in the syllogism that infers that the moon is eclipsed because it casts no shadows during full moon, the cause (eclipse) is inferred from an effect that is co-exstensive with it (casting no shadows during full moon), and thus the argument qualifies as a demonstration quia inmediata (or that-demonstration of type 1b).35 All of this accords with Grosseteste’s

maioris extremitatis simpliciter aut in quantum est in subiecto suo primo” (emphasis ours). The Latin expression per se translates Aristotle’s καθ᾿αὑτό. 33 “Probatio per signum: et signum huius est [etc…]” The use of the probatio per signum is parallel to the expression σημεῖον δέ which in classical authors introduces a proof of an anticipated conclusion: see Perilli (1991), 156 n.13. 34 Cf. Aristotle, APo B 8, 93a30–35. 35 Cf. Robert Grosseteste, Comm. in APo II.2, ed. Rossi, 333–334, where Aristotle’s argumentation is followed quite closely: “Huius autem explanatio per exemplum est talis. Cum causa defectus lune sit interpositio terre secundum lineam rectam inter solem et lunam, querere an defectus sit vel an luna sic deficiat, est querere sicut medium an oppositio terre sit secundum lineam rectam inter solem et lunam; et hoc est querere diffinitionem defectus. Deficere namque est habere umbrosum interpositum quod prohibeat r­ eceptionem illuminationis […] sicut cum scimus quod luna deficit propter hoc quod in plenilunio non proicit umbram; cum tamen nichil sit medium quod interpositum est inter nos et lunam per quod prohibeatur eius illuminatio a terra, scimus solum quod deficit et nondum ­scimus propter quid.”

Demonstration through Signs in 13th-Century Commentaries

211

extensional analyses in I.6 and I.12. At this point Grosseteste makes the following observation: The above mentioned middle, through which we know that the moon is eclipsed, does not express the cause, but only a sign; that the moon during full moon does not project any shadow of things onto the surface of the earth, even though the air between us and the moon is clear and no cloud is interposed, is a sign of the eclipse and not its cause; rather it is because it is eclipsed that it cannot project any shadow.36 Here Robert clearly assimilates the convertible effect to the sign and considers it as the middle term in a demonstration quia of type 1b (quia inmediata). The very same identification between effect and sign that surfaces negatively in II.5 (because there the signum is turned into an effectus) emerges here positively (because here the effectus is turned into a signum). Whether this should induce us to a “semiotic” reading of the other passages in his commentary where no such assimilation is made, and in general of the distinction between the two kinds of demonstration, is hard to say. His rendering of Aristotle’s σημεῖον at APo B 17, 99a3 as “effectus” rather than as “signum” is a clear indication that such semiotic reading would constitute an overinterpretation. On the other hand, the occurrence of “signum” just examined shows that the “removal of the sign” is not complete in Grosseteste’s analysis of scientific demonstration.37 However incomplete, such removal will markedly influence all subsequent commentaries on the Posterior Analytics. We conclude this section on Robert Grosseteste’s commentary on the Posterior Analytics with an analysis of his discussion about the distinction between scientia and other lower forms of knowledge, such as opinio and fides, a discussion which contains echoes of earlier debates in theology and logic about degrees of knowledge.38 We also examine Grosseteste’s use of the word intentio, which marks his dependence on Avicenna. The term opinio, Grosseteste 36

Robert Grosseteste, Comm. in APo II.2, ed. Rossi, 334: “Medium autem supra dictum quo scimus quia luna deficit non dicit causam, sed signum solum; quod enim luna in hora plenilunii non facit umbram rerum erectarum super superficiem terre, cum tamen aer sit purus inter nos et lunam et non sit nubes interposita, signum est defectus et non causa, immo quia deficit ideo non potest umbram facere.” 37 Umberto Eco spoke of the “removal of the sign” from the history of philosophy in Eco (1997) (the article was written at the end of the 1980s, when research into the history of semiotics had just begun), which was then followed by Manetti (1992). See also Marmo (2017) for some critical observations on the topic. 38 See supra, §4.2.

212

chapter 5

explains, has three senses: a common sense (communiter), a proper sense (proprie), and a more proper sense (magis proprie). In its common sense, the term indicates any knowledge that is accompanied by assent (cognitio cum assensu); in this sense it is equal to fides and has a greater generality than science and opinion in the proper and more proper senses, being the genus of which these are the species.39 In the proper sense, opinio is the acceptance of a part of a contradiction accompanied by the fear of the other part (cum timore alterius):40 taking the objects of cognitive states (designed by the term opinio) as equivalent to propositions (to which assent may or may not be given), opinion in the proper sense is the knowledge associated with a proposition which contradicts another proposition, to which assent is given in a manner that is not entirely free from doubts, so that one is thus led to fear or suspect that the c­ ontradictory proposition may be true. In this sense opinion differs from science, and one and the same content may be the object of opinion and of science, not for the same knowing subject but for different knowing subjects.41 In the more proper sense opinio is the acceptance of a true contingent proposition as such, and in this sense what is the object of science cannot be the object of opinion.42 As Robert later explains, the difference between opinion in the proper sense and opinion in the more proper sense consists in that the former does not perceive material and mutable things in their essential purity, but it mixes them up with their images (phantasmata): it is like when someone who is affected by jaundice or by an excess of bile (cholericus) thinks that all visible things have a yellowish 39

40

41

42

Robert Grosseteste, Comm. in APo I.19, ed. Rossi, 278: “opinio tripliciter dicitur, communiter, scilicet, proprie et magis proprie. Opinio autem dicta communiter est cognitio cum assensu, et sic est idem quod fides, et secundum hoc opinio est genus scientie et opinionis proprie et magis proprie.” Subsequent attestations of this definition of opinio (about which see Porro 2015) depend on Avicenna (Liber de anima seu sextus de naturalibus) and on Isaac Israeli, who in turn depends on Avicenna. The dependence is indicated by the use of the term formido instead of timor (cf. Porro 2015, 210 n. 2). The substitution may suggest either a second-hand knoweldge of Avicenna or a quotation from memory from Avicenna, whose De anima was already in circulation and exerted a certain influence upon the development of ­psychology. Robert Grosseteste, Comm. in APo I.19, ed. Rossi, 278–279: “Opinio vero proprie dicta est acceptio unius partis contradictionis cum timore alterius, et secundum hoc non est scientia opinio. Tamen secundum hoc idem est scibile et opinabile, quia nichil prohibet quin necessarium scibile credatur, cum suspicione tamen quod contradictio eius possit esse vera; sed secundum hoc non est possibile ut idem homo sciat et opinetur simul unum et idem, sed unum et idem est scibile et opinabile simul a diversis.” Robert Grosseteste, Comm. in APo I.19, ed. Rossi, 279: “Magis proprie vero dicitur opinio acceptio veri contingentis in quantum huiusmodi, et secundum hoc non est idem scibile et opinabile.”

Demonstration through Signs in 13th-Century Commentaries

213

color (iudicat omnia visa citrina). By contrast, opinion in the more proper sense corresponds to the vision of material and mutable things, perceived in their material conditions, but in as much as they are mutable.43 Science differs from opinion also in this last sense, because according to Aristotelian and Neoplatonic definitions it is an acquired habit that is about universal things by means of necessary premises, and is not concerned with mutable things that can be given in perception. Finally, the intellectus as perception of the indemonstrable principles is distinguished from both opinion and science.44 What we have here, then, is not a gradual progression from opinio to scientia through the intermediate degree of fides, as it was for the authors of the second half of the twelfth century.45 Rather, in Grosseteste we have a taxonomy in which the genus is the first sense of opinio (= fides) as knowledge accompanied by assent, which in its turn divides into the two other senses of opinio, scientia and opinio in its most proper sense. The definition of opinio (in the proper sense) may derive from the definition given by Avicenna in his Liber sextus de naturalibus (De anima).46 This is not the only clue that points to that work, however. Grosseteste’s use of the term intentio is also quite interesting and, we believe, certainly to be connected to some works by Avicenna that were in circulation since the twelfth century, the 43

Robert Grosseteste, Comm. in APo I.19, ed. Rossi, 280–281: “Opinio vero proprie dicta est visus anime qui, cum cadit super res intelligibiles et scibiles, non capit eas in puritate sua, sed commiscet cum eis phantasmata rerum materialium transmutabilium […] Et assimilatur hec opinio visui corporali qui transit per pupillam infectam vel perspicuum infectum usque ad coloratum, et non apprehendit coloratum sicut est in se, sed apprehendit ipsum secundum dispositionem infecti per quod transit, sicut visus icterici vel cholerici iudicant omnia visa citrina eo quod transit per pupillam infectam cholera citrina, et colorem qui est in oculo concernit cum colorato extra. […] Opinio autem magis proprie dicta est visus rerum materialium transmutabilium in suis conditionibus materialibus secundum quas sunt transmutabiles.” 44 Robert Grosseteste, Comm. in APo I.19, ed. Rossi, 281–282: “Dicit ergo Aristotele quod scibile differt ab opinabili et scientia ab opinione, quia scientia est habitus acquisitus super res universales per necessaria que non possunt aliter se habere; unde manifestum est quod scientia non est circa res transmutabiles que cadunt sub signatione sensibili, quia si circa eas esset scientia, ipse essent inpermutabiles. Opinio vero est cira transmutabili. At vero neque intellectus est scientia aut opinio, quia intellectus est principium scientie, quod non convenit scientie aut opinioni. Et iterum scientia non est indemonstrabilis, sed opinio immediate propositionis, hoc est intellectus, est indemonstrabilis, et ita intellectus non est scientia vel opinio, que est acceptio immediate propositionis non necessarie, supple, est indemonstrabilis, et in hoc differt a scientia.” 45 Cf. supra, §4.2. 46 Avicenna Latinus, Liber de anima seu sextus de naturalibus v, c. 1, ed. Van Riet, 79.45–46: “Sententia autem est conceptio definita vel certissima, opinio vero est conceptio ad quam acceditur cum formidine alterius partis.”

214

chapter 5

Liber de anima47 and the Liber de philosophia prima. Besides the more o­ bvious sense of intentio as “will,” the term also occurs in the definition of the universale ambiguum: If the subject of the conclusion is actually found in those things in which it is possible that it is found by virtue of its own nature, it either is an entirely univocal universal, or is an ambiguous universal, that is something that is said of its inferior things according to multiple ways, for example according to a principal and a secondary sense or according to a greater or a lesser force. If then it is an ambiguous universal, it cannot be named by means of a truly unique name. If it is said of different inferior things, on the one hand it maintains its proper conceptual unity, on the other hand it loses it; and therefore, although the name is sometimes unique according to the voice, it is not according to the intention.48 It should be evident that in this context intentio cannot mean “will”; rather, it has the meaning that the Arabs attribute to the term mana’, namely “concept” or “signification.” The substitution of the pair nomen and ratio of the Boethian translation49 with the pair vox and intentio may have an Arabic source (which we have not been able to identity) and corresponds to the use of the expression secundum intentionem made by al-Ghazālī in his Logica to explain the difference between univoca, diversivoca, multivoca, aequivoca and convenientia or

47 48

On the circulation and diffusion of the Liber de anima cf. Hasse (2000). Robert Grosseteste, Comm. in APo I.5, ed. Rossi, 118–119: “Si vero subiectum conclusionis sit repertum actualiter in hiis in quibus possibile est per naturam suam ut reperiatur, aut ipsum est universale univocum penitus aut ipsum est universale ambiguum, dictum scilicet de suis inferioribus secundum modos diversos, utpote secundum prius et posterius vel secundum fortius et debilius. Si itaque ipsum sit universale ambiguum, ipsum est innominabile nomine vere uno. Dictum enim de diversis inferioribus ex parte aliqua retinet unitatem intentionis et ex parte alia diversitatem intentionis, unde licet nomen forte sit aliquando unum secundum vocem, non tamen est penitus unum secundum ­intentionem.” 49 Cf. Cat 1a1–4, AL I.1, 5: “Aequivoca dicuntur quorum nomen solum commune est, ­secundum nomen vero substantiae ratio diversa, ut animal homo et quod pingitur. Horum enim solum nomen commune est, secundum nomen vero substantiae ratio diversa; si enim quis assignet quid est utrique eorum quo sint animalia, propriam assignabit ­utriusque rationem.”

Demonstration through Signs in 13th-Century Commentaries

215

ambigua,50 which latter will be called analoga by subsequent logicians and philosophers.51 In other passages reference is clearly made to intentio as the natural ­meaning of a word, and in the context of the analysis of nominal definitions (explicans intentionem nominis) it is said that names like tragelaphus (the classical Aristotelian example of an empty name), while they do not refer to anything existent, can nonetheless be defined.52 In the following passage from I.10 Avicenna’s definition of the object of logic is quoted almost verbatim: Dialectic […] as a science and a part of philosophy has its own object, namely the second intentions that are applied to first intentions, in so far as through them one goes from what is known to what is unknown.53 Other indications of Grosseteste’s knowledge and use of Avicenna’s Liber de anima are the expression intentio estimata or extimata,54 occurring in at least two passages, and the hint to a system of internal senses of II.6: The particular sense apprehends individuals, and the common sense expresses a judgment, and sense is a receptive faculty. And among sensitive beings there is a faculty that retains that which is perceived through the senses and the intentiones that are received from 50

51 52 53

54

Logica Algazelis I.5, ed. Lohr, 245–246: “Divisio quinta est quod dictiones intentionum sunt quinque modis. Sunt enim univoca, diversivoca, multivoca, aequivoca et convenientia. (1) Univoca sunt, ut haec dictio ‘animal’ convenit homini et equo secundum eandem intentionem indifferenter, sine magis et minus, sine prius et posterius […] (5) Convenientia sunt media inter univoca et aequivoca, ut ‘ens’ quod dicitur de substantia et accidente. […] Esse vero prius habet substantia; deinde accidens, mediante alio. Ergo est eis esse secundum prius et posterius. Hoc dicitur ambiguum, eo quod aptatur ad hoc et ad hoc.” The literature on analoga is quite abundant: see Libera (1989), Marmo (1994), 304–328, and, more recently, Ashworth (2013). See Robert Grosseteste, Comm. in APo I.8, ed. Rossi, 157 (in the space of few lines the expressions “intentio nominis vulgata est” and “eorum (scil. nominum) significatio est vulgata” are used as synonyms); II.2, ed. Rossi, 323 (tragelaphus); II.2, ed. Rossi, 333. Robert Grosseteste, Comm. in APo I.10, ed. Rossi, 171–172: “Dialetica […] in quantum ipsa est scientia et pars philosophie habeat subiectum proprium, scilicet secundas intentiones que apponuntur intentionibus primis, in quantum per eas pervenitur de cognito ad incognitum […].” Cf. Avicenna, Lib. de phil. prima I, 2: “Subiectum vero logicae, sicut scisti, sunt intentiones intellectae secundo, quae apponuntur intentionibus intellectis primo” (ed. Van Riet, I, 10.73–74). Rossi’s edition has the variant opponuntur, but apponuntur (from codd. OdW) is certainly to be preferred. Robert Grosseteste, Comm. in APo I.14, ed. Rossi, 215; II.6, ed. Rossi, 404 (see the text quoted below).

216

chapter 5

the estimative from sensible forms; and this faculty of retention is called memory. Memory in this sense is common to both the imagination, which retains the sensible forms, and memory properly so called, which retains the intentiones received from the estimative .55 The occurrences of intentio are left untranslated because, as will be seen ­further on,56 together with the estimative faculty this notion plays a special role in Avicenna’s theory of knowledge—which does not correspond to the sense of “signification/concept”—and it had an important role in shaping the development of a theory of animal intelligence and of the capacity of brute animals to make inferences from signs. 2

Robert Kilwardby

In chronological order, the second Latin commentary on the Posterior Analytics that has reached us in a complete form is that of Robert Kilwardby, Master of Arts in Paris, which probably dates to the 1240s.57 The commentary is divided into lectiones, which are opened by a lemma taken from the Greek-Latin translation of James of Venice—sometimes recourse is also made to the translation of Ioannes and to the Arabic-Latin translation of Gerard of Cremona, as we shall see—followed by the divisio textus (the part that organizes, also syntactically, the portion of text which is commented on), by the sententia (the meaning of each passage, sometimes also accompanied by the expositio litterae, in case the text of the translation is particularly difficult), and sometimes closed 55

Robert Grosseteste, Comm. in APo II.6, ed. Rossi, 404: “Sensus enim particularis est apprehensivus singularium et sensus communis iudicativus, et est sensus potentia receptiva. Et in quibusdam habentium sensum est potentia retentiva eorum que recipiuntur in sensu et intentionum extimatarum ex formis sensatis, et hec retentiva vocatur memoria. Hic enim dicimus memoriam communiter ad imaginativam, que retinet formas sensatas, et ad memoriam proprie dictam, que retinet intentiones extimatas.” 56 See infra, §7.2.3. 57 For Kilwardby’s works in general see Lewry (1978); for his commentary on the Posterior Analytics see Gauthier (1989), 57*–58*; Cannone (2002); Corbini (2012). A critical edition of Kilwardby’s Notule Libri Posteriorum is being prepared by P.B. Rossi and L. Campi, whom we thank for the generosity with which they provided some textual anticipations. We also thank Debora Cannone that has given us her permission to read and reproduce some parts of her doctoral thesis containing a complete transcription of the ms. ­Cambridge, Peterhouse 205 (C), corrected (up to ad APo A 28) on the ms. Venezia, Bibl. Marciana, Z.L. 240 (V) and on the ms. Paris, Bibl. Nationale de France, lat. 6576 (P); for a description of the manuscripts see Cannone (2002), 72–74.

Demonstration through Signs in 13th-Century Commentaries

217

by notabilia or quaestiones devoted to specific textual problems, according to the standard procedure of medieval university teaching.58 Kilwardby makes frequent use of Grosseteste’s commentary—from which also come citations from Philoponus—and of Themistius’ paraphrase.59 One first important thing to be observed is that Kilwardby’s characterization of the topic and scope of the Posterior Analytics is based on the distinction, which we have met in Alexander and Themistius,60 between the “logical” and the “ontological” senses in which the premises of an argument may be the cause of the conclusion: In the syllogism as such the premises are cause of the conclusion only in inference, in the demonstrative they are both in inference and in being.61 The Prior Analytics treat of the syllogism in general, in which the premises are the cause of the conclusion only in the logical sense (in inferendo tantum); the Posterior Analytics treat of the demonstrative syllogism, which add to the first logical requirement the further condition that the premises should be the cause of the conclusion in the ontological sense as well (tam in inferendo quam in essendo). All demonstrative syllogisms are syllogisms but not vice versa.62 No such distinction is found in Grosseteste. We saw in the previous section that Grosseteste’s fourfold typology in I.12 is Aristotelian, while that in I.6 is Philoponean. Both are fully, even if implicitly,

58 Cf. Cannone (2002), 74–76. 59 Cf. Rossi (1978) and Cannone (2002), 76–78. 60 Cf. supra, §§2.1, 2.2. 61 Robert Kilwardby, Notule libri Posteriorum, Prologus, ed. Cannone, II, 9–10: “In s­ illogismo simpliciter sunt (V; est ed.) premisse (V; prius ed.) causa conclusionis in inferendo ­tantum, in demonstrativo vero tam in inferendo quam in essendo.” 62 The same distinction is used to demarcate the scope of the Prior from that of the Posterior Analytics in an anonymous commentary that is certainly dependent on Kilwardby (Firenze, Biblioteca Nazionale Centrale, Conventi Soppressi J.V.51; cf. Brumberg-­Chaumont 2015): “Ad hoc dicendum quod syllogismi qui determinantur in libro isto [= APo] dicuntur posteriores respectu syllogismorum libri Priorum et causa eius est quoniam scientia procedit per causam inferendi et essendi. Scientia Priorum per causam inferendi tantum” (quoted in Brumberg-Chaumont 2015, 90 n. 1); “...duplex est resolutio: quaedam est quae est in causam essendi et inferendi, et haec est in demonstrativis et est quaedam alia quae est in causam inferendi tantum et haec salvatur in omni syllogismo, et topico et demonstrativo et peccante in materia.” (ibid., quoted in Brumberg-Chaumont 2015, 94 n. 1).

218

chapter 5

extensional. Kilwardby provides no Philoponean typology in his commentary on APo A 6. In his commentary on APo A 13, however, he says: In the first part proceeds thus: he first claims that to know that and to know why differ, and also that within the same science the difference is twofold […]. The first difference that he gives is that we have science of the that when the syllogism is not through the immediate but through the mediate, and this can be twofold, namely either through a mediate cause or through a mediate effect. And he adds a reason by saying that the science of the why is through a proximate and immediate cause, but the science of the that is not in this way […] The second difference is that we have science of the that when is through the immediate but not through a cause, but through an immediate effect, when is convertible and better known to us, because it is not inconvenient that when cause and effect convert, the effect is better known to us than the cause.63 Kilwardby interprets section (i) of APo A 13 (“not from immediates”) as referring both to a mediate cause and to a mediate effect. Arguments from either a mediate cause or a mediate effect are not propter quid; they are both quia; the only propter quid argument is that from an immediate cause, and this is what Aristotle says in sections (ii) and (iii) (“from immediates”); the argument from an immediate effect is also quia. Two things should be noticed. First, the whole discussion suggests that “immediate” and “mediate” are taken to somehow correspond to “convertible” and “non-convertible,” respectively, which is precisely the manner we conjectured sections (i) and (ii) of APo A 13 should be interpreted. That Kilwardby is taking “immediateness” extensionally can be doubted on the basis of the fact that in saying that a quia demonstration can also be per effectum immediatum, dummodo sit convertibilis et notior quo ad nos, he is thereby implicitly 63

Robert Kilwardby, Not. lib. Post. I.28, ed. Cannone, II, 166–167: “In prima parte sic procedit: primo dicit quod differt scire quia est et scire propter quid est, et primo quod est differentia dupliciter in eadem scientia, […] Prima differentia, quam ponit, est quod scientia quia est quando fit sillogismus non per inmediatum sed per mediatum, et hoc potest esse dupliciter, scilicet uel per causam mediatam, uel per effectum mediatum. Et addit rationem, dicens quod scientia propter quid est per causam proximam et inmediatam, sed scientia quia modo iam dicto non fit […]. Secunda differentia est quod scientia quia est quando fit per inmediatum sed non per causam, sed per effectum inmediatum, dummodo sit conuertibilis et notior quo ad nos, quia non est inconueniens, cum causa et effectus conuertantur, effectum esse notiorem nobis quam causam.”

Demonstration through Signs in 13th-Century Commentaries

219

distinguishing the immediateness condition from the convertibility condition. However, when he later connects section (iv), where Aristotle announces a middle term that is more extended than the major, to section (i), where ­Aristotle presents the first of his two that/why distinctions (“not from immediates”),64 the suggestion is that he takes “not from immediates” in section (i) to refer to non-convertibile terms, and thus that he takes the immediateness condition to correspond to the convertibility condition. In an earlier passage propter quid demonstrations are said to be per immediata, id est per causam propriam et proximam,65 where the adjective propriam unmistakably suggests convertibility. In neither Grosseteste nor Kilwardby the extensional interpretation is explicit; but neither is it in Aristotle, as we know. And yet the extensional interpretation is the only one that can make sense of Kilwardby’s analysis of APo A 13, where immediateness and mediateness divide arguments precisely as convertibility and non-convertibility of cause and effect do. In the second place, like in Grosseteste’s Philoponean typology ad A 6 and unlike Grosseteste’s Aristotelian typology ad A 13, Kilwardby here takes into consideration an effect that is more extended than the cause. With regard to the case announced in section (i) of APo A 13, Kilwardby says: Then he exemplifies the first mode of science and demonstration of the that, namely that there is no demonstration through a mediate , and exemplifies only that in which the effect is shown through a remote and mediate cause, and proceeds thus, saying that in those ­demonstrations in which a transcendent middle term is taken, which is more extended and remote, only in these cases there is demonstration of the that and not of the why, whether the transcendent middle term be cause or effect, neither this way nor the other way around it is said a demonstration of the why.66 64 65

66

“cum dicit, amplius quibus [78b14 = section (v)] determinat modum primum” (Robert Kilwardby, Not. lib. Post. I.28, ed. Cannone, II, 167); cf. also I.28, ed. Cannone, II, 169. Robert Kilwardby, Not. lib. Post. I.19, ed. Cannone, II, 114. Here we follow again manuscript V, which has propter quid, rather than C and P, which have quia, because the former, not the latter, is per immediata, id est per causam propriam et proximam (cf. Not. lib. Post. I.19, ed. Cannone, II, 114, apparatus). Robert Kilwardby, Not. lib. Post. I.28, ed. Cannone, II, 169: “Consequenter exemplificat de primo modo scientie uel demonstrationis quia, scilicet quod non sit demonstratio per mediatum (V; medium ed.), et exemplificat tantum ubi per causam remotam et mediatam ostenditur effectus, et procedit sic, dicens quod in demonstrationibus ubi ponitur medium trascendens quod est in plus et remotum, in illis solum est demonstratio quia et non propter quid, quia siue illud medium trascendens sit causa siue effectus,

220

chapter 5

Kilwardby seems not to take section (iv) as falling under section (i). He certainly takes section (v) to fall under it. And this immediately involves an identification of the “transcendent middle term,” which is “more extended and remote” than the major, with the “non-immediateness” announced in section (i), and thus an extensional interpretation of it: the “non-immediateness” of section (i) is the “mediateness” of the middle term of this passage, which is clearly taken extensionally. This “mediateness” in turn may either be of the cause or of the effect, i.e., either the cause is more extended than the effect or the effect is more extended than the cause. Kilwardby notices that Aristotle offers an example of the former (cause more extended than the effect) but not of the latter (effect more extended than the cause). In neither case, he adds, there is demonstratio propter quid. Thus, he does have in mind a Philoponean typology, for he admits the case of a more extended effect. But since his purpose here is to explain the Aristotelian typology of APo A 13, he is forced to drop this component of the Philoponean typology. Given that the more extended effect is dropped, the upshot of Kilwardby’s taxonomy is the same as in Grosseteste, and thus is Aristotelian. When cause and effect convert, there is demonstration propter quid from the cause and quia (of type 1b) from the effect. Here the examples of section (iii) (twinkling planets and the sphericity of the moon) are made. (The explanation of twinkling planets consists in a long quotation from Grosseteste.67) When cause and effect do not convert, there can be affirmative syllogism from the effect to the cause (no example of the type 2a is offered, just like in Aristotle) and negative syllogism from the negation of the cause to the negation of the effect (non-breathing walls, type 2b). Like Grosseteste, Kilwardby says nothing about the semiotic dimension of quia demonstrations. Like Grosseteste, Kilwardby refers to the distinction between science and demonstration quia and propter quid also in his discussion of APo A 6, 75a16– 17,68 without however going into any detail. What is interesting for us, also because of what it reveals about Kilwardby’s sources, is rather his comment on

67 68

nec sic nec econuerso dicitur propter quid demonstratio.” V has demonstratio per mediatum, but Cannone opts for medium, which makes little sense in this context. Robert Kilwardby, Not. lib. Post. I.28, ed. Cannone, II, 167–169. Cf. Robert Grosseteste, Comm. in APo I.12, ed. Rossi, 190–191. Robert Kilwardby, Not. lib. Post. I.19, ed. Cannone, II, 114: “Et nota quod Aristotiles non demonstrat circulariter, licet demonstrat necessitatem principiorum per necessitatem conclusionis, et econuerso, quia una istarum demonstrationum est per causam efficientem, uel materialem, alia uero per causam finalem; uel una est demonstratio propter quid et reliqua demonstratio quia, et ita per aliam et aliam uiam docetur, quare non est ­simpliciter circulus.”

Demonstration through Signs in 13th-Century Commentaries

221

APo A 6, 75a31–34, the passage containing the first mention of sign-inferences in the Posterior Analytics. Here is again the passage in Barnes’ translation: For what is incidental is not necessary (συμβεβηκότα οὐκ ἀναγκαῖα), so that you do not necessarily know why the conclusion holds (οὐκ ἀνάγκη τὸ συμπέρασμα εἰδέναι διότι ὑπάρχει)—not even if it is the case always but not in itself, as for example in syllogisms through signs (οὐδ᾿ εἰ ἀεὶ εἴη, μὴ καθ᾿ αὑτὸ δέ, οἷον οἱ διὰ σημείων συλλογισμοί).69 We saw in the first Chapter that this passage, and that which precedes it (APo A 6, 75a28–31, in which Aristotle argues that the conclusion and the premises of a demonstration must be καθ᾿αὑτό) involve several exegetical difficulties. What seemed sufficiently clear is that the whole passage is founded upon the opposition between a καθ᾿αὑτό and a κατὰ συμβεβηκός demonstration, and that the reference to the συλλογισμοὶ διὰ σημείων has to be interpreted with that contrast in mind: a sign-inference is “accidental” in this sense, that it does not proceed through the appropriate cause and thus does not show why something is.70 According to Kilwardby, what Aristotle is saying at APo A 6, 75a28– 31 is that proper demonstrations derive καθ᾿αὑτό, i.e., necessary, conclusions from καθ᾿αὑτό, i.e., necessary, premisses. He then interprets APo A 6, 75a31–34 as containing a possible quibbling objection (cavillatio) to this and Aristotle’s answer to the objection. […] since there still remains a quibbling objection against that proposition, removes it so that it can be accepted without that quibble. The quibbler would say that it is not necessary that the demonstration derives from necessary premisses, since in these the middle term can be an inseparable accident, which nonetheless would not be a per se accident, and therefore would not inhere necessarily according to the sense that Aristotle gives to “inhere necessarily,” that is, according to the first or second way of per se predication. For Aristotle has earlier argued that there is a corruptible contingent middle term, then it is impossible that it makes us know in this way; and this holds of the separable accident but not of the inseparable accident: for always inheres, and cannot not inhere, and therefore nothing was said against it.71 69 Aristotle, APo A 6, 75a31–34; transl. Barnes, modified. 70 Cf. supra, §1.6. 71 Robert Kilwardby, Not. lib. Post. I.19, ed. Cannone, II, 117: “[…] quia adhuc restat una cauillatio contra illam propositionem, ut penitus accipi possit sine illa calumpnia, remouet

222

chapter 5

The objection runs like this: contrary to what Aristotle says (that καθ᾿αὑτό, i.e., necessary, conclusions must be demonstrated from καθ᾿αὑτό, i.e., necessary, premises), it is possible to demonstrate from an inseparable accident, i.e., to have a demonstration in which the middle term is an inseparable accident of the minor term. For example: “any colored thing is a body; every man is colored; therefore, every man is a body,” in which the conclusion is necessary but the premises are not because the middle term (coloratum) is an inseparable accident, but not a καθ᾿αὑτό, i.e., necessary, accident of the minor. Kilwardby offers a second example in support of the cavillatio, which is based on another translation (Gerard of Cremona’s translation from the Arabic) and on a parallel passage in Themistius’ paraphrase (also translated from the Arabic by Gerard). Gerard has the following translation of APo A 6, 75a31–34: Et questiones accidentales (quoniam non sunt necessarie) non est via ad hoc ut contingat eas scire ex necessitate; neque etiam si essent ex ­accidentibus inseparabilibus, verumtamen non essent per se. Sicut ­sillogismi qui sunt sumpti ex vestigiis et signis.72 It is clear that the συμβεβηκότα of 75a31 include those “inseparable accidents” that are “always but not per se.” This is also the manner in which Kilwardby interprets the text. Themistius made the following comment on this passage: Otherwise, accidents are not necessary, not only the things that can hold and not hold , but also those that always hold together , but not in itself. Since also the syllogisms through signs take middle terms that always hold together with the thing; indeed “having milk” always holds of “having given birth,” and “smoke” of “fire”; and yet we are not entitled to call those demonstrative in the strict sense, because what is primary is syllogized through what is secondary.73

eam. Adhuc enim diceret cauillator quia non est demonstratio ex premissis necessariis ex necessitate, quia poterit in ipsa esse medium accidens inseparabile, quod tamen non est accidens per se, et ita non inerit ex necessitate secundum quod Aristotiles accipit ex necessitate inesse, scilicet solum primo modo uel secundo per se. Cum enim supra arguebat Aristotiles esse medium contingens corruptibile, ergo non potest esse quod ita facit scire; bene tenet de accidente separabili sed de accidente inseparabile non: semper enim inerit, et non potest non inesse, et ideo contra tale non fuit prius disputatum.” 72 Translatio Gerardi, AL IV.1–4, 202.14–18. 73 Themistius, In APo, ed. Wallies, CAG 5.1, 17.18–23. Cf. supra, §2.2.

Demonstration through Signs in 13th-Century Commentaries

223

Now, in the second example of the cavillatio, Kilwardby follows Themistius and Gerard’s translation in equating “inseparable accidents” and “accidental signs,” an equation which in fact simply makes Aristotle’s own reference to sign-syllogisms more explicit: Or alternatively, according to what is suggested by the other translation and by Themistius, if an accidental sign, like “having milk,” is taken as the middle term and through this it is shown that a certain woman has given birth: this predicate, “to have given birth,” always inheres in this subject who “has milk,” and yet corresponds to none of the mode of per se inherence.74 According to Kilwardby, then, APo A 6, 75a31–34 contains the cavillatio that inseparable accidents may serve as middle terms in a demonstration as well as Aristotle’s answer to it. Kilwardby’s version of Aristotle’s answer to the cavillatio has the following syllogistic form: He removes the objection as follows: the middle term in a demonstration makes us know per se a per se attribute of the subject and the reason why it holds; but no inseparable accident makes us know per se a per se attribute of the subject and the reason why it holds; therefore, no such accident can be the middle term in a demonstration.75 The cavillator objects that an inseparable accident can be the middle term of a demonstration: the examples of the colored body and of the lactating woman are cases in point. But Aristotle answers this objection by saying that no accident, not even an inseparable accident, makes us know why something holds of something else (i.e., makes us know per se a per se attribute of the subject and the reason why it holds): through such a middle term, as Aristotle says at APo A 6, 75a34–35, you do not “understand per se (καθ᾿αὑτό) something that holds per se (καθ᾿αὑτό), nor will you understand why it holds.”

74

75

Robert Kilwardby, Not. lib. Post. I.19, ed. Cannone, II, 117: “Uel aliter, secundum quod uult alia translatio et Themistius, signum accidentale, sicut habens lac, si ponatur pro medio et per hoc ostendatur aliquam peperisse: semper enim inest hoc predicatum ‘peperisse’ huic subiecto ‘habens lac’, et tamen nullo modo inherendi per se.” Robert Kilwardby, Not. lib. Post. I.19, ed. Cannone, II, 117: “Remouet ergo hanc cauillationem sic: medium in demonstratione facit scire per se passionem de subiecto per se et propter quid; sed nullum accidens inseparabile facit scire per se passionem de subiecto per se et propter quid; ergo nullum accidens tale potest esse medium in demonstratione.”

224

chapter 5

Kilwardby’s exploration of the cavillatio and of Aristotle’s answer to it is interesting for several reasons. In the first place, the example of “inseparable accident” or “accidental sign” that Kilwardby uses is the lactating woman of APr B 27. As we saw, Themistius uses that very same example in his own comment on APo A 6, and Kilwardby, who had access to Gerard’s translation of Themistius, explicitly refers to it, even though Kilwardby’s formulation (habens lac, peperisse) is not precisely the same as in Gerard’s Latin version of Themistius (esse ei lac, jam sit feta). No such example is found in Grosseteste. In the second place, Kilwardby did not read Greek and had only indirect access to the Latin-Arabic translation of Themistius’ paraphrase. We saw that in his comment on APo A 6 Themistius takes the syllogism through signs mentioned by Aristotle in that chapter as a demonstration that is not κυρίως, and we noticed that this idea depends on Alexander.76 Now, in the translation from the Arabic that Kilwardby is using, κυρίως becomes vere:77 a demonstration propter quid is “truly” a demonstration, while a demonstration quia is not a “true” demonstration at all. This is not the same thing as to say that they are demonstrations in a proper and in a secondary sense, respectively. In point of fact, in the passage from κυρίως to vere any reference to a secondary standard of demonstration is lost. Perhaps a direct access to Themistius’ Greek text might have brought Kilwardby closer to the Greek interpretation of that-demonstrations. In the third place, there is a strong similarity between the passage from ­Themistius on APo A 6 and what is probably a gloss (perhaps itself inspired by Themistius, as the occurrence of the adverb vere suggests) which may have slipped into the Arabic text and which is reported in the Toledo ­manuscript but not in the Cambridge manuscript that formed the basis of Minio-­Paluello’s ­edition of the translatio Gerardi.78 After 75a31–34 (quoted above) the gloss adds:

76 Cf. supra, §2.2. 77 Themistius, Paraph. sup. APo I.6, ed. O’Donnell, 263: “In syllogismis enim compositis, qui sunt per impressiones et significationes, etiam inveniuntur cum terminis mediis res existentes simul semper in re. Inde quod invenimus in muliere ut sit ei lac cum hoc ut jam sit feta, et fumus est cum igne. Verumtamen isti syllogismi etiam compositi non licet nobis ut dicamus vere quod sint demonstrativi, quoniam ipsi concludunt ex re postrema quod est antiquius ea.” (cf. Themistius, In APo, ed. Wallies, CAG 5.1, 17.1–23) 78 Cf. also Elamrani-Jamal (2000), 122, where a French translation of the Arabic gloss is provided. The Arabic gloss is in the anonymous translation of the Posterior Analytics but not in Matta’s. Hugonnard-Roche (1999) has argued that the anonymous translation has Themistius as its source; cf. also Bertolacci (2007), 71.

Demonstration through Signs in 13th-Century Commentaries

225

It is not up to us to say that these are truly demonstrative, because they conclude what is precedent from what follows. For the delivery is first and then the milk, and first is the fire and then the smoke; and it is possible that are absent and the science is not removed; hence will not be necessary.79 The examples are the same as we find in Themistius, and even the formulation is similar. The last part of this gloss, however, is quite puzzling. What does it mean that the signs can be removed without detriment of the science? Is the scientia that non removetur to be regarded as scientia quia or scientia propter quid? We saw that in his comment on APo A 13, 78b11–13 Themistius considers fire and smoke as non-convertible with one another, so that from the presence of smoke it is possible to infer the presence of fire (that-­demonstration), while from the presence of fire it is not possible to infer the presence of smoke (impossibility of a why-demonstration).80 In this context, the removal of the sign would entail both the impossibility of a that-­demonstration (because there would be no premise for it) and the impossibility of a why-­demonstration (because the effect is not coextensive with the cause and thus not inferable from it). On the other hand, having milk and having born a child are convertible, so that the removal of the sign entails the impossibility of the that-demonstration but still leaves open the possibility of a why-­demonstration. Perhaps the glossator only meant that when the sign or accident of anything is removed, since it is precisely only something that follows the thing accidentally, the possibility of a science of the thing is not endangered. Be that as it may, it is clear that there is a connection with the example of the lactating woman of APr B 27 and that it is mediated by Themistius. In what follows we shall track the fortune of this example still further. The second and last mention of signs in the Posterior Analytics is in B 17. As we know from the previous section, Grosseteste obliterates the assimilation of accidents to signs and simply speaks of “effects.” Kilwardby says:

79

AL IV.1–4, 202.18–23: “Non est nobis ut dicamus vere quod ipsi sunt demonstrativi, quoniam concludunt antecedens per ultimum: quoniam prius est partus et postea lac, et prius est ignis et postea fumus; hec enim possibile est ut tollantur et non removetur scientia, ergo non erit necessaria.” 80 Cf. supra, §2.2.

226

chapter 5

if there is to be demonstration per se and in the primary sense and not through a sign, that is a probable middle term, nor through an accidental middle term, it can be that there are multiple causes of it.81 It will be recalled that the Greek commentators, Themistius included, had interpreted the passage in the sense that when Aristotle says that in some cases the causes can be multiple, he is talking of the “logical cause” of the conclusion, not of the “ontological cause,” which must be unique.82 Kilwardby’s use of medium probabile as an explanation of signum points to a different interpretation (though one that is not inconsistent with Themistius’ position). A sign-­argument in the second figure, like the one that infers that a woman is pregnant from her being pale, is precisely an argument in which from the effect it is not possible to go back to a unique cause: the paleness is not necessarily caused by pregnancy; it might be caused by illness. Paleness is in this case a probable sign of pregnancy, and in this syllogism the sign really functions as medium probabile. The syllogism is not deductively valid; it is a probable argument, not a necessary one. A comprehensive evaluation of Kilwardby’s contribution to the topic must await the critical edition of his commentary on the Posterior Analytics. As we shall see in the next Chapter, the qualification of the signum as medium p­ robabile is consistent with Kilwardby’s tendency to ascribe sign-inferences to dialectics rather than to the theory of science. 3

Albert the Great: New Arabic and Latin Sources

With Albert the Great, the author of a monumental paraphrase of Aristotle’s works and especially of the Organon,83 a period begins which is marked by the influence of Arabic works. It has been pointed out that Albert often uses ideas and theories of Arabic philosophers and shows to have had access to texts that have thereafter been lost.84 His commentary on the Posterior Analytics is no

81

Robert Kilwardby, Not. lib. Post. II.31; ed. Cannone, II, 487: “si fiat demonstratio per se et primo et non secundum signum quod est medium probabile neque secundum medium accidentale, potest esse quia eiusdem sunt plures causae.” 82 Cf. supra, §§2.1, 2.2. 83 Albert’s paraphrases of both Analytics were composed between 1257 and 1263; those of the Topics and the Sophistici Elenchi after 1267; cf. Brumberg-Chaumont (2013), 373; Weisheipl (1980), 40. 84 Cf. Marmo (1990), 161, about the place of the Rhetoric and the Poetic in the Organon.

Demonstration through Signs in 13th-Century Commentaries

227

exception. Like in his other logical works, Albert also uses earlier Latin commentaries, especially that of Robert Kilwardby.85 Among the lost commentaries on the Posterior Analytics mentioned by Albert there are those of Alexander of Aphrodisias, Porphyry, Boethius, and al-Fārābī. Some items of Alexander’s lost commentary were considered above.86 However, we believe that Albert’s testimonies have not yet been taken into sufficient consideration for the reconstruction of Alexander’s lost commentary. Three passages in Albert allude to it. In the first of these Alexander is mentioned along with Themistius with regard to the definition of suppositio (ὑπόθεσις), i.e., a postulate from which conclusions can be derived on the model of Euclid’s Elements: “Positions” are of two kinds: that which assumes a proposition independently of its being affirmative or negative (namely with the being in affirmation and non-being in negation) is called “supposition” when is immediate, and Alexander and Themistius say of it that it is used by one who demonstrates because it is proved and demonstrated, although it is mediated, as it can be seen in the suppositions of Euclid in the first book of his Geometry. That which does not signify whether something exists or not, and nonetheless poses it, is the definition, as it can also been seen in the first book of Geometry.87 Themistius, although with different terms (translated from the Arabic), offers the same distinction in the second chapter of his paraphrase of the first book, but without mentioning Alexander,88 which suggests that Albert’s reference to Alexander is independent of Themistius in this case. In a second passage 85 Cf. Ebbesen (1981c). 86 Cf. supra, §2.1. 87 Albert the Great, Liber Posteriorum Analyticorum I.2.3, ed. Borgnet, 30a: “Positionis autem sunt duae differentiae: una enim quae quamlibet partem sive affirmativam sive negativam accipit enuntiationis (dico autem esse in affirmativa, vel non esse in negativa) vocatur suppositio quando est immediata, de qua dicit Alexander et Themistius, quod utitur ea demonstrator ut probata et demonstrata, quamvis sit mediata, sicut patet de suppositionibus Euclidis in primo Geometriae. Quae vero sine hoc est, quod esse aliquid vel non esse non significet et tamen ponitur, diffinitio est, sicut ibidem patet in primo Geometriae.” 88 Themistius, Paraph. sup. APo I.2, ed. O’Donnell, 250: “Et positio quidem habet duas species, quarum una dicitur definitio et altera dicitur radix posita. Et definitio est sermo qui non enuntiat de re quod ipsa sit aut quia non est, quamvis quandoque sequatur ut illa res, cujus definitionem affert aliquis, sit […]. et ejus alia species sicut diximus est radix posita. Et communicat omnis radix posita quia non pendet per scientiam naturalem ex scientiis

228

chapter 5

­ lexander is mentioned along with al-Fārābī and Porphyry: the reference in this A case might be to “Alexander” (Philoponus/Michael of Ephesus),89 but it could also be an indirect reference to the Aphrodisiensis via al-Fārābī or ­Porphyry (assuming however that Albert had also access to Porphyry’s lost commentary, about which more below).90 Alexander is associated with Themistius and al-Fārābī a third time in connection with the problem whether there can be demonstration about corruptible entities.91 Themistius refers to Alexander’s commentary slightly earlier, but only with respect to the universality of the premises of demonstration;92 hence, his commentary cannot be the source that informed Albert of Alexander’s opinion in this regard. The possibility that al-Fārābī may have reported Alexander’s position remains open, and it appears quite unlikely that these references are to “Alexander”/Philoponus. Given that al-Fārābī’s commentary is also missing, the question must remain open. Also open are the questions whether Albert had access to Porphyry’s

cognitionis; verum non ponit eam nisi positione auctor syllogismi et facit eam propositionem. Quod est quia non evacuatur quin sit secundum quod est res aut non est […].” 89 Cf. supra, §§2.7, 4.2. 90 Albert the Great, Lib. Post. An. I.2.9, ed. Borgnet, 46b–47a: “Scias autem quod Alfarabius super locum istum in commentum aliquantulum sequens Porphyrium et Alexandrum, aliter dicit […].” This passage is examined by Chase (2007), 23–33, with regard to Porphyry’s commentary. Chase assumes (29 n. 31) that the allusion to Alexander is actually a reference to Philoponus/Michael of Ephesus, which would be without value if the reference depends on Arabic sources or on Porphyry’s lost commentary: the confusion between Ephesius and Aphrodisiensis, as Ebbesen (1996) has shown with regard to logic, seems to be a peculiarity of the Latin West. With regard to other works, some confusion between the passages attributed to Alexander and those of Philoponus is also in Arabic philosophy; cf. Sorabji (1990), 190–194, with regard to the Physics, Metaphysics, and De caelo, and Hasnawi (1994), with regard to the De aeternitate mundi contra Proclum; cf. also Bertolacci (2007), 84–85 n. 50. 91 Albert the Great, Lib. Post. An. I.2.17, ed. Borgnet, 62b–63a: “Ex quo ulterius concluditur, quod corruptibilium quae sunt singularia, non est demonstratio: sed, sicut dicit Alfarabius in commento, alia ratiocinatio est de talibus ex causis materialibus, quae non est demonstratio, quamvis in hoc demonstrationi in aliquo sit similis, et in hoc quod concludit. Neque de talibus, singularibus scilicet et corruptibilibus, est scientia, quae simpliciter scientia est, secundum quod scire in antehabitis diffinitum est. Sed sic est de eis sicut secundum accidens. Et exponens Alfarabius dicit. Sic est de eis scientia sicut sunt: sunt autem per casum et fortunam quae sunt causae per accidens: sic ergo scientia est de ipsis: et haec non est scientia per se, sed habet aliquod accidens ad scientiae acceptionem, scilicet per materialem diffinitionem per quam per accidens scitur quod scitur. Quamvis autem haec [op]positio sit Alfarabii et etiam Themistii et Alexandri.” Cf. Aristotle, APo A 8, 75b24–25. 92 Themistius, Paraph. sup. APo I.8, ed. O’Donnell, 266; cf. Themistius, In APo, ed. Wallies CAG 5.1, 20.15. Cf. Aristotle, APo A 8, 75b21–24.

Demonstration through Signs in 13th-Century Commentaries

229

lost commentary (if there was one) and whether al-Fārābī informed him about that.93 With regard to Boethius’ commentary, one is led to suspect that there is a mistake of attribution: Albert normally uses James of Venice’s translation and quotes both from the other translation from the Greek (translatio Ioannis) and from Gerard of Cremona’s translation from the Arabic (translatio arabica).94 Yet, while he never mentions James (not even as the author of a translation from the Greek), in several places the translation used is attributed to Boethius.95 The impression is that Albert simply does not know who authored the translation that he is commenting on, and that he simply took him to be the translator par excellence of Aristotle’s Organon. His references to a commentary by ­Boethius in those same places suggest that here he was misinformed, too: if like the translation this commentary could also be attributed to James, one could infer that still at the beginning of the 1260s some such commentary was in circulation, although mistakenly attributed to Boethius.96 The only thing that is relatively certain is that Albert had access to the translation of al-Fārābī’s Great Commentary on the Posterior Analytics,97 to the so-called Logica ­Algazelis, and, likely, also to Avicenna’s Kitāb al-Burhān, which has both Themistius’s paraphrase and Philoponus’ commentary among its sources:98 these works may well have served as links between Albert and the Greek

93 94

95

96 97 98

Chase’s (2007) arguments for either solution are not conclusive; they do not dispel Ebbesen’s doubts about the reliability of Albert’s testimony; cf. Ebbesen (1976), 88; quoted in Chase (2007), 22 n. 5. Cf. Albert the Great, Lib. Post. An. I.2.13, ed. Borgnet, 50a–b; : “Tamen Boetii translatio habet ‘quam singularia’ [= translatio Iacobi, AL IV, 14.24 74a7–8], quam Boetius exponit in commento. Nos autem utramque exponemus litteram: primo quidem si littera est extra singulare (ut habet Arabica translatio quam exponit Alfarabius)”; I.5.8, ed. Borgnet, 145a (again, translatio Boethii); II.2.5, ed. Borgnet, 177a–b (translationes); II.2.5, ed. Borgnet, 179b: “Hujus enim est expositio Commenti Arabici: et in hanc magis consentit Boetii translatio et etiam translatio Joannis.”; II.2.7, ed. Borgnet, 183b (alia translatione); ed. ­Borgnet, 184a–b (translatio Arabica). Albert the Great, Lib. Post. An. I.2.13, ed. Borgnet, 50a–b: “Dicimus quod oberramus hanc deceptionem, hoc est, secundum hanc deceptionem: primo quidem cum tale sit accipere universale cujus universalis a superiori differens nihil est (aut extra) singulare: ideo quod extra suum unicum singulare nihil de universali invenitur, quam sit ipsum suum singulare. Tamen Boetii translatio habet quam singularia, quam Boetius exponit in commento. Nos autem utramque exponemus litteram.” Up to now, no traces of this commentary has been found; research on thirteenth-century commentaries on the Posterior Analytics, to a large extent still unedited, are not much developed, though; cf. Ebbesen (2015). See Zonta (1998), 221–222; and Janssens (2010). See Strobino (2012).

230

chapter 5

commentators. Albert’s references to and citations of al-Fārābī are abundant;99 less numerous are those to Avicenna.100 None of these, however—at least to our knowledge—has anything to do with those passages of the Posterior Analytics that bear on the distinction between that- and why-demonstrations or that mention syllogisms through signs. 3.1 Arabic Theories of Semiotic Demonstrations Studies on the Arabic commentaries on the Posterior Analytics are few101 and do not allow those who have no access to the Arabic editions to form a comprehensive picture of the Arabic reception of the Greek tradition and its debt to it. The following brief overview will show, however, that there is some continuity between the Greek and the Arabic commentators with regard to the problems of the present study. In his Kitāb al-Burhān (“Book of Demonstration”) al-Fārābī (c. 872–951 CE) distinguishes three kinds of demonstrations: (1) demonstration of existence (burhān al-anna, corresponding to the demonstration of the that); (2) demonstration of the cause (burhān al-limā, corresponding to the demonstration of the why); (3) absolute demonstration (which is at the same time of existence and of the cause).102 The demonstration of existence is also called dalāʾil, “sign,”

99

Cf. Albert the Great, Lib. Post. An. I.2.1, ed. Borgnet, 22b; I.2.9, 46b–47a (discussed by Chase 2007); I.2.13, ed. Borgnet, 50b–51a; I.2.17, ed. Borgnet, 62b–63b, 64b; I.3.3, ed. Borgnet, 75b; I.3.4, ed. Borgnet, 76a; I.5.8, ed. Borgnet, 145a, 146b; II.1.1, ed. Borgnet, 156a, 157b; II.2.2, ed. Borgnet, 168b; II.2.5, ed. Borgnet, 177b, 179a–b; II.2.7, ed. Borgnet, 182a–183b; II.2.12, ed. Borgnet, 195a. 100 Cf. Albert the Great, Lib. Post. An. I.1.1, ed. Borgnet, 3a–b; I.1.2, ed. Borgnet, 4a; I.1.3, ed. Borgnet, 9b, 11b; II.1.1, ed. Borgnet, 156b. 101 See Marmura (1965); Marmura (1990); Maróth (1994); Hugonnard-Roche (1999); ­Hugonnard-Roche (2002); Strobino (2012); Strobino (2015); Strobino (2016); Strobino (2019); Strobino (2021). For a recent overview of Arabic logic see Hasnawi and Hodges (2017) and El-Rouayheb (2017). 102 “There are three types of certain knowledge. One is certainty about only the existence of a thing, that is, knowing that something exists, which one group calls knowing that a thing is. The second type is certainty about only the cause for the existence of a thing, which one group calls knowing why something is. The third type is the first two types together. It is precisely by means of one of these three types of investigation that one seeks to understand the things that are investigated through certain principles. Clearly, when we seek to discover just the cause of something, we must necessarily already know that the thing exists, and [so] the type of knowledge that is most properly termed ‘certain knowledge’ is the one that is a combined certainty about both existence and cause.” (Al-Fārābī, Kitāb al-Burhān, transl. in McGinnis and Reisman 2007, 67–68). Cf. Cerami (2015), 324; Strobino (2019), 44.

Demonstration through Signs in 13th-Century Commentaries

231

because in such demonstration the middle term is a sign of the ­conclusion.103 Al-Fārābī also observes that “every demonstration is a cause for the knowledge derived from it, although not all of them provide the knowledge of the cause of the existence of something,”104 an observation that is clearly reminiscent of Alexander’s and Themistius’ distinction between the “logical” and the “ontological” senses in which the premises of an argument may be the cause of the conclusion.105 In his own Kitāb al-Burhān Avicenna (c. 980–1037 CE) also presents a taxonomy of demonstrations, but one that does not coincide with al-Fārābī’s.106 The main division is between a demonstration of the why (burhān limā) and a demonstration of the that (burhān al-inna). These are described as follows: If a deduction gives the assertion that such-and-such is such-and-such, without giving the cause [of the fact that] such-and-such is such-andsuch in [the realm of] existence in the same way in which it gives the cause of the assertion, then it is a that-demonstration. If it gives at the same time the cause of the two things—in such a way that, just as the middle term in [the deduction] is a cause of the assertion that the major belongs to the minor or is denied of it in the proof, so it is a cause of the fact that the major belongs to the minor or is denied of it in existence itself—then this demonstration is called a why-demonstration.107 103

“As for the demonstrations which give the causes only, these consist of matters whose existence is already known to us, either by themselves, through the senses, or through those demonstrations called signs [dalāʾil]. It then remains for us, once their existence is known, to seek their causes. Now the causes of things are known either through sense, through signs, or through demonstrations” (al-Fārābī, Kitāb al-Burhān, transl. in Nasr and Aminrazavi 2008, 148). Celli (2018) has argued that while in the Arabic translation of the Rhetoric the terms σημεῖον and τεκμήριον do not have a technical and uniform translation, a substantially uniform translation appears in the Arabic version of the Prior Analytics, where σημεῖον is translated as ‘alāma (but with dalīl in the margin), while τεκμήριον is transliterated as taqmaryūn. Al-Fārābī, Avicenna, and Averroes seem to reserve ‘alāma for the σημεῖον, and dalīl for both τεκμήριον and σημεῖον (which covers both refutable and irrefutable signs). See also Daiber (2004) and Bertolacci (2007), 76 n. 33. 104 Al-Fārābī, Kitāb al-Burhān, transl. in McGinnis and Reisman (2007), 68. 105 Cf. supra, §§2.1, 2.2. 106 Here we follow Strobino (2021), ch. 9. Strobino offers a reconstruction of both Burhān I, 7 and Burhān III, 3, containing two distinct but largely coincident taxonomies of demonstrations. Burhān I, 7 contains Avicenna’s own systematic treatment of demonstrations, Burhān III, 3 contains a discussion and interpretation of APo A 13. Here we refer ­especially to the taxonomy of Burhān I, 7. See Strobino (2021), 285–287, for an overview of the ­relations between Burhān I, 7 and Burhān III, 3. 107 Avicenna, Burhān I, 7; transl. in Strobino (2021), 266.

232

chapter 5

It should be evident that the distinction between why- and that-­demonstrations is here framed in terms of the Alexandrian and Themistian distinction between the “logical” and the “ontological” senses in which the premises may be said to be the cause of the conclusion, which as just noticed we also find in al-Fārābī: if the premises are the cause of the conclusion (the “assertion that the major belongs to the minor or is denied of it”) only in the logical sense (“in the proof”), then the demonstration is of the that; if the premises are the cause of the conclusion in the ontological sense (“in existence itself”), then the demonstration is of the why. In the Dānesh-Nāma (in Persian, “Book of Science”), after having made the usual distinction between the truly demonstrative syllogism, or “demonstration through the cause,” and the demonstration of existence, Avicenna observes that while all demonstrations are demonstrative “through the cause” if with “cause” we intend the cause of assent or the cause of affirmation, yet not all syllogisms are “through the cause” in the sense of being conducted through the cause of the existence of the state of things expressed in the conclusion. For example, if it is proved that there is fire because there is smoke, the demonstration is “through the cause” in the sense that the existence of the smoke makes us infer the existence of the fire, but not because the existence of the smoke is the cause of the existence of the fire. On the other hand, if it is proved that something is burned because there is fire, the demonstration is “through the cause” in the sense that the existence of the fire is the cause of the burning. In this second case, the “cause” is both the cause of the affirmation and the cause of the existence of the thing.108 Both why-demonstrations and that-demonstrations are then subdivided into sub-species. Why-demonstrations may be of two species: a first species, 108

Cf. Dubouclez (2008), 157–159. Both the distinction between “logical cause” and “­ontological cause” and the tripartite division of demonstrations (causal, factual, and semiotic demonstrations) are also discussed in the logical section of Al-Kitāb al-Ishārāt wa l-­tanbīhat (Book of Remarks and Admonitions): “If the middle term is the cause in the thing itself for the existence of the judgment which is the relation of the parts of the conclusion to each other, then the demonstration is a causal demonstration, since it gives the cause of assenting to the judgment, and the cause of the existence of the judgment. Thus, it gives the cause with no restriction. If the middle term is not such, but is the cause of the assent only—thus giving the reason for the assent without giving the reason for the existence—then the demonstration is called ‘factual demonstration,’ since it indicates the factuality of the judgment in itself, without its cause in itself. If, in the factual demonstration, the middle term, in addition to not being a cause of the relation of the two terms of the conclusion, is an effect of the relation of these two terms and is better known to us, then it is called ‘indicative’ (dalilan).” (Avicenna, Al-Kitāb al-Ishārāt wa l-tanbīhat I, 9, 5, 485–487; transl. in Inati 1984, 154–155).

Demonstration through Signs in 13th-Century Commentaries

233

called “absolute demonstrations [of the why],” in which the middle term is both the cause of the major term and of its belonging to the minor, and a second species, which has no specific name, in which the middle term is the cause of the major term’s belonging to the minor but not of the major term itself. An example of absolute why-demonstration comes from medicine: the putrefaction of the bile (middle term) is both the cause of the major (fever on alternate days) and of its belonging to the minor (some individual). An example of non-absolute why-demonstration is the following: humanity (middle term) may be the cause of the belonging of animality (major term) to some individual, but is not in itself the cause of the major (humanity is not the cause of animality). That-demonstrations are also of two species: the first species is when the middle term is neither a cause nor an effect of the major; this is called by Avicenna “absolute that-demonstration” and is itself of two sub-species: one is when middle term and major term are effects of one common unstated cause, the other is when middle term and major term are effects of the minor term.109 An example of the former is the inference of encephalitis in a man from his producing cloudy viscous urine; the urine is neither the cause nor the effect of encephalitis, but only something related to or coexstensive to it. In other words, encephalitis and cloudy viscous urine are both effects of a common hidden cause (the motion of heated humours toward the head and their evacuation from it).110 As we know, Themistius is the only one among the Greek commentators to have explicitly considered an inference from an effect to another effect of a common cause; his example was the infection of the trachea and the heat of the body, which are both effects of fever from either of which the latter can be inferred. We saw that Themistius only remarks that either of two converting effects δείκνυται the other, but he does not say that either is a σημεῖον of the other (even though, we noticed, a case can be made in support of this view).111 Like Themistius, Avicenna does not seem to regard his first sub-species of “absolute that-demonstration” as having anything to do with signs. The other of the two species of that-demonstration is called “sign” (dalīl) and corresponds to the “standard” Aristotelian inference of a cause from an effect of it. Two examples of dalīl demonstration are astronomical: the sphericity of the moon inferred from its waxing (from APo A 13), and the interposition

109 Cf. Strobino (2021), 267–269. 110 Cf. McGinnis (2010), 44–45; Strobino (2021), 272. 111 Cf. supra, §2.2.

234

chapter 5

of the earth inferred from the eclipse of the moon (from APo B 16).112 A third example is the inference of fire from the burning of wood, which reminds one of the example of carbon and fire as coexstensive effect and cause that Themistius uses in his comment on APo B 17.113 A fourth example comes again from medicine: the inference of the putrefaction of the bile from the occurrence of tertian fever is an inference of the cause from a (non-coextensive) effect of it. The inversion of this latter (the inference of tertian fever from the putrefaction of the bile) is an example of absolute demonstration of the why.114 Avicenna’s typology is not prima facie extensional, even if it may be construed in extensional terms. In his Long Commentary on the Posterior Analytics Averroes (1126–1198) distinguishes three kinds of demonstration in a way that agrees quite closely with al-Fārābī but not with Avicenna.115 In commenting on APo A 2, where Aristotle gives his definition of demonstration,116 Averroes mentions the three species of the genus demonstration: the demonstration of the fact, the demonstration of the cause, and the demonstration that gives both the fact and the cause.117 His explanation of the latter species, called absolute demonstration or demonstration simpliciter, involves Alexander’s and Themistius’ distinction between the “logical” and the “ontological” cause of the conclusion; the premises of an absolute demonstration must be the cause of the conclusion in both ways.118 112 Cf. Strobino (2021), 273. 113 Cf. supra, §2.2. 114 Cf. McGinnis (2010), 45–46; Strobino (2021), 273. 115 On Averroes’ typology of demonstrations and doctrine of sign-inferences see Elamrani-Jamal (2000); Hugonnard-Roche (2002); Dubouclez (2008), 159–168; Cerami (2015), 316–336. Elamrani-Jamal (2000), 115–119, also discusses Averroes’ commentaries on the Prior Analytics and the Rhetoric. 116 Cf. supra, §1.6. 117 Averroes, Aristotelis Opera I, GC in APo, c. 8, 130A; transl. Mantinus: “Et haec est differentia, per quam distinguitur syllogismus demonstrativus a syllogismo dialectico, quaecunque species fuerit trium demonstrationum, hoc est demonstratio existentiae, aut demonstratio causae, aut quae componitur ex duabus dispositionibus simul, hoc est, quae praebet existentiam et causam simul.” Transl. from the Arabic in Di Giovanni (2009), 105: “And this differentia is that by which demonstrative syllogism is differentiated from dialectical syllogism, no matter which of the three kinds of demonstration it is, whether a demonstration of the fact, a demonstration of the cause, or that which brings the two things together, namely that which gives both the fact and the cause.” Cf. also Averroes, Aristotelis Opera I, GC in APo, c. 95, 158D. 118 Averroes, Aristotelis Opera I, GC in APo, c. 8, 131A; transl. Mantinus: “Haec est differentia, per quam distinguitur demonstrationem simpliciter, hoc est, quae praebat existentiam et causam simul, a demonstratione signi [...] quoniam oportet demonstrationem habere propositiones cum his duabus conditionibus, hoc est, quod sint causa conclusionis et

Demonstration through Signs in 13th-Century Commentaries

235

In a demonstration from a sign, by contrast, the (ontological) cause is inferred from the effect; here the premises are causes of the conclusion only in the ­logical sense.119 Averroes’ commentary on APo A 13 sheds some further light on his conception of the tripartition. When cause and effect convert (the case discussed in sections (ii) and (iii) of that chapter), if the effect is better known than the cause, the inference of the cause from the effect is a demonstration of existence, while the inference of the effect from the cause is a demonstration of the cause. If by contrast the cause is better known than the effect, the inference (arguably, of the effect from the cause) can only be an absolute demonstration or demonstration simpliciter. These correspond to why-demonstration (type 1a) and that-demonstration of type 1b. Averroes clarifies in what sense a demonstration simpliciter differs from a demonstration of the cause: both infer the effect from the cause, but the demonstration simpliciter infers from

cause quod sciamus conclusionem. Quemadmodum si sciat, quod hoc in loco est lumen, propterea quod in ipso est ignis: quoniam cognitio quod in ipso est ignis, est causa cognitionis, quod in ipso est lumen, et causa quod sit lumen. Atqui erunt ambae propositiones cum hac conditione in syllogismo demonstrativo, cum terminus medius erit causa conclusionis quod sit, et causa ut cognoscamus ipsam.” Our transl. from Latin: “This is the difference through which absolute demonstration, that is, that which proves existence and cause at once, is distinguished from the demonstration through a sign […] it is necessary for the demonstration to have premises which satisfy these two conditions, namely they must be causes of the conclusion, and causes of our knowledge of the conclusion. As when we know that in this place there is light because in the same place there is fire. In fact our knowledge that there is fire is the cause of our knowledge that there is light and is the cause of light. Then in a demonstrative syllogism the premises are such that the middle term is cause of the conclusion as to its existence and cause of our knowledge of it.” 119 Averroes, Aristotelis Opera I, GC in APo, c. 8, 131A, transl. Mantinus: “Sed in signo medius terminus est tantummodo causa, ut cognoscamus conclusionem: non autem, ut conclusio sit extra intellectum, quemadmodum si monstraremus, quod hoc in loco est ignis, propterea quod in ipso est fumus: quoniam cognitio, quod fumus in ipso sit, est causa cognitionis, quod ignis sit, non autem causa, quod ignis sit. Sed res se habet in contrarium, quoniam ignis est causa, ut fumus sit.” Our transl. from Latin: “But in the sign the middle term is cause only of our knowledge of the conclusion, but is not cause of the conclusion’s being the case outside the intellect. As when we prove that in this place there is fire because in the same place there is smoke. In fact our knowledge that there is smoke is the cause of our knowledge that there is fire, but is not the cause of the fire: the thing is rather the opposite, namely that the fire is cause of the smoke.” In the commentary on APo A 6, demonstration (i.e., absolute demonstration) is contrasted with sign-inferences and both the example of the lactating woman of APr B 27 and, again, the example concerning fire and smoke are used to illustrate the contrast; cf. Averroes, Aristotelis Opera I, GC in APo, c. 55, 146B.

236

chapter 5

a better known cause while the demonstration of the cause infers from a less known cause. Averroes then considers the case of non-converting cause and effect (the case announced in section (iv) of APo A 13). We noticed that Aristotle considers a cause that is more extended than the effect, because the converse arrangement allows no valid demonstration of the that. For Aristotle, when the cause is more extended than the effect there can be a positive ­demonstration of the cause from the effect (that-demonstration of type 2a) and a negative demonstration of the effect from the cause (that-demonstration of type 2b).120 Themistius’ example of the former is: if from the fact that a woman has given birth we infer that she has had intercourse with a man; the argument is a that-demonstration, because the cause (intercourse with a man) is inferred from a sign or effect of it (giving birth), and there cannot be a why-­ demonstration, because the cause is more extended than the effect.121 Unlike Aristotle and Themistius, Philoponus considers also the specular case in which it is the effect to be more extended than the cause. The consideration of this case is peculiar to Philoponus, and we have called the typology that it yields “Philoponean,” in contrast to the “Aristotelian” that does not include this case. We saw that even though the example that he uses is the pale woman of APr B 27, Philoponus does not seem to consider the argument from a more extended effect as a semiotic inference: he limits himself to say that in this case there is a why-demonstration but not a that-demonstration.122 Like Philoponus, Averroes takes this latter case (effect more extended than the cause) to only allow a demonstration simpliciter, i.e., an inference of a less known effect from a better known cause; no less known cause can be inferred from a better known effect when the effect is more extended than the cause, because the argument would not be deductively valid. Finally, Averroes considers the former case (cause more extended than the effect). Here, the less known cause can be inferred from the better known effect and the inference qualifies as a demonstration of the sign. But no “causal” inference is possible from a more extended cause to one of its effects, as it would again produce a deductively invalid argument.123 It is evident that Averroes’ typology is both extensional and Philoponean. 120 Cf. supra, §1.6.1. 121 Cf. supra, §2.2. 122 Cf. supra, §2.3. 123 Averroes, Aristotelis Opera I, GC in APo, c. 96, 159C–D; transl. Mantinus: “Consequentia in hac mensura ex antecedente et consequente, causa et causatum inveniutur ­secundum tres species. Aut quod sequantur ex se invicem consequentia aequali. Et hoc, cum ­fuerit causatum notius apud nos, quam causa, per illud componitur existentia tantum. Deinde possibile est, ut accipiatur causa, et monstretur per ipsam demonstratione causae

Demonstration through Signs in 13th-Century Commentaries

237

Like Themistius and Avicenna, Averroes also considers the case of c­ onverting effects of the same cause. Themistius is explicitly mentioned in this context. Averroes’ example comes again from medicine but is not the same as Themistius’: irregular pulse and the absence of urine concoction (concotionis urinae ablatio) are both effects of putrid fever, and from either the other can be inferred. No such inference, however, counts as a demonstration if not accidentally.124 e­ xistentia causati de subiecto. Et sit ibi demonstratio causae tantum, quemadmodum declarabit Aristoteles postea. Quod si fuerit causa notior causato, tunc adducetur in hac specie demonstratio simpliciter tantum. Species autem secunda consequentiae est, ut sequatur posterius ex priori, hoc est causatum ex causa, et non convertatur res. Et in hac species non adducitur, nisi demonstratio simpliciter tantum: et hoc, cum fuerit causam notior. Quod si non fuerit notior, non adducetur ibi demonstratio penitus, etsi esset causatum notius apud nos. […] Atqui species tertia est contraria huius, hoc est, ut prius sequatur ex posteriori, hoc est ex causati causam [ex causa causatum ed.], et non convertatur. Et in hoc utique accidet demonstratio signi tantum.” Our transl. from Latin: “the consequence between antecedent and consequent, cause and effect, is of three ­species. Either they follow from one another: in this case, if the effect is better known to us than the cause, through that [i.e., the effect] there is demonstration of existence only. Then it is possible that we take the cause and show through it in a demonstration of the cause the existence of the effect of the subject. And here we have demonstration of the cause only, as Aristotle says later. Because if the cause were better known than the effect, under this species there will be a demonstration simpliciter only. The second species of consequence is when what is posterior follows from what is prior, that is the effect from the cause, and they do not convert. And in this species only a demonstration simpliciter is produced: and this because the cause is better known. Because if it were not better known, it would not produce a demonstration in the complete sense, even though the effect were better known to us. And the third species is contrary to this, that is, when what is prior follows from what is posterior, that is the cause from the effect and they do not convert. And in this case there can only be a demonstration from a sign.” Hugonnard-Roche (2002) only focuses on sign-inferences in which cause and effect are convertible, and thus neglects Averroes’ more fine-grained taxonomy; Dubouclez (2008), 163–165, considers a parallel threefold typology in the Epitome in libros logicae where the difference between demonstration simpliciter and demonstration of the cause is that the former is based on the convertibility of cause and effect. This is in tension with the passage just quoted, where the demonstration simpliciter is when cause and effect do not convert and yet the latter is inferable from the former. Moreover, neither typology seems to agree with Averroes’ comments on APo A 13 discussed above, where the demonstration simpliciter differs from a demonstration of the cause in that the former infers from a better known cause while the latter infers from a less known cause. The matter is certainly worthy of a careful examination which falls outside the scope of the present study. 124 Averroes, Aristotelis Opera I, GC in APo, c. 99, 161A–B; transl. Mantinus: “Nos vero ­invenimus Themistius posuisse demonstrationes, que exhibent existentiam trium specierum. […] Tertiam vero, quae monstrat posterius per posterius, quemadmodum qui monstrat, quod aegri huius urina est inconcocta, [quoniam] pulsus ipsius est diversus: et

238

chapter 5

Averroes’ typology of demonstrations plays a special role in his Great Commentary on Aristotle’s Physics.125 It will be recalled that in Physics A 1 Aristotle claims that the method of investigation must start from what is better known and clearer for us (the effect) and proceed from this to what is better known and clearer by nature (the cause), and that both Philoponus and Simplicius interpret this passage by reference to that lower kind of demonstration that they call “tekmeriodic.”126 This claim is in overt tension with the “strong” conception of demonstration that Aristotle presents in the Posterior Analytics and especially in APo A 2, which has to start from what is better known and clearer by nature (the cause) and proceed to what is better known and clearer to us (the effect). Averroes resolves the tension by distinguishing the method of discovery, in which we proceed from effect to cause, from the method of exposition, in which we proceed from cause to effect. The distinction is reminiscent of what Philoponus says in commenting on the very same passage, i.e., that Aristotle is implicitly distinguishing a “demonstrative” (discovery-like) from a “didactic” (exposition-like) method.127 What Aristotle is describing in Physics A 1—Averroes suggests—, is the method of discovery, while what he discusses in the Posterior Analytics is the method of exposition.128 The method of discovery is what the Greek-Arabic tradition labelled “sign” and corresponds to Aristotle’s that-demonstration. When in Physics A 1 Aristotle refers to a method of investigation starting from what is better known and clearer to us, the reference is actually to semiotic demonstrations:

hoc, [quoniam] diversitas pulsus, et concoctionis urinae ablatio, ambo sunt res causatae a febre putredinis, et ea posteriores aequaliter. Huiuscemodi enim syllogismi non sunt demonstrationes, nisi per accidens.” Our transl. from Latin: “We find that Themistius divides demonstrations that exhibit existence into three species. […] The third species is that which shows that which is posterior through that which is posterior, as for example that which shows that someone is ill whose urine is not concocted, because the pulse is irregular: and this, because the irregularity of pulse and the absence of urine concoction are both things caused by putrid fever, and both equally posterior to it. Syllogisms of such kind are not demonstrations, if not by accident.” 125 Averroes, Aristotelis Opera IV, GC in Phys. I, c. 2, 7A–D; cf. also the Middle Commentary, in Aristotelis Opera IV, 434G–H. See Elamrani-Jamal (2000), 113, for a quotation from the Epitome to the Physics in which the same tripartite division of demonstrations is given. On Averroes’ physics see Glasner (2009). 126 Cf. supra, §2.4. 127 Cf. supra, §2.4. 128 See Cerami (2015), 241–252, 287–288, 318–319; Barnes (1981) would agree that the P­ osterior Analytics is concerned with exposition and teaching, not with discovery; cf. supra, ­Chapter 1, footnote 101

Demonstration through Signs in 13th-Century Commentaries

239

After having shown that it is necessary for the physicist to provide the knowledge of causes and of elements, he begins to declare the way that leads to the knowledge of the causes of natural things and the nature of the demonstrations that provide the causes of natural things. And then he says: “the way to them,” namely the way that leads to the knowledge of the causes of natural things goes from accepted propositions from things that are posterior in being, which are better known and clearer to us, to conclusions that are prior in being, which are better known and clearer by nature and more concealed from us: and this is the type of demonstrations that is called sign.129 The typology of demonstrations also forms the backdrop of the debate between Avicenna and Averroes about the epistemology of physics and the subject matter of metaphysics.130 Avicenna based his argument concerning the subject-matter of metaphysics on three principles that he drew from the Posterior Analytics: (i) every science deals with a genus of things (its subject-matter) whose existence it takes for granted;131 (ii) every science has only one genus of things or subject-matter with which it deals;132 (iii) (in the formulation given in Abū Bišr Mattā’s translation, which Avicenna was using) the proper principles of each science cannot be demonstrated.133 Through the implicit or explicit application of these three principles Avicenna is led to claim that the subject matter of metaphysics is being qua being, not God or the four causes. He also claims that the proof of God’s existence is dealt with in metaphysics in the form of a “demonstration of the that” or “demonstration from a sign”(dalīl). The physical proof (from the existence of movement) of Physics Θ is only an 129 Averroes, Aristotelis Opera IV, GC in Phys, I, c. 2, 6 K8–L11; transl. Mantinus: “Cum declaravit quod oportet naturalem largiri cognitionem causarum et elementorum, incoepit declarare viam inducentem ad cognitionem causarum rerum naturalium et naturam demonstrationum largientium causas rerum naturalium. Et deinde dicit: Et via ad illa, id est via, inducens ad cognitionem causarum rerum naturalium, est de propositionibus acceptis ex rebus posterioribus in esse, quae sunt notiores et manifestiores apud nos, ad conclusiones priores in esse, quae sunt notiores et manifestiores apud naturam et latentiores apud nos: et est modus demonstrationum qui dicitur signum.” 130 On these topics see Bertolacci (2007); Di Giovanni (2009); Di Giovanni (2014), 66–76; Cerami (2014). 131 Aristotle, APo A 10, 76b11–16. “Subject-matter” is the meaning given to the expression ὑποκείμενον of APo A 9, 76a12, since Alexander of Aphrodisias; cf. Bertolacci (2007), 66 n. 11. 132 Aristotle, APo A 28, 87a38–39. 133 Aristotle, APo A 9, 76a8–17. Translations from the Arabic of the three principles are in Bertolacci (2007), 65–68.

240

chapter 5

anticipation with a merely propaedeutic function: the real proof of God’s existence is in the section of the Šifā devoted to metaphysics,134 where it is based on the finiteness of the chain of causes (material, formal, efficient, final) of Met Α 2.135 Averroes criticizes Avicenna’s argument: he considers the physical proof of Physics Θ as a semiotic demonstration that proves the existence of the subject matter of metaphysics on the basis of signs, and rejects the idea that metaphysics may establish the existence of God or of primary matter.136 Avicenna’s mistake is to think that principle (iii) applies to all types of demonstrations, while it only applies to absolute and causal demonstrations, but not to semiotic demonstrations: Avicenna contends that the natural speaks exclusively of the matter that is proximate to any being, and that only the first philosopher takes first into account. He was wrong. As he heard in the Posterior Analytics that no master of a discipline demonstrates the causes of the subject-matter that he takes into account—since, if he did demonstrate them by means of things that are prior to these causes, would pertain to a superior genus, and, thus, the clarification would belong to a superior discipline different , which takes into account the genus that contains the subject-matter of this discipline—as he heard this, he regarded it as impossible in the three ways of demonstration, i.e., demonstration as such, demonstration quia, and demonstration propter quid. But this is not so. For this is impossible only in a demonstration as such, and in a demonstration propter quid. In a demonstration quia, on the contrary, it is not impossible, as 134 Avicenna, Šifā, Ilāhiyyāt VIII.1–3 135 Bertolacci (2007), 78–84. 136 Averroes, Aristotelis Opera IV, GC in Phys, II, 47G–H; transl. Mantinus: “Et qui dicit quod prima Philosophia nititur declarare entia separabilia esse, peccat: haec enim entia sunt subiecta primae Philosophiae, et declaratum est in Posterioribus Analyticis quod impossibile est aliquam scientiam declarare suum subiectum esse, sed concedit ipsum esse, aut quia manifestum est per se, aut quia est demonstratum in alia scientia. Vnde Auicenna peccauit maxime, cum dixit quod primus Philosophus demonstrat primum principium.” Transl. in Bertolacci (2007), 86: “Whoever contends that first philosophy tries to show the existence of separable beings, is wrong. For these beings are the subject-matter of the first philosophy, and it is maintained in the Posterior Analytics that no science can show the existence of its own subject-matter, but takes its existence for granted, either because it is evident by itself, or because it is demonstrated in another science. Therefore, Avicenna made the greatest mistake as he said that the first philosopher demonstrates the First Principle’s existence.” Cf. Bertolacci (2007), 86–87; Di Giovanni (2014), 69–76.

Demonstration through Signs in 13th-Century Commentaries

241

Aristotle did with regard to the demonstration of the first matter and the First Mover in this book. If this concerns proper accidents of the being, it will be a demonstration pertaining to natural philosophy. If, on the other hand, it will concern proper accidents of being as such, it will be a demonstration pertaining to metaphysics. It is evident that the first matter cannot be properly shown to be existent except by means of a proof in natural philosophy. the First Mover cannot be shown to be existent except by means of a proof in natural philosophy.137 While the proper principles of each science cannot be demonstrated through an absolute or a causal demonstration, they can be demonstrated by means of a semiotic demonstration (or “a proof in natural science,” as Bertolacci translates signum naturale). In point of fact, the method in all sciences—with the exception of mathematics—is to proceed from things that are better known to us and less known by nature to things that are better known by nature, and this is precisely what Aristotle says at the beginning of the Physics.138 3.2 Albert the Great on Signs In Albert the Great’s paraphrase of the Posterior Analytics we find traces of the Greek exegetical tradition. In his comment on APo A 6 Albert argues that demonstration cannot proceed through accidental middle terms, because these are not necessary;139 nor can it proceed through inseparable accidents: 137 Averroes, Aristotelis Opera IV, GC in Phys, II, c. 22 56M–57B; transl. Mantinus: “Avicenna autem dicit quod naturalis non loquitur nisi de materia propinqua unicuique enti; de prima [materia] autem non considerat nisi primus philosophus. Et peccavit: cum enim audivit in Posterioribus quod nullus artifex demonstrat causas sui subiecti de quo considerat—quoniam, si demonstraret eas per res priores illis causis, tunc erit de genere superiori, quare illa declaratio erit de alia arte superiori quae considerat de genere continente subiectum illius artis—et, cum hoc audivit, existimavit hoc esse impossibile in tribus modis demonstrationum, scilicet in demonstratione simpliciter, et demonstratione quia, et demonstratione propter quid. Et non est ita: hoc enim non est impossibile nisi in demonstratione simpliciter et demonstratione propter quid; in demonstratione autem quia non est impossibile, sicut fecit Aristoteles in demonstratione primae materiae et Primi Motoris in hoc libro. Quae, si fuerit de accidentibus propriis entis, erit demonstratio naturalis; et si fuerit de accidentibus propriis entis simpliciter erit demonstratio metaphysica. Et videtur quod prima materia non potest declarari esse proprie nisi per signum naturale. Primus autem Motor impossibile est ut declaretur esse nisi per signum naturale.” Transl. in Bertolacci (2007), 89. 138 This idea is clearly expressed in Averroes’ Great Commentary on Met Z; cf. Cerami (2014), 458; Elamrani-Jamal (2000), 114. 139 Albert the Great, Lib. Post. An. I.2.16, ed. Borgnet, 60a: “accidentalia enim media non necessaria sunt: et ideo per talia non necesse est scire conclusionem secundum scientiam

242

chapter 5

Inseparable accidents too are not per se, even though there are syllogisms through them, as in the case of middle terms that are signs and not causes through which , for example: whoever has milk in the breast has given birth; she has milk in the breast, therefore she has given birth. Or: every body is colored; this is colored; therefore, this is a body. The conclusion is necessary, but is not per se, and from propositions that are not per se. Consequently, even if the conclusion were per se and necessary, and the premises and the middle term are not per se, but are such accidental signs from which syllogisms are constructed, this per se, that is, such conclusion that is thereby predicated of the subject through a sign (because of which such conclusion is per se), since anyone that so concludes, concludes through a sign, he does not know per se, nor does he know the why: to know the why is to know the cause; and this middle term is not cause, but sign.140 It will be recalled141 that in Kilwardby the two examples are alternative ­illustrations of the cavillatio: the first example (omne coloratum etc.) is of a middle that is an inseparable accident of the minor term, but nothing is said about its being a “sign,” while the second example (quaecumque habet lac etc., which ­Kilwardby takes from the alia translatio and from Themistius) is of an ­inseparable accident that is a sign of the major term’s predicating of the minor. Unlike in Kilwardby, in Albert the two examples are straightforwardly assimilated: both are inseparable accidents that are also signs. Accidents that are signs are also mentioned later in Albert’s commentary. Section II.2.8 contains a discussion of one of the crucial problems of the second book of the Posterior Analytics, namely whether it is possible to construct a definition from a demonstration, given that definitions cannot in general be propter quid: neque ostenditur per accidentalia, quod conclusio semper sit et aeterna si praemissae sint non per se. Et haec quidem de communiter accidentibus.” 140 Albert the Great, Lib. Post. An. I.2.16, ed. Borgnet, 60a: “Accidentia autem inseparabilia sunt etiam non per se, quamvis per ipsa syllogismi sint sicut per media quae sunt signa non causa propter quid, sicut, quaecumque lac habet in uberibus peperit: haec lac habet in uberibus: ergo peperit. Vel sic, omne coloratum est corpus: hoc est coloratum: ergo hoc est corpus. Conclusio est necessaria, sed non per se, et ex propositionibus quae non sunt per se: unde et si conclusio sit per se et necessaria, et propositiones et medium sint non per se, sed sint talia accidentia signa, ex quibus sunt syllogismi, hoc per se, hoc est, talem conclusionem quae sic per signum de subjecto praedicatur (propter quod talis conclusio per se est) quia taliter concludens concludit per signum, non sciet per se, neque sciet propter quid: propter quid enim scire est causam scire: tale autem medium non est causa, sed signum.” 141 Cf. supra, §5.2.

Demonstration through Signs in 13th-Century Commentaries

243

demonstrated. In this context, since the question concerning the existence of anything (quaestio quia est/si est) must precede the question concerning its cause (quaestio propter quid), Albert inquires into the different ways in which the knowledge of existence can be attained. One of the ways in which this happens is through an accidental middle “which is a sign rather than a cause.”142 We saw in the previous sections that Grosseteste’s and Kilwardby’s accounts of APo A 13 contain typologies of demonstrations which are implicitly extensional. Albert’s is explicitly extensional. This is his commentary on section (i) of APo A 13. On one way it is said science of the that if there is demonstrative ­syllogism through that which is not middle , i.e., if it is through a mediate middle ; such middle is not a middle , because it is not immediate; the middle must be immediate, and this is only transcendent and not convertible with the extreme; such is no sufficient and proximate cause; and thus such a middle is not taken as the primary cause, that is, proximate and convertible; through such transcendent middle only a science of the that is produced; but that which is science of the why is produced by a middle that is the primary, i.e., the proximate cause and essential to the conclusion. In the second way there is demonstration of the that in the same science when in a demonstration that which is not middle is taken as middle , that is, something immediate but which is not middle in that such immediate is not the cause, as when there is demonstration through an immediate effect that is convertible with the cause; for it is through converting or through convertible and proximate, and so through the better known to us; nothing indeed prohibits that of terms that equally and convertibly predicate (like proximate cause and effect) that which is not the cause but the effect is better known to us; and thus in so far as instruction is necessary it is more useful to demonstrate through the effect than through the cause; and for this reason there is demonstration through a science of the that.143 142

143

Albert the Great, Lib. Post. An. II.2.8, ed. Borgnet, 184b: “Procedamus igitur in illo et videamus quibus modis sciamus si est vel quia est. Dicamus igitur quod aliquando si est vel quia est habemus aliquando secundum accidens, hoc est, per medium accidentale quod potius est signum quam causa.” Albert the Great, Lib. Post. An. I.3.6, ed. Borgnet, 82b–83a: “Uno quidem modo dicitur­ scientia quia si fiat syllogismus demonstrativus per id quod est non medium, hoc est, si fiat per mediatum medium: tale enim medium est non medium, quia non est i­mmediatum:

244

chapter 5

The whole passage is only intelligible if medium is taken to mean “middle term convertible with the major that expresses the cause of the major.” For if it is so taken, then something can fail to be a medium either because is not convertible with the major or because it does not express the cause of the major. These two cases correspond to the two differences between quia and propter quid demonstration that Aristotle discusses in APo A 13. According to Albert, the first case is the one discussed by Aristotle in section (i) of APo A 13, which Albert clearly thinks involves non-convertible terms and where “immediate” is equivalent to “convertible.” A proximate cause is immediate, i.e., convertible with the effect; a middle term that is convertible with the major and which expresses the cause of it is a medium in the specified sense; but if it is not convertible, it is not a medium. The first kind of demonstratio quia that Albert considers is that from a non-proximate, i.e., non-convertible cause. The second case is the one discussed by Aristotle in sections (ii) and (iii) of APo A 13, which involves convertible terms; here the middle term of the argument fails to be a medium in the specified sense because it is not the cause but the effect, and the argument is again a demonstratio quia. The analysis that follows shows that Albert’s typology is Aristotelian, not Philoponean. His examples of the case of converting terms are non-­twinkling planets and the sphericity of the moon, from section (iii) of APo A 13. Here, both a propter quid demonstration (type 1a) and a quia demonstration of type 1b are possible. Then he says that when cause and effect do not convert, there may be either an inference from the effect, or an inference from the cause. As to the former, while no example is provided (just like in Aristotle in section (iv)), Albert has arguably a case in mind in which the cause is more extended than the effect and is inferred from it (type 2a), because otherwise no inference from the effect to the cause would be a deductively valid syllogism. The demonstratio immediatum autem debet esse medium, et hoc est tantum transcendens medium et non convertibile cum extremis: hoc enim non erit sufficiens et proxima causa: tunc enim in tali medio non accipitur prima causa, hoc est, proxima et convertibilis: per tale igitur transcendens medium non generatur nisi scientia quia: sed quae est scientia propter quid, est scientia generata ex medio quod est prima, hoc est, proxima et essentialis ­conclusionis causa. Alio vero modo secundo fit demonstratio quia in eadem scientia, quia, quando in demonstratione accipitur pro medio id quod non est medium, hoc est, aliquid quod est immediatum, sed est non medium in hoc quod immediatum est non causa, ut quando fit demonstratio per immediatum effectum et cum causa convertibile: tunc enim fit per convertentia sive per convertibilia et proxima, et sic per notius quoad nos: nihil enim prohibet inter ea quae aeque et convertibiliter praedicantur (sicut causa proxima et causatum) id quod est non causa, sed effectus, esse notius quoad nos: et tunc quoad instructionem necessariam utilius est demonstrare per effectum quam per causam: et ideo tunc per hanc scientiam quae est quia erit demonstratio.”

Demonstration through Signs in 13th-Century Commentaries

245

quia from a non-convertible effect is weaker, he says, than that from a convertible effect.144 As to the latter, here the example is the non-breathing wall of section (v), which is the inference of the negation of the effect from the negation of a more extended cause (type 2b).145 Both type 2a and type 2b involve a cause that is more extended than the effect; like Aristotle, Albert makes no mention of an effect that is more extended than the cause. The typology that he has in mind is authentically Aristotelian. Like Grosseteste and Kilwardby, he calls propter quid only the argument from a medium, i.e., from a convertible cause, and calls quia the argument from a convertible effect (1b), that from a less extended but better known effect (2a), and that from the negation of a more extended cause (2b). We saw that in Grosseteste’s and Kilwardby’s accounts of APo A 13 no explicit association is made between demonstrations quia of either type and sign-­ inferences. Albert does make some such an association with regard to converting cause and effect. He says that the inference of the sphericity of the moon from its phases—in which it sometimes appears in sickle shape and sometimes in a double horn shape (corniculata)—amounts to “demonstrating the cause of the effect through a sign (per signum effectus causam demonstrare).”146 The remaining quia demonstrations (types 2a and 2b) are not associated with sign-inferences in the same way. The association between that-demonstrations and signs is very feeble in Albert. The passages in which signs are mentioned are few and the matter is not spelled out in any detail. In this he has followed the Latin interpreters (Grosseteste and Kilwardby) and not the Greek-Arabic tradition. There is however a trace of a distinction that was crucial for the Greek interpreters of the Posterior Analytics: that between the logical and the ontological sense in which 144

145

146

Albert the Great, Lib. Post. An. I.3.6, ed. Borgnet, 83b: “In quibus autem demonstrationibus media quae sunt effectus, non convertuntur cum causa, eo quod non est effectus immediatus, et tamen medium est effectus et non causa, et effectus tamen ille mediatus notior quoad nos: si fiat demonstratio per talem effectum, iterum erit demonstratio per talem effectum demonstratio quia, et non demonstratio propter quid: sed debilioris virtutis erit haec demonstratio quam si fiat per effectum immediatum.” Albert the Great, Lib. Post. An. I.3.6, ed. Borgnet, 83b–84a: “Amplius autem secundo modo fit demonstratio quia in his in quibus medium quod est causa, ponitur extra extrema excellens utrumque extremorum: in talibus enim medium est causa remota non convertibilis et non sufficiens ad causandum effectum secundum seipsam.” Albert the Great, Lib. Post. An. I.3.6, ed. Borgnet, 83a–b: “Iterum fit per effectum demonstratio quia, ut si demonstret aliquis in astrologia quod luna circularis sit sive sphaerica per incrementa, hoc est, per modum incrementorum et decrementorum, quod corniculata sunt et sphaericitatem lineae ostendunt, quod est per signum effectus causam demonstrare.”

246

chapter 5

the premises of an argument may be said to be the cause of the conclusion. It is in Albert’s commentary on APo B 17, containing the second and last mention of sign-inferences that Aristotle makes in that work. We know that the Greek commentators interpret Aristotle’s claim that in some cases the causes can be multiple in the sense of the “logical cause,” not of the “ontological cause,” which must be unique. We also saw above that Kilwardby’s explanation of APo B 17 points to a different interpretation. Albert seems to agree with the Greek explanation: the shedding of leaves is the effect, not the cause, of having broad leaves; the inference of the latter from the former is an inference of the cause from the effect, and the middle term in this case is only the cause of the inference (causa consequentiae), but not of the thing inferred (causa consequentis).147 The feebleness of the association between signs and demonstrations in Albert’s work is confirmed by that portion of Albert’s commentary on Aristotle’s Physics in which the debate between Avicenna and Averroes about the possibility of knowing prime matter and God is reported.148 On the one hand, Albert seeks a solution that might reconcile the two positions; on the other hand, he exposes his ideas about the epistemological status of physics demonstrations. As we know,149 Averroes’ objection to Avicenna concerns the third principle, i.e., that the proper principles of each science cannot be demonstrated. Avicenna’s mistake, says Averroes, is to think that this principle applies to all types of demonstrations, while it only applies to absolute and causal demonstrations, but not to semiotic demonstrations, so that the existence of prime matter and of God can be demonstrated in physics by means of demonstrations from signs. After having reported Averroes’ position and his criticism of Avicenna,150 Albert proposes to distinguish an absolute sense of materia prima (simpliciter) from a physical sense (ens transmutabile). Physics treats of matter in the absolute sense neither through the cause nor through a sign: for when the demonstration is through a sign it is necessary that that sign be convertible just as the proper effect with the cause: but in the whole of physics there is no sign convertible with the matter, as matter is part of being and subdivides 147

Albert the Great, Lib. Post. An. II.4.7, ed. Borgnet, 222a: “Causa autem consequentiae et non consequentis (quae est medium) est folio fluere.” 148 Albert the Great, Physicorum Libri VIII, II.1.10, ed. Borgnet, 112b–113b. The passage is ­partially quoted in Bertolacci (2014), 421–422. 149 Cf. supra, §5.3.1. 150 Albert the Great, Phys. Lib. II.1.10, ed. Borgnet, 112b–113a.

Demonstration through Signs in 13th-Century Commentaries

247

it (prime matter simpliciter); consequently, the physicist demonstrates nothing through a demonstration of the that; and this is Avicenna’s position.151 Matter in the second sense falls under the genus of natural beings as principles and substrata of natural things, and physics demonstrates its existence by means of a physical sign, since it has in itself a convertible sign, namely the transmutability of things.152 It is thus evident that Averroes’ accusation of ­Avicenna is unfounded and that “there is no falsity in Avicenna’s words” (nulla est falsitas in verbis Avicennae).153 The association of the sign with the convertible effect unmistakably points to the first type of that-demonstration (type 1b), the only one that Albert associates with sign-inferences in his commentary on APo A 13. This is probably Albert’s only reference to the use of sign-inferences in ­physics. Unlike Averroes, who as we saw was happy to ground the whole of physics upon demonstrations of the that or sign-inferences, Albert regards physics as a discipline with a high epistemological status that needs to be grounded upon causal and universal why-demonstrations. It is in support of this idea that Albert also seeks to show that in physics one proceeds from what is at once better known to us (and less known by nature) and more universal. He appeals to the famous distinction between the three states of universals154 and argues that the physical universal must be distinguished from the universal in the plain sense: the latter, on which mathematical and metaphysical demonstrations are based, corresponds to the universal a re (or post rem), and 151

152

153 154

Albert the Great, Phys. Lib. II.1.10, ed. Borgnet, 113a: “quoniam, quando demonstratio est per signum, oportet quod signum illud sit convertibile sicut proprius effectus causae: sed in tota physica non est signum convertibile cum materia secundum quod ipsa est pars entis dividentis ipsum; ergo de illa nihil demonstrat physicus per demonstrationem quia: et haec est sententia Avicennae.” Albert the Great, Phys. Lib. II.1.10, ed. Borgnet, 113a: “Est autem materia secundo prima, quae est in genere prima dicta a physicis: et hoc est principium subiectum rerum naturalium: et bene verum est, quod scientia universalis physica cum sit perfecta, devenit in consideratione sua usque ad primum subiectum et primam formam physicorum. Et hanc declarat physicus per signum physicum, quia in se habet signum convertibile cum ipsa, quia est rei transmutabilis, ut dictum est.” Slightly earlier, in Phys. Lib. II.1.9, ed. Borgnet, 112a, Albert had opposed matter as part of the totality of being, which is not proportional to the form and constitutes no principle of natural entities because it is not affected by privation and motion (and this is the subject matter of metaphysics) and matter that is proportional and united to the form (and this is the subject matter of physics). Albert the Great, Phys. Lib. II.1.10, ed. Borgnet, 113b. About which see de Libera (1998), who shows that Albert takes this idea from Neoplatonic and Arabic sources.

248

chapter 5

is the abstract conception of things that resides in the understanding and is not accessible to the senses; the former corresponds to the universal in re, i.e., to the natura communis that exists in individuals.155 Through sensible perception, assisted by reason or by the estimative faculty, we can grasp the physical or in re universal.156 In his commentary on the second book of the Physics, Albert associates the sign convertible with the thing signified and the “proper” effect convertible with its cause. This might suggest the assumption on Albert’s part of some ­distinction between “proper” and “common” signs. Although not explicitly stated, the implicit assumption of some such distinction can be inferred by reading the passage just mentioned together with another passage from the commentary on the first book, where Albert criticizes the Heracliteans for thinking that physics has not the status of a scientia. While discussing the second ratio, which calls into question the possibility of a univocal definition of natural beings functioning as the middle term of a causal demonstration, Albert offers the following additional objection: If then you claim, says Heraclitus, that uses natural persuasions which are taken not through essential causes, but through common signs, I will say that such persuasions do not produce science unless they are reduced to demonstrations; yet cannot be reduced to demonstrations within physics; therefore, in physics there will be never science about any object of inquiry, but only some forms of belief (existimatio).157 The use of existimatio in this context is quite interesting. In the introduction to his logical writings Albert—inspired by his Arabic sources, in turn influenced by the Greek commentators—had adopted the so-called “enlarged” conception of logic, which includes both rhetoric and poetics, and had distinguished the several parts of logic that treat of argumentation (ratiocinatio) by 155 156

157

Albert the Great, Phys. Lib. I.1.6, ed. Borgnet, 12b–13b. Albert the Great, Phys. Lib. I.1.6, ed. Borgnet, 12a–16a. Albert here uses Aristotle’s example of the child who is unable to detect individual differences and confuses every man for his father, and Avicenna’s example of something seen from a distance, which is first judged to be a substance, then an animal, then a man, and finally an individual. Albert the Great, Phys. Lib. I.1.2, ed. Borgnet, 4b: “Si autem tu dicas, inquit Heraclitus, quod habet naturales persuasiones non per causas essentiales sumptas, sed per signa communia, dicam quod talis persuasio non facit scientiam, nisi reducatur ad demonstrationem aliquam; sed non potest reduci in genere physicae ad modum demonstrationis; ergo numquam erit scientia de aliquo quaesito in physicis, sed tantum existimatio quaedam.”

Demonstration through Signs in 13th-Century Commentaries

249

specifying their instruments and cognitive effects. For example, rhetoric uses signs and produces that sort of belief that Albert calls praesumptio; poetics uses fictions (ficta) that produce attraction or repulsion in the audience; dialectics (dealt with in the Topics) proceeds from what is probable and should produce opinion; demonstrative logic (dealt with in the Posterior Analytics) proceeds from essential causes (demonstrations of the why) and should produce science; sophistry proceeds through fallacious argumentations (what appears to be but is not) and should produce deception.158 In a later passage Albert orders these cognitive effects into a succession that suggests a decreasing degree of certainty that each possesses: opinio, fides, existimatio and suspicio.159 (These are later mentioned by Aquinas in his classification of the parts of logic.) In a parallel passage of the commentary on the Physics, then, Albert returns to the connections between cognitive effects and disciplines having a weak epistemological status, and specifies that only those disciplines which use demonstrations have science as their effect, while others, which make use of dialectics and rhetoric, do not have science as effect but only opinio, suspicio, or praesumptio.160 The connection between the existimatio (as weak adhesion to the content of a cognition) and the persuasive argumentations based on common signs (typical of dialectics and rhetoric), which we have seen is explicitly made in the passage quoted above, has further important developments in the commentaries on the Prior Analytics and the Sophistici Elenchi.161 One more indication. Albert’s commentary on the second part of APo A 13 is about the difference between the two kinds of demonstrations (propter quid and quia) in distinct and subordinate sciences. James of Venice’s translation runs like this: Huiusmodi autem sunt quecumque sic se habent ad invicem, et quod alterum sub altero est, ut speculativa ad geometriam et machinativa ad stereometriam et armonica ad arithmeticam et apparentia ad 158

Albert the Great, Super Porphyrium de V universalibus I.4, ed. Santos Noya, 6. We use the conditional in the case of dialectics, demonstrative logic, and sophistry because unlike Aquinas after him, Albert does not explicitly designate their respective cognitive effects. On this topic and for further bibliographic references see Marmo (1990) and Marmo (2013). 159 Albert the Great, Super Porphyrium de V universalibus I.4, ed. Santos Noya, 6: “Adhuc autem per hoc quod inveniendi quodlibet scitum scientia est per habitudines unius ad alterum, quae topicae sive locales vocantur, quibus intellectus vel opinio vel fides vel existimatio vel suspicio locatur in alio, quod jam intus habetur in animo quaerentis.” 160 Albert the Great, Phys. Lib. I.1.4, ed. Borgnet, 10b. 161 See infra, §§6.1.1, 6.2.

250

chapter 5

astrologicam. Fere autem univoce sunt harum quedam scientiarum, ut astrologia mathematica que et navalis est, et armonica mathematica que est et secundum auditum.162 In Aristotle’s Greek, the first part of the passage163 deals with the relation between objects and disciplines, not with that between superordinate and subordinate disciplines; the “objects” of the subordinate disciplines are expressed by substantivized adjectives in the neuter plural—τὰ ὀπτικά, τὰ μηχανικά, τὰ ἁρμονικά, τὰ φαινόμενα, literally, “that which is visible,” “that which is mechanic,” “that which is harmonic,” “that which appears [to the senses]”—while the disciplines superordinate to those that deal with these objects are expressed by nouns or polyrhematic expressions (πρὸς γεωμετρίαν, στερεομετρίαν, ἀριθμητικήν scil. ἐπιστήμην, ἀστρολογικήν scil. ἐπιστήμην). Quite regularly, Latin translators render the former with substantivized adjectives, some of which can also be regarded as names of disciplines on the condition that the subject scientia is made explicit: (scientia) speculativa, machinativa, armonica. The only exception to this is apparentia, which is the literal translation of the participle of φαίνομαι, which is used by Aristotle and which seems never to have been used as the name of a discipline. The names of the disciplines that deal with these objects are then listed in the second part of the passage: ἀστρολογία μαθηματική, (ἀστρολογία) ναυτική, ἀρμονικὴ μαθηματική, (ἀρμονικὴ) κατὰ τὴν ἀκοήν.164 Grosseteste’s paraphrase of the first part of the passage is quite liberal. It gives some coherence to the discussion about the disciplines and makes their several objects explicit by means of paraphrases:

162 Aristotle, APo A 13, 78b35–79a2, translatio Iacobi, AL IV, 31. Cf. the translatio Ioannis, AL IV, 130: “Talia autem sunt quecumque ita se habent ad invicem quod sit alterum sub altero, sicut inspectiva ad geometriam, et machinativa ad stereometriam, et armonica ad arismeticam, et apparentia ad astronomiam. Pene autem equivoce sunt quedam istarum scientiarum, sicut astrologia et mathematica et nautica, et armonica et mathematica et que est secundum auditum.” (emphasis ours). Cf. also the translatio Gerardi, AL IV, 214: “Et huiusmodi scientie sunt omnes scientie quarundam quarum forma apud alias est hec forma quam narro, et est ut sit una duarum scientiarum sub altera, sicut scientia de aspectibus sub geometria, et scientia machinarum apud scientiam corporum, et scientia compositionis cantus apud scientiam numeri, et apparentia apud scientiam stellarum. Harum autem scientiarum nomina fere sunt univoca, sicut scientia stellarum doctrinalis et illa qua utitur ars nautica, et sicut scientia cantus doctrinalis apud illam que est in cordis.” (emphasis ours). See below (footnote 167 for a translation into English. 163 Aristotle, APo A 13, 78b37–39. 164 Aristotle, APo A 13, 78b40–79a2.

Demonstration through Signs in 13th-Century Commentaries

251

like the science that is based on the lines and the figures of the rays is subordinate to geometry, which is based on figures tout court, and the science of the composition of machines, like architecture and other mechanic sciences, is under the science of corporeal figures, and the science of consonant sounds is under arithmetic, and the science that is possessed by navigators in directing the course of ships by means of the apparition of the stars is subordinate to astronomy.165 Grosseteste distinguishes the objects from the disciplines based on them, and his liberal paraphrases allow an interpretation of the text that is both intelligible and consistent. Kilwardby, on the contrary, introduces a note to explain Aristotle’s examples. On the one hand, he regards machinativa as the name of the discipline that deals with the construction of houses and towers. On the other hand—perhaps as the result of a misunderstanding of Grosseteste’s commentary—he regards apparentia as the name of a discipline, too: “‘appearance’ is the name of the art of directing the course of ships by means of the experience drawn from the disposition and the collocation of the stars (in the sky)” (Apparentia est ars rectificandi cursus nauium per experientiam a dispositione et a situ stellarum accepta).166 Albert follows Kilwardby in taking Aristotle’s neuter plurals167 as the names of the subordinate disciplines rather than the name of their objects. Having treated of the scientia machinativa (which should properly be called scientia de ingeniis, or engineering) and of harmonica, Albert concludes as follows: And like nautical science (which is called “appearance”) relates to astrology as regards that part which deals with angles and the diversity of the

165

Robert Grosseteste, Comm. in APo I.12, ed. Rossi, 194: “velut scientia que erigitur super lineas et figuras radiosas est sub geometria, que erigitur super figuras simpliciter, et scientia compositionis machinarum, ut architectura et alie machinative, est sub scientia figurarum corporalium, et scientia consonantiarum sub arithmetica, et scientia quam habent naute in dirigendo cursum navium per apparitionem stellarum subalternatur astrologie.” 166 Robert Kilwardby, Notule lib. Post. I.28, ed. Cannone, II, 172. 167 Jonathan Barnes seems to be following the Latin tradition, taking the names of the objects as names of their sciences: “These are the cases which are related to each other in such a way that the one falls under the other, e.g., optics to geometry, mechanics to solid geometry, harmonics to arithmetic, star-gazing to astronomy. Some of these sciences bear almost the same name as one another—e.g., mathematical and nautical astronomy, and mathematical and acoustical harmonics” (Barnes 1993, 21).

252

chapter 5

visible aspect : nautical is modeled and subordinated to it according to what appears in the stars.168 As we shall see in what follows,169 Kilwardby’s and Albert the Great’s interpretation of the term apparentia in this context paves the way for Giles of Rome to make some interesting remarks about nautical art as a discipline that actually employs signs or as an applied semiotics. 4

Thomas Aquinas and the Question Commentaries

Aquinas wrote a literal exposition of the Posterior Analytics during his Parisian period, between 1271 and 1272, before moving to Naples. In all probability it was published only around 1275,170 after Aquinas’ death, and had a great success at the Faculty of Arts in Paris.171 In this section we shall see that Aquinas and the question commentaries produced in Paris at the end of the thirteenth century confirm the substantial disconnection between demonstratio quia and sign-inferences which characterizes the Latin reception of the Posterior Analytics, in opposition to the Greek-Arabic tradition which had straightforwardly assimilated the two notions. 4.1 Aquinas Like his predecessors, Aquinas mentions signs and sign-syllogisms very rarely. The few mentions of signs in his commentary on the Posterior Analytics are remarkable for the examples that are used more than for the theory that they illustrate. The first mention occurs, quite naturally, in the section on APo A 6. Following Aristotle quite closely, Aquinas argues that if the premises of an argument are always true and necessary, but not per se, the conclusion is not demonstrated; this happens in the syllogisms from signs, “in which the ­conclusion, though per se, is not known per se or through the cause.”172 The 168

Albert the Great, Lib. Post. An. I.3.7, ed. Borgnet, 85a: “Et sicut scientia navalis (quae apparentia vocatur) se habet ad astrologiam quantum ad illam partem quae est de angulis et de diversitate aspectus: ad hanc enim navalis secundum apparentiam in stellis vias navium imaginatur et dirigit.” 169 See infra, §5.5. 170 Cf. Gauthier (1989), 55*–59*, 73*–77*. 171 On one aspect of this success, namely the diffusion of the model of an “enlarged” logic of Neoplatonic and Arabic origins, cf. Marmo (1990). 172 Thomas Aquinas, Expositio libri Posteriorum. Editio altera retractata I.14, ed. Gauthier, 54b–55a: “Vlterius autem ostendit quod etiam si premissa essent semper et necessaria, set

Demonstration through Signs in 13th-Century Commentaries

253

explanation is little more than a paraphrase of Aristotle, but the example is new: if the conclusion “any element is corruptible” is inferred from the premise “any element mutates through time,” the inference is through a sign (per signum), because neither is this premise the cause of the conclusion nor does it contain a per se predication. (The major premise should be something like “anything mutable through time is corruptible.”) Like Grosseteste, Kilwardby, and Albert the Great, Aquinas interprets APo A 13 as involving a taxonomy of demonstrations, only one of which is propter quid. Much like Albert, Aquinas takes APo A 13 to be based on the assumption that a propter quid demonstration has to satisfy two conditions, namely it has to be “from the cause” and “from immediates,” and that quia demonstrations fail to satisfy either or both these conditions. Section (i) of APo A 13 is about quia demonstrations not satisfying the immediateness condition, while sections (ii) and (iii) is about quia demonstrations not satisfying the causal condition. Now, with regard to section (i), Aquinas takes it to be illustrated in section (v) by the second-figure argument about non-breathing walls, which involves a cause that is more extended than the effect (and a that-demonstration of type 2b). With regard to the causal condition, Aquinas assumes that Aristotle is discussing cases not satisfying it in sections (ii), (iii), and (iv), with this difference, that while (ii) and (iii) concern convertible effects, and thus demonstrations quia of type 1b, in which only the causal requirement is not satisfied, section (iv) concerns non-convertible effects and thus demonstrations quia of type 2a (for 2b is discussed under section (i)), in which both the causal and the immediateness conditions are not satisfied. His analysis of section (iv) is quite interesting: Then he shows that a demonstration through a non-convertible effect is quia. He says, therefore, that even in those syllogisms in which the middles are not converted with the extremes, and in which an effect rather than a cause is taken as the middle better known to us, even in those cases the demonstration is quia and not propter quid. If the middle be such that it can be converted with the major extreme and it exceeds the minor, then obviously it is a fitting syllogism; for example, if one proves that Venus is near because it does not twinkle. On the other hand, if the minor exceeded the middle, it would not be a fitting syllogism: for one cannot conclude universally of stars that they are near because they non per se, non tamen sciretur de conclusione ‘propter quid’, sicut patet in sillogismis qui fiunt per signa, in quibus conclusionem, quae est ‘per se’, non scit aliquis ‘per se’, neque ‘propter quid’ […].”

254

chapter 5

do not twinkle. Quite the contrary is true in comparison to the major term: for if the middle is in less things than is the major term, the syllogism is fitting, as when it is proved that someone has a sensible soul on the ground that he is capable of progressive local motion. But if it is in more, then the syllogism is not fitting, for from an effect which can proceed from several causes, one of them cannot be concluded. Thus, one cannot conclude from a rapid pulse that he has a fever.173 When a middle convertible with the major extreme and exceeding the minor expresses an effect, the inference is a quia demonstration of type 1b. In Aristotle’s example, the minor term (the class of planets in general) may also be taken to convert with the middle (in an astronomical context, anything not twinkling is a planet and vice versa), while here the minor term, being only a member of that class (Venus), does not convert with the middle. When a middle term converting with the major and less extended than the minor expresses an effect, we do not have a valid syllogism. For example, one cannot conclude universally (i.e., in the first figure) that stars are near because they do not twinkle. For the middle (not twinkling) is less extended than the minor term (stars), and thus the minor premise would have to be converted (in an astronomical context anything not twinkling is a heavenly body or “star” but not vice versa), and this would produce a deductively invalid third-figure syllogism. Since it is deductively invalid, it is no demonstration at all. When a middle term less extended than the major expresses an effect, we have a valid syllogism. (Aquinas’ example—the inference that someone has a sensible soul because he is capable of local motion—makes it clear that the

173 Aquinas, Expositio lib. Post. I.23, ed. Gauthier, 86b: “Deinde cum dicit: In quibus autem media etc., ostendit quod sit demonstratio ‘quia’ per effectum non conuertibilem, dicens quod in illis etiam sillogismis in quibus media non conuertuntur cum extremis, et accipitur ut notius quo ad nos, scilicet loco medii quod non est causa, set magis effectus, demonstratur quidem ‘quia’, set non ‘propter quid’. Et quidem si tale medium conuertatur cum maiori extremitate et excedat minorem, manifestum est quod conueniens fit sillogismus, sicut si probetur de Venere quod sit prope quia non scintillat. Si autem e converso minor terminus esset in plus quam medium assumptum, non esset conueniens sillogismus: non enim potest de stella uniuersaliter concludi quod sit prope per hoc quod non scintillet. In comparatione autem ad maiorem terminum est e converso: nam si medium sit in minus quam maior terminus, conueniens fit sillogismus, sicut si per hoc quod est moueri motu progressivo probetur de aliquo quod habeat animam sensibilem. Si autem sit in plus, non fit conueniens sillogismus. Nam ab effectu, qui a pluribus causis procedere potest, non potest una illarum concludi, sicut non potest concludi, quod aliquis habeat febrem, ex citatione pulsus.” Transl. Larcher, modified.

Demonstration through Signs in 13th-Century Commentaries

255

minor can also be less extended than the middle.) Using a particular animal, say the donkey, for the minor term, the syllogism is like this: Major premise: Omne quod movetur motu progressivo habet animam sensibilem Minor premise: Omnis asinus movetur motu progressivo Conclusion: Omnis asinus habet animam sensibilem This syllogism has the form of a demonstratio quia of type 2a. The example used by Themistius and Philoponus to illustrate it is the inference of the sexual intercourse from the fact of having given birth, or the inference of fire from the presence of smoke. When a middle term is more extended than the major and expresses an effect, there can be no valid syllogism. The example has the form of a deductively invalid second-figure syllogism and of the second-figure sign-inference treated by Aristotle in APr B 27. Major premise: Omne quod habet febrem habet pulsum excitatum Minor premise: Hic habet pulsum excitatum Conclusion: Hic habet febrem When things stand in this way, only the inference from the cause to the effect is deductively valid, and Philoponus is the only one to add it to the inventory of demonstrations. But Aquinas is considering it as the inference from the effect, and so considered, it is deductively invalid, and, again, no demonstration at all. Aquinas’ analysis of section (iv) of APo A 13 (“from a non-convertible effect”) has thus the following result: of four possible cases, only two constitute deductively valid inferences from the effect. If the middle expressing the effect is convertible with the major but not with the minor, the inference is of type 1b; if the middle expressing the effect is less extended than the major, the inference is of type 2a. No “Philoponean” inference involving a more extended effect is considered by Aquinas. His typology is Aristotelian. In none of the cases under examination does Aquinas say that the effects are “signs” of their cause. But he does say so in his comments on the second and last occurrence of sign-inferences in the Posterior Analytics. This time the example comes from ethics. We know that in APo B 16–17 Aristotle discusses the convertibility of cause and effect. Aquinas observes that when anything is the per se cause of something else, cause and effect are convertible. When on the contrary the effect is common to more than one cause there is

256

chapter 5

no convertibility. This is the case explicitly excluded in Aquinas’ discussion of section (iv) of APo A 13, but emerges in his discussion of APo B 16–17. In this case, Aquinas says, the middle term is a sign or an accident. The example is the inference of blameworthiness from excess (of courage, in the brave) or deficiency (in the timid). Since the inference of the cause from the effect is deductively invalid, here only the inference of the effect from the cause is possible in the form of two why-syllogisms in which the middle term expresses the cause (excess or deficiency): omnis qui habet superhabundanciam est uituperabile (every B is A) omnis audax habet superhabundanciam (every D is B) omnis audax est uituperabilis (every D is A) omnis qui habet defectus est vituperabile (every C is A) omnis timidus habet defectum (every E is C) omnis timidus est vituperabilis (every E is A) If there is the cause, then there must be the effect (rem esse): if there is either excess or deficiency, we can infer that there will be blameworthiness. But it is impossible to construct a syllogism of the that from terms having these relations. If there is the effect, it is necessary that there be one cause, but no inference to one determined cause can be made: if there is blameworthiness, it is impossible to determine whether it is due to excess or to deficiency.174 This is the case explicitly considered by Philoponus in his analysis of APo A 6 and of the second part of APo A 13 and not considered by Aquinas in his analysis of APo A 13; it is the explicit consideration of this case that distinguishes a Philoponean from an Aristotelian typology of demonstrations. In the following lecture (II.19) the same example is used again to illustrate a sign or accident which is taken as middle term in a syllogism and which is unable to determine the cause: However, if one does not take as the inferring cause that which is per se the middle of demonstration, but some sign or accident is used as the middle, then it does happen that of one effect several causes, as it were, are taken in different things, as is clear in the example given earlier. For 174 Aquinas, Expositio lib. Post. II.18, ed. Gauthier, 237b: “[…] set existente re, necesse est quidem quod aliqua causarum sit, non tamen necesse est quamlibet causam esse (sicut posito quod aliquid sit uituperabile, non est necesse quod sit in superhabundancia, set necesse est quod uel sit in superhabundancia uel in defectu).”

Demonstration through Signs in 13th-Century Commentaries

257

the per se cause why something is blameworthy is that it is not according to reason. But to be excessive or defective is a sign of that which is not according to reason.175 Again, there can be a causal demonstration from the cause to the effect, but there can be no demonstration from the effect to the cause, because there can be multiple causes of the same effect. When terms are so related as in Aquinas’ ethical example, only the inference of the more extended effect from the cause is possible; but this does not qualify as a demonstration from a sign because a cause is not, in general, a sign of the effect. Why-syllogisms of this sort only occur in Philoponean typologies of demonstrations, but are absent in Aristotelian typologies. By contrast, the converse inference from the more extended effect to the cause would count as a deductively invalid sign-syllogism in the second figure. None of the commentators on the Posterior Analytics has dared to admit into the realm of the theory of demonstration a deductively invalid form of reasoning. There are demonstrations of a lower kind, of course, but none of them is defective in form. If semiotic demonstrations are to be admitted, they have to qualify as τεκμήρια, not σημεῖα in the strict sense. Deductive validity is still the golden standard of the Aristotelian theory of science. No association between demonstration and sign-inference is made in ­Aquinas’ commentary on the first book of the Physics.176 By contrast, in the commentary on Boethius’ De trinitate, Aquinas identifies the demonstratio signi with the method ex posterioribus of Phys A 1: 175 Aquinas, Expositio lib. Post. II.19, ed. Gauthier, 239a-b: “Si uero non accipiatur quasi causa inferens id quod est per se medium demonstrationis, set accipiatur pro medio aliquod signum uel aliquod accidens, tunc contingit unius effectus accipi quasi plures causas in diuersis, ut patet in exemplo superius posito; per se enim causa quod aliquid sit uituperabile, est esse preter rationem rectam, set quod aliquid sit superhabundans uel deficiens, est signum eius quod est preter rationem rectam.” Transl. Larcher. 176 Yet there is a reference to Averroes’ equivalence between demonstratio quia and demonstratio signi in the commentary on the seventh book: “Sed dicit Averroes quod ista demonstratio non est de genere demonstrationum simpliciter, sed de genere demonstrationum quae dicuntur demonstrationes signi, vel demonstrationes quia, in quibus est usus talium conditionalium” (In Phys VII, lec. 1 n. 889). The argument in question is that of Phys H 1 intended to prove that everything that is in motion must be moved by something. The argument is an argument “through the impossible,” and according to Averroes any such argument is not a demonstration in the proper sense (propter quid, absolute or simpliciter) but only a demonstration quia or signi. According to Aquinas, by contrast, the argument is a proper demonstration propter quid because it shows the cause of the conclusion: “sed videtur dicendum quod non sit demonstratio quia, sed propter quid; continet enim causam quare impossibile est aliquod mobile movere seipsum” (ibid.); see Kukkonen (2002).

258

chapter 5

as the rational soul comes to the knowledge of the intelligibles, which are best known by nature, starting from what is perceptible, which is best known to us, so natural science proceeds from what is better known to us and less known by nature, as is evident from the first book of the Physics, and the demonstration that starts from the sign or effect is the one most used in natural science.177 Just like the cognition of the intelligible (better known by nature) derives from the cognition of what is sensible (better known to us), so in natural science one proceeds from what is better known to us to what is better known by nature. This method, announced in Phys A 1, is that of the demonstration of a cause from its effect, which here Aquinas, in agreement with the Greek-Arabic ­tradition, qualifies as a demonstratio per signum. Here the explicit reference to the demonstratio quia of APo A 13 is absent; yet talking of a demonstratio per signum vel effectum is ipso facto to accept the identification of demonstratio quia (which is per effectum) and sign-inference (which is per signum). It has also to be recalled, in conclusion, that Aquinas uses the distinction of APo A 13 between demonstratio quia and demonstratio propter quid in the Summa theologiae precisely in the context of the demonstration of God’s existence. The demonstration is twofold. One is that which through the cause and is called of the why, and this is accomplished through what simply precedes. The other is realized through the effect and is called demonstration of the that, and this proceeds through what is better known to us; since an effect is better known to us than its cause, we proceed through the effect to the knowledge of the cause. From any effect, the existence of its cause can be demonstrated (provided that its effects are better known), since, depending the effect on the cause, once the effect is in existence, its cause must pre-exist. Consequently, that God exists, since He is not known to us in itself, is demonstrable through the effects that are known to us.178 177 Aquinas, Super Boethius De Trinitate III, qu. 6, art. 1, com. 3: “sicut anima rationalis a sensibilibus, quae sunt nota magis quoad nos, accipit cognitionem intelligibilium, quae sunt magis nota secundum naturam, ita scientia naturalis procedit ex his, quae sunt nota magis quoad nos et minus nota secundum naturam, ut patet in I Physicorum, et demonstratio, quae est per signum vel effectum, maxime usitatur in scientia naturali.” 178 Aquinas, Summa theologiae I, qu. 1, art. 2: “duplex est demonstratio. Una quae est per causam, et dicitur propter quid, et haec est per priora simpliciter. Alia est per effectum, et dicitur demonstratio quia, et haec est per ea quae sunt priora quoad nos, cum enim

Demonstration through Signs in 13th-Century Commentaries

259

God, better known by nature, is the cause of effects that are better known to us. The demonstration of God’s existence is accordingly from the effects to their cause, and is a demonstration quia rather than propter quid. In order for a demonstration propter quid of God’s existence to be possible one should proceed from the cause of God; but God is the uncaused cause, and therefore does not admit of a demonstration propter quid. The famous five demonstrations of God’s existence that Aquinas expounds in the third article of the second question are in fact demonstrationes quia that proceed from the existence of God’s effects (the existence of motion, the existence of efficient causes, the existence of the possible and the necessary, the existence of degrees in things, and the existence of an end in the action of things) to the existence of their cause (God).179 4.2 Question Commentaries Given the almost exceptionless silence about sign-inferences in the literal ­commentaries since Grosseteste, it is not surprising that subsequent ­question commentaries (which are rather more selective in the topics treated, as they only focus on the problems that are more pressing in a certain period or those that are of some interest to the master who authors the commentary or who proposes the questions) leave not much space to the syllogismi or demonstrationes per signa. Among the seven question commentaries that we have consulted—those by James of Douai (Iacobus de Duaco), Gerard of Nogent (Gerardus de Nogento), Anonymus Cordubensis, Anonymus Monacensis (only on APo A), Anonymus Brugensis, Simon of Faversham and Radulphus Brito,180

179 180

effectus aliquis nobis est manifestior quam sua causa, per effectum procedimus ad cognitionem causae. Ex quolibet autem effectu potest demonstrari propriam causam eius esse (si tamen eius effectus sint magis noti quoad nos), quia, cum effectus dependeant a causa, posito effectu necesse est causam praeexistere. Unde Deum esse, secundum quod non est per se notum quoad nos, demonstrabile est per effectus nobis notos.” On the Five Ways as arguments from effect to cause see Martin (1997), esp. ch. 6. It is thanks to generosity of Sten Ebbesen, who allowed us to see his complete transcriptions of these documents (with the exception of Faversham’s and Brito’s), that we have been able to verify the character of the debate about the distinction between demonstration quia and demonstration propter quid in the question commentaries of the second half of the thirteenth century. These commentaries are preserved in the following mss.: Iacobus de Duaco, Quaest. sup. APo, ms. Klosterneuburg, Stiftsbibliothek, CCI 274, 148ra–161va (K); Gerardus de Nogento, Quaest. sup. APo, ms. Paris, Bibl. Nationale de France, Lat. 16170, 113rb–127va; Anonymus Cordubensis, Quaest. sup. APo, ms. Cordoba, Biblioteca del Excellentissimo Cabildo, 52, 80va–100rb; Anonymus Monacensis, Quaest. sup. APo I, ms. München, Staatsbibliothek, clm 14460, 239ra–242ra; Anonymus Brugensis, Quaest. sup. APo, ms. Brugge, Stedelijke Openbare Bibliotheek, 509, 59ra–75va.

260

chapter 5

spanning from the 1270s to the end of the century—only James of Douai’s commentary treats of sign-syllogisms. According to Gauthier (1989), James of Douai composes his commentary between 1275 and 1280, when Aquinas’ Expositio is already in circulation at the Faculty of Arts in Paris. James mentions the syllogismi per signa in a question devoted to accidents, in which reference is made to APo A 6, 75a31–34.181 He also makes some interesting observations on sign-inferences in the context of his discussion of the demonstratio quia. The question is whether a demonstratio quia is a demonstration or not.182 One argument in support of a negative answer is that the dialectician uses signs; since the effect that is the middle term in a demonstratio quia is a sign of its cause, the demonstratio quia is a dialectical syllogism, not a demonstrative syllogism.183 A reply to this argument follows the determinatio in which the master restates the distinction between why- and that-demonstrations and points out that like a demonstratio propter quid, a demonstratio quia does produce certitude (as opposed to opinion, which is the cognitive effect of dialectical arguments).184 There is no graduality between demonstratio quia and demonstratio ­propter quid. According to James, their difference is neither in the kind of ­knowledge that they produce, nor in the necessity of the inference; rather, the difference consists in the means that produce the certitude (cause or effect as middle

181

182 183

184

We read the quaestiones veteres by Simon of Faversham in John Longeway’s edition; we consulted those by Radulphus Brito in the mss. indicated in Appendix A. Iacobus de Duaco, Quaest. sup. APo I.34 (u. accidens sit necessarium), K 153va–b, trascr. Ebbesen: “Praeterea, dicit Aristoteles quod si sit aliqua propositio quae sit semper et non per se, et fiat syllogismus ex illis(!) non erit demonstratio si ei non addatur alia necessaria, sicut syllogismi sunt per signa. Videtur ergo innuere quod aliqua sint semper quae sunt accidentia et aliqua // non sunt semper nisi necessaria. Videtur ergo quod accidens potest esse necessarium.” Iacobus de Duaco, Quaest. sup. APo, I.45 (u. demonstratio quia sit demonstratio), K 155va–b. Iacobus de Duaco, Quaest. sup. APo I.45, K 155va, trascr. Ebbesen: “Praeterea. ­Syllogismus dialecticus secundum quod talis non est demonstrativus, sed demonstratio quia est ­syllogismus dialecticus, nam syllogismus qui est per signa videtur esse dialecticus; nunc autem effectus est signum suae causae.” Iacobus de Duaco, Quaest. sup. APo I.45, K 155va, trascr. Ebbesen: “Ad hoc dicendum quod talis(?) ostensio demonstratio est, nam talis(?) processus certitudinem inducit de quaestione et non solum opinionem. Ex hoc enim quod luna recipit lumen secundum figuram circularem, ex hoc certus est aliquis quod luna est sphaericae figurae, unde ista demonstratio non est dialectica, quia dialectica solum facit opinionem, ista vero certitudinem eo quod effectus necessarius est respectu suae causae.”

Demonstration through Signs in 13th-Century Commentaries

261

terms and premises of the syllogism).185 A demonstratio quia, he says, produces certitude by means of either convertible or non-convertible effects, and by means of either proximate or remote effects (sive fiat per effectum convertibilem vel non, sive per effectum propinquum sive remotum).186 It is not clear whether James takes “convertible” to be equivalent to “proximate” and “non-convertible” to be equivalent to “remote.” Were it so, the second disjunctive condition (sive per effectum propinquum sive remotum) would be a reformulation of the first (sive per effectum convertibilem vel non). In any case, neither “non-convertible” nor “remote” effects can have a wider extension than the cause, because James is clear that in a demonstration we have the certitude that the conclusion cannot be otherwise, and this is only possible in deductively valid arguments from effects convertible with their cause (i.e., that-demonstrations of type 1b). The reply to the argument in support of the negative answer then distinguishes between two kinds of signs: To the argument that there is a sign that produces certitude about what it signifies, and this pertains to demonstration; and another sign that once posed does not necessitate that also what it signifies is posed, nor does it produce certitude about what it signifies, and this sign has to be considered by the dialectician.187 This is one of the few passages of a commentary on the Posterior Analytics in which knowledge through signs is credited with a certain demonstrative and scientific quality. This is done by means of the distinction between necessary signs, which necessitate the thing signified (the τεκμήριον of APr B 27, the that-demonstrations of APo A 13), and non-necessary signs, which do not necessitate the thing signified (the σημεῖον in the strict sense of APr B 27). Only these latter belong to dialectics. As we shall see in the next Chapter, for most 185

186

187

Iacobus de Duaco, Quaest. sup. APo I.45, K 155va–b, trascr. Ebbesen: “Unde differentia est inter demonstrationem propter quid et quia: demonstratio enim propter quid facit scire effectum et certitudinem effectus per causam, et est effectus propter causam expressam per demonstrationem propter quid; demonstratio quia vero // facit certitudinem quia ita est, non tamen facit certitudinem causae propter quid ita est.” Iacobus de Duaco, Quaest. sup. APo I.45, K 155vb, trascr. Ebbesen: “Unde omnis demonstratio quia sive fiat per effectum convertibilem vel non, sive per effectum propinquum sive remotum, si tamen(?) certitudinem inducit ita quod se habere non potest aliter apud illum qui hoc credit, demonstratio est.” Iacobus de Duaco, Quaest. sup. APo I.45, K 155vb, trascr. Ebbesen: “Ad aliud quod aliquod est signum quod inducit de suo significato certitudinem, et tale pertinet ad demonstrationem; et est aliud signum quo posito non oportet quod ponatur significatum nec faciens certitudinem de significatum, et tale signum habet considerare dialecticus.”

262

chapter 5

commentators of the logica nova, signs belong to dialectic or rhetoric, not to the theory of scientific demonstration. James’ position is different. After all, this agrees with what he says in the prooemium of his commentary, where he speaks of a graduality among the disciplines that use the methods of dialectic, rhetoric, and poetics, which produce—according to Aquinas, whom Iacobus is here following—opinio, suspicio, and aestimatio respectively.188 In subsequent questions (I.46–47), James discusses about the knowledge of the cause from its effect, but in this case he never qualifies the effect as a sign, although he clearly connects it to the demonstration of the that. The same happens with the other Parisian Masters of Arts who discuss the question whether the demonstration of the that is a demonstration at all: utrum demonstratio quia sit demonstratio (simpliciter, some add).189 Since these works are not literal expositions, their authors are not committed to display a full typology of that-demonstrations. Some, such as Simon of Faversham and Radulphus Brito, however, recall en passant the distinction between the proof that moves from an immediate effect (type 1b) and the proof that has as its middle term a remote cause (type 2b, according to the example of the non-breathing wall recalled by Brito).190 5

Giles of Rome between Astrologers and Sailors

Giles of Rome’s commentary, composed in 1285,191 is a literal commentary. It follows Aristotle’s text closely and tries to give a rational justification for its structure by means of a minute divisio textus followed by several notanda (annotations) e dubitationes.192 As far as the distinction between demonstratio 188 189

Cf. Marmo (1990), 175–176. Cf. Gerardus de Nogento, Quaest. sup. APo, ms. Paris, Bibl. Nationale de France, Lat. 16170, 122rb-va (u. possit esse aliqua demonstratio per effectum procedens, where this type of demonstration is clearly a that-demonstration); Anonymus Cordubensis, Quaest. sup. APo, ms. Cordoba, Biblioteca del del Excellentissimo Cabildo, 52, 99va-rb (u. demonstratio faciens scire quia sit demonstratio); Anonymus Brugensis, Quaest. sup. APo, ms. Brugge, Stedelijke Openbare Bibliotheek, 509, 70rb (u. demonstratio quia sit demonstratio simpliciter); Simon of Faversham, Quaest. sup. APo I.53, ed. Longeway, 252–254 (u. demonstratio quia sit demonstratio simpliciter); Radulphus Brito, Quest. sup. APo I.68 (Appendix A). 190 See Radulphus Brito, Quest. sup. APo I.68, §3.2 (Appendix A). 191 Cf. Donati (1990), 71. 192 For a detailed analysis of Giles’ divisio textus see Bertagna (2002); Bertagna (2003); Bertagna (2004). A presentation of the commentary and of its contents is in Marmo (2016), 244–254.

Demonstration through Signs in 13th-Century Commentaries

263

propter quid and quia is concerned, Giles follows earlier commentators and in particular Aquinas, but with a greater attention than the latter to the coherence of Aristotle’s text.193 Like Albert and Aquinas, Giles gives two conditions that have to be satisfied for a (deductively valid) syllogism to be a demonstration of the why: the syllogism should be (i) from the cause and (i) from an immediate middle term.194 Any syllogism not satisfying either or both conditions is a that-demonstration: For a demonstration of the why two are required and both must be realized together in it, namely that this demonstration be through the cause and that it be through an immediate cause, that is, proper and convertible. Consequently, we have demonstration of the that either if it is not through the cause but through the effect, or if it is through the cause but not through an immediate and convertible cause. There can be a third mode of demonstration of the that, in case satisfies neither condition, that is, in case it is neither through the cause but through an effect nor through a proper and convertible effect. Therefore, all demonstration is either through the cause or through the effect; and through the cause is twofold, either through a mediate or an immediate ; and also through the effect is twofold, either through a proper and convertible effect or through an improper and non-convertible effect. Since therefore demonstration can be of four modes, one mode is the demonstration of the why, when it is demonstration through an immediate cause; three other modes are demonstrations of the that. It has also to be noted that when the Philosopher determines two modes, in those two modes the third is comprehended; for if one mode of the that is that in which an immediate is not taken, and another mode of the that is when the cause is not taken, it is necessary that the third mode of the that is one which fails in both, that is in which neither an immediate nor the cause is taken.195 193 194 195

Cf. Bertagna (2003), 184–185. Giles of Rome, Super Libros Posteriorum Analyticorum, f4’rb. Giles of Rome, Super Libros Posteriorum Analyticorum, f4’rb–va: “Ad demonstrationem propter quid duo requiruntur et oportet ambo illa concurrere, videlicet quod talis demonstratio sit per causam et quod sit per causam immediatam, id est propriam et convertibilem. Igitur erit demonstratio quia vel si non est per causam, sed per effectum, vel si est per causam, non tamen per causam immediatam et convertibilem. Posset etiam esse tertius modus quia, ut si deficeret in utrisque, quod nec sit per causam sed per effectum nec sit per effectum proprium et convertibilem. Omnis ergo demonstratio vel est per causam

264

chapter 5

Two terminological observations are in order. In the first place, the expression “proper and convertible” has to be taken as a hendiadys; i.e., proprium and convertibile mean the same thing (and indeed a proprium or property is convertible on Aristotelian principles); for otherwise the cases would multiply, and there is no evidence of any such multiplication in Giles’ analysis.196 In the second place, there can be no doubt that with “immediate” and “mediate” Giles means “convertible” and “non-convertible,” respectively. It is true that in saying per causam dupliciter, vel per mediatam vel per immediatam; et per effectum dupliciter, vel per effectum proprium et convertibilem vel per effectum non proprium et non convertibilem he seems to distinguish the immediateness condition (which is ascribed to the cause) from the convertibility condition (which is ascribed to the effect). And yet, in saying per causam immediatam, id est propriam et convertibilem Giles himself shows that he is taking “immediate” to mean “convertible.” Perhaps the terminological difference is only due to the attempt to preserve Aristotle’s vocabulary as much as possible. Thus, notwithstanding some terminological oscillations, Gile’s interpretation of APo A 13 is markedly extensional. There are therefore two conditions that a middle term has to satisfy in order to be the middle term of a propter quid demonstration: it must be convertible (with the major) and cause (of the major). A middle term may fail to satisfy either or both the convertibility or the causality condition, and in that case the syllogism is quia. There are therefore three types of quia demonstrations, and the resulting typology is fourfold. Yet, Giles’ fourfold typology is neither Aristotelian nor Philoponean. Let us see why. A syllogism may satisfy both the convertibility and the causality condition, i.e., may be such that its middle term is the “immediate cause.” This is the only propter quid demonstration (type 1a), and according to Giles this is the case discussed in sections (ii) and (iii) of APo A 13. Reversing a propter quid demonstration yields a quia demonstration from an “immediate effect,” i.e., from a middle term that satisfies the convertibility but not the causality condition. It

196

vel est per effectum; per causam dupliciter, vel per mediatam vel per immediatam; et per effectum dupliciter, vel per effectum proprium et convertibilem vel per effectum non proprium et non convertibilem. Cum ergo quattuor modis possit esse demonstratio, uno modo est demonstratio propter quid, cum est demonstratio per causam immediatam; tribus aliis modis erit demonstratio quia. Notandum etiam quod cum Philosophus assignaverit duos modos in illis duobus modis comprehenditur tertius: nam si est unus modus quia qui non accipitur immediatum, est alius modus quia qui non accipit causam, oportet quod si tertius modus quia qui deficit in utrisque, id est qui non accipit causam, nec immediatum.” Cf. Bertagna (2003), 274 n. 25.

Demonstration through Signs in 13th-Century Commentaries

265

is the prototypical quia demonstration (type 1b) illustrated by Aristotle’s astronomical examples. A syllogism may satisfy the causality condition but not the convertibility condition. Such a syllogism is “not from immediates,” i.e., it falls under the case announced in section (i) of APo A 13; but since it does satisfy the causality condition, it is from a “mediate cause,” i.e., from a cause more extended than the effect. According to Giles, it is the case discussed by Aristotle in section (v) of APo A 13, where the inference is from the negation of the cause to the negation of the effect (that-demonstration of type 2b, exemplified by the non-breathing wall). Rather than taking section (iv) of APo A 13 as involving, like section (v), a cause more extended than the effect that can positively be inferred from it (in a that-demonstration of type 2a), Giles takes that section as involving an effect that is more extended than the cause. He reasons as follows: if the non-­ breathing wall of section (v) illustrate a negative inference from a cause more extended than the effect, then there must be also an inference from a more extended effect. For otherwise Aristotle would have failed to see that some quia demonstrations satisfy neither of the conditions that he set. Since Giles does not consider section (iv) as involving the positive inference of a more extended cause from the effect, and since he does consider an inference involving a more extended effect, his typology is not Aristotelian. Philoponus, on his part, does consider a more extended effect, but only regards it as allowing an inference from the cause to the effect. This, we noticed, is precisely the difference between the Aristotelian and the Philoponean typologies: the Aristotelian typology is based on two extensional cases (converting cause and effect, and cause more extended than the effect), while the Philoponean typology is based on three extensional cases (converting cause and effect, cause more extended than the effect, and effect more extended than the cause); unlike the ­Aristotelian, the Philoponean typology includes no that-­demonstration in the second figure when the cause is more extended, an extensional case that Aristotle however does consider; and unlike the Philoponean, the ­Aristotelian typology does not include a why-demonstration from a more extended cause to the effect because that extensional case is not considered by Aristotle. Giles’ typology is neither Aristotelian nor Philoponean. He says: It has to be said that one effect may follow from multiple causes, as for example drying may be the effect of the sun and fire. Thus such effect which is produced by multiple causes exceeds any of those causes and if it is such as to be better known than its cause, as it is better known to me that something is dried than that there is fire, we can argue from such

266

chapter 5

effect to its cause not affirmatively […] but negatively. We say that whatever does not dry is not fire.197 To say that the effect is more extended than the cause is to say that one and the same effect may be caused by more than one cause, i.e., that it has m ­ ultiple causes. Something dry may have been dried by the sun or by the fire. The inference of either cause from the effect is thus deductively invalid (it has the form of the invalid second-figure sign-argument of APr B 27). Yet, the cause can be validly inferred from the effect negatively (i.e., in the second figure): the major extension of the effect does not allow the inference of one of its causes; but its negation allows the inference of the negation of any of its causes; if something is not dry I can infer that it has not been dried by the sun or by the fire.198 Not only is Giles considering a case not considered by Aristotle (a more extended effect); he is also connecting this case to what Aristotle says in section (iv), i.e., that when cause and effect are not convertible and the effect is better known than the cause the inference is of the that and not of the why. This gives to Giles’ interpretation a peculiar symmetry: he interprets section (iv) as involving a negative inference from a more extended effect, and section (v) as involving a negative inference from a more extended cause. In other words, like Philoponus and unlike Aristotle, he considers three extensional cases (converting cause and effect, cause more extended than the effect, and effect more extended than the cause); unlike Philoponus but like Aristotle with more extended causes, he allows a second-figure that-demonstration from the more extended effect. The typology that results is found in none of the previous commentators on APo A 13; it is, we may say, peculiarly “Aegidian.” In order to justify the inclusion of the demonstratio quia among scientific demonstrations, i.e., those that satisfy the requirements of APo A 2, Giles claims in a dedicated dubitatio199 that even though the demonstratio quia is not

197

Giles of Rome, Sup. Lib. Post., f4’’rb: “Dicendum quod unus effectus potest sequi ex multis causis, utputa desiccare potest esse effectus solis et ignis. Talis ergo effectus qui efficitur ex multis causis excedit quamlibet illarum causarum et si sit talis effectus notior sua causa ut si notius est mihi quod aliquid sit desiccat[iv]um quam quod sit ignis poterimus arguere a tali effectu ad suam causam non affirmative […] sed negative. Dicemus enim quicquid non desiccat non est ignis.” 198 Cf. Marmo (2016), 245–246; and Bertagna (2003), 276. 199 Giles of Rome, Sup. Lib. Post., fa’va: “Dubitaret forte aliquis utrum demonstratio quia faciat scire.” See extensive quotations in Bertagna (2003), 286–287.

Demonstration through Signs in 13th-Century Commentaries

267

the highest and most powerful species of demonstration (potissima),200 yet in some sense it does satisfy those requirements: knowing through an immediate and convertible effect amounts in a way to knowing through what is true, immediate, prior to, better known than, and cause of the conclusion (ex veris et immediatis et ex prioribus et notioribus et ex causis conclusionis): He who demonstrates through the proper effect demonstrates from what is true, because it is true that this effect exists; he demonstrates from what is immediate, because the proper effect is immediately related to the cause; he demonstrates from what is prior and better known not in absolute sense but for us (there is no demonstration through the effect if those effects are not prior and better known to us). […] and this amounts to demonstrating from the causes of the conclusion, not through the cause of being but from the cause of inferring: for the effect is not the cause for which the cause is, but it can be the cause for the inference and the conclusion of the cause.201 It is clear that the species of demonstratio quia that Giles has in mind in this passage is that which proceeds from a convertible effect (type 1b). Giles is attempting to show that the requirements of APo A 2 are somehow fulfilled by this type of demonstratio quia. The occurrence of an effect, if true, is no less true than the occurrence of a cause; and just as the cause is immediate when it converts with the effect, the effect is immediate when it converts with the cause. It is therefore true that a demonstratio quia of this type is from true and immediate premises. The other two requirements, that the premises should be prior to and better known than the conclusion, are also satisfied by this type of demonstratio quia if, following Aristotle, we consider priority and knowability to be relative to us and not absolute or with respect to nature. The fifth requirement, that the premises should be causes of the conclusion, is satisfied by this type of demonstratio quia if we take “cause” in the logical rather than in the ontological sense. Here appeal is made to the distinction, which originated 200 Giles devotes a short treatise to this kind of demonstration and to its medium (ed. in Pinborg 1976, 254–268; cf. Longeway 2002). 201 Giles of Rome, Sup. Lib. Post., fa’va: “Demonstrans enim per effectum proprium demonstrat ex veris, quia verum est talem effectum esse; et demonstrat ex immediatis, quia ex quo effectus proprius habet se immediate ad causam; demonstrat ex prioribus et notioribus non simpliciter sed quoad nos (numquam est enim demonstratio per effectus nisi effectus illi sint priores et notiores nobis) […] etiam hoc demonstrare est ex causis conclusionis, non ex causis in essendo sed ex causis in inferendo: effectus enim non est causa quod causa sit sed potest esse causa quod causa inferatur et concludatur.”

268

chapter 5

with Alexander of Aphrodiasis and was then employed in both the Greek and the Arabic commentary tradition, between the logical and the ontological interpretation of the causal requirement of APo A 2.202 We saw that Kilwardby appeals to some such distinction in the attempt to demarcate the subject matter of the Prior Analytics (syllogism and logical cause) from that of the Posterior Analytics (demonstration, both logical and ontological cause).203 We also saw that Albert uses a similar distinction in his explication of APo B 17 (there can be multiple causes when “cause” is taken in the logical sense).204 Giles uses this distinction in order to “save” demonstrations quia from the exclusion from the realm of scientific demonstrations: a demonstratio quia of type 1b does satisfy the requirements of APo A 2, if they are granted some flexibility, i.e., if, among other things, “cause” is taken in the logical rather than in the ontological sense. Yet only this type of demonstratio quia is credited with scientific dignity in the context of this dubitatio. Since Giles does not consider the positive quia demonstration of a more extended cause from the effect (type 2a), for him all quia demonstrations other than the prototypical type are negative, i.e., are in the second figure: the that-demonstrations from a more extended cause (type 2b) and that from a more extended effect (the peculiarly “Aegidian” type) make us know only negatively. These satisfy the requirements of APo A 2 only in an imperfect way; they are not demonstrations in the absolute sense (simpliciter), but only in a relative sense (secundum quid).205 For Giles, as for his predecessors, effects are simply effects. Yet, slightly later in the work, in the context of a discussion of subordinate and superordinate sciences, Giles acknowledges that some scientific objects are investigated through signs. The sciences in questions are again astronomy and nautical science (or apparentia, as Kilwardby mistakenly calls it). In all the cases listed in APo A 13, 78b37–79a2 the object of the superordinate science is more general than that of the subordinate science. This also holds of astronomy and nautical science. In this context apparentia gets an additional meaning:

202 Cf. supra, §§2.1, 2.2, 5.3.1. 203 Cf. supra, §5.2. 204 Cf. supra, §5.3.2. 205 Giles of Rome, Sup. Lib. Post., fa’va: “Ostensum est ergo quomodo demonstratio per effectum convertibilem facit scire ex prioribus et notioribus; demonstrationes vero quia per causam remotam vel per effectum non convertibilem non faciunt scire affirmative et quod hoc sit, sed negative et quod hoc non sit. Tamen eo ipso quod aliquo modo faciunt scire aliquid participant de conditionibus que requiruntur ad sciendum et secundum hoc possunt dici demonstrationes non simpliciter, sed secundum quid.” Cf. Bertagna (2003), 286–288.

Demonstration through Signs in 13th-Century Commentaries

269

in this way apparentia, that is nautical science, is related to astronomy: for astronomy considers the motion of the stars in the absolute sense, nautical science considers this type of motion through some m ­ anifestations and through some sensible signs: for it considers in this way the motion of the stars in as much as they serve the art of navigation; the motion of the stars in this sense is subsumed under the motion of the stars in the absolute sense.206 In this passage the term apparentia occurs once as the name of the discipline (feminine singular noun) and a second time with the meaning of “phenomena that appear to the senses” (feminine plural noun). Later it occurs as an adjectival present participle in the expressions per quedam signa apparentia and aliqua signa apparentia.207 What are the “sensible signs” that nautical science is concerned with? Giles explains that both mathematical astronomers and nautical astronomers are concerned with atmospheric variations (de serenitate et tempestate). Yet, the former considers them from the point of view of celestial causes (­conjunctions of stars that affect the weather on earth), while the latter considers them through their signs and sensible manifestations, like lunar halos, a red sky or the intensity of the red color of Mars.208 206 Giles of Rome, Sup. Lib. Post., fa’’’ra: “hoc etiam modo se habet apparentia, id est navalis, ad astrologiam: nam astrologia considerat motus astrorum simpliciter, navalis vero ­considerat huiusmodi motus per quasdam apparentias et per quedam signa sensibilia: considerat enim hoc modo motus astrorum prout deservit ad artem navigandi; motus autem astrorum sic sumptus est sub motu astrorum sumpto simpliciter.” 207 See next footnote. 208 Giles of Rome, Sup. Lib. Post., fa’’’rb: “Notandum autem quod de serenitate et de tempestate considerat astrologus et navalis, sed astrologus considerat de talibus secundum causas, quia considerat motus et situs astrorum a quibus causantur serenitas et tempestas; navalis autem considerat de talibus secundum quedam signa sensibilia et secundum quasdam apparentias. Notandum quod astrologia est duplex: una que considerat solum motus et cursus astrorum, alia practica et iudicialis que secundum motus astrorum iudicat serenitates et tempestates et alia que hic inferius accidunt. Ista autem astronomia iudicialis est quasi uniuoca ad navalem, quia id quod considerat navalis modo grosso et sensibili et per quedam signa apparentia, ut puta quia luna facit circulum vel quia rubet celum, astronomia iudicialis considerat modo subtiliori, ut per motus et situs astrorum, ut quia tales planete ad invicem coniungentur, vel quia talis planeta erit in tali puncto et ideo hoc et hoc eveniet. […] Dubitaret forte aliquis quomodo in talibus dicuntur fere univoce scientie subalternantes et subalternate. Dicendum quod univoca sunt quorum nomen commune est et ratio substantie eadem; ratio autem sumitur ex forma et quia illam eandem formam quam considerat scientia superior modo abstracto considerat scientia inferior et subalternata modo sensibili et per applicationem ad materiam,

270

chapter 5

Giles also devotes some observations to the problem of determinism, which seems to be implied by the subordination of the two disciplines. The problem is solved by appealing to Ptolemy, according to whom the judgments of the astronomer satisfy two conditions: they are general (and not particular) and are intermediate between the possible and the necessary.209 Now when something happening on earth depends on free will and is therefore not fully determined, the first of Ptolemy’s conditions explains how it is possible for astrological previsions to be compatibile with the absence of full determinism: it is possible because they are general and do not concern particular individuals.210 For example: if someone by means of astrology should foresee abundance in the production of wine , he should not judge that Peter or John will be drunk, since by means of free will they could avoid drunkenness. He should rather provide a universal judgement, saying that many will be drunk because of the abundance of wine. If he then should descend to special persons, he would fall into greater error.211

ideo una est fere univoca alteri. Scientia enim navalis quedam astrologia est, quia per ea que videt in astris iudicat de tempestate et serenitate astrorum; ergo astrologia navalis et astrologia mathematica conveniunt in nomine, quia quelibet est astrologia et musica mathematica et secundum auditum conveniunt in nomine, quia quelibet est musica, et conveniunt etiam in ratione quia per eadem astra iudicat de serenitate et tempestate astronomia navalis per que iudicat astronomia mathematica; non tamen est simpliciter et proprie univoca hec et illa, quia non iudicat eodem modo: nam astronomia autem navalis considerabit per astra serenitatem et tempestatem considerando aliqua signa apparentia in astris, ut puta quia luna facit circulum vel quia mars oritur nimis rubicundus.” (our emphases). 209 Giles of Rome, Sup. Lib. Post., fa’’’va: “Dicendum quod Ptolemeus in Centiloquio suo duas conditiones dat iudicio astronomorum: una est quod debent astronomorum iudicia esse in universali non in particulari, alia est quod talia iudicia sunt media inter possibile et necessarium.” 210 Giles of Rome, Sup. Lib. Post., fa’’’va: “Si autem que hic inferius aguntur dependent ex libero arbitrio, tunc ibi est adhibenda secunda conditio, videlicet quod iudicia astronomorum sunt in universali et non in particulari: nam liberum arbitrium corporum ­celestium directe subditum esse non potest, ideo debet tale iudicium in particulari.” 211 Giles of Rome, Sup. Lib. Post., fa’’’va: “si quis per atrologiam cerneret quod deberet esse copia vini, ideo non deberet iudicare quod Petrus vel Ioannes erunt ebrii, quia per liberum arbitrium possent ab ebrietate cavere. Sed in universali verius iudicium darent dicendo quod plures erunt ebrii hoc anno propter copiam vini. Si autem descenderent ad personas speciales posset eis accidere maior deceptio.”

Demonstration through Signs in 13th-Century Commentaries

271

Even when something happening on earth does not depend on free will, astronomy cannot yield necessary judgements (the second of Ptolemy’s conditions), because the realization of the effects of the stars depends on the disposition of matter, so that a certain effect due to the disposition of the stars may be blocked by the indisposition of matter. For it is not necessary that the effects (the meteorological changes) have the same uniformity as their causes (the motions of the stars), since the disposition of matter to receive certain effects is independent of the celestial movements. It follows that the judgement about what happens on earth and does not depend on free will is more than possible (where with “possible” it is meant that which is neutral in respect of its outcomes, possibile quod est ad utrumlibet) and less than necessary (where with “necessary” it is meant that which always happens in the same way).212 Giles’ observations about the semiotic method of nautical science cannot be generalized and extended to all those subordinate disciplines that make some use of that-demonstrations. The occasion for this semio-nautical digression was offered by the peculiar interpretation that the Latin commentators that we have met have given of the term apparentia, which as we noticed is the Latin translation of the Greek substantivized participle τα φαινόμενα. Giles has two dubitationes about the second and last mention of sign-inferences in the Posterior Analytics (B 17 99a3):213 the first is whether one and the same effect can have multiple per se causes.214 The question is debated in some of the question commentaries and receives a unanimous negative answer: of one and the same effect there is only one per se cause, where with “per se cause” it is meant that which constitutes the middle term in a demonstration of the

212

213 214

Giles of Rome, Sup. Lib. Post., fa’’’va: “Et ut hoc adaptemus ad propositum dicimus quod ea que hic inferius aguntur vel dependent ex libero arbitrio vel non. Quod si non dependent sicut tempestas, serenitas, ubertas, sterilitas, de talibus poterunt iudicare astronomi ita tamen quod eorum iudicium erit plus quam possibile quod est ad utrumlibet et minus quam necessarium quod est semper. Nam motus celi presupponit dispositionem materie, ita quod ex eodem situ syderum non semper contingit idem effectus si materia non sit eodem modo disposita; et quia potest propter indispositionem materie impediri talis effectus ex motu celi non est necessarium iudicium de effectibus istorum inferiorum. Quare si dicatur quod ipsa dispositio materie dependet ex motu celi ita quod redeuntibus syderibus ad eundem punctum redibit eadem dispositio materie et per consequens idem effectus, dici debet quod non oportet dare tantam equalitatem nec tantam uniformitatem in effectibus quantam damus in causis. Vnde non oportet semper si in tanto tempore talis coniunctio syderum quod semper in illo tempore redeat talis dispositio materie.” Giles of Rome, Sup. Lib. Post., q2rb. Giles of Rome, Sup. Lib. Post., q2rb: “Dubitaret forte aliquis utrum eiusdem effectus sint plures cause per se.”

272

chapter 5

why.215 The second dubitatio is whether, taking a sign as cause, there can be multiple causes of the same effect. To our knowledge, no other commentator discusses this point.216 The first argument to the second dubium is that if there is one per se cause of one and the same effect, then the same thing holds of the sign.217 Giles’ answer is different, however, as both the cause per accidens and the sign are to be taken here as “causes” in the logical sense only (causa non in essendo sed in inferendo).218 With respect to accidental causes, Giles offers two examples. One is geometrical: if we say that the cause of a triangle having three sides is that it is the first plane figure, i.e., that to which all other plane figures can be reduced, the cause is only accidental: there can be other causes of that property, and none of the syllogisms that can be constructed by means of them would be a proper causal demonstration, i.e., would proceed from the per se cause of the property to be demonstrated.219 The non-geometrical example runs like this: if a man builds a house he is the per se cause of the house; but since the man can be white, musician, beautiful, etc., these properties are only causes per accidens of the house.220 The same holds of the sign: if a sign is taken as cause (i.e., as the logical cause of the conclusion), then there can be multiple causes of the same thing. 215

Giles of Rome, Sup. Lib. Post., q2rb-va; Gerard of Nogent, Quaest. sup. APo II.15, Paris, BnF, lat. 16170, 127rb-va; Simon of Faversham, Quest. vet. sup. APo I.53, ed. Longeway, 252–254; Radulphus Brito, Quest. sup. APo II.25, B 458rb [see abbreviation in Appendix A]. 216 Giles of Rome, Sup. Lib. Post., q2va: “Ulterius forte dubitaret aliquis utrum si accipiatur signum pro causa possint esse plures cause eiusdem .” 217 Giles of Rome, Sup. Lib. Post., q2va: “Et videtur quod non. Nam demonstratio per signum est demonstratio per effectum; sed eadem ratio est de effectu et de causa; si ergo est una causa per se causa unius effectus, erit unum per se signum unius cause; non ergo aliter deberet loqui de causa quam de signo.” 218 Giles of Rome, Sup. Lib. Post., q2va: “Dicendum quod signum et causa per accidens possunt habere rationem cause non in essendo sed in inferendo.” 219 Giles of Rome, Sup. Lib. Post., q2va-b: “quod autem cause per accidens possint esse plures non est difficile videre, ut puta si de habere tres assignaremus causam in triangulo quia est principium rectilinearum, vel quia est illa figura ad quam stat resolutio omnium figurarum: multa enim talia possemus assignare que essent cause inferendi; per quodlibet enim horum possemus inferre habere tres de triangu//lo, ut si diceretur: omne principium figurarum habet tres; triangulus est huiusmodi; ergo etc.; sic etiam omne ad quod stat resolutio figurarum rectilinearum ; triangulus est huiusmodi; ergo etc. Sed tales cause sunt per accidens, quia accidit principio figurarum habere tres, quia non habet tres triangulus ut est principium figurarum et ut est prima figura, nec habet tres ut ad eam stat resolutio aliarum figurarum.” 220 Giles of Rome, Sup. Lib. Post., q2vb: “Possunt ergo eiusdem rei esse plures cause per accidens, immo si edificator facit domum per se, et edificator est albus, musicus, pulcher, omnia ista erunt cause per accidens.”

Demonstration through Signs in 13th-Century Commentaries

273

This, it will be recalled, is precisely the solution advanced by Alexander and Themistius in their discussion of APo B 17.221 A comparable solution is also offered by Albert the Great in his commentary.222 According to Giles, a “sign” is anything through which we are led one way or another to the knowledge of a thing, and nothing prevents a sign from being defective while still remaining a sign:223 according to the Philosopher the syllogisms through signs are deficient. For weak and incomplete effects are called signs and also signs in the proper sense; this is not true of the cause, because what causes in a weak and incomplete way is not properly a cause. Since there can be multiple non-equivalent effects of one and the same cause, it is not inconvenient to conclude the same thing through multiple signs, as in the case of someone who is an adulterer; from this cause several effects can follow: that he embellishes and adorns himself, that he often wanders about at night; and from all these effects taken as many signs one could infer that he is an adulterer. Signs and accidental causes of the same thing can therefore be multiple; but the per se cause is unique.224 The example of the adulterer comes from Soph El 5, where it illustrates the semiotic variety of the fallacy of the consequent, which has the form of the second-figure sign-syllogism of APr B 27.225 The inference is a fallacy because when there can be distinct causes of one and the same effect (or, extensionally, when the effect is more extended than either of its possible causes) no inference from the effect to the cause is a deductively valid inference. We noticed that in his commentary on APo A 13 Giles allows a negative inference from a 221 Cf. supra, §§2.1, 2.2. 222 Cf. supra, §5.3.2. 223 Giles of Rome, Sup. Lib. Post., q2vb: “Et quod dictum est de causa per accidens veritatem habet de signo: nam eiusdem rei possunt esse plures cause, si accipiatur signum pro causa. Nam signum dicitur illud per quod aliquo modo ducimur in cognitionem rei, unde non est contra rationem signi quod deficiat.” 224 Giles of Rome, Sup. Lib. Post., q2vb: “nam secundum sententiam Philosophi sillogismi per signa deficiunt. Ipsi ergo effectus diminuti et incompleti vocantur signa et etiam proprie dicuntur signa; non autem sic est de causa: nam quod incomplete et diminute causat non est proprie causa; cum ergo effectus non equati possint esse plures eiusdem cause, non est inconveniens per plura signa unum et idem concludere, ut si quis est adulter ex hac causa poterunt sequi omnes hii effectus: quod se componat et ornet, et sit errabundus de nocte; ex quibus omnibus effectibus tamquam ex quibusdam argueretur esse hunc adulterum. Signa ergo et cause eiusdem rei possunt esse plures; sed causa per se est una.” 225 Cf. supra, §§1.3, 1.7, 2.7. Cf. also infra, §§6.1, 6.2.

274

chapter 5

more extended effect. By contrast, here Giles imagines that one and the same cause (not different possible causes of an effect) may have distinct effects (not one effect more extended than either of its possible causes); extensionally speaking, he has a case in mind in which the cause is more extended than either of its effects. In this case, the negative inference from either effect to the cause is valid; it is a that-demonstration of type 2a. Thus, if we take “cause” in the logical sense, this case offers a positive answer to the question that opens APo B 17, i.e., whether there can be multiple causes of one and the same thing. But ontologically either cause and effect are convertible or the cause is more extended than the effect. A proper sign is an incomplete and weak effect from which a more extended cause can be inferred. But an incomplete and weak cause, i.e., a cause that is less extended than its effect, is no cause at all. 6 Conclusion No systematic association is made in the commentaries on the Posterior Analytics of the thirteenth century between that-demonstrations and sign-­inferences. This calls for some explanation, that we shall advance in the conclusions of this study. What we find in these commentaries is a sort of removal or obliteration of the semiotic nature of this kind of demonstration. This sharply distinguishes the Latin from Greek-Arabic tradition of the Posterior Analytics, where such association, inaugurated by Alexander of Aphrodisias, is systematically made and becomes an accepted interpretative scheme. Notwithstanding the general reticence of Latin commentators of the ­thirteenth century on the semiotic dimension of demonstrations, in their commentaries some echoes of the Greek-Arabic heritage are clearly detectable. In the first place, Grosseteste’s contrast between a maxime demonstratio and a demonstratio dicta per posterius is clearly dependent on the contrast between κυρίως and δευτέρως demonstrations that we find in Alexander, Themistius, and Philoponus. Some such contrast dominates all attempts at a general taxonomy of demonstrations, be they made with the exegetical intention of elucidating Aristotle (typically, APo A 13) or with some more systematic purpose. In the second place, the distinction, which we find in both the Greek and the Arabic commentators, between the “logical” and the “ontological” senses in which the premises of an argument may be causes of the conclusion, is also operative in some of the Latin commentaries. Thus, we find it in Kilwardby, where it helps determining the difference in subject matter between Prior Analytics (syllogism, logical sense only) and Posterior Analytics (demonstration, logical and ontological sense). It is found in Albert the Great, where it helps

Demonstration through Signs in 13th-Century Commentaries

275

explaining the meaning of APo B 17, in which Aristotle seems to be saying that in sign-inferences the cause inferred may be multiple: according to Albert, the cause can be multiple if it is taken in the logical sense (causa consequentiae), but not if it is taken in the ontological sense (causa consequentis). It is found in Giles of Rome, where it helps seeing that a demonstration quia does deserve the title of demonstration: in a demonstratio quia the requirement that the premises be causes of the conclusion still holds; only, “cause” has to be taken in the logical sense. In the third place, signs and sign-inferences do make some sporadic appearance in these commentaries. Thus, Grosseteste, who never mentions sign-­ arguments, and even departs from all current translations and renders the σημεῖον of APo B 17 as “effectus” rather than as “signum,” yet does make a reference to the contrast between causes and signs in his comments on APo B 8 (medium […] non dicit causam, sed signum). In his comments on APo A 6, in a passage that directly depends on Themistius, Kilwardby mentions “accidental signs” and associates them with the “inseparable accidents” discussed in that chapter; like Themistius, he also uses the example of the lactating woman of APr B 27, and so does Albert in his own commentary on the model of Kilwardby. Albert, on his part, describes the astronomical example of APo A 13 as one in which it is possible per signum effectus causam demonstrare. There is a mention of signs in Aquinas’ comments on the second and last occurrence of sign-inferences in the Posterior Analytics (B 17): an effect that is more extended than the cause (i.e., that may have more than one cause) is a sign. This time the example comes from ethics. Excess or deficiency cannot be inferred from blameworthiness (effect) in a that-syllogism, but it is possible to infer blameworthiness from both excess and deficiency in a why-syllogism. Sign-inferences make one single, feeble appearance also in Albert’s ­commentary on the Physics, which since late antiquity is a classical place for discussions about the compatibility of the method of natural science with the theory of demonstration of the Posterior Analytics. Aristotle’s methodological declaration in Phys A 1, according to which we start from what is better known to us, was taken by Greek and Arabic commentators to be incompatible with the strong notion of demonstration (why-demonstration) but compatible with the weaker notion (that-demonstration). For Albert, in order for a demonstratio signi or quia to be possible in physics, the sign or effect should be convertible with the cause; but the cause in physics is prime matter, and nothing is convertible with it. Like Avicenna and against Averroes, Albert claims that demonstrations in physics are not demonstrationes quia. Aquinas promotes no assimilation between demonstrations quia and sign-inferences in his own commentary on the Physics, but in the commentary on Boethius’ De trinitate

276

chapter 5

he straightforwardly identifies the demonstratio signi with the method ex posterioribus of Phys A 1. If this identification is considered along with Aquinas’ use of demonstrations quia in the five proofs of God’s existence in the Summa theologiae, one is naturally led to suppose that the whole of Aquinas’ theological argument is based on signs; a supposition that remains such, as Aquinas, like his Latin predecessors, is characteristically reticent to see any demonstration sub specie semiotica. One explanation for the reluctance or hesitance to explicitly discuss or mention sign-inferences, especially in connection with the demonstratio quia and the scientia founded upon it, is in the assumed association between signs and forms of knowledge and inference lower than science, either because though deductively valid yet signs fail to conclude from the cause to the effect, as in proper demonstrations, or because, like Aristotle’s second- and third-figure sign-syllogisms, they are simply deductively invalid. In the second Chapter we distinguished the “Aristotelian” typology of demonstrations, which is the one that Aristotle presents in APo A 13, from the “Philoponean” typology, which Philoponus presents in his commentary on APo A 6 and then again in his commentary on sections (ii), (iii), and (iv) of APo A 13. The difference, we observed, is that the Aristotelian typology is based on two extensional cases: converting cause and effect (arguments of types 1a and 1b) and cause more extended than the effect (arguments of types 2a and 2b); effects more extended than their causes are excluded. By contrast, the Philoponean typology is based on three extensional cases: converting cause and effect (corresponding to arguments of types 1a and 1b of the Aristotelian typology), cause more extended than the effect (corresponding to arguments of type 2a of the Aristotelian typology), and effect more extended than the cause (no corresponding argument in the Aristotelian typology). Arguments of type 2b are not included in the Philoponean typology. Both the Aristotelian and the Philoponean typologies are extensional. The Latin commentaries on the Posterior Analytics examined in this ­Chapter offer typologies of demonstrations that are invariably extensional, even if sometimes only implicitly so. Grosseteste’s typology in I.12 (ad APo A 13) is Aristotelian, that in I.6 (ad APo A 6) is Philoponean. Both are implicitly extensional. In his commentary on APo A 13, Kilwardby shows that he has a Philoponean typology in mind, but in the course of the analysis he drops the peculiarly Philoponean component of it (the argument from a more extended effect) and follows Aristotle (and Grosseteste) quite closely; the result is an Aristotelian typology that is implicitly extensional. Albert the Great’s analysis of APo A 13 is likewise based on an Aristotelian typology that is explicitly extensional. Aquinas’ analysis is also explicitly extensional; he offers a special analysis of section (iv) of APo A 13, whose upshot however remains within the

Demonstration through Signs in 13th-Century Commentaries

277

exegetical and conceptual limits of the Aristotelian typology. Giles of Rome is the only one among the Latin commentators on the Posterior Analytics to have taken the case of a more extended effect into account, i.e., the case that only Philoponus among the Greeks had considered and whose consideration distinguishes the Philoponean from the Aristotelian typology. Yet, unlike Philoponus, who only allows a positive, first-figure why-demonstration to the more extended effect, Giles allows a negative, second-figure that-­ demonstration from the more extended effect. The resulting typology is found in none of the previous commentators on APo A 13, and should be considered as peculiarly “Aegidian” (see Fig. 4). With one single exception, no one of the demonstrationes quia recognized by the Latin commentators (1b, 2a, 2b, and the “Aegidian” from the more extended effect) is associated with sign-inferences by these authors. The exception is the already-mentioned passage in which Albert the Great describes the astronomical example of APo A 13, which instantiates the “prototypical” demonstratio quia, as one in which it is possible per signum effectus causam demonstrare. Apart from this exception—which occurs in the context of the fourfold taxonomy, i.e., in the most appropriate place for a theory of semiotic demonstrations—, and apart from the few references to signs and sign-inference (which occur in contexts other than the taxonomy, as indicated above), the Latin tradition of the Posterior Analytics has failed to produce a doctrine of semiotic demonstrations as the one that we find in both late-ancient Greek commentaries and in the Arabic treatises.

Figure 4 Typologies of demonstrations in APo Latin commentaries

CHAPTER 6

Thirteenth-Century Parisian Commentaries on the logica nova about Inferences from Signs The commentaries on the Posterior Analytics of the thirteenth century do not give much space to semiotic demonstrations. As Giles of Rome’s discussion of the scientia navalis indicates, signs and sign-inferences enter the discussion only accidentally. In the conclusions of the previous Chapter, we suggested that a likely reason for this reticence towards signs, especially in connection with the demonstratio quia and the scientia founded upon it, is in the assumed association between signs and forms of knowledge lower than science. This attitude towards sign-inferences is confirmed by the commentaries on Boethius’ De differentiis topicis and the first commentaries on the Topics, where signs are intrinsically connected to probability, fallibility, and even fallacious reasoning. In the 1230s–1240s Nicholas of Paris offers a description of dialectic that is quite standard in the commentaries on Boethius’ De differentiis topicis. Dialectic is an inventive discipline, in opposition to demonstrative logic that is “­judicative” or “resolutive” (i.e., analytic): this science [i.e., that of the Topics] is said “inventive” in so far as it teaches to find the middle term through exterior signs, i.e., through the loci [i.e., argumentative places] which are fallible signs. As if someone should find something reddish yellow and because of the reddish yellow sign should think to have found gold, and this through exterior signs. Likewise is this science which proceeds according to opinion and probability; because of this, this science is said to be “inventive.” But the demonstrative science [of the Posterior] and the Prior [Analytics] is said to be “resolutive” and not “inventive”; although it teaches to find the middle term, it does not teach to find it through exterior signs, but through necessary causes.1 1 Nicholas of Paris, Notule Topicorum Boethii, ms. München, Staatsbibliothek, Clm 14460, 152va–b: “ista scientia [scil. Topicorum] dicitur inventiva, eo quod docet invenire medium per signa exteriora, id est per locos, que quidem signa sunt fallibilia. Sicut si aliquis invenit aliquid rubeum propter signum rubeum credit se invenisse aurum, et hoc per signa exteriora. Similiter est de ista scientia que procedit secundum opinionem et probabilitatem; et propter hoc ista scientia dicitur esse inventiva. Sed scientia // demonstrativa et Priorum dicitur resolutoria et non inventiva, quamvis doceat invenire medium, quia non docet ipsum © koninklijke brill nv, leiden, 2023 | doi:10.1163/9789004546974_008

280

chapter 6

Of a similar tone are the observations made by other more or less coeval commentators. As it has been shown,2 the question concerns not only the epistemological status of the subject matter dealt with in the Analytics and in the Topics, but more generally the epistemological status of those disciplines that make use of scientific demonstration, in contrast to those that follow a dialectical method: the former are judicative, the latter inventive; the former demonstrate and produce judgments that show the derivation of something from its cause, the latter seek a middle term which is not a cause but a sign, and as such only probable and fallible.3 The present Chapter is organized as follows. The first part (§6.1) deals with those areas of logic where there seems to be no reticence to speak about signs or where there is an explicit theory of the sign. This first part is in turn divided into four sub-sections: §6.1.1 is devoted to the commentaries on APr B 27, which as we know contains Aristotle’s official theory of sign-inferences; §6.1.2 examines the only thirteenth-century commentary to the parallel sections of Rhetoric A 2, while §6.1.3 examines the commentaries on the interpolated passage in Peter of Spain’s Summulae logicales, which we have already met in Chapter 4; finally, §6.1.4 is about the debate on the epistemological status of a science that is explicitly regarded as relating to signs, i.e., physiognomics, in the last decade of the thirteenth century. The second part of the Chapter (§6.2) is devoted to the commentaries on Boethius’ De differentiis topics, to the commentaries on Peter of Spain’s Tractatus V (De locis), on the locus a communiter accidentibus, and to the commentaries on chapt. 5 of the Sophistici Elenchi, on the fallacy of the consequent. It is also divided into two sub-sections; the first, §6.2.1, deals with commentaries and logic textbooks of the first half of the century; the second, §6.2.2, examines textbooks and commentaries of the second half.

invenire per signa exteriora, sed per causas necessarias.” Quoted in Marmo (1994), 20–21. See infra, §6.2.1, for an analogous passage from the same commentary. 2 See Brumberg–Chaumont (2015) for an examination of this problem in Kilwardby and Albert the Great. 3 Cf. Robert Kilwardby (or Oxford-Robert), Scriptum super libro Topicorum, ms. Oxford, Bodleian Library, Canon. misc. 403, 182va (in Green-Pedersen 1973, 29–30 = A.10 in Green-Pedersen 1984, 386–387); Anonymous, Commentum super librum Topicorum “Supposita divisione,” ms. Todi, Biblioteca Comunale, 54, 61rb (= A.8 in Green-Pedersen 1984, 385): “licet [scil. scientia Posteriorum et Priorum] doceat invenire medium, non propter hoc debet dici inventiva, cum non procedat per signa. Ad hoc enim quod sit inventiva oportet quod procedat per signa. Si enim servum fugitivum queras et nescias signum, si obviaueris ei non cognosces ipsum”; the example of the fuggitive servant comes from Themistius (cf. Themistius, In APo, ed. Wallies, CAG 5.1, 246–247); Albert the Great, Liber Topicorum I.1.2, ed. Borgnet, 241b–242a. Cf. also Green-Pedersen (1973), 7–8 n. 14; Green-Pedersen (1984), 131, 242 n. 22, for further references.

13th-Century Parisian Commentaries on the logica nova

1

281

Signs in Commentaries on Prior Analytics B and in Other Texts

1.1 The Commentaries on Prior Analytics B 27 The Prior Analytics were translated into Latin by Boethius at the beginning of the sixth century but were not read or used for centuries.4 The first traces of it or of syllogistic in general date to the twelfth century. In his Dialectica Abelard quotes some passages from Prior Analytics A.5 By the middle of the century the situation has changed and the influence of this work has become evident. John of Salisbury, a pupil of Abelard, shows some direct acquaintance with the Prior Analytics in his Metalogicon.6 As shown by Sten Ebbesen, references to the Prior Analytics are also found in the treatises on fallacies of the second half of the twelfth century.7 The first Prior Analytics literal commentary that has reached us (though incomplete), by the so-called “Anonymus Aurelianensis III,” also dates to the second half of the century (circa 1160s–1180s).8 Authors of logical treatises like the Dialectica Monacensis (first decades of the thirteenth century) must have had a first-hand knowledge of it. Yet, “we have to wait till about 1240 before it becomes obvious that teaching the Prior Analytics had become established practice in schools at university level.”9 The first complete literal commentary on the Prior Analytics that we possess is that of Robert Kilwardby, composed in the 1240s. Before discussing Kilwardby, however, it is opportune to say something of two other works that are either slightly earlier than or coeval with Kilwardby’s commentary, and which reflects the status of logic teaching during the 1230s and 1240s. The first is Peter of Spain’s Tractatus, better known as Summulae logicales. Peter of Spain was probably a Castilian member of the Dominican order. He composed his logic textbooks at the beginning of the 1230s, most likely in Northern Spain.10 Peter devotes the whole of Tractatus IV to syllogisms, which constitutes in fact a summary of Prior Analytics A, and moves the discussion of some of the topics 4 5 6

7 8 9 10

On the fortune of the Prior Analytics in the Latin West see Ebbesen (2010). On Abelard and the Prior Analytics see Martin (2010). John of Salisbury, Metalogicon IV.5, ed. Hall and Keats-Rohan, 144: “Deinde quid instantia, quid icos, quam propositionem probabilem dicit et si eius possit esse instantia, id est non perpetuo optineat, ut matres amare, nouercas inuidere. Quid item signum, et quomodo enthimema constet ex icotibus et signis. Postremo agit de cognitione naturarum.” Ebbesen (2010), 98–99. Christina Thomsen Thörnqvist edited this commentary in 2015. Ebbesen (2010), 101. See the several conjectures made about Peter in de Rijk (1968); de Rijk (1969); de Rijk (1970); de Rijk (1971); de Rijk (1972); Meirinhos (1996); D’Ors (1997); D’Ors (2001); D’Ors (2003); Tugwell (1999); Tugwell (2006) in reply to D’Ors; Figliuolo (2010).

282

chapter 6

of Prior Analytics B, like enthymeme, induction, and example, to Tractatus V. We shall return below to Tractatus V (De locis) and VII (De fallacis) and to the commentaries on this work composed in Southern France in the 1250s.11 The second work is the so-called “Guide de l’étudiant” or Ripoll Compendium edited by Lafleur (1992) on the basis of one manuscript.12 This work probably reflects the examination practices at the Faculty of Arts in Paris around the middle of the century. The questions usually asked in examinations are ordered and paired with corresponding answers. As far as logic is concerned, the Compendium follows the standard disposition and ordering of Aristotle’s Organon (which however does not match with that of the 1252 statute of the English nation in Paris13), in which the ars vetus (Isagoge, Categories and De interpretatione) is followed by the Prior Analytics, the Posterior Analytics, then by the Topics and the Sophistici Elenchi.14 Both Prior Analytics A and B are included, which shows that both must have been an integral part of the philosophical curriculum in Paris in the 1230s and 1240s. There are eight questions on Prior Analytics B, each with dedicated argumentations and replies. The topics covered by this part include: the inference from falsehood; circular demonstration—also dealt with in the Posterior Analytics, to which reference is made—; syllogisms ex impossibili and ex oppositis; question begging; the relationship between enthymeme and syllogism (with references to induction and objection—instantia), and, finally and most importantly for us, the ycos (the Latin correspondent of εἰκός, likelihood). The question about the ycos concerns the relation between dialectic/logic and rhetoric, because it is assumed that the ycos concerns the rhetorician, not the dialectician.15 Unfortunately, the text 11 See infra, §§6.1.3, 6.2.2. On earlier commentaries on the Summulae see de Rijk (1969); de Rijk (1970); Rosier-Catach and Ebbesen (1997); Ebbesen and Rosier-Catach (2000); Ebbesen (2021). Some earlier logical treatises, composed between the end of the twelfth and the beginning of the thirteenth centuries, both French and English, do have a part on syllogistic but mention some of the notions of Prior Analytics B (induction, example, and enthymeme) just after syllogisms; this suggests a connection with the manner this matter is discussed in Boethius’ De differentiis topicis II.2.16–19, 23–24 (cf. Excerpta Norimbergensia, in LM II.2, 119; Ars Emmerana, LM II.2, 163–164; Ars Burana, LM II.2, 194; Introductiones Parisienses, LM II.2, 362–363; Logica “Ut dicit,” LM II.2, 394; Logica “Cum sit nostra,” LM II.2, 434; Dialectica Monacensis, LM II.2, 487–488). 12 Ms. Barcellona, Arxiu de la Corona d’Aragó, Ripoll 109, 134ra–158vb. 13 Quoted in Ebbesen (2010), 102 n. 22; the statute required that the teaching of the logica nova should begin with the Topics, followed by the Sophistici Elenchi, and end with the Analytics (Chartularium Universitatis Parisiensis, ed. H. Denifle and E. Chatelain, Paris: Delalain, 1889, I, 201) 14 On the section about the logica nova, see Ebbesen (1997). 15 Anonymus, Ripoll Compendium, §742, ed. Lafleur, 194: “Item queritur quare agitur de ycotibus, cum ycota tangant materiam specialem rethorum.”

13th-Century Parisian Commentaries on the logica nova

283

of the reply is not wholly perspicuous and the editor’s emendations are of not much help; here we maintain some and add others: To this we reply that here intends to show the definition of the enthymemes that above all proceed from signs and ycota:16 these are propositions that can be proved through signs, from which rhetoricians above all argue; therefore, shows from which enthymemes are mostly formed; that is, from ycota.17 The author seems to argue as follows: ycota are propositions that can be proved by means of inferences from signs; on the one side, rhetoricians are especially concerned with inferences from signs (from which ycota are proved); on the other side, dialecticians use enthymemes that have as premises such ycota. There seems to be something like a “cascade” grounding of the premises used by rhetoricians and dialecticians: the first ones prove ycota from signs, the second ones prove their conclusions from ycota. As we shall see in the next section, Kilwardby offers a different interpretation of the relationship between sign and ycos, and an interpretation of the ouverture of APr B 27 that will become standard: he explains the meaning of ycos on the basis of its assonance with another Greek term, εἰκῶν (“image”), rendered as ycon, which although etymologically connected with εἰκός (from ἔοικα, “to be similar”), had a quite different meaning in Greek. In general (and this is especially true of the second half of the thirteenth century), question commentaries focus on the first book of the Prior Analytics and leave the material of the second book out of account.18 When they do deal with that material, they usually omit treatment of the sign definition and classification that Aristotle gives in APr B 27 on the basis of the syllogistic figures.19 16

Here, as in the quotations from Kilwardby (infra, §6.1.1.1), we use the untranslated ycos and its plural ycota. 17 Anonymus, Ripoll Compendium, §742, ed. Lafleur, 194: “Ad hoc dicimus quod intendit hic ostendere rationem entimematum que maxime procedunt a signis et ycotibus, que sunt propositiones probabiles per signa ex [entimematibus] maxime arguunt rethores; igitur ostendit (-at, ms.) ex quibus maxime habent esse entimemata: quia ex ycotibus.” Lafleur propose to insert ut after rhetores to match with the subsequent subjunctive ostendat; yet, this would not accord with the plural subject rethores, and should be rather connected with the subject of the first subordinate clause, Aristoteles. 18 Ebbesen (2010), 105. 19 Cf. the list of questions recorded in Ebbesen (2010), III, 109–133: of the three Parisian commentaries examined by Ebbesen, only that by Simon of Faversham has a quaestio on the enthymeme (Quaestiones libri Priorum II.14, cf. Appendix D), which we examine below (infra, §6.1.2).

284

chapter 6

1.1.1 Robert Kilwardby on Enthymemes, Signs, and “Images” Kilwardby’s Notule libri Priorum, a literal exposition of the Prior Analytics, is the earliest thirteenth-century commentary to have reached us, and is also the earliest complete Latin commentary on that work. Kilwardby’s commentary is of great interest to us also because the preliminary divisio textus that it contains sheds further light on why signs are so marginal in logic, over and above the question of the close relation of signs to such weaker cognitive effects as opinio, praesumptio or suspicio and to areas of logic like dialectic and rhetoric that are peripheral to demonstrative science. Kilwardby’s commentary is composed of seventy-seven lectiones on Prior Analytics A and B. These lectiones have roughly the same structure and organization as those on the Posterior Analytics: division of the text and of the portion of it commented in the lectio, exposition of the sense of the text (sententia), then notabilia or quaestiones.20 Before examining the comments on APr B 27, let us have a look at the way in which the overall structure of the Prior and Posterior Analytics is presented by Kilwardby. We noticed in the previous Chapter that a parallel passage in his commentary on the Posterior Analytics is the occasion for an application of the distinction between the logical and ontological senses of “cause”: in the syllogism as such the premises are the logical cause of the conclusion only; in a demonstration they also are the ontological cause of it. The exposition of APr A 4 (lectio 10) has two competing versions of the division of the subject matter of both Analytics.21 The highest nodes of the division are identical in both versions: the difference between the Prior and the Posterior Analytics is that the former deal with syllogism and the latter with demonstration; then, APr A and B 1–21 deal with syllogism as such or in itself, while APr B 22–27 deal with “ancillary matters”:22 “in prima [i.e., in toto libro Priorum] determinat de sillogismo, in secunda (cum dicit Quando conuertuntur extremitates [APr B 22]) de quibusdam sillogismo annexis et in ipsum reducendis.”23 The subject matter of the last part of Prior Analytics B is said to be incomplete argumentations that are reducible to the syllogism (de quibusdam rationibus incompletis in sillogismum reducibilibus), namely induction (and example) and enthymeme.24 The two final lectiones (76 e 77) are devoted 20 Cf. supra, §5.2. 21 See Thom and Scott (2015), xviii. 22 Thom and Scott (2015), xvii. 23 Robert Kilwardby, Notule libri Priorum, lec.10, ed. Thom and Scott, 176. Cf. Not. lib. Priorum, lec. 71, ed. Thom and Scott, 1470: “Determinato de sillogismo, in hac parte intendit de quibusdam ratiocinationibus sillogismo annexis et in sillogismum reducibilibus.” 24 Robert Kilwardby, Not. lib. Priorum, lec. 72, ed. Thom and Scott, 1500 (on APr B 23). Kilwardby deals with induction in the sequel of lec. 72 (ed. Thom and Scott, 1502–1517) and

13th-Century Parisian Commentaries on the logica nova

285

to APr B 27: the first is on the enthymeme in itself (secundum eius substantiam), the second on the discovery of the sign that constitutes the middle in an enthymeme (determinat inventionem signi quod est medium in entimemate).25 One first thing to be noticed concerns the translation used by Kilwardby. The editors of the Notule observe that it is difficult in general to tell which of the two recensiones of Boethius’ translation, the recensio Florentina and the recensio Carnutensis, was the one used by Robert, since some lemmata come from the one and some lemmata come from the other.26 The last part of the commentary certainly follows the recensio Carnutensis: the opening words of the chapter, “Ycos autem et signum non est idem” correspond (spelling notwithstanding) to the Chartres version.27 The Chartres version represents an earlier version of Boethius’ translation in which some technical terms of the original Greek are simply transliterated. In the recensio Florentina the term ikos (here ycos) of the Carnutensis is changed into verisimile.28 Kilwardby, like the author of the Ripoll Compendium,29 seems to be unaware of this alternative translation, and therefore proposes a definition of it on the basis of the translation available to him and with reference to an etymological explanation in circulation at the time: Now, an ycos he defines as follows: An ycos is a plausible proposition. […] And note that an ycos is the same as an image; whence it is rightly said that an ycos is probable because, just as an image is assimilated to the thing in external shape (though not internally) and represents the thing according to the exterior shape, in the same way the probable represents the thing according to the external shape.30 with example in lec. 73 (ed. Thom and Scott, 1519–1528); then he treats of arguments that are opposite to induction and example, i.e., reduction (deductio) and objection (instantia) (lec. 74, ed. Thom and Scott, 1530–1557). 25 Robert Kilwardby, Not. lib. Priorum, lec. 76, ed. Thom and Scott, 1558. 26 Cf. Thom and Scott (2015), lxxv–lxxvi. On the two recensiones see Minio Paluello’s introduction (1962) to the edition of the Prior Analytics in the Aristoteles Latinus. 27 AL III.2, 189 = APr B 27, 70a10–11. 28 AL III.1, 137. 29 Cf. supra, §6.1. 30 Robert Kilwardby, Not. lib. Priorum, lec. 76, ed. and transl. Thom and Scott, 1558–1561, modified: “‘Ycotem’ autem sive ‘ycon’ sic diffinit: Ycos est propositio probabilis. […] Et nota quod ycos idem est quod ymago. Unde probabile bene dicitur ycos, quia sicut ymago assimilatur rei in exteriori figura quamuis non interius, et representat rem ipsam secundum figuram exteriorem, sic probabile representat ipsam rem secundum figuram exteriorem.” Both the Latin text and the English translation are from Thom and Scott. We depart from the translation in two cases: we leave ycos untranslated (the editor’s translation

286

chapter 6

Kilwardby’s etymological argument, according to which ikos/ycos is connected to ikon/ycon on the basis of morphological affinity, is also found in Eberhard of Béthune’s Graecismus, a grammar textbook composed in verse during the first decades of the thirteenth century and quite widespread at the time: “Ast diuisio sit idios, fit ab hoc ‘idiota,’ // Icos imago sit, quod probat ‘iconia’.”31 The definition of the sign is drawn verbatim from Aristotle: “propositio demonstratiua, necessaria uel probabilis” (“demonstrative proposition necessary or probable”).32 (Slightly later Kilwardby returns to a detail of the text that here is neglected.) The inclusion of the probable in the description of the sign, in opposition to the necessary, is reminiscent of the Ps-Philoponus-1. According to Aristotle, signs in the wide sense of APr B 27, 70a3 and 70b1 divide into τεκμήρια and σημεῖα in the strict sense of 70b4. At Rhet A 2, 1357b4–5 the σημεῖον in the strict sense is said to have no name (ἀνώνυμον).33 Ps-Philoponus-1 says that the σημεῖον ἀνώνυμον is rather ὁμώνυμον with the genus, i.e., with the σημεῖον in the wide sense, and identifies the σημεῖον ὁμώνυμον with the εἰκός.34 Kilwardby seems to agree. In his commentary on APr B 27 the term signum is taken in three distinct senses. On the one hand, signum is the common genus (in tota communitate sua) comprising the middle terms of enthymemes as species. Since enthymemes are syllogisms, and syllogisms come in three figures, signa in this generic sense can accordingly be taken in three ways corresponding to the three figures. This corresponds to Aristotle’s σημεῖον in the wide sense. In the second place, the signum antonomastice is only the middle term of a first-figure sign-enthymeme. This is also called prodigium (which is Boethius’ translation of τεκμήριον in both recensiones). Kilwardby offers the following etymological explanation for the denomination: prodigium derives from pre digitis, namely from “what is at hand,” something which is so evident that it can be touched “with the fingers.” (The editors of the Notule translates prodigium with “index,” is likelihood) in order to emphasize that the term is unusual and in need of an explicative definition; we also translate imago as image rather than as appearance. 31 Eberhard of Béthune, Graecismus, 8.181–182, ed. Wrobel, 40. The etymology is also given in the Glosse on the Graecismus, in which also another etymology is mentioned according to which ycos/icos is connected to scientia as a constitutive morpheme, like in politica (polis + ycos); cf. Anonymus, Glosa super Graecismus Eberhardi Bethunensis, Prol., 3, ed. Grondeux, 172: “Dicitur autem rhetorica a “resis” quod est “ornatus” et “icos” quod est “scientia” uel “imago,” unde magistri loquentes ornate et lepide rhetores appellantur”; cf. 4.2.1, ed. Grondeux, 220, for politica. 32 Robert Kilwardby, Not. lib. Priorum, lec. 76, ed. Thom and Scott, 1560–1561. 33 Cf. supra, §1.4. 34 Cf. supra, §2.5.

13th-Century Parisian Commentaries on the logica nova

287

but in spite of Kilwardby’s etymological argument we feel that “evidence” would be more appropriate. We leave it untranslated for now.) In the third place, signum can be taken to apply only to the middle terms of second- and third-figure sign-enthymemes: these are “signs” in an unqualified sense (signum simpliciter or absolute dictum) and correspond to Aristotle’s σημεῖον in the strict sense. Like in the Ps-Philoponus-1, second- and third-figure signs are called ycota. Kilwardby discusses the relation between ycos and signum under the heading of the third dubium (que sit differentia ycotis et signi). If signum is taken in the first, generic sense, then the relation between signum and ycos is the relation of the genus to one of its species.35 But if signum is taken in the second sense (prodigium), then the relation between signum and ycos is the relation of two coordinate species (or cohyponyms), and only the former is properly called a “sign.”36 Kilwardby then observes that the adjective probabile used in the definition of ycos has to be taken both for what is genuinely probable and for what only appears to be probable; as we shall see in a moment, according to Kilwardby the third-figure sign is genuinely probable while the second-figure sign is only apparently probable and actually only sophistical. It is in this generic sense—as covering both real probability and apparent probability— that probabile has to be taken in the definition of the sign: “A sign is a proposition that is necessary,” i.e., a sign that is in the first figure, namely a prodigium, “or probable,” i.e., a sign that is an ycos. And because in neither of these ways is it a genuine demonstrative proposition, he says “a sign wants to be” etc., as if he said: “it claims to demonstrate,” even though it does not do so. And “demonstrative” is there taken generically for that which is an ostensive sign: does not always show anything, even though it may seem to show.37 Like Ps-Philoponus-1, W.D. Ross, and Myles Burnyeat,38 Kilwardby takes Aristotle’s contrast at APr B 27, 70a7 between ἀναγκαία and ἔνδοξος to correspond 35 36 37

Robert Kilwardby, Not. lib. Priorum, lec. 76, ed. Thom and Scott, 1568. Robert Kilwardby, Not. lib. Priorum, lec. 76, ed. Thom and Scott, 1570. Robert Kilwardby, Not. lib. Priorum, lec. 76, ed. and transl. Thom and Scott, 1568–1571, modified: “‘Signum est propositio necessaria’ pro signo quod est in prima figura, scilicet prodigio, ‘uel probabilis’ pro signo quod est ycos. Et quia neutro modo istorum est uere demonstratiua propositio, dicit ‘signum uult esse’ etc., quasi dicat: pretendit demonstrare quamuis non faciat. Et accipitur ibi ‘demonstratiua’ communiter pro eo quod est ostensiuum signum; autem non semper ostendit quamuis uideatur ostendere.” 38 Cf. supra, §1.2.

288

chapter 6

to the contrast between τεκμήριον and σημεῖον. But since neither a τεκμήριον/ prodigium nor a σημεῖον/ycos can be the middle term of a demonstration in the proper sense, demonstrativa (propositio) has to be taken in a generic sense: a sign, either prodigium or ycos, “demonstrates” in this sense if it either shows something (prodigium) or only appears to show something (ycos); but in neither case there is demonstration in the proper sense. That is the reason why a sign of either species vult esse (βούλεται εἶναι) a demonstration but is not so.39 In describing the three species of signs Kilwardby expands Aristotle’s examples of enthymemes into full-fledged syllogisms by making explicit the implicit premise. Each example is preceded by some remarks about the middle term in each figure. With regard to the first figure, Kilwardby claims that “the middle term or sign is convertible” (medium siue signum est conuertibile) with the predicate of the implicit major premise (Omnis mulier habens lac peperit, habens lac being the middle term), i.e., with the predicate of the conclusion. With regard to the third figure, he claims that the middle term or sign is less extended (est in minus) than the predicate of the implicit minor premise40 (Pittacus est sapiens, Pittacus being the middle term), i.e., than the subject of the conclusion. With regard to the second, it is claimed that the middle term has greater extension (in plus est) than the subject of the implicit major premise (Quecumque peperit pallida est, pallida being the middle term), i.e., than the predicate of the conclusion.41

39

40 41

We feel we can exclude that Kilwardby’s interpretation derives somehow from the glosses that are in the margin of the manuscript of the recensio Florentina (independently of the identity of their author), given the lexical difference with the translation that Kilwardby was using: in the glosses the term used is verisimile, not ycos/ikos (cf. AL III.4, 369: “Signum vel firmum est vel infirmum. Firmum autem secondum naturam est, et dicitur signum proprie, vel secondum figuram syllogimorum et dicitur prodigium; tale est signum in prima figura. Rursum, infirmum vel secondum materiam est, et dicitur verisimile, vel figuras, et dicitur monstrisimile; in orationibus tale est signum in secunda et tertia figura.”). There is a debate between Shiel (1982; 1990) and Ebbesen (1990b; 2010, 100–101) about who was responsible for the translation of these glosses: Shiel thinks it was Boethius, Ebbesen thinks that they derive from some Byzantine compilation connected to the Ps-Philoponus-1 and does not accept the hypothesis of the Boethian authorship. Robert Kilwardby, Not. lib. Priorum, lec. 76, ed. Thom and Scott, 1562: “qui arguunt entimematice in hiis maiorem exprimunt et minorem subticent quia manifesta est. Et hoc est Quoniam autem sapientes [APr B 27, 70a16].” In presenting these examples, Kilwardby uses the expression velle/vult (the βούλεται of APr B 27, 70a21) only for the sign in the second figure: “Et dicit quod illud uult esse per secundam figuram quia pretendit sillogismum secunde figure apparenter, sed non est sic cum sit ex affirmatiuis.” (Robert Kilwardby, Not. lib. Priorum, lec. 76, ed. Thom and Scott, 1562).

13th-Century Parisian Commentaries on the logica nova

289

This may sound problematic. The definition of the sign at APr B 27, 70a6–9 makes it clear that a sign is a proposition (or premise, πρότασις). Yet, here and elsewhere Kilwardby explicitly says that the sign is the middle term. One may argue that both the Posterior Analytics and the commentaries on it seem to assume that signs/effects and causes are sub-propositional components rather than full-fledged propositions; in the classical example from APo B 16 “interposition” (in a why-demonstration) and “eclipse” (in a that-demonstration) are middle terms, not propositions. Kilwardby clearly oscillates between the two positions, with a tendency to favour the idea that the sign is the syllogistic middle term.42 In any case, the two positions are equivalent: for to say that “interposition” is the middle term of a why-demonstration of the eclipse is to say that it is its occurrence or inherence in some subject that constitutes the premise through which the occurrence or inherence of the eclipse in that subject is established. Likewise, to say that “having milk” is the middle term of a sign-argument that concludes to giving birth is to say that it is its occurrence or inherence in some subject that constitutes the premise through which the occurrence or inherence of giving birth in that subject is established. In any case, the occurrence or inherence of a term can only be expressed propositionally. Signs are middle terms, namely propositions containing middle terms; and a proposition containing a middle term is the premise (πρότασις) of an argument. The translation into English of APr B 27, 70a10 “entimema est sillogismus ex ycotibus et signis” as “enthymeme is a syllogism composed from likelihoods and signs” is not decisive here: a syllogism can be “composed” of signs both in the sense of having premises that are signs (sign in the propositional sense) and in the sense of having middle terms that are signs (sign in the sub-propositional sense). Kilwardby also points out that the prodigium or first-figure sign is productive of real knowledge (facit scire), while the third-figure sign is refutable (solubile) because from singular premises it cannot conclude universally. Of the second-figure sign Kilwardby says that it is neither necessary nor probable, but simply sophistical, since it derives an affirmative conclusion from affirmative premises, which is impossible in the second figure (as he had pointed out earlier in connection with the instantia of APr B 24).43 This is the difference, 42 43

Cf. also Robert Kilwardby, Not. lib. Priorum, lec. 76, ed. Thom and Scott, 1566: “entimema primo fit per medium quod est signum quando subticetur una propositio manifesta.” And passim. Robert Kilwardby, Not. lib. Priorum, lec. 76, ed. Thom and Scott, 1564. Cf. lec. 75, ed. Thom and Scott, 1548: “Consequenter ex hoc quod dixit per secundam figuram non sillogizari affirmatiue [69a3], concludit correllarie quod argumentum a signo per hanc secundam figuram non fit quia argumentum a signo concludit affirmatiue, et non ostenditur affirmatiue per secundam.”

290

chapter 6

mentioned above, between a sign that is really probable and one that merely appears to be probable: the third-figure sign, though not necessary, is probable; the second-figure sign is only apparently probable, but actually only sophistical. As we shall see, second-figure signs will return with all their bulky weight in the discussion of the fallaciae.44 Like the anonymous author of the Ripoll Compendium, Kilwardby addresses the question whether signs belong to logic and dialectic;45 his answer to this question involves some of the distinctions that he had made so far: […] signs may be of two types, because they are either so-called without any qualification, as are signs in the second or third figure, or they are prodigia. Now, signs in the first of these senses, and the corresponding enthymemes, pertain primarily to the rhetorician, and this is what Aristotle means at the start of the Posterior Analytics [A 1, 71a9]. But signs in the second sense, and the corresponding enthymemes, pertain to the dialectician and to the demonstrator. And so the enthymeme in itself is a genus common to argumentations pertaining to the dialectician and the demonstrator and the rhetorician. And thus determinations have to be made about it here.46 Here signum is said to be dupliciter, i.e., in the second and third senses specified above: prodigium and ycos. The prodigium concerns logic and science, 44 Cf. infra, §6.2. 45 Robert Kilwardby, Not. lib. Priorum, lec. 76, dub. 1, ed. Thom and Scott, 1562–1564: “Dubitatur hic de pertinentia huius partis quia cum entimema sit ratiocinatio contracta ad materiam, pertinet enim ad rethoricam secundum Aristotelem in principio Posteriorum, non debet hic determinari ubi determinatur de sillogismo simpliciter et in communi, et cum hoc queritur ad quem pertineat entimema.” Other dubitationes raised about APr B 27 concern the reduction of the enthymeme to the syllogism (dub. 2, ed. Thom and Scott, 1566–1568), the difference between enthymeme and syllogism (dub. 4, ed. Thom and Scott, 1570), the difference between ycos and signum, which we have discussed above (dub. 3, ed. Thom and Scott, 1568–1570), and the problem of interpreting the plural ex ycotibus et signis (dub. 5, ed. Thom and Scott, 1572). 46 Robert Kilwardby, Not. lib. Priorum, lec. 76, ed. and transl. Thom and Scott, 1566–1567: “[…] signum dupliciter est, quia uel absolute dictum, sicut signum in secunda et tertia figura, uel signum quod est prodigium. Signum autem primo modo dictum pertinet ad rethoricum primo et entimema secundum ipsum, et hoc intendit Aristoteles in principio Posteriorum. Signum autem secundo modo dictum, et entimema secundum ipsum, ad dialecticum et demonstratorem. Et ita entimema in se est genus commune argumentandi pertinens ad dialecticum et demonstratorem et rethoricum, et ideo hic habet determinari.”

13th-Century Parisian Commentaries on the logica nova

291

while the ycos concerns rhetoric. As we will see later, the relevance of signs in the definition of the border between dialectic and rhetoric emerges again after the translation into Latin of the Rhetoric made by William of Moerbeke at the end of the 1260s and with the commentary composed by Giles of Rome at the beginning of the 1270s.47 1.1.2 Albert the Great on Inferential Signs Albert the Great wrote his paraphrases on the Analytics between 1257 and 1263 and made large use of Kilwardby’s commentaries, where available. Unlike two logical works of the 1250s, the so-called Communia “Visitatio” and Communia “Feminae,” which have a part on Prior Analytics B but fail to mention the enthymemes ex icotibus et signis,48 Albert devotes to this topics the last three chapters of the last treatise of his Liber Priorum.49 Albert’s prologue does not explain the organization of the treatise but contains some observations about the subject matter of the Prior and the Posterior Analytics: the former deal with the syllogism simpliciter and its formal principles; the latter deal with demonstration and its real principles;50 the syllogism simpliciter is inferens and not probans like the demonstrative syllogism.51 The syllogism simpliciter is the genus; the demonstrative, dialectical, and sophistical (and tentative) syllogisms are the species, which differ for the matter they are “contracted” in, namely the propositions they move from: demonstrative syllogisms move from necessary propositions, dialectical syllogisms from probable propositions, and sophistical syllogisms from apparent propositions (sophistical syllogisms imitate vocally the appearance of dialectical syllogisms).52 As we shall see below, Albert does not stick to this picture of syllogistic form and syllogistic species in his subsequent works, especially in his paraphrases of the Topics and Sophistici Elenchi (composed after 1267).53 47 Cf. infra, §6.1.2. 48 Cf. Ebbesen (2002), 201–203 (Communia “Visitatio”) and 242–245 (Communia “Feminae”). 49 Albert the Great, Liber Priorum II.7.8–10, ed. Borgnet, 802a–809b. 50 Albert the Great, Liber Priorum I.1.1, ed. Borgnet, 460a. 51 Albert the Great, Liber Priorum I.1.1, ed. Borgnet, 461a. Cf. Brumberg-Chaumont (2013), 377–378. 52 Albert the Great, Liber Priorum I.1.1, ed. Borgnet, 459a. 53 See the monumental Brumberg-Chaumont (2013). Brumberg-Chaumont (2015) and (2016) also point out that Albert’s position on this does not coincide with Kilwardby’s: for Kilwardby the matter of the syllogism simpliciter is the “transcendental” terms (the letters used as variables), while for Albert the syllogism simpliciter is only a form that exists in its more concrete instances and species; cf. Albert the Great, Liber Elenchorum I.1, ed. Borgnet, 525b–526a, in Brumberg-Chaumont (2015), 272 n. 29; cf. also Brumberg-Chaumont (2013), 384–409.

292

chapter 6

Albert’s interpretation of APr B 27 is roughly the same as Kilwardby’s: the signum in the generic sense (Aristotle’s σημεῖον in the wide sense) comprises signs in all of the three figures; the signum in the proper sense (Aristotle’s σημεῖον in the strict sense), called icos, only applies to signs in the second and third figure; the sign in the first figure is called prodigium (Albert’s etymological explanation is almost identical to Kilwardby’s: prae digitis ostensum). Then it is necessary to notice the difference between the icos and the sign: and we have to say that the sign can be said in the generic and in the proper sense. In the generic sense a sign is anything that on the basis of its appearance (which it exhibits to the knowing subject) claims that something else is inferable from itself; and in this sense the icos is contained under the sign, as a species under its genus; and in this way there is sign in any figure. The icos in the proper sense is in the second and third […] Assuming the sign in the proper sense, then the sign is that which in a manifest manner and almost demonstrating or showing leads to the thing signified: and in this sense the sign is called prodigium, as if shown “before the fingers.”54 The sign in the generic sense, and a fortiori its species (the prodigium and the icos), have a decidedly inferential nature: a sign is something from which something else can be inferred, either necessarily or probably. Not only this: the qualification ex sui specie may be an allusion to the traditional, Augustinian definition of the sign: “Signum est enim res praeter speciem, quam ingerit sensibus, aliud aliquid ex se faciens in cogitationem uenire.”55 Augustine’s definition is quoted almost verbatim slightly earlier, where it is followed by Aristotle’s definition: The sign is that which, independently of the appearance offered to the knowing subject, leads to something of which it is the sign; and therefore according to its signification purports (vult) to be a demonstrative 54

Albert the Great, Liber Priorum II.7.8, ed. Borgnet, 803a–b: “Unde notanda est differentia icotis et signi: et dicendum quod signum dicitur communiter et proprie. Signum quidem communiter dictum est omne illud quod ex sui specie (quam cognoscenti exhibet) aliud praetendit quod inferri potest ex ipso: et sic icos continetur sub signo, sicut species sub genere; et hoc modo signum est in omni figura. Icos autem proprie in secunda et tertia. […] Proprie autem sumptum signum, tunc signum est quod ostensibiliter et quasi demonstrando sive ostendendo ducit in rem significatam: et sic dicitur signum prodigium, quasi prae digitis ostensum.” 55 Augustine, De doctrina christiana II.1.1, ed. Martin, 5–7.

13th-Century Parisian Commentaries on the logica nova

293

proposition either necessary or probable. I say “purports” because, in virtue of the disposition of the sign and its relation to the thing signified, sometimes leads to the essential cause, and then it purports to be a necessary proposition, even though in itself and as such it is not so; by contrast, sometimes it leads to what is generically associated with the things and extrinsically adherent to it, and then it purports to be a probable proposition.56 The quasi-Augustinian definition (signum est quod, praeter speciem quam cognoscenti offert, ad aliquid ducit cuius est signum) and the Aristotelian definition (signum est propositio demonstrativa, vel necessaria vel probabilis) are here associated, perhaps for the first time in the history of Western semiotics. The operation of ducere (“leading”) that occurs in Albert’s definition corresponds to the argumentatio or ratiocinatio that is the object of logic according to Albert (who follows Avicenna in this57). In Albert’s commentary on Porphyry, logic is said to be the rational instrument through which we make the unknown known.58 The operation of ducere, then, is the inferential process that is mentioned in the first of the passages quoted here and in the Aristotelian definition.59 56

Albert the Great, Lib. Priorum II.7.8, ed. Borgnet, 803a: “Signum autem est quod, praeter speciem quam cognoscenti offert, ad aliquid ducit cuius est signum: et ideo sui significatione vult esse propositio demonstrativa, vel necessaria vel probabilis. Dico autem vult, quia aptitudine signi et relatione ad signatum, aliquando ducit in causam essentialem, et tunc vult esse propositio necessaria, quamvis secundum se et secundum sui rationem non sit ita; aliquando autem ducit in ea quae communiter sunt in re et extrinsecus adhaerentia, tunc vult esse propositio probabilis.” 57 Avicenna, Logyca I.2 (3), 2va: “Logyca [...] est speculatio rerum [...] per quas deuenitur ad cognitionem incogniti.” 58 Albert the Great, Super Porph. 4, ed. Santos Noya, 6: “Cum autem logica sit scientia contemplative docens, qualiter et per quae devenitur per notum ad ignoti notitiam, oportet necessario quod logica sit de huiusmodi rationis instrumento, per quod acquiritur per notum ignoti scientiam in omni eo quod de ignoto notum efficitur. Hoc autem est argumentatio, secundum quod argumentatio est ratiocinatio mente arguens et convincens per habitudinem noti ad ignotum de ignoti scientia.” (Also in Robert 2013, 469 n. 6). See Robert (2013) for an evaluation of this thesis and its medieval reception. 59 Cf. Albert the Great, Liber Priorum II.7.8, ed. Borgnet 803a: “Id enim quo existente in praesenti, res est, et infertur ex ipso; vel quo facto in praeterito, res facta est in praeterito; vel quo posterius facto, indicat factum esse aliquid, sicut pallor conceptum factum indicat: aut id quod indicat, quoniam erit res illo prius facto, sicut in aegroto tremor in labro inferiori factus indicat vomitum futurum, hoc dicitur signum.” This is clearly a re-elaboration of Boethius’ Latin version of the definition (like Kilwardby, Albert seems to be using the Recensio Carnutensis) with the addition of two examples: the former is modelled after Aristotle’s example of second-figure sign, the latter is likely taken from medical literature.

294

chapter 6

We saw in the previous section the Kilwardby oscillates between a propositional and a sub-propositional notion of “sign.” Albert’s emphasis on the inferential process is explicit, but the reference to the Augustinian definition does not by itself imply anything about whether the sign is the premise or the middle term. It appears that Albert is more cautious than Kilwardby in identifying the sign and the middle term of the syllogism to which the enthymeme is reduced. He first illustrates the difference between enthymeme and syllogism by saying that an enthymeme is substantially (substantialiter or secundum rem) a syllogism whose premises are probable propositions (ex icotibus in secunda et tertia figura) or necessary propositions (ex signis sive prodigiis in prima figura). Then he claims that the “moods” of the enthymeme depend on the fact that “the sign (which is almost the middle term of the enthymeme) can be taken in three ways according to the position and order of terms”60 that compose it. Albert adds the remark in parenthesis (“which is almost the middle term of the enthymeme”) in order to distance himself from any straightforward identification of the sign with the middle term (sub-propositional notion of sign). And yet such identification is confirmed by the description of the three species of signs which follows: as the middle term is taken in the figures according to the difference of its position: for either the position of the sign is taken as the middle term is taken in the first figure, which for position and order of the terms is the middle, part of one and totality of the other; or it is taken as the middle term is taken in the second figure, in which the middle term is outside the extremes as a common predicate of multiple ; or it is taken as the middle term is taken in the third figure, as the one common subject of multiple predicates.61

60 61

Here is the text from the Recensio Carnutensis: “quo existente vel quo facto prius vel posterius futuro facta est res, signum est vel esse vel fuisse vel quoniam erit” (AL III.2, 189). Albert the Great, Liber Priorum II.7.9, ed. Borgnet, 803b: “Modi autem quibus fiunt enthymemata ex hoc inveniuntur, quod signum (quod est quasi medium enthymematis) tripliciter secundum positionem et ordine terminorum accipitur.” Albert the Great, Liber Priorum II.7.9, ed. Borgnet, 803b–804a: “quoties enim medium secundum diversitatem positionis accipitur in figuris: aut enim positio signi accipitur ut in prima figura accipitur medium, quod positione et ordine terminorum est medium, ut pars unius et totum alterius; aut accipitur sicut medium accipitur in figura secunda, in qua medium est extra extrema ut unum commune praedicatum de pluribus; aut accipitur sicut accipitur medium in tertia, ut unum commune subjectum substans pluribus praedicatis.”

13th-Century Parisian Commentaries on the logica nova

295

Albert’s determination of the middle term of the first figure is both “positional” and “extensional”: the middle term of the first figure is intermediate positione et ordine because it is intermediate in the standard formulation of the first figure; it is extensionally intermediate because it is more extended than, and thus predicable of, the minor, and less extended than, and thus subject of predication by, the major. As we know from the first Chapter, in Barbara the extensional definition of the middle term is equivalent to the predicative definition: that which is less extended is subject, that which is more extended is predicate. But since as we know this equivalence does not hold with respect to the other figures, Albert follows Aristotle in giving a “purely” predicative definition of the middle term in the second and third figure: in the second the middle term is predicate in both premises, in the third is subject in both premises (the extra extrema of the second figure is also interpretable in the predicative sense). Quite naturally, Albert’s examples are the same as Aristotle’s. There is however a little variation on the example of the first figure probably explained by Albert’s acquaintance with the books De animalibus, i.e., the collection of the ten books of the Historia animalium, the De partibus animalium, and the De generatione animalium which Michael Scot had translated from the Arabic in 1215.62 In the third book of the Historia mention is made of the practice of rubbing with nettles the udders of goats that had not given birth so as to obtain a liquid quite similar to the milk obtained from goats that have given birth.63 In his paraphrase Albert refers to Aristotle’s observation and adds a personal note: And I have myself seen many women doing the same on their own breasts; some were widows, other virgins, and from all breasts the milk came out abundantly.64 This biological detail is not without logical import. In his commentary on the milk example of APr B 27 Albert observes: Having milk is a sign, not a cause: because if also a woman that has not given birth rubs her breast with nettle and salt, she will have milk in the 62

On the entrance of the De animalibus in the thirteenth century, and for further references, see Rossi (2017). 63 Aristotle, Historia Animalium Γ 20, 522a7–11. 64 Albert the Great, De animalibus libri XXVI, III.2.9, §171, ed. Stadler, 353: “Et ego vidi hoc facere multas mulieres in suis propriis uberibus et erant quaedam viduae et quaedam virgines et de omnibus uberibus lac exivit abundanter.”

296

chapter 6

breast, but her breast will not produce it abundantly. In this manner we have an enthymeme in the first figure from a convertible sign in the implicit major premise: because it is believed to be manifest.65 The reference to the “cause” is relevant in this context, because it connects Aristotle’s discussion of enthymemes (in which the notion of “cause” plays no explicit role) to the contrast between signs and demonstrations that characterizes the commentaries on the Posterior Analytics. Yet Albert’s argument is not wholly clear. On the one hand, the fact that an “artificial” lactation can be induced in women seems to undermine the validity of the first-figure sign or prodigium; the sign is not convertible with its “cause” in the implicit major premise: all those who have given birth have milk, but not all who have milk in their breasts have given birth, precisely because we admit the possibility of artificial lactation. On the other hand, in the final part of the passage Albert does state that there is convertibility between cause and sign. Perhaps the point is the following: the possibility of artificial lactation does not undermine the validity of the inference; it only shows that the milk is not the cause (in the ontological sense) of having given birth. Albert may have thought as follows: if the milk were the cause of having given birth, then there should be no cases of milk in the breast that are not cases of having given birth; but since there are such cases, as shown by artificial lactation, the milk cannot be the cause of having given birth. By so arguing, however, Albert does not see that he is implicitly admitting that the sign in this case is not convertible with the cause and thus cannot qualify as a τεκμήριον/prodigium, but only as a σημεῖον/ycos. If this is so, then “signum” in this passage has to be taken in Aristotle’s strict and Albert’s “proper” sense, and in particular as a second-figure sign. Another explanation of the puzzle is the following: it is one thing to have “proper” milk, i.e., the abundant quantity that only women who have given birth have; another thing is to have “improper” milk, i.e., the lesser quantity artificially induced in women who have not given birth. If this is the case, then “proper” milk is after all a τεκμήριον/prodigium of having given birth, for it is convertible with its cause. As we shall see in what follows, Albert returns to the example of artificial lactation in his commentary on the Sophistici Elenchi.66

65

Albert the Great, Liber Priorum II.7.9, ed. Borgnet, 804a: “Lac autem habere signum est, et non causa: quia si etiam ea quae non peperit fricet mamillas urtica et sale, lac habebit in mamillis, sed non ubertim fundent illud mamillae ipsius. Sic ergo fit enthymema in prima figura ex signo convertibili tacita majori propositione: eo quod illa reputatur manifesta.” 66 See infra, §6.2.2.

13th-Century Parisian Commentaries on the logica nova

297

Albert’s observations will also have a role in the weakening of the status of sign inferences in later discussions.67 Slightly later in the same chapter Albert considers what Aristotle says about the difference in strength and validity among the three species of sign-enthymemes: the sign in the first figure is irrefutable and perfect in form according to the figure, the mood, and the matter;68 the signs in the second and third figure are refutable even when they move from true premises and draw true conclusions. Their problem is that they are defective in form: the sign-enthymeme in the third figure is defective in form because it has two singular or particular premises (Pittacus is wise, Pittacus is excellent) from which nothing follows syllogistically;69 the sign-enthymeme in the second figure is defective in form because it has two affirmative premises and this combination never yields a valid syllogism in this figure,70 or as he observed earlier, “there is no sign in the second figure.”71 Kilwardby had already argued that the enthymeme in the second figure is sophistical and thus no genuine syllogism at all. Albert specifies that it is an instance of the fallacia consequentis.72 As we shall see in what follows, it is precisely in the tradition of the commentaries on the fallacia consequentis that we find further interesting observations on the sign in the second figure.73 67 See infra, §6.1.3. 68 The matter of the syllogism is the two propositions and three terms of which it is composed. In this circumstance, Albert exemplifies the first figure by means of a reformulation of the example of the third figure, changing studiosus into ambitiosus: “Omnis ambitiosus liberalis; Pittacus est ambitiosus; ergo Pittacus est liberalis.” (Albert the Great, Liber Priorum II.7.9, ed. Borgnet, 805a). 69 Actually, the reference to the form of second-figure syllogisms is implicit. Albert’s treatment of second-figure sign-enthymemes is close to his prologues to the Topics and Sophistici Elenchi (cf. Brumberg-Chaumont 2013, 384–409), where he does not seem to accept that the syllogism simpliciter is the genus of which demonstrative, dialectical, and sophistical syllogisms are the species. 70 Albert the Great, Liber Priorum II.7.9, ed. Borgnet, 805b: “numquam sic se habentibus terminis fit syllogismus in secunda figura.” 71 Albert the Great, Liber Priorum II.7.9, ed. Borgnet, 804b: “quia sic arguitur affirmative et in secunda figura nihil affirmative concluditur: propter quod in ante habitis dictum est quod in secunda figura non est signum.” The reference is to Albert the Great, Liber Priorum II.7.7, ed. Borgnet, 801b: “Et quia secunda figura affirmative non concludit; a signo autem non trahitur argumentum nisi affirmative; idcirco a signo non syllogizatur in secunda figura, et signum in ea (a quo arguatur) non est.” 72 Albert the Great, Liber Priorum II.7.9, ed. Borgnet, 805b: “numquam sic se habentibus terminis fit syllogismus in secunda figura: non enim sequitur per virtutem syllogismi secundae figurae, quod si quaecumque peperit (eparit, ed.) pallida est (pallida autem est haec) quod hanc parere sit necesse: sed est fallacia consequentis.” 73 See infra, §6.2.1.-2.

298

chapter 6

One last observation.74 Just like Kilwardby, Albert observes that while first-figure signs fall within logic or the theory of demonstration, second- and third-figure signs belong to rhetoric: the enthymeme from a prodigium pertains to the dialectician or demonstrator, according to the diversity of the matter, either probable or necessary. By contrast, the enthymeme from the sign in the generic sense pertains to the rhetorician, as Aristotle says in the first book of the Posterior Analytics.75 The reference is probably to APo A 1, where Aristotle says that the division between syllogism and induction also applies to rhetorical argumentations, which divide into examples (rhetorical inductions) and enthymemes (rhetorical syllogisms).76 But, of course, that passage can hardly be taken as saying that probable enthymemes belong to rhetoric. Be that as it may, Albert’s remark brings us to the only thirteenth-century commentary on Aristotle’s Rhetoric that has reached us in a complete form: that of Giles of Rome. 1.2 Giles of Rome’s Commentary on Rhetoric A 2 As we know from the first Chapter, Rhetoric A 2 contains a treatment of sign-inferences that is somehow parallel to, and perhaps genetically dependent on, APr B 27.77 The text of the Rhetoric becomes available to the Latin West during the second half of the thirteenth century, when both a first anonymous translation from the Greek and the translation from the Arabic made by Hermann the German (Hermannus Alemannus) (completed around 1256) enter into circulation. The anonymous translation from the Greek has scarce diffusion.78 That from the Arabic is better known: it is quoted by Roger Bacon, Albert the Great, and Thomas Aquinas. A second translation from the Greek, made by William of Moerbeke aroud 1269, is adopted as textbook for university teaching and is the basis for the first commentary on the Rhetoric that we have, the

74

For now, we leave out the last chapter of Albert’s Liber Priorum, which deals with physiognomics; we shall return to that infra, §6.1.4. 75 Albert the Great, Liber Priorum II.7.9, ed. Borgnet, 806a: “pertinet enthymema ex prodigio vel ad dialecticum vel ad demonstratorem, secundum diversitatem materiae probabilis vel necessariae. Enthymema autem ex signo communiter accepto pertinet ad rhetorem, ut dicit Aristoteles in primo Posteriorum.” 76 Cf. supra, §§1.1, 1.2. 77 Cf. supra, Chapter 1, footnote 83. 78 Cf. Schneider (1978), xxviii.

13th-Century Parisian Commentaries on the logica nova

299

one composed by Giles of Rome between 1272 and 1273.79 Giles uses the earlier translations, though not systematically, as aids to interpretation.80 When Giles decides to produce a commentary on Aristotle’s Rhetoric, this work is almost unknown to the Latin West. While for his work on the Sophistici Elenchi and the Posterior Analytics Giles could draw from a quite established tradition of commentaries and series of questions, there was nothing at all which could guide him in the difficult task of commenting on the Rhetoric. He was also quite young at the time; that on the Rhetoric is probably one of his earliest works. Nevertheless, his commentary has a great success: it is transmitted, fully or partially, by more than twenty manuscripts, especially of the fourteenth century, which are preserved in several European libraries. Like Giles’ other Aristotelian commentaries, this is a literal exposition and has the typical structure of literal expositions. Notabilia or declarationes inserted in the explanation of the text only occur in the first and second books. After having suggested a reformulation of Rhet A 2, 1357a32–33 that should bring to the fore its implicit assumptions and its relationship to the preceding sections, Giles embarks onto a lengthy discussion about signs and the relation between signum and ycos which differs in some important ways from Kilwardby’s and Albert the Great’s interpretations of APr B 27.81 According to Giles, there are three species of sign: i) the sign that can be reconstructed as a first-figure syllogism and which always allows to infer the thing signified; the example is the Aristotelian lactating woman; ii) the sign that can be reconstructed as a second-figure syllogism, which exceeds the thing signified (in plus est signum quam signatum) and allows the inference of the thing signified for the most part (ut in pluribus); the example here is wandering about at night as sign of being a thief (it is the example of Soph El 5, to which we return below); iii) the sign that can be reconstructed as a third-figure syllogism, in which two properties that are connected in one subject are inferred to always be connected; the example here is the standard one of Pittacus, who is wise and learned.82 79

On Giles’ commentary see Marmo (2016); Marmo (2018); on Giles’ life and works and for further bibliographic references see Briggs (2016). 80 Cf. Marmo (1998). 81 Cf. supra, §§6.1.1.1, 6.1.1.2. 82 Giles of Rome, Expositio super Rhetoricam Aristotelis, lec. 6, 9va: “Ad evidentiam autem dictorum est notandum signum tripliciter posse sumi, secundum tres figuras sillogismorum. Sumitur enim primo signum in prima figura, et huiusmodi signum semper infert signatum, sicut lac habere est signum peperisse; et tunc formetur sic sillogismus: Quecumque habet lac peperit; hec habet lac; ergo etc. In secunda autem figura accipitur signum quando in plus est signum quam signatum, et ut in pluribus signum signatum infert,

300

chapter 6

At first Giles seems to accept Kilwardby’s and Albert the Great’s interpretation according to which the first-figure sign is called prodigium (but also retinerium, about which more below) and is irrefutable, while second- and third-figure signs are called ycos because in both arguments the premises and the conclusion are only probable. But this is not Giles’ considered view: the sign in the third figure has no specific name and is simply described as “non-necessary sign”;83 the ycos for Giles is only the sign in the second figure. Like his predecessors, Giles explains the etymology of ycos through reference to images; he also characterizes this kind of sign as signum similitudinarium.84 At this point Giles offers a terminological dilemma that involves a reconsideration of APr B 27 itself. On the one hand, if we take signum as the opposite of ycos, then the former includes both first- and third-figure signs; this seems to be Giles’ own terminological position; none of the authors so far considered seems to have given to the term “sign” this extension. On the other hand, if ycos covers third-figure signs as well, like in Kilwardby and Albert the Great, then signum must refer to the first figure only; in this case the contrast between necessary (first figure) and probable (second- and third-figure) signs would reflect

83 84

licet non semper sicut esse errabundum de nocte est signum furis; potest tamen quis esse errabundus absque eo quod sit fur; et tunc formetur sic sillogismus: fur est errabundus; hic est errabundus; ergo etc. In tertia autem figura sumitur signum quando aliqua duo habentia aliquem ordinem ad se invicem ex eo quod se concomitantur in aliquo credimus quod se concomitentur in omnibus, ut sapientia habet quendam ordinem ad studiositatem sive ad bonitatem. Nam Socrates inter cetera auxilia dicit sapientiam esse maximum auxilium ad vitandum peccatum, quia ergo videmus quod aliquis homo particularis, ut puta Pithacus est sapiens et studiosus, credimus sapientes studiosos esse. Formetur ergo sic sillogismus: Pithacus est sapiens; Pithacus est studiosus; ergo sapientes sunt studiosi.” See infra, Appendix B, §6.1.4. Quotations from the 1515 editions are hardly reliable and have been corrected on two manuscripts: Paris, Bibliothèque Nationale de France, Lat. 16681, 10v–11v (XIII) [= P1] and Paris, Bibl. de la Sorbonne, 120, 12rb–13ra (XIV) [= S] (see a provisional edition of about a half of lectio 6 in Appendix B). Outside Appendix B, variants are not registered. This sounds as an inversion of what Aristotle says at Rhet A 2, 1357b4–5, i.e., that the non-necessary sign has no name: τὸ δὲ μὴ ἀναγκαῖον ἀνώνυμον. Giles of Rome, Exp. sup. Rhet., lec. 6, 9va: “Istorum autem signorum signum in prima figura, eo quod de necessitate concludit, dicitur prodigium, id est magnum signum, sive retinerium, quia hominem retinet et terminat eo quod non contingat solvere, nec est in eo possibilis evasio. Signum vero in secunda figura, et maxime cum est in pluribus, dicitur ycos, quasi imago vel similitudinarium: nam si non est necessarium quod posito tali signo ponatur signatum, est tamen verisimile et probabile. Signum vero in tertia figura etiam ycos dici potest, quia verisimile est sapientes studiosos esse; tamen quia non habet proprium nomen dicitur signum non necessarium, quia non est necessarium quod aliqua duo habentia aliquem ordinem ad se invicem se concomitantur in aliquo quod se concomitentur simpliciter.” See infra, Appendix B, §6.1.

13th-Century Parisian Commentaries on the logica nova

301

the contrast in the definition of the enthymeme between εἰκός-enthymemes and σημεῖον-enthymemes: λέγεται γὰρ ἐνθυμήματα ἐξ εἰκότων καὶ σημείων.85 But if, as Giles proposes, ycos is only the sign in the second figure, then what follows the definition in the text of the Rhetoric86 is susceptible of a better explanation. Aristotle specifies that the ycos is what happens for the most part and is contingent, and is related to the thing signified as the universal to the particular: Here takes the ycos as the sign in the second figure and is found in something in which the thing signified is not found, like wandering about at night is ycos of being a thief, for it is more universal than this, so that there may be someone who wanders about at night and is not a thief; even if some thief were found who does not wander about at night so that wandering about at night and being a thief were related as what exceeds and what is exceeded, this would not be relevant; it is sufficient for this that wandering about at night be ycos of being a thief for some guy who is not a thief.87 Giles thinks that in order for a sign to qualify as an ycos it is sufficient that it be more extended than that which it signifies; wandering about at night is true of thieves but also of non-thieves; it is not relevant, Giles says, that not all thieves wander about at night. This seems implausible: if neither all those who wanders about at night are thieves nor all thieves wander about at night, how should one be justified in inferring from one’s wandering about at night that s/he is a thief? Giles thinks that a confirmation of the idea that the ycos is only the sign in the second figure comes from the continuation of the passage. Here Aristotle says that of signs one behaves like the universal to the particular, another as the particular to the universal.88 If σημεῖον at Rhet A 2, 1357b1 is taken in the wide sense, then the sign that is as the particular to the universal should include both second- and third-figure signs. But Giles apparently thinks that since the second-figure sign is an ycos, and since ycota have just been treated 85 Aristotle, Rhet A 2, 1357a32–33. 86 Aristotle, Rhet A 2, 1357a34–b1. 87 Giles of Rome, Exp. sup. Rhet., lec. 6, 9vb: “Accipit enim hic ycotem prout dicit signum in secunda figura et reperitur in aliquo in quo non reperitur signatum, ut esse errabundum est ycos ad esse furem, cum sit universalius quam ipsum, et sit aliquis errabundus qui non est fur; quod si etiam reperitur fur qui non est errabundus ita quod errabundus et fur sic se habent sicut excedentia ad excessa, nichil ad propositum; sufficit ad hoc quod errabundus sit ycos ad furem esse aliquem talem qui non sit fur.” See infra, Appendix B, §6.2.1. 88 Aristotle, Rhet A 2, 1357b1–3.

302

chapter 6

by Aristotle, then σημεῖον at 1357b1 should be taken in his (i.e., Giles’) sense, i.e., as comprising first- and third-figure signs (and excluding ycota). Then, the sign that behaves like the universal to the particular is the first-figure sign, that which behaves like the particular to the universal is the third-figure sign. Of this, the latter is not necessary and has no name, the former is necessary and is called retinerium, while in APr B 27 it was called prodigium, that is “great sign.”89 Where does the weird appellation retinerium come from?90 Its origins are in the Greek τεκμήριον which William of Moerbeke had merely transliterated into tecmerium/tekmerium (Rhet A 2, 1357b4–5).91 However, the manuscript of the Latin translation used by Giles is corrupt. University copyists, who did not understand the word, had proposed bizarre variants. It is a pity that the text edited in the Aristoteles Latinus gives no indication of this. Slightly later, in the apparatus of the edition of the Rhetoric, there are two distinct readings of the translation of τέκμαρ, which Aristotle indicates as the root of τεκμήριον: tecinar (according to mss. TzWl) and recinar (Pä).92 The latter reading is taken from a manuscript quite close to S (used here, see infra Appendix B), and could explain Giles’ interpretation, even though Schneider’s edition gives no variant for tecmerium. The point is that S reads retinerium (together with Pä 77vb) instead of tecmerium, and retinar instead of tecmar. Since consonants c and t in thirteenth- and fourteenth-century Gothic script are often indistinguishable, we believe that retinar rather than recinar could be the correct reading of 89

Giles of Rome, Exp. sup. Rhet., lec. 6, 9vb: “Dicit ergo quod signorum hoc quidem sic se habet ut aliquod singularium ad universale quantum ad signum in tertia figura, ubi particulariter concluditur intentum. Nos autem ex illo particulari inferimus universale, ut quia Socrates est sapiens et studiosus inferimus omnes sapientes esse studiosos. Hoc autem ut aliquod universalium ad particulare quantum ad signum in prima figura, ubi concluditur universaliter intentum. Istorum autem signorum unum est necessarium sicut signum in prima figura, aliud non necessarium, ut signum in tertia. Signum necessarium vocatur retinerium quasi hominem retinens et terminans, quia cum sit insolubile nescit homo quo fugiat. In secundo autem Priorum vocatur prodigium, quasi magnum signum. Signum vero non necessarium non habet nomen secundum differentiam, id est non habet nomen proprium, secundum quod distinguatur et differat ab aliis.” See infra, Appendix B, §6.2.2.1.2. 90 Here we follow Marmo (2018), 137–140. 91 Cf. translatio Guillelmi in AL XXXI.1–2, 167: “Horum autem quod quidem necessarium ­tecmerium.” 92 The manuscripts used by Schneider in his edition of the Latin version of William of Moerbeke are the following: Oz = Eton College 129 (ca 1300); Wl = Wolfenbüttel. Bibl. ducale, ms. 488 (ca 1300). Schneider proposes a selection of variants of the university tradition (which often has a wrong text); these are taken from mss. Tz = Toledo, Bibl. del Capitolo 47.10 (ca 1280); Pä = Paris, Bibl. Nat., lat. 16583 (ms. S, used here, corresponds to Pf in his stemma and appears very close to Pä).

13th-Century Parisian Commentaries on the logica nova

303

Pä. Giles confirms this hypothesis: he takes the name retinerium quite seriously and explains it by means of the following etymological argument: The necessary sign is called retinerium, almost as if it should restrain and determine the man, for since it is insoluble the man is unable to escape […] the necessary sign is the retinerium. For when they think they cannot reply to what is said, then they think it is a retinerium, in as much as it is shown and determined. For according to the old language of the Greeks retinar is the same as term, or tecmar according to another version. These signs are said necessary in as much they bind the man by restraining and determining him.93 Giles explains the weird appellation by appealing to the logical necessity of the sign in the first figure. He also refers to another manuscript, which has the correct reading, tecmar (while the 1515 edition and other manuscripts have detinar). We mentioned that this approach to the text is typical of Giles of Rome: he does not limit himself to one manuscript but uses at least another witness and earlier translations—the vetus translatio from the Greek and the littera arabica.94 Even if his use of these sources is not systematic, in his commentary there are more than ninety explicit references to each of the two translations, and we believe there may be still others. Two final observations: i) Giles’ notion of sign is coherently propositional, not sub-propositional; nowhere does Giles suggest that the sign is the middle term rather than the proposition containing the middle term; ii) Giles’ propositional notion of sign might explain the absence of any reference to the Augustinian definition: while this absence is curious in the work of an Augustinian monk, yet it may be the effect of the perception, on Giles’ part, of its irreducibility to the Aristotelian notion, which after all was the subject of his commentary.

93

94

Giles of Rome, Expositio, lec. 6, 9vb–10ra: “Signum necessarium vocatur retinerium quasi hominem retinens et terminans, quia cum sit insolubile nescit homo quo fugiat […] signum necessarium est retinerium. Nam quando putant non contingere solvere quod dictum est, tunc vere putant retinerium esse, eo quod ostensum et terminatum sit. Nam secundum antiquam linguam grecorum retinar idem est quod terminus vel tecmar secundum aliam litteram. Dicuntur enim talia signa necessaria eo quod hominem necessitent retinendo eum et terminando.” See infra, Appendix B, §6.2.2.1.1–2. Cf. Marmo (1998); the same attitude is also present in other commentators, like Kilwardby (cf. supra, §5.2).

304

chapter 6

1.3  The Enthymeme ex signis et ycotibus in the Commentaries on Peter of Spain’s Tractatus V and in a Question on Enthymemes The distance between the Augustinian (with its variants) and the Aristotelian definition of the sign is remarkable. The distance between the two models is also evidenced by the interpolation in the text of Peter of Spain’s Tractatus V that we mentioned above.95 We now quote it again in order to advance a hypothesis about the time and place at which the interpolation may have occurred: Aristotle has thus defined the enthymeme: the enthymeme is formed starting from ycota and from signs; ycos means the same as “probable proposition”; the sign, instead, according to the sense in which it is understood here, is the same thing as “demonstrative proposition which is either necessary or probable,” and this happens when we infer .96 Here both the definition of the sign and that of the ycos point to APr B 27. But there is a further detail: in the Latin version of the sign definition in APr B 27 it is said that the sign vult esse propositio demonstrativa, “wants (or purports) to be a demonstrative proposition.” We saw that in his comment on APr B 27 Kilwardby observes that a sign, whether necessary or probable, vult esse (βούλεται εἶναι) a demonstration but is not so. Yet in presenting his examples of signs in the three figures, Kilwardby uses the expression velle/vult (the βούλεται of APr B 27, 70a21) only of the sign in the second figure.97 Now, the absence of the modal qualification in the interpolation to Tractatus V may indicate a dependence on Kilwardby’s commentary. If this is correct, then the interpolation cannot be earlier than the 1250s, when Kilwardby’s work has become a reference for subsequent commentators.98 As mentioned, Peter’s Tractatus 95 Cf. supra, §4.1. 96 Petrus Hispanus, Tract. V.3, ed. de Rijk, 57, app: “Aristotiles sic diffinit entimema: Entimema est ex ycotibus et signis; ycos autem idem est quod propositio probabilis; signum autem, secundum quod hic sumitur, idem est quod propositio demonstrativa vel necessaria vel probabilis et hoc est inferendo.” Emphasis in transl. added. 97 Cf. supra, §6.1.1.1 and footnotes 37 and 41. 98 A further support for the hypothesis of a dependence on Kilwardby is the reply to the objection that follows the text added in the manuscripts H (Milano, Bibl. Ambrosiana, H.64 inf.) and R (Bibl. Apostolica Vaticana, Reg. Lat. 1731), those used by de Rijk for the critical edition: “Si quis obiciat quod debet diffiniri sic entimema est ex ycote et signo cum non sit nisi una propositio inferens que est ycos et signum secundum diversa ad hoc dicendum quod licet sit tantum una propositio inferens habet tamen in se virtutem duarum propositionum quia habet in se virtutem suam propriam et illius que intelligitur et sic est una secundum substantiam et sunt due propositiones secundum virtutem et

13th-Century Parisian Commentaries on the logica nova

305

(1230–1231) has some success as textbooks for the training to logical teaching in Dominican studia99 and in the universities. Starting maybe from the 1250s the Tractatus is commented in Southern France,100 and in the 1280s also in Paris (and then in Bologna, upon the Parisian model, where it enters into the university statutes as commentary text).101 In the statutes of the University of Paris of the thirteenth century there is no trace of the use of Peter’s Tractatus as introduction to logic. De Rijk has suggested that the reason of this is probably that the Tractatus arrived in Paris in the 1260s–1270s, after having spread in Southern France and Northern Italy, as shown by the oldest manuscripts in our possession.102 The first Parisian commentary, limited to the first five Tractatus, seems to have been that by Simon of Faversham.103 Simon’s commentary is preserved in four manuscripts: (1) ms. 429 of the Biblioteca Antoniana of Padova (1ra–27rb), attributed by a later hand to Magister Simon in the upper margin of the first column; (2) ms. Lat. 16126 of the Bibliothèque Nationale de France in Paris (77ra–90rb), which contains an incomplete copy but says in the colophon (92rb): Explicit scriptum tractatuum magistri Petri Hyspani compilatum a magistro Symone ad iuuenum instructionem; (3) ms. clm 14697 of the Bayerische Staatsbibliothek of München (1ra–48rb) without attribution; (4) Milano, Bibl. Ambrosiana, F.56 ideo dicit in plurali quod ex ycotibus et non ex ycote et similiter ex signis et non ex signo.” (Tract. V.3, ed. de Rijk, 57, app.). Kilwardby has a similar solution, cf. Not. lib. Priorum, lec. 76, dub. 4, ed. Thom and Scott, 1570: “Deinde queritur de diffinitione entimematis. Falso enim dicitur esse sillogismus, ut uidetur, cum sint modi diuersi argumentandi et sillogismus exprimat duas propositiones, entimema autem unam. Et dicendum quod substantialiter idem est sillogismus et entimema quamuis non sit in entimemate expressio utriusque propositionis.” The convergence may also be explained as dependence on a common source, but we are unable to verify this hypothesis. The Glossae Salmantinae seem to be the first to have read the text with the interpolation on the enthymeme; according to the anonymouys commentator ycos and signum are almost synonymous; they differ only from the point of view of their consideration (Anon., Glossae Salamantinae super Tractatus Petri Hispani, ms. Paris, Bibl. Nat. de France, lat. 6433, 216va: “eadem propositio dicitur esse ycos et signum, sed secundum aliam et aliam rationem dicitur ycos et signum.”). 99 Cf. D’Ors (1997); Maierù (1994), 11–12; Brumberg-Chaumont (2019). 100 On the commentary attributed to a no better specified Robertus Anglicus, see de Rijk (1969); as it has been pointed out in Ebbesen and Rosier (1997), Rosier and Ebbesen (2000), and Ebbesen (2021), they are two distinct authors, neither of whom can be identified with Kilwardby. We shall return to this series of commentaries (infra, §6.2.1). 101 On the commentaries on Peter of Spain in Bologna, e in Italy in general, see Maierù (1992) and (1994). 102 See de Rijk (1972), xcvi–xcviii. 103 See de Rijk (1968).

306

chapter 6

sup.104 The attribution to Simon of Faversham is especially founded on the several references to Albert the Great, which are also the source of the dating to the 1270s–1280s. There is however no sufficient evidence in support of this attribution and therefore of the dating. The author of the commentary may be rather the same person who authored another commentary attributed to Magister Simon: the earliest commentary on Martin of Dacia’s Modi significandi. We shall refer to the author as “Master Simon.” A confirmation of the dating, however, comes from the fact that it certainly had influence upon Gentilis of Cingoli, who was student in Paris in the 1280s and who would bring to Bologna both the practice of using the first five Tractatus of Peter of Spain as introduction to logic (just like Master Simon did) and that of teaching speculative grammar by commenting upon Martin of Dacia’s Modi significandi. The second commentary that will be object of examination here is preserved in one single copy in the ms. clm 6726 of the Bayerische Staatsbibliothek of München (1r–39v); it is written on paper in only one column by a hand of the fifteenth century and without attribution. In the colophon it is titled: Notule super Tractatus Petri Hispani (39v).105 Master Simon’s commentary is important because its author is aware that the copy of the Tractatus in his hands contains unauthentic portions of the text: following a usual practice among commentators, he has compared his text with older and therefore more reliable copies of the work and has detected some discrepancies. One of these concerns precisely the interpolation discussed above: Then follows: The Enthymeme, in which the author gives the definition of the enthymeme. And it is divided in two : first, he gives his own definition of the enthymeme, and in the second place he gives Aristotle’s definition. The second here (if you have the same text : Aristotle so defines . But this is not the author’s text.106 104

105 106

De Rijk (1968) has published several passages from this commentary, following especially the Paduan manuscript (which appears to be derived from a better ancestor). The München manuscript has several interpolations and a quite different text of the commentary on Tractatus II (De universalibus). This at least suggests a double redaction of the commentary, testified by the two manuscripts (Padova and München). Further research is needed for a better understanding of the relationships between the four witnesses. The Milan manuscript has been added in de Rijk (1972), L n. 2 (unfortunately we haven’t been able to examine it). For a more detailed description of both commentaries cf. Marmo (forthcoming). Master Simon, Expositio super Tractatus Petri Hispani V, ms. Pd = Padova, Bibl. Antoniana, 429, 22ra: “Deinde sequitur: Entimema [V.3, 56.16], in qua auctor ponit diffinitionem

13th-Century Parisian Commentaries on the logica nova

307

For our purposes, however, Master Simon’s commentary is a bit disappointing, as it only treats of two problems. The first is about the definition of the enthymeme, of which he also provides the etymology; the second is about the possibility of reducing the enthymeme to the syllogism. As to the first problem, Simon defines the enthymeme as a truncated, diminished, and incomplete syllogism. We saw in the first Chapter that both Alexander and Philoponus take an enthymeme to be a syllogism with one premise omitted.107 According to Master Simon, the etymology of this term (from en-, “in,” and -thimos, meaning mens, “mind”) suggests that “in every enthymeme one proposition is kept in mind,” be it the minor (like in the enthymeme “Every man is animal, hence Socrates is animal”) or the major premise (like in the enthymeme “Every man is animal, hence every man is substance”).108 With regard to the second problem, the possibility of a reduction of the enthymeme to the syllogism seems to be hindered by their formal opposition (qua distinct species of the genus argumentation), for nothing of this sort can be reduced to its opposite. In order to answer to this objection, it is necessary to introduce a distinction that comes from the modistic theory of second intentions (for enthymemes and syllogisms are clearly second intentions). On the one hand, in so far as enthymeme and syllogism designate complex second intentions, the enthymeme cannot be reduced to the syllogism because they are formally distinct (and this supports the objection). On the other hand, in so far as they designate the “things” to which second intentions are attributed, or their objects,109 the enthymeme can be reduced to the syllogism, which latter constitutes the main species of entimematis. Et dividitur in duas: primo ponit diffinitionem entimematis propriam, secundo ponit diffinitionem entimematis secundum Aristotelem. Secunda ibi (si habetis illam litteram): Aristoteles sic diffinit [V.3, 57, app.]. Sed non est littera auctoris.” Quoted in de Rijk (1968), 100; Pa = Paris, BNF, Lat. 16126, 88vb. This passage occurs in the München ms. (M) in an abbreviated form and without questioning its authenticity (as mentioned, M might be a witness of a distinct version, maybe earlier): “Consequenter sequitur: Entimema, in qua auctor manifestat ipsum entimema, ponendo diffinitionem eius.” (M 40rb). 107 Cf. supra, §1.2. 108 Master Simon, Exp. sup. Tract. V, M 40rb; Pa 88vb; Pd 22ra: “Nota quod enthimema est sillogismus deminutus et incompletus et dicitur ab ‘en’ quod est ‘in’ et ‘thimos’ quod est ‘mens,’ quia semper in omni enthimemate retinetur una propositio in mente: vel minor ut ‘homo est animal, ergo Sortes est animal,’ vel maior ut ‘omnis homo est animal, ergo omnis homo est substantia,’ hic retinetur maior que est ‘omne animal est substantia’.” See the text in Appendix C with the apparatus of variants. The minor of the first enthymeme is of course “Socrates is man”; the major of the second is “Every animal is substance.” It is interesting to note that ms. M, probable witness of an earlier version, gives a completely different etymology: “‘timeiria’(?) quod est ‘retinere’,” which may be an echo of the commentary of Giles of Rome, Expos. sup. Rhet., 9vb and 10ra. 109 This is a typical argumentative step in modistic works.

308

chapter 6

argumentation, and that with respect to which the other species are to be compared. In this sense, not only the enthymeme, but also induction can be reduced to the syllogism.110 The question on enthymemes in Simon of Faversham’s commentary on the Prior Analytics is about a related topic. It is the last question of his commentary. The author inquires whether the enthymeme is or is not a syllogism. In connection with the often quoted sentence from APr B 27, “entimema est sillogismus ex ycotibus et signis,” Simon refers to the parallel passage in Rhet A 2, which we have examined above.111 According to Simon, the enthymeme is a syllogism in substance (Albert’s terminology), even though it lacks a premise, which is implicitly assumed because evident.112 Also, like the syllogism the enthymeme is based on principles, like the dici de omni and the dici de nullo.113 However, although it is a syllogism in substance, the enthymeme is defective in matter and in form. It is defective in matter because it moves from probable rather than from true and necessary premises (which is what is meant by Aristotle’s claim that the enthymeme est ex ycotibus et signis): speculative sciences, which alone are sciences in the proper sense, proceed from necessary premises, and therefore make use of the syllogism in its most perfect and efficient form: practical sciences proceed from what is probable and thus from enthymemes. The enthymeme is defective in form because in it the disposition of the propositions does not conform to its full vocal expression.114 The 110 Master Simon, Exp. sup. Tract., V, M 40rb; Pa 88vb; Pd 22ra–b; see infra, Appendix C. 111 Cf. supra, §6.1.2. 112 Simon of Faversham, Questiones libri Priorum II.15: “Dicendum quod entimema est sillogismus: idem enim est substantialiter sillogismus et entimema, nec in alio est differentia nisi quod in sillogismo explicatur sive exprimitur utraque propositio; in entimemate autem quandoque una exprimitur et alia subticetur. Subticetur quidem, quia ipsa est evidens.” (See infra, Appendix D, §3.1). 113 Simon of Faversham, Quest. lib. Priorum II.15: “Quod autem entimema sit sillogismus patet, quia omnis ratiocinatio que confirmatur per illa principia per que tenet sillogismus unde sillogismus est, est vere sillogismus; sed entimema tenet per illa principia per que tenet sillogismus unde sillogismus est, scilicet per dici de omni et dici de nullo.” (See infra, Appendix D, §3.2). 114 Simon of Faversham, Quest. lib. Priorum II.15: “Et ad hoc advertens Philosophus, primo Rethoricorum et hic, dicit quod entimema est sillogismus ex ycotibus et signis; entimema ergo est sillogismus, tamen in quantum una propositio subticetur, non est sillogismus evidens. Ideo aliqualiter deficit a sillogismo et quia in omni genere imperfectum reducitur ad perfectum, ideo entimema ad sillogismum reducitur. Tunc autem ad sillogismum reducitur cum illa propositio que deficit exprimitur. Deficit autem entimema a sillogismo in duobus, scilicet in materia et forma. In materia, quia sillogismus secundum quod accipitur in suo esse potissimo est ex propositionibus veris et necessariis; sed entimema non sic, sed ex probabilibus solum. [...] Differt etiam entimema a sillogismo in forma: si

13th-Century Parisian Commentaries on the logica nova

309

enthymeme is not therefore a syllogism in its most perfect and complete being (in suo esse potissimo); it is a syllogism ex ycotibus et signis. This is the reason why demonstrative sciences make use of syllogisms and not of enthymemes.115 Apart from this, there are no special remarks about signs and ycota in Simon’s commentary. The difference of approach between Master Simon and Simon of Faversham in their discussion of the relation between enthymeme and syllogism also suggests a difference in authorship. A somewhat more interesting case for our theme is the commentary by another Anonymous of Munich. On the basis of the affinity between this commentary and the doctrines of Radulphus Brito, it has been suggested that its author may be the young Brito.116 The Anonymous makes no mention of the inauthenticity of the interpolation about the enthymeme (as he does with other portions of the text117), but offers some interesting remarks. One is about the ycos, which is characterized as a proposition having an appearance of truth in the eyes of everyone, the majority, or the wise. The term ycos is, again, etymologically connected to images and visuality. The example, however, is puzzling: “the woman who has milk in the breast has given birth” (mulier que habet lac in mamillis peperit), i.e., the τεκμήριον of APr B 27 and Rhet A 2. It is an ycos, according to the author, because no one has ever seen a woman with milk in the breast who has not given birth. This proposition represents a reality, and once proved it is regarded as known and true, or at least probable.118 The annotation formam sillogismi vocemus debitam ordinationem propositionum secundum vocalem expressionem, et ita differt a sillogismo secundum formam quia in entimemate non exprimitur vocaliter nisi una propositio.” (See infra, Appendix D, §3.5). Simon here refers to the notions of syllogistic form and matter that we find in Albert the Great’s prologue to the Prior Analytics paraphrase, cf. supra, §6.1.1.2. 115 Simon of Faversham, Quest. lib. Priorum II.15: “Et tu dices: nonne dictum est quod entimema est sillogismus? Et modo dicis quod differt a sillogismo. Dico quod entimema non est sillogismus accipiendo sillogismum in suo esse potissimo, sed cum hac additione ‘ex ycotibus et signis’; unde sillogismi sunt in demonstrativis, entimemata vero non. Sic igitur patet quomodo entimema est sillogismus /O 138va/ et quomodo non quicumque, quia non sillogismus in suo esse potissimo, sed est sillogismus ex ycotibus et signis.” (See infra, Appendix D, §3.6). 116 See Marmo (forthcoming). 117 Anonymous, Notule super Tractatus Petri Hispani, ms. München, Staatsbibliothek, clm 6726, 12v and 22r, where he mentions an antiquus textus as opposed to a new and interpolated one. 118 Anonymous, Not. sup. Tract., 31v: “Nota: ycos dicitur propositio representans que habet apparentiam et videtur vera et probabilis vel omnibus vel pluribus vel sapientibus et maxime notis, ut illa propositio ‘mulier que habet lac in mamillis peperit’ potest dici ycos, quia videtur esse nota in sua apparentia, quia non est visa mulier habens lac in mamillis que non peperit(?); et est ycos gratia dictionis(?) quia interpretatur ymago: ymago

310

chapter 6

suggests that in this context ycos is to be taken as the major premise (proved or probable) of an enthymeme. The Anonymous further observes that the sign is said “correlatively to the thing signified” (correlative ad signatum). He mentions some topical rules that may be applied in this case: “a relative term, once posed [i.e., affirmed], poses its correlative, and once destroyed [i.e., negated], destroys its correlative” (relatiua posita se ponunt et perempta se perimunt). When this topical rule is applied to the relation sign-thing signified, we get the conclusion “your sister has given birth” from the premise “your sister has milk in the breast,” thanks to the proposition “the woman who has milk in the breast has given birth.”119 The “sign” here is the major, not the minor, premise, which is the proposition that states the correlation of two facts, one of which is “sign” (in the standard sense) of the other. The text is not wholly perspicuous on this point. Yet the Anonymous’ claim that “sign” means “the necessity of inference” (signum dicit necessitatem illationis)120 seems to go in the same direction: for the major premise is precisely the rule that governs the illative derivation of the conclusion from the minor premise (or, when expressed as a conditional, the illative relation between antecedent and consequent), and thus can with some justice be said to express the necessity of the inference. This practice of calling “sign” not the minor but the major proposition is quite original, or at least is found nowhere else in coeval commentaries.121 1.4 Physiognomics as scientia de signis Both Kilwardby and Albert the Great close their commentary/paraphrase of the Prior Analytics with a chapter devoted to the physiognomic section of APr B 27, titled “On the discovery of the sign that is the middle term in an enthymeme” in both commentaries. After having mentioned some of the questions discussed by Kilwardby at the end of his own commentary,122 Albert, like representat rem cuius est ymago, ut ymago beati Nicolai. Ista autem propositio que dicitur ycos representat rem ita quod statim probata videtur esse nota et vera et probabilis et per se nota.” 119 Anonymous, Notule super Tractatus Petri Hispani V, 31v: “propositio dicitur signum quo (-a, ms.) posito (-a, ms.) de necessitate ponitur et reliquum, ut hec propositio ‘mulier habens lac in mamillis peperit’, primo dicitur signum quia sequitur ad istam(?) de necessitate ‘soror tua peperit’, quia apparet ad sensum quod soror tua habet lac in mamillis.” 120 Anonymous, Notule super Tractatus Petri Hispani V, 31v. 121 Further research is needed on the Bologna commentaries. Since the majority of them dates to the fourteenth century (cf. Maierù 1992, 502–503), they fall outside the temporal scope of the present investigation. 122 Cf. Robert Kilwardby, Not. lib. Priorum, lec. 77, dub. 1 and 3, ed. Thom and Scott, 1582: why the investigation is not about the discovery of the middle for induction and example, and whether it concerns the logician as such or also the dialectician and the demonstrator.

13th-Century Parisian Commentaries on the logica nova

311

Kilwardby before him, explains that there can be physiognomic inferences if two conditions are met. Actually, as we saw above, the conditions posed by Aristotle are three: (i) body and soul are altered simultaneously by nature; (ii) there is a one-to-one correspondence between bodily affections or signs and spiritual affections; (iii) both the spiritual affection and the bodily affection or sign are “proper” to a kind.123 Aristotle specifies that “the sign is proper (ἴδιον) in this sense, that it is proper of the whole kind, but not that it is proper of one kind, as we usually say,”124 and we noticed that this sense is incompatible with that of non-essential property convertible with a subject that is used in the Topics. We also saw that Aristotle suggests that the second part of condition (iii)—that a bodily affection or sign is “proper” to a kind of animals—derives from the first part of condition (iii) together with (i), because if body and soul are altered simultaneously, to a “proper” affection of the soul there will correspond a “proper” sign of it.125 Kilwardby, and Albert the Great after him, must have perceived that the third of Aristotle’s conditions partly derives from the first, and this is probably the reason why they mention two conditions only. Here is Kilwardby’s formulation of the two conditions: “Prima suppositionum est quod passio naturalis signum habet in subiecto cuius est, secunda est quod unius passionis sit unum signum” (“The first assumption is that a natural affection has a sign in its subject; the second is that there is a single sign of a single affection”).126 Albert follows Kilwardby quite closely on this.127 But both also assume that the “sign” has to be proper in the sense of APr B 27, i.e., it must belong universally to one species and non-universally to some other. Following Ross, we also saw that Aristotle’s discussion on physiognomics can only make sense if we assume that he is talking of inferring natural affections in men from the presence in man of certain signs that in other species are constantly associated with those natural affections. The peculiar sense of ἴδιον, which both Kilwardby and Albert recognize, is crucial in this respect: we can infer that S is a sign of A in a species (human being) to which S belongs non-universally on the ground that S is a sign of A in a species to which S belongs universally (lion). Kilwardby gives the opposite interpretation: he thinks that Aristotle seeks to show “this [i.e., large extremities] to be a sign of courage in the lion through the fact that it is a sign of courage in other animals 123 Aristotle, APr B 27, 70b6–14. 124 Aristotle, APr B 27, 70b18–20; transl. Smith. 125 Cf. supra, §1.5. 126 Robert Kilwardby, Not. lib. Priorum, lec. 77, ed. and transl. Thom and Scott, 1574–1575. 127 Albert the Great, Liber Priorum II.7.10, ed. Borgnet, 807a.

312

chapter 6

in which it does not inhere universally.”128 The doubt then is raised (dubium 7) concerning the possibility of an inference in the other direction, from the lion to the human being (which is Ross’ and our interpretation). But then there is a doubt because it seems that by the same argument it could be shown that having large extremities is a sign of courage in other animals, by virtue of the fact that it is a sign of courage in the lion, and the converse can be shown by this reasoning. And it should be said: No. For courage and the having of large extremities inheres universally in the lion, but in man it does not inhere in all. And so from the differences between those that have large extremities and those that do not in the same genus, it can be argued that this is a sign of strength in the lion, but not conversely.129 Kilwardby’s point is that in order to be able to formulate the major proposition that “large extremities are a sign of courage,” the association between large extremities and courage has to be determined with respect to the ­species to which it belongs non-universally: it is because human beings with large ­extremities are courageous while human beings without large extremities are not, that we discover that the association is valid and that justifies the transferring of it to the species to which the natural affection belong universally (lions). Albert follows Kilwardby quite closely also here.130 Ross would concede Kilwardby’s point, however: “We can also reason back from the species only some of whose members have P1 [large extremities] to that all of whose members have it.”131 The next dubium (no. 8), practically identical in Albert, substantiates and clarifies the point:

128 129

130 131

Robert Kilwardby, Not. lib. Priorum, lec. 77, ed. and transl. Thom and Scott, 1587. Robert Kilwardby, Not. lib. Priorum, lec. 77, dub. 7, ed. and transl. Thom and Scott, 1586– 1587: “Sed tunc dubitatur quia uidetur quod eadem ratione posset ostendi habitus magnarum extremitatum signum fortitudinis esse in alio animali per hoc quod est signum fortitudinis in leone, qua ratione econuerso ostendi potest. Et dicendum quod non. Leoni enim uniuersaliter inest tam fortitudo quam habitus magnarum extremitatum, homini autem non omni inest, et ideo per differentias eorum qui habent magnas extremitates ad illos qui non habent in eodem genere, argui potest in leone illud esse signum fortitudinis, sic autem non se habet econuerso.” Albert the Great, Lib. Priorum II.7.10, ed. Borgnet, 807b–808a. Ross (1949), 502.

13th-Century Parisian Commentaries on the logica nova

313

But further, it seems that his technique is null. For it seems to show the same thing from itself. For it shows the affection from the sign and conversely the sign from the affection. Hence it shows the same thing from itself. And it should be said that it shows the sign from the affection and conversely, but not in the same thing nor in the same way, and so it is not inappropriate. For it shows the sign from the affection but not in the affection’s proper subject, whereas it shows the affection from the sign in its proper subject. Further, the two demonstrations are produced in different ways, because the sign is shown from the affection by way of sense-experience, but the affection is shown from the sign by way of syllogism. And thus the two demonstrations are produced in different things and in different ways—which is not inappropriate.132 Even though sign and affection are convertible and thus in principle provable through one another, physiognomics is not circular. The reason is that the sign is inferred from the affection in the species to which the sign (and the affection, given convertibility) belong non-universally (large extremities are inferred from courage in men), while the affection is inferred from the sign in the species to which sign and affection belong universally (courage is inferred from large extremities in lions). Kilwardby also specifies that only the second direction is a proper syllogistic inference, while the first direction is simply sense perception (per viam sensus). This is problematic. For either what is “shown” in human beings is that some of them have large extremities; this is indeed the direct product of sense perception and not the indirect product of inference “from the affection”; or what is shown is that courageous human beings have large extremities, but this is hardly a matter of sense perception only. Perhaps Kilwardby means that once we have come to know that some human beings are courageous while others are not, we verify by sense perception that the former have large extremities while the latter have not. This is the only meaning of the solutio that supports the idea that the inference (or perhaps

132

Robert Kilwardby, Not. lib. Priorum, lec. 77, dub. 8, ed. and transl. Thom and Scott, 1586– 1589: “Sed adhuc uidetur quod ars sua nulla. Ostendit enim, ut uidetur, idem per seipsum. Ostendit enim passionem per signum et econuerso signum per passionem, quare ostendit idem per seipsum Et dicendum quod ostendit signum per passionem et econuerso, sed non in eodem nec eodem modo et ideo non est inconueniens. Ostendit enim signum per passionem in subiecto non proprio passionis, ostendit autem passionem per signum in subiecto eius proprio. Adhuc diuersimode fit hec ostensio et illa quia signum ostenditur per passionem per uiam sensus, passio autem per signum per uiam sillogismi. Et ita in diuersis et diuersimode fit hec ostensio et illa, quod non est inconueniens.”

314

chapter 6

the mere perception) of the association in human beings is the basis for the inference of the association in lions. Aristotle says that physiognomic inferences are drawn in the first figure. Since the only kind of sign in this figure is the τεκμήριον discussed in the first part of APr B 27, Kilwardby and Albert are justified in thinking that the sign on which a physiognomic inference can be based is a prodigium. Kilwardby has a dubium (no. 2) about this, easily resolved by pointing out that only signs of this type are necessary and yield knowledge. Moreover, Aristotle is very clear that in physiognomic inferences the major premise has to be convertible (condition (ii)), and we know that the convertibility of sign and thing signified is precisely what characterizes the sign in the first figure. Is physiognomics a logical discipline? Kilwardby has a dubium also on this (no. 3). The problem is whether or not physiognomic investigations belong to logic, since the logician is concerned not with things but with the concepts of things (intentiones rerum), which of course is an implicit reference to Avicenna’s definition of the object of logic (explicitly referred to in the De ortu scientiarum of 1252).133 The answer is that natural affections do belong to logic, even though the logician is concerned with natural things only in general and not as such or according to their principles.134 Kilwardby does not know the pseudo-Aristotelic Physiognomics and therefore cannot go beyond the few remarks that he makes. As we shall see in a moment, for Radulphus Brito, who is credited with being the author of a series of questions on the Physiognomics,135 physiognomics establishes relationships between external signs and natural affections. Albert the Great returns to the semiotic nature of physiognomics, and in particular to the last section of APr B 27, in his paraphrase of the books De animalibus (roughly coeval with his works on the Prior and the Posterior Analytics, 1258–1262), at the end of the section on human physiognomics:136 These are then the signs of physiognomics that show the natural regime of human beings’ life not always with necessity but frequently and with probability. These signs, then, in human beings and in animals, only refer to those affections that inhere naturally, which moving from the body reach to the soul, and not those that are only in the soul, like music and

133 134 135 136

Robert Kilwardby, De ortu scientiarum, §459, ed. Judy, 157. Robert Kilwardby, Not. lib. Priorum, lec. 77, ed. Thom and Scott, 1582–1584. Cf. Costa (2011), 162–165. Albert the Great, Lib. de animal. I.2–3, ed. Stadler, 46–223.

13th-Century Parisian Commentaries on the logica nova

315

geometry, but rather like anger, desire and the like. And this is what Aristotle claims at the end of the Prior Analytics […].137 As it happens in some of his other works, Albert’s physiognomic digression is based on his knowledge of “new” sources. In particular, Albert appears to know the De physiognomonia liber of the so-called “Anonymus Latinus” (sixth century, but re-appeared in the twelfth), the Liber ad Almansorem of al-Razi or Rasis, the Secretum secretorum attributed to Aristotle, and (perhaps) the Liber Phisionomie of Michael Scot, which constitutes the canon of medieval physiognomics.138 At the beginning of his physiognomic digression Albert tells the following story, taken from the Secretum secretorum. In order to verify the ability of the physiognomer Philemon, some disciples of Hippocrates go to Philemon with a drawing portraying their master. On inspecting the drawing, Philemon concludes that the man portrayed is lascivious and lustful, which conclusion disturbs the disciples. Having told about Philemon’s conclusion to Hippocrates, they are puzzled by their master’s answer: Philemon is right, but the wise Hippocrates claims to have fought and defated his own inner nature, for the sake of philosophy and moral life.139 According to Jole Agrimi,140 Albert’s treatment of physiognomics, based as it is on anatomy and the description of exterior signs, is a stepping stone in the history of physiognomics and of the university reception of the pseudo-Aristotelian Physiognomonics, as it favoured the adoption of the latter as textbook for the teaching of this science. Another important step in this direction is made by Peter of Abano, who in 1295, in Paris, writes a compendium of the pseudo-Aristotelian Physiognomonics which “facilitates the circulation [of the work] in the intellectual milieu in the margins of university teaching, first in Paris, then in Padua.”141 In a later work, the Lucidator, physiognomy is presented as a science subordinate to astrology: 137

Albert the Great, Lib. de animal. I.3.7, ed. Stadler, 223: “Haec igitur sunt signa physonomiae quae regimen physicum vitae hominum non quidem semper ex necessitate, sed frequenter et probabiliter ostendunt. Haec autem signa in hominibus et animalibus non referuntur nisi ad eas passiones quae naturaliter insunt, quae incipiunt a corpore et perveniunt ad animam, et non ad illas quae sunt animae solius, sicut est musica, et geometria, sed potius sicut est ira et concupiscentia et huiusmodi. Et hoc est quod dicit Aristoteles in fine secundi priorum Analeticorum […].” 138 On the beginnings of physiognomics in the Latin West see the articles by Jole Agrimi collected in Agrimi (2002); for its earliest phase see esp. Agrimi (2002), 101–108. 139 Cf. Lib. de animal. I.2.2, ed. Stadler, 46. Cf. also Roger Bacon, Secretum secretorum IV.1, ed. Steele, 165–166; Agrimi (2002), 116; Costa (2011), 164 n. 125. 140 Cf. Agrimi (2002), 117. 141 Agrimi (2002), 120.

316

chapter 6

Physiognomy is contained under natural science, as even its name denotes: called from “physis” nature and “nomos” law. From a law and a coordination of nature it happens that a power similar to a certain form of a body is impressed upon the soul. And there exists such a science of natural affections and of accidental of the body that induce reciprocal transformations to the dispositions of both, as I have shown in my Compendium of physiognomy.142 Peter had given the same etymological explanation in his Liber compilationis physionomie. There he had also criticized an alternative etymological explanation according to which the second part of the name of the discipline derives from “onoma” rather than from “nomos.”143 In the third part of the Liber, after a recognition of the signs that can be drawn from the observation of bodies, he explains and determines the causes of those signs, thus making of physiognomy a genuine scientia propter quid: he first describes universal and primary causes (connected to astronomy, chapters 1–3) and then particular and secondary causes (connected to medicine, chapters 4–5).144

142

143

144

Peter of Abano, Lucidator dubitabilium astronomiae, ed. Federici Vescovini, 122: “physionomia sub naturali contenta scientia, ut etiam nomen denotat: a ‘physis’ natura dicta et “nomos” lex. Ex quadam namque lege ac cohordinatione nature inest quod talis corporis forme similis anime imprimatur potentia. Que siquidem scientia existit passionum anime naturalium corporisque accidentalium habitum vicissim permutantium utriusque, ut in Physionomie declaravi compilatio.” Cf. also Paschetto (1985). On Peter’s life and works see Federici Vescovini (1988), 21–36. Cf. Peter of Abano, Liber compilationis physionomie, part. 1, cap. 2, decisio 1, where an identical definition of physiognomics is given; decisio 2, which refers to APr B 27; and decisio 3, about the interpretation of the name: “A nonnullis autem dicta est phisionomia a phisis greca lingua natura et onoma nomen, eo quod ipsam naturam nominet. Sunt et alii nature grecantes quod determinatio vel lex existat nature, a phisis et nomos quod est lex. Ex quadam namque ordinatione et lege nature inest quod talis corporis forma uel potentia anime imprimatur et econtra.” The alternative etymology criticized by Peter is contained in Peter of Spain’s Questiones super De animalibus (cf. Agrimi 2002, 117). Peter of Abano, Liber compilationis physionomie, pars 3, cap. 1. In the Conciliator differentiarum philosophorum et medicorum, diff. 8, s.l., 1490, b3r–v (composed in 1303 and revised in 1310), Peter addresses some issues of Aristotelian philosophy of science. In particular, he associates the Galenian via resolutiva and via compositiva with the Aristotelian demonstratio propter quid and demonstratio quia, respectively. He also refers to the threefold Averroistic distinction between demonstration of the cause, demonstration of the sign, and absolute demonstration; see supra, §5.3.1. Crisciani and Agrimi (1992), 193–201 have also conjectured Peter’s dependence on Taddeo Alderotti and his reading of the commentary by Haly Abbas on Galen’s Techne; cf. also Crisciani and Agrimi (1988), ch. 2.

13th-Century Parisian Commentaries on the logica nova

317

Among the texts of the last decade of the thirteenth century there is a series of questions on the Physiognomonics that is preserved in a Florentine manuscript containing several works by Radulphus Brito. In his doctoral dissertation, Iacopo Costa has conjectured that this series of questions is also authored by Brito, especially on the basis of the affinity of the first question with a similar question of the so-called “Vatican Commentary” on the Nicomachean Ethics authored by Brito.145 In the first question, Brito deals with the epistemological status of physiognomics (or physionomia, as it is called in his work), which he characterizes as “conjecture or knowledge of natural customs through exterior signs” (coniecturatio vel cognitio de moribus naturalibus per signa exteriora).146 In answering the question, Brito illustrates the following three points: i) what is physiognomics; ii) there can be scientific knowledge of natural customs; iii) physiognomics is not as certain as other sciences. (i) As to the first point, following the usual pratice in this sort of works, Brito provides an etymolological explanation of the term physionomia: according to him, this term derives from physis, which means “nature or natural customs,”147 and from nomos, meaning “rule” or “speech”: physionomia means speech on ­natural customs.148 (ii) The second point establishes that mores or natural inclinations are intelligible entities having properties and principles or causes that can be determined through demonstration, so the answer must be positive. In support of this second point Brito tells the story about the disciples of Hippocrates that we have met in Albert the Great’s De animalibus.149 (iii) The third point is of much relevance for us: if physiognomics is a conjectural science that investigates human beings’ natural inclinations from exterior signs, it cannot be a

145 146 147

148 149

We shall not push this line of investigation any further in this book, but it is certainly worth further study. Costa (2011), 162–165. Radulphus Brito, Questiones libri De physionomia, ms. Firenze, Bibl. Nazionale Centrale, Conv. Soppr. E.I.252, 232vb. See the complete text in Appendix E; a transcription is also in Costa (2011), 164–165; the list of questions is in Costa (2011), 357–358. In other works, as in the Questiones super Metaphysicam, Proemium, ms. Firenze, Biblioteca Nazionale Centrale, Conv. Soppr., E.I.252, 265rb, Brito shows that he knows the meaning of physis, namely nature. It is likely that the text of his questions on the Physionomia is corrupted here and that sermo should be changed into something like natura vel mos naturalis (see infra, Appendix E) Radulphus Brito, Quest. lib. De phys., q. 1, 232vb (see infra, Appendix E, §3.1). Radulphus Brito, Quest. lib. De phys., q. 1, 232vb–233ra (see infra, Appendix E, §3.2). The text (again) appears to be corrupt: the disciples are first said to be Galen’s pupils, but when they return to their master, his name is Hippocrates. The debate about what requirements have to be satified by a discipline in order to be considered a science was quite traditional; for a close example (concerning astrology), cf. Peter of Abano, Lucidator, diff. 1.3, ed. Federici Vescovini, 133 (with four requirements rather than three).

318

chapter 6

demonstrative science in the strict sense (propter quid) since it does not proceed from the causes: In the third place I say that this science is not so certain as some others, like mathematics and many other natural sciences, because, although some other sciences first demonstrate through the effect, yet in the end they demonstrate through the causes. And such science is certain. This science by contrast investigates the properties through the effects, without determining the causes. And yet it is necessary to determine the causes. And I shall do so.150 In his replies to the opposite argument, i.e., that there can be no sciences of natural inclinations, Brito focuses on two central issues. In the first place, science must be necessary, i.e., must proceed from necessary premises and reach necessary conclusions; this is clear from the Posterior Analytics. Brito’s reply is that this only holds of maximally certain sciences, like mathematics; in some other sciences it is sufficient that the connection between cause and effect is only frequent or for the most part (ut in pluribus). If it is counter-objected that such inclinations are investigated from signs that do not necessitate the animal to have certain inclinations, Brito counter-replies that in fact this happens frequently, especially with those signs that belong to the fundamental parts of the body (like the head, discussed at length by Albert the Great).151 In the second place, to the objection that physiognomics does not demonstrate from the causes and therefore is not a science, Brito replies that only perfect sciences demonstrate from the causes (thus implying that physiognomics is an imperfect science), and that Aristotle speaks of both universal and particular causes. The final section of the quaestio—which is closer to a collection of notes for a possible discussion than to a proper treatment of the subject—Brito offers some alternative replies: Aristotle may have neglected causal demonstrations in this case, because they belong to the mathematician or astrologer; he may 150

151

Radulphus Brito, Quest. lib. De phys., q. 1, 233ra: “Tertio dico quod ista scientia non est ita certa sicut quedam alie scientie, scilicet mathematice et plures alie naturales, quia licet forte quedam scientie primo demonstrent per effectus, tamen ultimate demonstrant per causas. Et talis scientia est certa. Ista autem scientia per effectus passiones investigat, causas non assignando; tamen oportet causas assignare. Et ego faciam.” See infra, Appendix E, §3.3. This is what Peter of Abano does, too, in his Liber compilationis phisionomie. Radulphus Brito, Quest. lib. De phys., q. 1, 233ra (see infra, Appendix E, Ad 1.2). In Albert’s Liber de animalibus several chapters are about the examination of the signs that are in man’s head, including the hair, the eyes, the ears, the jaw, the lips, and the neck (I.2.2–11, ed. Stadler , 48–92).

13th-Century Parisian Commentaries on the logica nova

319

have meant to leave to others the development of the discipline and the discovery of the causes; he may have regarded physiognomics as an imperfect science; finally, the book in which physiognomics is treated as a perfect science has not yet been translated, like many others after all.152 2 The locus a communiter accidentibus and the Fallacy of the Consequent We have dealt with the Latin translations of the logica nova at the beginning of Chapter 4 and with the commentaries on the Posterior Analytics in Chapter 5. As far as the commentaries on the Sophistici Elenchi and the treatises (or sections thereof) devoted to fallacies are concerned, there is a remarkable continuity between the schools of the twelfth century and the faculties of arts of the new universities of the thirteenth century. Following a tradition that dates back to the second half of the twelfth century,153 new introductions to logic are composed in the first half of the thirteenth century: the Tractatus or Summulae logicales of Peter of Spain (ca. 1230), the Introductiones in logicam of William of Sherwood, composed between the 1230s and the 1240s,154 the Summulae dialectices of Roger Bacon, probably composed at Oxford during the 1240s–1250s,155 and the Summa Lamberti of Lambert of Lagny (or Auxerre), composed in the 1250s in Southern France.156 As mentioned, Peter of Spain’s Tractatus are object of teaching and commentary in Southern France in the 1240s; in the 1280s they are taught in Paris, and in the 1290s in Bologna after the Parisian, modistic model, according to which only the first five treatises are commented while the treatises on the theory of suppositio are neglected.157 Commentaries on the treatises on the loci (Tract. V) and fallacies (Tract. VII)

152 153 154 155 156 157

Radulphus Brito, Quest. lib. De phys., q. 1, 233ra (see infra, Appendix E, Ad 1.3). Quaestio 16 is devoted to the Aristotelian example of large extremities as sign of courage (239rb–vb), but without any reference to APr B 27. See de Rijk’s investigations into the Logica modernorum: de Rijk (1962) = LM I; de Rijk (1967) = LM II.1 Cf. Brands and Kann (1995), xv. Cf. de Libera (1986); de Libera (1987). Lambert of Auxerre, Logica (Summa Lamberti), ed. Alessio. Cf. Alessio (1971); de Libera (1981). In Bologna sometimes the seventh treatise on fallacies is added, and sometimes it is substituted by the so-called Fallaciae Santi Thomae; on the Bologna commentaries, see Maierù (1992).

320

chapter 6

contribute to the debates about signs and semiotic demonstrations together with the works on Boethius’ De differentiis topicis and the Sophistici Elenchi. The commentaries on Boethius’ De differentiis topicis have a much older tradition, one which is older than the eleventh century.158 Unlike Nicholas of Paris’ commentary, the only one composed at the middle of the century,159 the commentaries of the second half of the twelfth century that we have been able to consult seem not to have been influenced by the logica nova.160 GreenPedersen suggested that the decline of the commentaries on the De differentiis topicis coincides with the re-discovery of Aristotle’s Topics and the success of Peter of Spain’s Tractatus; the latter, in particular, contain in the fifth treatise a sort of summary of the second book of Boethius’ Topics and may have substituted it in teaching curricula.161 The last commentary on Boethius’ De differentiis topicis, authored by Radulphus Brito in the form of a question commentary, is from the 1290s and represents a true anomaly.162 Given the connections and the reciprocal influence between the commentaries on Boethius’ Topics and those on Aristotle’s Sophistici Elenchi, we shall follow a (roughly) chronological rather than work-based order of presentation: we first examine the texts composed between the end of the twelfth and the first half of the thirteenth century (§6.2.1) and then those of the second half of the thirteenth century (§6.2.2). 2.1  Logic Textbooks and Commentaries between the End of the Twelfth and the First Half of the Thirteenth Centuries Already in the logic textbooks of the last decades of the twelfth century edited by de Rijk in his monumental Logica Modernorum, the section devoted to dialectic is often occupied by a sketchy exposition of Boethius’ De differentiis topicis. For instance, the Introductiones Parisienses (c. 1170 according to de Rijk163)

158 159

See Green-Pedersen (1984), 123–126. Of the three that remain, this is the only one we have been able to examine; cf. Green-Pedersen (1984), 427–429 (B.18–B.20); the last is Nicholas’, about which more below. 160 We consulted the commentaries on the De differentiis topicis of Boethius contained in the ms. Paris, Bibl. Arsénal 910, 34ra–54vb (B.13) and 58ra–82vb (B.14) (url: https://gallica .bnf.fr/ark:/12148/btv1b52513289s?rk=42918;4; last access: November 11, 2020): the only example that is discussed is the one proposed by Boethius (cf. 51rb and 78vb), while, as we shall see, in Nicholas of Paris’ commentary further examples are introduced which are connected to the text of the logica nova. For a list of these commentaries see Green-­ Pedersen (1984), 425–427 (B.13–B.17). 161 Green-Pedersen (1984), 125. 162 Questions edited in Green-Pedersen (1978). 163 LM II.1, 447.

13th-Century Parisian Commentaries on the logica nova

321

illustrate the fundamental concepts of the discipline in the section devoted to the loci: A Topic, as Themistius says, is the foundation of an argumentation, that is its solidity, in so far as it gives strength to the argumentation. Just like when we seek something we resort to the Topic where we think it can be found, so when we want to argue we resort to the maxim or to the difference of the maxim, so as to find argumentations in abudance. A maxim is a general rule, like this: “Of whatever the species so is the genus.” The difference of the maxim is the relation that subsists between the genus and the species or the other way around, or between a simple principle and another simple principle. Simple principles are the things signified by these terms: genus, species, difference, property, accident.164 This follows Boethius quite closely as well as the classification of the loci into intrinsic, extrinsic, and intermediate. The locus a communiter accidentibus falls in the first class. The loci intrinseci are in turn divided in two groups: those deriving from substance (a substantia) and those deriving from what is concomitant to substance (a concomitantibus substantiam).165 The former are 164

165

LM II.2, 365: “Locus, ut dicit Tymisteus, est sedes argumenti, idest firmitudo, eo quod ministrat vires argumento. Et dicitur locus a quadam similitudine. Sicut enim nos querentes aliquid recurrimus ad locum ubi credimus illud invenire, ita si velimus argumentari, recurrimus ad maximam sive ad differentiam maxime ut inde habundanter argumentemus. Maxima vero est regula communis, ut hec: ‘de quocumque species, et genus.’ Differentia maxime est habitudo generis ad speciem vel econverso, sive alterius simplicis principii ad simplex principium. Simplicia principia sunt significata horum terminorum: genus, species, differentia, proprium, accidens.” We translate argumentum as “argumentation,” even though Boethius distinguishes between argumentatio as the linguistic expression of an argument and argumentum as its conceptual content; cf. De diff. top. I, PL 64, col. 1174C: “Argumentum est ratio rei dubiae faciens fidem. Non uero idem est argumentum et argumentatio: nam uis sententiae ratioque ea quae clauditur oratione cum aliquid probatur ambiguum, argumentum uocatur; ipsa uero argumenti elocutio argumentatio dicitur.” Transl. Stump: “An argument is a reason (ratio) producing belief regarding a matter in doubt. Argument and argumentation are not the same, however; for the sense (vis sententiae) and the reason enclosed in discourse (oratio) when something uncertain is demonstrated is called the argument; but the expression (elocutio) of the argument is called the argumentation.” There is here a slight divergence from Boethius, who describes the distinction as follows: “Eorum uero locorum qui ab his ducuntur terminis de quibus in quaestione dubitatur (i.e. loci intrinseci), duplex est modus: unus quidem ab eorum substantia, alter uero ab his quae substantiam eorum consequuntur” (De diff. top. II, PL 64, col. 1186D). The verb consequi is substituted by the verb concomitari, which may obscure the consequentiality between substance and the property from which inferences are drawn. Yet the verb

322

chapter 6

themselves sub-divided in three sub-types: from the definition (or from what is defined), from the description (or from what is described), and from the interpretation of the name (or from what is interpreted).166 Those deriving from what is concomitant to substance are sub-divided in seven sub-types: from the whole, from the part, from the cause, from generation, from corruption, from uses, and from associated accidents (literally: from what inheres commonly).167 The example of locus a communiter accidentibus made by Boethius is the wise who never repents for what he did, since repentance is always accompanied by bad deed: since bad deed does not belong to the wise, neither does repentance.168 By contrast, the example used by the author of the Introductiones Parisienses derives from Soph El 5, 167b6–9, where it illustrates the fallacy of the consequent.169 Here Boethius’ Topics, a classic of the logica vetus, is thus brought into connection with one of the works of the logica nova. The Topic from associated accidents, like: “It has rained on the ground, therefore it is wet.” The rule is: to that to which belongs one of the common accidents, to it the other belongs as well.170 Unlike in Soph El 5, 167b6–8, where the antecedent is invalidly inferred from the consequent, here the argument is not fallacious, as the consequent (est madida) is validly inferred from the antecedent (est compluta). The formulation of the rule is positive, while in Boethius it was negative.171

comitari is used by Boethius himself in his explanation of the example of locus a communiter accidentibus (De diff. top. II, PL 64, col. 1190B; see infra, footnote 168). 166 Introd. Paris., LM II.2, 365. 167 Introd. Paris., LM II.2, 367. 168 Boethius, De diff. top., II, PL 64, 1190B: “A communiter accidentibus argumenta fiunt quoties ea sumuntur accidentia, quae relinquere subiectum uel non possunt uel non solent, ut si quis hoc modo dicat: Sapientem non poenitebit, poenitentia enim malum factum comitatur. Quod quia in sapiente non conuenit, ne poenitentia quidem.” Transl. Stump: “Arguments arise from associated accidents when we consider accidents which cannot or generally do not leave their subject. For example, if someone speaks in this way: a wise man will not repent, for repentance follows on a bad deed; but since [doing] a bad deed does not belong to a wise man, neither does repentance.” 169 Cf. supra, §1.7. 170 Introd. Paris., LM II.2, 369: “Locus a communiter accidentibus ut: ‘terra est compluta; ergo est madida.’ Regula: cui adest unum communiter accidentium, eidem convenit reliquum.” 171 Boethius, De diff. top. II, PL 64, 1190B: “Maxima propositio: Cui non inest aliquid, ei nec illud quod eius est consequens inesse potest.” Transl. Stump: “The maximal proposition: what follows from something which does not inhere in a thing cannot inhere in that thing either.”

13th-Century Parisian Commentaries on the logica nova

323

According to de Rijk, the Introductiones Parisienses belong to the same milieu as two other, slightly later Oxonian treatises which constitute the basis for the future development of the so-called “contextual approach” typical of the English (Oxford) theory of suppositio, as opposed to the continental (Paris) theory:172 the Logica “Ut dicit” and the Logica “Cum sit nostra.” In both these works, the example of locus a communiter accidentibus is the adulterer of Soph El 5, 167b9–12. Here is the relevant passage from the Logica “Cum sit nostra”: The Topic from associated accidents, like this: “He is dressed up, therefore he is an adulterer.” Whence Topic from associated accidents. Maxima: to what inheres some accident, inheres another accident that properly follows it.173 Unlike the example of the terra madida in the Introductiones Parisienses, which qualifies as the valid inference of the consequent from the antecedent, here, as in Soph El 5, the inference is fallacious, for it invalidly infers the antecedent from the consequent. Yet it is not presented as a fallacy. The two accidents (being dressed up and being an adulterer) are regarded as following one another properly (proprie consequitur). Which one properly follows which is not clearly stated, but if the rule has to be applied to the example, it is the antecedent (adulter) that properly follows the consequent (comptus), which given the truth of the conditional can only mean that the antecedent is inferred (though invalidly) from the consequent. As we saw and as will become clear in what follows, in the commentaries on the Sophistici Elenchi and in the treatises on fallacies, this inference is regarded as a fallacy and indeed precisely as the fallacy of inferring the antecedent from the consequent of a true conditional. For the moment, however, the link between the locus and the fallacy remains implicit, based as it is only on the example.

172 173

LM II.1, 416–447., On the Paris/Oxford split see, besides the classical de Rijk (1972) and de Libera (1982), also Rosier-Catach and de Libera (forthcoming). Logica “Cum sit nostra,” LM II.2, 440: “Locus a communiter accidentibus, ut hic: ‘iste est comptus; ergo est adulter.’ Unde locus a communiter accidentibus. Maxima: cuicumque inest aliquod accidens, et ei inerit aliquod aliud quod proprie consequitur.” Cf. Logica “Ut dicit,” LM II.2, 405, where the formulation of the rule should cover (problematically) both the constructive and the descructive use of the maxim: “A communiter a­ ccidentibus constructivus, ut ‘iste est comptus; ergo est adulter.’ Econverso destructivus. Maxime utriusque: cui inest aliquod accidens proprium, et illud inerit cuius est accidens.” On the same lines William of Sherwood, Introductiones in logicam, ed. Brands and Kann (1995), 112.

324

chapter 6

Some further developments of the doctrine of the locus a communiter accidentibus are in the Dialectica Monacensis, whose original should date back to the last decades of the twelfth century:174 We proceed with the Topic from associated accidents, or from associated things, of which we have finally to treat. Associated accidents are said those that neither are usually separated nor can be separated from the same subject. Those that are not usually separated, like being a mother and loving ; those that cannot be separated, like giving birth and having had an intercourse with a man. Moreover, associated accidents are threefold, according to Cicero. For sometimes obtain at the same time, sometimes at different times. At the same time, like being a mother and loving . At different times, in two ways according as what is associated or associated accident is with respect to the past or the future. With respect to the past, as in “If she has given birth, she has had intercourse with a man.” With respect to the future, as in “She has conceived, therefore she will give birth.”175 Unlike the Oxonian textbooks just considered, in which the examples refer to the tradition of the Sophistici Elenchi, here the examples refer to the tradition of Boethius’s Topics.176 The example of the sexual intercourse, in particular, has a long history, which we have told in previous Chapters: it originates in the Greek commentators and was used by Boethius in his De hypotheticis syllogismis, by twelfth-century commentators of Cicero’s De inventione, and by

174 Cf. LM II.1, 414. Ebbesen and Iwakuma (1993), 9, are favourable to a later dating, but not later than 1225. 175 Dialectica Monacensis, LM II.2, 545: “Sequitur de loco a communiter accidentibus, sive ab adiunctis. De quo ultimo dicendum est. Dicuntur autem communiter accidentia que nec solent nec possunt relinquere se circa idem subiectum; non solent, ut esse matrem et diligere; non possunt, ut parere et cum viro concubuisse. Attenduntur autem communiter accidentia tripliciter, ut dicit Cicero. Quandoque enim in eodem tempore, quandoque in diversis. In eodem ut esse matrem et diligere. In diversis autem dupliciter [Uno modo] secundum quod unum adiunctum sive communiter accidens respectu preteriti vel futuri. Respectu preteriti, ut ‘si parit, cum viro concubuit.’ Respectu futuri, ut ‘hec concipit, ergo pariet.’” The expression “uno modo” is probably to be deleted, as it is not paired by a “secundo/alio modo.” 176 See supra, footnote 160. The rules (maximae) on which the inferences are based are both affirmative (constructive), and negative (destructive); cf. Dial. Mon., LM II.1, 545–546. Cf. also supra, §4.2.

13th-Century Parisian Commentaries on the logica nova

325

Simon of Tournai in his Institutiones in sacram paginam.177 In the Dialectica Monacensis this example is formulated as a conditional proposition (si parit, cum viro concubuit), while the second example has the form of an inference (hec concipit, ergo pariet).178 The second example is of course no conversion of the first, as this would produce a false conditional (si cum viro concubuit, pariet). Unlike the first, the second example involves two convertible propositions (parit, concipit) and thus allows convertibility between antecedent and consequent (hec parit, ergo concipit). A further difference between the Dialectica Monacensis and the Oxonian textbooks with regard to the account of the locus is that unlike the Oxonian textbooks the Dialectica accepts that some of these inferences are founded on probable premises or premises that occur for the most part (nec solent relinquere) (much like in Aristotle’s εἰκός-enthymeme), while others are necessary (nec possunt relinquere), according to a distinction that is solidly present in both the rhetorical and dialectical tradition. None of the texts so far examined, however, make any mention of “signs” in connection with the locus a communiter accidentibus. There is an additional difference between the Dialectica Monacensis and the Oxonian textbooks. The Dialectica has a section on the fallacies, and so constitutes a complete introduction to logic, both vetus and nova. The account of fallacies in the Dialectica is characterized by the distinction between causa apparentiae and causa falsitatis (which will become causa non existentiae or defectus) of the fallacy itself.179 Yet, in the discussion of the fallacia secundum consequens the author makes no reference to the doctrine of the loci. Such reference is made, by contrast, in the Fallaciae Londinenses and in the Fallaciae 177 Cf. supra, §§2.2, 2.3, 3.4, 4.3. 178 Pinborg (1972, 75) noticed that twelfth-century formulations of the syllogism accept both the conditional form (“If P1 and P2, then C”) and the inferential or argumentative form (“P1, P2; ergo C”). The difference is not without importance, however, because “conditionals make statements whereas inferences do things with statements” (King 2001, 118). Conditionals are true or false, inferences are valid or invalid. However, their equivalence is granted by the principle of conditionalization, explicitly formulated already in the Ars Emmerana: “A qualibet enim argumentatione transformari potest conditionalis propositio, sicut a qualibet conditionali sumi potest argumentatio. Verbi gratia: ‘celum est rotundum // ergo celum est volubile’; ab hac argumentatione transformari potest conditionalis hec: ‘si celum est rotundum, celum est volubile’; et huius conditionalis dictum est: ‘si celum est rotundum, celum esse volubile’” (LM II.2, 164). Some such principle of conditionalization or “medieval deduction theorem” is operative in fourteenth-century theories of consequentiae; cf. King (2001); for an overview on consequences, see Moody (1953); Boh (1982). 179 Cf. Ebbesen and Iwakuma (1993), 6.

326

chapter 6

Lemovicenses.180 The author of the Dialectica introduces a twofold division of the fallacy of the consequent. After this it is necessary to know that there are two general modes of the fallacy of the consequent. For there are two modes of inferring with necessity in a conditional proposition, that is from the affirmation of the antecedent to the affirmation of the consequent, and from the negation of the consequent to the negation of the antecedent. According to this there are two non-necessary modes, of which one is from the negation of the antecedent to the negation of the consequent, and the other from the affirmation of the consequent to the affirmation of the antecedent.181 The two fallacies (affirming the consequent AC, denying the antecedent DA) are simply inversions of the two valid inference schemes modus ponens (affirming the antecedent) and modus tollens (denying the consequent).182 The anonymous author of a Tractatus de fallaciis preserved in a Munich manuscript (clm 14763)183 follows the Dialectica quite closely. It not only refers to the two causes of the fallacy (apparentiae and falsitatis),184 but also offers examples of the twofold typology: 180 Cf. Fallacie Londinenses, LM II.2, 676, where common accidents are mentioned with regard to the example of the adulterer, and the loci a simili and a proportione are referred to with regard to the two other species of the fallacy of the consequent; cf. also Anonymus, Fallaciae Lemovicenses, in Ebbesen and Iwakuma (1993), 39: “Possunt enim illa in diversis locis esse divisim.” 181 Dial. Monac., LM II.2, 589: “Post hec sciendum quod duo modi generales sunt paralogismorum secundum consequens. Sunt enim duo modi arguendi necessarii in conditionali, scilicet a positione antecedentis ad positionem consequentis vel a destructione consequentis ad destructionem antecedentis. Iuxta quos sumuntur duo non-necessarii, quorum unus a destructione antecedentis ad destructionem consequentis, reliquus a positione consequentis ad positionem antecedentis.” 182 Cf. supra, §3.4. 183 It corresponds to SE28 contained in the ms. München, Bayerische Staatsbibliothek, clm 14763, 123vb–125ra (Ebbesen 1993, 156): it is the third part of a series of introductions to logic (121rb–129vb) whose structure does not match Peter of Spain’s Tractatus (I. De enunciatione et eius partibus, 121rb; II. De locis, 122ra; III. De fallaciis, 123vb; IV. De ­equipollentiis, 125ra; V. De universalibus, 125rb; VI. Sincategoremata, 126ra; VII. De predicamentis, 126vb; VIII. De oppositis, 128rb; Notanda, 129va–b—perhaps this latter is not part of the work). 184 Tract. de fallaciis, ms. München, BSB, clm 14763, 124va: “Sequitur de fallacia consequentis. Consequens est quod aliquis aliud arguit consequentiam convertendo, cum conversionem habere non potest, ut ‘si est aurum, est rubeum’ ergo ‘si est rubeum, est aurum.’ Causa apparentie istius fallacie est idemptitas primi in secundo, diversitas vero eorumdem

13th-Century Parisian Commentaries on the logica nova

327

There are two species of this fallacy: the first derives from the fact that one argues from the affirmation of the consequent, as in “If is gold, then it is yellow; but it is yellow, therefore, it is gold,” and is realized against this rule: once the consequent is destroyed, the antecedent is also destroyed, but not the other way around. The second species derives from the fact that one argues from the destruction of the antecedent, as in “If is a human being, it is an animal; but it is not a human being; therefore, it is not an animal,” and is realized against this rule: once the antecedent is affirmed, the consequent is also affirmed, but not the other way around.185 Given a true conditional, it is possible to infer validly the consequent from the antecedent (modus ponens) or the negation of the antecedent from the negation of the consequent (modus tollens). The two species of fallacies are invalid inversions of these rules (AC and DA). Other treatises move from the formulation of the rules and raise doubts as to the denomination of the fallacy or the validity of the bipartition. For example, the author of the Fallaciae ad modum Oxoniae, a treatise which was with all probability a part of the Logica “Cum sit nostra” and also somehow connected to the Dialectica Monacensis,186 asks why the fallacy is called “of the consequent” rather than “of the antecedent,” since according to its standard bipartition one species of it is from the affirmation of the consequent and the other from the negation of the antecedent.187 The answer is quite complex and considers several examples. The basic idea is that the species from the negation of the antecedent (DA) falls under the species from the affirmation of the consequent (AC), and this justifies the choice of the name. Later commentators

185

186 187

causa falsitatis, ut patet in auro et rubeo: nam rubeum idem est cum auro, sed aurum non est idem cum rubeo.” Tract. de fallaciis, ms. München, BSB, clm 14763, 124va: “Due sunt species istius fallacie: prima provenit ex eo quod argumentatur a positione consequentis, ut ‘si est aurum, est rubeum; sed est rubeum, ergo est aurum,’ et fit contra hanc regulam: destructo consequente, destruitur antecedens; sed non convertitur. Secunda species provenit ex eo quod arguitur a destructione antecedentis, ut ‘si est homo, est animal; sed non est homo; ergo non est animal,’ et fit contra hanc regulam: posito antecedente ponitur consequens; sed non econverso.” Cf. Kopp (1985), xv–xxi. Fallaciae ad modum Oxoniae, ed. Kopp, 138: “Sed quaero, quare ista fallacia dicitur fallacia consequentis et non fallacia antecedentis, cum fit a destructione antecedentis ita bene sicut a positione consequentis.” (ms. N) (SE33 in Ebbesen 1993, 158).

328

chapter 6

will make a similar appeal to this sort of justification.188 In the Fallaciae ad modum Oxoniae the argument seems to be the following: the fallacy from the negation of the antecedent non homo est, ergo non animal est is modelled after the valid inference non animal est, ergo non homo est, which is a sound instance of the locus a genere (and given the true conditional si est homo, est animal, it is also an instance of modus tollens). Now, in the valid inference non animal est, ergo non homo est, non animal est is the antecedent and non homo est is the consequent. Therefore, when in the fallacy non homo est, ergo non animal est, one says non homo est one is actually affirming the consequent of the corresponding converse inference. So when one negates the antecedent one actually affirms the consequent (of the converse valid inference).189 The author seems not to perceive that, mutatis mutandis, the same is true of the other species of this fallacy, the one from the affirmation of the consequent. Of this species, too, we might say that when one affirms the consequent one actually affirms the antecedent (of the converse inference in modus ponens). Moreover, if one accepts the explanation in these terms, we are also forced to dismiss the bipartition itself; the author of the Fallaciae does not appreciate the taxonomic import of this move. William of Sherwood’s Introductiones in logicam offers a different typology of this fallacy. On the one hand, there are the fallacious inferences of a superior term from an inferior by means of negation (“It is not a human being; therefore, it is not an animal”) and of an inferior term from a superior by means of affirmation (“It is an animal; therefore, it is a human being”); on the other hand, there is the fallacy of inferring from affirmative premises in the second figure.190 A discussion about the name of the fallacy, similar to that of the Fallaciae ad modum Oxoniae, is offered by the anonymous author of a commentary on the Sophistici Elenchi, composed between the 1220s and the middle of the century 188 An echo of this justification is in one of the objections in Brito’s commentary on the Sophistici Elenchi, as we shall see; cf. infra, §6.2.2. 189 Fallaciae ad modum Oxoniae, ed. Kopp, 138–139: “Dicendum quod ubi est fallacia consequentis, semper a positione consequenti, verbi gratia hic est fallacia a destructione antecedentis: ‘non homo est, ergo non animal est’, quia sequitur econverso ‘non animal est, ergo non homo est’ per locum a genere, et non sic; ergo quod ‘non animal ’ antecedens est, ‘non homo ’ consequens, quia cum dicit ‘non homo ’ ponit consequens, ‘non animal ’ concludit antecedens, et sic est fallacia consequentis a positione consequentis.” 190 Cf. William of Sherwood, Introd. in log., ed. Brands and Kann, 212. This reference could be to second-figure invalid sign-arguments as presented in APr B 27, but there are no indications of this.

13th-Century Parisian Commentaries on the logica nova

329

and preserved in another Munich manuscript.191 It is a literal commentary followed by short questions for each section of the text. The first quaestio on the fallacy of the consequent is about the name (de eius nominatione). There are no pro and con arguments, like in the standard questions of the second half of the century; once the problem and the reason why it emerges are posed (in the form of an objection), the author goes directly to the solution: according to a general rule, the name is always given from what is superior in dignity, and since the consequent is superior to the antecedent, this is the reason why the fallacy is said to be “of the consequent” and not “of the antecedent.” An alternative solution is that the fallacy is so named after its motivation (principium motivum): we are deceived because the inference or the conditional is modelled after a valid inference rule.192 As it is repeatedly declared in many other treatises, “the fallacy of the consequent is a deception that depends on us, because we think that an inference converts but it does not.”193 Another quaestio is devoted to a discussion of Aristotle’s examples in Soph El 5. According to the Anonymus Monacensis, the inference “He wanders about at night, therefore he is an adulterer or a thief” is no fallacy of the consequent, and neither does Aristotle think that it is. As stated, the inference is to a disjunctive antecedent (adulterer or thief) from a single consequent (wandering about at night). By contrast, Aristotle’s example has a disjunctive consequent: Volentes enim ostendere quoniam adulter, quod adiunctum est, accipiunt quoniam compositus aut quoniam in nocte videtur errabundus. (Soph El 5, 167b9–11, AL VI.1, 13.11) The Anonymous seems to argue that Aristotle means that the fallacy of the consequent only occurs if the properties that “follow” (secuntur) the thief or the adulterer are taken in disjunctive form, i.e., if the consequent is disjunctive. Consider the following true conditional: “If a man is a thief, then he either wanders about at night, or lives on robbery, or is often together with evil persons, or has no income, or etc.” Given this conditional, the inference of the 191 192 193

Anonymus Monacensis, Comm. sup. Soph El, ms. München, BSB, clm 14246, 1ra–16r; 20ra–48rb (SE34 in Ebbesen 1993, 158; see infra, Appendix F for a transcription of q. 1); 16r–19va contain a prologue to Averroes’ De substantia orbis. Anonymus Monacensis, Comm. Soph El, q. 1, ms. München, BSB, clm 14246, 13ra (see infra, Appendix F). Peter of Spain, Tractatus VII.156, ed. de Rijk, 170, uses the same terminology. Dial. Monac., LM II.2, 589: “Fallacia consequentis est deceptio proveniens ex parte nostri ex hoc quod nos putamus consequentiam converti que non convertitur.” Cf. Fallaciae ad modum Oxoniae, ed. Kopp, 135–136; and so on.

330

chapter 6

disjunctive consequent from the single antecedent (“This man is a thief, therefore he either wanders about at night, or lives on robbery, or is often together with evil persons, or has no income, or etc.”) is a valid inference. The converse inference of the single antecedent from the disjunctive consequent (“He either wanders about at night, or lives on robbery, or is often together with evil persons, or has no income but expends too much, or etc., therefore he is a thief”) is a true fallacy of the consequent.194 Or perhaps there is a probabilistic reasoning behind his argument. Since an inference is invalid or is a fallacy (and its corresponding conditional is false) when the premise is true and the conclusion false, and since a conjunctive proposition has more probability to be true than an atomic proposition, then an inference with a disjunctive premise and an atomic conclusion (like “He either wanders about at night, or lives on robbery, or is often together with evil persons, or has no income, or etc., therefore he is a thief”) has more probability to be a fallacy than an inference with an atomic premise and a disjunctive conclusion (like “This man is a thief, therefore he either wanders about at night, or lives on robbery, or is often together with evil persons, or has no income, or etc.”). Here the probability of the premises and the conclusion of each inference is considered independently of the truth of the conditional that serves as the major premise of the argument in each case. Given the truth of that conditional, the former inference is a fallacy and the latter a valid argument independently of the probability of its premises and conclusion. The example of the thief was introduced by Philoponus, who split Aristotle’s single example at Soph El 5, 167b9–12 (both fancy dressing and wandering about at night as signs of being an adulterer) into two: fancy dressing is a sign of being an adulterer, wandering about at night the sign of being a thief. In the same split form it was used by Michael of Ephesus’ commentary on the

194

Anonymus Monacensis, Comm. Soph El, q. 1, ms. München, BSB, clm 14246, 13ra–b: “ibi non est // fallacia consequentis ‘iste est errabundus de nocte, ergo est adulter vel latro,’ sicut obiectum fuit, nec in alio exemplo, nec auctor hoc vult, scilicet, quod +hoc uiteret(?)+ sit ibi fallacia con. Sed auctor innuit quod adiuncta que secuntur latronem sive adulterum sumuntur sub disiunctione—et non quodlibet per se divisim—et ex illis sic sumptis inferatur illud cui adiungitur et tunc est fallacia consequentis. Verbi gratia ‘iste est errabundus de nocte vel vivit ex rapto vel consequitur pravam societatem vel nichil lucratur et satis expendit, ergo est latro’, hic est fallacia consequentis: sequitur enim econverso, quia si est latro, habet aliquam istarum proprietatum. Et sic debet intelligi illud quod dicit auctor et non eo modo quo obiectum fuit.” (The first part of the text is different in the other witness, ms. Admont, Bibliothek des Benediktinerstifts, 241, 32ra; furthermore the text has several problems and requires emendation; see infra, Appendix F).

13th-Century Parisian Commentaries on the logica nova

331

Sophistici Elenchi.195 In the Anonymus Monacensis it probably occurs for the first time in a Latin work, while it is absent in Boethius. A commentary on the Sophistici Elenchi attributed to Robert Kilwardby196 offers a different interpretation of the passage and makes use of the example of the thief in the Philoponean split form. According to Kilwardby(?), Aristotle first presents the fallacies deriving from the affirmation of the consequent and then those deriving from the negation of the antecedent. The first species197 is itself of two sub-species: those fallacies whose converse inference (consequentia) is necessary and those whose converse inference is probable.198 Examples of the former sub-species are the inference that bile is honey because it is yellow199 and that it has rained because the earth is drenched.200 As we saw, these are cases in which sense perception influences opinion.201 The converse inferences—which Kilwardby(?) actually expresses as conditional propositions— are valid, i.e., the corresponding conditional propositions are necessarily true: si est mel, est rubeum; si terra est depluta, ergo est madida. The inference of the antecedent (mel, depluta) from the consequent (rubeum, madida) is a fallacy deriving from the affirmation of the consequent. The other sub-species is when the converse inference is probable. According to Kilwardby(?), these are the demonstrationes secundum signa that are used in rhetoric.202 The examples are the following: Then he provides the matter of the two fallacies by saying that when they want to show that someone is an adulterer, they assume that which is added to being an adulterer, i.e., that he is dressed up, and from that they infer that he is an adulterer. Or in order to show that someone is a thief,

195 Cf. supra, §§2.4, 2.7. The thief appears also in Peter of Spain, Tractatus VII.158, ed. de Rijk, 171, but not in connection with nightly activities. 196 Cf. Lewry (1982), 43–46. Ebbesen (1993), 158 (on SE35), and Brumberg-Chaumont (2016), 109–113, have some doubts on this attribution. 197 We shall see that Kilwardby(?), like some previous commentators, considers the distinction to be groundless. 198 See the text from two mss. in Appendix G, div. textus. Two other witnesses have extracts only; cf. Ebbesen (1993), 158. 199 Soph El 5, 167b5–6. 200 Soph El 5, 167b6–8. 201 Cf. supra, §4.2. 202 This second sub-species is differentiated from the first by Aristotle’s introduction at Soph El 5, 167b8–9 of rhetorical demonstrations from signs: “Et in rethoricis quae secundum signum sunt demonstrationes ex adiunctis sunt.” (AL VI.1, 13.9).

332

chapter 6

they assume what is added to being a thief, i.e., that he wanders about at night, and from that they infer that he is a thief.203 The author then presents the two examples in the form of deductively invalid second-figure syllogisms with the conditional as major premise: (i) si aliquis est adulter, ipse est comptus; sed iste est comptus; ergo iste est adulter; (ii) si aliquis est fur, est errabundus de nocte; sed iste est errabundus de nocte; ergo iste est fur.204 Like in Kilwardby’s authentic commentaries the explanation of the littera is followed by dubitationes. They are six in total and concern questions that are quite standard in this tradition. Here we consider only those that are relevant to our topic. The first is about the denomination of the fallacy.205 The author’s solution is different from those we have met in previous commentaries: With regard to the first doubt, we have to say that in general the Topic, whether dialectical or sophistical, takes its denomination from the middle term. This is evident in dialectical Topics: when the middle term of inference is the definition, then we have the “Topic from the definition”; when it is the definitum, we have the “Topic from the definitum,” and so on. The same applies to sophistical Topics: when the middle term is equivocal, then we have the “Topic from equivocity”; when the middle term is accidental with respect to the extremes, we have the “Topic from the accident,” and so on. Therefore, in general every Topic takes its denomination from the middle term: but in this Topic the middle term is always consequent with respect to the other extreme, and thus this Topic takes its name from the consequent and not from the antecedent.206 203 Robert Kilwardby(?), Comm. in Soph El, ad Soph El 5, 167b10ff: “Postea dat materiam duorum paralogismorum dicens quod volentes ostendere quod aliquis sit adulter, accipiunt quod adiunctum est adultero, scilicet quod sit comptus, et ex hoc inferunt ipsum esse adulterum. Aut ad ostendendum quod aliquis sit fur accipiunt quod adiunctum est furi, scilicet quod sit errabundus de nocte, et ex hoc inferunt ipsum esse furem.” See infra, Appendix G, div. textus. 204 The fallacy deriving from the negation of the antecedent, whose example is Melissus’ argument for the infinity of the world (Soph El 5, 167b13–18), is not relevant here. 205 Robert Kilwardby(?), Comm. in Soph El, dub. 1: “quare magis denominatur locus iste a consequente quam ab antecedente?” See infra, Appendix G, Ad 1. 206 Robert Kilwardby(?), Comm. in Soph El, dub. 1, Ad 1: “Ad primum dicendum quod locus universaliter tam dialeticus quam sophisticus recipit suam denominationem a medio. Hoc patet in locis dialeticis: cum enim medium inferens est diffinitio, tunc est locus a diffinitione; cum autem \est/ diffinitum, tunc est locus a diffinito, et ita de aliis. Similiter in locis sophisticis: quando enim medium est equivocum, est locus equivocationis; quando autem medium est accidentale respectu extremorum, tunc est locus accidentis,

13th-Century Parisian Commentaries on the logica nova

333

The middle term of inference (medium inferens) is either coextensive to, and thus convertible with, the extreme that is inferred (illatum), or it is not. If it is, the inference is valid and there is no fallacy of the consequent: of convertible terms, neither can be said to be consequent upon the other. If the middle term is less extended than the illatum, we have again a valid inference (the hyponym implies the hypernym but not vice versa). If the middle term is more extended than the illatum the former can be said to be a consequent of the latter (e.g., wandering about at night is more extended than being a thief and a consequent of it); the inference of an illatum less extended than the middle term is a fallacy which is correctly said to be “from the consequent.”207 The second doubt is about the examples offered in the explanation of the littera: Aristotle seems to suggest that the converse of the fallacy is always necessary and this seems to be patently false, as it is evidenced by the example of the adulterer: the conditional “If he is an adulterer, then he is smartly dressed” is not, on the author’s opinion, necessarily true.208 In point of fact, Aristotle does not suggest that the converse in each example is necessary. Rather, as Boethius argues in his Topics, some inferences are necessary and not probable, some probable and not necessary, some are both necessary and probable, and some neither necessary nor probable: the converse of the fallacy of the consequent may thus be true or probable without being necessary: it may be true that an adulterer is smartly dressed, but is not necessary that he be so.209 et ita de aliis. Ergo generaliter omnis locus recipit suam denominationem a medio termino; sed in hoc loco semper est medius terminus consequens ad alterum extremorum, et ideo denominatur locus iste a consequente, ab antecedente vero minime.” See infra, Appendix G. 207 Robert Kilwardby(?), Comm. in Soph El, dub. 1, Ad 1: “Si inferens et illatum sint in eque, tunc bonum est argumentum et non incidit fallacia consequentis. In convertibilibus enim non cadit consequens. Si inferens sit in minus et illatum in plus, tunc est bonum argumentum ab inferiori ad superius affirmando et non est tunc fallacia consequentis. Si vero medium inferens sit in plus et illatum in minus, tunc est semper fallacia consequentis et est semper medium consequens ad aliquod extremorum. Et ita patet quare magis denominatur iste locus a consequente quam ab antecedente.” See infra, Appendix G. 208 Robert Kilwardby(?), Comm. in Soph El, dub. 2, Ad 2: “Patet ergo quod ipse semper velit conversam consequentiam in paralogismo consequentis esse necessariam. Sed in hoc videtur quod ipse innuat falsum: dicit enim in littera quod hic est fallacia consequentis ‘ille est comptus, ergo est adulter’; nec tamen est consequentia conversa necessaria: non enim est necesse ad hoc ut aliquis sit adulter quod ipse sit comptus.” See infra, Appendix G. 209 Robert Kilwardby(?), Comm. in Soph El, dub. 2, Ad 2. See infra, Appendix G. An alternative solution is to define the locus with regard to the best example of it, i.e., the first species, from the affirmation of the consequent, and is then extended to the other species by way of analogy (ibid.). The same is true for Roger Bacon, Summulae dialectices, 3.3.2.2, §647,

334

chapter 6

The third doubt is about the relationships between sophistical loci on the one hand, and dialectical and rhetorical loci on the other. It is divided into two parts and has two distinct answers. With regard to the opposition between loci sophistici and loci dialectici, the author argues that what is added (adiuncta) can be either proper or common. What is proper follows necessarily that to which it is added and converts with it. An example of this is having milk and giving birth, which of course is the example of irrefutable sign in APr B 27. The author remarks that Aristotle calls such signs prodigia (which as we know is Boethius’ translation of τεκμήριον) or “signs in the first figure,” and that Boethius and Themistius (according to what Boethius says in the De diff. top.) have placed the locus ex adiunctis among dialectical loci.210 What is common is a sign that has a greater extension than that to which it is added, and these are called “signs in the second figure” in APr B 27. The example is the paleness in the woman from which it is inferred that she has given birth: this is a fallacy of the consequent. The author knows and understands APr B 27 quite well: he straightforwardly and correctly associates the deductively invalid second-figure sign-syllogism with the fallacy of the consequent, and the deductively valid first-figure sign-syllogism with the inferences ex adiunctis that Boethius places among dialectical argumentations. These latter are similar to the inferences from the antecedent (like in the example “She has given birth, therefore she had intercourse with a man”) which are necessary inferences.211 The author also makes an observation that should be somehow connected to the Anonymus Monacensis: But this adjunct occurs in two ways in an argumentation, because either one single common adjunct is assumed in order to infer that to which it is added, and in this case there is always fallacy of the consequent, like in “She is pale, therefore she has given birth”; or multiple of those adjuncts are assumed in order to infer that to which they are added, and in this case we have a sound argumentation and there is no fallacy of the consequent.212

ed. de Libera, 263, who grants to the converse of the fallacy some degree of probability, which is enough for the dialectician. 210 Boethius, De diff. top. III, PL 64, col. 1198A–B, 1200B–C. 211 Boethius, De diff. top. III, PL 64, col. 1198B–D and 1200B–C. 212 Robert Kilwardby(?), Comm. in Soph El, dub. 3, Ad 3.1: “Sed adhuc tale adiunctum contingit esse dupliciter in argumento, quia aut accipitur unum solum adiunctum commune ad inferendum illud cuius est adiunctum, et tunc semper fit fallacia consequentis, ut ‘hec est pallida, ergo peperit’; aut accipiuntur plura huiusmodi adiuncta ad inferendum illud

13th-Century Parisian Commentaries on the logica nova

335

We saw above that according to the Anonymus Monacensis, given a true conditional with a disjunctive consequent, the inference of the disjunctive consequent from the single antecedent is a valid inference, while the converse inference of the single antecedent from the disjunctive consequent is a fallacy of the consequent. Here the argument is rather that the inference of a single antecedent from a single consequent is a fallacy, while the inference of a single antecedent from a conjunctive consequent may qualify as a valid argument. Take the conditional “If she has given birth, she is pale.” Here the consequent is more extended than the antecedent, and thus the inference from the consequent to the antecedent is invalid. But now consider a conjunctive consequent, like “she is pale, depressed, has cramps in the uterus, has a pelvic prolapse, etc.” While each of the conjuncts may be singularly more extended than the antecedent, they may be collectively as extended as it (or at least they may approximate its extension). In this case, the inference from the conjunctive consequent to the single antecedent may qualify as a valid inference (or approximately so). With regard to the opposition between loci sophistici and loci rhetorici, the objection is that since Boethius’ locus ex adiunctis (or a communiter accidentibus) belongs to rhetoric and is a sound argumentation, there exists no locus sophisticus (or fallacia) secundum consequens. The reply is that rhetorical argumentation is based on common signs that hold ut frequentius and seeks to induce trust or suspicatio in the audience.213 The idea of a conjunctive adiunctum is here evoked again: if only one sign or adiunctum is taken, the inference is a fallacy of the consequent; if multiple signs or adiuncta are taken, the inference is sound.214

213 214

cuius sunt adiuncta, et tunc est bonum argumentum et non accidit fallacia consequentis.” See infra, Appendix G. As mentioned (supra, §6.1.2), in Aquinas’ and Giles of Rome’s commentaries on the ­Posterior Analytics and the Rhetoric, suspicatio or suspicio is the cognitive effect per antonomasia of rhetorical argumentation. We simplify a bit. Actually, the author argues that when only one sign or adiunctum is taken, it can be taken either cum circumstantiis, which produces a good argument, or sine circumstantiis, which produces the fallacy of the consequent. No example is given of the two cases. Cf. Robert Kilwardby(?), Comm. in Soph El, dub. 3.2, Ad 3.2: “Sed distinguendum est: aut enim sumuntur plura adiuncta ad inferendum illud cuius sunt adiuncta, et tunc est bonum argumentum; aut sumitur tantum unum et hoc contingit dupliciter: aut enim illud adiunctum sumitur cum circumstantiis, et sic est bonum argumentum rethoricum, secundum quod habetur in quarto Topicorum Boetii quod questio rethorica involuta circumstantiis; aut sine circumstantiis, et sic est semper fallacia consequentis.” See infra, Appendix G.

336

chapter 6

One last observation concerns the number of the species of this fallacy. We saw that in the Fallaciae ad modum Oxoniae the fallacy deriving from the negation of the antecedent falls under that deriving from the affirmation of the consequent, but the taxonomic consequences of this move are not appreciated in that context. The author of the commentary attributed to Kilwardby and Roger Bacon in his Summulae dialectices do consider those consequences. The former claims that the two species of this fallacy are substantially identical (sunt idem modus in substantia), since in a valid inference the negation of the antecedent follows from the negation of the consequent, and therefore is “consequent” in this sense.215 Here of course the author conflates the consequent of the conditional proposition in a modus tollens (“B” in “If A, then B”) with the conclusion of it (“not-A”). On similar lines, Bacon argues that there is only one species of fallacy of the consequent, which he identifies with that deriving from the affirmation of the consequent. If given the true conditional “If Socrates is a body, then he is a substance,” we make the inferences “Socrates is not a body, therefore he is not a substance” (DA) and “Socrates is a substance, therefore he is a body” (AC), “we have the same mode , that is from the affirmation of the consequent (AC), because just as substance is consequent of body, so ‘non-body’ is consequent upon ‘non-substance’.”216 The commentary on Boethius’ Topics by Nicholas of Paris (an author coeval with or slightly later than Kilwardby) also goes in the direction of an association between the locus a communiter accidentibus, the fallacia secundum consequens, and the second-figure sign-syllogism of APr B 27. His last question on the loci intrinseci concerns precisely the connection between fallacy of the consequent and associated accidents. The objection here is that in the Sophistici Elenchi Aristotle qualifies the locus a communiter accidentibus as a fallacy of the consequent, thus implying that such locus does not belong to dialectic.217 The reply distinguishes between the inference from a single adiunctum (a communiter accidente) and the inference from the conjunction of multiple adiuncta (a communiter accidentibus). The latter is a dialectical argument and 215

216 217

Robert Kilwardby(?), Comm. in Soph El, dub. 5, Ad 5: “destructio enim antecedentis est consequens ad destructionem consequentis; et ita cum prius ponitur destructio antecedentis et infertur destructio consequentis, prius ponitur consequens et deinde infertur antecedens.” See infra, Appendix G. Roger Bacon, Summ. dial., 3.3.2.2, §645, ed. de Libera, 263. Nicholas of Paris, Not. Top. Boethii, ms. München, BSB, clm 14460, 158vb: “Octavo et ultimo queritur de loco a communiter accidentibus. Dicit enim Aristotiles in libro Elenchorum quod in tali loco est fallacia consequentis, ergo non est locus dyaleticus.” (= B.20; cf. Green-Pedersen 1984, 428–429).

13th-Century Parisian Commentaries on the logica nova

337

not a fallacy of the consequent.218 A single sign or adiunctum yields no suspicio about what it signifies, while multiple signs or adiuncta do yield suspicio: In order for the inference to be valid multiple signs are necessary, as if we said “He is dressed up, wanders about at night, is prodigal and lustful, therefore he is an adulterer,” this is a valid inference. Thus, when Aristotle says that here there is the consequent, he means that we infer from one accident only; when he [i.e., Boethius] says that it is a dialectical Topic, he means from multiple And so one does not contradict the other.219 The point made is the same as in the author of the commentary on the Sophistici Elenchi attributed to Kilwardby: the inference from a conjunctive consequent to a single antecedent is a valid inference (and is correctly dealt with in dialectic), while the inference from a single consequent to a single antecedent is invalid and is rather a fallacy (and is correctly dealt with in the Sophistici Elenchi).220 218

Nicholas of Paris, Not. Top. Boethii, ms. München, BSB, clm 14460, 158vb: “Ad hoc dicendum quod sicut vult Aristotiles in libro Elenchorum, volens probare quod est adulter ostendit per illud quod est adiunctum, et non (ideo, cod.) dicit quod fiunt per adiuncta; ideo quia quando fit per adiuncta (-um, cod.), tunc est ille locus dyaleticus qui dicitur a communiter accidentibus et non a communiter accidente. Unde dico quod, cum dicitur ‘est comptus, ergo est adulter’ est fallacia consequentis, quia non est ibi locus dyaleticus a communiter accidentibus, sed a communiter accidente, qui non valet. Et hoc est quia unum signum non dat suspicionem de suo subiecto, sed plura signa.” In those years (1247–1250), Roger Bacon mentions the examples of the mother loving her children (from Boethius) and the examples of the adulterer and the thief (from the Sophistici Elenchi) with regard to the locus a communiter accidentibus; cf. Summ. dial., 3.2.2, §320, ed. de Libera, 229. Likwise does Lambert of Lagny (or Auxerre), who distinguishes between common accidents that are sometimes concomitant and sometimes not, like being dressed up (the text has corruptus, certainly to be emended to comptus) and being an adulterer, and common accidents that follow one another temporally, like repent (penitere), which must follow some evil action (deliquisse); cf. Summa Lamberti, ed. Alessio, 132–133. 219 Nicholas of Paris, Not. Top. Boethii, ms. München, BSB, clm 14460, 158vb: “Unde ad hoc quod sequatur oportet apponere plura signa, ut si dicatur ‘iste est comptus, iste est errabundus de nocte et est prodigus et est luxuriosus, ergo est adulter,’ tunc bene potest sequi. Unde cum Aristotiles dicit quod ibi est consequens, intelligit cum infertur ab uno accidente; cum vero iste dicit quod est locus dyaleticus, intelligit a pluribus. Et sic unus non contradicit alterum.” 220 The Summe Metenses, attributed to Nicholas of Paris and composed between 1240 and 1260 (SE42; cf. Ebbesen 1993, 160), while commenting on the Boethian traditional examples of the locus a communiter accidentibus (mater est, ergo diligit filium, and peperit, ergo cum viro concubuit) mentions some remarkable exceptions: “Medea que licet mater,

338

chapter 6

One last remark which closes the circle. An annotation in the lower margin of the Munich manuscript that contains Nicholas’ commentary, as a gloss on what Nicholas says about the locus a communiter accidentibus, recalls the distinction of APr B 27 between the sign in the first-figure (signum prodigium) and that in the second figure (signum non prodigium); the former is exemplified by the classical “She has milk, therefore she has given birth”; the latter by the equally classical “She is pale, therefore she has given birth”; this latter is qualified as a fallacy of the consequent.221 2.2  Logic Textbooks and Commentaries from the Second Half of the Thirteenth Century In his discussion of the locus a communiter accidentibus Peter of Spain had explained that there are two species of associated accidents: those that frequently or occasionally go together, like comptus and adulter, and those that always and invariably go together, like penitere and deliquisse.222 The first species is illustrated through the example of the Sophistici Elenchi (like in the Logica “Ut dicit” and the Logica “Cum sit nostra”), while the second through the example of Boethius’ De differentiis topicis. With regard to the fallacy of the consequent, Peter had pointed out that the “principle of motivation” (principium motivum) of the fallacy is the similarity between the valid inference and its converse, and that its “principle of defect” (principium defectus) is the falsity of the converse inference.223 The species of this fallacy are three according to Peter: from the affirmation of the consequent (AC, a positione consequentis), like in “If it rains, the earth is drenched; the earth is drenched; therefore, it has rained”;224 from the circumstances that are connected with some kind of persons, like in “If he is an adulterer, then he is fancily dressed or wanders about tamen non dilexit, sed filios morti tradidit; similiter de beata Virgine que virum non cognovit, Christum tamen peperit.” (ms. Paris, Bibl. Nat. de France, Lat. 11412, 30vb). Medea is also mentioned by Giles of Rome, Exp. sup. Rhet. I, lectio 15, 25vb. 221 Nicholas of Paris, Not. Top. Boethii, ms. München, BSB, clm 14460, 158vb, mg. inf.: “Duplex est signum, scilicet signum prodigium et signum non prodigium; sed nunc(?) signum quod est prodigium bene infert(?) suum subiectum, unde sequitur ‘si habet lac, ergo peperit’; signum vero(?) non prodigium suum subiectum non infert, unde non sequitur ‘est pallida, ergo peperit,’ et est fallacia consequentis(?) […]” (The last line is almost entirely deleted and perhaps only readable with a Wood’s lamp). 222 Peter of Spain, Tract. V.26, ed. de Rijk, 70; the rules are in affirmative form (communiter accidentium si posterius inest, et primum) and in negative form (si communiter accidentium primum non inest, neque posterius); cf. Tract. V.26, ed. de Rijk, 70–71. 223 Peter of Spain, Tract. VII.156, ed. de Rijk, 170. 224 Peter of Spain, Tract. VII.157, ed. de Rijk, 170–171. Robert Kilwardby(?), Comm. in Soph El, div. textus, has the same formulation of the example. Cf. infra, Appendix G.

13th-Century Parisian Commentaries on the logica nova

339

at night; he is fancily dressed or wanders about at night; therefore, he is an adulterer”;225 from the negation of the antecedent, like in “If it is done, it has a principle; it is not done; therefore, it has not a principle.”226 Among the earliest commentaries on Peter of Spain’s Tractatus there are three which are attributed to a not-better-specified “Robertus Anglicus.” As shown by Sten Ebbesen and Irène Rosier-Catach, he is not to be identified with Kilwardby, nor is he an Englishman.227 They probably date to the 1250s and 1260s (for they are influenced by debates following the commentary on the Sophistici Elenchi attributed to Kilwardby) and were probably composed in Southern France around the University of Montpellier.228 They form a chronological sequence (R, then V, then T).229 With regard to the locus a communiter accidentibus,230 the picture that they offer is influenced by the debate reconstructed above and adds nothing special to what is already in Peter of Spain. With regard to the comments on the Tractatus VII on the fallacy of the consequent, the situation is quite the same: there are many original examples that are not in the commented text, but they are offered in the context of a discussion about the rules that distinguish valid from invalid inferences, which the most recent witness (the Todi manuscript) raises from two to six.231 None of these commentaries seems to know the interpolation which we examined above concerning the enthymema and the ycos.232 Slightly later or coeval is Albert the Great’s paraphrase of the Sophistici Elenchi, his Liber Elenchorum. Albert opens the discussion about the fallacy of the 225 226

Peter of Spain, Tract. VII.158, ed. de Rijk, 171. Cf. supra, §6.2.1 (Anonymus Monacensis). Peter of Spain, Tract. VII.159, ed. de Rijk, 171–172 (with regard to Melissus’ argument about the infinity of the world). 227 Cf. Ebbesen and Rosier-Catach (1997); Rosier-Catach and Ebbesen (2000); cf. also Ebbesen (2021), where a new manuscript is considered (R) which probably contains the least recent of the versions that we have. 228 Thanks are due to Sten Ebbesen, who kindly checked and collated some passages for us. 229 R = (“the Remnant manuscript”) Lubbock, Texas Tech University, ms. 0894; V = Biblioteca Apostolica Vaticana, Lat. 3049; T = Todi, Biblioteca comunale, 54 (cf. Ebbesen (2021)). 230 Ms. V, consulted at https://digi.vatlib.it/view/MSS_Vat.lat.3049, distinguishes two kinds of common accidents, with some new examples: “Quarto notandum quod communiter accidentia dicuntur duobus modis. Uno modo secundum prius et posterius, vel uno modo secundum verba de presenti et preterito, ut ‘pellis est, ergo animal fuit’; et de istis loquitur in littera. Alio modo dicuntur accidentia convertibilia, ut ‘corpus est, ergo locus est’; et sic in talibus tenet locus affirmative et negative et est maxima: si convertibilium accidentium unum inest, et reliquum; et si unum non inest, sic (fit, V) et reliquum.” The text of the least recent witness (R) is not much different. In the third manuscript, containing a later redaction (T), this annotation does not occur. 231 Cf. ms. Todi, Bibl. Com. 54, 22rb. 232 See supra, §§4.1, 6.1.3.

340

chapter 6

consequent with some preliminary observations. In the first place, antecedens has to be taken in the logical sense of a proposition which, once posed (quo posito), allows to infer another proposition (the consequens) either probably or necessarily. The inference is necessary when the consequent is included (either according to reason or according to the reality of things) in the antecedent, namely when the predicate of the consequent holds of the predicate of the antecedent according to the first, second, or the fourth mode of per se inherence.233 The inference is probable when the predicate of the consequent usually holds of the predicate of the antecedent, as in the case of the adulterer (to which we return in a moment) or in conditionals like “If a pauper talks with a rich man, then he is asking something from him” (si loquitur cum divite pauper, petit aliquid ab illo) or “If they have enemies in common, then they are friends” (ambo amici, si eiusdem ambo inimici).234 In the second place, Albert examines the distinction, which originates with Boethius and which is employed in the commentary attributed to Kilwardby, between the different kinds of inference. The classification is connected by him to the disciplines corresponding to each kind: some inferences are necessary and not probable, and these are proper to demonstrative disciplines; some are probable and not necessary, and these are proper to dialectical disciplines; some are both necessary and probable but with reference to distinct middle terms (no example of discipline is provided for this kind of inference); some are neither necessary nor probable, and these are proper to rhetorical and poetic disciplines.235 According to Albert, in the fallacy of the consequent the “cause of appearance” (causa apparentiae) is the identity between the antecedent and the consequent “that is in it [i.e., in the antecedent] either necessarily, probably, or conjecturally”: identity is here to be taken as intensional inclusion of the consequent in the antecedent, i.e., as the intensional inclusion of the hypernym (“animal”) in the hyponym (“human being”). The validity of the inference from the latter to the former (“It is a human being, therefore it is an animal”) misleads us into thinking that the converse inference from the former to the latter (“It is an animal, therefore it is a human being”) is also valid. By contrast, the cause of the invalidity or of the non-existence of this inference (causa defectus

233

234 235

Albert the Great, Liber Elencorum I.3.15, ed. Borgnet, 584a. In the first sense of per se, the predicate is said per se of the subject in so far as the former is part of the definition of the latter; in the second sense, the predicate is said per se of the subject in so far as the latter is part of the definition of the former; in the fourth sense, Albert says, the predicate is said per se of the subject in so far as the latter is the cause of the former. Cf. supra, §§1.6, 5.2. Albert the Great, Liber Elencorum I.3.15, ed. Borgnet, 584a. Ibidem.

13th-Century Parisian Commentaries on the logica nova

341

sive non existentiae) is that the antecedent is not such if not potentially.236 The first species of this fallacy is that which produces wrong opinions from sense perception; some classical examples come from Soph El 5, 167b5–8: the inference that bile is honey because it is yellow and that it has rained because the earth is drenched. Albert, following Kilwardby(?), claims that the valid inference that is the converse of the fallacy is necessary.237 Probable inferences, by contrast, are used in rhetoric (in rhetoricis demonstrationes, hoc est, probationes sive ostensiones) and are based on common rather than on proper signs; these derive from predicates that are associated with some subject (ex adiunctis) which Cicero calls “associated accidents” (communiter accidentia).238 Albert illustrates this species of the fallacy by means of an example that re-unites the adulterer and the thief (which Philoponus and the Anonymus Monacensis had split into two distinct examples) into one single argument: when rhetors want to show or prove that someone is an adulterer, they assume that common predicate which is commonly added to the adulterer, or an associated accident of the adulterer, like that he is elegant, and embellished and fancily dressed, and that he often looks at other men’s women, or that he wanders about at night: from which the suspicion is generated that he is an adulterer and a thief.239 236 Albert the Great, Liber Elencorum I.3.15, ed. Borgnet, 585a–b: “Causa autem apparentiae in hac fallacia est identitas antecedentis cum consequente, quod vel necessario vel probabiliter vel suspicabiliter est in ipso: ex qua creditur quod sicut consequens infertur ex antecedente, ita e converso consequens inferat antecedens. Causa vero defectus sive non existentiae est diversitas consequentis ab antecedente in quo non est antecedens, nisi in potentia: et ideo non potest inferri ex ipso.” 237 Albert the Great, Liber Elencorum I.3.15, ed. Borgnet, 585b–586a. 238 Albert the Great, Liber Elencorum I.3.15, ed. Borgnet, 586a: “Similiter autem in materia in qua consequentia conversa non est necessaria, sed probabilis vel suspicabilis tantum, sicut in rhetoricis demonstrationes (hoc est, probationes sive ostensiones) quae sunt secundum signa communia non propria: fiunt enim ex adjunctis praedicatis alicui subjecto, quae dicuntur a Tullio ‘communiter accidentia’.” 239 Albert the Great, Liber Elencorum I.3.16, ed. Borgnet, 586a: “volentes enim ipsi rhetores ostendere sive probare, quoniam aliquis est adulter, illud praedicatum commune quod communiter adjunctum est adultero, sive communiter accidens est adultero, accipiunt, ut quoniam compositus est et ornatus et comptus, et saepe respicit ad uxorem alterius, aut quoniam in nocte videtur errabundus: ex quo suspicio generatur, quod sit adulter et latro.” The adjective compositus is Boethius’ rendering of καλλωπιστής (AL VI.1, 13.11: “Volentes enim ostendere quoniam adulter, quod adiunctum est accipiunt, quoniam compositus aut quoniam in nocte videtur errabundus.”). As we saw above, it is usually substituted by comptus, with the same meaning. It has also to be noted that just like the alleged Kilwardby, Albert frames the fallacies in syllogistic terms: “Et potest sic formari

342

chapter 6

The connection of the fallacy of the consequent with both Boethius’ Topics and APr B 27 is evident and explicitly emphasized. Albert goes far beyond Boethius and his commentators in saying that the argument from communiter accidentibus, when the accidents or adiuncta are “proper” (i.e., as extended as, and thus convertibe with, the subject in which they inhere), namely “signa and ycotae,” concludes in the first figure: It has to be known that in such cases, as Boethius says, the locus from what is added or from associated accidents, when what is added are assumed to be proper, since these are signs and icotae, concludes in the first figure, like this: whoever has milk in the breast, without the breast having been rubbed with salt and nettle, has given birth; this one does have milk in the breast; therefore, she has given birth. I say “without the breast having been rubbed,” because Aristotle says that if a vergin, or even a man with large breast, have the breast rubbed with salt or nettle, that person will have milk in the breast; but it will be light and in modest quantity and not sufficient for lactation.240 The example is that of the lactating woman of APr B 27, with the qualification that the milk should not have been induced artificially by rubbing the breast with nettle. The qualification is reminescent of Albert’s commentary on the Prior Analytics.241 However, while in that context the example of artificial lactation was invoked to support the idea that the milk is the sign and not the cause of giving birth (or at least so we argued), here the possibility of artificial lactation is explicitly introduced as an exception clause (asbque confricatione mammillarum) that preserves the deductive validity of the inference. In any case, the passage quoted is puzzling for its terminology. One would expect the “signs” that conclude in the first figure to be called prodigia.242 On the contrary, paralogismus: si aliquis est adulter, ipse est comptus et politus; sed iste est comptus et politus; ergo est adulter. Vel sic: si aliquis est fur, iste est errabundus de nocte; sed iste est errabundus de nocte; ergo est fur” (Albert the Great, Liber Elencorum I.3.16, ed. Borgnet, 586a). 240 Albert the Great, Liber Elencorum I.3.16, ed. Borgnet, 586a–b: “Sciendum quod in his talibus, sicut dicit Boetius, locus ab adjunctis sive communiter accidentibus, quando adjuncta accipiuntur propria, quia ista sunt signa et icotae, concludit in prima figura, ut hic: quaecumque habet lac in mammillis, absque confricatione mammillarum cum sale et urtica, peperit; haec sic habet lac in mammillis; ergo peperit. Dico autem ‘absque confricatione mammillarum,’ quia dicit Aristoteles quod si virgini vel etiam viro habenti mammillas magnas cum sale vel urtica confricentur mammillae, lac habebit in mammillis; sed tenue erit et modicum et non sufficiens ad lactandum [locandum, ed.].” 241 Cf. supra, §6.1.1.2. 242 Like in the margins of Nicholas of Paris’ commentary on Boethius’ Topics; cf. supra, §6.2.1.

13th-Century Parisian Commentaries on the logica nova

343

Albert calls them signa and ycotae. In his paraphrase of the Prior Analytics, signum in the proper sense is only the prodigium; second- and third-figure signa are rather icota (or icotae). Here he seems happy to call first-figure signs icotae. When the accidents are common (i.e., more extended than the subject in which they inhere) the inference is in the second figure and qualifies as a fallacy of the consequent. The example here is the pale woman of APr B 27.243 Albert observes that if the locus a communiter accidentibus is to have any validity, the sign or accident has to be taken in conjunction with other signs or accidents; in this manner the common sign or accident becomes proper and the inference valid.244 This observation certainly derives and reflects previous commentaries and treatises, in which the connection between the fallacy of the consequent, Boethius’ Topics and APr B 27 is made explicit. Like Kilwardby(?) and Nicholas of Paris before him,245 Albert seeks to save this dialectical locus from falling within the domain of fallacies by allowing a conjunctive consequent. Semiotic inferences from conjunctive consequents are used in several disciplines: In this way one argues in rhetoric and in physiognomics, and in other demonstrative sciences like astronomy, and in the others in which one demonstrates from signs.246 Albert points out that such inferences are not necessary according to the necessity of the premises or conclusion (necessitas antecedentis et consequentis) but according to the necessity of the inference itself (necessitas consequentiae). Albert also observes that the necessity of such inferences is sufficient for the production of the cognitive effect that is adequate to those disciplines (ad 243

Albert the Great, Liber Elencorum I.3.15, ed. Borgnet, 586b: “Si autem sint signa et adjuncta in secunda figura quae communia sunt praedicata, ut esse pallidam, et adjunctum ad ea quae peperit, ut dicit Aristoteles in fine secundi Priorum, et solum accipiatur unum tale accidens vel adjunctum, tunc praedicatum communius erit, quam quod possit inferre subjectum: et tunc erit fallacia consequentis.” 244 Albert the Great, Liber Elencorum I.3.15, ed. Borgnet, 586b: “Et ideo si debeat esse locus a communiter accidentibus, tunc oportet quod tale adjunctum accipiatur cum circumstantiis personae: quia cum multis talibus acceptum erit proprium, et infert subjectum, quod solum unum adjunctum inferre non poterit.” The expression cum circumstantiis personae comes from Cicero’s rhetoric, whose teaching was in vogue in the twelfth century but already in decadence at the beginning of the thirteenth; cf. Fredborg (1987); Marmo (1997a), 142–145. 245 Cf. supra, §6.2.1. 246 Albert the Great, Liber Elencorum I.3.16, ed. Borgnet, 586b: “et sic arguitur in rhetoricis et in physiognomicis, et aliis scientiis demonstrativis, sicut in astronomia, et in aliis in quibus ex signis demonstratur.”

344

chapter 6

faciendam aestimationem, judicium vel suspicionem), which is clearly inferior to the cognitive effect proper to demonstrative science in the primary sense.247 Giles of Rome’s commentary on the Sophistici Elenchi was composed around 1274 and is a literal commentary that follows Aristotle’s text quite closely. With regard to the fallacy of the consequent, Giles focuses on two issues: its pertinence to the Sophistici Elenchi and its denomination.248 After the exposition of the divisio textus of Soph El 5, Giles presents the dubium according to which an argument from the affirmation of the consequent amounts to an argument from affirmative premises in the second figure, which is the worthless combination for a sound syllogism (inutilis coniugatio) that Aristotle treats in APr A 9; for this reason, the fallacy of the consequent is not of pertinence to the Sophistici Elenchi.249 In his solution of the dubium Giles claims that consequens (or fallacia consequentis) may be taken either as a deviation with respect to syllogism as such (simpliciter), and in this sense it is of pertinence to the Prior Analytics; or as grounded on a false maximal proposition (que uni et eidem sunt eadem, inter se sunt eadem:250 things identical to a third are identical to each other), and in this sense it is of pertinence to the Sophistici Elenchi.251 247 Albert the Great, Liber Elencorum I.3.15, ed. Borgnet, 586b: “Sciendum etiam quod tales consequentiae non sunt necessariae secundum necessitatem antecedentis et consequentis, quamvis satis necessariae sint ad faciendam aestimationem judicium (judicio, ed.) vel suspicionem (suspicioni, ed.): et hoc vocatur hic consequentiae necessitas: quia, sicut dicit Boetius generaliter loquens de omni argumento, argumentum est ratio rei dubiae faciens fidem, fidem vocans quamcumque credulitatem.” In this context, no reference is made to the scientia quia; this is coherent with the substantial even if not complete disconnection of scientia quia from sign-inference in Latin Aristotelianism (cf. supra, Chapter 5). This text probably needs emendation. 248 Giles of Rome, Expositio super libros Elenchorum, 20rb–21vb. 249 Giles of Rome, Expos. sup. lib. El., 20va: “Dubitaret forte aliquis utrum de fallacia consequentis determinari habeat in hoc libro. Et videtur quod non: dictum est enim ea que determinantur in hoc libro esse obliquitates sillogismi dialetici; sed arguere a positione consequentis est arguere ex puris affirmativi in secunda figura; sed hec est obliquitas sillogismi simpliciter et est inutilis coniugatio, et de ea determinatur in libro Priorum, capitulo nono; non ergo debet hic tractari de ea.” 250 Cf. Soph El 6, 168b31–33, transl. Boethii, AL VI.1, 16.24–25: “nam quae uni et eidem eadem, et sibi invicem probamus esse eadem; propter quod fit secundum consequens elenchus.” 251 Giles of Rome, Expos. sup. lib. El., 20va: “Respondeo dicendum quod consequens dupliciter potest accipi: primo ut est pura obliquitas sillogismi simpliciter, et sic est inutilis coniugatio et de ea habet tractari in libro Priorum; secundo, potest considerari consequens ut habet specialem maximam cui innititur: innititur enim illi maxime ‘que uni et eidem sunt eadem, inter se sunt eadem’, ut patebit in illo capitulo AUT SIC DIVIDENTES [Soph El 6, 168a17]. Et quia huiusmodi maxima ut ibi declarabitur non est necessaria, sed apparens et sophistica, ideo consequens ut innititur tali maxime est locus sophisticus.” Cf. Giles of Rome, Expos. sup. lib. El., 25va, where he discusses the maxima in question.

13th-Century Parisian Commentaries on the logica nova

345

The second dubium, about the classical problem of the fallacy’s denomination, also addresses the problem of the typology of fallacies of this kind, i.e., whether there are two species of it, one from affirming the consequent (AC) and one from denying the antecedent (DA). Giles follows the path opened by the Fallaciae ad modum Oxoniae: this fallacy always derives from AC. The reason is that the more a term in its affirmative form is specific, the more general it is in its negative form: if animal is more extended than homo, non-homo is more extended than non-animal, and what is more extended always follows from what is less extended (“If human being, then animal,” but not vice versa). Thus, animal is the consequent of homo and non-homo is the consequent of non-animal. Therefore, the inference of non-animal from non-homo (that is from the negation of the antecedent) is in fact an inference from AC. The name of the fallacy is accordingly correct.252 The strategy here is the same as in earlier commentators: the fallacy from DA is also from AC, if with “consequent” we mean the conclusion of the converse valid inference. The fallacy is one in form (from AC), although in matter there are three species of it, according to the several matters to which it is applied (per applicationem ad diversam materiam): that which derives from sense perception (honey and drenched earth); moral and rhetoric sciences (the adulterer; the thief is absent, as it was absent in Aristotle); speculative and syllogistic science (Melissus’ argument for the infinity of the world).253

252 Giles of Rome, Expos. sup. lib. El., 20va: “Ulterius forte dubitaret aliquis, cum hec fallacia non solum fiat a positione consequentis, sed a destructione antecedentis, quare potius nominata est consequentis quam antecedentis. Dicendum quod si bene consideramus hec fallacia semper fit a positione consequentis. Nam quanto specialius est aliquid affirmative sumptum, tanto negatum generalius efficitur: ut si animal est in plus quam homo, non-homo erit in plus quam non-animal, et quia semper illud quod est in plus sequitur ad id quod est in minus; sed animal est consequens ad hominem, non-homo erit consequens ad non-animal; negatio ergo facit de antecedente consequens et de consequente antecedens; antecedens ergo destructum est consequens ad antecedens negatum: arguere ergo a destructione antecedentis est arguere a positione consequentis. Merito ergo hec fallacia nominata est consequens, quia quodammodo semper per eam arguitur a positione consequentis.” A similar justification is given by Roger Bacon, Summ. dial., 3.3.2.2, §645 (see supra, §6.2.1). 253 Giles of Rome, Expos. sup. lib. El., 20va–b.

346

chapter 6

Modistic question commentaries focus roughly on the same problems (denomination,254 relationship with the fallacia accidentis,255 and typology256); they occasionally use the example of the adulterer.257 As we shall see in a moment, during the last decade of the thirteenth century Radulphus Brito returns to the connection between fallacia consequentis, locus a communiter accidentibus and the semiotic typology of APr B 27 in one of the questions devoted to the fallacy of the consequent in his commentary on the Sophistici Elenchi. Before turning to Brito, however, it is interesting to say something about the two modistic commentaries on Peter of Spain’s Tractatus that we met earlier,258 which go in the same interpretive direction (not without problems, however). While commenting on the locus a communiter accidentibus, Master Simon embarks onto a brief discussion about the question whether this locus is instrinsic or not. The only argument against a positive answer is that this locus is based on the relation between distinct accidents and that distinct accidents are necessarily extraneous to one another; the locus cannot therefore be intrinsic.259 In his determinatio Simon specifies that there are two kinds of accidents: (i) “proper accidents,” which derive from the essential principles of a species (as any proprium in the Porphyrian sense does, e.g., capability to laugh with respect to man); (ii) accidents that derive from individual principles 254 Anonymus-SF, Quaestiones super Sophisticos Elenchos, q. 100 (de sua nominatione), ed. Ebbesen, 233–235; Simon of Faversham, Quaestiones novae super libro Elenchorum, q. 33 (u. sit fallacia distincta contra alias: denomination and types), ed. Ebbesen et al., 188–191; Anonymous of Prague, Quaestiones super Sophisticos Elenchos, q. 38 (u. fallacia consequentis debeat nominari antecedentis vel consequentis), ed. in Murè (1997–1998). 255 Anonymus-SF, Quaest. sup. Soph El, q. 101 (u. consequens sit pars accidentis), ed. Ebbesen, 235–236; Simon of Faversham, Quaest. nov. sup. lib. El., q. 34 (u. consequens sit pars accidentis), ed. Ebbesen et al., 191–194. 256 Anonymus-SF, Quaest. sup. Soph El, q. 102 (de numero modorum), ed. Ebbesen, 236–237; Simon of Faversham, Quaest. nov. sup. lib. El., q. 35, (u. ubicumque est fallacia consequentis necesse sit consequentiam conversam bonam esse), ed. Ebbesen et al., 194–198; q. 36 (u. arguendo a positione consequentis ad positionem antecedentis sit bona consequentia), 198–200; q. 37 (u. arguendo a destructione antecedentis ad destructionem consequentis sit bona consequentia), 200–203; Anonymous of Prague, Quaest. sup. Soph El, q. 39 (u. possimus arguere a superiori ad inferius affirmando); q. 40 (u. valeat processus ab inferiori ad superius negando), ed. in Murè (1997–1998). 257 Cf. Simon of Faversham, Quaest. nov. sup. lib. El., q. 35, ed. Ebbesen et al., 194, 197. 258 Cf. supra, §6.1.3. 259 Magister Simon, Scriptum Tractatuum magistri Petri Hyspani, ad V.26: “Aliquis dubitaret utrum locus a communiter accidentibus sit locus intrinsecus. Et videtur quod non, quia ille locus /Pd/ in quo consequens est extra essentiam antecedentis, non est intrinsecus; sed in loco a communiter accidentibus est huiusmodi, quia talis fundatur super habitudinem unius accidentis ad alterum; sed unum accidens est extra essentiam alterius; ergo etc.” See infra, Appendix C.

13th-Century Parisian Commentaries on the logica nova

347

(e.g., whiteness and the like). Since these are founded upon common physical complexions (e.g., cold complexion produces white skin, hot complexion produces dark skin), they are called “common accidents.”260 The locus in question is based on common (or associated) accidents. According to Simon, in inferences that move from the locus a communiter accidentibus there are two sorts of processes. In the first, one infers a simple (i.e., a single categorical) conclusion from multiple premises, like in the inference that someone is a thief from the conjunctive premise that he wanders about at night, seeks to mislead, and has a low income. This is a valid inference. In the second process one infers a simple conclusion from a simple premise, and this is itself twofold: either from common accidents that constantly or essentially go together (essentialiter et inseparabiliter concomitantur), like in ille penitet, ergo deliquit, and here again we have a valid inference; or from common accidents that do not constantly or essentially go together, like in ista mulier dat lac, ergo est corrupta. For Simon this last species is a fallacy of the consequent. Simon here refers to Albert the Great’s commentary on the Sophistici Elenchi261 and to the artificial production of milk in a virgin (or in a male with a large breast) by rubbing with nettles and vinegar (but Albert says “nettle and salt” in his commentary on the Prior Analytics).262 Like in Albert, the example illustrates a sign in the first figure. In Simon, however, the example is slightly more complex and contains an echo of the example peperit, ergo cum viro concubuit of the earlier tradition.263 The inference ista mulier dat lac, ergo est corrupta is in fact the condensation into one single inferential step of a chain of several inferences: this woman has milk, therefore she has given birth; she has given birth, therefore she has had intercourse with a man; she has had intercourse with a man, therefore she has lost her virginity (this is the corruptio hinted at). What is also remarkable is that while in Albert’s commentary on the Sophistici Elenchi the possibility of artificial lactation is introduced as an exception clause (asbque confricatione…) 260 Magister Simon, Scriptum Tractatuum magistri Petri Hyspani, ad V.26: “Ad hoc dico quod hic locus est intrinsecus. Ad cuius intellectum nota quod duplicia sunt accidentia: quedam sunt propria que consecuntur principia essentialia speciei et illa dicuntur proprie propria, ut risibile est proprium hominis; alia sunt accidentia que causantur ex principiis individui, ut album et consimilia. Quia, secundum quod vult Avicenna, ista accidentia fundantur super complexiones, quia si homo est frigide complexionis, tunc est albus; si autem est calide complexionis, tunc est niger, quia Albertus dicit quod caliditas est mater nigredinis, frigiditas vero mater albedinis: et quia tales complexiones sunt communes, ideo accidentia talia que causantur ex hiis dicuntur ‘communia’.” See infra, Appendix C. 261 Cf. supra, §6.2.1. 262 Cf. supra, §6.1.1.2. 263 Cf. supra, §3.4.

348

chapter 6

that preserves the deductive validity of the inference, in Simon the possibility of artificial lactation is what explains the invalidity of the inference. The fate of the example of first-figure sign-syllogism of APr B 27 is quite singular indeed: some knowledge of the books De animalibus and of the practice of udders rubbing with nettle on Albert’s part has the effect in Master Simon of turning the most secure and infallible of the signs, the τεκμήριον or prodigium, into the weakest of all, the one that yields the fallacy of the consequent.264 These and other problems are addressed by Radulphus Brito in two of his works: the questions on the second book of Boethius’ De differentiis topicis, composed in the 1280s or 1290s, and the questions on the Sophistici Elenchi, with all probability one of the last works that he composed before turning to theology.265 Question II.17 on the De differentiis topicis is about the last two loci intrinseci that Boethius treats following Themistius: the locus ab usibus and the locus a communiter accidentibus. With regard to both Brito’s question is the same as Master Simon’s: are they actually loci intrinseci? With regard to the second locus, Brito’s arguments agree with Simon’s: common accidents that are related in this locus are reciprocally extraneous, like the blooming of my garden and the blooming of yours; if one wanders about at night or dresses fancily (from Soph El, but by this time an integral part of the traditional inventory of examples for the locus a communiter accidentibus), these are inferential signs (signa illativa) that infer something from which they are distinct and separate, and upon them no locus intrinsecus can be constructed; regret and crime are opposed, and there is not locus intrinsecus between them, either.266 In his determinatio Brito distinguishes among several senses in which two 264 The last commentary on Peter of Spain that we have considered above (maybe authored by Radulphus Brito) has a poorly intelligible text, but it appears to be in consonance with Master Simon; cf. Radulphus Brito(?), Notule super Tract., ms. München, BSB, 6726, 37v: “COMMUNITER ACCIDENTIA [V.26, 70.15]. Determinat de loco a communiter accidentibus et primo distinguit communiter accidentia; secundo alterum membrum eligit. ET AB HIIS [V.26, 70.20]. Primo ponit unum membrum distinctionis; secundo alterum, ibi ALIA AUTEM SUNT [V.26, 70.18]. Primo dicit communiter accidentia sunt que concomitantur, hoc est que conveniunt alicui etiam ab extra, ut sint accidentia, et hoc communiter. Et hoc duobus modis: ut accidens commune est quod quandoque est et quandoque non, ut supra habemus(?), ut comptum esse sequitur adulterum (ad alterum, ms.) esse, vel velle placere puellis, sed semper non sequitur, quia aliquando fit gratia honestatis; et aliquis (aliquando?) non sumitur locus dyaleticus sed(?) sophisticus. Ita errare de nocte sequitur furem esse, sed non semper, quia aliquis circuit de nocte ut costodiat a furibus vel ut fornicetur.” Here there are no speculations about the sign in the first figure. 265 For some hypotheses about the internal chronology of Brito’s logical works see Ebbesen and Marmo (forthcoming). 266 Raduphus Brito, Quaestiones super libro Topicorum Boethii II.17, ed. Green-Pedersen and Pinborg, 61.

13th-Century Parisian Commentaries on the logica nova

349

c­ ommuniter accidentia can be taken in this locus: one can be a sign of the other, or it can be cause of the other, or they can both derive from one and the same cause. An illustration of the first is a reformulation of the thief example: Somehow this [insufficient income] disposes to theft, because now he has not enough to spend, and it is a sign that he will thieve; therefore, these are probable signs that someone will thieve: this man spends more than he gets and nobody gives it to him, and likewise for other circumstances, is a sign that he is a thief.267 Insufficient income is a sign of being a thief.268 The other two senses are exemplified as follows. Regret is caused by crime, or at least the former follows from the latter and so are both accidents that inhere in the same subject. Both the blooming in my garden and in yours of flowers of the same kind derive from the same cause, namely the sun (plus some other agent that is not specified and which is the proximate cause of the blooming).269 In all these cases, the 267 Radulphus Brito, Quaest. sup. lib. Top. Boethii II.17, ed. Green-Pedersen and Pinborg, 62: “Modo hoc disponitur ad furtum postea, quia nunc non habet unde expendat, cuius signum est quod postea furetur, unde ista sunt signa probabilia quod aliquis furetur: iste plus expendit quam lucratur nec aliquis dat sibi, et sic de aliis circumstantiis, signum est quod ipse sit latro.” The editors indicate a lacuna in the text immediately preceding this passage, where there must have been some sign of being a thief like the one given within parenthesis in the translation. 268 Cf. supra, §6.2.1: the same sign is taken into account by the Anonymus Monacensis (see infra, Appendix F). 269 Radulphus Brito, Quaest. sup. lib. Top. Boethii II.17, ed. Green-Pedersen and Pinborg, 62: “Vel /184rb/ unum est causa alterius, sicut delictum et poenitentia, unde ex delicto sequitur poenitentia, quia unicuique inerit poenitentia ex delicto; tamen non accipiuntur ut unum est causa alterius, sed unum concomitatur ad alterum circa unum subiectum. Aliquando ambo communiter accidentia sunt causata ab aliquo tertio, sicut quod haec herba floreat in horto meo et consimilis in horto tuo, ista sunt causata ab aliquo tertio, quia causa utriusque est idem accessus solis ad utrumque, et etiam postquam iste effectus consimilis sequitur, oportet quod istae non solum sunt idem in agente primo, sicut in sole; sed in agente particulari, quia sol non agit nisi quia determinetur eius actio per agens particulare. Ergo ex quo est ibi consimilis effectus oportet quod ibi sit consimilis dispositio, quae est causa magis proxima istius effectus.” Here Brito seems to suggest that between repentance and bad deed there is no relationship of efficient causality, and that the two accidents are permanently connected, so that if there is one (repentance) there must be the other (bad deed): it is a sort of presupposition that we may explain in terms of frame semantics. The passage (and the one quoted in the body of the text) is singularly similar to what the Anonymous of Munich says in his Notule sup. Tractatus Petri Hispani with regard to the locus a communiter accidentibus, immediately after the text quoted above in footnote 264 (ms. München, BSB, 6726, 37v): “Nota de communiter

350

chapter 6

relation (habitudo) between the two accidents, whether sign and signified thing, cause and effect, or effects of a common (remote) cause, always realizes an intrinsic locus, even though from the point of view of its instrinsic nature (de intrisecitate) it is the weakest of all and is thus examined at the end.270 We close the present Chapter with an examination of Brito’s quaestio I.48 of his Quaestiones super Sophisticos Elenchos. This question is about a problem that is also discussed by Giles of Rome in his Expositio and by Simon of Faversham (q. 33) in his second series of question. The question is whether the fallacy of the consequent is a locus sophisticus and whether it should then be distinguished from other fallacies. Some of the arguments against a positive answer are similar to those used by Giles and Simon. The first one, taken from Giles, is that if the inference is in the second figure with two affirmative premises, there is an unproductive disposition of the premises (inutilis coniugatio), which is not a fallacy, because it concerns a formal and not a material aspect of the inference.271 The second argument is close to the one used by Simon: since there is no fallacy of the antecedent, there can be no fallacy of the consequent.272 accidentibus quod possunt se comitare unum ad alterum duobus modis: ut unum sequitur ex altero tanquam ex qualitatibus(?) que sunt signa propria, ut si dicatur de aliquo quando/quod(?) iste \cum/ \re(liquit?)/ [misit] ei modicum, puta X marcas, cum ipse autem uno (vero?) XXX expendit et nec(?) arte aliquid lucratur nisi aliquis sibi donat, sequitur universaliter ergo furtum vel latrocinium perpetrauit; quandoque alterum habet se ad alterum sicut causa ad effectum, ut “penitet, ergo deliquit”: delictum non est causa penitentie; quandoque ambo habent quandam causam est(rinsecam?) aut sunt quedam accidentia quorum unum sequitur ad alterum ut penitere sequitur delinquere: cum enim quis peccat opus est ut peniteat si tamen agnoscit (agnossit, ms.) se peccasse. Et ab hiis sumitur hic locus dyaleticus. Et si vis describere: tunc locus est habitudo unius communiter accidentis ad reliquum. Et est maxima propositio per se nota explicans habitudinem, ut si Sortes penitet sequitur quod deliquit. Vnde pecata hic +sub(iectum?) effectu[[s]] facta(?)+ nephanda.” Notwithstanding the uncertainties in our reading of the manuscript, it is not difficult to notice that the two texts are very close, and this can only support the conjecture that they might have the same author. 270 Radulphus Brito, Quaest. sup. lib. Top. Boethii II.17, ed. Green-Pedersen and Pinborg, 62–63. 271 Radulphus Brito, Questiones super Sophisticos Elenchos I.48, 1.1: “Quia ubi est inutilis coniugatio non est locus sophisticus; in fallacia consequentis est inutilis coniugatio, ergo etc. Maior patet, quia inutilis coniugatio pertinet ad librum Priorum et per consequens non est fallacia que pertinet ad librum Elenchorum. Minor patet: in secunda figura arguendo ex affirmativis fit fallacia consequentis et est inutilis coniugatio, ut patet primo Priorum.” Parwana Emamzadah is preparing an edition of Britos’s questions on the Elenchi: we thank her for the revision of our working edition of q. I.48 in Appendix H; see supra, Giles of Rome, Exp. sup. El., 20va. 272 Radulphus Brito, Questiones super Sophisticos Elenchos I.48: “Item, non habemus fallaciam antecedentis, /B/ ergo nec consequentis; antecedens patet, consequens declaratur:

13th-Century Parisian Commentaries on the logica nova

351

Quite naturally, this leads to an argument, the third, that contains a clear echo of the discussions on the denomination: dialectical loci are named after what infers, not after what is inferred; since it is always the antecedent that infers the consequent, there must be a locus sophisticus of the antecedent, not of the consequent.273 The fourth argument, then, relies on the similarity of rhetorical and sophistical loci. The former are subordinated to dialectical loci and thus are distinguished, like the dialectical, from the sophistical. So, if it is true that whenever there is a fallacy of the consequent there is a rhetorical locus, then this locus cannot be sophistical.274 Also, since the fallacy of the consequent is obtained from associated accidents, it must be a locus a communiter accidentibus that is dialectical and not sophistical.275 In the determinatio Brito explains that the fallacy of the consequent is a locus sophisticus. This is confirmed by what Aristotle says in the Sophistici Elenchi and by the earlier tradition, in which to each locus sophisticus there correspond both the cause of appearance and the cause of defect: since both causes are given for the fallacy of the consequent too, it must be sophistical.276 Following the tradition, Brito explains that there are two species of this fallacy: one from AC and one from DA.277 As he then clarifies in reply to the second and third argumentation (Ad 1.2–3), even if the species are two, the quia sicut in consequentia est consequens ita antecedens.” See infra, Appendix H, §1.2. Cf. Simon of Faversham, Quaest. nov. sup. lib. El., q. 33, ed. Ebbesen et al., 133. 273 Radulphus Brito, Questiones super Sophisticos Elenchos I.48: “Item, locus dialecticus debet denominari /S/ ab inferente; sed inferens est antecedens; ergo magis debet esse locus sophisticus antecedentis quam consequentis.” See infra, Appendix H, §1.3. About this Brito has the same solution as the Anonymous of Prague, Quaest. sup. Soph El, q. 38, ed. in Murè (1997–1998). 274 Radulphus Brito, Questiones super Sophisticos Elenchos I.48: “Item, ubi est locus rethoricus non est locus sophisticus; sed ubi est fallacia consequentis est locus rethoricus; ergo etc. Maior patet, quia locus rethoricus et dyaleticus secundum essentiam sunt idem, nec differunt nisi sicut commune et contractum sub communi, secundum Boethium, in quarto Topicorum suorum; sed locus dyaleticus et sophisticus non sunt idem, sed similes, ergo nec rethoricus et sophisticus . Probatio minoris: quia, secundum Philosophum, fallacia consequentis fit ex adiunctis; modo ex adiunctis est locus rethoricus; ideo etc.” See infra, Appendix H, §1.4. 275 Radulphus Brito, Questiones super Sophisticos Elenchos, I.48: “Item, locus dyalecticus est ex communiter accidentibus; ergo non erit locus sophisticus; sed fallacia consequentis fit ex communiter accidentibus; ergo fallacia consequentis non est locus sophisticus.” See infra Appendix H, §1.5. 276 Here Brito goes back to his predecessors’ discussion of the two causes: cf. infra, Appendix H, §3.1. 277 Radulphus Brito, Questiones super Sophisticos Elenchos I.48: “Sed notandum est quod duo sunt modi istius fallacie: unus est a positione consequentis et alius a destructione antecedentis.” See infra, Appendix H, §3.2.

352

chapter 6

fallacy takes its name from the consequent. The reason of this is that the premises from which one infers (inferens) is always the real consequent (quod in veritate est consequens): in the fallacy animal currit, ergo homo currit, the premise is the consequent (i.e., the conclusion) of the valid inference homo currit, ergo animal currit. Here it is evident that both the objector and Brito are assuming that a valid inference can be expressed in conditional form, so that the premise becomes the antecedent and the conclusion the consequent of a conditional proposition. It is also clear that with consequens Brito means quod in veritate est consequens, i.e., the consequent of the true conditional proposition, while the objector must mean the conclusion of the fallacy (or its “consequent” when it is expressed as a conditional proposition). In fact, the objector of the third argument simply conflates the premise of the fallacious argument with the antecedent of the corresponding conditional. If indeed the fallacious inference animal currit, ergo homo currit (whose major premise is the true conditional si homo currit, animal currit) is cast in the form of the false conditional proposition si animal currit, homo currit, then the premise of the fallacious inference becomes the “antecedent” of the false conditional. And in this sense, since any argument is from its premises, in this case too it is from the antecedent. But this “antecedent” is actually the consequent of the true conditional proposition si homo currit, animal currit. “Consequent” in this context has almost invariably the meaning of quod in veritate est consequens, i.e., of the consequent of the true conditional proposition. Mutatis mutandis, the same holds of the species from DA.278 Like Roger Bacon, Simon of Faversham, and others, and unlike Kilwardby(?) and Albert the Great, Brito argues that it is not needed that the converse of the fallacy of the consequent be always valid (consequentia semper bona); it is sufficient that it be probable.279 In reply to the arguments contra, Brito follows Giles of Rome almost verbatim and distinguishes two senses of the fallacia consequentis; in one sense, it is a deviation from the syllogism and as such it falls under the Prior Analytics. In another sense, in so far as the cause of its appearance of validity is added to the explanation of its invalidity, it falls under the Sophistici Elenchi.

278 Brito’s qualification quod in veritate est consequens may be an indication that he has something like the logical/ontological distinction in mind: in a true conditional that which is consequent logically is also so ontologically. In any case, none of our medieval commentators on the Sophistici Elenchi seems to have made any use of this distinction. 279 Radulphus Brito, Questiones super Sophisticos Elenchos I.48: “Item, notandum est quod in fallacia consequentis non oportet alteram consequentiarum semper esse bonam, sed sufficit quod sit probabilis.” See the continuation infra, Appendix H, §3.3.

13th-Century Parisian Commentaries on the logica nova

353

In answer to the fourth argument, according to which from adiuncta one can only produce rhetorical loci, Brito replies: Among the things that are added, some are proper and others common. Proper are those which necessarily follow the thing to which they are added, like “having milk” is related to “giving birth”; and these are called prodigia by Aristotle at the end of the Prior Analytics; and in this case we have a dialectical or rhetorical Topic. By contrast, common are those which have a greater extension than the thing to which they are added, like “this is pale, therefore she has given birth”; and in this case we have precisely the fallacy of the consequent.280 However—and here Brito relies on the tradition discussed above—these latter adiuncta may either be taken singularly, and this produces the fallacy of the consequent, or they may be taken in conjunction with other features (plura adiuncta), and this produces a respectable rhetorical argument.281 He has no examples of this, but we have met several above that perfectly illustrate the case. With regard to the locus a communiter accidentibus, Brito also restates the Boethian distinction between that which always follows (penitere from deliquisse) and that which sometimes follows and sometimes not: the former produces a good dialectical argument, the latter a fallacy of the consequent.282 Brito’s work on the Sophistici Elenchi is certainly dependent upon and influenced by the long traditions of commentaries on Boethius’ De differentiis 280 Radulphus Brito, Questiones super Sophisticos Elenchos, I.48: “ex adiunctis quedam sunt propria et quedam communia. Propria sunt illa que necessario sequuntur rem cuius sunt adiuncta, sicut ‘habere lac’ se habet ad ‘parere,’ et talia vocat Aristotiles, in fine Priorum, ‘prodigia,’ et ibi est locus dyaleticus vel rethoricus. Communia autem sunt in plus quam res cui sunt adiuncta, sicut ‘ista est pallida, ergo peperit’; et in talibus est bene fallacia consequentis.” See infra, Appendix H, Ad 1.4. 281 Radulphus Brito, Questiones super Sophisticos Elenchos I.48; “Sed adhuc notandum est quod ista communia adiuncta dupliciter possunt accipi, quia aut accipitur unum solum adiunctum ad inferendum illud cuius est adiunctum, et tunc est fallacia consequentis, ut ‘est pallida, ergo peperit’; aut accipiuntur plura adiuncta ad inferendum illud cuius sunt adiuncta, et bene tunc fit argumentum rethoricum et non fallacia consequentis.” See infra, Appendix H, Ad 1.4. Cf. Robert Kilwardby(?), Comm. in Soph El, dub. 3.2, see infra, Appendix G (and cf. supra, §6.2.1). 282 Radulphus Brito, Questiones super Sophisticos Elenchos I.48: “Per idem patet ad aliam, quia communiter accidentia quedam sunt semper consequentia, et in talibus est locus dyaleticus; alia sunt que quandoque sequuntur, et quandoque non, et in talibus est fallacia consequentis.” See infra, Appendix H, Ad 1.5.

354

chapter 6

topicis, on the Prior Analytics, and on the Sophistici Elenchi. In this tradition, signs sometimes play the role of “glue” that connect the three intellectual threads and their heritage, allowing the transfer of notions and examples from one domain to the other. In Brito, however, signs almost disappear, and this constitutes somehow a step back to the beginning of the century. 3 Conclusion Kilwardby’s is the first complete Latin commentary on the Prior Analytics. Kilwardby used both the recensio Florentina and the recensio Carnutensis of the Boethian translation, but in the part on B 27 he certainly follows the Carnutensis, which uses ikos for εἰκός. Like the anonymous author of a Greek commentary (Ps-Philoponus-1), Kilwardby and Albert the Great take the ycos not as the premise of one of the two species of enthymemes, the other being sign-enthymemes, but as a species of sign-enthymeme, and identify it with the second- and third-figure signs (Aristotle’s σημεῖα in the strict sense). For Aristotle a sign is the premise of an enthymeme. Both Kilwardby and Albert oscillate between a propositional and a sub-propositional notion of “sign” (sign as the premise of an enthymeme, and sign as the middle term of the syllogism), with Albert being more inclined towards the identification of the sign with the middle term. In Albert, but not in Kilwardby, the Aristotelian definition of the sign (which has a propositional size) merges with the Augustinian definition. For Kilwardby the third-figure sign is probable, while the second-figure sign is only apparently probable and really sophistical; in either case, the probabilitas of ycota (in Kilwardby’s sense of second- and third-figure signs) contrasts with the certainty of prodigia (first-figure signs), and this difference is reflected in a disciplinary divorce: for both Kilwardby and Albert the prodigium concerns logic and science, while the ycos concerns rhetoric only. The examples are in both commentaries the very same as Aristotle’s. But with regard to the lactating woman as illustration of the prodigium, Albert’s specification Lac autem habere signum est, et non causa makes the reference to the contrast between sign and cause quite evident. That contrast plays no role in the official account of signs in APo B 27. It is rather an echo of the opposition between why-demonstrations (through the cause) and that-demonstrations (through the effect) in the Posterior Analytics, and especially of the manner in which that contrast is explained by the Greek and then the Arabic commentators: as a contrast between causal and semiotic demonstrations. Conversely, Kilwardby does make the point that a sign of both the necessary and the probable species vult esse (βούλεται εἶναι) a demonstration without being so. But this observation is not followed by the

13th-Century Parisian Commentaries on the logica nova

355

further observation, which Kilwardby might have made, that necessary signs, though not proper (i.e., causal) demonstrations, may still be regarded as demonstrations of a lower kind. None of these authors makes a point like this. Nor is any such point made by Kilwardby or Albert in their treatment of the physiognomic section of APr B 27. Kilwardby observes (though his observation is not free from ambiguities) that when certain conditions concerning the relation between bodily signs and spiritual affections obtain, a physiognomic inference can go in two directions: one can infer the affection from the sign or the sign from the affection; taking the affection to be the unobservable cause of an observable effect, the two directions might be associated with the two kinds of demonstration of APo A 13: by a why-demonstration we infer the sign from the affection, and by a that-demonstration we infer the affection from the sign. But no such association is made by Kilwardby. In both Kilwardby and Albert the Great physiognomic is an applied semiotics that is conceptually disconnected from the Aristotelian theory of demonstration. In general, the situation is symmetrical to that observed for the Posterior Analytics tradition: just as the demonstratio quia is associated with sign-inference only sporadically and quite unsystematically in the Latin commentaries on the Posterior Analytics, so no reference to demonstrations of a lower kind or to semiotic demonstrations is made in the context of the Latin commentaries on APr B 27. The silence about the theory and taxonomy of demonstrations within the theory of signs of APr B 27 is matched by a corresponding silence about the theory of signs within the theory and taxonomy of demonstrations of the Posterior Analytics Similar conclusions hold of the Rhetoric and the Summule. The first Latin commentary on the Rhetoric that have been preserved is that by Giles of Rome. Unlike Kilwardby and Albert the Great, Giles considers the ycos to be the sign in the second figure only. Giles thinks that this idea agrees with Aristotle’s treatment of both likelihood- and sign-enthymemes in the Rhetoric. In this perspective, only first- and third-figure signs are signa in the proper sense (as opposed to ycota); the first-figure sign is called a prodigium or retinerium (which despite Giles’ etymological audacity simply derives from a corrupt reading of the Latin tecmerium for τεκμήριον); the third-figure sign is simply referred to as “non-necessary sign.” Unlike what happens in the commentaries on the Prior Analytics, Giles’ notion of sign is coherently propositional This certainly marks a certain distance from the Augustinian definition, which Giles might have taken to be incompatible with the Aristotelian, propositional notion. No reference is made by Giles to the theory of demonstration of the Posterior Analytics and to the taxonomy of demonstrations; enthymemes are rhetorical syllogisms, not demonstrative or scientific syllogism; the distance

356

chapter 6

between theory of signs and theory of demonstration could not be greater. The same holds of the commentaries on Peter of Spain’s Tractatus V: while they generally contain original interpretations of, and interesting variations over, Aristotle’s analysis of signs in APr B 27, none of them connects that analysis to the theory of demonstration of the Posterior Analytics. There is one single but important exception to the general impermeability of these two areas of the Aristotelian oeuvre. In a series of questions on the pseudo-Aristotelian Physiognomics, Radulphus Brito makes the observation that since physiognomics is a conjectural science that investigates human natural inclinations from their exterior signs, it cannot be a demonstrative science in the strict sense, like mathematics is, as it does not proceed from the causes to the effects; it rather proceeds from the effects (the exterior signs) to their causes (the natural inclinations). He does not say that explicitly, but the idea clearly implied here is that physiognomic sign-inferences are demonstrations of the that. After all, one of the types of that-demonstrations that he recognizes in his discussion about the validity of quia demonstrations283 is from proximate effects. APr B 27, the official theory of sign-inferences (including physiognomic sign-inferences) and APo A 13, the official account of that-demonstrations, are here only implicitly connected. The tradition of commentaries on the Prior Analytics converge in the thirteenth century with two other traditions: the commentaries on Boethius’ De differentiis topicis, and the commentaries on the Sophistici Elenchi. Signs and sign-inferences, together with their typical examples, surface here and there within these three traditions and sometimes play the role of “glue” connecting different domains and their heritage, thereby allowing the transfer of notions and examples from one domain to the other. Particularly interesting in this regard are the reflections presented in these texts regarding the relationship between the fallacy of the consequent and the locus a communiter accidentibus. The problem arises precisely from the use of the same repertoire of examples at the beginning of the thirteenth century in the dialectical-rhetorical and sophistical domains: in particular the example of those who wander about at night, perhaps following in the footsteps of Philoponus (but there is no textual evidence of this possible dependence), is interpreted as a sign of being a thief and no longer a further sign of being adulterous. The basic need is to distinguish probable valid inference, which can be used in dialectical and rhetorical contexts, from the fallacy that must instead be rejected. The solutions are at least two, advanced by the different authors in the first half of the century. 283 Cf. infra, Appendix A, §3.2.

13th-Century Parisian Commentaries on the logica nova

357

The first one is that of the Anonymus Monacensis who considers the inference of being a thief from the disjunction of its possible signs (wandering at night or accompanying criminals or earning little and spending too much) to be false, while he considers the converse as correct (the one which goes from being a thief to having one of those properties or behaviors). The second one is adopted by the author of the commentary on the Sophistici Elenchi attributed to Kilwardby and by Nicholas of Paris (in his commentary on Boethius’s De differentis topicis) and is followed by other masters who later commented on the Sophistici Elenchi (such as Radulphus Brito) : the locus a communiter accidentibus consists in inferring from a plurality of signs (or accidents), taken in conjunction, a certain property (being a thief from wandering at night and being prodigal and being lustful and so on), while the fallacy of the consequent consists in inferring that same property (being a thief) from one of these signs only; in the first case the inference is valid and can be safely used in dialectic, in the second it is incorrect and must be rejected. Kilwardby(?) also makes explicit the connection of this distinction with that between signs in the first figure (prodigium) and signs in the second figure of APr A 27, with the consequence of also bringing back the necessary inferences, such as that of the lactating woman—susceptible of a placement within a typology of demonstrations—in the field of dialectic. This consequence is also clearly at work in Radulphus Brito’s discussion on the subject, where he considers the inference from the sign in the first figure (prodigium) as a dialectical or rhetorical locus. Within the dialectical and sophistical branches of thirteenth-century Latin Aristotelism, signs are never connected, either explicitly or implicitly, with the theory of demonstration. One reason for this disconnection is again to be found in the assumed association between signs and forms of knowledge lower than science, either because though deductively valid they are not demonstrative (like first-figure sign-syllogisms), or because they are simply deductively invalid and thus belong to probable and even fallacious reasoning (like second- and third-figure sign-syllogisms). The taxonomies of signs of the 1260s did not produce any real change in this panorama. This is the topic of the next Chapter.

CHAPTER 7

Thirteenth-Century Classifications of Signs While twelfth-century classifications of signs appear especially, though not exclusively, in theological works,1 by the middle of the thirteenth century they also appear in logic and linguistics: sign taxonomies are often put forth as introductions to the proper logical and grammatical analysis, both in standard treatises as well as in other works that do not have the standard form of an academic treatise. In this Chapter we shall examine two examples of thirteenth-century sign taxonomies. One is contained in the commentary on the first sixteen books of Priscian’s Institutiones grammaticae (1250s) once attributed to Robert Kilwardby (pseudo-Kilwardby on the Priscianus maior).2 The other is in Roger Bacon’s De signis (1267), a part of his Opus maius that was rediscovered at the end of the 1970s by Jan Pinborg and his collaborators, together with other works connected to the De signis.3 In both these works the influence of the debates about sign-inferences emerges with peculiar clarity, even though with remarkable differences in each. 1  Scientiae de signis and Natural Signs in the Pseudo-Kilwardby’s Commentary on the Priscianus maior The author referred to as the pseudo-Kilwardby is an anonymous grammarian probably active in the 1250s4 whose commentary on the Priscianus maior is preserved in some Cambridge manuscripts that also contain some authentic works by Kilwardby.5 With his work we move to grammar, where the references 1 Cf. supra, §4.3. 2 A partial edition is in Fredborg et al. (1975). 3 Cf. Fredborg et al. (1978). An anticipation of the classification is in the Communia naturalium, composed in the early 1260s (ed. Steek, I), in the Opus tertium (1267, ed. Brewer), and in the late Compendium Studii Theologiae (1292, ed. and transl. Maloney). We return to these works infra, §7.2. 4 Cf. Pinborg (1975), 5+. 5 Cambridge, University Library, Peterhouse 191, 1r–111v (thirteenth century); Cambridge, University Library, Peterhouse 206, 308–329 (thirteenth/fourteenth centuries); Cambridge, University Library, Kk III.20, 25r–224r + 228v–229v (fifteenth century); cf. Pinborg (1975), 2+. The first manuscript also contains Kilwardby’s commentaries on the Priscianus minor (books 17 and 18 of Priscian’s Institutiones, 112r–229v), on Donatus’ Barbarismus (230r–250v, likely non-authentic), and on Priscian’s De accentu (251r–258v; ed. Lewry); the second manuscript © koninklijke brill nv, leiden, 2023 | doi:10.1163/9789004546974_009

360

chapter 7

to Augustine’s semiotics are usually not frequent. As pointed out by Pinborg, the pseudo-Kilwardby’s sources are quite heterogeneous: they include not only several works by Aristotle—among which the Posterior Analytics (as we are about to see)—and Augustine, but also Avicenna, al-Ghazālī, Averroes, John of Damascus and Anselm of Canterbury.6 Like Simon of Tournai, the pseudoKilwardby offers an original classification of signs that seeks to combine distinct points of view and different sources of inspiration. In his prologue, he deals with the epistemological status of grammar in the context of a broader discussion on the possibility of a “science of signs” (scientia de signis), and it is here that he offers his own classification of signs. The prologue of the commentary opens with two crucial quotations: one from APo A 2, 71b25–26, which presents the idea that only what exists (ens) can be known (quod non est non contigit scire), and another from Augustine’s De doctrina christiana (omnis scientia aut est de rebus significatis aut de signis),7 which introduces a sketchy classification of the sciences according to the principles of derivation of their objects: nature, will, and reason. From nature derive natural objects, dealt with in the scientia naturalis; from will, together with the faculty of choice, derive moral objects, like good and evil actions and dispositions, dealt with in the scientia moralis; from reason derive rational objects, like discourses, dealt with in the scientia rationalis.8 This sketchy classification of the sciences is followed by a dubitatio: “whether there can be a science of signs” (an possit esse scientia de signis). Three arguments are offered in support of a negative answer which are quite strong and echo some of the questions examined in earlier Chapters: (i) according to the Posterior Analytics, sciences deal with universal objects, not with individual ones; now according to Augustine’s definition, a sign is something sensible; since anything sensible

contains Kilwardby’s commentaries on the logica vetus and nova, and on the Nicomachean Ethics. 6 Cf. Pinborg (1975), 4+–5+. 7 Ps.-Kilwardby, Commentum super Priscianum maiorem, 1.0, ed. Fredborg et al., 1. Cf. Augustine, De doctrina christiana I.2.2, ed. Martin, 7. 8 Ps.-Kilwardby, Comm. sup. Prisc. mai., 1.0, ed. Fredborg et al., 2: “In easdem tres partes potest dividi scientia a parte principiorum rerum de quibus sunt scientiae. Sunt enim tria rerum principia, scilicet natura communiter dicta, voluntas cum eligentia, et ratio. Natura est principium rerum naturalium. Voluntas cum eligentia rerum moralium ut habituum bonorum vel malorum et operationum. Ratio est principium rationalium ut sermonum. De rebus prima modo est scientia naturalis, de rebus secundo modo moralis, de rebus tertio modo scientia rationalis, et sic patet divisio scientiae per comparationem ad principia rerum de quibus est.”

13th-Century Classifications of Signs

361

is individual, there can be no science of signs.9 (ii) Signs are fallible and uncertain, as it appears from rhetoric; but a science whose aim is certainty cannot be based on what is fallible and uncertain.10 (iii) Like propositions, signs may be false; but there can be no science of falsity.11 The solution that the pseudo-Kilwardby offers of this complex dubitatio moves from a general classification of signs. The main division is between natural and conventional signs. It must be observed that this distinction does not derive from Augustine’s distinction between signa naturalia and data, since the latter are characterized as including signs that are produced by an animated being with an intention to signify. The distinction between natural and conventional signs is rather founded on the Aristotelian-Boethian tradition of the De interpretatione, and the commentaries on it, in which words, which signify by convention (as the Aristotelian κατὰ συνθήκην was traditionally interpreted to imply), are distinguished from the voices of the beasts, which are also taken to signify something, but not by convention.12 The distinction between natural and conventional signs is furthemore theoretically grounded on the distinction between natural or real relations (relatio realis) and mind-dependent relations (relatio rationis), which was traditionally adopted and used by medieval philosophers in many different fields, from logic to theology.13 Unlike Bacon,14 the pseudo-Kilwardby does not subdivide natural signs so as to have a species of them cover inferential natural signs. According to him, all inferential signs are alike in nature and are, like in the Greek commentators, 9 Ps.-Kilwardby, Comm. sup. Prisc. mai., 1.0, ed. Fredborg et al., 2: “Nulla scientia est de sensibilibus. Sed signa sunt sensibilia. Ergo nulla scientia est de signis. Maior patet ex primo Posteriorum ubi dicitur quod singularium non est scientia. Minor patet per definitionem signi sumptam ab Augustino in libro De Doctrina Christiana, quae est: Signum est res quae praeter speciem quam ingerit sensibus aliud facit in cognitionem venire, et sic signum habet speciem quam ingerit sensibus et omne tale est sensibile et sic patet minor.” 10 Ps.-Kilwardby, Comm. sup. Prisc. mai., 1.0, ed. Fredborg et al., 2: “Ad idem: Nullus habitus infallibilis est de fallibilibus et incertis. Sed scientia est habitus infallibilis, ut habetur ex primo Posteriorum. Ergo etc. Sed signa sunt fallibilia et incerta, ergo non est scientia de signis; quod signa sint fallibilia et incerta patet in signis rhetoricis.” 11 Ps.-Kilwardby, Comm. sup. Prisc. mai., 1.0, ed. Fredborg et al., 3: “Ad idem: Nulla scientia est de falso. Sed signorum quaedam sunt vera, quaedam falsa. Ergo non est scientia generaliter de signis. Maior patet ex primo Posteriorum, quia quod non est non contingit scire. Falsum autem non est. Minor patet discurrendo per signa diversa; orationum enim quaedam sunt verae, quaedam falsae et sic de aliis signis.” 12 Cf. Mora-Márquez (2015), for an introduction to this rich tradition, which we do not discuss in the present work. 13 On the medieval theories of relations, see Henninger (1989) and, for a recent update, Marenbon (2016) and Brower (2018). 14 Cf. infra, §7.2.2.

362

chapter 7

effects that are signs of their causes. In some cases, the effect or sign has the same extension as its cause and is thus convertible with it; in other cases, the effect or sign has not the same extension as its cause and is not convertible with it. Signs may also be distinguished into those that belong to the physical world (in genere naturae) and those that belong to the moral world (in genere moris). This latter subdivision should not be conflated with or reduced to the higher division into natural and conventional signs: there are both physical and moral natural signs.15 Smoke and the eclipse are both physical natural signs. Smoke is a sign that is not convertible with the thing it signifies (fire). It will be recalled that smoke as a sign of fire was exactly the example of a cause more extended than the effect that Themistius makes in his commentary on APo A 13: all occurrences of the smoke are occurrences of the fire, but not all occurrences of the fire are occurrences of the smoke; in this case, Themistius says, there is demonstration of the cause through the sign but not of the sign through the cause.16 The pseudo-Kilwardby does not say whether his second example of physical sign, the eclipse, illustrates a sign that is convertible with the thing it signifies (the interposition of an astronomical body).17 This is the standard example from APo B 16, 98b18–19, where it illustrates the relationship between syllogism of the why and syllogism of the that in which cause and effect are convertible.18 An example of a moral natural sign (whether convertible or not is not clear) is the pleasure one experiences in doing certain things, which is taken as the sign of a disposition of the will.19 The example comes from a passage in the

15 Ps.-Kilwardby, Comm. sup. Prisc. mai., 1.0, ed. Fredborg et al., 3: “Signorum enim quaedam significant aliquid ex institutione et quaedam significant naturaliter ut effectus generaliter sive sit convertibilis sive non convertibilis cum sua causa est signum suae causae. Quod patet tam in genere naturae quam in genere moris.” 16 Cf. supra, §2.2. The example of the smoke as sign of fire is also in Philoponus’ commentaries on the Posterior Analytics, on the De Anima (cf. supra, §2.3), and on the Physics (cf. supra, §2.4), in the ps-Philoponus-1’s commentary on Prior Analytics B 27 (cf. supra, §2.5), and in the ps-Philoponus-2’s commentary on Posterior Analytics B (cf. supra, §2.6). 17 Ps.-Kilwardby, Comm. sup. Prisc. mai., 1.0, ed. Fredborg et al., 3: “In genere naturae fumus est signum ignis non convertibile et defectus luminis sive eclipsis a corpore luminoso est signum interpositionis tenebrosi corporis.” Cf. John Duns Scotus, Reportata Parisiensia IV, d. 1, q. 2, n. 3, ed. Wadding, 546, who makes use of the same example in order to distinguish signs that always have their meaning with them (efficacia et vera) from signs that can be false (like propositions). Cf. also Marmo (2010), 195. 18 Cf. supra, §2.1. 19 Ps.-Kilwardby, Comm. sup. Prisc. mai., 1.0, ed. Fredborg et al., 3: “Similiter in genere moris delectatio, quae est in operationibus, est signum habitus voluntarii, sicut dicit Philosophus in secundo Ethicorum ubi dicit quod oportet signa facere habituum delectationem vel tristitiam in operationibus.”

13th-Century Classifications of Signs

363

Nicomachean Ethics.20 The pseudo-Kilwardby adds an explicit reference to the first mention of signs in the Posterior Analytics21 as a justification for the association between demonstration from the effect and sign-inferences: And so, it is evident that in general the effect is a sign of its cause. This is why the Philosopher in the first book of the Posterior Analytics calls the demonstrations made through the effect “syllogisms through signs,” in the part : “Since it is necessary in each kind.”22 We know from the second Chapter that the association between the ἀπόδειξις τοῦ ὅτι and sign-inference is the hallmark of the Greek and Arabic traditions of the Posterior Analytics. The pseudo-Kilwardby appears to have been more markedly influenced by that tradition than were the Latin commentators of the Posterior Analytics.23 A natural sign is the effect of a cause and from it that cause can be inferred, whether or not cause and effect are convertible. The problem that the pseudo-Kilwardby does not address (while Bacon does, as we shall see), is whether the sign-inference so produced is necessary or probable, and consequently which kind of cognitive effects such inference generates. Conventional signs are of two species: those that both signify and sanctify, like the signs of divine law (sacraments),24 and those that signify only. These latter are divided according to the nature of the “signifier” into “vocal” signs (voces), i.e., linguistic signs, and “real” signs, i.e., things not produced by the phonatory apparatus which are taken as signs of something else, like the gestures or bodily movements used by monks to communicate without speaking, or the circle used to advertise that wine is sold in a tavern (circulus vini), or the

20 Aristotle, Eth Nic B 2, 1104b3–5. 21 Aristotle, APo A 6, 75a28–34. 22 Ps.-Kilwardby, Comm. sup. Prisc. mai., 1.0, ed. Fredborg et al., 3: “Et sic patet quod effectus generaliter est signum suae causae. Unde Philosophus primo Posteriorum demonstrationes factas per effectum vocat syllogismos per signa in illa parte: QUONIAM AUTEM EX NECESSITATE SUNT CIRCA UNUMQUODQUE” [APo A 6, 75a28]. 23 See supra, Chapter 5. 24 In all probability, the so-called sacraments of the Old Testament (sacramenta veteris legis), like circumcision, are in the class of signa instituta ad significandum et sanctificandum quantum ad aliquod tempus, discussed in the Summa fr. Alexandri I (in Alexander of Hales, Summa theologica, ed. Collegium S. Bonaventurae, I, 748b–749b). Here the pseudo-Kilwardby speaks only of signa divinae legis without going into theological details.

364

chapter 7

images used as shop signs.25 While the signs that both signify and sanctify are dealt with in sacramental theology,26 linguistic signs are the object of the disciplines of the Trivium (grammar, logic, and rhetoric). The question remains as to what discipline should deal with gestural languages27 or commercial signs, such as the circulus vini. From the pseudo-Kilwardby’s classification it clearly emerges that there can be distinct “sciences of signs” according to the kind of sign that is taken into consideration, and that some sciences deal with linguistic signs, others with natural signs; physics and ethics in particular deal with natural signs in a manner that is perfectly consonant with the idea of a “semiotic” demonstratio quia. The pseudo-Kilwardby’s sign typology is summarized in Figure 5. The dubitatio concludes with replies to each of the three arguments in support of a negative answer to the question “whether there can be a science of signs.” We proceed in inverse order. The reply to (iii) contains a reference to a text that is quite common in the theological tradition28 but unusual in a grammatical commentary. The pseudo-Kilwardby uses a distinction between the accidental and the essential truth of the sign that is taken from the De veritate 2 of Anselm of Canterbury:29 To the third it is necessary to say, with respect to the minor premise, that the truth of the sign is twofold. One is essential to the sign qua sign, and this truth is attributed to it by the act of signification. For when a sign signifies that which it must signify, whether this exists or not, the sign is true because it signifies that which it is made to signify. And this truth is essential to the sign and has no opposite if not by negation, since this truth is the essentiality itself of the sign. Being can only be opposed to non-being. Another truth is accidental to the sign, which is attributed to the sign in virtue of the thing signified, for example a sentence is said to be true not only because it signifies that which it is made to signify (and this is its essential truth), but when it signifies that what 25 Ps.-Kilwardby, Comm. sup. Prisc. mai., 1.1.1, ed. Fredborg et al., 3–4. The pseudo-Kilwardby speaks of imaginationes, which we take to be “images,” even though this is against the standard idea in the Middle Ages about the naturality of images (cf. Bacon’s typology, infra §7.2.2). 26 Cf. Maierù (1981), 57–59; Maierù (1999); Rosier-Catach (2004). 27 The English monk Bede the Venerable (672/3–735 CE) composed a treatise on the language of gestures: the De loquela per gestum digitorum, PL 90, col. 685–697. 28 Cf. Rosier-Catach (2004), 82–85 (with reference to Richard Fishacre and Bonaventure of Bagnoregio). 29 De veritate 2, ed. Schmitt, I, 179.

13th-Century Classifications of Signs

365

is is and that what is not is not, and this is accidental truth to which one opposes falsity as a contrary or as a privation. With regard to this kind of truth and of the falsity that is opposed to it, some signs are true and some other false. But there is never a science of false signs in as much as they are false, but in as much as they are signs, and in this manner essential truth is attributed to them.30 As far as essential truth is concerned, there are no false or empty signs: a sign that is devoid of essential truth is a non-sign, which is negatively opposed to the sign just like what exists is negatively opposed to what does not exist. A sign qua sign must be significant, if its essential truth is considered. There can therefore be a science of contingently false signs; not qua false, however, but qua signs which, independently of their contingent falsity, are essentially true, i.e., are significant (whether by nature or by convention). The reply to (ii) involves the distinction between the act of signification and the cognitive effect (or judgment) generated in the knowing subject (or recipient). The argument is parallel to that about essential truth. Signs are infallible in as much as they always signify that which they are made to signify, for otherwise they would not be signs. However, the cognitive habit that they generate

30 Ps.-Kilwardby, Comm. sup. Prisc. mai., 1.1.1, ed. Fredborg et al., 5: “Ad tertium dicendum respiciendo ad minorem quod duplex est veritas signi. Quaedam est essentialis signo in quantum signum est, et haec veritas debetur ei ab actu significandi. Cum enim significat signum id quod debet significare sive id sit sive non sit, verum est signum quia significat illud quod natum est significare. Et haec veritas est signi essentialis et non habet oppositum nisi per negationem, quia haec veritas est signi ipsius essentialitas. Enti autem non opponitur nisi non ens. Alia est veritas signi accidentalis quae debetur signo ratione rei significatae, verbi gratia oratio dicitur vera non solum quia significet id quod nata est significare, et haec est veritas essentialis, sed quando significat quod est esse et quod non est non esse, et haec veritas est accidentalis cui opponitur falsitas contrarie vel privative. Et loquendo de tali veritate et falsitate sibi opposita, signorum quaedam sunt vera, quaedam falsa. Sed numquam est scientia de signis falsis in quantum falsa sunt, sed in quantum signa sunt, et hoc modo debetur eis veritas essentialis.” An alternative solution is offered which allows the possibility that one and the same discipline might know what is true and what is false, the former as an aim to pursue and the latter as an obstacle to avoid: “Vel potest dici aliter quod scientia potest esse alicuius dupliciter, aut sicut subiecti, et sic non entis et falsi non est scientia, vel sicut oppositi subiecto et sic tam non entis quam falsi potest esse scientia. Oppositorum enim eadem est disciplina ut dicit Philosophus, unius tamquam eligendi et alterius tamquam fugiendi et sic tam verorum quam falsorum signorum potest esse scientia, sed verorum sicut subiecti, falsorum sicut oppositi” (Comm. sup. Prisc. mai., 1.1.1, ed. Fredborg et al., 5).

366

chapter 7

is not always science but can sometimes be somehow weaker, like opinion and imagination.31 The replies to (i) are multiple and theoretically substantial. The pseudoKilwardby indicates at least two distinct strategies to deal with this objection. According to the first strategy [1], the sign can be taken either [1.1] qua sign, and as such it is an object of the understanding to which—according to the Augustinian-like definition—it leaves something (aliquid derelinquit), or [1.2] according to its substance, and this is in turn twofold: either [1.2.1] according to its material and sensible being, and therefore as an individual and concrete token, or [1.2.2] as an universal that is abstracted from its realizations or tokens, and therefore as a type.32 The second strategy [2] follows an approach already in use in theology33 and claims that the Augustinian definition has to be corrected because it neglects that concepts are not sensible and yet are signs: being sensible is not an essential or definitional feature of signs anymore, and can sometimes be parenthesized.34 The latter strategy [2], as we shall see in the next section, is the one adopted by Roger Bacon. The first strategy [1] appears to be based upon a conception of the science of signs that is quite close to Hjelmslev’s “denotative semiotics,” i.e., a structure or language in which a system of expression is correlated to a 31 Ps.-Kilwardby, Comm. sup. Prisc. mai., 1.1.1, ed. Fredborg et al., 4: “Ad secundum dicendum quod minor duplex est eo quod signa possunt dupliciter considerari, uno modo quantum ad actum significandi et sic sunt infallibilia, eo quod semper significant ea quae nata sunt significare, aliter enim non essent signa. Alia modo possunt considerari quantum ad ea quae significantur per ipsa quantum ad actum iudicandi per ipsa, et sic quandoque sunt falsa et fallibilia, et habitus generatus per signa secundum quod huiusmodi non est habitus qui est scientia sed potius phantasia vel opinio.” On cognitive habits lower than science see supra, §§4.3, 6.1.1.1 and 6.2.1. 32 Ps.-Kilwardby, Comm. sup. Prisc. mai., 1.1.1, ed. Fredborg et al., 3: “Ad primum obiectum dicendum quod minor est duplex, quia signum potest dupliciter accipi. Uno modo sub ratione signi et est sic obiectum intellectus apud quem aliquid derelinquit, sicut habetur ex ultima parte definitionis signi superius positae. Alio modo secundum substantiam et hoc dupliciter, uno modo secundum esse materiale et sensibile et sub ratione qua est hic et nunc, et sic est sensibile, et hoc modo non est scientia de signis. Alio modo potest considerari signum sub ratione universalis abstracti a particularibus signis, et sic cum habeat rationem universalis potest esse scientia de signis.” The argument contains an allusion to a sign definition that is alternative to Augustine’s. This latter was quite known and widespread and, here as elsewhere, implicitly considered to be equivalent to that of the De doctrina christiana (about which see infra, §7.2.1). 33 Cf. Rosier-Catach (2004), 47; Marmo (2010), §1.2.2. 34 Ps.-Kilwardby, Comm. sup. Prisc. mai., 1.1.1, ed. Fredborg et al., 3: “Potest etiam dici quod ista definitio non est universaliter vera de quolibet signa quia passiones animi sunt signa rerum et tamen non ingerunt speciem suam sensibus.” Along similar lines, Bacon criticizes the common definition of the sign and offers his own; cf. infra, §7.2.1.

13th-Century Classifications of Signs

367

system of content, where the structure can be manifested in several distinct substances (both of expression and of content) and in which neither of the two planes is in its turn a semiotics (or a language).35 Physics as the science of bodies and motion or ethics as the science of right and wrong may be considered as denotative semiotics or languages. Now, the science of signs in the sense [1.1] is any discipline which can be expressed in a language and which has not language itself as its subject matter, since what it represents is the system of content or a portion of it. Solution [1.2] makes it explicit what assumptions a general semiotics, like that of Umberto Eco, makes about its object: (a) a sign is not a physical entity, the physical entity being at most the concrete occurrence of the expressive pertinent element; (b) a sign is not a fixed semiotic entity but rather the meeting ground for independent elements (coming from two different systems of two different planes and meeting on the basis of a coding correlation). Properly speaking there are no signs, but only sign-functions.36 Both (a) and (b), universality of the method of investigation and relational conception of the sign, are among the assumptions of Modistic semiotics and grammatical theory.37 As to the possibility of a general semiotics, the pseudo-Kilwardby’s solutions do not constitute an absolutely positive answer. Signs can certainly be the object of a science; not of one single science, though, but of multiple sciences each characterized by a distinct epistemological status; these special semiotics are not sciences in the higher and stronger sense

Figure 5 The classification of signs in the pseudo-Kilwardby

35 36 37

Cf. Hjelmslev (1961), 122. Eco (1975), 49. Cf. Marmo (1994), ch. 3; Marmo (2010), §5.2.

368

chapter 7

(­scientiae propter quid), but sciences that make use of demonstrations or ­syllogisms through signs (scientiae quia). A general semiotic, according to the pseudo-Kilwardby, only concerns the genus (signs), of which it merely provides a definition and a general taxonomy. 2 Roger Bacon’s De signis: A New Definition and Classification of Signs Thanks to its connections with theological debates, Bacon’s De signis (1267) takes another turn. The work cannot be properly defined as a logic treatise, even though it deals with many problems traditionally discussed in logical treatises and commentaries.38 It is actually a fragment of a larger encyclopedic work dedicated to Pope Clement IV (1265–1268) and written (in different and increasingly abridged versions) with the aim of raising awareness in the Pope about the most pressing problems of Christianity and the solutions proposed by its author. Roger Bacon was Master of Arts in Paris around the middle of the century and had produced works in grammar and logic, together with commentaries on several of Aristotle’s works in metaphysics and natural philosophy, notwithstanding the prohibition to do so that religious authorities had imposed in order to preserve the orthodoxy of the new institution.39 After his return to Oxford, Bacon entered the Franciscan Order, and this justifies his interest in the theological problems that are addressed in his De signis.40 The first part of the De signis contains both an analysis of the notion of sign which follows the tendency of theological discussions of the first half of the century in emphasizing its relational nature (§7.2.1), and a complete classification of signs (§7.2.2), which Bacon would modify in 1292, just before his death, in his Compendium studii theologiae. Among intentional signs or signa data Bacon includes a species of natural signs used by non-human animals. 38

39

40

In a resumé of this part of the Opus majus, the so-called Opus tertium, Bacon says that this treatise is a part of grammar that has not yet been composed in the Latin world (Opus Tertium, 27, ed. Brewer, 100: “Post haec addidi intentionem alterius partis grammaticae quae non est adhuc composita nec translata. [...] Et est de compositione linguarum et de impositione vocum ad significandum, et quomodo significant per impositionem et per alias vias.” See Denifle and Chatelain (1889), 78–79, for the letter by the papal legate Robert of Courçon that prohibits the teaching of Aristotle’s works in natural philosophy: “non legantur libri Aristotelis de methafisica et de naturali philosophia, nec summe de eisdem.” For an introduction to this work, see Rosier-Catach (2022).

13th-Century Classifications of Signs

369

The examination of this species of signs (§7.2.3) shows that not only human beings but also other animals make use of signs, and this in turn implies that non-human animals too, according to a tradition that originates with Avicenna, are capable of inference and reasoning. 2.1 The Relational Nature of Signs and the Pivotal Role of the Interpreter The pseudo-Kilwardby’s classification of signs is implicitly based on a dyadic conception of signification and on the traditional distinction between natural relations and mind-dependent relations, which correspond to natural and conventional signs, respectively. Bacon’s classification is based on different principles. In the first place, he uses the distinction between simple and double relations, which comes from the theological tradition of the commentaries on the Sentences of Peter Lombard.41 Simple relations are dyadic relations that hold between two relata, a terminus a quo and a terminus ad quem. The Dominican Richard Fishacre, in all probability the first to have made this ­distinction, illustrates the first member of this distinction by means of the participle positum and the verb lucere:42 positum involves the relation between the action (of posing) and the direct object of the action (the object posed), while lucere involves the relation between the action (of emanating light) and the source of the light as grammatical subject (which is implicit in intransitive verbs like lucere).43 By contrast, double relations are actually triadic. Fishacre’s examples in this case are the participle datum and the verb illuminare. Datum involves three terms, namely the object given, the subject who gives, and the person to whom something is given. In the terms of the medieval theory of relations, this is a double dyadic relation, composed of a first dyadic relation between the subject of the action and the direct object of the action, and a second dyadic relation between the subject of the action and the indirect object of the action, each relatum being expressed by a distinct grammatical case, i.e., nominative, accusative, and dative, respectively.44 The same analysis holds of illuminare, which involves an object enlightened, an object that sheds light, and a (somewhat implicit) subject that experiences the lightening (and can therefore see where he puts his feet, for example). According to Fishacre, the term “sign” involves precisely such a double dyadic relation between three 41 42 43 44

Cf. Rosier-Catach (1994), 112–122; (2004); Marmo (2010), chs. 1 and 4. Cf. Richard Fishacre, Commentum super Sententias IV, d. 1 (see infra, footnote 45 Fishacre does not explain these two examples, so the above explanation is our reconstruction. A double dyadic relation is in fact a triadic relation which is expressed as the combination of two dyadic relations.

370

chapter 7

terms: the object functioning as sign, that which it signifies, and the entity that receives and interprets the sign qua sign (which we may call the “interpreter” of the sign).45 Fishacre claims that the Augustinian definition of the sign46 is an explicit statement of this triadic structure: on the one hand we have the (dyadic) relation between sign and thing signified (corresponding to the part of the definition mentioning aliquid aliud), which we label “R1”; on the other hand, there is the relation between the sign and the interpreter (corresponding to faciens in cognitionem47 venire), which we label “R2.”48 Fishacre also adds that in natural signs R1 is essential while R2 is accidental: smoke is a sign of fire (which is its cause) even if nobody sees it or takes it as a sign. In conventional signs neither relation is prior to the other: conventional signs are made to signify something (R1) to someone (R2) and both are perpetual even if accidental.49 Bonaventure of Bagnoregio, a Franciscan theologian who taught in Paris in the 1240s, takes up and simplifies Fishacre’s distinction. He claims that the essential in every sign, whether natural or conventional, is the relation to what is signified by the sign (R1) and not to whom the sign appeals (R2): “as a consequence the circle above the tavern is always a sign, even if nobody sees it.”50 The debate about the doubly dyadic (or triadic) structure of signs forms the backdrop against which the incipit of Bacon’s De signis has to be placed: 45

46 47 48 49

50

Richard Fishacre, Comm. sup. Sent. IV, d. 1: “Sciendum quod hoc nome signum relativum est, et nominum relativorum quaedam significant unicam relationem, quaedam duplicem; unicam ut ‘positum’ (ponitur cod.), duplicem ut ‘datum,’ quod dicit relationem et ad dantem et ad accipientem. Similiter ‘lucere’ significat habitudinem unicam, scilicet ad lucentem, sed ‘illuminare’ duplicem. Sic signum, ut aestimo, si proprie accipiatur significat relationem unam ad significatum et aliam ad eum cui significat.” (The transcription of Joseph Goering quoted in Rosier-Catach 2004, 94 is slightly corrected here). De doctrina christiana II.1.1, ed. Martin, 32: “Signum est enim res, praeter speciem quam ingerit sensibus, aliquid aliud ex se faciens in cogitationem venire.” The term cognitio (“knowledge” or “cognition”) regularly substitutes cogitatio (“thought”) in Scholastic versions of Augustine’s definition. We follow Cesalli and Rosier-Catach (2018) here. Some relevant passage of Fishacre’s work can be read in Rosier (1994), 116–117 nn. 81–82; Rosier-Catach (2004), 94. Cf. also the commentary to the French translation of the De signis in Rosier-Catach et al. (2022). That a sign involves two dyadic relations amounts to its being a triadic relational structure. On this, thirteenth-century authors agree with Peirce; cf., e.g., Peirce (1932–1958), II, §274. For Peirce, however, a triadic relation cannot be reduced to a combination of dyadic relations. “Unde circulus super tabernam semper est signum, etiam si nullus aspiciat” (Bonaventure, Commentarius in quartum librum Sententiarum Petri Lombardi, d. 1, pars I, art. un., q. 2, ed. Collegium S. Bonaventurae, 15a). On the history of the example of the circulus vini, see Rosier-Catach (2020).

13th-Century Classifications of Signs

371

A sign stands in the category of relation and is spoken of essentially with respect to that [an interpreter] to which it signifies, because it [the interpreter] sets that [the sign] in act when the sign is in act, and in potentiality when it is in potentiality. Unless someone could conceive through a sign, it [the sign] would be useless and empty. Indeed, it would not even be a sign, but would remain a sign only in substance and would not have the essence of a sign, just as the substance of a father [i.e., a man] remains after his child is dead, but not the relationship of paternity. And even though there be a vocal sound or a circle for wine or something else actually imposed for something and instituted for it, so that it could represent and signify it to something else [an interpreter], nevertheless if there is nothing [no interpreter], to which it actually signifies, it is not actually a sign, but one only potentially.51 The prominence here given to the interpreter is a novelty in medieval semiotics. It has been observed that such prominence is not without consequences upon Bacon’s linguistic and semiotic doctrines; for example, his explanation of the semiotic functioning of the famous circulus vini differs from Bonaventure’s precisely in virtue of the emphasis on the role of the interpreter;52 another example is Bacon’s idea that words are continually and implicitly “re-imposed” by speakers, and according to him this is the hidden engine of the working of language.53 51

52 53

Roger Bacon, De signis I, §1, ed. Fredborg et al., 81–82: “Signum est in praedicamento relationis et dicitur essentialiter ad illud cui significat, quoniam illud ponit in actu cum ipsum signum sit in actu, et in potentia cum ipsum est in potentia. Quia nisi posset aliquis concipere per signum, cassum esset et vanum, immo non erit signum, sed maneret signum solum secundum substantiam signi et non esset in ratione signi, sicut substantia patris manet quando filius est mortuus et non relatio paternitatis. Et quamvis sit vox vel circulus vini vel aliud actu impositum [respectu] alicui et institutum eidem quatenus possit repraesentare et significare alii, tamen si non sit cui actu significetur non est signum in actu sed in potentia tantum.” Transl. Maloney, modified. It has to be noted that while the English and French translators assume the occurrence of illud in quoniam illud ponit in actu to refer to the interpreter as direct object of the verb ponit, we take it to refer to the sign, so that the sense of the utterance is the following: “whenever there is an interpreter of a given sign, then the sign is in act (illud ponit in actu), whenever there is no actual but only a potential interpreter, then the sign is in potentiality (in potentia).” On which see the comments on De signis I, §1 and §147, in Rosier-Catach et al. (2022), 261–265 and 375–379. Cf. Fredborg (1981b); Marmo (2010), §§6.1.1, 7.2; see also the comments on De signis IV.3, §§154–161 in Rosier-Catach et al. (2022), 381–390, in part. 387, where it is oberved that the pseudo-Kilwardby is an earlier model (Comm. sup. Prisc. mai., 2.1.1a, 52; 2.1.1.b–4b, 60 and 63).

372

chapter 7

In De signis I, §2, Bacon discusses the traditional definition of the sign, somehow connected to the Augustinian definition, and offers his own. As mentioned, the Augustinian definition was already called into question by theologians. According to its traditional definition, a sign is a sensible and therefore concrete thing (with all the consequences for a possible scientia de signis discussed by the pseudo-Kilwardby) which cannot embrace those signs through which angels communicate (Fishacre) or those concepts that Aristotle calls “similitudes of the things” and which are the same for all (pseudo-Kilwardby). But while the problems of the traditional definition had not been sufficient for its dismissal, Bacon subjects it to radical criticism: A sign, moreover, is something that, once presented to a sensory faculty or an intellect, designates something to that intellect, because not every sign is offered to a sensory faculty, as the common description of sign would have it. One sort is presented to the intellect alone, as Aristotle bear witness, who says that the soul’s experiences (passiones) are signs of things. These experiences are the very habits and species of things existing within the intellect, and so they are presented to the intellect alone so as to represent things outside to the intellect.54 Bacon’s re-definition of the sign clearly distinguishes the two relations that constitute it: the relation to the thing signified (aliquid) (R1) and the relation to the mind of the interpreter (intellectui) (R2). Unlike in Bonaventure and the logico-semantic tradition of the treatises on suppositio, in Bacon the essential semiotic relation is that between sign and interpreter, not that between sign and object. Without an interpreter that receives and actualizes it, the sign remains a pure potentiality, just like of a father who survives his sons there remains only the substance but not the relation (paternitas) that makes of him a father in act.55 But the real novelty of Bacon’s definition is that ­allowance is explicitly made in it for signs that are only intelligible and 54

55

Roger Bacon, De signis I, §2, ed. Fredborg et al., 82: “Signum autem est illud quod oblatum sensui vel intellectui aliquid designat ipsi intellectui, quoniam non omne signum offertur sensui ut vulgata descriptio signi supponit, sed aliquod soli intellectui offertur, testante Aristotele, qui dicit passiones animae esse signa rerum quae passiones sunt habitus ipsi et species rerum existentes apud intellectum, et ideo soli intellectui offeruntur, ita ut repraesentant intellectui ipsas res extra.” Transl. Maloney. This is in agreement with Umberto Eco’s idea that a text (as a species of complex sign) “presupposes its addressee as a necessary condition not only of its actual communicative effectiveness, but also of its own significative potentiality” (Eco 1979, 52–53; our transl.); cf. also Marmo (2017), 116–118.

13th-Century Classifications of Signs

373

not sensible: concepts are signs but are not given to sense perception. Aristotle says that concepts (passiones animae) are images of the things. The same is true for Bacon, who takes concepts to be signs of the things in one of the manners of natural signs.56 To be precise, Bacon should have included in his definition of the sign also a reference to the estimative part of the brain, for in non-human animals this part has a similar function as intellect has in humans, i.e., it is what allows non-human animals of the same species to communicate with each other and to understand natural inferential signs.57 2.2 Bacon’s Sign Classification and Inferential Signs The main division of Bacon’s semiotic taxonomy is into natural signs and signs produced by an animated being with the aim of signifying something (signa ordinata or data ab anima).58 In this section we focus on the former, among which fall inferential signs; we return to the latter in the next section. This first main division of signs precisely corresponds to that made by Augustine in the De doctrina christiana II.1.1. In the Compendium studii theologiae, his latest work, Bacon claims to have originally made the distinction independently of Augustine and that recognition of Augustine’s priority only came later.59 The claim is hardly believable: at least as early as the Communia naturalium (begun around 1260)60 signs of the second species are called signa data,61 which is precisely the terminology used by Augustine, and they are opposed to the signa naturalia, like in the De doctrina christiana. Even if Bacon had no direct access to Augustine’s work, which in point of fact is never cited in the Communia naturalium, yet he must have had indirect access to it through the commentaries on the fourth book of the Sentences, like Bonaventure’s: the 56

See Marmo (2010), §4.2.2, for an analysis of this species of signs and the apories concerning them. 57 See infra, §7.2.3. 58 Roger Bacon, De signis I, §3, ed. Fredborg et al., 82: “Signorum autem quaedam sunt naturalia, quaedam ordinata ab anima ad significandum.” Cf. §8 for evidence that datum and ordinatum (ab anima) are used interchangeably. 59 Cf. Roger Bacon, Compendium studii theologiae II.1.25, ed. Maloney, 56: “Et, licet antequam vidi librum beati Augustini De doctrina christiana, cecidi per studium propriae inventionis in divisionem signorum, quam postea inveni in principio secundi libri De doctrina christiana, dico eius auctoritate, licet explico dicta eius ratione et exemplis, quod signum secundum est a natura vel datum ab anima.” 60 Cf. Hackett (1997), 22; Maloney (2013), 1 n. 2, correctly observes that the part on signs, too, is datable to the early 1260s. 61 Roger Bacon, Liber primus Communium naturalium Fratris Rogeri II.4.3, ed. Steele, I, 119: “Et per hanc viam patet notabilis divisio signorum, quoniam signum quoddam est datum ab anima, et quoddam est naturale.”

374

chapter 7

De signis certainly depends on the discussion therein contained about the essentiality of the relation of the sign to the object (R1) and to the interpreter (R2).62 Among natural signs, which are signs in virtue of their own essence and not in virtue of the intention of an animated being, Bacon distinguishes three classes of signs: (1) those that are inferentially connected to the thing signified; (2) those that have a likeness to the thing signified; (3) those that are effects of a cause.63 Here we focus on the first and third classes. The third class of signs, those that are effects of a cause, seems to contain an echo of late-ancient Greek interpretations of the Posterior Analytics. The only two examples that Bacon offers are also in Augustine, namely the footprint as the sign of an animal (vestigium est signum animalis) and the smoke as a sign of fire (fumus est signum ignis).64 The latter, it will be recalled, is often used by the Greek and Arabic commentators to illustrate the “semiotic demonstration” of the presence of fire from that of smoke. Bacon then makes an observation that somehow connects his taxonomical investigations to the question—which originates with APo A 2 and which constitutes the backdrop of subsequent discussions about demonstrations of a lower kind—of the status of those sciences that proceed from what is better known to us. Bacon says: For an effect, compared to its cause, is more taken to be a sign than vice versa, because an effect is better known to us, and a sign has to be better known to us than what is signified, because we come to a knowledge of what is signified by recognizing a sign.65 62 63

64 65

Pace Maloney (2013), 18–25 (with further references). See some further arguments in ­Rosier-Catach (2022), 81–83, and Rosier-Catach et al. (2022), 268–269. Roger Bacon, De signis I, §§4–6, ed. Fredborg et al., 82–83: “Naturalia autem dicuntur, quia ex essentia sua et non ex intentione animae signi rationem recipiunt. [§4] Et haec dividuntur in tria genera: primum est quando aliquid dicitur signum propter hoc quod < aliud > necessario vel probabiliter infert. […]. [§5] Secundus modus signi naturalis est quando non propter illationem aliquam significatur aliquid, sed propter conformitatem et configurationem unius rei ad aliud in partibus et proprietatibus […]. [§6] Tertium autem genus reperitur ut universaliter effectus respectu suae causae […]. Cf. Comm. natural. II.4.3, ed. Steele, I, 119–120; Comp. stud. theol. II.1.26–29, ed. Maloney, 56. (As we shall see, in this latter work Bacon reduces the three classes of natural signs to two by associating those that are effects either with the first or with the second class.) Roger Bacon, De signis I, §6, ed. Fredborg et al., 82. Roger Bacon, De signis I, §6, ed. Fredborg et al., 83: “Effectus enim magis ponitur esse signum respectu causae quam e converso, quoniam effectus magis est notus nobis et signum habet esse magis notum nobis quam significatum, quia per notitiam signi devenimus

13th-Century Classifications of Signs

375

Bacon specifies that an effect is a sign of its cause in as much as the former is better known than the cause. Signhood, one may say, is directly proportionate to knowability. This leaves open the possibility that causes too may be signs of their effects, if and in so far as they are better known than those effects. Since however effects are typically better known than their causes, they are more often signs of those causes than the other way around. This is in some agreement with Simon of Tournai but in disagreement with the commentaries on the logica nova and on Boethius’ Topics.66 Bacon also specifies that there is no inconvenience in the fact that the relations between cause and effect and between sign and thing signified are in the same objects. The difference between the two relations (cause-effect and sign-thing signified) is somewhat analogous to that which Fishacre sees in the participles positum and datum; the relation between cause and effect relates two elements independently of the fact that they are known (like positum/ponere, causatum/causare is a dyadic or bivalent verb); by contrast, the relation between sign and thing signified relates three elements, namely the sign, the thing signified, and the interpreter of the sign. A signum is a triadic relation obtained by coupling two dyadic relations (sign-thing signified and sign-interpreter): as Bacon remarks at the beginning of the fragment on signs we are considering, it is the second dyadic relation that is essential, for if there is no interpreter there can be no signification. On the contrary, there can be a causal relation without the presence of an observer. It has to be noticed that in the last work that Bacon devotes to signs, the Compendium studii theologiae, the third class of natural signs (3), those that are effects of their cause, is dropped. This happens in all probability because some of these signs can be classified with those of the first class (1), i.e., those that function by inference (the smoke as the sign of fire seems to fit this ­category quite well, but there is no mention of it in the Compendium), while others can be classified with those of the second class (2), i.e., those that are even partially similar to their object (the footprint being a case in point, because it is similar to a part of the impressor).67 in cognitionem significati.” Transl. Maloney, modified. We take habet esse magis notum quam significatum not as a qualification of the being (esse) of a sign in comparison to the being of the thing signified, but more simply as a common way of saying “a sign ought to be or has to be better known than the thing signified,” a circumlocution which is, by the way, quite common in English, too. Cf. the French translation in Rosier-Catach et al. (2022), 101. 66 Cf. supra, §§4.3, 5.3, 5.4, 6.2. 67 Roger Bacon, Comp. stud. theol. II.1.29, ed. Maloney, 56: “Secundus modus signi naturalis est quod repraesentat per configurationem et expressionem similitudinis, ut vestigia

376

chapter 7

Bacon’s analysis and illustration of the first class of natural signs (1), those that function inferentially, in both the De signis and the Compendium are highly interesting and deserve a detailed account. These signs are inferential in the sense of APr B 27, i.e., in the sense that they are premises of probable or necessary inferences. They can further be distinguished according as they signify something present, future, or past. This is also reminiscent of APr B 27, where signs are said to signify things that are, that have been, or that will be.68 We thus have six classes: 1.1.1 necessary signs of something present; 1.1.2 necessary signs of something future; 1.1.3 necessary signs of something past; 1.2.1 probable signs of something present; 1.2.2 probable signs of something future; 1.2.3 probable signs of something past. It is worth having a closer look at Bacon’s examples for each of these sub-classes, in order not only to determine their remote sources,69 but also to show that they are part of the more general debate about the cognitive value of signs and the epistemic status of the disciplines relying upon them. [1.1.1] Necessary signs of something present: a. “[...] to have large limbs in the case of an animal, e.g., a lion or another, is a sign of strength” (Si ergo attendamus rationem signi penes consequentiam et illationem necessariam, et hoc respectu praesentis, sic habere magnas extremitates in animali, ut in leone et alio, est signum fortitudinis).70 The example clearly derives from the physiognomic section of APr B 27 and the commentaries on it (Kilwardby and Albert the Great, in particular), as well as from the commentaries on the pseudo-Aristotelian Physiognomica.71 It is also found in the Secretum secretorum, to which Bacon seems to have been working in the decade following the composition of the Opus maius (and the De signis).72 rerum et imagines, et ea quae aliis sunt similia. Ut vestigium pedis in nive significat illud cuius est […].” Cf. Marmo (1997c), 144. 68 Cf. supra, §1.2. 69 This was done in Marmo (1997c), 145–146. 70 Roger Bacon, De signis I, §4, ed. Fredborg et al., 82; transl. Maloney. Cf. Comm. nat. II.4.3, ed. Steele, I, 120: “habere magnas extremitates [est signum] respectu presentis”; Opus tertium, 27, ed. Brewer, 100: “quaedam sunt per concomitantiam signatorum, ut habere magnas extremitates, est signum fortitudinis”; Comp. stud. theol. II.1.27, ed. Maloney, 56: “Signum vero quod repraesentat signatum per illationem seu consequentiam naturalem et necessariam potest esse […] respectu praesentis, ut ‘Habet extremitates magnas; ergo est fortis.” 71 Cf. supra, §§1.5, 6.1.4. 72 Secretum secretorum IV.15, ed. Steele, 171 (“et earum [tibiarum] grossicies significat audaciam et fortitudinem.”). On the date of Bacon’s edition and commentary of the Secretum, cf. Williams (1997), esp. 372–373.

13th-Century Classifications of Signs

b.

c.

73 74 75 76 77 78

377

“and likewise the ability to teach is a sign that a person is knowledgeable” (et sic scientis est posse docere).73 The example comes from Aristotle’s Metaphysics (A 1, 981b7); it is used by some others74 and circulates in Aristotelian florilegia.75 “and the crow of a rooster, naturally moved to crow, is a sign of the hour of the night” (et cantus galli moti naturaliter ad cantandum est signum horae noctis).76 The example also occurs in Bacon’s Summule dialectices with a slight difference: the nominal phrase (cantus galli) is turned into an infinitive (gallum cantare), with the specification that the crow of the rooster (cantus galli) as such signifies nothing to us (it is a “significant voice” only for his conspecifics); it is rather the fact that the rooster is crowing (gallum cantare) that signifies something to us, i.e., that it is a certain time (of the night), just like a red sky in the morning signifies rain.77 The example and its accompanying remarks might be connected to what Albert the Great says about animals in the eighth book of his De animalibus. Albert observes, like he had done in the De homine, that before raining ants gather in their anthill and thus may be taken to “foresee” future events. The De homine specifies that the ants cannot be said to “feel” or “know” the forthcoming rain from its causes (for this can happen only thanks to reason); but that they so act is caused by a purely mechanical process: when the elements are altered because of the forthcoming rain, the bodies of the ants are also subject to alteration, and move or stand accordingly per instinctum naturae; this gives us the appearance of an anticipation of future events.78 A similar “mechanism” explains, Roger Bacon, De signis I, §4, ed. Fredborg et al., 82; transl. Maloney. Cf. Comm. nat. II.4.3, ed. Steele, I, 120 (“et posse docere est signum scientis”). Cf., e.g., Thomas Aquinas, Summa theologiae IIa–IIae, q. 181, a. 3. Auctoritates Aristotelis, in Hamesse (1974), 1.8, 115. Roger Bacon, De signis I, §4, ed. Fredborg et al., 82; transl. Maloney. Cf. Comm. nat. II.4.3, ed. Steele, I, 120 (“et cantus galli est signum certe hore noctis”). Roger Bacon, Summ. dial. II.2.1.1, §23, ed. de Libera, 222: “Similiter cantus galli nihil proprie nobis significat tanquam vox significativa, sed gallum cantare significat nobis horas, sicut rubor in mane significat nobis pluviam.” Albert the Great, Lib. de animal. VIII.4.1, ed. Stadler, 627: “Deprehendunt autem formicae frigus et pluvias et ventos tempestatum: cuius signum est, quod ante ortum talium se ad casas recolligunt.” Cfr. De homine, ed. Anzulewicz and Söder, 316b–317a: “Et si obicitur quod quaedam bruta fugiunt futura et non praesentia tantum et praesignant aliquando futura, sicut formicae latentes in foraminibus praesignant futuram pluviam, dicendum quod hoc non fit ex aliqua apprehensione futuri, sed potius ex instictu naturae, ut dicit Avicenna [V.1, 75–76]. Cum enim immutantur elementa ad eandem futuram pluviam vel futuram serenitatem vel aliquid huiusmodi, immutantur corpora talium animalium, ex qua immutatione vel moventur vel quiescunt per instinctum naturae, et ex hoc habetur

378

chapter 7

according to Albert’s commentary on the Book of Job, the behaviour of the roosters that crow at certain hours of the night.79 This should also explain the link between the crowing of the rooster and the red sky at morning on the basis of some meteorological mechanism, which is perhaps the object of astrology.80 [1.1.2] Necessary signs of something future: “the dawn is a sign of sunrise” (Si vero respectu futuri, sic aurora est signum ortus solis).81 In the fifth part of the Opus maius, devoted to optics, Bacon explains the manner in which the sun that is about to rise produces auroral light: When the sun is close to rising, and this is when it is in the 18th degree of the circumference of its orbit below the horizon, according to the teaching of Ptolemy in the Almagest, then his rays touch the air that is closer to us and enter into the upper and lateral part of the terrestrial shadow; so, the illuminated air can produce a stronger species for the eyes that begin to see it; and the more it gets illuminated, the more it becomes visible.82 To this astronomical phenomenon (the apparent movement of the sun along a circular orbit) one should add the effect produced on the propagation of light

79

80 81 82

prognosticum aliquid de futuro.” This might echo the peculiar Themistian case of converting effects of the same cause, the better known of which points to the other; cf. supra, § 2.2. Albert the Great, Commentarii in Job, ed. Weiss, 455: “vel quis dedit gallo intelligentiam? [Job 38, 36] Intelligentiam vocat aestimationem, quam habet gallus de horis distinguendis; ad immutationem enim solis ab angulis caeli in mane, meridie, vespere, media nocte, et etiam ad mutationem aurae per dispositionem factam in aere cantat gallus, et etiam alia animalia, quae circa regimen suae vitae non sollicitantur, et ideo facile deprehendunt impressiones factas in corporibus suis vel a motu caeli vel a dispositione aeris et ad illas moventur ad vociferandum vel tacendum.” Thanks are due to Stefano Perfetti for the consultation on Albert the Great, that among other things has pointed to this text (about which see Perfetti 2018, 83 and 85). On the aestimativa see infra, §7.2.3. We return to this below. Roger Bacon, De signis I, §4, ed. Fredborg et al., 82; transl. Maloney. Cf. Comm. nat. II.4.3, ed. Steele, I, 120: “aurora est signum futuri ortus solis”; Comp. stud. theol. II.1.28, ed. ­Maloney, 56: “vel respectu futuri, ut ‘Aurora est signum ortus solis cito venturi’.” Roger Bacon, Opus maius V (De perspectiva), 2.3.1, ed. Bridges, II, 102: “quando sol appropinquat ad ortum, et hoc est quando est in decimo octavo gradu circuli suae depressionis sub horizonte, secundum quod Ptolemaeus docet in Almagesti, tunc radii ejus cadunt in aere propinquiori ad nos, et ingrediuntur summitatem umbrae et latera ejus, et sic potest aer illuminatus propinquior facere speciem fortiorem ad oculum, et incipit videre eum, et magis videtur secundum quod propinquior illustratur.”

13th-Century Classifications of Signs

379

by the density of the air that is closer to the observer, as shown in the Liber de crepusculis.83 The visibility of sunlight before the sunrise occurs not because of the reflection or division (fractio) of light in the clouds, but because of an accidental species of the light that is produced when the rays pass through the air thick with vapours and clouds, just as it happens to the sunbeam that enters in the house through a window and produces an accidental species that illuminates everything.84 Like in the preceding examples of the red sky at morning as a sign of rain and of the crowing of the rooster as indicating a certain hour of the night, here it is the astronomical dynamics and the mechanism of propagation of light that guarantees the necessity of the inference. [1.1.3] Necessary signs of something past: “to have a supply of milk for nourishing an infant is a sign of childbirth in a woman” (Si respectu praeteriti, sic habere lactis copiam ad nutriendum infantem est signum partus in muliere).85 We know that this example comes from APr B 27 and that it has a long history afterwards, being used in distinct domains (logic, dialectic, sophistry, and then rhetoric) and with different emphases on its cognitive import. This will be made explicit by Bacon at the end of his inventory of natural signs of the first class. [1.2.1] Probable signs of something present: a. “red dreams are sign of a choleric or sanguine temperament, dreams with water a phlegmatic temperament, black ones of a melancholic one” (respectu praesentis, sic somnia rubea sunt signa colerae vel sanguinis dominantis, aquatica fleumatis, nigra melancholiae).86 The example does not occur in the parallel sections of the Communia naturalium and of the Compendium studii theologiae. It is both in Avicenna’s Canon87 and in coeval medical treatises, like those of Arnald of

83

On the attribution of this work to Abu ‘Abd Allāh Muḥammad ibn Mu‘ādh al-Jayyāni (­Arabic mathematician who lived in Sourthern Spain in the eleventh century) rather than to Alhazen, cf. Sabra (1967). 84 Likely, Bacon is here referring to the refraction of light through a means that is thicker than the one from which the ray comes. 85 Roger Bacon, De signis I, §4, ed. Fredborg et al., 82; transl. Maloney. Cf. Comm. nat. II.4.3, ed. Steele, I, 119–120: “Primus modus signi naturalis est habere lac signum partus respectu prereriti.”; Comp. stud. theol. II.1.27, ed. Maloney, 56: “respectu praeteriti, ut ‘Habet lac, ergo peperit’.” 86 Roger Bacon, De signis I, §4, ed. Fredborg et al., 82; transl. Maloney, modified: the adjective aquatica in this context—especially as compared to its source, i.e., Avicenna’s Canon, see below—does not refer to the colour of the dreamt things but to the dreamt things themselves. 87 Avicenna, Canon medicinae I, fen. 2, doctr. 3, cap. 7 (De signis dominii cuiuslibet ­humorum).

380

chapter 7

Villanova.88 Avicenna uses these examples in the context of his treatment of the symptoms of excess of humours in bodily channels and of strength of the faculties.89 Among the several symptoms (whose list is provided, which includes the colour of the face and of the tongue, the presence of pimples and the feeling of heaviness in the eyes), there are dreams, their colours, and the kinds of objects dreamt: And the dreams which signify this are as when a man in his dreams sees red things and a lot of blood coming out of his body or swimming in blood and the like. The signs of dominant phlegm are unduly paleness and being soft […] And the dreams in which one sees waters and rivers, snow and rain, and cold: they all signify that . The signs of dominant choleric humour are the yellow tinge in skin and conjunctiva, bitter taste […] And dreams in which one sees fires and yellow flags, and things that are not yellow appear yellow, conflagration or hot bath or sun, and the like: they all signify that . The signs of dominant atrabilious humour are an emaciated body and the whole body dark […] And the terrifying dreams from fear of darkness and torture, and terrifying black things.90 88

Arnald of Villanova, Expositiones visionum que fiunt in somniis IV, 632: “Ut si phlegma abundaverit in corpore alicuius et in somno destillare incipiat per scapulas et per membra, talis se videt in somno per pluviam madefactum, licet in corpore bene disposito pluvia significet doctrinam ab aliquo vel impetrationem a Deo vel aliquo Domino: nubes etiam spiritum gravans caput, sapientiam designabit. Si vero cholera multum abundet in corpore incendia, stellae cadentes et corruscationes apparebunt; et si cum hoc grossus intercipiatur ventus, cum tonitru apparebit. Si vero melancholia abundet, apparent terribilia magna, comestio acetosorum, incubus, et consimilia huic proportionata humori. Si vero sanguis abundet, res rubeae cum aliquibus eorum, quae pertinent ad choleram, apparebunt.” 89 Avicenna, Canon medicinae I, fen. 2, doctr. 3, cap. 6: “humor etiam dominans cognoscitur per significationes ipsius quas nominabimus.” Transl. Gruner: “Which of the humours it is which is dominant in such cases is discerned by the signs which now follow.” There follows a list including dreams, their colors, and their objects as signs of the excess dominance of a given humours over the others. 90 Avicenna, Canon medicinae I, fen. 2, doctr. 3, cap. 7 (1490); transl. Gruner: “Et somnia que illud significant sicut quando homo in somniis res videt rubeas aut sanguinem multum ex suo corpore exire aut se in sanguinem natare aut hiis similia. Dominii vero phlegmati significationes sunt albedo in colore superflua et laxitas […] Et somnia in quibus videntur aque et flumina et niues et pluvie et frigus demonstrant illud. Significationes autem dominii cholere rubee sunt color et oculorum citrinitas et os amaritudo […] Et somnia in quibus videntur ignes et vexilla citrina et videre res que non sunt citrine citrinas et videre

13th-Century Classifications of Signs

b.

c.

d.

381

“Similarly, to be a mother is a sign of love [for her children]” (Sic esse matrem est signum dilectionis).91 This is one of the Boethian examples of locus a communiter accidentibus that we met in the Summe Metenses attributed to Nicholas of Paris.92 The link between dialectic and this locus is made explicit by Bacon at the end of De signis I, §4. “and to be flashy and too adorned is a sign of pride and lewdness” (et esse comptum et nimis ornatum est signum superbiae et lasciviae).93 The example does not occur in this formulation in the parallel section of the Compendium studii theologiae. It comes from Soph El 5 but is often used as one of the examples of locus communiter accidentibus, and is thus a connector of dialectic and sophistry.94 “and wandering too much by night is a sign of a robber” (et esse errabundum multum de nocte est signum latronis).95 As we know,96 the example of the thief does not occur in Soph El 5 but only in the Greek and Latin commentaries. Again, this is a sign of Bacon’s dependence on the earlier tradition, where logic (Prior Analytics), dialectic (Boethius’ De diff. top.) and sophistry (Sophistici Elenchi) are intertwined.

[1.2.2] Probable signs of something future: a) “then a red in the morning is a sign of rain the same day” (Si vero respectu futuri, sic rubedo in mane est signum pluviae eadem die);97

incensionem aut calorem balnei aut solis, aut hiis similia, significant illud. Dominii vero cholere nigre significationes sunt corporis macies et ut sit fuscus […] Et somnia terrorem facientia ex tenebris et cruciatu et rebus nigris et terroribus.” In Gruner’s translation, §500, the signs are shown in a table. 91 Roger Bacon, De signis I, §4, ed. Fredborg et al., 82; transl. Maloney. Cf. Comm. nat. II.4.3, ed. Steele, I, 120: “Secundum vero convenientiam probabilem […] respectu presentis esse matrem est signum dileccionis”; Comp. stud. theol. II.1.28, ed. Maloney, 56: “Si vero sit signum naturale per consequentiam probabilem, tunc potest esse […] respectu praesentis, ut ‘Est mater, ergo diligit’.” 92 Cf. supra, §6.2.1. 93 Roger Bacon, De signis I, §4, ed. Fredborg et al., 82; transl. Maloney. Cf. Comm. nat. II.4.3, ed. Steele, I, 120: “et esse errabundum de nocte est signum furis vel luxuriosi,” where the example is only alluded to by the term luxuriosus. 94 Cf. supra, §§6.2.1, 6.2.2. 95 Roger Bacon, De signis I, §4, ed. Fredborg et al., 82; transl. Maloney. Cf. Comm. nat. II.4.3, ed. Steele, I, 120: “et esse errabundum de nocte est signum furis vel luxuriosi.” 96 Cf. supra, §§2.7, 6.2.1, 6.2.2. 97 Roger Bacon, De signis I, §4, ed. Fredborg et al., 82; transl. Maloney. Cf. Comp. stud. theol. II.1.28, ed. Maloney, 56: “vel respectu futuri […] rubedo in mane est signum pluviae in illa die.”

382

chapter 7

b)

“and a red in the evening is a sign of fair wheather in the next day” (et rubedo in vespere est signum serenitatis in crastino).98 Both examples should come from meteorological treatises. Meteorology was regarded as a branch of astrology, on the model of Giles of Rome’s idea of a scientia navalis.99 [1.2.3] Probable signs of something past: “then for the ground to be wet is a sign of a past rain” (Si vero respectu praeteriti, sic terram esse madidam est signum pluviae praeteritae).100 This comes from Soph El 5, too, and in the earlier tradition of the De diff. topicis and of the logic textbooks it occurs as example of locus a communiter accidentibus.101 In the last sentence of De signis I, §4, the connection is explicitly made between the above examples [1.2] and the locus a communiter accidentibus: “Et secundum haec signa probabilia currit locus a communiter accidentibus. (“And the Topic from associated accidents runs in accord with these probable signs”).”102 It was observed in Marmo (1997c) that Bacon’s classification of inferential signs, along with the theory of connotation, may be considered as a development and an expansion of the discussions about probable inferences contained in the commentaries on Boethius’ De diff. top. and the logical treatises of the first half of the thirteenth century, like Peter of Spain’s Tractatus themselves. If connotation, which is a special mode of signification often used by theologians (according to Bacon’s claim in the Opus tertium and the Comp. stud. theol.103), is a case of natural inferential sign, then the range of application of this species of signs is indefinitely extended to anything that can be inferred from real relations; the inferences dealt with in the commentaries on the De diff. topicis, like the loci a toto and a parte, as well as the loci founded on natural relations, whether metalinguistically codified or not (e.g., species to genus, property to 98

Roger Bacon, De signis I, §4, ed. Fredborg et al., 83; transl. Maloney. Cf. Comm. nat. II.4.3, ed. Steele, I, 120: “et respectu futuri rubedo aeris vepertina est signum pluvie”; Comp. stud. theol. II.1.28, ed. Maloney, 56: “rubedo in sero est signum serenitatis in crastino.” 99 Cf. supra, §5.5. There was a Liber imbrium, attributed to Hermann of Carinthia (cf. Burnett 2004, 85 n. 2), of which there seems to be no trace in Bacon’s works, though. 100 Roger Bacon, De signis I, §4, ed. Fredborg et al., 83; transl. Maloney. Cf. Comm. nat. II.4.3, ed. Steele, I, 120: “Secundum vero convenientiam probabilem, terram esse madidam est signum pluvie preterite”; Comp. stud. theol. II.1.28, ed. Maloney, 56: “Si vero sit signum naturale per consequentiam probabilem, tunc potest esse respectu praeteriti, ut ‘Terra est madida, ergo pluit’.” 101 Cf. supra, §§6.2.1, 6.2.2. 102 Roger Bacon, De signis I, §4, ed. Fredborg et al., 83; transl. Maloney, modified. Cf. Comp. stud. theol. II.1.28, ed. Maloney, 56. 103 Opus tertium, 27, ed. Brewer, 101; Comp. stud. theol. II.3.66, ed. Maloney, 74.

13th-Century Classifications of Signs

383

species, relata of a relation, and so on), would thus fall in the scope of natural inferential signs: Next one should consider further that a name imposed for some thing outside a mind can signify at the same time many things outside a mind, and in philosophy these are called “things co-understood,” and among theologians “things connoted.” Every thing which accompanies the name of something by natural and necessary consequence is co-­understood and connoted in it, since otherwise would not necessarily accompany , as exemplified in “ a creature; therefore a Creator” […] And every proper attribute connotes its subject, as “ capable of laughing; therefore a human being.” And every universal connotes an indeterminate particular; an indeterminate particular and a determinate one connote a species; a species its genus; a related entity connotes the other of the correlatives […]. And such is the case with an unlimited number of others that they accompany others by natural consequence; therefore are connoted and co-­ understood through them and because of this a name will signify them.104 According to this passage, as well as to parallel passages in the De signis and in the Opus tertium,105 a word that has received an imposition with regard to 104 Roger Bacon, Comp. stud. theol. II.3.66, 74; ed. Maloney, 74–75, 78–79 (transl. slightly modified): “Deinde diligenter considerandum est ulterius quod nomen impositum alicui rei soli extra animam potest multa simul significare extra animam, et haec vocantur in philosophia ‘cointellecta,’ et apud theologos ‘connotata.’ Omne enim quod naturali et necessaria consequentia sequitur ad nomen alicuius, cointelligitur et connotatur in eo, quia aliter non sequeretur ad ipsum necessario, ut ‘Creatura; igitur Creator’ […]. Et omne accidens proprium connotat suum subiectum, ut ‘Risibile; ergo homo.’ Et omne universale connotat particulare vagum; et particulare vagum et signatum connotant speciem; et species genus; et relatum connotat alterum correlativorum […]. Et sic de infinitis aliis est quod naturali consequentia concomitantur alia; ergo connotantur et cointelliguntur per ea, quapropter nomen significabit ea.” It was observed in Marmo (1997c), 149, that while in the De signis (III.5, §103, ed. Fredborg et al., 116) Bacon acknowledges his debts to al-Ghazālī’s Logic (and to Avicenna which is the latter’s source), in the Compendium he rather points to the convergence between Arabic logic and Western theology. 105 De signis III.5, §102, ed. Fredborg et al., 116: “Sed alios modos analogiae inveniemus quando scilicet unica impositione facta sub uno actu significandi plura intelliguntur per vocem, quorum uni soli facta est impositio, et quia illud habet respectum [ad aliud aliquod] ad multa, habet vox comparationem ad omnia ea, non quia eis fiat impositio sed solum isti rei quae habet necessariam dependentiam ad illa, et significabit ad placitum cui rei imponitur, naturaliter autem et primo modo signi naturalis talia quae intelliguntur < per> primum significatum.” Cf. Opus tertium, 27, ed. Brewer, 101: “Et quando univoce

384

chapter 7

a thing existing outside the soul and which signifies that thing by convention, can signify many other things according to the first mode of natural signification (i.e., as a natural sign of the first species) without requiring a new imposition. This is possible precisely because anything is in relation with many others, with which it is coexistent. (The simultaneity of the terms is one of the essential requirements of real relations in the Aristotelian theory of relations.) Inferential signification can “map” real relations and be superimposed on them, as well as on causal relations. It is thus possible that a word that is uniquely imposed to signify one thing happens to co-signify naturally many other things that are in some relation with that thing conventionally signified. The signification relation that overlaps with and is superimposed on the natural relation (of causality, of part to whole, of membership, hierarchical order, etc.) may be represented in Table 2, where it is illustrated by the example of the father-son relation:106 Table 2  Significations and relations

1.1 signum 1.2 pater 2. |the father| 3.1 signum 3.2 si pater est 4. pater

repraesentat stat pro is in relation to infert ergo connotat

significatum |a man who has generated a son| |the son| significatum (connotatum) filius est filium

There is a substantial difference between signification [1.2] and signification [4]. The former rests upon an act of original imposition and concerns the relation (created by the intellect of the impositor) between a linguistic item and something existing outside the soul. By contrast, the latter concerns both the relation between language and world, and the relation between linguistic items: since someone is a father only when he actually has a son, the name that signifies his being a father leads the interpreter (always presupposed in any process of signification) to think of the son and to infer the existence of the l­ atter from the existence of the former, or—when all this finds a linguistic expression—to infer from an existential proposition about the father an existential proposition about the son [3.2]. Secondary signification (or connotation) is built upon

106

significat, et tamen simul multa significat, declaravi quod naturaliter et non ad placitum significat illa. Et illa sic significata naturaliter sint connotata apud theologos.” See Marmo (1997c), 149.

385

13th-Century Classifications of Signs

the real relation between one significatum (the object |father|) and the other (the object |son|) [2]. Inferential signification as well as the secondary relation of signification or connotation (i.e., the natural signification of the first species) may be expressed in multiple ways. Bacon expresses this relation in three different ways in three of his works (Table 3). The example is the Boethian one of a mother who loves her children: Table 3  Distinct expressions of secondary signification

Signum

Significatum

Modality

Bacon’s work

a.

dilectionis

metalinguistic

De signis

b.

esse matrem est signum si mater est,

diligit

Summule dialectices

c.

est mater,

ergo diligit

conditional proposition inference

Compendium studii theologiae

A natural inferential sign can be expressed (a) either by making explicit use of the term signum, so that the relation of coexistence (or any other natural relation) is semiotized, i.e., transformed into a semiotic relation; signum here takes on a metalinguistic sense, i.e., is a metalinguistic description of the dictum (object language); (b) or by a conditional form, in which the antecedent is a sign of the consequent; (c) or by an inferential form, in which the premise is a sign of the conclusion. These different ways are clearly considered as equivalent. However, if we consider Bacon’s definition of the sign, we can make a step further: expression (a) involves an interpreter (whether human or not; see the next section) capable of turning a natural relation into a cultural or cognitive relation, i.e., into a relation of signification.107 In Bacon’s semiotics natural signs are, among humans, prototypically the product of a lexicalization, i.e., of the linguistic expression of natural relations, or, among non-human animals, the result of a cognitive-inferential process which involves a peculiar faculty, the aestimativa. In conclusion, it is also necessary to notice that the sign is not simply reducible to an absolute thing (res absoluta), i.e., a substance, a quantity, or a quality, 107

This may perhaps also hold for the pseudo-Kilwardby’s distinction between convertible and non-convertible natural signs; see supra, §7.1.

386

chapter 7

but can also be a situation or state of things (such as esse multum errabundum) expressed by an infinitive dictum, in which case it would have a propositional structure and could be regarded as a distant and indirect heir of the stoic λεκτόν.108 2.3  The aestimativa: Intentional and Inferential Signs in Non-Human Animals According to Avicenna, the ability of non-human animals to “understand” advantageous and disadvantageous situations depends on a special power called “estimative” (al-wahm), which receives non-sensible forms (e.g., hostility or friendliness) and produces instinctive judgments. This power is discussed by Avicenna in several of his works devoted to the soul, its functions, and its internal organization. Estimative power is part of the sensitive soul of both human and non-human animals. By means of it Avicenna seeks to account for some peculiar aspects of animal behaviour and of some natural inclinations to form opinions in human beings:109 in particular, the appeal to estimative power plays a crucial role in the classification of premises in several of Avicenna’s logical works, in his discussion about the division of the sciences, in his religious and moral works (where it is claimed that estimative power may have noxious effects), in the explanation of animal apperception and other forms of self-consciousness, and in the theories about the making of fictional ideas and the epistemic dimension of ethical precepts.110 The existence of such internal sensitive power finds its justification in its own objects, according to the principle that for each kind of object there must be a distinct power or faculty adequate to it. So while the five external senses are deputed to perceive the forms or images of proper and common “sensibles,” non-sensible forms require a specific power: these are the so-called “intentions” (ma‘ānī, lit. “meanings”) that always go together with sensible forms but are not reducible to them. In general, the Arabic term ma‘ān indicates any object of a cognitive power (it might be what we call “lexical meaning,” or a form or image, or intelligible universal), and is far from clear why Avicenna uses the 108 109

110

On the problematic connections between dictum/dicibile and λεκτόν see Ebbesen (2007), 144–145, who in absence of a clear lineage of derivation of the former from the latter makes appeal to the notion of “parallel evolution” that is used in biology. On this see Black (1993); Black (2000), 59–62; Black (2005), 314–316; Kemp and Fletcher (1993); Pormann (2013) (for Avicenna’s medical works); Mousavian and Fink (2020). In a pioneering work on the topic (Wolfson 1935) the paternity of the notion was attributed to al-Fārābī; Black (2000), 69–70 n. 1, has shown that the works considered by Wolfson are spurious and later than Avicenna. Cf. Black (1993), 220. See also Sebti (2020), 103–112.

13th-Century Classifications of Signs

387

same term also for the forms that are the object of estimative power. Its Latin version (intentio) will have much success and will receive a peculiar interpretation. A definition of the non-sensible intentions that are the object of the estimative power is not provided; Avicenna rather resorts to examples that illustrate how behaviour is consequent upon estimation. So a sheep perceives the wolf’s hostility and the lamb’s friendliness, and this explains the sheep’s consequent and opposite behaviours in the two cases. Another example is the dog’s running away as soon as he sees a stick in a man’s hand.111 Notwithstanding the criticisms of al-Ghazālī and Averroes, Avicenna’s theory of the articulation of internal senses and the inferential ability of non-­human animals is generally accepted in the Latin West, especially in c­ onsequence of the translation of the so-called Liber sextus de naturalibus or Avicenna’s De anima112 and of parts of the Kitāb al-Šifā’ (especially the section on animals which Michael Scot had translated in 1232 and which circulated along with the translation of Aristotle’s De animalibus).113 In several passages of his works, Bacon deals with the articulation of internal sense; he specifies its role in the perceptual process and bases on it a genuine theory of animal intelligence. Besides Aristotle, his main sources are not only Avicenna and Averroes, but also Alhazen (Ḥasan ibn al-Haytham, ca. 965–ca. 1040) and Alkindi (Abu Yūsuf Yaʻqūb ibn ʼIsḥāq aṣ-Ṣabbāḥ al-Kindī, ca. 801–873), whose optical investigations were of fundamental importance, as well as Robert Grosseteste’s works on light (which contain several references to the latter).114 Bacon takes from Avicenna the organization and the localization of internal senses in human beings (common sense, imagination, estimative power, cognitive power, and 111 Avicenna, Kitāb al-Najāh (Book of Salvation), II.6, ed. Fakhry, 200–202 (Engl. transl. Rahman, 30–31); Kitāb al-Šifā’ (Book of the Cure), IV.1, ed. Rahman, c165–167. One can read the Latin translation in Avicenna Latinus, Liber de anima seu sextus de naturalibus, ed. Van Riet, IV.1, 2 (the dog and the stick) and 6–8 (the lamb and the wolf); Al-Išārāt wa-al-tanbīhāt, ed. Forget (Engl. transl. Inati, 125); further references in Black (1993); Black (2000). 112 On which see the introduction to the edition in Van Riet (1972), 91*–105*, and D’Alverny (1982), 444–446, 451 (now in D’Alverny 1994, VII, with identical pagination). 113 Cf. D’Alverny (1982), 455–457 (= D’Alverny 1994, VII). On the translation of several parts of the Kitāb al-Šifā’ in the twelfth century, see D’Alverny (1952). 114 On animal rationality, see Oelze (2019). For a summary of Avicenna’s contribution, al-Ghazālī’s and Averroes’ criticisms, and their reception in Latin authors, esp. Albert the Great and Aquinas, see Marmo (2020), with further references, to which we should add Di Martino (2008) and Toivanen (2020) on the social function of estimative power. On Alhazen in particular, see Sabra (1978); and on his contribution to geometrical optics, see Lindberg (1976). On the connection between Bacon and Robert of Grosseteste, see ­Lindberg (1983a), xlix-lvi, and Tachau (1988), 7.

388

chapter 7

memory), but combines these with the virtus distinctiva, which for Alhazen is the fundamental element in the elaboration of perceptual data (intentiones) and which is placed in the final part of the sensitive soul (ultimum sentiens).115 According to Alhazen, this power governs two of the three kinds of sensible knowledge that are identified in his treatise on optics (translated into Latin between the end of the twelfth and the beginning of the thirteenth centuries116 with the title of De aspectibus or Perspectiva).117 1. The first kind occurs when sight perceives colours and light and is thus limited to the perception of proper sensibles, through the power of the sense organ alone (solo sensu).118 2. The second kind occurs when sight perceives two objects of similar shape: the similarity or difference between two shapes, in the same or in distinct individuals, cannot be perceived through the sense organs alone but requires some comparison; when for example one perceives the transparency of a stone that is between our eyes and a source of light, our eye is not powerful enough and must resort to an inferential process (non est comprehensio solo sensu, sed est comprehensio per rationem) that compares different sensible data.119 3. The third kind occurs in the cases of recognition (ma’rifa), which involves memory and takes place in an imperceptible lapse of time: perceptual inferences of the second kind, when repeated in time and accumulated, become cases of recognition; the premises of such inferences are so wellknown that can be taken for granted, so that the inferential process is instantaneous and the perception of the conclusion immediate.120

115 116 117

118 119

120

Roger Bacon, De multiplicatione specierum I.2, ed. Lindberg, 36. Cf. Sabra (1989), lxxiii-iv. A critical edition of the Latin translation has not yet been published. We consulted the edition of 1572 (Opticae thesaurus). It has been regularly observed that the Latin text does not always correspond to the original Arabic, which we consulted in the English translation by Sabra (1989). Ibn al-Haytam, Optics II.3.1; Engl. transl. Sabra, 126; Opticae thesaurus II.3, 30. Ibn al-Haytam, Optics II.3.2-14; Engl. transl. Sabra, 126–128 (“[this] is not a perception by pure sensation, but rather a perception by inference”: the Latin term ratio should not in this context be taken as “reason” but as “argumentation”: slightly later the translator uses the hendiadys “by judgement (al-tamyīz) and inference (qiyās),” rendered in Latin as distinctione et ratione); Opticae thesaurus II.3, 30. Ibn al-Haytam, Optics II.3.18-31; Engl. transl. Sabra, 128–133. The Latin translation renders the perception through recognition by the expression per cognitionem (Opticae thesaurus II.3, 30-32). The link with signs is quite interesting, and may allude to the doctrine of signs of APr B 27.

13th-Century Classifications of Signs

389

Alhazen does not deal with non-human animals. His examples are all about humans: the recognition of written language in reading, the children who picks out the most enjoyable or most beautiful of two objects that have been offered to him. One is thus led to think121 that the sensible perception that is based on inference or recognition rests on some activity of reason, which is latent in the reader and in the child (who is however predisposed to exercise it). One could thus think that for Alhazen the whole of these perceptual modalities is proper to human beings, and that non-human animals, at least those endowed with memory, can exercise only the first and the third. As we shall see in a moment, Bacon goes much farther than this: he straightforwardly identifies Alhazen’s virtus distinctiva with Avicenna’s cogitativa, and attributes to it the capacity to judge about accidental sensibles by means of estimative power and memory.122 He then credits non-human animals (of which he makes several examples) with a genuine power of inferential perception. Such inferential perception is instinctive and natural, and yet according to Bacon the animals’ ability to communicate is based on it. Alhazen’s optics constitutes the model of Bacon’s theory of the multiplication of the species, which is a general theory of causality of natural agents: species is defined as “the first effect of anything acting according to nature.”123 A species is the image of its own cause, to which it is similar by nature, and therefore belongs to the second class of natural signs.124 As such it is called either imago and similitudo, or idolum—mirror image—or fantasma and simulacrum—dreamt object.125 As a natural image, the species has a lower ontological status than its cause (in this sense, it is also called intentio). Bacon 121 122

123 124

125

Cf. Federici Vescovini (2005), 84. Roger Bacon, De multiplicatione specierum I.2, ed. Lindberg, 36–38: “virtus distinctiva, que est cogitativa, cuius esse est in media cellula cerebri, iudicat de hiis sensibilibus, tam propriis quam communibus, mediante sensu communi et particulari, qui solum de p ­ artibus anime sensitive vocantur a vulgo nomine sensus, et quia de sensibilibus per accidens eadem cogitativa iudicat mediante estimatione et memoria et non mediante sensu communi et particulari.” Roger Bacon, De multiplicatione specierum I.1, ed. Lindberg, 2: “Species autem non sumitur hic pro quinto universali apud Porphyrium, sed transumitur hoc nomen ad designandum primum effectum cuiuslibet agentis naturaliter.” Roger Bacon, De signis I, §6, ed. Fredborg et al., 83: “Secundus modus signi naturalis est quando non propter illationem aliquam significatur aliquid, sed propter conformitatem et configurationem unius rei ad aliud in partibus et proprietatibus, ut imagines et picturae et similitudines et similia et species colorum et saporum et sonorum et omnium rerum tam substantiarum quam accidentium, quoniam omnia haec sunt configurata et conformata aliis.” Cf. Comm. nat. II.4.3, ed. Steele, I, 120; Comp. stud. theol. II.1.29, ed. Maloney, 56. Roger Bacon, De multiplicatione specierum I.1, ed. Lindberg, 4.

390

chapter 7

specifies that this should not mislead us into thinking that then the species has a merely spiritual being in opposition to corporeal beings, as maintained by several coeval authors (among whom Aquinas) who somehow thereby misinterpret the doctrines of Averroes. By contrast, as Bacon claims in several passages, what is meant is that species have no sensible nature, i.e., they are not grasped by any of the senses, nor are they perceived as such, and are therefore closer to spiritual entities: but they are corporeal, because they are the effects of corporeal things.126 Alhazen is again the source of Bacon’s answer to the question as to which objects produce species which might explain the working of sensible knowledge in man and non-human animals. Bacon’s answer is that “proper sensibles” can produce them. But while Alhazen’s concerns were limited to optics and therefore to light and colors (as the sensibles that are proper to sight), Bacon, without departing from the model of light irradiation, yet extends to all proper sensibles the power to produce effects-species in the means (in medio), which are then propagated like light.127 The consequences of Bacon’s doctrine are the following. i. Common sensibles are unable to produce species; among them Bacon includes the remaining twenty intentiones which Alhazen lists among the aspects of things that are grasped by sight, namely: distance and position, solidity, shape, size, separation, continuity, number, motion, rest, roughness, softness, opacity, shadow, obscurity, beauty, ugliness.128 Only light and colors are grasped in virtue of sensation alone (type 1); the remaining aspects only through comparison and inference from light and colors (type 2). ii. This may cause some problems for Bacon’s identification of the virtus distinctiva with the virtus cogitativa. For Avicenna allows the common sense to compose and divide sensible intentions (proper and common) into global sensible images of the object perceived. But the aestimativa or the cogitativa are not yet at work at this stage, as they are of a higher order and are introduced precisely for the perception and elaboration of non-sensible intentions, like the relations of usefullness/uselessness and friendliness/hostility, and not even in this case do they operate inferentially according to Avicenna. By contrast, for Alhazen common sensibles 126

Roger Bacon, Opus majus V.1, d. 6.3–4, ed. Bridges, II, 40–45; De multiplicatione specierum III.2, ed. Lindberg, 192. Cf. Lindberg (1983), lxvii. 127 Cf. Roger Bacon, Opus majus V.1, d. 1.3, ed. Bridges, II, 6. 128 Ibn al-Haytam, Optics II.3.44; Engl. transl. Sabra, 138 (Opticae thesaurus II.3, 34). Cfr. Roger Bacon, Opus majus V.1, d. 1.3, ed. Bridges, II, 6; De multiplicatione specierum I.2, ed. ­Lindberg, 40.

13th-Century Classifications of Signs

391

derive from proper sensibles (of sight) in virtue of the inferential work of the virtus distinctiva. Bacon seems not to grasp the difference between these two positions. iii. According to Bacon, relations, like common sensibles and the last six categories, do not produce species, namely effects that influence perception:129 in this case the distance from Avicenna is even greater, for according to the latter, estimation is specialized in grasping relations as non-sensible intentiones. iv. If, however, relations (friendliness/hostility) are not productive of species that multiply in the means and along the nerves up to the brain, how can the sheep perceive the hostility of the wolf and run away? Bacon’s answer resumes some elements that are already in Albert the Great,130 and collocates them into the completely new framework of the multiplication of species. Besides proper sensibles, substances too are capable of producing effects, i.e., species that multiply in the means and are transferred along with the species of proper sensibles, but are grasped by estimative power only: substance produces a sensible species, not however by the five external senses or by the common sense. Yet can be had by the cogitative and the estimative by which the sheep feels the species of the complexion of the wolf that corrupts and damages the organ of the estimative; and, therefore, runs away from the wolf at its first sight, even if it has never seen a wolf. And this is the species of a noxious substance and hostile to the sheep; and by contrast, the substance of the friendly and useful substance of another sheep strengthens the organ of the estimative, and so a sheep does not run away from another.131

129 130 131

Roger Bacon, De multiplicatione specierum I.2, ed. Lindberg, 40. Cf. Marmo (2020), 88–94. For an account of this problem in Aquinas and Gregory of Rimini, see Perler (2012). Roger Bacon, De multiplicatione specierum I.2, ed. Lindberg, 24: “substantia facit speciem sensibilem, non tamen a sensibus exterioribus quinque nec a sensu communi. Sed tamen haberi potest a cogitatione et estimatione quibus ovis sentit speciem complexionis lupi inficientem et ledentem organum estimative; et ideo fugit lupum primo aspectu, licet numquam prius viderit eum. Et hec est species substantie nocive et inimice ipsi ovi; et econtrario species substantie amice et convenienti alterius ovis comfortat organum estimative, et ideo non fugit una ovis aliam.” Cf. Opus majus V.1, d. 1.4, ed. Bridges, II, 7–8; Comm. nat. I.2.1, ed. Steele, I, 17.

392

chapter 7

What is implicit here, but will be made explicit later, is that substances or substantial forms can have contrary substances and forms, and so can act upon and harm one another.132 In the Opus majus, Bacon calls Alhazen’s distinction between the three kinds of vision (solo sensu, scientia et syllogismo)133 into question. In particular, he wonders whether or not inferential capacities derive from reason (anima intellectiva et rationalis) and therefore belong exclusively to human beings. His answer is negative, and is supported by several examples illustrating the behaviour of an animal which presupposes both the use of memory (connected to recognition—ma’rifa in Arabic—rendered in Latin by scientia or cognitio) and the application of inferential processes (qiyās, here rendered by syllogismus). The dog recognizes the face of a man already seen; monkeys and other animals can distinguish not only the objects of different kinds, but also individuals of the same kind: they can discriminate and categorize, we might say. Since they are able to grasp common sensibles like motion and rest through sight, brute animals are able to “reason”: the dog that sees a stick in the hands of a man runs away to avoid being beaten; predatory animals lurk when the prey is still, and chase it when it runs away. As Alhazen had observed (regarding children), this kind of inference involves neither the ability to form syllogisms according to the figures and the modes, nor that of distinguishing the premises from the conclusion, as these latter abilities (together with metalinguistic and metacognitive awareness) are the privilege of rational souls.134 Non-human animals rather possess a certain ability to gather into unity a plurality of data (collatio plurium ad unum) thanks to a natural instinct (quadam industria naturali et instinctu naturae) that is not preceded by deliberation (sine deliberatione), a process in which the plurality is the premise and the unity the conclusion: And it is so in infinite , in which brute animals think many things ordered with regard to one thing to which they tend, as if they argued in themselves a conclusion from premises. But they do not ­dispose the process of their thinking according to the moods and the figures , nor do they deliberately distinguish the latter 132 133 134

Roger Bacon, De multiplicatione specierum I.2, ed. Lindberg, 26–28 (with reference to ­ ristotle’s De generatione et corruptione, where Bacon also clarifies that the point of view A adopted here is not that of logic, according to which substances have no contraries). Cf. Tachau (1993), 660. Cfr. Roger Bacon, Opus majus V.2, d. 3.8, ed. Bridges, II, 127–129; cf. Opus majus V.1, d. 1.4, ed. Bridges, II, 9.

13th-Century Classifications of Signs

393

from the former. And neither are they aware they are making this kind of discourse, since their thinking proceeds only from intuition and natural instinct.135 Bacon uses the same terminology in the De signis, when he explains the workings of the voces that non-human animals exchange in communication: these sounds are signa data (intentional signs) just as human words, but unlike human words they are significative not thanks to will (or ad placitum) but without the deliberation of reason and without a choice of the will, neither at our pleasure nor for a purpose, but rather suddenly, without no noticeable time lag, by a kind of natural instinct and impulse due to the nature and power of an agent acting naturally.136 Similar distinctions are made in the Communia naturalium, where Bacon says that “anything acting without the deliberation of reason and without the choice of will is called a natural agent because it acts upon natural instinct.”137 Human beings, too, which are substantiae rationales, perform several actions in this way, and with respect to these actions they can be said to act according to nature. Some of their actions take place without the intervention of the apprehensive power, like those that concern the preservation of the individual or of the species, e.g., eating and procreating. Other actions take place with some form of apprehension and of inclination of the will: if they are carried out through a conscious choice, then they cannot be said to be natural. In the De signis Bacon classes conventional intentional (data) signs under this heading, whether they are sounds produced by humans (like words) or are objects

135

136

137

Roger Bacon, Opus majus V.2, d. 3.8, ed. Bridges, II, 129: “Et sic est de infinitis, in quibus bruta animalia cogitant multa per ordinem respectu unius rei quam intendunt, ac si arguerent apud se conclusionem ex praemissis. Sed decursum suae cogitationis non disponunt in modo et figura, nec ex deliberatione distinguunt ultima a primis. Nec percipiunt se huiusmodi discursum facere, quia ex solo intuitu et instinctu naturali decurrit cogitatio eorum.” Roger Bacon, De signis I, §8, ed Fredborg et al., 83: “sine deliberatione rationis et sine electione voluntatis, nec ad placitum, nec ex proposito sed quasi subito per privationem temporis sensibilis et quodam instinctu naturali et impetu naturae et virtutis naturaliter agentis.” Transl. Maloney. Roger Bacon, Comm. nat. II.4.1, ed. Steele, I, 108: “omne agens sine deliberatione racionis et sine eleccione voluntatis dicitur agens naturale, quia instinctu naturali agit.”

394

chapter 7

shown in shops for commercial purposes.138 Still other actions are realized without any choice; they are “natural,” too, but in a different sense: nature is said in two senses: in a general sense, in so far as it is a force acting without the deliberation of reason and the choice of the will; in a more specific and restricted sense, in so far as it is a force acting in opposition to the soul; so is intended by Aristotle in the second book of the De anima; but in the second book of the Physics it is intended in the first sense.139 In De signis I, §§12–14,140 Bacon applies this distinction to the one between natural signs (of the three classes) and intentional signs that function naturally: in the former, nature is identified with the susbtance or essence of things themselves (as opposed to the soul) which allow to infer something (first class), to represent something by similarity (second class), or to determine the cause from the effect (third class). In the latter, nature is intended as a force acting without deliberation and is a principle of motion and rest (with reference to Phys B 1, 192b8–11). Intermediate between these signs are interjections, which on the one hand are among the parts of speech and thus are conventional, but on the other hand are motivated by passions that lead man to act instinctively.141 Among intentional signs that function naturally (in the second sense) Bacon includes the sounds that animals exchange in communication: animal communication, too, is a consequence of the very same force that, on the one hand, leads brute animals to make things that resemble those produced by human intelligence (the net woven by spiders, the hexagonal cells of honeycombs

138

139

140 141

Roger Bacon, De signis I, §7, ed. Fredborg et al., 83: “Signum vero ordinatum ab anima et ex intentione animae recipiens rationem signi est duplex: Unum sit ab anima cum deliberatione rationis et electione voluntatis, sive ad placitum, sive ex proposito, et huiusmodi est signum institutum ab intellectu ut linguae et idiomata et circulus vini et res expositae venditionis in fenestris venditorum positae pro signis, non solum ad repraesentandum alia, sed se ipsa, ut panis in fenestra et cetera comestibilia, et similiter arma et lorae et sellae et omnes res huiusmodi quae in signum venditionis exponuntur secundum omnem diversitatem artificum et artium mechanicarum.” Roger Bacon, Comm. nat. II.4.1, ed. Steele, I, 111: “natura dicitur duobus modis: uno modo generaliter, ut est virtus operans sine deliberatione racionis et eleccione voluntatis; aliter specialiter dicitur et [di]stricte, ut est virtus operans divisa contra animam, sic accipit Aristoteles, secundo De anima; set secundo Physicorum accipit priori modo.” Ed. Fredborg et al., 85–86. Roger Bacon, De signis I, §11, ed. Fredborg et al., 84; Comm. nat. II.4.1, ed. Steele, I, 110–111. On interjections cf. Rosier-Catach (1992) and (1994), ch. 2.

13th-Century Classifications of Signs

395

made by bees, nests built by swallows);142 on the other hand, the same force allows brute animals to interpret natural signs according to a judgment power (estimative power) that is typical of non-human animals. 3 Conclusion In the classifications of signs of the thirteenth century we see traces of the Greek-Arabic idea of semiotic demonstration. We examined two important examples of thirteenth-century sign taxonomies. In the pseudo-Kilwardby’s commentary on Priscian the problem of a classification of signs is closely connected with that about the possibility of a science of signs. Signs are either natural or conventional, according to a distinction between natural and mind-dependent relations that is usually linked to the Aristotelian-Boethian tradition of the De interpretatione and the commentaries on it. The influence of the tradition of the Posterior Analytics becomes visible in the ­pseudo-Kilwardby’s treatment of natural signs: a sign in this sense is the effect of a cause from which the latter can be inferred. Natural signs may be convertible or non-convertible with the thing they signify, and may be physical or moral. Unlike conventional signs, natural signs are inferential signs: the model is that of the demonstratio quia in which the cause is inferred from the effect. The first of the two passages of the Posterior Analytics in which sign-inferences are mentioned (APo A 6) is explicitly cited by the pseudo-Kilwardby in support of the identification of the demonstrationes per effectum with the syllogismi per signa. Unlike the pseudo-Kilwardby, Roger Bacon adopts the Augustinian distinction between signa naturalia and signa data, but like the pseudo-Kilwardby’s, Bacon’s taxonomy of natural signs contains echoes of the Greek-Arabic doctrine of semiotic demonstrations. Bacon’s natural signs are either grounds of probable or necessary inferences, likenesses of an object, or effects of a cause. An effect is a sign because it is better known than its cause. Being better known than its cause, the effect is the ground for inferring that cause; the third class overlaps with the first (and is accordingly omitted in Bacon’s later account). The first class of signs, inferential signs, is implicitly modeled after APr B 27: signs are either probable or necessary (i.e., σημεῖα in the strict sense or τεκμήρια), and related to the present, the past, or the future. Probable signs are explicitly associated with the locus a communiter accidentibus of the Boethian 142

Roger Bacon, De signis I, §12, ed. Fredborg et al., 85; Comm. nat. II.4.1, ed. Steele, I, 111.

396

chapter 7

tradition and exemplified by inferences taken from Soph El 5, thus confirming the close connection between Bacon’s semiotic endeavour and the tradition of commentaries and textbooks that we examined in the previous Chapters. In the sign taxonomies of Bacon, the Aristotelian notion of sign (premise of an argument) and its late-ancient reconstruction (premise of a demonstration from the effect to the cause) becomes one kind of signs among others within the Augustinian general distinction between natural and intentional signs. Signs in the Aristotelian sense are natural signs; linguistic signs are not inferential in themselves, but can naturally infer (i.e., connote) whatever their signified things are linked to. Furthermore, in Bacon, as language can also metalinguistically express inferential relations: “natural” signs in the Aristotelian sense (premises of arguments, grounds of inference and demonstration) are codified by “conventional signs” (words and sentences). Inferential signs, in Bacon’s semiotics, are not reserved to human beings: Bacon’s analysis, thanks to various influences (from Augustine to Avicenna and Alhazen) includes both non-human animal communication and understanding. Adapting to non-human animals Alhazen’s osbervations about children and acknowledging that all animals have a special faculty (the aestimativa) specialized in the reception of insensible intentions (or species), Bacon can ground both non-human animal communication through intentional natural signs and non-human animal inferential abilities on natural instinctive reactions. While the pseudo-Kilwardby outlines a compartimentalization of the semiotic disciplines (applied semiotics), implicitly denying the possibility of a general semiotics, Bacon shows that semiotics as a discipline should be contained in an extended grammar, yet to be written, that includes an analysis of different kinds of signs and which develops several suggestions from a variety of well established fields of philosophical inquiry.

CHAPTER 8

Conclusion The story that we have told in this book is about the cognitive and scientific value assigned to signs within the Aristotelian tradition up to the end of the thirteenth century. We saw that Aristotle’s explicit theory of signs in the Prior Analytics (APr B 27) is only implicitly connected to the theory of scientific demonstration, and that conversely his theory of scientific demonstration in the Posterior Analytics, while it allows for a strong and a weak sense of “demonstration”—why-demonstrations and that-demonstrations, respectively—yet seems to leave little room to signs: sign-inferences only make a feeble appearance in two passages (in APo A 6 and APo B 17) in which they seem to be contrasted with proper demonstrations (or demonstrations in the strong sense, i.e., why-demonstrations). We also noticed that unlike the theory of signs of the Stoics, Aristotle’ theory of signs in the Prior Analytics is not epistemic, in contrast to his theory of demonstration in the Posterior Analytics, which makes some use of epistemic notions (an effect is better known than its cause). Starting with Alexander of Aphrodisias, Aristotle’s Greek commentators explicitly connected the theory of signs of APr B 27 to the theory of demonstration of the Posterior Analytics, thereby projecting the epistemic dimension of the latter onto the former. According to this interpretation, the prototypical that-demonstration of APo A 13, that in which cause and effect are convertible (which we classified as type 1b), is to be identified with the deductively valid sign-inference of APr B 27, which Aristotle calls τεκμήριον. Alexander’s followers, Themistius and Philoponus, accept this interpretation and develop it into distinct typologies of that-demonstrations. The that-demonstration that is so identified with the sign-inference is called by Philoponus a “tekmeriodic demonstration,” a denomination that also surfaces in Philoponus’ and Simplicius’ commentaries on the ouverture of the Physics, where Aristotle had said that physical investigations move from what is better known to us, and thus, the commentators added, from effects and signs. The Arabic developments of the theory of demonstration heavily depend on the Greeks, and it is no surprise to see that sign-inferences have accordingly a prominent role in their typologies. In contrast to the Arabic tradition, the Latin reception of these theories is practically null. Although the reception and integration of the Greek commentaries on the logica nova is well documented, and although in that context the term demonstratio (at least in some domains) has the inferential, and even the syllogistic sense of the Aristotelian © koninklijke brill nv, leiden, 2023 | doi:10.1163/9789004546974_010

398

chapter 8

demonstration, yet the first commentaries on the Posterior Analytics in the first half of the thirteenth century (Grosseteste and Kilwardby) accurately and systematically avoid to connect the epistemic dimension of sign-inferences (which after all had been widely discussed in theology, esp. sacramental) to Aristotle’s theory of scientific knowledge and demonstration. This disconnection, which characterizes with almost no exceptions the tradition of the Posterior Analytics in the thirteenth century, is not causal. Rather, on the one hand it appears to derive from the widespread distrust of signs and of knowledge through signs, certainly in its turn dependent on its connection with ­argumentative forms of a lower kind or having a lower degree of strength, like those treated in rhetoric and dialectic. On the other hand, that disconnection is perhaps explainable by reference to the rather early diffusion of the Sophistici Elenchi in the Latin West, in whose fifth chapter the “demonstrations through signs” are regarded as fallacious and thus to be rejected. Even in those places of the Latin commentaries on the Posterior Analytics in which mention is made of sciences that make use of signs, like Giles of Rome’s scientia navalis, these are often fortuities, sometimes produced by interpretive mishaps (it is the case of apparentia or scientia navalis in Kilwardby), rather than systematic connections that depend on late-ancient literature. Not even the strong influence that the Arabic commentators had on Albert the Great was sufficient to determine him to consider physical investigation as somehow connected to sign-inferences and semiotic knowledge. Sign-inferences are discussed in commentaries on other departments of the Organon. Besides those on the De Interpretatione, locus classicus of the analysis of linguistic signs—already well-researched and therefore not discussed in this book—interesting analyses are in the few commentaries on APr B 27, and in the treatment of both the locus a communiter accidentibus and the fallacy of the consequent in the commentaries on Sophistici Elenchi 5 and on Peter of Spain’s Tractatus V, which is devoted to the loci. In all these contexts the general mistrust for signs and sign-inferences that was evoked above finds a decisive confirmation. On the one hand, the commentaries on the Prior ­Analytics of Kilwardby and Albert the Great take the theory of signs to be conceptually disconnected from the theory of demonstration. What is more, the logical validity and cognitive stability of the τεκμήριον itself seem to deteriorate: the example of the milk in the breast of APr B 27, which necessarily signifies that a woman has given birth, is not without exceptions once allowance is made for artificial production of milk, as Albert says in both his commentary on the Prior ­Analytics and that on the Sophistici Elenchi. On the other hand, signs are definitely connected with dialectical and rhetorical argumentations, which yield forms of knowledge that fall short of the requirements of scientific

Conclusion

399

demonstration: opinion or conjecture—suspicio—and even to fallacious argumentation, which yields no knowledge at all and has to be rejected. The problem in this context has become that of distinguishing fallacious reasoning based on signs (whose prototypical form is the fallacy of the consequent) from valid dialectical arguments. If our reconstruction is correct, then, one may put the matter as follows. In the Greek-Arabic tradition the theory of signs of APr B 27 is used both explicitly and implicitly within the theory of demonstration of the Posterior Analytics. The tradition of the Posterior Analytics is permeable to the Prior Analytics: the examples, the analyses, and the terminology of the latter is fully integrated into the former. By way of contrast, in the Latin West there is a symmetric “impermeability”: with the few exceptions that we have documented, the commentaries on the Posterior Analytics make no use of the semiotic notions of APr B 27, and conversely the commentaries on the Prior Analytics make no use of the categories and typologies of the Posterior Analytics. In sum, if our reconstruction is correct, one may speak of Greek-Arabic permeability and Latin impermeability between the Prior and the Posterior Analytics in semiotic matters. A notable exception to this trend is both in the pseudo-Kilwardby’s commentary on Priscian and in Roger Bacon. In the context of a discussion on the epistemology of grammar, the pseudo-Kilwardby claims that a general scientia de signis is possible and that distinct specific sciences of signs do exist: the traditional disciplines of the trivium (esp. grammar and logic), natural science (dealing with signs convertible and non-convertible with their own cause)— and this is the place where an otherwise quite uncommon reference to APo A 6, where sign-syllogisms are mentioned, is clearly made—and moral science (which goes from behaviour and physical reaction as effects to the emotion that causes it). Roger Bacon—a decidedly atypical author but one who was nonetheless closely connected to the tradition of commentaries on logic and dialectic— devotes to signs an important part of his project for a reform of Christianity (Opus maius). His classification of signs, comparable only to Abelard’s and Simon of Tournai’s in the twelfth century, has many sources, among which Augustine (not only the De doctrina christiana but also the De dialectica) and Aristotle, as well as Arabic medicine, physiognomics, astrology, and—last but not least—theology. Inferential signs deserve a special attention, and constitute an essential element of Bacon’s theory of connotation, which is the mode of sign-inference typical of theology. The distinction between necessary and probable inferences, while it occurs in the context of Bacon’s analysis of signs, is not sufficient to re-open the dossier about demonstration, so to say. Unlike Simon of Tournai, Bacon does not connect the idea of a sign that is a cause

400

chapter 8

(in case the cause is better known than the effect) to why-demonstrations, nor the idea of a sign that is an effect (typically better known than the cause) to that-demonstrations; he does not distinguish in this context the necessity of the consequence from the necessity of the consequent, and thereby does not release necessary inferential signs from the heavy mortgage of a generalized cognitive mistrust. The contribution that the reception of the logica nova made on discussions about signs was not the focus of our previous investigation into sign theories in the thirteenth century.1 One historiographical commonplace that formed the basis of that investigation was that the medieval notion of sign is substantially and exclusively derived from the Augustinian definition, which originated and was initially adopted in theology but soon reached grammar and logic, too.2 The present study, which rarely discusses the Augustinian definition, constitutes a partial correction of that common place, as it focuses on a theory of signs that was highly sensitive to the reception of the Aristotelian Organon— even though the innovations of the Greek commentators in matters semiotic where not inherited by the Latins—and of Boethius’ dialectic and rhetoric; a theory of signs whose subject-matter is the notion of “inferential sign,” which have or may have a certain cognitive and scientific (demonstrative) value, and which is independent and—in some contexts at least—alternative to the Augustinian and theological notion. 1 Marmo (2010). 2 Leblanc (2021), 239 and n. 4.

Appendix

Thirteenth-Century Unedited Texts on the Typology of Demonstrations and Sign-Inferences This appendix brings together some unpublished texts referred to above, in particular in chapter 6 of this book. These texts are presented here for the first time, in transcription from a witness or, in some cases, by collating two or more manuscripts. The responsibility for the transcriptions and the choice of variants are completely mine. The working editions reproduce the words of the manuscripts, trying to respect their orthography (although not their punctuation or paragraphing). All numbers are, however, spelled out and the choice between c and t, u and v has been normalized. Names or titles of classical and medieval authors or texts have been normalized, too. At the beginning of each appendix, I have indicated the handwritten witnesses, their sigla and, when available online, their URL at my last access date (Sept. 22nd, 2022). If necessary, these preliminary notes will be preceded by additional introductory notes. I owe my deepest thanks to Sten Ebbesen and Christina Thomsen Thörnqvist who shared with me their digital copies of some manuscripts, and to Parwana Emamzadah, who checked my working edition of Radulphus Brito’s question I.48 on the Sophistici Elenchi (Appendix H) while preparing her own critical edition. C. Marmo

A

Radulphus Brito, Questiones super Posteriora Analytica, I.68.

P1 = Paris, Bibliothèque Nationale de France, lat. 14705, 89vb (see on Gallica: https:// gallica.bnf.fr/ark:/12148/btv1b9067142t?rk=21459;2); P2 = Paris, Bibliothèque Nationale de France, lat. 16609, 20vb-21ra (dated on february, 3rd, 1300) (see on Gallica: https://gallica.bnf.fr/ark:/12148/btv1b9067744q?rk=21459;2); B = Bruxelles, Bibliothèque Royal “Albert Ier” 2910 (3540–47), 433va-b. Utrum demonstratio quia sit demonstratio simpliciter /P1 89vb/ /P2 20vb/ /B 433va/ Consequenter queritur circa illam partem SED QUIA DIFFERT PROPTER QUID ET QUIA [A 13, 78a22] utrum demonstratio quia sit demonstratio simpliciter.

© koninklijke brill nv, leiden, 2023 | doi:10.1163/9789004546974_011

402

Appendix

1. Arguitur quod sic. 1.1 Quia illa demonstratio que est ex primis, veris et immediatis est demonstratio simpliciter; sed demonstratio quia est huiusmodi, quantum ad illam que procedit per effectum; ideo etc. Maior patet per diffinitionem demonstrationis. Minor patet, quia illa demonstratio que procedit per effectum immediatum est ex primis, veris et immediatis, quia illi effectus sunt primi effectus et sunt immediati et veri.1 1.2 Item, illa demonstratio que facit scire rem est demonstratio simpliciter; demonstratio quia facit scire rem;2 ergo etc. Maior patet, quia finis demonstrationis est facere3 scire. Minor patet, quia quedam est demonstratio quia que fit per causam remotam, et ista facit scire rem simpliciter, quia scire est per causam primam; modo causa universalis et remota est causa prima; ergo demonstratio que fit per istam causam maxime facit scire. 2. Oppositum arguitur. Quia omnis demonstratio simpliciter est ex causis et4 immediatis; sed demonstratio quia vel non est ex causis vel non est ex5 immediatis; ideo etc. Probatio minoris: quia demonstratio quia6 vel est per causas remotas et mediatas7 vel per effectus immediatos, qui non sunt cause. 3. Ad istam8 questionem dico quod demonstratio quia non est demonstratio simpliciter; secundo dico quod est demonstratio incompleta et secundum quid. 3.1 Primum declaratur sic, supponendo duo: primo quod unumquodque ens habet propriam operationem, in quantum cum9 potest est illud, cum autem non potest non est illud nisi equivoce,10 secundum Philosophum,11 quarto12 Metheororum; secundo suppono quod operatio propria demonstrationis est facere scire. Tunc arguo:13 quod non facit scire simpliciter non est demonstratio simpliciter; sed demonstratio quia non

1 2 3 4 5 6 7 8 9 10 11 12 13

effectus et sunt immediati et veri] et veri et immediati P2 facit scire rem] est huiusmodi P2 facere] om. P2 et] om. P1 ex] om. P2 quia] om. B et mediatas] immediatas P2; om. B istam] om. P2 cum] om. B nisi equivoce] om. B secundum Philosophum] ut habetur sicut(?) P2 quarto] in fine quarti B Tunc arguo] om. P2

Appendix

403

facit scire simpliciter;14 ergo etc. Maior patet per suppositionem factam,15 quia16 sicut facit scire sic est demonstratio, quia sicut aliquid potest in suam operationem ita17 est illud; modo18 facere scire est propria operatio demonstrationis; cum ergo potest facere scire /B 433vb/ rem simpliciter19 est demonstratio20 simpliciter, et quod non facit scire rem simpliciter non est demonstratio simpliciter. Minor declaratur, quia demonstratio quia21 vel procedit per causas remotas vel per effectus immediatos; modo res non scitur per causas remotas vel per22 effectus proximos, sed magis scitur per causas propinquas et immediatas; ideo etc. 3.2 Secundum declaratur: quia illa demonstratio que facit aliqualiter scire rem et imperfecte est demonstratio secundum quid et imperfecta; sed demonstratio quia est huiusmodi;23 /P2 21ra/ ideo etc. Maior patet, quia sicut aliquid24 facit scire rem25 ita est demonstratio. Minor declaratur, quia demonstratio quia vel procedit per causas remotas vel per effectus immediatos.26 Si procedat27 per causas remotas, sic facit scire rem incomplete, quia sciendo28 rem per causam remotam solum scitur confuse et indeterminate, quia29 talis causa non est ad tale effectum determinata, sicut si sciam quod paries non respirat per hoc quod non est animal: non esse animal est causa remota non respirandi. Eodem modo si aliquid sciatur per effectum immediatum, istud scire non est perfectum, cum non sit per causam nec ex prioribus simpliciter, sed solum ex prioribus30 quoad nos. Ad 1. Tunc ad rationes.

14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

scire simpliciter] hoc P2 suppositionem factam] inv. P1 quia] quod P2 aliquid potest in suam operationem ita] potest aliquis in propriam operationem P2 modo] om. P2 simpliciter] om. B P1 est demonstratio] inv. B demonstratio quia] om. B P1 per] om. P2 est huiusmodi] facit scire /21ra/ rem secundum quid et imperfecte P2 est huiusmodi; ideo etc. Maior patet, quia sicut aliquid] om. B rem] om. B P2 immediatos] propinquos B P2 procedat] om. P2 sciendo] scire B quia] om. B solum ex prioribus] om. P2

404

Appendix

Ad 1.1 Ad primam. Cum dicitur “illa demonstratio que est ex primis etc.”, dico quod demonstratio que est per effectus immediatos potest esse31 ex veris et immediatis, non tamen est32 ex causis quod requiritur ad scire simpliciter. Ad 1.2 Ad aliam. Cum dicitur “illa demonstratio que facit scire etc.”, verum est si facit scire33 simpliciter; et cum dicitur “demonstratio quia facit scire rem34 simpliciter,” falsum est; et cum dicitur “ista accipit causas remotas35 et iste sunt prime,” verum est: sunt prime universales; et cum dicitur “prime cause faciunt maxime scire rem,” dico quod non accipiuntur36 ibi prime cause, id est maxime universales, sed prime cause id est37 proxime et immediate. Unde licet ad esse effectus magis faciant cause universales, tamen effectus non assimilatur cause universali, sed magis cause particulari, sicut homo non assimilatur soli qui est causa universalis eius, sed magis assimilatur38 homini qui est causa particularis eius.39 Et ideo effectus magis habet sciri per causam particularem quam per causam universalem, quia causa particularis est determinata ad talem effectum; causa autem universalis non est sic determinata ad aliquem effectum.40 Ad 2. Responsio in oppositum bene probat quod demonstratio quia non est demonstratio simpliciter, tamen bene est demonstratio incompleta et imperfecta.

B Giles of Rome (Aegidius Romanus), Expositio super Rhetoricam Aristotelis, lectio 6, ad Rhet A 2 1357a22–29 ed = Venetiis, per Georgium Arrivabenum, 1515 (die VI mensis Januarii); P = Paris, BNF, Lat. 16681, 10v-11v (XIII) (see on Gallica: https://gallica.bnf.fr/ark:/12148/ btv1b10033381h?rk=21459;2); S = Paris, Bibl. de la Sorbonne, 120, 12rb-13ra (XIV). Lectio 6 Quoniam autem sunt pauca [Rhet A 2 1357a22–29]. 31 32 33 34 35 36 37 38 39 40

esse] om. B est] om. B scire] rem add. B rem] om. B causas remotas] inv. B accipiuntur] -itur P2 maxime universales, sed prime cause id est] om. P2 assimilatur] om. P2 eius] om. P2 Unde licet… aliquem effectum] om. B

Appendix

405

In parte ista ostendit Philosophus ex quibus habeant esse41 entimema42 et exemplum. Et duo facit, quia primo ostendit ex quibus est entimema; secundo declarat quomodo habeat fieri exemplum. Secunda pars ibi: Exemplum autem. Circa primum duo facit: nam primo ostendit entimema esse43 ex ycotibus et signis, secundo declarat quid est44 ycos et quid signum. Secunda pars ibi: Ycos quidem enim. Circa primum tria facit, quia primo dicit eorum ex quibus sunt entimemata quedam esse necessaria, plurima tamen esse ut in pluribus et quod conclusiones assimilantur principiis sive45 premissis; secundo dicit hoc esse manifestum ex libro Priorum; tertio concludit signum et ycotem ex quibus est entimema esse idem quod necessarium et in pluribus. Secunda ibi: Palam auteM nobis. Tertia ibi: Entimemata autem. 6.1.1 Dicit ergo46 primo quod pauca sunt necessaria ex quibus sunt rethorici sillogismi; multa autem sunt de quibus iudicia et considerationes contingit aliter47 habere, quasi diceret quod sillogismi rethorici raro habent premissas necessarias; ut plurimum habent eas contingentes. Et est ratio: quia huiusmodi sillogismi ut plurimum sunt de hiis que homines agunt, consiliantur et tractant; que autem aguntur omnia sunt talis generis, id est generis48 contingentis; nihil enim horum, ut contingens est dare,49 ex necessitate habet esse; igitur ut plurimum entimemata habent premissam contingentem. Et sicut est in premissis, ita est in conclusionibus: nam conclusa non necessaria sed contingentia et accidentia ut in pluribus necesse habent sillogizari ex talibus alteris, id est ex talibus premissis que /ed 9va/ sint ut in pluribus; autem, pro ‘sed’, sed50 conclusa51 necessaria sillogizantur ex necessariis. 6.1.2 Deinde cum dicit: Palam autem nobis [1357a29–32], ostendit Philosophus52 hoc53 esse manifestum ex Analeticis, id est ex libro Priorum. Nam ibi ostensum est conclusiones necessarias esse ex necessariis; alia autem ex aliis. Et quia in rethorica sunt pauce conclusiones necessarie, multe autem ut in pluribus, manifestum est quod

41 42 43 44 45 46 47 48 49 50 51 52 53

habeant esse] om. ed entimema] emptimema S passim esse] om. ed est] om. ed principiis sive] om. P ed ergo] om. S ed habere] se add. ed id est generis] om. ed contingens est dare] consequens est dicere S ed sed] om. ed conclusa] cum conclusa non S Philosophus] om. P hoc] om. ed

406

Appendix

ea ex quibus sunt entimemata et sillogismi rethorici hec, id est pauca, erunt necessaria, plu/S 12va/rima autem dicuntur esse ut in pluribus. 6.1.3 Deinde cum dicit: Entimema autem [1357a32]. Ex eo quod entimemata sunt ex ycotibus et signis, cum habitum sit ea54 esse ex necessariis et his que sunt in pluribus, concludit utrumque horum, id est ycotem et signum, esse idem utrique dictorum, id est necessario et ei quod est ut in pluribus, quia signum idem est55 quod necessarium, ycos autem est idem quod esse in pluribus. 6.1.4 Ad evidentiam autem dictorum56 est57 notandum signum tripliciter posse sumi, secundum tres figuras sillogismorum. Sumitur enim primo signum in prima figura, et huiusmodi signum semper infert58 signatum, sicut lac habere est signum peperisse; et tunc formetur sic sillogismus: Quecumque habet lac peperit; hec habet lac; ergo etc. In secunda autem figura accipitur signum quando in plus est signum quam signatum, et59 ut60 in pluribus signum signatum infert,61 licet non semper,62 sicut esse errabundum de nocte est signum furis; potest tamen quis esse errabundus absque eo quod sit fur; et tunc formetur sic sillogismus: fur est errabundus;63 hic est errabundus; ergo etc. In tertia autem figura sumitur signum quando aliqua duo habentia aliquem ordinem ad se invicem ex eo quod se /P 11r/concomitantur64 in aliquo credimus quod se concomitentur65 in omnibus, ut sapientia habet quendam ordinem ad studiositatem sive ad bonitatem. Nam Socrates inter cetera auxilia dicit sapientiam66 esse maximum auxilium ad vitandum peccatum, quia ergo videmus67 quod aliquis homo particularis, ut puta Pithacus68 est sapiens et studiosus, credimus sapientes studiosos esse. Formetur ergo sic sillogismus: Pithacus est sapiens; Pithacus est studiosus; ergo sapientes sunt studiosi. Istorum autem signorum signum in prima figura, eo69 quod de necessitate 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69

ea] om. P ed idem est] inv. P ed dictorum] et dicendorum add. P ed est] om. P ed infert] refert ed et] om. S ed ut] tunc ed signatum infert] sit natum inferre S non semper] vere simpliciter ed errabundus] de nocte add. ed concomitantur] concomitentur P; comitentur ed concomitentur] comitentur ed sapientiam] scientia S; scientiam ed ergo videmus] inv. P Pithacus] Phitacus S; Pytachus ed eo] est eo S; et ed

Appendix

407

concludit,70 dicitur71 prodigium, id est magnum signum,72 sive retinerium, quia hominem retinet et terminat eo quod non contingat73 solvere, nec est in eo possibilis evasio. Signum vero in secunda figura,74 et maxime75 cum est in pluribus, dicitur ycos, quasi imago vel similitudinarium: nam si non est necessarium quod posito tali signo ponatur signatum, est tamen verisimile et probabile. Signum vero in tertia figura etiam ycos76 dici potest, quia verisimile est sapientes studiosos esse; tamen quia non habet proprium nomen dicitur signum non necessarium, quia non est necessarium quod aliqua duo77 habentia aliquem ordinem ad se invicem se concomitantur78 in aliquo quod se concomitentur79 simpliciter. 6.1.5 Advertendum tamen quod, licet omnibus istis80 modis sumatur signum, ut tamen81 signum dividitur contra ycotem vel nominat solum signum in prima figura, vel nominat signum in prima et tertia figura.82 Dictum est enim quod ycos dupliciter sumitur:83 uno modo ut nominat solum signum in secunda84 figura, alio modo85 prout cum hoc86 comprehendit signum in87 tertia figura. Si ergo ycos sumatur ad secundam et tertiam figuram, signum88 divisum contra ycotem comprehendit solum signum in prima figura sive signa necessaria: et sic accipit signum Philosophus et ycotem, cum dicit quod necessarium est idem quod signum et ycos idem89 quod esse in pluribus, et quod entimema90 quia constat91 ex ycotibus et signis constat ex necessariis et ex hiis que sunt in pluribus.

70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91

concludit] concludat S ed dicitur] dicimus ed magnum signum] inv. P ed contingat] om. S figura] est add. P et maxime] om. ed etiam ycos] inv. ed duo] non add. ed concomitantur] concomitantia ed concomitentur] ad invicem add. et del. P omnibus istis] inv. ed ut tamen] attamen ed figura] om. P ed sumitur] sumi potest P secunda] prima ed modo] vero S cum hoc] om. ed in] secunda et add. ed signum] om. ed idem] id est ed entimema] -ta ed constat] constant ed

408

Appendix

Sed92 ex hoc etiam apparere potest quomodo intelligendum sit quod ea ex quibus sunt entimemata raro sunt /S 12vb/ necessaria, ut /ed 9vb/ plurimum93 sunt ut in pluribus. Non enim intendit Philosophus loqui de necessario simpliciter, nec istud capitulum debet reduci ad generationem sillogismorum ex necessario vel ad capitulum de mixtione ex necessario et contingenti, sed ipse94 vult dicere quod rethores, cum arguunt per signa,95 raro dant signa infallibilia; sed ut96 plurimum dant signum ut in pluribus. Propter quod istud capitulum97 ad secundum Priorum ubi determinantur98 de entimemate reduci habet. Cum igitur tales sint conclusiones quales sunt premisse, sicut rethores raro arguunt per signa infallibilia, conclusiones eorum raro sunt infallibiles; ut plurimum autem debent esse ut in pluribus. Si vero ycos dicat solum signum in figura secunda, sic signum divisum contra ycotem comprehendit signum necessarium, ut signum in prima, et non necessarium, ut signum in tertia; et sic loquitur Philosophus de signo infra, cum dividit ipsum in signum necessarium et non necessarium. 6.2 Deinde cum dicit: Ycos quidem [1357a34], determinat de ycote et signo, et duo facit, quia primo determinat de ycote, secundo de signo; secunda pars ibi: Signorum autem. 6.2.1 Dicit ergo quod ycos quidem99 est quod fit in pluribus, et non, sicut quidam diffiniunt, ycos est quod fit simpliciter vel quod fit in omnibus; sed ycos, sive tale signum quod fit100 circa contingentia aliter se habere, sic se habet ad illud ad quod est ycos, id est ad signatum, sicut universale ad particulare. Accipit enim hic ycotem prout dicit signum in secunda figura et reperitur in aliquo in quo non reperitur signatum,101 ut esse errabundum est ycos ad esse furem,102 cum sit universalius quam ipsum, et sit aliquis errabundus qui non est fur; quod103 si etiam reperitur fur qui non est errabundus ita quod errabundus et fur sic se habent sicut excedentia ad excessa, nichil

92 93 94 95 96 97 98 99 100 101 102 103

Sed] om. P plurimum] vero add. ed ipse] om. P ed signa] signum ed; signum add. et del. P sed ut] secundum ed istud capitulum] id ed determinantur] terminatur ed quidem] om. S ed fit] om. S signatum] figuratum ed furem] add. a.m. s.l. P quod] quia ed

Appendix

409

ad propositum; sufficit ad hoc quod errabundus104 sit ycos ad furem esse aliquem105 talem qui non sit106 fur. 6.2.2 Deinde cum dicit: Signorum autem [1357b1], determinat de signo. Et primo dividit signum,107 secundo ostendit quomodo utrumque signum se habet ad entimema108 vel ad sillogismum rethoricum. Secunda pars ibi: Adhuc autem. Circa primum duo facit, quia primo distinguit signum, secundo specialiter determinat de signo necessario; secunda pars ibi: Necessaria quidem igitur. 6.2.2.1.1 Dicit ergo quod signorum109 hoc quidem110 sic se habet ut aliquod singularium ad universale quantum ad signum111 in tertia figura, ubi particulariter concluditur intentum. Nos autem ex illo particulari inferimus universale,112 ut quia Socrates est sapiens et studiosus inferimus omnes sapientes esse studiosos. Hoc autem ut aliquod universalium ad particulare quantum ad signum in prima figura, ubi concluditur universaliter intentum. Istorum autem113 signorum unum est necessarium sicut signum114 in prima figura, aliud non necessarium, ut signum in tertia. Signum necessarium vocatur retinerium quasi hominem retinens et terminans, quia115 cum sit insolubile116 nescit homo quo fugiat. In secundo autem Priorum vocatur prodigium, quasi117 magnum signum. Signum vero non necessarium non habet nomen secundum differentiam,118 id est non habet nomen proprium, secundum quod distinguatur et differat119 ab aliis. 6.2.2.1.2 Deinde cum dicit: Necessaria quidem [1357b5], specialiter120 determinat de signo necessario dicens ea ex quibus /ed 10ra/ est sillogismus dicuntur necessaria eo

104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120

ita quod errabundus et fur… ad hoc quod errabundus] om. S aliquem] aliqualem S ed sit] est ed signum] om. ed entimema] -ta ed signorum] signum ed quidem] quod ed signum] signatum ed Nos autem ex illo particulari inferimus universale] om. S ed autem] om. S ed sicut signum] om. S ed quia] et ed insolubile] solubile S ed quasi] quia S ed non habet… differentiam] om. ed distinguatur et differat] distinguitur et differt ed specialiter] om. S ed

410

Appendix

quod tale signorum, id est signum necessarium, est retinerium. Nam quando putant non contingere solvere quod dictum est, tunc vere121 putant retinerium esse, eo quod ostensum et terminatum sit.122 Nam secundum antiquam linguam grecorum retinar idem est quod terminus /S 13ra/ vel tecmar123 secundum aliam litteram. Dicuntur enim talia signa necessaria eo quod hominem necessitent retinendo eum124 et terminando. 6.2.2.2 Deinde cum dicit: Adhuc autem [1357b10], comparat predicta signa125 ad entimema et tria facit, quia primo ostendit quomodo signum non necessarium comparatur126 ad entimema, secundo quomodo necessarium, tertio epilogat. Secunda pars ibi: Hoc autem et si quis; tertia ibi:127 Quid igitur est ycos. 6.2.2.2.1 Dicit ergo quod hoc quidem signorum quod se habet ut singulare ad universale, id est signum128 /P 11v/ in tertia figura, adhuc, id est preter hoc quod non est necessarium, est etiam insillogizabile. Habet enim sic fieri huiusmodi signum: ut si quis dicat sapientes iustos esse,129 quia Socrates, qui nunc est sapiens, iustus est. Hoc igitur est signum non necessarium, ideo solvendum est quod dictum est. Nam etsi verum sit quod concluditur, insillogizabile tamen est: nam dato quod premisse vere sint, non est necessarium conclusionem veram esse, quia non valet gratia forme, licet contingenter vel ex alia causa veritatem habere possit. 6.2.2.2.2 Deinde cum dicit: Hoc autem [1357b14], ostendit quomodo se habet signum necessarium ad sillogismum. Nam tale signum sillogizabile est.130 Est enim hoc signum: si quis dicat egrotat quia131 febricitat, ut accipiamus febricitare132 non prout est species egritudinis, sed prout dicit aliquod signum inseparabiliter egritudinem concomitans; tale etiam signum est cum dicitur: peperit quia lac habet. Istud enim signum necessarium est, et solum tale signum est retinerium; et cum verum sit, insolubile est. Nam cum tale signum verificatur133 de aliquo, de necessitate verificatur134 signatum, 121 122 123 124 125 126 127 128 129 130 131 132 133 134

vere] fere S sit] om. S ed tecmar] detinar P ed eum] eos S predicta signa] predictum signum ed comparatur] operatur ed Hoc autem et si quis; tertia ibi] om. ed signum] om. S esse] ecce ed est] om. ed quia] qui ed febricitare] -tantem ed verificatur] inficiatur ed verificatur] inficiatur ed

Appendix

411

et ideo est insolubile, quia non potest esse quod135 aliquis febricitet nisi egrotet. Et ideo addit quod hoc signum se habet ut universale ad particulare, quia semper universaliter concludit intentum, ut si quis dicat: febricitare signum est egritudinis;136 spissim autem respirare non est tale signum respectu febricitationis. Nam etsi verum sit aliquem spissim respirare, non tamen propter hoc sequitur quod febricitet; immo solvendum est, quod137 contingit138 spissim respirantem non febricitare. Vel aliter et melius: per hoc quod dicit “hoc autem ut139 universale ad particulare” possumus intelligere signum in secunda figura, ubi140 signum est universalius quam signatum. Nam141 spissim respirare est in plus quam egrotare. Notandum ergo quod tam in secunda figura quam in prima reperitur habitudo universalis ad particulare, aliter tamen et aliter: nam in secunda signum se habet ut universale et signatum ut particulare, cum ibi medium se habet ut signum predicetur142 et maior extremitas subiciatur que se habet143 ut signatum. In prima144 autem totum est econverso, ut patet intuenti. 6.2.2.2.3 Deinde cum dicit: Quid igitur est145 (1357b21–25), epilogat dicens quid igitur est ycos et quid signum et quid retinerium et que differentia inter ipsa dictum est nunc; tamen in Analeticis, id est in libro Priorum, ut in secundo, dictum est146 de hiis magis manifeste:147 ibi148 etiam de ipsis dictum est; propter quam causam hec quidem insillogizabilia sunt, ut signa non necessaria; hec autem sillogizata, ut illa que sequuntur ex signis necessariis. (…)

135 136 137 138 139 140 141 142 143 144 145 146 147 148

quod] quia P est egritudinis] esse egritationis P quod] quia P contingit] convenit ed hoc autem ut] ut S; hoc autem vult ed ubi] ut P ed Nam] in add. ed predicetur] proceditur ed se habet] inv. ed prima] figura add. ed est] ycos add. S dictum est] om. S manifeste] dictum est add. S ibi] ubi S

412 C

Appendix

Magister Simon, Expositio super Tractatus Petri Hispani V

I mainly follow P+Pd, since M appears to witness another version of the same commentary. References in square brackets are to de Rijk’s edition of Peter of Spain’s Tractatus (1972). P = Paris, BNF, Lat. 16126, 88vb-89ra; 92rb (see on Gallica: https://gallica.bnf.fr/ ark:/12148/btv1b9067843n/f5.item); Pd = Padova, Bibl. Antoniana, 429, 22ra-va; 26rb-va; M = München, Staatsbibliothek, clm 14697, 40rb-vb; 46rb-va (see on MDZ: https:// www.digitale-sammlungen.de/en/view/bsb00103973?page=,1). /M 40rb/ /P 88vb/ /Pd 22ra/ ARGUMENTATIONIS QUATUOR SUNT SPECIES149 [V.3, 56.10]. In qua150 ponit divisionem argumentationis.151 Et dividitur in quatuor: primo ponit ergo152 divisionem argumentationis, et de primo membro153 prosequitur; in secunda de secundo, ibi: INDUCTIO; in tertia de tertio, ibi: ENTIMEMA; in quarta de quarto, ibi: EXEMPLUM. Ponit ergo divisionem argumentationis et patet.154 Sufficientia autem155 istarum specierum potest sic patere:156 quia157 in omni argumentatione158 manifestatur159 virtus conclusionis prius ignota; ignotum autem non potest manifestari ex ignotis equaliter; ergo omnis argumentatio procedit ex notioribus ad conclusionem.160 Sed hoc fit dupliciter:161 vel162 ex notioribus163 simpliciter vel164 quoad nos; si primo modo,165 hoc est dupliciter: vel ex notioribus simpliciter166 quantum ad principia 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166

QUATUOR SUNT SPECIES] om. Pd; SUNT SPECIES] om. P qua] auctor add. M divisionem argumentationis] inv. M ergo] om. Pd membro] om. M P Et dividitur in quatuor… Ponit ergo divisionem argumentationis et patet] om. M autem] om. P potest sic patere] sic accipitur M quia] quod M argumentatione] argumento M manifestat] manifestatur M prius ignota… ad conclusionem] om. M Sed hoc fit dupliciter] Et hoc dupliciter manifestatur M vel] om. M notioribus] notantibus M vel] aut ex notioribus M primo modo] simpliciter M vel ex notioribus simpliciter] aut M

Appendix

413

complexa et sufficientia;167 vel ex notioribus simpliciter quantum168 ad principia incomplexa et insufficientia. Si primo modo, hoc est sillogismus; si secundo modo169 sic est enthimema;170 si autem procedit171 ex notioribus nobis vel172 /M 40va/ quoad nos,173 hoc est dupliciter: vel procedit174 ex principiis complexis et sufficientibus, et sic est inductio;175 vel procedit ex incomplexis et insufficientibus,176 et sic est exemplum. In exemplo enim procedit a singularibus ad probandum particulare, et sic proceditur a principiis insufficientibus; sed quia inductio177 recipit omnia particularia contenta sub aliquo universali, ideo procedit ex principiis sufficientibus.178 Deinde membra divisionis declarat et primo remittit nos ad diffinitionem sillogismi prius positam. Deinde sequitur INDUCTIO179 [V.3, 56.12], in qua180 ponit diffinitionem inductionis181 etc. Ad cuius evidentiam182 est notandum, secundum Boethium in Topicis suis,183 quod duplex est inductio: completa et incompleta.184 Completa185 est illa186 in qua a singularibus sufficienter enumeratis proceditur ad totum187 universale, et dicitur188

167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188

principia (-um P) complexa et sufficientia] principia completa, sic est sillogismus M vel ex notioribus simpliciter] si autem M incomplexa et insufficientia; si primo modo, hoc st sillogismus; si secundo modo] incompleta M enthimema] quia enthimema est sillogismus imperfectus add. M si autem procedit] si M nobis vel] om. M nos] et add. Pd procedit] pro ordine M inductio] introtuctio(?) P completis et sufficientibus… et insufficientibus] om. M; incomplexis et insufficientibus] inv. P inductio] introductio P In exemplo enim procedit… ideo procedit ex principiis sufficientibus] om. M; sufficientibus] insufficientibus P Deinde sequitur INDUCTIO] Consequenter sequitur illa pars: INDUCTIO EST M qua] parte auctor add. M inductionis] reductionis P Ad cuius evidentiam] Ad evidentiam huius P secundum Boethium in Topicis suis] om. M completa et incompleta] quedam completa, quedam incompleta M; complexa et incomplexa P Pd Completa] ut add. M; Complexa P Pd illa] que a veritate non deficit et add. M in qua a singularibus… ad totum] que procedit a particularibus sufficienter enumeratis ad totum M dicitur] quasi add. P

414

Appendix

‘completa’189 quia a veritate non deficit, et hoc patet190 in littera. Incompleta191 est illa in qua a pluribus particularibus ad aliud192 particulare proceditur et dicitur ‘incompleta’193 quia a veritate deficit,194 verbi gratia195 qui scit196 potare potator est, qui scit197 legere lector est,198 qui scit docere doctor est, ergo qui scit199 malum malus est, hoc non sequitur, immo falsum est. Talis enim potest esse bonus quamvis sciat malum: et hoc est quod vult Alanus in suo libro De planctu nature, ubi dicit quod mali notitia expediens est200 ad cautelam.201 Item scire malum202 non est malum, sed potius operari. De hac inductione secunda non intendit auctor hic, sed de completa.203 Nota etiam quod duplex est progressio: quedam est progressio corporalis, secundum quam204 aliquid movetur de loco ad locum205 vel progreditur, et in[tro]ductio non est talis progressio;206 alia207 est progressio non corporalis, sed mentalis et rationis208 secundum quam a particularibus progreditur ad universalia, et sic auctor sumit hic209 ‘progressionem’.210 Unde supple litteram sic: Inductio est progressUS, supple mentalis et a ratione factus.211

189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211

completa] complexa P Pd et dicitur ‘completa’ quia a veritate non deficit, et hoc patet] ut auctor exemplum ponit M Incompleta] Incomplexa P Pd aliud] om. P incompleta] incomplexa P Incompleta est illa… a veritate deficit] Alia autem est inductio incompleta, ut est illa que a veritate deficit et procedit a pluribus particularibus ad aliud particulare M verbi gratia] ut Pd scit] sic Pd potare potator est, qui scit] om. M est] qui scit cantare cantor est add. M scit] om. P expediens est] inv. P cautelam] carcelia(?) P. Cf. Alanus, De planctu naturae:, ed. Häring, 836.98: “mali cognitio, expediens est ad cautelam.” malum] male P Talis enim potest esse bonus… sed de completa] om. M quam] quem(?) M de loco ad locum] a loco isto ad locum a[[d]]lium add. M vel progreditur, et in[tro]ductio non est talis progressio] om. M alia] autem add. M non corporalis, sed mentalis et rationis] rationalis M hic] om. M progressionem] et non primo modo add. M Unde supple litteram sic: Inductio est progressUS, supple mentalis et a ratione factus] om. M

Appendix

415

Deinde212 sequitur: ENThIMEMA [V.3, 56 16], in qua213 ponit diffinitionem enthimematis et dividitur in duas: primo facit quod dictum est; secundo reducit enthimema ad sillogismum, ibi: SCIENDUM QUOD OMNE ENThIMEMA [V.3, 57.3]. Prima adhuc in duas: primo214 ponit diffinitionem enthimematis propriam; secundo215 ponit diffinitionem enthimematis secundum Aristotelem; secunda ibi, si habetis illam litteram: ARISTOTILES SIC DIFFINIT: sed non est littera auctoris.216 Nota quod enthimema est sillogismus217 deminutus et incompletus218 et dicitur219 ab ‘en’ quod est ‘in’220 et ‘thimos’221 quod est ‘mens’,222 quia semper in omni enthimemate223 retinetur una propositio224 in mente:225 vel minor ut ‘homo est animal, ergo Sortes est226 animal’, vel maior ut ‘omnis homo227 est animal, ergo omnis homo est substantia’, hic retinetur maior que228 est ‘omne animal est substantia’.229 Deinde sequitur SCIENDUM [V.3, 57.3] ubi reducitur enthimema in sillogismum.230

Deinde] Consequenter M qua] auctor add. M facit quod dictum… in duas: primo] om. P secundo] secundum Pd ponit diffinitionem enthimematis… littera auctoris] manifestat ipsum enthimema, ponendo diffinitionem eius M 217 sillogismus] truncatus(?) add. P 218 est sillogismus deminutus et incompletus] om. M 219 dicitur] denominatur M 220 in] non M 221 thimos] timos Pd 222 ‘thimos’ quod est ‘mens’] ‘timeiria’(?) quod est ‘retinere’ M (cf. Aegidius Romanus, Expos. sup. Rhet. I, supra, Appendix C). 223 in omni enthimema] ibi M 224 retinetur una propositio] inv. P 225 in mente] om. M 226 est] homo add. et del. P 227 homo] om. P 228 que] qui P 229 vel minor ut ‘homo est animal… ‘omne animal est substantia’] aliquando maior, verbi gratia ‘omnis homo est animal, omnis homo est substantia’ hic removetur maior que est ‘omne animal est substantia’; aliquando minor ut ‘omnis homo currit, ergo Sortes currit’, hic retinetur illa minor que est ‘Sortes est homo’ M 230 Deinde sequitur… sillogismum] Item auctor dicit quod enthimema reducitur ad ipsum sillogismum M 212 213 214 215 216

416

Appendix

Sed de hoc aliquis dubitaret /Pd 22rb/ et videretur alicui quod231 non esset232 verum, quia quandocumque233 aliqua duo sunt formaliter234 et in235 specie ex opposito236 distincta,237 istorum unum238 ad alterum reduci non potest; sed enthimema et sillogismus sunt huiusmodi, quia sunt diverse species argumentationis;239 ergo unum non potest reduci ad alterum et sic dictum auctoris non videtur valere.240 Oppositum patet per Philosophum241 et per auctorem in littera.242 Iuxta quod243 est notandum quod enthimema et sillogismus possunt considerari dupliciter: uno modo possunt considerari formaliter in quantum nominant quasdam intentiones secundas, sic enthimema non potest in sillogismum reduci244 et hoc patet per rationem in contrarium prius adductam, et confirmatur etiam sic: simile est de intentionibus complexis et incomplexis; sed in245 intentionibus complexis numquam246 una reducitur ad aliam; ergo etc. Secundo modo enthimema et sillogismus possunt considerari magis materialiter in quantum nominant res istis intentionibus247 subiectas vel obiectas, et sic quelibet species argumentationis potest reduci ad sillogismum. Et huius248 ratio249 est, quia, secundum Philosophum in libro250 Methafisice,251 in unoquoque252 quod] hoc add. M esset] est M quandocumque] quando M sunt formaliter] inv. M in] in add. P ex opposito] om. M distincta] om. P istorum unum] inv. et add. distincte(?) P argumentationis] argumentum(?) Pd unum istorum non potest… videtur valere] enthimema ad sillogismum reduci non potest M 241 Philosophum] in secundo Priorum add. M 242 et per auctorem in littera] om. M Pd 243 Iuxta quod] Ad cuius evidentiam M; quod] illud Pd 244 in sillogismum reduci] reduci in sillogismo Pd 245 in] om. P 246 complexis numquam] incomplexis in quantum/inquam Pd 247 intentionibus] ita add. Pd 248 uno modo possunt considerari… ad sillogismum. Et huius] vel quantum ad intentionem vel etiam quantum ad rem intentioni subiectam, sive formaliter et materialiter. Si (Sed M) sillogismus et enthimema considerantur formaliter, vel quantum ad intentionem, sic unum ad alterum non reducitur. Cuius ratio iam dicta est, quia sic sunt ex opposito et formaliter distincta. Si autem considerantur materialiter vel quantum ad rem, sic enthimema et omnes alie species argumentationis /M 40vb/ ad sillogismum reducuntur. Cuius M 249 ratio] idem P 250 in libro] om. P; in quarto M 251 Arist., Metaph. XI (I) 1 1052b18–19, 31–32 (Auct. Arist. 1 (239), p. 135). 252 unoquoque] quocumque M 231 232 233 234 235 236 237 238 239 240

Appendix

417

genere est recipere253 aliquod primum et minimum254 quod est metrum255 et mensura omnium aliorum in illo genere, verbi gratia in genere entium substantia est primum ad quod omnia alia entia256 reducuntur; similiter257 in genere colorum color albus est258 primum minimum259 ad quod omnes260 alii colores reducuntur; similiter in entibus rationis, ut est261 gramatica, littera est primum ad quod omnia alia262 reducuntur; ergo etiam in genere263 argumentationis erit dare aliquod264 primum, hoc autem non potest esse nisi sillogismus, quia sillogismus265 est quidam discursus rationis266 a premissis ad conclusionem sive a particularibus ad universale que sunt quedam entia rationis. Similiter inductio267 procedit a particularibus sufficienter enumeratis ad universale vel a particularibus ad particulare, et sic268 est in aliis. Et sic inductio,269 enthimema et omnes alie possunt reduci ad sillogismum.270 Unde ratio in oppositum habet veritatem eo modo quo dictum est. Nota. Adhuc de diffinitione questionis dubitatur utrum questio sit dubitabilis propositio. Et videtur quod non, quia271 multi sunt qui dubitant de ista propositione ‘utrum ens sit ens’, et hec propositio est una illarum que per se sunt note; ergo etc. Preterea, propositio et conclusio272 sunt unum, ut auctor dicit; sed multe sunt propositiones de quibus non dubitatur; ergo etc. Oppositum patet per auctorem. Ad cuius evidentiam est notandum quod questio est nomen verbale terminatum in -tio; unde deberemus dicere ‘quesitio’; sed per sincopam dicimus ‘questio’. Sed 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272

est reperire] om. M; et recipere P et minimum] om. M metrum] modus Pd entia] om. M similiter] est add. Pd est] est add. P minimum] om. M omnes] om. P est] in Pd entibus rationis… ad quod omnia alia] ad litteram omnia M; omnia alia] alia/omnia(?) P in genere] inter species M aliquod] quod sit add. M quia sillogismus] om. P rationis] ieprens(?) P inductio] introductio P sic] similiter Pd inductio] introductio P hoc autem non… possunt reduci ad sillogismum] ad quod omnes alie species argumentationis reducantur add. M quia] se sunt note ergo etc. preterea conclusio et propositio add. et del. P propositio et conclusio] inv. P

418

Appendix

secundum Petrum elye super Priscianum et secundum Philosophum sexto Topicorum, omne nomen verbale terminatum in -tio est equivocum; unde potest importare actionem agentis et passionem patientis et rem passam, verbi gratia ‘lectio’ significat actionem legentis et passionem rei lecte et rem lectam; ergo etiam ‘questio’, cum sit nomen verbale, potest habere respectum ad querentem et ad animam componentem vel dividentem, quia questio est quedam intentio secunda fundata super complexum ut dubitatum; tale autem complexum est obiectum intellectus componentis et dividentis, et potest habere respectum ad rem quesitam et ad scientiam sive cognitionem que est passio rei quesite. Unde sicut se habet scientia ad scientem sic questio ad animam. Ex hoc ad propositum. ‘Questio’ importat motum rationis, sed motus rationis debet proportionari motui nature; sed ad motum naturalem tria concurrunt, videlicet terminus a quo et terminus ad quem et mobile, ergo etiam concurrent ad questionem: terminus enim ad quem questionis est scientia et terminus a quo est res quesita, mobile est idem quod movere de re quesita ad animam. Sed, secundum Themistium super primum Posteriorum273 in omni questione reali aliquid debet esse274 notum et aliquid ignotum. Quod declarat in patre familias querente servum fugitivum quem si non cognosceret non posset invenire, etiam si ipsum haberet /P 89ra/ in presenti non eum apprehenderet; ergo etiam in ratione(?) questionis275 debet esse aliquid notum et aliquid ignotum. Unde querens est motivum inter scientem et ignorantem. Per hoc ad rationes. Ad primam, dico quod licet iste propositiones ‘ens est ens’ et consimiles276 non sint dubitate ex parte rei, tamen ex parte querentis. Ad secundum, dico quod licet questio et propositio sint unum in subiecto, id est in obiecto, differunt tamen formaliter, id est secundum diversas intentiones earum; et ideo oportet quod si multe sint propositiones non dubitate quod ergo etiam sint questiones non dubitate, quia questio addit super propositionem hanc differentiam ‘dubitabilis’. Deinde sequitur EXEMPLUM EST [V.3, 58.4], in qua ponit diffinitionem exempli et apparet in littera.277 /Pd 22va/ Deinde278 sequitur:279 LOCUS EST SEDES ARGUMENTI280 [V.4, 58.11–12] (…) 273 274 275 276 277 278 279 280

Posteriorum] Priorum Pd aliquid debet esse] debet esse aliquid Pd ratione(?) questionis] questione rationis Pd consimiles] similes Pd Nota. Adhuc de diffinitione questionis… in littera] om. M; sed cf. M 41rb-va Deinde] Consequenter M sequitur] illa pars add. M ARGUMENTI] om. P

Appendix

419

/M 46rb/ /P 92rb/ /Pd 26rb/ Deinde sequitur: COMMUNITER ACCIDENTIA281 [V. 26, 70.15], in qua282 prosequitur de loco a communiter accidentibus. Unde nota283 quod communiter accidentia sunt et dicuntur284 illa que eidem insunt et quorum285 unum raro potest reperiri286 /M 46va/ sine287 altero. Aliquis dubitaret utrum locus a communiter accidentibus sit288 locus intrinsecus. Et videtur quod non, quia ille locus /Pd 26va/ in quo289 consequens est extra essentiam antecedentis,290 non est291 intrinsecus; sed in loco a292 communiter accidentibus est huiusmodi,293 quia talis294 fundatur super habitudinem unius accidentis295 ad alterum; sed unum accidens est extra essentiam296 alterius; ergo etc.297 Oppositum patet per auctorem.298 Ad hoc299 dico quod hic locus est300 intrinsecus. Ad cuius intellectum nota301 quod duplicia sunt accidentia: quedam sunt propria que consecuntur principia essentialia302 speciei303 et illa dicuntur proprie propria,304 ut risibile est proprium hominis; alia sunt accidentia que causantur ex305 principiis individui,306 ut album et consimilia.307 Quia, 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307

ACCIDENTIA] antecedentia(?) Pd passim qua] auctor add. M nota] notandum M et dicuntur] om. M quorum] om. M potest reperiri] invenitur M sine] om. M sit] esset M ille locus in quo] quando M antecedentis] ibi add. M est] locus add. M a] om. M huiusmodi] cuius ratio est add. M talis] tales Pd accidentis] antecedentis P Pd quia terminus fundatus… extra essentiam] ibi sunt accidentia diversa, ideo unum non est essentia M etc.] non facit locum intrinsecum add. M auctorem] in littera add. M Ad hoc] om. M locus est] inv. M intellectum nota] evidentiam est notandum M essentialia] om. M; eius sententialia Pd speciei] immediate add. M propria] accidentia add. M ex] a M individui] et talia dicuntur accidentia communia add. M consimilia] similia M

420

Appendix

secundum quod vult Avicenna, ista accidentia fundantur super complexiones,308 quia si homo est frigide complexionis, tunc est albus;309 si autem est310 calide complexionis,311 tunc est niger,312 quia Albertus dicit quod caliditas est mater nigredinis, frigiditas vero mater albedinis: et quia tales complexiones sunt communes, ideo accidentia talia que causantur ex hiis dicuntur ‘communia’. Et quia ille locus potissime tenet313 in communiter accidentibus, unde314 nota315 quod in loco316 a communiter accidentibus duplex fit317 processus. Quidam enim est processus a pluribus ad unum, ut ‘iste est errabundus in nocte et318 multum deludit et paucos redditus habet,319 ergo est fur’, et super talem habitudinem fundatur locus dyaleticus intrinsecus, videlicet a communiter accidentibus.320 Alius est processus quando ab uno proceditur ad unum, et hoc dupliciter: vel enim illa essentialiter et inseparabiliter se321 concomitantur322 vel non; si primo modo, sic super ista fundatur locus dyaleticus intrinsecus,323 ut ‘ille324 penitet, ergo deliquit’;325 si autem non essentialiter se concomitentur,326 sic super ista327 fundatur locus sophisticus ut ‘ista mulier dat lac, ergo est corrupta’,328 hec est fallacia consequentis,329 sicut vult Albertus330 super Elenchos: dicit enim331 quod virgines possunt dare lac et viri, licet modice

308 complexiones] et quia complexiones sunt communes, ideo etiam sequitur talia accidentia sunt communia. Quod autem fundentur super complexiones patet add. M 309 est albus] inheret sibi albedo M 310 est] om. M 311 complexionis] om. M 312 est niger] nigredo M 313 tenet] om. Pd 314 quia Albertus dicit… tenet in communiter accidentibus, unde] etc. M 315 nota] etiam add. M 316 unde nota quod in loco] ideo de locis Pd 317 fit] est M 318 et] om. M 319 et multum deludit et paucos redditus habet] paucos habet redditus et multum deludit Pd; multum deludens et paucos redditus habens M 320 et super talem habitudinem… a communiter accidentibus] om. M 321 essentialiter et inseparabiliter se] se essentialiter a M 322 concomitantur] comitantur Pd 323 intrinsecus] et etiam super illud unum processit exemplum de isto secundo M 324 ille] om. M 325 deliquit] deliquid M, delinquid P 326 non essentialiter se concomitentur] ista accidentia essentialiter se non respiciunt M 327 ipsa] ea Pd; ista M 328 est corrupta] peperit M 329 hec est fallacia consequentis] hoc non sequitur M 330 Albertus] om. P 331 sicut vult Albertus super Elenchos: dicit enim] Albertus enim dicit M

Appendix

421

quantitatis;332 et docet hoc experimento facere.333 Dicit enim si accipiantur urtice et ponatur ad acetum334 et tunc, si confricetur mammilla virginis335 vel etiam viri,336 tunc dabit lac, tamen modice quantitatis.337 Tamen quia ille locus potissime tenet quando procedimus a pluribus ad unum, ideo dicitur in plurali ‘a communiter accidentibus’.338 Ad rationem in oppositum. Maior concedatur. Ad minorem339 per interemptionem.340 Ad probationem: tu dicis quod sint diversa, concedo quod sint diversa secundum rationem; et ideo super ista fundatur locus a concomitantibus substantiam. Deinde sequitur QUID AUTEM SIT LOCUS EXTRINSECUS [V.27, 71.4].341 (…)

D

Simon of Faversham, Questiones libri Priorum, II.15

O = Oxford, Merton College 292, 138rb-va; Mi = Milano, Bibl. Ambros. C.161.Inf., 64rb-va. Utrum entimema sit sillogismus Queritur circa partem illam in qua Philosophus determinat de pluribus argumentationibus342 que habent reduci ad sillogismum; determinat autem ibi de inductione et entimemate et exemplo; et aliis omissis queratur de entimemate utrum343 entimema sit sillogismus. 1. Et arguitur quod non. 1.1 Quia omnis sillogismus est ex duabus propositionibus; sed entimema non est ex duabus propositionibus, sed ex una tantum; ideo etc.

et viri, licet modice quantitatis] om. M experimento facere] inv. M accipiantur urtice et ponantur ad acetum] accipiatur urtica et ponatur ad acetum P confricetur mammilla virginis] fricetur mammilla mulieris vel virginis M vel etiam viri] om. M tamen modice quantitatis] sed in modicum similiter est de viris M dicitur in plurali ‘a communiter accidentibus’] auctor istum locum denominat in plurali numero scilicet (sed, ms.) locum a communiter accidentibus M 339 ad minorem] minor dicatur M 340 interemptionem] et add. M 341 QUID AUTEM SIT LOCUS EXTRINSECUS] DE LOCIS EXTRINSECIS [V.27, 71.3] M; EXTRINSECUS] om. Pd 342 argumentationibus] argumentis Mi 343 utrum] scilicet add. Mi 332 333 334 335 336 337 338

422

Appendix

1.2 Item, illud quod ex opposito distinguitur contra sillogismum non est sillogismus; sed entimema est species argumentationis distincta contra sillogismum: dicit enim Boethius quod quatuor sunt species argumentationis, scilicet sillogismus, inductio, entimema et exemplum; ideo etc. 2. Oppositum arguitur. Omnis ratiocinatio que fit in modo et figura est sillogismus; sed entimema fit in modo et figura; ergo etc. 3.1 Dicendum quod entimema est sillogismus: idem enim est344 substantialiter sillogismus et entimema, nec in alio est differentia nisi quod in sillogismo explicatur sive exprimitur utraque propositio; in entimemate autem quandoque una exprimitur et alia subticetur. Subticetur quidem, quia ipsa est evidens: si enim arguatur sic ‘iste vicit olimpia, ergo iste est coronandus’, maior est manifesta et ideo subticetur. Est autem345 maior manifesta, quia planum est quod omnis qui vicit olimpia est coronandus. Hec autem est maior. 3.2 Quod autem entimema sit sillogismus patet, quia omnis ratiocinatio que confirmatur per illa principia per que tenet sillogismus unde sillogismus est, est vere sillogismus; sed entimema tenet per illa principia per que tenet sillogismus unde sillogismus est, scilicet per dici de omni et dici de nullo. Entimema autem habet /Mi 64va/ maiorem et minorem, licet habeat unam expressam et aliam intellectam quandoque; ex quo igitur habet maiorem et minorem, licet unam expressam et aliam subintellectam, et minor debet sumi sub maiore, manifestum quod ibi est sumptio sub. Omnis autem sumptio sub est per dici de omni et dici de nullo, ideo etiam entimemata tenent per hec principia; quare etc. 3.3 Item, ratiocinatio illa que concludit primum de tertio per medium et fit in modo et figura est sillogismus; sed entimema est huiusmodi: si enim arguatur sic ‘homo currit, ergo Sortes currit’ subticetur minor et tamen concluditur maior de tertio per medium; ideo etc. 3.4 Item, hoc declaratur. Sillogismus est ens rationis: est enim de intentionibus secundis que non sunt causate nisi a ratione, et ideo perfecta ratio sillogismi videtur consistere in debita ordinatione346 propositionum secundum intellectum absque omni

344 est] om. O 345 autem] enim Mi 346 ordinatione] sillogismorum add. et del. Mi

Appendix

423

expressione vocali; illud ergo quod quantum ad esse intellectum347 habet omnia illa que requiruntur ad formam sillogismi unde sillogismus, est complete sillogismus; sed348 entimema quantum ad esse intellectum habet omnia illa que requiruntur ad naturam sillogismi unde sillogismus; ideo etc. 3.5 Et ad hoc advertens Philosophus, primo Rethoricorum et hic, dicit quod entimema est sillogismus ex ycotibus et signis; entimema ergo est sillogismus, tamen in quantum una propositio subticetur, non est sillogismus evidens. Ideo aliqualiter deficit a sillogismo et quia in omni genere imperfectum reducitur ad perfectum, ideo entimema ad sillogismum reducitur.349 Tunc autem ad350 sillogismum reducitur cum illa propositio que deficit exprimitur. Deficit autem entimema a sillogismo in duobus, scilicet in materia et forma. In materia, quia sillogismus secundum quod accipitur in suo esse potissimo est ex propositionibus veris et necessariis; sed entimema non sic, sed ex probabilibus solum.351 Et quia ita est, ideo scientie speculative que procedunt ex necessariis utuntur sillogismo; practice vero352 que procedunt ex probabilibus utuntur entimemate; et propter hoc alicubi in libris suis scientias sillogisticas distinguit contra rethoricas, per ‘sillogisticas’ intendens speculativas. Et ideo secundum ipsum rethorice scientie non proprie utuntur sillogismo in suo esse potissimo. Differt etiam353 entimema a sillogismo in forma: si formam sillogismi vocemus debitam ordinationem propositionum354 secundum vocalem expressionem, et ita differt a sillogismo secundum formam quia in entimemate non exprimitur vocaliter nisi una propositio. 3.6 Et tu dices: nonne dictum est quod entimema est sillogismus? Et modo dicis quod differt a sillogismo. Dico quod entimema non est sillogismus accipiendo sillogismum in suo esse potissimo, sed cum hac additione ‘ex ycotibus et signis’; unde sillogismi sunt in demonstrativis, entimemata355 vero non. Sic igitur patet quomodo entimema est sillogismus /O 138va/ et quomodo non quicumque, quia non sillogismus in suo esse potissimo, sed est sillogismus ex ycotibus et signis.

347 348 349 350 351 352 353 354 355

intellectum] om. Mi sed] et add. Mi entimema ad sillogismum reducitur] ad sillogismum reducitur entimema Mi ad] in O probabilibus solum] propositionibus solum ex probabilibus Mi vero] non Mi etiam] autem Mi ordinationem propositionum] ordinem propositionem(?) O entimemata] entimema Mi

424

Appendix

3.7 Et si dicas: sicut se habet exemplum ad inductionem sic se videtur habere entimema ad sillogismum; sed exemplum non est inductio; ergo etc. Et356 apparet ad istud quod non est simile, quia in entimemate et sillogismo est similis processus, in exemplo vero et inductione non. In entimemate et sillogismo est similis processus, quia sicut sillogismus concludit primum de tertio per medium, sic entimema; in inductione vero357 et exemplo non est similis processus, quia inductio procedit a parte ad totum, exemplum358 vero a parte ad partem. Item, inductio concludit primum de medio per tertium, exemplum vero concludit primum de medio359 per simile tertio; nichilominus exemplum ad inductionem reducitur, et entimema ad sillogismum. Iste enim sunt species argumentationis ad quas omnes alie reducuntur, unde Philosophus dicit in littera quod sillogismo et inductione credimus quibuscumque credimus. Ad 1. Ad rationes. Ad 1.1 Ad primam dico quod maior vera est sic: vel expressis vel intellectis; unde quamvis entimema non sit ex duabus propositionibus expressis, est tamen ex una expressa et alia subintellecta. Et hoc sufficit ad hoc quod sit sillogismus. Ad 1.2 Ad aliam, concedo maiorem eo modo, et ad minorem dico quod non distinguitur contra sillogismum unde sillogismus est, sed contra sillogismum qui procedit ex necessariis ita quod entimema dicatur sillogismus procedens ex solis probabilibus; sillogimus autem absoluto nomine dicatur procedens ex veris et necessariis. Expliciunt questiones super360 librum Priorum disputate a magistro Symone de Faverisham.361

E

Radulphus Brito(?), Questiones libri De physionomia, q. 1

See also Costa (2011), 164–165, for a transcription of this question. F = Firenze, BNC, Conv. Soppr. E.I.252, 232vb-233ra

356 357 358 359 360 361

Et] om. Mi in inductione vero] vero inductione Mi exemplum] inductio O primum de medio] de medio; a.m. del. et corr. primum de medio in mg. super] supra Mi Faverisham] H(us)timit(us)(?) correxit add. Mi

Appendix

425

Utrum de moribus naturalibus possit esse scientia Circa librum De physionomia queratur primo utrum de moribus naturalibus possit esse scientia. Secundo, dato quod sic, utrum ista scientia sit moralis vel naturalis et sic consequenter. 1. De primo arguitur quod non. 1.1 Quia de partibus non est scientia; sed mores naturales sunt huiusmodi; quare etc. Maior apparet primo Posteriorum et septimo Metaphysice. Minor patet, quia et mores fleumatici sunt particulares et etiam colerici; ideo etc. Maior apparet primo Posteriorum et septimo Metaphysice, ubi dicitur quod corruptibilium est opinio, scientia autem necessariorum. Minor apparet quia signa †impedimenta(?)† [possunt] per que ista scientia traditur in tales mores non necessario secuntur ad talem dispositionem corporis. 1.2 Item, 362 de illis non est scientia de quibus nichil scitur nisi per signa; sed de moribus naturalibus nichil scitur nisi per signa; ideo etc. 1.3 363 Maior364 apparet primo Posteriorum et in primo Physicorum, ubi dicitur quod scire est per causam. Minor apparet, quia365 scientia huiusmodi est tradita per signa extrinseca corporis; hec autem sunt affectus anime; quare etc. 2. Oppositum dicit Philosophus in textu. 3. Tria dicantur ad questionem. Primo quid est Physionomia; secundo quod de [hu] moribus naturalibus possit esse scientia; tertio quod ista scientia non est ita certa366 sicut multe alie scientie.

362 363 364 365 366

Cf. infra, Ad 1.2. Cf. infra, Ad 1.3. Maior] Minor F quia] quod F certa] incerta F

426

Appendix

3.1 Physionomia non est aliud quam coniecturatio vel cognitio de moribus naturalibus per signa exteriora. Et dicitur a ‘physis’ grece quod est ‘natura’ vel ‘mos naturalis’367 latine et ‘nomos’ quod est regula , quasi sermo de [hu]moribus naturalibus. 3.2 Secundo dico ad questionem quod de [hu]moribus est scientia sicut de passionibus. Quia de illis potest esse scientia que sunt entia intelligibilia habentia causas et principia per que possunt determinari; sed mores naturales sunt huiusmodi; ergo etc. Maior apparet, quia ad hoc quod de aliquo sit scientia oportet quod sit ens, quia de non ente non est scientia, primo Posteriorum. Secundo oportet quod sit intelligibile, quia scientia est habitus intellectivus, sexto Ethicorum. Et habet causas et principia oportet, ut apparet primo Posteriorum et primo Physicorum. Minor declaratur, quia mores naturales habent causam naturalem. Primo, habet causam naturalem sive subiectum, sicut animal vel homo est subiectum eorum, quia per aptitudines naturales homines vel animalia inclinantur ad diversa opera, quandoque ad audaciam, quandoque ad furtum, et consimilia. Habent etiam causas effectivas, sicut corpora supercelestia et generantia que dant [hu]mores. Vel secundum quosdam, subiectum primum est causa efficiens morum naturalium per modum esse et non per modum transmutationis. Et hoc est secundum illos qui ponunt quod subiectum se habet in duplici genere cause respectu proprie passionis, scilicet materialis et efficientis. Causa finalis istorum est operatio. Alia instrumentalis sanguis,368 calor et similia et signa colorum et dispositionis, ita quod mores consecuntur animal ratione anime sensitive et intellective, non vegetative. Causam formale non habent, quia sunt ipsemet quedam forme, et forme non est forma. Sic ergo apparet secundum, scilicet quod de istis est scientia. Vnde secundum Philosophum in De secretis, Phylomon primo adinvenit istam scientiam, multum habens eam in honore. Unde ibi in fine369 recitatur quod scolares Yppocratis370 scripserunt figuram Yppocratis371 in pergameno et ibant ad Phylomonem et quesiverunt qualis conditionis est iste. Ille autem dixit quod incontinens e luxuriosus et male morigeratus . Et hiis auditis scolares Yppocratis372 voluerunt ipsum interficere. Et ipse dixit: nescivi cuius figura erat, sed iudicavi secundum artem: quid ergo petitis michi? Illi autem recedentes istud dixerunt Yppocrati. Respondens Yppocras dicit: ita est. Tamen sibi cavebat ut dixit et posuit rationem regi/233ra/men sui corporis. Hiis autem auditis

367 natura vel mos naturalis] sermo F 368 sanguinis(?) F 369 Secr. secr. IV.1, 165. 370 Galieni F 371 Galieni F 372 Galieni F

Appendix

427

scolares Yppocratis erant contempti de Philomone. Sic ergo apparet quod de moribus naturalibus est scientia. 3.3 Tertio dico quod ista scientia non est ita certa sicut quedam alie scientie, scilicet mathematice et plures alie naturales, quia licet forte quedam scientie primo demonstrent per effectus, tamen ultimate demonstrant per causas. Et talis scientia est certa. Ista autem scientia per effectus passiones investigat, causas non assignando; tamen oportet causas assignare. Et ego faciam. Sic ergo sit dictum ad questionem. Ad 1. Tunc ad rationes. Ad 1.1 Ad primam. Cum dicitur “de partibus non est scientia,” concedo; et cum dicitur “mores naturales sunt etc.”, interimo; et ad probationem, cum dicitur quod non solum hic determinatur de moribus in specie humana, sed de moribus cuiuslibet hominis puta collerici, fleumatici et talis figure, dico quod licet hic determinetur de moribus hominis in communi, quia non de moribus Sortis vel Platonis, sed de moribus cuiuslibet talis figure et complexionis hic determinatur, licet forte ista considerare373 sit magis particularis quam considerare mores secundum se. Ad 1.2 Ad aliam. Cum dicitur “omnis scientia est necessaria,” dico quod verum est— scientia omnino certa, sicut est mathematica, scientia autem que est certissima, sicut apparet secundo Metaphysice. Et cum dicitur “ista non est huiusmodi,” dico quod ymmo, ut est in pluribus, licet non omnino et hoc sufficit. Et tu dicis quod non, quia determinatur per signa que non necessitant animal ad tales mores, dico quod accidit ut in pluribus, quod signa in partibus principalioribus talia coaptant animal ad tales mores. Et hoc sufficit ad hoc quod de aliquo sit scientia. Ad 1.3 Ad tertiam. Cum dicitur “omnis scientia est per causas,” dico quod verum est— scientia perfecta. Ad minorem, cum dicitur “ista scientia non est huiusmodi,” dico quod ymmo, quia aliquo modo Aristoteles assignavit causas universales et particulares, licet non omnes. Forte autem hoc dimisit, quia hoc pertinet ad mathematicos vel ad astrologos. Vel forte volebat quod homines essent attenti circa istam scientiam inquirendo causas; ideo dimisit assignare causas particulares; tamen causas naturales satis assignavit. Vel posset dici quod non ita perfectam scientiam hic tradidit, sicut in aliis libris fecit. Et hoc per causas dictas. Vel forte non est translatum adhuc, sicut multa alia opera Aristotelis ad nos non pervenerit. Et sic ad illud. 373

considerare] -tive F

428

Appendix

F Anonymus Monacensis, Commentum super Sophisticos Elenchos, qq. 1–4 I mainly follow M, except for q. 2bis which M omits. In particular, I follow M—before its corrections—at the end of q. 4, since these corrections (corresponding to the A version), transforming a disjunctive proposition into a conjunctive one, make the text inconsistent. A = Admont, Bibliothek des Benediktinerstifts, 241, 31vb-32ra; M = München, BSB, clm 14246, 13ra-b (see on MDZ: https://www.digitale-sammlungen. de/en/view/bsb00046853?page=,1). /A 31vb//M 13ra/

Postea374 queritur de fallacia consequentis, et primo375 de eius nominatione,376 scilicet377 quare potius dicitur378 fallacia consequentis quam antecedentis. Quia non videtur ratio: fit enim hec fallacia a destructione antecedentis sicut a positione consequentis.379 Et potest dici quod consequens est dignius quam antecedens, et a digniori debet fieri nominatio.380 Vel aliter dicendum quod381 non nominatur fallacia consequentis quia fit382 a positione consequentis, quia sic383 eadem ratione fallacia antecedentis nominaretur,384 ut obiectum est, quia aliquando fit385 a destructione antecedentis, nec iterum sic nominatur386 quia peccat in eo quod est non sequi conclusionem ex premissis, quia sic eadem ratione plures alie fallacie387 nominarentur fallacia consequentis; sed appellatur sic388 a suo principio motivo: decipiuntur enim propter consequentiam bonam389 tamquam390 principium motivum. 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390

Postea] Circa secundum A primo] queritur add. A nominatione] nomine A scilicet] et primo queritur A dicitur] appelletur A Quia non videtur ratio… a positione consequentis] om. M consequens est dignius… fieri nominatio] a digniori denominatur: consequens autem dignius est antecedente A dicendum quod] quia A quia fit] eo quod fiat A sic] om. A fallacia antecedentis nominaretur] inv. A ut obiectum est, quia aliquando fit] cum fiat A nec iterum sic nominatur] et iterum non dicitur fallacia consequentis A sic eadem ratione plures alie fallacie] plures fallacie eadem ratione A sic] fallacia consequentis A bonam] om. A tamquam] propter add. A

429

Appendix

M

A

Postea queritur de unitate istius loci, quia sicut diversi sunt loci dialetici procedendo ab inferiori ad superius, et econverso, quia unus est locus a specie, alius autem est locus a genere, similiter videtur quod procedendo a superiori ad inferius affirmando et econverso negando sunt duo loci sophistici.

Postea queritur de unitate, cum locus a superiori ad inferius sit unus locus dialeticus, locus ab inferiori ad superius alius dialeticus locus ab illo secundum speciem differens. Videtur similiter quod procedere a superiori ad inferius affirmando et ab inferiori ad superius negando faciant duos locos sophisticos. [Vel propter quid non]

Et dicendum391 quod loci dialetici diversificantur penes392 diversam intentionem393 inferentis et illati,394 et quia inferius et superius—sive genus et species—sunt diverse395 intentiones, ob hoc sunt396 diversi loci dialetici;397 sed fallacie distinguuntur penes principia motiva et quia idem est principium motivum, sive arguatur M

A

a superiori ad inferius affirmando sive econverso negando, etiam unus locus [locus] secundum speciem quocum \illorum duorum/ modorum [[at]] generat.

a positione consequentis sive a destructione antecedentis, et erit unus locus sophisticus secundum speciem. Et sic patet solutio.

Hoc habito secundo queretur de sufficientia paralogismorum huius fallacie, quia cum fiat fallacia consequentis ab insufficienti et ab inferiori ad superius398 negando dicendum] est add. A penes] diversitatem add. et del. M diversam intentionem] diversitatem A illati] secundum intensionem add. A diverse] et alie add. A sunt] erunt A dialetici] va- diversificantur penes diuersitatem inferentis et illati secundum intentionem -cat add. et del. A 398 superius] superiori A 391 392 393 394 395 396 397

430

Appendix

et a superiori ad inferius affirmando, et huiusmodi modos non tangat, videtur esse insufficiens. Ad hoc dicendum est quod omnis paralogismus huius fallacie aut est a positione consequentis aut a destructione antecedentis, et uterque istorum dicit auctor; et ponit in littera quod omnis paralogismus consequentis ad aliquem istorum modorum reducitur. Et ex hoc patet quod arguendo ab insufficienti iste modus reducitur ad illum qui est a positione consequentis aut ad illum qui est a destructione antecedentis: si enim fit ab insufficienti affirmative, reducitur illa argumentatio ad illum modum qui est a positione consequentis; si autem fiat negative, reducitur ad illum [ad illum] modum qui est a destructione antecedentis. Item, iste modus arguendi qui est ab inferiori ad superius negando continetur sub illo modo qui est a destructione antecedentis; ille qui est a superiori ad inferius affirmando continetur sub illo modo qui est a positione consequentis. et sic patet quod sufficienter tangit omnes modos huius fallacie.399

Consequenter queritur de eis que sunt in littera. Et primo de hoc quod dicit fallaciam fieri ex sensu circa opinionem, quomodo istud habet400 intelligi et istud idem401 iam402 aliquo modo patuit in sententia, tamen sic potest obici quia hec prepositio ‘ex’ denotat causam materialem ex qua, ergo—ut videtur—“sensus est materia ex qua sunt deceptiones,”403 quod nichil est dictu. Si autem exponatur sic:404 ex sensu,405 id est post sensum, ita quod hec prepositio ‘ex’ denotet ordinem et sumatur una prepositio pro alia, et huius ratio potest esse406 quia sensus decipitur primo407 iudicans rubeum esse mel408 et opinio, que est quedam virtus, accipit a sensu eo modo quo habet sensus; et ita possunt deceptiones fieri409 in opinione.

399 400 401 402 403 404 405 406 407 408 409

Hoc habito secundo… modos huius fallacie] om. M habet] habeat A idem] om. A iam] in add. A deceptiones] sive fallacie add. A Si autem exponatur sic] Si dicatur quod fallacia dicitur fieri A sensu] circa opinionem add. A potest esse] ex predictis est A primo] om. A rubeum esse mel] fel esse mel eo quod utrumque est rubeum A possunt deceptiones fieri] potest (patet, ms.) fieri deceptio A

431

Appendix M

A

Sed hoc [p(…) non] videtur esse contra Aristotelem in secundo De anima qui dicit quod sensus non decipitur etc. Propter hoc queritur quomodo ista littera habet exponi.

Si ita respondeatur, tunc videtur ista responsio esse contra Aristotelem in libro De anima qui dicit quod sensus non decipitur, et ita videtur solutio nulla. Propter hoc queritur de expositione illius verbi.

Ad hoc intelligendum410 est quod est quidam411 sensus communis qui accipit a quolibet sensu412 particulari, et de omnibus que apprehenduntur a sensibilibus particularibus413 iudicat;414 cum ergo aliquis per visum percipiat415 [recipiat] in melle ruborem et iterum per gustum sapiat416 quoniam dulce sit,417 sensus aliquis418 noscens419 ab istis particularibus ponit mel cum rubore et ruborem cum melle iudicans omne rubeum esse mel, et similiter omne dulce esse mel et econverso, et decipitur ille sensus; postea420 alia virtus que est opinio quedam accipit, hoc est421 a sensu communi,422 eo modo quo sensus habet,423 et ita similiter decipitur opinio ponens mel /A 32ra/ esse rubeum et econverso. Et ita patet quod sensus communis primo decipitur et post424 sensum communem abstrahens425 ab illo. Et hoc modo426 potest exponi verbum illud quod fallacie, id est deceptiones, fiunt circa opinionem ex sensu, id est post sensum,

410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426

intelligendum] dicendum A est quidam] inv. A sensu] om. A a sensibilibus particularibus] in sensu A iudicat] indicat A passim percipiat] om. A sapiat] quantum add. M sit] om. A sensus aliquis] inv. A noscens] nesciens A postea] alie virtutes add. et del. M est] om. A communi] et nonnisi add. A habet] habuit A post] opinio est A abstrahens] attrahens A hoc modo] ex hoc A

432

Appendix

ut hec prepositio dicat427 ordinem,428 vel429 terminum a quo, ut430 sensus sit:431 illud a quo. M

A

Ad illud autem quod obicitur quod sensus non decipitur etc., dicendum quod sensus particularis non decipitur in proprio obiecto, quia particularis sensus non iudicat; sed sensus communis iudicat et in iudicando decipitur. Et de isto intelligendum quod dicit hic.

Ad aliud quod obicitur quod sensus non decipitur, distinguendum duplicem sensum: communem et particularem. Particularis sensus non decipitur in proprio suo obiecto, quia particularis sensus non iudicat, et de tali sensu intelligit Aristoteles; sed communis sensus qui iudicat iudicando (ind-, ms.) decipitur, et de isto intelligendum est hic.

Item potest queri:432 cum soli sophiste pertineat433 uti fallaciis istis, videtur quod non rethorico;434 male ergo ponit exemplum de paralogismis huius fallacie in materia rethorica, sed in435 dialetica deberet ponere.436 Item,437 dicit quod hic est fallacia consequentis:

ut hec prepositio dicat] ita quod ‘ex’ denotat A ordinem] et non causam materialem ut dictum est prius add. A vel] [ex] prepositio ‘ex’ dicet A ut] sit add. et del. M sit illud] fallacie, id est deceptiones fiunt cira opinionem tamquam ad terminum ad quem ex sensu, id est tamquam termino add. A 432 Item potest queri] Postea A 433 pertineat] conveniat A 434 rethorico] rethoriquo M 435 in] materia add. A 436 ponere] exemplum tantummodo add. A 437 Item] ipse add. A 427 428 429 430 431

433

Appendix M

A

‘iste est com

tus, ergo adulter’ vel ‘iste est errabundus de nocte, ergo est adulter’, consequentia non sequitur econverso, quare mentitur dicendo quod ibi est fallacia consequentis.

iste est errabundus de nocte, ergo est adulter et latro’: secundum quod comptus (coopertus, ms.) est adulter, secundum quod est errabundus de nocte est latro; sed consequentia non sequitur econuerso: ‘iste est adulter, ergo est errabundus de nocte’; nec in alio exemplo, quare non ibi est fallacia consequentis, cuius oppositum innuit.

Ad primum dicendum quod sophista438 arguit in omni materia sicut et dialeticus, unde bene concedendum439 quod rethor in eo quod rethor440 non utitur fallaciis; sed in eo quod sophista. Si obiciatur sic441 quod in omnibus paralogismis huiusmodi vel442 huius fallacie non debeat443 ponere exempla in materia rethorica ex quo non utitur fallaciis, dicendum quod bene obiceret444 si solum rethor argueret in materia rethorica,445 sed hoc non est verum, immo et \sophista/ [sophistica].446

M

A

Ad aliud dicendum quod ibi non est /13rb/ fallacia consequentis ‘iste est errabundus de nocte, ergo est adulter vel latro’, sicut obiectum fuit, nec in alio exemplo, nec auctor hoc vult, scilicet, quod hoc vitaret sit ibi fallacia consequentis.

Ad illud quod postea obicitur dicendum quod hic non est fallacia consequentis ‘iste est errabundus de nocte, ergo est latro’, quia non sequitur econuerso, sicut obiectum fuit. Item similiter nec in alio exemplo, nec illud vult auctor, scilicet quod hoc modo sit ibi fallacia consequentis.

438 439 440 441 442 443 444 445 446

sophista] sophistica A concedendum] est add. A rethor] retor M; recthor A sic] tunc A huiusmodi vel] om. A debeat] deberet A obiceret] obiceres A solum rethor argueret in materia rethorica] rethor in materia rethorica solum argueret A et \sophista/ [sophistica] ] in materia sophistica et non in eo quod retor, sed in eo quod sophista A

434

Appendix

Sed auctor innuit quod adiuncta que secuntur latronem sive adulterum sumuntur sub disiunctione—et non quodlibet per se divisim447—et ex illis sic sumptis inferatur illud cui adiungitur et tunc est fallacia consequentis. Verbi gratia ‘iste est errabundus de nocte vel448 vivit ex rapto vel449 consequitur pravam societatem vel450 nichil lucratur et satis expendit,451 ergo est latro’, hic est fallacia consequentis: sequitur enim econverso, quia si est latro, habet aliquam452 istarum proprietatum. Et sic debet intelligi illud quod dicit auctor et non eo modo quo obiectum fuit.453

G

Robertus Kilwardby(?), Expositio super libros Elenchorum,

C = Cambridge, Peterhouse 205, 295rb-296rb; P = Paris, BNF 16619, 22vb-23vb (see on Gallica: https://gallica.bnf.fr/ark:/12148/ btv1b525112607.r=16619?rk=21459;2). QUI AUTEM SECUNDUM CONSEQUENS [Soph El 5 167b1ff.]. In hac parte determinat de loco sophistico secundum consequens et dividitur in duas, in quarum prima dat causam universalem secundum quam contingit decipere in hac fallacia, in secunda cum dicit SEPE ENIM declarat illam causam per exempla; dat ergo causam454 universalem huius loci dicens quod elenchus apparens qui fit secundum consequens fit eo quod putant respondentes consequentiam converti que non convertitur. Et hoc manifestat: quia enim cum antecedens est, de necessitate sequitur quod sit consequens, putant respondentes quod cum consequens est, similiter necesse sit antecedens esse;455 hoc tamen non oportet. Et hec est QUI AUTEM SECUNDUM CONSEQUENS. Et intellige per ‘illud’ semper consequens /C 295va/ per ‘hoc’ et ‘alterum’ semper antecedens. Et tunc plana est sententia littere. Hoc habito declarat istam causam per exempla et dividitur hec pars in duas, in quarum prima ponit paralogismos peccantes a positione consequentis; in secunda, cum dicit SIMILITER AUTEM ET IN SILLOGISTICIS, ponit unum paralogismum peccantem 447 sumuntur sub disiunctione et non quodlibet per se divisim] et non quodlibet secundum se divisum A 448 vel] del., et add. s.l. M; et A 449 vel] del., et add. s.l. M; et A 450 vel] et M 451 expendit] expedit M 452 aliquam] aliam M 453 obiectum fuit] obicitur A 454 per exempla… causam] om. C 455 necesse sit antecedens esse] antecedens esse necesse sit P

Appendix

435

a destructione antecedentis. Pars prima habet duas, in quarum prima dat orationes in quibus consequentia conversa est necessaria; in secunda, cum dicit ET IN RETHORICIS, dat orationes in quibus consequentia conversa est tantum probabilis. In parte prima sic procedit: dicit quod deceptiones que456 sunt circa opinionem, id est457 deceptiones que accidunt eo quod opinatur consequentiam converti que458 non convertitur fiunt ex sensu, id est ex cognitione sensitiva; et hoc manifestat dicens quod quia mel rubeum est,459 ideo suspicati sunt sepe homines fel esse mel, cum videant fel esse rubeum, sicut est mel. Et similiter quia accidit terram, cum depluta est, fieri madidam, opinamur pluisse quando videmus terram esse madidam; quod tamen non est necessarium. In hoc ergo dedit materiam460 duorum paralogismorum quorum primus sic potest formari si placet: si est mel, est rubeum; et hoc est rubeum (demonstrato felle); ergo fel est mel. Secundus paralogismus potest sic formari: si terra est depluta, ergo est madida; sed est madida; ergo est depluta. In utroque istorum paralogismorum est fallacia consequentis a positione consequentis. Et hoc est UNDE ET QUE TERRA. Consequenter dat materiam paralogismorum in quibus consequentia conversa non est necessaria, sed tantum probabilis. Et habet hec pars duas particulas secundum quod dat primo duas orationes et secundo, cum dicit PLURIBUS AUTEM, manifestat defectum in illis. Proponit ergo sic: dicit quod quidam paralogismi huius fallacie sunt ex adiunctis que quidem adiuncta sunt in rethoricis461 demonstrationes secundum signa, et sunt huiusmodi adiuncta accidentia que ut frequentius concomitantur suum subiectum. Et hoc est ET IN RETHORICIS. Postea dat materiam duorum paralogismorum dicens quod volentes ostendere quod aliquis sit adulter accipiunt quod adiunctum est adultero,462 scilicet quod sit comptus, et ex hoc inferunt ipsum esse adulterum; aut ad ostendendum quod aliquis sit fur acci/P 23ra/piunt quod adiunctum est furi, scilicet quod sit errabundus de nocte, et ex hoc inferunt ipsum esse furem. In hoc ergo tetigit materiam duorum paralogismorum, quorum primus sic potest formari: si aliquis est adulter, ipse est comptus; sed iste est comptus; ergo iste463 est adulter; secundus potest sic formari: si aliquis est fur, est errabundus de nocte; sed iste est errabundus de nocte; ergo iste464 est fur. Et hoc est VOLENTES ENIM.

456 457 458 459 460 461 462 463 464

que] qua C id est] et P que] cum P rubeum est] inv. P dedit materiam] dividit materia C rethoricis] vel add. P adultero] adverbio C iste] om. P iste] om. P

436

Appendix

Hoc habito manifestat defectum in duabus orationibus iam positis dicens quod peccant quia hec adiuncta insunt465 pluribus quibus predicatum non inest, et intellige per ‘predicatum’ illud cui insunt adiuncta; et quia ita est quod adiuncta conveniunt pluribus quam ea quorum sunt adiuncta, ideo non sequitur quod466 de quocumque predicatur adiunctum de eodem467 predicetur illud cuius est adiunctum. Et hoc est PLURIBUS AUTEM. Hoc habito sequitur pars illa468 in qua dat unam orationem secundum consequens peccantem a destructione antecedentis; et primo dat orationem, secundo ut ibi NON NECESSE EST AUTEM, manifestat eius peccatum. Procedit ergo sic: dicit quod fit quandoque fallacia consequentis in orationibus factis ad modum sillogismi, sicut se habet ratio Melixi per quam voluit ostendere mundum esse infinitum. Et potest ratio eius sic formari: omne quod est factum habet principium; mundus non est factus; ergo mundus non habet principium; est igitur infinitus.469 Et hoc est SIMILITER AUTEM. In hac ratione sic procedit: primo ponit conclusionem, cum dicit QUONIAM INFINITUM; secundo minorem, ibi SUMENS QUIDEM, id est assumens pro minori; tertio probationem minoris, ibi NAM EX NICHILO; quarto declarationem /C 295vb/ minoris, ibi QUOD AUTEM FACTUM EST;470 quinto resumit minorem et infert conclusionem suam cum conclusione ulteriori, cum dicit SI ERGO NON EST. Probatio autem minoris quam innuit potest esse talis: (…)

1. Dubitatur hic primo: cum deceptio in ista fallacia proveniat ex ydemptitate que est inter antecedens et consequens, quare magis denominatur471 locus iste a consequente quam ab antecedente? 2. Similiter cum hoc queratur de causa universali decipiendi secundum hunc locum: dicit enim quod sicut cum antecedens est, necesse est consequens, putamus quod cum consequens est, necesse est antecedens esse, patet ergo quod ipse semper velit conversam consequentiam in paralogismo consequentis esse necessariam; sed in hoc videtur quod ipse innuat falsum: dicit enim in littera quod hic est fallacia consequentis ‘iste est

465 466 467 468 469 470 471

insunt] sunt P quod] add. in mg. P eodem] eo C illa] om. C infinitus] -um C P EST] om. C denominatur] nominatur C

Appendix

437

comptus, ergo est adulter’; nec tamen est consequentia conversa necessaria: non enim est necesse /P 23rb/ ad hoc ut aliquis sit adulter quod472 iste sit comptus. 3.1 Adhuc autem cum in dictis exemplis sit locus dialeticus et locus dialeticus necessariam habeat consequentiam; nunc igitur cum ipso coincidet locus sophisticus consequentis,473 et locus iste inter omnes locos maxime474 impedit consequentiam. 3.2 Adhuc locus ab adiunctis est locus rethoricus secundum quod dicitur in quarto Topicorum Boetii, quod argumenta rethorica sumuntur ab adiunctis persone et negocio; locus autem rethoricus debet facere suspicionem vel fidem; et si hoc est,475 ergo non deficiet a consequentia; non ergo erit ibi fallacia consequentis. 4. Adhuc dubitatur de hoc quod dicit in manifestando defectum talium paralogismorum. Dicit enim quod adiuncta insunt multis quibus non insunt predicata: nonne adiuncta in dictis paralogismis sunt predicata? Constat quod sic. Videtur igitur quod idem dicit476 ac si diceret “hec adiuncta insunt multis quibus hec adiuncta477 non insunt”; sed hoc nichil est dictu, quare apparet sermo suus vanus. 5. Adhuc autem dubitatur de478 hoc quod dicit manifestando defectum ultimi paralogismi: debet enim ostendere hoc argumentum479 peccare ‘mundus non est factus, ergo non habet principium’, et dicit hanc consequentiam non valere ‘mundus habet principium, ergo est factus’; hoc nichil videtur ad propositum; aut si sit ad propositum queritur quomodo et quare magis manifestaret peccatum predicti480 paralogismi in suo converso quam in se. 1. Ad primum dicendum quod locus universaliter tam dialeticus quam sophisticus recipit suam denominationem a medio. Hoc patet in locis dialeticis: cum enim medium inferens est diffinitio, tunc est locus a diffinitione; quando autem est diffinitum, tunc est locus a diffinito; et ita de aliis. Similiter in locis sophisticis: quando enim medium est equivocum, est locus equivocationis; quando autem medium est accidentale respectu extremorum, tunc est locus accidentis; et ita de aliis. Ergo generaliter 472 473 474 475 476 477 478 479 480

quod] ut C consequentis] om. C inter omnes locos maxime] maxime inter omnes locos P est] om. P quod idem dicit] oratio idem dicere C multis quibus hec adiuncta] add. in mg. P de] ad C ostendere hoc argumentum] hoc argumentum ostendere P predicti] dicti P

438

Appendix

omnis locus recipit suam481 denominationem a medio termino; sed in hoc loco semper est medius terminus consequens ad alterum extremorum482 et ideo denominatur483 locus iste a consequente; ab antecedente vero minime. Quod autem medium /C 296ra/ in isto loco semper sit consequens respectu unius extremi sic patet: quando aliquid infertur ex alio, medium inferens aut est in eque cum suo484 illato, aut est inferius eo, aut superius. Extraneum enim non potest esse, cum debeat aliud inferre. Si inferens et illatum sint in eque, tunc bonum est argumentum et non incidit fallacia consequentis. In convertibilibus enim non cadit consequens. Si inferens sit in minus et illatum in plus, tunc est bonum argumentum ab inferiori ad superius affirmando et non est tunc fallacia consequentis. Si vero medium inferens sit in plus et illatum in minus, tunc est semper fallacia consequentis et est semper medium consequens ad aliquod extremorum. Et ita patet quare magis denominatur iste locus a consequente quam ab antecedente. 2. Ad secundum potest dici quod quando Aristoteles dicit “si cum hoc est, necesse est illud esse” etc., non intendit consequentiam semper esse necessariam, sed veram; potest enim consequentia esse vera licet non sit necessaria, sicut vult Boethius in Topicis suis, nisi distinguit quod argumentorum alia sunt necessaria et non probabilia, alia probabilia et non necessaria, alia probabilia et necessaria, alia nec probabilia nec necessaria. Vel potest dici aliter, sicut vult Aristoteles in sua Metaphysica: omne anologum si debeat diffiniri aut describi, describitur prout est in illo in quo primo et per se salvatur; sed hec fallacia potissime salvatur in primis paralogismis qui scilicet fiunt iuxta primum modum, et in talibus est consequentia conversa necessaria. Convenienter ergo dedit causam universalem decipiendi /P 23va/ per hanc fallaciam in potissimo esse huius fallacie. 3. Ad tertium autem, quia bipertita est oppositio, ideo bipertita est responsio. 3.1 Quantum enim ad hoc quod opponit de sillogismo dialetico, dicendum quod adiuncta quedam sunt propria et quedam communia; propria sunt illa que necessario consecuntur ea quorum sunt adiuncta et convertuntur cum illis, sicut habere lac se habet ad parere, et485 talia vocat Aristoteles in fine Priorum signa prodigia sive signa in prima figura; et de huiusmodi adiunctis sive signis intelligit Boethius cum dicit quod

481 482 483 484 485

suam] om. P extremorum] extremum C denominatur] denotatur C suo] om. C et] ad P

Appendix

439

Cicero486 et Themistius487 posuerunt locum ab adiunctis esse locum dialeticum; adiuncta autem communia sunt signa que sunt in plus quam ea quorum sunt adiuncta, et talia vocat Aristoteles in libro Priorum signa in secunda figura, ut pallida esse est signum ad peperisse, et cum tali adiuncto bene potest fieri fallacia consequentis. Sed adhuc tale adiunctum contingit esse dupliciter in argumento, quia aut accipitur unum solum adiunctum commune ad inferendum illud cuius est adiunctum, et tunc semper fit fallacia consequentis, ut ‘hec est488 pallida, ergo peperit’; aut accipiuntur plura huiusmodi adiuncta ad inferendum illud cuius sunt adiuncta, et tunc est bonum argumentum, et non accidit fallacia consequentis. 3.2 Ad hoc autem quod opponit de argumento rethorico dicendum quod re vera tale argumentum infert necessario ad faciendum fidem489 vel suspicionem. Fiunt autem talia argumenta ut frequentius ex signis consequentibus, sed distinguendum est: aut enim sumuntur plura adiuncta ad inferendum illud cuius sunt adiuncta, et tunc est bonum argumentum, aut490 sumitur tantum unum, et hoc contingit dupliciter: aut enim illud adiunctum sumitur cum circumstanciis,491 et tunc492 est bonum argumentum rethoricum secundum quod habetur in quarto Topicorum Boethii quod questio rethorica est involuta circumstanciis; aut sine circumstanciis, et sic est semper fallacia consequentis. 4. Ad quartum dicendum quod per predicatum intendit maiorem extremitatem que maxime habet rationem predicati: est enim illud quod de altero ostenditur. Et ita patet satis intentio illius493 littere. 5. Ad quintum dicendum quod duplex potest esse ratio quare non manifestavit peccatum illius rationis in se sed in suo antecedente. Una quia eadem est bonitas et idem peccatum alicuius argumenti et sui conversi; ut ergo illud hic significaret, manifestavit peccatum eius in sua conversa et non /C 296rb/ in se. Et ita magis significat hoc modo faciendo quam aliter. Alia ratio potest esse de eodem quod hoc fecit ut significaret quod idem modus in substantia est arguendo a positione consequentis et a destructione antecedentis: destructio494 enim antecedentis est consequens ad destructionem 486 487 488 489 490 491 492 493 494

Cicero] Cithero(?) C Themistius] Chomentissimus(?) P est] om. P fidem] finem C P aut] cum P circumstancii] circumstancia P tunc] sic P illius] om. P destructio] destructo C

440

Appendix

consequentis; et ita cum prius ponitur destructio antecedentis et infertur destructio consequentis, prius ponitur consequens et deinde infertur antecedens. Patet igitur quod isti modi paralogizandi sunt idem modi in substantia et ad hoc significandum manifestavit495 Aristoteles peccatum unius in altero. 6.1 Consequenter queritur que est causa apparentie et que causa non existentie in hoc loco. 6.2 Et simul cum hoc queratur qui et quot sunt modi paralogizandi secundum hunc locum. 6.1 Et dicendum ad primum quod causa apparentie in hoc loco est idemptitas antecedentis ad consequens, quia enim tanta est idemptitas antecedentis ad consequens quod posito antecedente de necessitate ponitur consequens; ideo credimus quod eadem est habitudo consequentis ad antecedens quod scilicet /P 23vb/ consequente posito de necessitate ponatur antecedens, cum tamen hoc non sit necesse. Causa vero non existentie est diversitas inter antecedens et consequens. 6.2 Ad secundum dicendum quod tantum duo sunt modi paralogizandi in hac fallacia: dicit enim Aristoteles quod fit hec fallacia cum putamus conversam converti que non convertitur. Supponit ergo in hoc loco semper duplicem esse consequentiam et super eosdem496 terminos. Dico: aut enim utraque consequentia est necessaria, aut altera tantum, aut neutra. Si utraque sit necessaria, tunc non decipitur qui putat consequentiam converti, et ita non accidit tunc fallacia consequentis. Si autem una sit necessaria et alia non, cum videt unam consequentiam esse necessariam et credit eius conversam497 esse necessariam, decipitur per fallaciam consequentis, et est primus modus a positione498 consequentis. Si autem neutra sit necessaria, cum apprehendit unam esse probabilem et credit suam conversam esse probabilem, tunc decipitur per fallaciam consequentis, et fit tunc secundus modus, ut accidit in argumentis ab adiunctis. 7. Et si queratur quare non sunt diversi modi penes positionem consequentis et destructionem antecedentis, dicendum quod sunt idem modus in substantia, sicut pretactum est.

495 496 497 498

significandum manifestavit] manifestandum significavit P eosdem] eodem P conversam] consequentiam C positione] petitione C

Appendix

H

441

Radulphus Brito, Questiones super Sophisticos Elenchos, I.48

See also the complete edition of these questions in Emamzadah (2022), I. B = Bruxelles, Bibliothèque Royale de Belgique, 3540–47, 530va-531rb; S = Salamanca, Biblioteca Universitaria, 2350, 189rb-vb. Utrum fallacia consequentis sit locus sophisticus Consequenter499 queratur circa fallaciam consequentis,500 et501 primo utrum sit locus sophisticus. 1. Arguitur quod non. 1.1 Quia ubi est inutilis coniugatio non est locus sophisticus; in fallacia consequentis est inutilis coniugatio, ergo etc. Maior patet, quia inutilis coniugatio pertinet ad librum Priorum et per consequens non est fallacia que pertinet ad librum502 Elenchorum. Minor patet: in secunda figura arguendo ex affirmativis fit503 fallacia consequentis et504 est inutilis coniugatio, ut patet primo Priorum. 1.2 Item,505 non habemus fallaciam antecedentis, /B 530vb/ ergo nec consequentis; antecedens patet, consequens declaratur: quia sicut in consequentia est consequens ita antecedens. 1.3 Item, locus dialeticus506 debet denominari507 /S 189va/ ab inferente; sed inferens est antecedens; ergo magis debet esse locus sophisticus antecedentis quam consequentis. 1.4 Item, ubi est locus rethoricus non est locus sophisticus; sed ubi est fallacia consequentis est locus rethoricus; ergo etc. Maior patet, quia locus rethoricus et dyaleticus secundum essentiam sunt idem, nec differunt nisi sicut commune et contractum sub communi, secundum Boethium, in quarto508 Topicorum suorum; sed locus ­dyaleticus 499 500 501 502 503 504 505 506 507 508

Consequenter] dictis(?) add. S consequentis] corr. ex accidentis B et] om. S librum] Priorum add. et del. S fit] con(stituit)ur(?) S et] est(?) B Cf. Simon de Faverisham, Quaest. novae sup. Soph El, q. 33, ed. Ebbesen et al., 189. dyaleticus] dyali’ticus B passim denominari] denominare B; ab in add. S quarto] 9(?) B

442

Appendix

et sophisticus non sunt idem, sed509 similes,510 ergo nec rethoricus et sophisticus . Probatio minoris: quia, secundum Philosophum, fallacia consequentis fit ex adiunctis; modo ex adiunctis est locus rethoricus; ideo etc. 1.5 Item, locus dyaleticus511 est ex communiter accidentibus; ergo non erit locus sophisticus; sed fallacia consequentis fit ex communiter accidentibus; ergo fallacia consequentis non est locus sophisticus. 2. In oppositum est Philosophus. 3.1 Ad hoc est dicendum quod fallacia consequentis est locus sophisticus. Cuius ratio est, quia quod habet causam apparentie et defectus est locus sophisticus; sed fallacia consequentis est huiusmodi; ideo etc. Maior patet, quia ista duo principaliter, scilicet causa apparentie et defectus, sufficienter constituunt locum sophisticum. Minor declaratur, quia causa apparentie istius fallacie est ydemptitas512 partialis antecedentis ad consequens: quia enim tanta est ydemptitas antecedentis ad consequens quod posito antecedente ponitur consequens, credimus quod eadem sit habitudo consequentis ad antecedens quod posito consequente ponatur antecedens, cum tamen non oporteat. Vel possumus dicere quod causa apparentie istius fallacie est ydemptitas bone consequentie ad malam, quia sicut videmus quod ad antecedens sequitur consequens, ita credimus econverso, /B 531ra/ cum tamen non sit necessarium. Causa autem defectus in ea est diversitas istarum consequentiarum vel diversitas antecedentis et consequentis. 3.2 Sed notandum est quod duo sunt modi istius fallacie: unus est a positione consequentis et alius a destructione antecedentis. 3.3 Item, notandum est quod in fallacia consequentis non oportet alteram consequentiarum semper esse bonam, sed sufficit quod sit probabilis. Et propter hoc, cum dicitur quod causa apparentie eius est ydemptitas bone consequentie ad malam, ibi accipitur ‘consequentia’ large pro vera consequentia vel pro513 probabili. Vel potest dici quod, quia consequentia dicitur principaliter de vera consequentia et ex consequenti de probabili,514 et frequentius fit ista fallacia et principalius ex ydemptitate antecedentis

509 510 511 512 513 514

idem sed] om. S; add. in mg. B similes] simili B; simul S dyaleticus] rethoricus B ydemptitas] ydempti B pro] om. S Vel potest dici… ex consequenti de probabili] om. B

Appendix

443

veri ad consequens;515 ideo dicitur quod hec fallacia fit ex eo quod creditur516 consequentia converti que non convertitur, vel ex ydemptitate antecedentis et consequentis. Et ad517 istam intentionem etiam dicit Aristoteles in littera quod si ad antecedens sequitur518 consequens credimus quod ad consequens sequatur antecedens. Ad 1. Ad rationes. Ad 1.1 Ad primam.519 Cum dicitur “ubi est inutilis coniugatio etc.”, dicendum quod consequens potest dupliciter considerari: uno modo ut est obliquitas pura520 sillogismi simpliciter et sic est inutilis coniugatio, et pertinet ad librum Priorum; alio modo ut addit aliquam causam apparentie per quam videtur521 bona /S 189vb/ consequentia, que non est bona, et sub ista ratione est locus sophisticus et pertinet ad librum Elenchorum. Ad 1.2–3 Ad aliam. Quando dicitur “non habemus fallaciam522 antecedentis; ergo etc.”, dicendum quod locus sophisticus debet denominari ab inferente. Modo dico quod in fallacia consequentis istud quod realiter est consequens habet rationem inferentis, sicut dicendo ‘homo currit, ergo animal currit’: hic est bona consequentia; sed si dicatur ‘animal currit, ergo homo currit’, hic est fallacia consequentis. et ibi inferens est ‘animal currit’ quod in veritate est consequens. Et ita debet dici fallacia consequentis. Eodem modo sic proceden/B 531rb/do a destructione antecedentis, sicut dicendo ‘non est homo, ergo non est animal’: hoc enim quod dico ‘non est homo’ est consequens secundum veritatem ad non esse animal, quia sequitur ‘non est animal, ergo non est homo’. Et ideo adhuc ibi inferens est illud quod est consequens, et ideo dicitur fallacia consequentis et non antecedentis. Ad 1.4 Ad aliam. Cum dicitur “ubi est523 locus rethoricus etc.”, concedatur; et cum dicitur “ex adiunctis est locus rethoricus etc.”, dicendum quod ex adiunctis quedam sunt propria et quedam communia. Propria sunt illa que necessario sequuntur rem cuius sunt adiuncta, sicut524 ‘habere lac’ se habet ad ‘parere’, et talia vocat Aristoteles, in fine 515 516 517 518 519 520 521 522 523 524

consequens] corr. B ex consequentis creditur] credatur S ad] ex sed del. B sequitur] sequatur S Ad primam] om. B pura] puri B videtur] corr. B ex ut non habemus fallaciam] om. S ubi est] om. B sicut] sic B

444

Appendix

Priorum, ‘prodigia’, et ibi est locus dyaleticus vel rethoricus. Communia autem sunt in plus quam res cui sunt adiuncta, sicut ‘ista est pallida, ergo peperit’; et in talibus est bene fallacia consequentis. Sed adhuc notandum est525 quod ista communia adiuncta dupliciter possunt accipi, quia aut accipitur unum solum adiunctum ad inferendum illud cuius est adiunctum, et tunc est fallacia consequentis, ut ‘est pallida, ergo peperit’; aut accipiuntur plura adiuncta526 ad inferendum illud cuius sunt adiuncta, et bene tunc fit527 argumentum rethoricum et non fallacia consequentis. Ad 1.5 Per idem patet ad aliam, quia communiter accidentia quedam sunt semper consequentia, et in talibus est locus dyaleticus; alia sunt que quandoque sequuntur, et528 quandoque non, et in talibus est fallacia consequentis. 525 526 527 528

est] om. S adiuncta] coniuncta S fit] sic S et] om. B

References CAG translations listed here are those that have been used in the present work. AHDLMA = Archives d’Histoire Doctrinale et Littéraire du Moyen Âge CIMAGL = Cahiers de l’Institut du Moyen-Âge Grec et Latin LCL = Loeb Classical Library

Sources Alan of Lille, Summa “Quoniam homines,” ed. P. Glorieux. AHDLMA 20, 1954, 113–364. Alan of Lille, Textes inédits, ed. M. Th. D’Alverny. Paris: Vrin, 1965. Albert the Great, Commentarii in Job, ed. M. Weiss. Freiburg i. B.: Herder, 1904. Albert the Great, De animalibus libri XXVI, 2 vols., ed. H. Stadler. Münster: Aschendorff, 1916–1920. Albert the Great, De homine, eds. H. Anzulewicz and J.R. Söder, in Alberti Magni Opera omnia, vol. 27.2. Münster: Aschendorff, 2008. Albert the Great, Liber Elenchorum (Opera omnia vol. 2), ed. A. Borgnet. Paris: Vives, 1890. Albert the Great, Liber Posteriorum Analyticorum (Opera omnia vol. 2), ed. A. Borgnet. Paris: Vives, 1890. Albert the Great, Liber Priorum Analyticorum (Opera omnia, vol. 1), ed. A. Borgnet. Paris: Vives, 1890. Albert the Great, Physicorum Libri VIII, (Opera omnia, vol. 3), ed. A. Borgnet. Paris: Vives, 1890. Albert the Great, Quaestiones de animalibus, ed. E. Filthaut, in Alberti Magni Opera omnia, vol. 12. Münster: Aschendorff, 1955. Albert the Great, Super Porphyrium de V universalibus, ed. M. Santos Noya, in Alberti Magni Opera omnia, vol. 1.1. Münster: Aschendorff, 2004. Alexander of Aphrodiasis, In Aristotelis Topicorum libros octo commentaria (CAG 2.2), ed. M. Wallies. Berlin: Reimer, 1891. Transl. On Aristotle Topics 1, ed. J.M. Van Ophuijsen. London: Bloomsbury, 2000. Alexander of Aphrodiasis, In Aristotelis Analyticorum Priorum Librum I commentarium (CAG 2.1), ed. M. Wallies. Berlin: Reimer, 1883. Transl. On Aristotle Prior Analytics 1.1– 7, eds. J. Barnes, S. Bobzien, K. Flannery, K. Ierodiakonou. London: Bloomsbury, 1991. Alexander of Hales, Summa theologica. Vol. 1. ed. Collegium S. Bonaventurae. Quaracchi, Florence: Collegium S. Bonaventurae, 1924. Algazel, Logica, ed. C.H. Lohr. Traditio 21, 1965, 223–290.

446

References

Alhazen, Opticae thesaurus. Alhazeni Arabis libri septem, nunc primum editi. Eiusdem liber De crepusculis et Nubium ascensionibus. Item Vitellonis Thuringopoloni libri X. Omnes instaurati, figuris illustrati et aucti, adiectis etiam in Alhazenum commentarijs, a Federico Risnero. Basel, 1572; repr. New York, 1972. Transl. The Optics of Ibn al-Haytam. Books I–III, ed. A.I. Sabra. London: The Warburg Institute and the ­University of London, 1989. Anselm of Canterbury, Cur Deus homo? (Opera omnia, vol. 2), ed. F.S. Schmitt. Rome, 1940. Anonymus, Ars Burana, ed. de Rijk, LM II.2, 175–213. Anonymus, Ars Emmerana, ed. de Rijk, LM II.2, 143–174. Anonymus, Commentum super librum Topicorum “Supposita divisione,” ms. Todi, ­Biblioteca Comunale, 54, 1r–56v. Anonymus, Dialectica Monacensis, ed. de Rijk, LM II.2, 453–638. Anonymus, Excerpta Norimbergensia, ed. de Rijk, LM II.2, 109–141. Anonymus, Fallaciae ad modum Oxoniae, ed. C. Kopp. PhD Dissertation, Universität zu Köln, 1985 (= SE33). Anonymus, Fallaciae Lemovicenses, eds. S. Ebbesen and Y. Iwakuma. CIMAGL 63, 1993, 3–42 (= SE23). Anonymus, Fallacie Parvipontane, ed. de Rijk, LM I, Appendix E, 545–609 (= SE17). Anonymus, Glosa super Graecismum Eberhardi Bethunensis, ed. A. Grondeux. ­Turnhout: Brepols, 2011. Anonymus, Glose in Aristotilis Sophisticos Elenchos, ed. de Rijk, LM I, Appendix A, 187–255 (= SE5). Anonymus, Glossae Salamantinae super Tractatus Petri Hispani, ms. Paris, Bibliothèque Nationale de France, Lat. 6433, 153ra–258vb. Anonymus, Introductiones Parisienses, ed. de Rijk, LM II.2, 353–373. Anonymus, Logica “Cum sit nostra,” ed. de Rijk, LM II.2, 413–451. Anonymus, Logica “Ut dicit,” ed. de Rijk, LM II.2, 375–411. Anonymus, Notae Dunelmenses V, eds. A. Grondeux and I. Rosier-Catach. Turnhout: Brepols, 2018. Anonymus (Radulphus Brito?), Notule super Tractatus Petri Hispani, ms. München ­Bayerische, Staatsbibliothek, clm 6726, 1r–39v. Anonymus, Ripoll Compendium (Guide de l’étudiant), ed. C. Lafleur. Québec: Faculté de Philosophie, Université Laval, 1992. Anonymus, Summa Sophisticorum Elencorum, ed. de Rijk, LM I, Appendix B, 257–457 (= SE6). Anonymus, Tractatus de dissimilitudine argumentorum, ed. de Rijk, LM I, Appendix C, 459–489 (= SE7). Anonymus, Tractatus de fallaciis, ms. München, Bayerische Staatsbibliothek, clm 14763, 123vb–125rb (= SE28).

References

447

Anonymus Aurelianensis I, Commentarium in Sophisticos Elenchos, ed. S. Ebbesen. CIMAGL 34, 1979b, i–xlviii, 1–200 (= SE13). Anonymus Aurelianensis II, De paralogismis, ed. S. Ebbesen. CIMAGL 16, 1976, 1–128 (= SE14). Anonymus Aurelianensis III, In Aristotelis Analytica Priora, ed. C. Thomsen ­Thörnqvist. Leiden: Brill, 2015. Anonymus Brugensis, Quaestiones super Analytica Posteriora, ms. Brugge, Stedelijke Openbare Bibliotheek, 509, 59ra–75va. Anonymus Cantabrigiensis, Commentarium in Sophisticos Elenchos, ed. S. Ebbesen. Copenhagen: Royal Danish Academy, 2019 (= SE15). Anonymus Cordubensis, Quaestiones super Analytica Posteriora, ms. Cordoba, Biblioteca del Excellentissimo Cabildo, 52, 80va–100rb. Anonymus Monacensis, Commentarium super Sophisticos Elenchos, ms. München, ­Bayerische Staatsbibliothek, clm 14246, 1ra–48rb (= SE34) (Excerpts in Appendix F). Anonymus Monacensis, Quaestiones super Analytica Posteriora I, ms. München, ­Bayerische Staatsbibliothek, clm 14460, 239ra–242ra. Anonymus Monacensis, Tractatus de fallaciis, ms. München, Bayerische Staatsbibliothek, clm 14763, 123vb–125ra (= SE28). Anonymus Parisiensis, Compendium Sophisticorum Elenchorum. (The Uppsala ­Version), ed. S. Ebbesen. CIMAGL 66, 1996, 253–312 (= SE8). Anonymus Praguensis, Quaestiones super Sophisticos Elenchos, ed. D. Murè, qq. 7–19, CIMAGL 68, 1998, 63–97; qq. 142, PhD Thesis, Università di Roma “La Sapienza,” 1997–1998 (= SE74). Anonymus-SF, Quaestiones super Sophisticos Elenchos, ed. S. Ebbesen. Copenhagen: G.E.C. Gad, 1977 (= SE64). Anselm of Canterbury, De veritate (Opera omnia, vol. 1), ed. F.S. Schmitt. Edinburgh: Nelson, 1946; repr. Stuttgart: F. Frommann, G. Holzboog, 1968. Apollonius Dyscolus, Περὶ συντάξεως (De la construction), ed. J. Lallot. Paris: Vrin, 1997. Aristotle, Meteorologica (LCL 397), transl. H.D.P. Lee. Cambridge, MA: Harvard University Press, 1952. Aristotle, On Rhetoric, transl. G.A. Kennedy. Oxford: Oxford University Press, 2007. Aristotle, On Sophistical Refutations (LCL 400), transl. E.S. Forster. Cambridge, MA: Harvard University Press, 1955. Aristotle, Parva Naturalia (LCL 288), transl. W.S. Hett. Cambridge, MA: Harvard ­University Press, 1957. Aristotle, Posterior Analytics, ed. and transl. J. Barnes. Oxford: Clarendon, 1993. Aristotle, Prior Analytics, ed. and transl. R. Smith. Indianapolis: Hackett, 1989. Aristotle, Topics. Books I and VIII with excerpts from related texts, ed. and transl. R. Smith. Oxford: Clarendon, 1997.

448

References

Arnald of Villanova, Expositiones visionum que fiunt in somniis (Opera omnia, vol. 1). Basileae: ex officina Pernea per Konradum Waldkirch, 1585. Augustine of Hippo, De doctrina christiana (Corpus Christianorum, Series Latina, vol. 3), ed. I. Martin. Turnholt: Brepols, 1962. Averroes, [Long Commentary on the Posterior Analytics] (Aristotelis opera cum Averrois commentariis, vol. 1.2). Venice: apud Junctas, 1562. Averroes, [Long Commentary on the Physics] (Aristotelis opera cum Averrois commentariis, vol. 4). Venice: apud Junctas, 1562. Avicenna, Canon medicinae. Venice: per Dionysium Bertocum, 1490. Transl. Canon of Medicine, ed. O.C. Gruner. London, 1930; repr. New-York: AMS, 1973. Avicenna, Kitāb al-Najāh, ed. M. Fakhry. Beirut: Dar al-’Afaq al-Jadidah, 1985. Transl. in Avicenna’s Psychology. An English Translation of Kitāb al-Najāh, ed. F. Rahman. Westport, CT: Hyperion Press, 1952. Avicenna, Kitāb al-Šifā’. Transl. in Avicenna’s De Anima, Being the Psychological Part of Kitāb al-Shifā’, ed. F. Rahman. London: Oxford University Press, 1959. Avicenna, Al-Išārāt wa-al-tanbīhāt, ed. J. Forget. Leiden: Brill, 1892. Transl. Remarks and Admonitions, ed. S.C. Inati. Toronto: Pontifical Institute of Mediaeval Studies, 1984. Avicenna Latinus, Liber de anima seu sextus de naturalibus, ed. S. Van Riet. Leuven: Peeters; Leiden: Brill, 1972. Avicenna Latinus, Liber de philosophia prima sive Scientia divina, vol. 1, ed. S. Van Riet. Leuven: Peeters; Leiden: Brill, 1977. Avicenna Latinus, Logyca. Venice: per Bonetum Locatellum, 1508. Bernardus Silvestris(?), Super sex libros Eneidos Virgilii, eds. J. and E. Jones. Lincoln, NE: University of Nebraska Press, 1977. Boethius, De hypotheticis syllogismis, ed. L. Orbetello. Brescia: Paideia, 1969. Boethius, De syllogismo categorico, ed. C. Thomsen Thörnqvist. Göteborg: University of Göteborg, 2008. Boethius, In Ciceronis Topica, PL 64, col. 1039D–1169. Boethius, De differentiis topicis, PL 64, col. 1173B–1215D. Transl. De topicis differentiis, ed. E. Stump. Ithaca, NY: Cornell University Press, 1978. Bonaventure of Bagnoregio, Commentarius in quartum librum Sententiarum Petri Lombardi (Opera omnia, vol. 4), ed. Collegium S. Bonaventurae. Quaracchi, Florence: Collegium S. Bonaventurae, 1889. [Cornificius seu Incertus auctor] Rhetorica ad C. Herennium (LCL 403), ed. G. Calboli. Vol. 1: Prolegomena, testo critico e traduzione, Berlin-Boston: De Gruyter, 2020 (first ed.: Bologna: Pàtron, 1969). Transl. H. Caplan. Cambridge, MA: Harvard University Press, 1964. Eberhard of Béthune, Graecismus, ed. J. Wrobel. Breslavia, 1887; repr. Hildesheim: Olms, 1987.

References

449

Gerard of Nogent (Gerardus de Nogento), Quaestiones super Analytica Posteriora, ms. Paris, Bibliothèque Nationale de France, Lat. 16170, 113rb–127va. Giles of Rome (Aegidius Romanus), De medio in demonstratione. ed. in Pinborg (1976). Giles of Rome, Super Libros Posteriorum Analyticorum. Venice, 1488. Giles of Rome, Expositio super Rhetoricam Aristotelis. Venice, 1515. (Excerpts in ­Appendix B). Giles of Rome, Expositio super Libros Elenchorum. Venice, 1496; repr. Frankfurt am Main, 1967 (= SE65). Grillius, Commentum in Ciceronis Rhetorica, ed. R. Jakobi. München: Saur, 2002. Hugh of St. Victor, Super Hierarchiam Dionisii, ed. D. Poirel. Turnhout: Brepols, 2015. James of Douai (Iacobus de Duaco), Quaestiones super Analytica Posteriora, ms. Klosterneuburg, Stiftsbibliothek, CCI 274, 148ra–161va. John Duns Scotus, Reportata Parisiensia, II–IV (Opera omnia, vol. 23), ed. L. Wadding. Paris: Vivès, 1894. John of Salisbury (Iohannes Saresberiensis), Metalogicon, eds. J.B. Hall and K.S.B. Keats-Rohan. Turnhout: Brepols 1991. Lambert of Auxerre, Logica (Summa Lamberti), ed. F. Alessio. Firenze: La Nuova Italia, 1971. Manegold of Lautenbach, Liber contra Wolfelmum, ed. W. Hartmann. Weimar: ­Hermann Bölhaus, 1972. Engl. transl. R. Ziomkowski. Leuven: Peeters, 2002. Marius Victorinus, Commenta in Ciceronis Rhetorica. Band I: Prolegomena; Band II: Kritischer Kommentar und Indices, ed. T. Riesenweber. Berlin: De Gruyter, 2015. Marius Victorinus, Explanationes in Ciceronis Rhetoricam, ed. A. Ippolito. Turnhout: Brepols, 2006. Master Simon, Expositio super Tractatus Petri Hispani, mss.: Padova, Biblioteca Antoniana, 429, 1ra–27rb; Paris, Bibl. Nationale de France, lat. 16126, 77ra–90rb; München, Bayerische Staatsbibliothek, clm 14679, 1ra–48rb; Milan, Bibl. Ambrosiana, F.56. sup. (Excerpts in Appendix C). Menegaldus, In Ciceronis Rhetorica glose, ed. F. Bognini. Firenze: SISMEL – Edizioni del Galluzzo, 2016. [Michael of Ephesus], Alexandri quod fertur in Aristotelis Sophisticos Elenchos commentarium (CAG 2.3), ed. M. Wallies. Berlin: Reimer, 1898. Nicholas of Paris, Notule Topicorum Boethii, ms. München, Staatsbibliothek, clm 14460, 152ra–166vb (= B.20; cf. Green-Pedersen 1984, 428–429). Nicholas of Paris, Summe Metenses, ms. Paris, Bibl. Nat. de France, Lat. 11412, 25r–40r (De fallaciis, 31r–35r = SE42) (Extracts in LM II.1, 473–478). Peter Abelard, Dialectica, ed. L.M. de Rijk. Assen: van Gorcum, 1959. Peter Abelard, Glossae super Perì Hermeneias, eds. K. Jakobi and C. Strub. Turnhout: Brepols, 2010.

450

References

Peter Abelard, Philosophische Schriften. I. Die Logica “Ingredientibus.” 1. Die Glossen zu Porphyrius, ed. B. Geyer. Münster im Westfalen: Aschendorff, 1919. Peter Abelard, Philosophische Schriften. II. Die Logica “Nostrorum petitioni sociorum.” Die Glossen zu Porphyrius, ed. B. Geyer. Münster im Westfalen: Aschendorff, 1933. Peter Abelard, Theologia Christiana, ed. E.M. Buytaert. Turnhout: Brepols, 1969. Peter Abelard, Theologia Scholarium, eds. E.M. Buytaert and C.J. Mews. Turnhout: ­Brepols, 1987. Peter Damian, De divina omnipotentia, ed. A. Cantin. Paris: Les Éditions du Cerf, 1972. Peter Damian, Die Briefe des Petrus Damiani, ed. K. Reindel. München: Monumenta Germaniae Historica, 1989. Peter Helias, Summa super Priscianum, ed. L. Reilly. Toronto: Pontifical Institute of Mediaeval Studies, 1993. Peter of Abano, Conciliator differentiarum philosophorum et medicorum, s.l., 1490. Peter of Abano, Liber compilationis physionomie. Padova: per Petrum Maufer, 1474. Peter of Abano, Lucidator dubitabilium astronomiae, ed. G. Federici Vescovini. Padova: Programma: 1+1, 1988. Peter of Spain, Tractatus, called afterwards Summule logicales, ed. L.M. de Rijk. Assen: van Gorcum, 1972. Philoponus, In Aristotelis Analytica Posteriora commentaria cum anonymo in librum I (CAG 13.3), ed. M. Wallies. Berlin: Reimer, 1909. Transl. On Aristotle Posterior Analytics 1.1–8, ed. R. McKirahan. London: Bloomsbury, 2008; On Aristotle Posterior Analytics 1.9–18, ed. R. McKirahan. London: Bloomsbury, 2012; On Aristotle Posterior Analytics 1.19–34, eds. O. Goldin and M. Martijn. London: Bloomsbury, 2012; On Aristotle Posterior Analytics 2, ed. O. Goldin. London: Bloomsbury, 2009. Philoponus, In Aristotelis Meteorologicorum librum primum commentarium (CAG 14.1), ed. M. Hayduck. Berlin: Reimer, 1901. Transl. On Aristotle Meteorology 1.1–3, ed. I. Kupreeva. London: Bloomsbury, 2011. Philoponus, In Aristotelis de anima libros commentaria (CAG 15), ed. M. Hayduck. Berlin: Reimer, 1897. Transl. On Aristotle On the Soul 1.1–2, ed. P. van der Eijk. London: Bloomsbury, 2005. Philoponus, In Aristotelis Physicorum libros tres priores commentaria (CAG 16), ed. H. Vitelli. Berlin: Reimer, 1887. Transl. On Aristotle Physics 1.1–3, ed. C. Osborne. London: Bloomsbury, 2006. Priscian, Institutionum grammaticarum libri, ed. M. Hertz. Lipsiae: Teubner, 1855. Pseudo-Aristotle, Rhetoric to Alexander (LCL 317), transl. D.C. Mirhady. Cambridge, MA: Harvard University Press, 2011. Pseudo-Kilwardby, Commenti super Priscianum maiorem extracta, eds. K.M. Fredborg, N.J. Green-Pedersen, L.O. Nielsen and J. Pinborg. CIMAGL 15, 1975, 1–146. Pseudo-Philoponus, In Aristotelis Anlytica Priora commentaria (CAG 13.2), ed. M. ­Wallies. Berlin: Reimer, 1905.

References

451

Radulphus Brito, Quaestiones super Analytica Posteriora, ms. Bruxelles, Bibliothèque Royale “Albert Ier”, 2910 (3540–47), 372ra–460ra. (q. II.25 = Appendix A). Radulphus Brito, Quaestiones super libro Topicorum Boethii, eds. N.J. Green-Pedersen and J. Pinborg. CIMAGL 26, 1978, 1–92. Radulphus Brito, Questiones libri De physionomia, ms. Firenze, BNC, Conv. Soppr. E.I.252, 232vb-242va (q. 1 = Appendix E). Radulphus Brito, Questiones super Metaphysicam, ms. Firenze, BNC, Conv. Soppr. E.1.252, 265–310; partial ed. in Ebbesen (2001). Radulphus Brito, Questiones super Sophisticos Elenchos, I.10–19, ed. S. Ebbesen. CIMAGL 68, 1998, 185–227 (I.48 = Appendix H); complete edition in Emamzadah (2022), I. Radulphus Brito, Sophisma “Omnis homo est omnis homo,” eds. N.J. Green-Pedersen and J. Pinborg. CIMAGL 26, 1978, 93–114. Robert Grosseteste, Commentarius in Posteriorum Analyticorum libros, ed. P.B. Rossi. Firenze: Olschki, 1981. Robert Kilwardby(?), Commentarium in Sophisticos Elenchos, mss.: Cambridge, Peterhouse 205, 277ra–344vb; Paris, Bibliothèque Nationale de France, lat. 16619, 1ra–71vb. (Excerpts in Appendix G). Robert Kilwardby, De ortu scientiarum, ed. A.G. Judy. London: British Academy; Toronto: The Pontifical Institute of Mediaeval Studies, 1976. Robert Kilwardby, Notule libri Posteriorum, ed. D. Cannone. PhD Thesis, Università degli Studi di Cassino and Università di Roma “La Sapienza,” 2003–2004. Robert Kilwardby, Notule libri Priorum, 2 vols., eds. and transl. P. Thom and J. Scott. Oxford: Oxford University Press for the British Academy, 2015. Robert Kilwardby, Notulae libri Prisciani De accentibus, ed. O.P. Lewry. Mediaeval Studies 50, 1988, 96–185. Robert Kilwardby, Scriptum super libro Topicorum, ms. Oxford, Bodleian Library, Canon. misc. 403. Roger Bacon, Communium naturalium libri, 3 vols. (Opera hactenus inedita, vols. 2–4), ed. R. Steele. Oxford, Clarendon, 1909–1913. Roger Bacon, Compendium studii theologiae, ed. and transl. Th.S. Maloney. Leiden: Brill, 1988. Roger Bacon, De multiplicatione specierum and De speculis comburentibus, ed. and transl. D. Lindberg. Oxford: Clarendon, 1983. Roger Bacon, De signis, eds. K.M. Fredborg, L.O. Nielsen and J. Pinborg. Traditio 34, 1978, 75–136. Engl. transl. On Signs, ed. Th.S. Maloney. Toronto: Pontifical Institute of Mediaeval Studies, 2013. Roger Bacon, Opus majus, 2 vols., ed. J.H. Bridges. Oxford: Clarendon, 1897–1900. Roger Bacon, Opus tertium (Opera hactenus inedita, vol. 1), ed. J. Brewer. London: ­Longman, 1859. Roger Bacon, Secretum secretorum (Opera hactenus inedita, vol. 5), ed. R. Steel. Oxford: Clarendon, 1920.

452

References

Roger Bacon, Summulae dialectices, ed. A. de Libera. I–II: De termino. De enuntiatione: AHDLMA 53, 1986, 167–289; III: De argumentatione: AHDLMA 54, 1987, 191–278. Rufinus of Aquileia, Commentarius in Symbolum Apostolorum, ed. M. Simonetti. ­Turnhout: Brepols, 1961. Sedulius Scotus, In Donati artem maiorem. In Priscianum. In Eutychem, ed. B. Lofstedt. Turnhout: Brepols, 1977. Simon of Faversham, Quaestiones libri Priorum, mss.: Milano, Biblioteca Ambrosiana C.161.Inf. 34vb-64va; Oxford, Merton College 292, 110ra-138va (q. II.14 = Appendix D) Simon of Faversham, Quaestiones super libro Elenchorum, eds. S. Ebbesen, T. Izbicki, J. Longeway, F. Del Punta, E. Serene, and E. Stump. Toronto: Pontifical Institute of Mediaeval Studies, 1984 (Quaestiones veteres super libro Elenchorum, 23–97; Quaestiones novae super libro Elenchorum, 99–233). Simon of Faversham, Quaestiones veteres super Analytica Posteriora, in Simon of Faverhsam, Quaestiones super libro Posteriorum, ed. and transl. by J. Longeway, longeway. wordpress.com, 2016. Simon of Tournai, Institutiones in sacram paginam. An Edition of His Introduction about Signification, ed. C. Marmo. CIMAGL 67, 1997, 93–103. Simon of Tournai, Institutiones in sacram paginam, ed. F. Siri. PhD Thesis, Università di Roma “La Sapienza,” 2011. Simplicius, In Aristotelis Physicorum libros quattuor priores commentaria (CAG 9), ed. H. Diels. Berlin: Reimer, 1885. Themistius, Analyticorum Posteriorum paraphrasis (CAG 5.1), ed. M. Wallies. Berlin: Reimer, 1900. Themistius, In Aristotelis Physica paraphrasis (CAG 5.2), ed. H. Schenkl. Berlin: Reimer, 1900. Transl. On Aristotle Physics 1–3, ed. R.B. Todd. London: Bloomsbury, 2012. Themistius, Paraphrasis of the Posterior Analytics in Gerard of Cremona’s Translation, ed. J. Reginald O’Donnell. Medieval Studies 20, 1958, 239–315. Thierry of Chartres, Commentarius super libros De inventione, ed. K.M. Fredborg. Toronto: Pontifical Institute of Mediaeval Studies, 1988. Thomas Aquinas, Expositio libri Posteriorum. Editio altera retractata, ed. R.-A. Gauthier. Rome: Commissio Leonina; Paris: Vrin, 1989. Thomas Aquinas, Summa Theologiae, ed. Commissio Leonina. Roma, 1888–1906. William of Champeaux(?), In De inventione, ms. York, Minster Library, XVI.M.7. William of Champeaux, Notae Dunelmenses II and IV, in Grondeux and Rosier-Catach, eds. (2017). William of Conches, Glose super Priscianum, mss.: Firenze, Bibl. Medicea Laurenziana, S. Marco 310, 1ra–82vb; Paris, BNF, lat. 15130, 1ra–137va; Oxford, Bodleian Lib., Laud. lat. 67, 15ra–19va. William of Sherwood, Introductiones in logicam. Einführung in die Logik, eds. H. Brands and C. Kann. Hamburg: Felix Meiner, 1995.

References

453

Studies Agrimi, Jole (2002). Ingeniosa scientia nature: studi sulla fisiognomica medievale. ­Tavarnuzze, Impruneta: SISMEL – Edizioni del Galluzzo. Alessio, Franco (1971). “Introduzione.” In Lambert of Auxerre, Logica (Summa L­ amberti), ed. F. Alessio, xi–lxiii. Firenze: La Nuova Italia, 1971. Allen, James. (2001). Inference from Signs. Ancient Debates about the Nature of Evidence. Oxford: Clarendon Press. Angioni, Lucas (2014). “Aristotle on necessary principles and on explaining X through the essence of X.” Studia Philosophica Estonica 7 (2), 88–112. Angioni, Lucas (2016). “Aristotle’s definition of scientific knowledge (APo 71b9–12).” Logical Analysis and History of Philosophy 19, 79–105. Angioni, Lucas (2018). “Causality and coextensiveness in Aristotle’s Posterior Analytics 1.13.” Oxford Studies in Ancient Philosophy 54: 159–185. Angioni, Lucas (2019). “Aristotle’s definition of syllogism in Prior Analytics 24b18–20.” Manuscript. Angioni, Lucas (2020). “Aristóteles e a necessidade do conhecimento científico.” Discurso 50 (2), 193–238. Ashworth, E. Jennifer (2008). Les théories de l’analogie du XIIe au XVIe siècle. Paris: Vrin. Barnes, Jonathan (1969). “Aristotle’s Theory of Demonstration.” Phronesis 14 (2), 123–152. Barnes, Jonathan (1970). “Property in Aristotle’s Topics.” Archiv für Geschichte der Philosophie 52 (2), 136–155. Barnes, Jonathan (1981). “Proof and the Syllogism.” In Aristotle on Science. The Posterior Analytics, ed. E. Berti, 17–60. Padova: Antenore. Barnes, Jonathan (1993). Aristotle. Posterior Analytics. 2nd edition. Oxford: Clarendon. Barnes, Jonathan (2016). “Les syllogismes dialectiques.” In Logique et dialectique dans l’Antiquité, eds. J.-B. Gourinat and J. Lemaire, 135–159. Paris: Vrin. Bellucci, Francesco (2018). “Signs and demonstration in Aristotle.” British Journal for the History of Philosophy 26 (3), 410–428. Bellucci, Francesco (2019). “Aristotelian Abductions: A Reply to Florez.” Transactions of the Charles S. Peirce Society 55 (2), 185–196. Bellucci, Francesco and Costantino Marmo (2018). “Sign and Demonstration in Late-ancient Commentaries on the Posterior Analytics.” CIMAGL 87, 1–33. Bertagna, Mario (2002). “La divisio textus nel commento di Egidio Romano agli Analitici Posteriori. Parte I.” Documenti e studi sulla tradizione filosofica medievale 13, 285–371. Bertagna Mario (2003). “La divisio textus nel commento di Egidio Romano agli Analitici Posteriori. Parte II.” Documenti e studi sulla tradizione filosofica medievale 14, 263–326.

454

References

Bertagna Mario (2004). “La divisio textus nel commento di Egidio Romano agli Analitici Posteriori. Parte III.” Documenti e studi sulla tradizione filosofica medievale 15, 439–486. Bertolacci, Amos (2007). “Avicenna and Averroes on the Proof of God’s Existence and the Subject-Matter of Metaphysics.” Medioevo. Rivista di storia della filosofia medievale 32, 61–97. Bertolacci, Amos (2018). “‘Averroes ubique Avicennam persequitur’: Albert the Great’s Approach to the Physics of the Šifā in the Light of Averroes’ Criticisms.” In The Arabic, Hebrew and Latin Reception of Avicenna’s Physics and Cosmology, eds. D.N. Hasse and A. Bertolacci, 397–431. Berlin: De Gruyter. Biondi, Paolo C. (2004). Aristotle. Posterior Analytics II.19. Introduction, Greek Text, Translation and Commentary. Saint-Nicolas: Les Presses de l’Université Laval. Black, Deborah L. (1993). “Estimation (Wahm) in Avicenna: The Logical and Psychological Dimensions.” Dialogue 32, 219–258. Black, Deborah L. (2000). “Imagination and Estimation: Arabic Paradigms and Western Transformations.” Topoi 19, 59–75. Black, Deborah L. (2005). “Psychology: Soul and Intellect.” In The Cambridge Companion to Arabic Philosophy, eds. P. Adamson and R.C. Tylor, 308–326. Cambridge: ­Cambridge University Press. Boh, Ivan (1982). “Consequences.” In The Cambridge History of Later Medieval ­Philosophy. From the Rediscovery of Aristotle to the Disintegration of Scholasticism, 1100–1600, eds. Kretzmann, N., A. Kenny, J. Pinborg, and E. Stump, 300–314. ­Cambridge: Cambridge University Press. Bolton, Robert (1995). “Aristotle’s method in natural science: Physics I.” In Aristotle’s Physics. A Collection of Essays , ed. L. Judson, 1–29. Oxford: Clarendon Press. Bonitz, Hermann (1870). Index Aristotelicus. Berlin: Reimer. Borgo, M. 2009. “Themistius on Demonstrative Premisses: A Reading of His Paraphrase of Posterior Analytics, 71b9–72a7.” Documenti e studi sulla tradizione filosofica medievale 20, 149–192. Briggs, Charles F. (2016). “Life, Works, and Legacy.” In A Companion to Giles of Rome, eds. C.F. Briggs and P.S. Eardley, 6–33. Leiden: Brill. Bronstein, David (2016). Aristotle on Knowledge and Learning. The Posterior Analytics. Oxford: Oxford University Press. Brower, Jeffrey E. (2018). “Medieval Theories of Relations.” In Stanford Encyclopedia of Philosophy, ed. E.N. Zalta (https://plato.stanford.edu/entries/relations-medieval/) Brumberg-Chaumont, Julie (2013). “Les divisions de la logique selon Albert le Grand.” In Ad notitiam ignoti. L’Organon dans la translatio studiorum à l’époque d’Albert le Grand , ed. J. Brumberg-Chaumont, 335–416. Turnhout: Brepols. Brumberg-Chaumont, Julie (2015). “Universal Logic and Aristotelian Logic: Formality and Essence of Logic.” Logica Universalis 9, 253–278.

References

455

Brumberg-Chaumont, Julie (2016). “La forme syllogistique et le problème des syllogismes sophistiques selon Robert Kilwardby.” In Formal Approaches and Natural Languages in Medieval Logic. Proceedings of the 19th European Symposium on Medieval Logic and Semantics, Geneva, June 12–16, 2012, eds. L. Cesalli, F. Goubier, and A. de Libera, 93–116. Barcelona: FIDEM. Brumberg-Chaumont, Julie (2017). “Form and Matter of the Syllogism in ­Anonymus Cantabrigiensis.” In The Aristotelian Tradition. Aristotle’s Works on Logic and ­Metaphysics and Their Reception in the Middle Ages, eds. B. Bydén and C. Thomsen Thörnqvist, 187–213. Toronto: Pontifical Institute of Mediaeval Studies. Brumberg-Chaumont, Julie (2019). À l’école de la logique. L’essor d’une norme intellectuelle, sociale et anthropologique au XIIIe siècle. Thèse d’Habilitation, EPHE, Paris. Burnett, Charles (2004). “Lunar astrology. The Varieties of Texts Using Lunar Mansions with Emphasis on Jafar Indus.” Micrologus 12, 43–133. Burnyeat, Myles F. (1981). “Aristotle on Understanding Knowledge.” In Aristotle on ­Science. The Posterior Analytics, ed. E. Berti, 97–139. Padova: Antenore. Burnyeat, Myles F. (1982). “The origins of non-deductive inference.” In Science and Speculation: Studies in Hellenistic Theory and Practice, eds. J. Barnes, J. Brunschwig, M.F. Burnyeat, and M. Schofield, 193–238. Cambridge: Cambridge University Press. Now in M. Burnyeat, Explorations in Ancient and Modern Philosophy, vol. 1, 112–151. Cambridge: Cambridge University Press, 2012. Burnyeat, Myles F. (1994). “Enthymeme: Aristotle on the logic of persuasion.” In Aristotle’s Rhetoric: Philosophical Essays. Proceedings of the Twelfth Symposium Aristotelicum, eds. D.J. Furley and A. Nehamas, 3–55. Princeton, NJ: Princeton University Press. Now in M. Burnyeat, Explorations in Ancient and Modern Philosophy, vol. 1, 152–201. Cambridge: Cambridge University Press, 2012. Caiazzo, Irene (2011). “Manegold, modernorum magister magistrorum.” In Arts du ­langage et théologie aux confins des XIe–XIIe siècles. Textes, maîtres, débats, ed. I. Rosier-Catach, 317–349. Turnhout: Brepols. Cannone, Debora (2002). “Le Notule Libri Posteriorum di Robert Kilwardby: il ­commento ad Analitici Posteriori, I, 4, 73a34–b24 (per se).” Documenti e studi sulla tradizione filosofica medievale 13, 71–135. Celli, Gaia (2018). “Avicenna and Aristotle’s Rhetoric: Lexical Options.” In Commenting on Aristotle’s Rhetoric from Antiquity to the Present. Commenter la Rhétorique d’Aristote, de l’Antiquité à nos jours, ed. F. Woerther, 89–115. Leiden: Brill. Cerami, Cristina (2014). “Signe physique, signe métaphysique. Averroès contre Avicenne sur le statut épistémologique des sciences de l’être.” In Nature et sagesse. Les rapports entre physique et métaphysique dans la tradition aristotélicienne, ed. C. Cerami, 429–474. Louvain: Peeters. Cerami, Cristina (2015). Génération et Substance. Aristote et Averroès entre physique et métaphysique. Berlin: De Gruyter.

456

References

Cesalli, Laurent and Irène Rosier-Catach (2018). “Signum est in praedicamento relationis. Roger Bacon’s Semantics Revisited in the Light of His Relational Theory of the Sign.” Oxford Studies in Medieval Philosophy 6, 62–99. Chiron, P. (2011). “Relative Dating of the Rhetoric to Alexander and Aristotle’s Rhetoric: A Methodology and Hypothesis.” Rhetorica 29 (3), 236–262. Crombie, Alistair Cameron (1953). Robert Grosseteste and the Origin of Experimental Science, 1100–1700. Oxford: Clarendon Press. D’Alverny, Marie-Thérèse (1952). “Notes sur les traductions médiévales d’Avicenne.” AHDLMA 19, 339–358. D’Alverny, Marie-Thérèse (1982). “Translations and translators.” In Renaissance and Renewal in the Twelfth Century, eds. R.L. Benson and G. Constable, 421–462. ­Cambridge, MA: Harvard University Press. Now in D’Alverny (1994), n. 2. D’Alverny, Marie-Thérèse (1994). La transmission des textes philosophiques et scientifiques au Moyen Age. Edited by C. Burnett. Aldershot: Variorum. D’Ors, Angel (1997). “Petrus Hispanus O.P., Auctor Summularum.” Vivarium 35 (1), 21–71. Spanish transl. “Petrus Hispanus O.P., Auctor Summularum.” Dicenda. Cuadernos de Filología Hispánica 19, 243–291. D’Ors, Angel (2001). “Petrus Hispanus O.P., Auctor Summularum (II): Further Documents and Problems.” Vivarium 39 (2), 209–254. Spanish transl. “Petrus Hispanus O.P., Auctor Summularum (II): Nuevos documentos y problemas.” Dicenda. Cuadernos de Filología Hispánica 25, 139–180. D’Ors, Angel (2003). “Petrus Hispanus O.P., Auctor Summularum (III): ‘Petrus Alfonsi’ or ‘Petrus Ferrandi’?” Vivarium 41 (2), 249–303. Spanish transl. “Petrus Hispanus O.P., Auctor Summularum (III): ¿‘Petrus Alfonsi’ or ‘Petrus Ferrandi’?” Dicenda. Cuadernos de Filología Hispánica 33, 35–89. Dahan, Gilbert (1980). “Notes et textes sur la Poétique au Moyen Age.” AHDLMA 47, 171–239. Daiber, Hans (2004). “The Limitations of Knowledge According to Ibn Sīnā. Epistemological and Theological Aspects and the Consequences.” In Knowledge and Science. Problems of Epistlloyemology in Medieval Philosophy, eds. M. Lutz-Bachmann, A. Fidora, and P. Antolic, 25–34. Berlin: Akademie Verlag. De Filippis, Renato (2022). Loquax pagina. La retorica nell’Occidente tardo-antico e alto-medievale. Roma: La città nuova. Denifle, H. and Chatelain, E. (1889). Chartularium Universitatis Parisiensis. Paris: Delalain. de Rijk, Lambert M. (1962). Logica Modernorum. A Contribution to the History of Early Terminist Logic. Vol. I. Assen: van Gorcum (= LM I).

References

457

de Rijk, Lambert M. (1967). Logica Modernorum. A Contribution to the History of Early Terminist Logic. Vol. II.1: The Origin and Early Development of the Theory of Supposition. Vol. II.2: Texts and Indices. Assen: van Gorcum (= LM II.1–II.2). de Rijk, Lambert M. (1968). “On the Genuine Text of Peter of Spain’s Summule logicales, II: Simon of Faversham (d. 1306) as a Commentator of the Tracts I–V of the ­Summule.” Vivarium 6, 69–101. de Rijk, Lambert M. (1969a). “On the Genuine Text of Peter of Spain’s Summule ­logicales, III: Two Redactions of a Commentary upon the Summule by Robertus Anglicus.” Vivarium 7, 8–61. de Rijk, Lambert M. (1969b). “On the Genuine Text of Peter of Spain’s Summule logicales, IV: The Lectura Tractatuum by Guillelmus Arnaldi, Master of Arts at Toulouse (1235–44). With a Note on the Date of Lambert of Auxerre’s Summule.” Vivarium 8, 120–162. de Rijk, Lambert M. (1970). “On the Genuine Text of Peter of Spain’s Summule logicales (Conclusion). V: Some Anonymous Commentaries on the Summule Dating from the Thirteenth Century.” Vivarium 8, 10–55. de Rijk, Lambert M. (1972). “Introduction.” In Peter of Spain, Tractatus, called a­ fterwards Summule logicales, ed. L.M. de Rijk, i-c. Assen: van Gorcum. Di Giovanni, Matteo (2009). “Demonstration and First Philosophy. Averroes on Met. Zeta as a Demonstrative Examination (al-faḥṣ burhānī).” Documenti e studi sulla tradizione filosofica medievale 20, 95–126. Di Giovanni, Matteo (2014). “The Commentator: Averroes’ Reading of the Metaphysics.” In A Companion to the Latin Medieval Commentaries on Aristotle’s Metaphysics, eds. F. Amerini and G. Galluzzo, 59–94. Leiden: Brill. Diller, H. 1932. “Ὄψις αδήλων τὰ φαινόμενα.” Hermes 67 (1), 14–42. Di Martino, Carla (2008). Ratio particularis: Doctrine des senses internes d’Avicenne à Thomas d’Aquin. Paris: Vrin. Di Piazza, Salvatore (2011). Congetture e approssimazioni. Forme del sapere in Aristotele. Milano: Mimesis. Dubouclez, Olivier (2008). L’invention de l’analyse. Généalogie d’un concept d’Aristote à Descartes. Doctoral Dissertation, Paris IV-Sorbonne. Dutmer, Evan (2020). “Aristotle’s Methodology for Natural Science in Physics 1–2: a New Interpretation.” Journal of Ancient Philosophy 14 (2), 130–146 Ebbesen, Sten (1976). “Anonymus Aurelianensis II, Aristotle, Alexander, Porphyry and Boethius. Ancient Scholasticism and 12th Century Western Europe.” CIMAGL 16, 1–128. Ebbesen, Sten (1977). “Jacobus Veneticus on the Posterior Analytics and Some Early 13th Century Oxford Masters on the Elenchi.” CIMAGL 21, 1–9.

458

References

Ebbesen, Sten (1981a). Commentators and Commentaries on Aristotle’s Sophistici Elenchi. A Study of Post-Aristotelian Ancient and Medieval Writings on Fallacies. 3 vols (Corpus Latinum Commentariorum in Aristotelem Graecorum 7.1–3). Leiden: Brill. Ebbesen, Sten (1981b). “Analysing Syllogisms or Anonymus Aurelianensis III – The (presumably) Earlier Extant Latin Commentary on the Prior Analytics and its Greek Model.” CIMAGL 37, 1–20. Now in Ebbesen (2008a), 171–186. Ebbesen, Sten (1981c). “Albert (the Great?) Companion to the Organon.” In Albert der Grosse. Seine Zeit, sein Werke, seine Wirkung (Miscellanea Mediaevalia, 14), ed. A. Zimmermann, 89–103. Berlin: De Gruyter. Now in Ebbesen (2009), 95–108. Ebbesen, Sten (1982). “Ancient Scholastic Logic as the Source of Medieval Scholastic Logic.” In The Cambridge History of Later Medieval Philosophy. From the Rediscovery of Aristotle to the Disintegration of Scholasticism, 1100-1600, eds. N. Kretzmann, A. Kenny, J. Pinborg, and E. Stump, 101–127. Cambridge: Cambridge University Press. Ebbesen, Sten (1990a). “Philoponus, ‘Alexander’ and the Origins of Medieval Logic.” In Aristotle Transformed. The Ancient Commentators and Their Influence, ed. R. Sorabji, 445–461. Ithaca, NY: Cornell University Press. Now in Ebbesen (2008a), 157–170. Ebbesen, Sten (1990b). “Boethius as an Aristotelian commentator.” In Aristotle Transformed. The Ancient Commentators and Their Influence, ed. R. Sorabji, 373–392. Ithaca, NY: Cornell University Press Ebbesen, Sten (1993). “Medieval Latin Glosses and Commentaries on Aristotelian logical Texts of the Twelfth and Thirteenth Centuries.” In Glosses and Commentaries on Aristotelian Logical Texts. The Syriac, Arabic and Medieval Latin Traditions, ed. C. Burnett, 129–177. London: The Warburg Institute and the University of London. Ebbesen, Sten (1996). “Anonymi Parisiensis Compendium Sophisticorum Elenchorum. The Uppsala Version.” CIMAGL 66, 253–312. Ebbesen, Sten (1997). “The Ars Nova in the Ripoll Compendium.” In L’enseignement de la philosophie au XIIIe siècle, ed. C. Lafleur, 325–352. Turnhout: Brepols. Ebbesen, Sten (2002). “Communia ‘Visitatio’ & Communia ‘Feminae’.” CIMAGL 73, 167–258. Ebbesen, Sten (2004) “Echoes of the Posterior Analytics in the Twelfth Century.” In Knowledge and Science. Problems of Epistemology in Medieval Philosophy, eds. M. Lutz-Bachmann, A. Fidora, and P. Antolic, 69–92. Berlin: Akademie Verlag. Ebbesen, Sten (2008a). Greek-Latin Philosohical Interaction: Collected Essays of Sten Ebbesen. Vol. 1. Aldershot: Ashgate. Ebbesen, Sten (2008b). “Fragments of ‘Alexander’s’ Commentaries on Analytica Posteriora and Sophistici Elenchi.” In Ebbesen (2008a), 187–201. Ebbesen, Sten (2009). Topics in Latin Philosophy from the 12th–14th centuries: Collected Essays of Sten Ebbesen. Vol. 2. Aldershot: Ashgate. Ebbesen, Sten (2010). “The Prior Analytics in the Latin West: 12th–13th Centuries.” Vivarium 48, 96–113.

References

459

Ebbesen, Sten (2012). Review of Interpreting Aristotle’s Posterior Analytics in Late Antiquity and Beyond, eds. F. de Haas, M. Leunissen, and M. Martijn (Leiden: Brill, 2010). Aestimatio 9, 355–366. Ebbesen, Sten (2015). “The Posterior Analytics 1100–1400 in East and West.” In Raison et démonstration. Les commentaires médiévaux sur les Seconds Analytiques, ed. J. Biard, 11–30. Turnhout: Brepols. Ebbesen, Sten (2018). “Michael of Ephesus on the Fallacy of Consequent.” CIMAGL 87, 34–38. Ebbesen, Sten (2021). “A New Version of ‘Robertus Anglicus’ on Peter of Spain.” CIMAGL 90, 384–500. Ebbesen, Sten and Costantino Marmo (forthcoming). “Introduction.” In Radulphus Brito, Quaestiones super librum Divisionum Boethii. Turnhout: Brepols. Ebbesen, Sten and Irène Rosier-Catach (2000). “Robertus Anglicus on Peter of Spain.” In Medieval and Renaissance Logic in Spain. Acts of the 12th European Symposium on Medieval Logic and Semantics, University of Navarre, Pamplona, May 26–30, 1997, eds. I. Angelelli and P. Pérez-Ilzarbe, 61–95. Hildesheim: Olms. Ebbesen, Sten and Yukio Iwakuma (1993). “Anonymi Fallaciae Lemovicenses.” CIMAGL 63, 3–42. Eco, Umberto (1975). A Theory of Semiotics. Bloomington: Indiana University Press. Eco, Umberto (1997). “History and Historiography of Semiotics.” In Semiotik/Semiotics. Ein Handbuch su den zeichentheoretischen Grundlagen von Natur und Kultur/A Handbook on the Sign-Theoretic Foundations of Nature and Culture. Vol. 1, eds. R. Posner, K. Robering, and Th.A. Sebeok, 730–746. Berlin: De Gruyter. Einarson, Benedict (1936). “On Certain Mathematical Terms in Aristotle’s Logic.” American Journal of Philology 57, 33–54. Elamrani-Jamal, Abdelali (2000). “La démonstration du signe (burhān al-dalīl) selon Ibn Rushd (Averroès).” Documenti e studi sulla tradizione filosofica medievale 11, 113–131. El-Rouayheb, K. (2017). “Arabic Logic after Avicenna.” In The Cambridge Companion to Medieval Logic, eds. C. Dutilh Novaes and S. Read, 67–93. Cambridge: Cambridge University Press. Emamzadah, Parwana (2022). Édition critique et étude doctrinale des Quaestiones super Sophisticos Elenchos de Radulphus Brito. I: Édition critique. II: Étude doctrinale. Thèse de doctorat ès lettres. Université de Genève, Département de Philosophie. Fausti, Daniela (2008). “Il segno e la prognosi nel Corpus hippocraticum (Prognostico e Prorretico I e II).” I quaderni del ramo d’oro on line 1, 258–278. Federici Vescovini, Graziella (1988). Il “Lucidator dubitabilium astronomiae” di Pietro d’Abano. Opere scientifiche inedite. Prefazione di E. Garin. Padova: Programma: 1+1. Federici Vescovini, Graziella (2005). “Alhazen, lo spazio percettivo del De aspectibus e l’immaginativa.” In Corpo e anima, sensi interni e intelletto dai secoli XIII–XIV ai

460

References

post-cartesiani e spinoziani, eds. G. Federici Vescovini, V. Sorge, and C. Vinti, 79–101. Turnhout: Brepols. Ferejohn, Michael T. (2013). Formal Causes. Oxford: Oxford University Press. Figliuolo, Bruno (2010). “A further Note on ‘Peter of Spain’.” Vivarium 48 (2), 368–369. Flórez, Jorge A. (2014). “Peirce’s Theory of the Origin of Abduction in Aristotle.” Transactions of the Charles S. Peirce Society 50 (2), 265–280. Fredborg, K. Margareta (1971). “The Commentary of Thierry de Chartres on Cicero’s De Inventione.” CIMAGL 7, 1–36. Fredborg, K. Margareta (1973). “The Dependence of Petrus Helias’ Summa super Priscianum on William of Conches’ Glose super Priscianum.” CIMAGL 11, 1–57. Fredborg, K. Margareta (1974). “Petrus Helias on Rhetoric.” CIMAGL 13, 31–41. Fredborg, K. Margareta (1976). “The Commentaries on Cicero’s De inventione and ­Rhetorica ad Herennium by William of Champeaux.” CIMAGL 17, 1–39. Fredborg, K. Margareta (1981a). “Some Notes on the Grammar of William of Conches.” CIMAGL 37, 21–41. Fredborg, K. Margareta (1981b). “Roger Bacon on impositio vocis ad significandum.” In English Logic and Semantics from the End of the Twelfth Century to the Time of ­Ockham and Burleigh. Acts of the 4th European Symposium on Medieval Logic and Semantics, eds. H.A.G.Braakhuis, C.H. Kneepkens, and L.M. de Rijk, 167–191. Turnhout: Brepols. Fredborg, K. Margareta (1987). “The Scholastic Teaching of Rhetoric in the Middle Ages.” CIMAGL 55, 85–105. Fredborg, K. Margareta (1988). “Introduction.” In Thierry of Chartres, Commentarius super libros De inventione, ed. K.M. Fredborg. Toronto: Pontifical Institute of ­Mediaeval Studies. Fredborg, K. Margareta (2009). “Petrus Helias’s Summa on Cicero’s De inventione.” ­Traditio 64, 139–182. Fredborg, K. Margareta (2015). “The De inventione Commentary by Manegold (of Lautenbach?) and its Place in Twelfth-Century Rhetoric.” In Public Declamations. Essays on Medieval Rhetoric, Education and Letters in Honor of M. Camargo, eds. G. Donavin and D. Stodola, 45–64. Turnhout: Brepols. Fredborg, K. Margareta, Niels J. Green-Pedersen, Lauge O. Nielsen and Jan Pinborg, eds. (1975). Roberti Kilwardby quod fertur Commenti super Priscianum maiorem extracta. CIMAGL 15, 1975, 1+–20+ and 1–146. Fredborg, K. Margareta, Lauge O. Nielsen, and Jan Pinborg (1978). “An Unedited Part of Roger Bacon’s ‘Opus Majus’: ‘De Signis’.” Traditio 34, 75–136. Gaetano, Fabrizio (2018) “τεκμαίρομαι nella storiografia di Erodoto: una proposta di lettura.” Aevum 92 (1), 3–16. Gauthier, René-Antoine (1989). “Introduction.” In Thomae Aquinatis Expositio libri Posteriorum. Editio altera retractata. Roma: Commissio Leonina; Paris: Vrin.

References

461

Glasner, Ruth (2009). Averroes’ Physics. A Turning Point in Medieval Natural Philosophy. Oxford: Oxford University Press. Gili, Luca (2011). La sillogistica di Alessandro di Afrodisia: Sillogistica categorica e sillogistica modale nel commento agli Analitici Primi di Aristotele. Hildesheim: Olms. Goldin, Owen (2009). “Introduction.” In Philoponus, On Aristotle Posterior Analytics 2, ed. O. Goldin, 1–10. London: Bloomsbury. Gramigna, Remo (2020). Augustine’s Theory of Signs, Signification, and Lying. Berlin: De Gruyter. Granger, Herbert (1981). “The Differentia and the Per Se Accident in Aristotle.” Archiv für Geschichte der Philosophie 63 (2), 118–129. Green-Pedersen, Niels J. (1973). “On the Interpretation of Aristotle’s Topics in the 13th Century.” CIMAGL 9, 1–46. Green-Pedersen, Niels J. (1984). The Tradition of the Topics in the Middle Ages. The ­Commentaries on Aristotle’s and Boethius’ “Topics.” München: Philosophia Verlag. Green-Pedersen, Niels J. and Jan Pinborg (1978). “Radulphus Brito: Commentary on Boethius’ De differentiis topicis and the Sophism ‘Omnis homo est’.” CIMAGL 26, i–viii. Grimaldi, William M.A (1972). Studies in the Philosophy of Aristotle’s Rhetoric. ­Wiesbaden: Steiner. Grimaldi, William M.A (1980a). Aristotle. Rhetoric I. A Commentary. New York: Fordham University Press. Grimaldi, William M.A (1980b). “Semeion, tekmerion, eikos in Aristotle’s Rhetoric.” American Journal of Philology 101 (4), 383–398. Grondeux, Anne and Irène Rosier-Catach, eds. (2018). Priscien lu par Guillaume de Champeaux et son école. Les Notae Dunelmenses (Durham, D.C.L., C.IV.29). Vol. 1: Introduction. Vol. 2: Edition critique des Notae Dunelmenses. Turnhout: Brepols. Hamesse, Jacqueline (1974). Les Auctoritates Aristotelis. Un florilège médiéval. Etude historique et édition critique. Louvain: Publications Universitaires; Paris: Béatrice Nauwelaerts. Hankinson, Jim (1997), “‘Semeion’ e ‘tekmerion.’ L’evoluzione del vocabolario di segni e indicazioni nella Grecia classica.” In I Greci. Storia cultura arte società. 2. II. Una storia greca. Definizione, ed. S. Settis, 1169–1187. Torino: Einaudi. Hartmann, Wilfried (1997). “Rhetorik und Dialektik in der Streitsschriftenliteratur des 11./12. Jahrhunderts.” In Dialektik und Rhetorik im frühen und hohen Mittelalter, ed. J. Fried, 73–95. München: Oldenbourg. Hasnawi, Ahmad and Wilfrid Hodges (2017). “Arabic Logic up to Avicenna.” In The Cambridge Companion to Medieval Logic, eds. C. Dutilh Novaes and S. Read, 45–66. Cambridge: Cambridge University Press.

462

References

Hasse, Dag Nikolaus (2000). Avicenna’s De Anima in the Latin West. The Formation of a Peripatetic Philosophy of the Soul, 1160–1300. London: Warburg Institute; Torino: Aragno. Henninger, Mark G. (1989). Relations, Medieval Theories 1250-1325. Oxford: Clarendon Press. Hjelmslev, Louis (1943). Omkring sprogteoriens grundlæggelse. København: Munksgaard. Transl. Prolegomena to a Theory of Language. University of Wisconsin, 1961. Holopainen, Toivo J. (1996). Dialectic and Theology in the Eleventh Century. Leiden: Brill. Hornblower, Simon (1987). Thucydides. Baltimore: Johns Hopkins University Press. Hornblower, Simon (1991). A Commentary on Thucydides. Vol. 1. Oxford: Clarendon Press. Hugonnard-Roche, H. (1999). “Averroès et la tradition des Seconds Analytiques.” In Averroes and the Aristotelian Tradition. Sources, Constitution and Reception of the Philosophy of Ibn Rushd (1126–1198), eds. G. Endress, J.A. Aertsen, and K. Braun, 172–187. Leiden: Brill. Hugonnard-Roche, H. (2002). “Logique et physique. La théorie aristotélicienne de la science interprétée par Averroès.” Medioevo. Rivista di storia della filosofia medievale 27, 141–164. Jakobi, Rainer (2005). Grillius. Überlieferung und Kommentar. Berlin: De Gruyter. Janssens, Jules (2013). “Albert le Grand et sa connaissance des écrits logiques arabes: une réévaluation du dossier Grignaschi.” In Ad notitiam ignoti. L’Organon dans la translatio studiorum à l’époque d’Albert le Grand, ed. J. Brumberg-Chaumont, 225–257. Turnhout: Brepols. Jeauneau, Edouard (1957). “L’usage de la notion de integumentum à travers les gloses de Guillaume de Conches.” AHDLMA 24, 35–100. Now in E. Jeauneau, Lectio Philosophorum. Recherches sur l’école de Chartres, 125–192. Amsterdam: Hakkert, 1973. Jeauneau, Edouard (1960). “Deux rédactions des Gloses de Guillaume de Conches sur Priscien.” Recherches de Théologie Ancienne et Médiévale 27, 212–247. Now in E. Jeauneau, Lectio Philosophorum. Recherches sur l’école de Chartres, 335–370. ­Amsterdam: Hakkert, 1973. Kemp, Simon and Garth J.O. Fletcher (1993). “The Medieval Theory of the Inner Senses.” American Journal of Psychology 106 (4), 559–576. King, Peter (2001). “Consequence as Inference: Medieval Proof Theory 1300–1350.” In Medieval Formal Logic, ed. M. Yrjonsuuri, 117–146. Dordrecht: Kluwer. Kopp, Clemens Reiner (1985). Die “Fallaciae ad modum Oxoniae.” Ein Fehlschlußtraktat aus dem 13. Jahrhundert. Inaugural-Dissertation sur Erlangung des Doktorgrades der Philosophischen Fakultät der Universität zu Köln. Kukkonen, Taneli (2002). “Alternatives to Alternative. Approaches to Aristotle’s ­Arguments per impossibile.” Vivarium 40 (2), 137–173. Lafleur, Claude, ed. (1992). Le “Guide de l’étudiant” d’un maître anonyme de la Faculté des Arts de Paris au XIIIe siècle. Québec: Faculté de Philosophie, Université Laval.

References

463

Leblanc, Hélène (2021). Théories sémiotiques à l’âge classique. Translatio signorum. Paris: Vrin. Lewry, P. Osmond (1978). Robert Kilwardby’s Writings on the Logica Vetus, Studied with regard to their Teaching and Method. Ph.D. Dissertation, Oxford University. Lewry, P. Osmond (1982). “Robertus Anglicus and the Italian Kilwardby.” In English Logic In Italy in the Fourteenth and Fifteenth Centuries. Acts of the Fifth European Symposium on Medieval Logic and Semantics, ed. A. Maierù, 33–51. Naples: Bibliopolis. Libera, Alain de (1981). “Le traité De appellatione de Lambert de Lagny (Lambert d’Auxerre).” AHDLMA 48, 251–285. Libera, Alain de (1986). “Les Summulae dialectices de Roger Bacon. I-II. De termino. De enuntiatione.” AHDLMA 53, 139–165 (edition at 167–289). Libera, Alain de (1987). “Les Summulae dialectices de Roger Bacon. III. De argumentatione.” AHDLMA 54, 171–190 (edition at 191–278). Libera, Alain de (1989). “Les sources Greco-Arabes de la théorie médièvale de l’analogie de l’être.” Les etudes philosophiques 3/4, 319–345. Libera, Alain de (1998). Porphyre, Isagoge. Texte grec et latin, traduction par A. de ­Libera et A. Ph. Segonds. Introduction et notes par A. de Libera. Paris: Vrin. Lindberg, David C. (1976). Theories of Vision from al-Kindi to Kepler. Chicago-London: The University of Chicago Press. Lindberg, David C. (1983). “Introduction.” In Roger Bacon’s Philosophy of Nature. A Critical Edition with English Translation, Introduction, and Notes, of De multiplicatione specierum and De speculis comburentibus, ed. D.C. Lindberg, xv–lxxxi. Oxford: Clarendon Press. Lloyd, Geoffrey (1989). “The Theories and Practices of Demonstration in Aristotle.” ­Proceedings of the Boston Area Colloquium in Ancient Philosophy 6 (1), 371–401. Lohr, Charles H. (1965). “Logica Algazelis: Introduction and Critical text.” Traditio 21, 223–290. Longeway, John (2005). “Medieval Theories of Demonstration.” In Stanford Encyclopedia of Philosophy, ed. E.N. Zalta (https://plato.stanford.edu/entries/­demonstrationmedieval/). Luhtala, Anneli (2000). “Early Medieval Commentary on Priscian’s Institutiones grammaticae.” CIMAGL 71, 115–188. Łukasiewicz, J. (1957). Aristotle’s Syllogistic from the Standpoint of Modern Formal Logic. Oxford: Clarendon Press. Magli, Patrizia (1988). Il volto e l’anima. Milano: Bompiani. Maierù, Alfonso (1981). “Signum dans la culture médiévale.” In Sprache und Erkenntnis im Mittelalter. 2 vols. (Miscellanea mediaevalia, 13/1–2), ed. W. Kluxen, I, 51–72. Berlin: De Gruyter. Maierù, Alfonso (1987). “Influenze arabe e discussioni sulla natura della logica presso i Latini fra XIII e XIV secolo.” In La diffusione delle scienze islamiche nel Medio Evo europeo, 243–267. Roma: Accademia Nazionale dei Lincei.

464

References

Maierù, Alfonso (1992). “I commenti bolognesi ai Tractatus di Pietro Ispano.” In L’insegnamento della logica a Bologna nel XIV secolo, eds. D. Buzzetti, M. Ferriani, and A. Tabarroni, 497–541. Bologna: Istituto per la Storia dell’Università di Bologna. Maierù, Alfonso (1994). University Training in Medieval Europe. Ed. and transl. by D.N. Pryds. Leiden: Brill. Maierù, Alfonso (1999). “Signum negli scritti filosofici e teologici fra XIII e XIV secolo.” In Signum. Atti dell’XI Colloquio Internazionale del Lessico Intellettuale Europeo, Roma, 8–10 gennaio 1998, ed. M.L. Bianchi, 119–141. Firenze: Olschki. Manetti, Giovanni (1993). Theories of the Sign in Classical Antiquity. Bloomington: ­Indiana University Press; or. ed. Milano: Bompiani, 1987. Manetti, Giovanni (1992). “Trame, nodi, repressioni. Umberto Eco e la storia della semiotica.” In Semiotica: storia teoria interpretazione. Saggi intorno a Umberto Eco, eds. P. Magli, G. Manetti, and P. Violi, 5–24. Milano: Bompiani Manetti, Giovanni (2013). In principio era il segno. Milano: Bompiani. Mann, Jill (2001). “Jean de Meun and the Castration of Saturn.” In Poetry & Philosophy in the Middle Ages. A Festschrift for Peter Dronke, ed. J. Marenbon, 309–326. Leiden: Brill. Marenbon, John (1997). The Philosophy of Peter Abelard. Cambridge: Cambridge ­University Press. Marmo, Costantino (1988). “From Analogical Points of View. On the Use of Analogy in Ancient Greek Medical Texts.” VS. Quaderni di Studi Semiotici 50/51, 19–37. Marmo, Costantino (1990). “Suspicio. A Key Word to the Significance of Aristotle’s Rhetoric in Thirteenth Century Scholasticism.” CIMAGL 60, 145–198. Marmo, Costantino (1994). Semiotica e linguaggio nella Scolastica: Parigi, Bologna, Erfurt 1270–1330. La semiotica dei Modisti. Roma: Istituto Storico Italiano per il ­Medioevo. Marmo, Costantino (1997a). “Retorica e Poetica.” In La filosofia nelle università. Secoli XIII–XIV, ed. L.M. Bianchi, 141–162. Firenze: La Nuova Italia. Marmo, Costantino (1997b). “Simon of Tournai on Inferential Signs.” In Vestigia, Imagines, Verba. Semiotics and Logic in Medieval Theological Texts (XII–XIV Century), Proceedings of the 11th Symposium on Medieval Logic and Semantics, University of San Marino, May 24–28, 1994, ed. C. Marmo, 61–82. Turnhout: Brepols. Marmo, Costantino (1997c). “Roger Bacon, Aristotle (and all the others) on Natural Inferential Signs.” Vivarium 35 (2), 136–154. Marmo, Costantino (1997d). “Simon of Tournai’s Institutiones in sacram paginam. An Edition of His Introduction about Signification.” CIMAGL 67, 93–103. Marmo, Costantino (1998). “L’utilizzazione delle traduzioni latine della Retorica nel commento di Egidio Romano.” In La Rhétorique d’Aristote. Traditions et commentaires de l’Antiquité au XVIIe siècle, eds. G. Dahan and I. Rosier-Catach, 111–134. Paris: Vrin.

References

465

Marmo, Costantino (2006). “Symbolum, simulacrum, imago, e altri termini collegati, nelle opere di Ugo di San Vittore.” VS. Quaderni di Studi Semiotici 102, 139–161. Marmo, Costantino (2010). La semiotica del XIII secolo, dalla teologia alle arti liberali. Milano: Bompiani. Marmo, Costantino (2013). “Logique élargie et sémiotique: Albert le Grand, Roger Bacon et Gilles de Rome.” In Ad notitiam ignoti. L’Organon dans la translatio studiorum à l’époque d’Albert le Grand, ed. J. Brumberg-Chaumont, 447–465. Turnhout: Brepols. Marmo, Costantino (2016). “Logic, Rhetoric, and Language.” In A Companion to Giles of Rome, eds. C.F. Briggs and P.S. Eardley, 212–254. Leiden: Brill. Marmo, Costantino (2017). “Eco’s Semiotics and Medieval Philosophy.” In The Philosophy of Umberto Eco, eds. S.C. Beardsworth and R.E. Auxier, 103–131. Chicago: Open Court. Marmo, Costantino (2018). “Le commentaire littérale de la Rhétorique d’Aristote par Gilles de Rome (1272–73).” In Commenting on Aristotle’s Rhetoric from Antiquity to the Present. Commenter la Rhétorique d’Aristote, de l’Antiquité à nos jours, ed. F. Woerther, 132–152. Leiden: Brill. Marmo, Costantino (2020). “Per uno studio sull’intelligenza animale nella Scolastica medievale: facoltà estimativa, inferenze e segni tra XIII e XIV secolo.” In La voce e il logos. Filosofie dell’animalità nella storia delle idee, ed. S. Gensini, 79–109. Pisa: ETS. Marmo, Costantino (forthcoming). “L’introduction à la logique d’après quelques commentaires modistes des Tractatus de Pierre d’Espagne à Paris et Bologne (fin XIII-debut XIV).” In L’Europe de la logique, ed. J. Brumberg-Chaumont. Turnhout: Brepols (colloque “Europe de la Logique,” org. A. de Libera, A. Romano and J. Brumberg-Chaumont, Collège de France, Paris, May 2018; video at: https://www.college-de -france.fr/site/alain-de-libera/symposium-2018-05-15-15h15.htm). Marmura, Michael E. (1965). “Ghazali and Demonstrative Science.” Journal of the ­History of Philosophy 3 (2), 183–204. Marmura, Michael E. (1990). “The Fortuna of the Posterior Analytics in the Arabic ­Middle Ages.” In Knowledge and the Sciences in Medieval Philosophy (Acta ­Philosophica Fennica 48), eds. M. Asztalos, J.E. Murdoch, and I. Niiniluoto, 85–103. Helsinki: Helsinki University Press. Maróth, M. (1994). Die Araber und die antike Wissenshaftstheorie. Leiden: Brill. Martin, Christopher J. (1997). Thomas Aquinas. God and Explanations. Edimburgh: Edimburgh University Press. Martin, Christopher J. (2010). “‘They had added not a single tiny proposition’: The Reception of the Prior Analytics in the First Half of the Twelfth Century.” Vivarium 48, 159–192. McKirahan, R. (2008). “Introduction.” In Philoponus, On Aristotle Posterior Analytics 1.1–8, ed. McKirahan, 1–8. London: Bloomsbury.

466

References

McGinnis, Jon (2010). Avicenna. Oxford: Oxford University Press. McGinnis, Jon and David C. Reisman, eds. (2007). Classical Arabic Philosophy. An Anthology of Sources. Indianapolis-Cambridge: Hackett. Meirinhos, José (1996). “Petrus Hispanus Portugalensis? Elementos para uma diferenciação de autores.” Revista Española de Filosofía Medieval 3, 51–76. Merlin Defanti, Stella (2020). Anaphora and deixis in Articles and Pronouns back to Apollonius Dyscolus and the Origin of a Theory. Roma: Il Calamo. Mignucci, Mario (1969). Gli Analitici Primi. Napoli: Loffredo. Mignucci, Mario (1975). L’argomentazione dimostrativa in Aristotele. Commento agli Analitici Secondi. Padova: Antenore. Mignucci, Mario (1981). “Hos epi to polu et nécessaire dans la conception aristotélicienne de la science.” In Aristotle on Science. The Posterior Analytics, ed. E. Berti, 173–203. Padova: Antenore. Minio-Paluello, Lorenzo (1957). “A Latin Commentary (? Translated by Boethius) on the Prior Analytics, and Its Greek Sources.” Journal of Hellenic Studies 77 (1), 93–102. Minio-Paluello, Lorenzo (1962). “Praefatio.” In Aristoteles Latinus. Vol. III.1–4. Analytica priora: translatio Boethii (recensiones duae), translatio anonyma, Pseudo-Philoponi aliorumque scholia, specimina translationum recentiorum, ed. L. Minio-Paluello Leiden: Brill. Minio-Paluello, Lorenzo (1968). “Praefatio.” In Aristoteles Latinus. Vol. IV.1–4. Analytica posteriora: translationes Iacobi, Anonymi sive Ioannis, Gerardi et recensio Guillelmi de Moerbeka, eds. L. Minio-Paluello and B.G. Dod Paris: Desclée de Brouwer. Minio-Paluello, Lorenzo (1972). Opuscula. The Latin Aristotle. Amsterdam: Hakkert. Minnis, A.J. and A.B. Scott (eds.) (1988). Medieval Literary Theory and Criticism, c. 1100– c. 1375: The Commentary Tradition. Oxford: Clarendon Press. Moody, Ernest (1953). Truth and Consequence in Mediaeval Logic. Amsterdam: North Holland. Mora-Márquez, Ana María (2015). The Thirteenth-Century Notion of Signification. The Discussions and Their Origin and Development. Leiden: Brill. Morrison, Donald (1997). “Philoponus and Simplicius on Tekmeriodic Proof.” In Method and Order in Renaissance Philosophy of Nature: The Aristotle Commentary Tradition, eds. D.A. Di Liscia, E. Kessler, and C. Methuen, 1–22. Aldershot: Ashgate. Moraux, Paul (1979). Le Commentaire d’Alexandre d’Aphrodise aux «Seconds Analytiques» d’Aristote. Berlin: De Gruyter. Murè, Dafne (1997–1998). Le quaestiones dell’Anonimo di Praga sugli Elenchi sofistici. PhD Thesis, Università di Roma “La Sapienza.” Murphy, James J. (1974). Rhetoric in the Middle Ages. A History of Rhetorical Theory from Saint Augustine to the Renaissance. Berkeley: University of California Press. Nasr, S.H. and Aminrazavi, M. (2008). An Anthology of Philosophy in Persia. Volume I. From Zoroaster to ʿUmar Khayyām. London: I.B. Tauris.

References

467

O’Donnell, J. Reginald (1958). “Themistius’ Paraphrasis of the Posterior Analytics in Gerard of Cremona’s Translation.” Medieval Studies 20, 239–315. Oelze, Anselm (2019). Animal Rationality. Later Medieval Theories 1250–1350. Leiden: Brill. Paschetto, Eugenia (1985). “La fisiognomica nell’enciclopedia delle scienze di Pietro d’Abano.” Medioevo. Rivista di storia della filosofia medievale 11, 97–111. Patzig, Günther (1968). Aristotle’s Theory of the Syllogism. Dordrecht: Springer; or. ed. Göttingen: Vandenhoeck & Ruprecht, 1963. Peirce, Charles S. (1932–1958). Collected Papers of Charles S. Peirce, 8 vols., eds. C. Hartshorne, P. Weiss, and A. Burks. Cambridge, MA: Harvard University Press. Perfetti, Stefano (2018). “Biblical Exegesis and Aristotelian Naturalism: Albert the Great, Thomas Aquinas, and the animal of the Book of Job.” Aisthesis 11 (1), 81–96. Perilli, Lorenzo (1991). “Il lessico intellettuale di Ippocrate. Semainein e tekmairesthai.” Lexicon Philosophicum 5, 153–180. Perler, Dominik (2012). “Why is the Sheep Afraid of the Wolf? Medieval Debates on Animal Passions.” In Emotion and Cognitive Life in Medieval and Early Modern P­ hilosophy, eds. M. Pickavé and L. Shapiro, 32–52. Oxford: Oxford University Press. Piazza, Francesca (2000). Il corpo della persuasione. L’entimema nella retorica greca. Palermo: Novecento. Piazza, Francesca and Salvatore Di Piazza, eds. (2011). Verità verosimili. L’eikos nel p­ ensiero greco. Milano: Mimesis. Pinborg, Jan (1972). Logik und Semantik im Mittelalter. Stuttgart-Bad Cannstatt: Frommann-Holzboog. Pinborg, Jan (1975). “Introduction to the text.” In Fredborg et al., eds. (1975), 1+–11+. Pinborg, Jan (1976), “Diskussionen um die Wissenschaftstheorie an der Artistenfakultät.” In Die Auseinandersetzungen an der Pariser Universität im XIII. Jahrhundert, ed. A. Zimmermann, 240–268. Berlin: De Gruyter. Poirel, Dominique (2013). Des symboles et des anges. Hugues de Saint-Victor et le réveil dionysien du XIIe siècle. Turnhout: Brepols. Pormann, Peter E. (2013). “Avicenna on medical practice, epistemology, and the physiology of the inner senses.” In Interpreting Avicenna. Critical Essays, ed. P. Adamson, 91–108. Cambridge: Cambridge University Press. Porro, Pasquale (2015). “Il timore dell’altra parte. Il ruolo della formido nei dibattiti scolastici sull’assenso (da Tommaso d’Aquino a Pietro Aureolo).” Archivio di Filosofia/ Archives of Philosophy 83 (1–2), 209–220. Reilly, Leo (1993). “Introduction and Bibliography.” In Petrus Helias, Summa super Priscianum. Vol. I, 1–56. Toronto: Pontifical Institute of Mediaeval Studies, Robert, Aurélien (2013). “Le débat sur le sujet de la logique et la réception d’Albert le Grand au Moyen Âge.” In Ad notitiam ignoti. L’Organon dans la translatio studiorum à l’époque d’Albert le Grand, ed. J. Brumberg-Chaumont, 467–512. Turnhout: Brepols.

468

References

Rosier, Irène (1992). “Interjections et expressions des affects dans la sémantique du XIIIe siècle.” Histoire Épistémologie Langage 14 (2), 61–84. Rosier, Irène (1994). La parole comme acte. Sur la grammaire et la sémantique au XIIIe siècle. Paris: Vrin. Rosier-Catach, Irène (2004). La parole efficace. Signe, rituel, sacré. Paris: Seuil. Rosier-Catach, Irène (2020) “‘Multa vocabula ceciderunt ab usu.’ Les mots, le cercle de vin, et le beneplacitum des locuteurs.” In Per Enrico Fenzi. Saggi di allievi e amici per i suoi ottant’anni, eds. P. Borsa et al., 25–41. Firenze: Le Lettere. Rosier-Catach, Irène (2022). “Introduction. Le De Signis de Roger Bacon” In Rosier-­ Catach et al. (2022), 47–85. Rosier-Catach, Irène and Alain de Libera (forthcoming). “The Oxford-Paris Split Revisited.” In Modes, Terms and Propositions. Continental versus British Traditions in Medieval Logic. Proceedings of the 22th European Symposium of Medieval Logic and Semantics, Düsseldorf, June 25–29, 2018, eds. Ch. Rode and C. Kann. Leuven: Peeters. Rosier-Catach, Irène and Sten Ebbesen (1997). “Two Roberts and Peter of Spain. Excerpts from the Vatican and Todi Commentaries.” CIMAGL 67, 200–288. Rosier-Catach, Irène, Alain de Libera, Laurent Cesalli and Frédéric Goubier (2022). Roger Bacon, Des signes. Avant-propos, introduction, texte latin, traduction et commentaire par I. Rosier-Catach, L. Cesalli, F. Goubier et A. de Libera. Paris: Vrin. Ross, William D. 1939. “The Discovery of the Syllogism.” The Philosophical Review 48 (3), 251–272. Ross, William D. 1949. Aristotle’s Prior and Posterior Analytics. Oxford: Clarendon. Rossi, Pietro B. (1978). “Tracce della versione latina di un commento greco ai Secondi Analitici nel Commentarius in Posteriorum Analyticorum libros di Roberto Grossatesta.” Rivista di Filosofia Neo-Scolastica 70 (3), 433–439. Rossi, Pietro B. (1981). “Introduzione.” In Robertus Grosseteste, Commentarius in Posteriorum Analyticorum libros, ed. P. Rossi, 7–88. Firenze: Olschki. Rossi, Pietro B. (2017). “L’entrata dei libri De animalibus nel Medioevo latino.” In La zoologia di Aristotele e la sua ricezione dall’età ellenistica e romana alle culture medievali. Atti della X “Settimana di Formazione” del Centro GrAL, Pisa, Novembre 18–20, 2015, eds. M.M. Sassi, E. Coda, and G. Feola, 237–268. Pisa: Pisa University Press. Sabra, A.I. (1967). “The Authorship of the Liber de crepusculis, an Eleventh-Century Work on Atmospheric Refraction.” Isis 58 (1), 77–85. Sabra, A.I. (1978). “Sensation and Inference in Alhazen’s Theory of Visual Perception.” In Studies in Perception. Interrelations in the History of Philosophy and Science, eds. P.K. Machamer and Robert G. Turnbull, 160–185. Columbus: Ohio State University Press. Sabra, A.I. (1989). “Introduction, Commentary, Glossaries, Concordance, Indices.” In The Optics of Ibn al-Haytham. Books I–III, vol. 2, ed. A.I. Sabra. London: The ­Warburg Institute and the University of London.

References

469

Schmücker, Lorenz (1984). In Barbarismum Donati. In Robert Kilwardby, In Donati artem maiorem III, ed. L. Scmücker. Brixen: Weger. Schneider, Bernd (1978). “Praefatio.” In Aristoteles Latinus. Vol. XXXI.1–2. Rhetorica. Translatio Anonyma sive Vetus et Translatio Guillelmi de Moerbeka, ed. B. Schneider Leiden: Brill. Schreiber, Scott G. (2003). Aristotle on False Reasoning. New-York: SUNY Press. Sebti, Meryem (2020). “Re-presentation in Avicenna’s Doctrine of Knowledge.” In The Internal Senses in the Aristotelian Tradition, eds. S.N. Mousavian and J.L. Fink, 83–113. Cham: Springer. Shiel, James (1982). “A Recent Discovery: Boethius’ Notes on the Prior Analytics.” Vivarium 20, 128–141. Shiel, James (1990). “Boethius’ Commentaries on Aristotle.” In Aristotle Transformed. The Ancient Commentators and Their Influence, ed. R. Sorabji, 349–372. Ithaca, NY: Cornell University Press. Smith, Robin (1989). Aristotle. Prior Analytics. Indianapolis: Hackett. Solmsen, Friedrich (1929). Die Entwicklung der aristotelische Logik und Rhetorik. Berlin: Weidmann. Solmsen, Friedrich (1941). “The Discovery of the Syllogism.” The Philosophical Review 50 (4), 410–421. Strobino, Riccardo (2012). “Avicenna’s Use of the Arabic Translations of the Posterior Analytics and the Ancient Commentary Tradition.” Oriens 40, 355–389. Strobino, Riccardo (2015). “What if that (is) why? Avicenna’s taxonomy of scientific inquiries.” In Aristotle and the Arabic Tradition, eds. A. Alwishah and J. Hayes, 50–75. Cambridge: Cambridge University Press. Strobino, Riccardo (2016). “Per Se, Inseparability, Containment and Implication. ­Bridging the Gap between Avicenna’s Theory of Demonstration and Logic of the Predicables.” Oriens 44, 181–216. Strobino, Riccardo (2019). “Varieties of Demonstration in Alfarabi.” History and Philosophy of Logic 40 (1), 42–62. Strobino, Riccardo (2021). Avicenna’s Theory of Science. Logic, Metaphysics, Epistemology. Oakland, CA: University of California Press. Stocks, J.L. (1933). “The Composition of Aristotle’s Logical Works.” The Classical Q ­ uarterly 27 (2), 115–124. Tachau, Katherine (1988). Vision and Certitude in the Age of Ockham. Optics, Epistemology, and the Foundations of Semantics: 1250–1345. Leiden: Brill. Thom, Paul and John Scott (2015). “Introduction.” In Robert Kilwardby, Notule libri P­ riorum, 2 vols., eds. and transl. P. Thom and J. Scott, I: viii–cxiii. Oxford: Oxford University Press for the British Academy. Todd, R.B. (2012). “Introduction.” In Themistius, On Aristotle Physics 1–3, ed. R.B. Todd, 1–8. London: Bloomsbury.

470

References

Toivanen, Juhana (2020). “Estimative Power as a Social Sense.” In The Internal Senses in the Aristotelian Tradition, eds. S.N. Mousavian and J.L. Fink, 115–136. Cham: Springer. Tugwell, Simon (1999). “Petrus Hispanus. Comments on Some Proposed Identifications.” Vivarium 37, 103–113. Tugwell, Simon (2006). “Auctor Summularum Petrus Hispanus OP Stellensis.” Archivum Fratrum Praedicatorum 76, 103–115. Van Riet, Simone (1972). “La traduction latine du De anima.” In Avicenna Latinus, Liber de anima seu Sextus de naturalibus, I–II–III, ed. S. Van Riet, 91*–132*. Leuven: Peeters; Leiden: Brill. Ward, John O. (1995). Ciceronian Rhetoric in Treatise, Scholion and Commentary. ­Turnhout: Brepols. Ward, John O. (2015). “Master William of Champeaux, and Some Other Early Commentators on the Pseudo-Ciceronian Rhetorica ad Herennium.” In Public Declamations. Essays on Medieval Rhetoric, Education and Letters in Honor of M. Camargo, eds. G. Donavin and D. Stodola, 21–44. Turnhout: Brepols. Weisheipl, James A. (1980). “The Life and Works of St. Albert the Great.” In Albertus Magnus and the Sciences. Commemorative Essays, ed. J.A. Weisheipl, 13–51. Toronto: Pontifical Institute of Mediaeval Studies. Williams, Steven J. (1997). “Roger Bacon and the Secret of Secrets.” In Roger Bacon and the Sciences. Commemorative Essays, ed. J. Hackett, 365–393. Leiden: Brill. Wolfson, Harry A. (1935). “The Internal Senses in Latin, Arabic, and Hebrew Philosophic Texts.” Harvard Thological Review 28, 69–133. Now in Studies in the History of Philosophy and Religion. Vol. 1, eds. I. Twersky and G.H. Williams, 250–314. Cambridge, MA: Harvard University Press, 1973. Zonta, Mauro (1998). “Al-Fārābī’s Commentaries on Aristotelian Logic: New Discoveries.” In Philosophy and Arts in the Islamic World. Proceedings of the 18th Congress of the Union Européenne des Arabisants et Islamisants, Leuven, September 3–9, 1996, eds. U. Vermeulen and D. De Smet, 219–232. Leuven: Peeters. Zuppolini, Breno (2021). “Immediacy in Aristotle’s Epistemology.” Phronesis 66, 111–138.

Index of Ancient and Medieval Names Note: When a name occurs both in the text and in footnote, only the page number is given but not the footnote number. Abelard. See Peter Abelard Alan of Lille 7, 193–195, 197, 200 Albert the Great 2, 49n127, 201n1, 202, 226–230, 241–252, 253, 263, 268, 273, 274–275, 276, 277, 280nn2–3, 291–298, 299, 300, 306, 309n114, 310–311, 312, 314–315, 317, 318, 339–344, 347, 352, 354–355, 376, 377, 378n79, 387n114, 391, 398 Alexander of Aphrodiasis 1, 4, 6, 8, 20, 21, 28, 48, 61n159, 65, 68, 69, 70–81, 82, 83, 85, 91, 94, 95, 96, 97, 99, 100, 101, 104, 106, 110, 114–115, 117, 123, 124, 125, 126, 129, 131–133, 134, 135, 181, 188, 195n74, 201, 207, 209, 217, 224, 227–228, 231, 234, 239n131, 268, 273, 274, 307, 397 Alexander of Hales 363n24 Alfarabi (al-Fārābī) 8, 227, 228, 229, 230–231, 232, 234, 386n109, Algazel (al-Ghazālī) 214–215, 360, 383n104, 387 Alhazen (al-Haytham) 11, 379n83, 387–389, 390, 392, 396, Ammonius 33n78, 96, 97, 123, 124 Anonymous of Munich (on Peter of Spain) 309–310, 349n269 Anonymus Aurelianensis I 6, 174, 178–193, 196, 199, 200 Anonymus Aurelianensis II 6, 174, 178–193 Anonymus Aurelianensis III 118, 174 Anonymus Brugensis 259, 262n189 Anonymus Cantabrigiensis 6, 174, 178–193, 194n74, 195, 199, 200 Anonymus Cordubensis 259, 262n189 Anonymus Monacensis (on Soph El) 329– 331, 334–335, 341, 349n268, 357 Anonymus Monacensis (on APo A) 259 Anonymus Parisiensis 174, 178n18 Anonymus Praguensis 346n254, 346n256, 351n273

Anonymus-SF 346nn254–256 Anselm of Canterbury 164, 360, 364, Antiphon of Rhamnus 33n7 Apollonius Dyscolus 5, 142, Aquinas. See Thomas Aquinas Aristotle 1–10, 13–68, and passim Arnald of Villanova 379–380 Augustine of Hippo 3, 177, 197, 292, 360, 361, 366n32, 370n47, 373, 374, 396, 399 Averroes (Ibn Rušd) 2, 8, 94n51, 133, 203, 231n103, 234–241, 246, 247, 257n176, 275, 329n191, 360, 387, 390 Avicenna (Ibn Sīnā) 2, 8, 94n51, 133, 201, 211, 212n40, 213, 215, 216, 229, 230, 231–234, 237, 239–241, 246, 247, 248n156, 275, 293, 314, 347n260, 360, 369, 377n78, 379, 380, 383n104, 386–387, 389, 390, 391, 396 Bede the Venerable 364n27 Bernardus Silvestris(?) 154 Boethius 9, 10, 65, 117, 118, 158n80, 159–162, 168, 169, 170, 173, 174, 175, 176, 227, 229, 257, 275, 279, 280, 281, 282n11, 285, 286, 288n39, 293n59, 320, 321, 322, 324, 331, 333, 334, 335, 336, 337, 338, 340, 341n239, 342, 343, 348, 353, 356, 357, 375, 381, 382, 400 Bonaventure of Bagnoregio 364n28, 370, 371, 372, 373, Cicero 5, 6, 137, 138, 141, 149, 151, 156, 159, 160, 161, 162, 166, 167, 168, 171, 172, 177n12, 184, 191n66, 194n74, 324, 341, 343n244 Eberhard of Béthune 286 Galen 317n149 Gerard of Nogent (Gerardus de Nogento) 259, 262n189, 272n215

472

Index of Ancient and Medieval Names

Giles of Rome (Aegidius Romanus) 2, 9–10, 49n127, 202, 252, 262–274, 275, 277, 279, 291, 298–303, 307n108, 335n213, 338n220, 344–345, 350, 352, 355, 382, 398 Grillius 156, 157–159, 162, 168, Hermann of Carinthia 382n99 Hermann the German (Hermannus Alemannus) 298 Herodotus 33n77 Hippocrates 3, 33n76, 315, 317 Hippocrates of Chio 18 Hugh of St. Victor 155–156 James of Douai (Iacobus de Duaco) 259, 260–262 John Duns Scotus 362n17 John Scotus (Eriugena) 143n24 John Philoponus. See Philoponus John of Salisbury (Iohannes Saresberiensis) 174, 281 Lambert of Lagny (or Auxerre) 202, 319, 337n218, Manegold of Lautenbach 138n8, 157, 165–166, 168, 170 Marius Victorinus 156–157, 166, 167 Martin of Dacia 306 Master Simon 10, 305–308, 309, 346, 348, Menegaldus 138–139, 166–168, 171 Michael of Ephesus 5, 6, 69, 129–131, 178n18, 179, 182n35, 188, 192, 194, 228, 330 Nicholas of Paris 10, 279, 320, 336–338, 342n242, 343, 357, 381 Peter Abelard 6, 148–154, 168–171, 172, 174, 197, 198, 281, 399 Peter Damian 157, 162–164, 165, 170 Peter Helias 141n18, 145n33, 146–148, 171 Peter of Abano 9, 315–316, 317n149, 318n150 Peter of Spain 10, 176, 177, 201–202, 280, 281–282, 304–305, 306, 316n143, 319, 320, 326n183, 329n192, 331n195, 338–339, 346, 348n264, 356, 382, 398 Philoponus 1, 2, 3, 4–5, 6, 7, 11, 46, 47n122, 48n126, 49, 51n134, 54, 57, 61, 65, 67, 69,

96–113, 115–116, 117, 123, 124, 126, 129, 131, 133, 134, 135, 156, 174, 178, 179n24, 182n33, 187n54, 188, 189, 195n74, 203, 204, 205, 206, 207, 208, 217, 228, 229, 236, 238, 255, 256, 265, 266, 274, 276, 277, 307, 330, 341, 356, 362n16, 397 Plato 17n15, 165n97 Porphyry 139, 154n64, 227, 228, 293, 389n123 Priscian 5, 11, 142, 143, 144, 145, 146, 147, 148, 153n61, 171, 359, 395, 399 Pseudo-Kilwardby 11, 359–368, 369, 371n53, 372, 385n107, 395, 396, 399 Pseudo-Philoponus-1 5, 9, 20, 25n48, 27n60, 69, 117–123, 133, 187n54, 195n74, 286, 287, 288n39, 354, 362n16 Pseudo-Philoponus-2 5, 123–129, 133, 195n74, 362n16 Radulphus Brito 9, 10, 259, 260n180, 262, 272n215, 309, 314, 317–319, 320, 328n188, 346, 348–354, 356, 357 Richard Fishacre 364n28 Robert Grosseteste 2, 7, 8, 49n127, 175, 201, 202–216, 217, 219, 220, 224, 225, 243, 245, 250–251, 253, 259, 274, 275, 276, 387, 398 Robert Kilwardby(?) 331–336, 338n224, 341, 343, 352, 353n281, 357 Robert Kilwardby 2, 7–8, 9, 10, 49n127, 173, 201, 202, 216–226, 227, 242, 243, 245, 246, 251, 252, 253, 268, 274, 275, 276, 280nn2–3, 281, 283, 284–291, 292, 293n59, 294, 297, 298, 299, 300, 303n94, 304, 305n98, 305n100, 310–314, 331, 332, 336, 337, 339, 340, 354–355, 357, 359, 360n5, 398 Roger Bacon 1, 11, 25n51, 132n150, 151n55, 173, 177n12, 202, 203, 298, 315n139, 319, 333n209, 336, 337n218, 345n252, 352, 359, 361, 363, 364n25, 366, 368–386, 387–395, 396, 399–400 Rufinus of Aquileia 155n70 Sedulius Scotus 143n24 Simon of Faversham 10, 259, 260n180, 262, 272n215, 283n19, 305, 306, 308–309, 346nn254–257, 350, 351n272, 352 Simon of Tournai 7, 149, 156, 162, 173, 183, 193, 195–199, 200, 325, 360, 375, 399

Index of Ancient and Medieval Names Simplicius 3, 5, 113, 116–117, 135, 238, 397 Themistius 1, 4, 5, 6, 7, 8, 11, 47, 48, 61n159, 69, 82–96, 97, 99, 103, 104, 105, 106, 107, 108, 109, 110, 113, 114, 115n101, 117, 124, 126, 127, 128, 129, 133–134, 135, 156, 195n74, 201, 203, 207, 217, 222, 223, 224, 225, 226, 227, 228, 229, 231, 233, 234, 236, 237, 238n124, 242, 255, 273, 274, 275, 280n3, 321, 334, 348, 362, 397

473

Thierry of Chartres 141, 156n72, 171, 174 Thomas Aquinas 2, 9, 49n127, 202, 249, 252–259, 260, 262, 263, 275–276, 298, 335n213, 377n74, 387n114, 390, 391n130 Thucydides 33n77 William of Champeaux 139–140, 143–144, 171 William of Conches 144, 145–146, 147, 171 William of Sherwood 319, 323n173, 328

Index of Modern Names Note: When a name occurs both in the text and in footnote, only the page number is given but not the footnote number. Editor and translator names are not indexed. Agrimi, J. 315, 316nn143–144 Alessio, F. 319n156 Allen, J. 3, 19n22, 20n29, 23n43, 25, 37n88, 65n168 Aminrazavi, M. 231n103 Angioni, L. 19n22, 45n119, 46n121, 47n123, 52, 56, 56nn149–150 Ashworth, E.J. 215n51 Barnes, J. 3, 19nn22–23, 21n31, 35n83, 39n97, 40n101, 41nn107–108, 42n114, 44n117, 46n121, 48n125, 50, 51nn134–135, 56n149, 60, 80n23, 221, 238n128, 251n167 Bellucci, F. 18n16, 61n159, 131n149 Bertagna, M. 262n192, 263n193, 264n196, 266nn198–199, 268n205 Bertolacci, A. 224n78, 228n90, 231n103, 239nn130–131, 239n133, 240nn135–136, 241, 246n148 Biondi, P.C. 41n105 Black, D.L. 386nn109–110, 387n111 Boh, I. 325n178 Bolton, R. 54n146 Bonitz, H. 24 Borgo, M. 82n30 Briggs, C.F. 299n79 Bronstein, D. 40n101 Brower, J.E. 361n13 Brumberg-Chaumont, J. 181nn30–32, 217n62, 226n83, 280n2, 291nn51–53, 297n69, 305n99, 331n196 Burnett, C. 382n99 Burnyeat, M.F. 3, 19n18, 20, 22n36, 24n47, 25, 34, 35n83, 40n101, 65, 287 Caiazzo, I. 138nn7–8, 157n76, 158n80, 166–167, 168 Cannone, D. 216n57, 217nn58–59, 220n66 Celli, G. 119n116, 231n103 Cerami, C. 115n103, 230n102, 234n115, 238n128, 239n130, 241n138

Cesalli, L. 370n48 Chatelain, E. 368n39 Chiron, P. 33n78 Crombie, A.C. 206 D’Alverny, M.-T. 387nn112–113 D’Ors, A. 281n10, 305n99 Dahan, G. 202n8 Daiber, H. 231n103 De Filippis, R. 138n6, 157n75 Denifle, H. 368n39 Di Giovanni, M. 234n117, 239n130, 240n136 Diller, H. 33nn76–77 Di Martino, C. 387n114 Di Piazza, S. 22n38, 33n76, 33n78 Dubouclez, O. 69n1, 232n108, 234n115, 237n123 Dutmer, E. 54n146 Ebbesen, S. 3, 70nn3–4, 117, 118, 123, 124, 130n144, 131, 173–174, 175nn7–9, 178, 179nn21–24, 180n28, 182nn33–36, 187nn53–54, 193, 201n2, 202n6, 203n11, 203nn14–15, 227n85, 228n90, 229n93, 229n96, 259n180, 281, 282n11, 282nn13–14, 283nn18–19, 288n39, 291n48, 305n100, 324n174, 325n179, 326n180, 326n183, 327n187, 329n191, 331n196, 331n198, 337n220, 339, 348n265, 386n108 Eco, U. 153n60, 211n37, 367n36, 372n55 Einarson, B. 28n61 Elamrani-Jamal, A. 224n78, 234n115, 238n125, 241n138 El-Rouayheb, K. 230n101 Emamzadah, P. 350n271 Fausti, D. 33n76 Federici Vescovini, G. 316n142, 389n121 Ferejohn, M.T. 45n119 Figliuolo, B. 281n10 Fletcher, G.J.O. 386n109

475

Index of Modern Names Flórez, J.A. 18n16 Fredborg, K.M. 138nn7–8, 139n9, 140nn10– 12, 141nn13–14, 141n18, 145nn32–34, 146n38, 156n72, 343n244, 359nn2–3, 371n53 Gaetano, F. 33n77 Gauthier, R.-A. 203, 216n57, 252n170, 260 Glasner, R. 238n125 Gili, L. 76n17 Goldin, O. 123, 124 Gramigna, R. 117n12 Granger, H. 51n135 Green-Pedersen, N.J. 280n3, 320nn158–162, 336n217 Grimaldi, W.M.A 25n48, 31n69, 33n78, 35n83 Grondeux, A 143n25, 144n29, 153n61 Hamesse, J. 377n75 Hankinson, J. 33n76, 33n78 Hartmann, W. 165n96 Hasnawi, A. 228n90, 230n101 Hasse, D.N. 214n47 Henninger, M.G. 361n13 Hjelmslev, L. 366, 367n35 Hodges, W. 230n101 Holopainen, T.J. 164 Hornblower, S. 33n77 Hugonnard-Roche, H. 224n78, 230n101, 234n115, 237n123 Iwakuma, Y. 324n174, 325n179, 326n180 Jakobi, R. 156n75 Janssens, J. 229n97 Jeauneau, E. 145nn32–34, 155n65 Kemp, S. 386n109 King, P. 325n178 Kopp, C.R. 327n186 Kukkonen, T. 257n176 Lafleur, C. 282, 283n17 Leblanc, H. 400n2 Lewry, P.O. 216n57, 331n196 Libera, A. de 215n50, 247n154, 319nn155–156, 323n172 Lindberg, D.C. 387n114, 390n126 Lloyd, G. 50

Longeway, J. 202n9, 267n200 Luhtala, A. 143n24 Łukasiewicz, J. 27n60 Magli, P. 37n88 Maierù, A. 202n6, 305n99, 305n101, 310n121, 319n157, 364n26 Manetti, G. 3, 33n77, 65n168, 211n37 Mann, J. 155n65 Marenbon, J. 149n47, 149n51, 153n61, 361n13 Marmo, C. 17n12, 131n149, 149n50, 155n66, 155n70, 177n12, 197n83, 211n37, 215n51, 226n84, 249n158, 252n171, 262n188, 262n192, 266n198, 280n1, 299nn79–80, 302n90, 303n93, 306n105, 309n116, 343n244, 348n265, 362n17, 366n33, 367n37, 369n41, 371n53, 372n55, 373n56, 376n67, 376n69, 382, 383n104, 384n106, 387n114, 391n130, 400n1 Marmura, M.E. 230n101 Maróth, M. 230n101 Martin, C.J. 259n179, 281n5 McKirahan, R. 97n57 McGinnis, J. 230n102, 231n104, 233n110, 234n114 Meirinhos, J. 281n10 Merlin Defanti, S. 142n19, 142nn21–22 Mignucci, M. 3, 19n18, 19n22, 22n38, 24n47, 26n58, 41n105, 41n107, 42n114, 50, 51nn134–135, 121n121 Minio-Paluello, L. 117, 118, 174, 175n7, 224, 285n26 Minnis, A.J. 193n72 Moody, E. 325n178 Mora-Márquez, A.M. 361n12 Morrison, D. 3, 55n147, 69n1, 108n83, 117n107 Moraux, P. 70, 77, 81n26, 82n30, 97n57, 123 Murè, D. 346n254, 346n256, 351n273 Murphy, J.J. 138n5 Nasr, S.H. 231n103 Oelze, A. 387n114 Paschetto, E. 316n142 Patzig, G. 19n22, 26n52, 26–27nn58–59, 28, 29 Peirce, C.S. 18n16, 370n49 Perfetti, S. 378n79

476 Perilli, L. 33n76, 33n78, 210n33 Perler, D. 391n130 Piazza, F. 20n28, 33n76, 33n78 Pinborg, J. 267n200, 325n178, 359, 360 Poirel, D. 155n66, 155n70, 156n73 Pormann, P.E. 386n109 Porro, P. 212n40 Reilly, L. 145n33, 146n38 Reisman, D.C. 230n102, 231n104 de Rijk, L.M. 178n17, 202nn5–6, 281n10, 282n11, 304n98, 305, 306n104, 307n106, 319n153, 320, 323 Robert, A. 293n58 Rosier-Catach, I. 143n25, 153n59, 153n61, 177n12, 197n82, 202n6, 282n11, 305n100, 323n172, 339, 364n26, 364n28, 366n33, 368n40, 369n41, 370n45, 370nn48–50, 371nn52–53, 374n62, 375n65, 394n141 Ross, W.D. 3, 14n4, 18n16, 19n18, 19n22, 24, 25, 28n61, 35n83, 37n88, 38, 42n114, 54, 65n169, 287, 311, 312 Rossi, P.B. 201n2, 202n10, 203, 206n21, 216n57, 217n59, 295n62 Sabra, A.I. 379n83, 387n114, 388n116 Schneider, B. 298n78, 302 Schreiber, S.G. 62n162

Index of Modern Names Scott, A.B. 193n72 Scott, J. 284nn21–22, 285n26 Sebti, M. 386n110 Shiel, J. 117, 288n39 Smith, R. 19n18 Solmsen, F. 35n83 Strobino, R. 229n98, 230nn101–102, 231nn106–107, 233nn109–110, 234n112, 234n114 Stocks, J.L. 35n83 Tachau, K. 387n114, 392n133 Thom, P. 284nn21–22, 285n26 Todd, R.B. 115n101 Toivanen, J. 387n114 Tugwell, S. 281n10 Van Riet, S. 387n112 Wallies, M. 4, 69, 70, 77, 96n55, 117, 118, 123, 130n144, 131 Ward, J.O. 138n6 Weisheipl, J.A. 226n83 Williams, S.J. 376n72 Wolfson, H.A. 386n109 Zonta, M. 229n97 Zuppolini, B. 44n117

Index of Manuscripts Admont, Bibliothek des Benediktinerstifts, 241 330n194, 428–434 Barcellona, Arxiu de la Corona d’Aragó, Ripoll 109 282n12 Brugge, Stedelijke Openbare Bibliotheek, 509 259n180, 262n189 Bruxelles, Bibliothèque Royal “Albert Ier” 2910 (3540–47) 401–404, 441–444 Cambridge, Peterhouse College 205 216n57, 434–440 Città del Vaticano, Biblioteca Apostolica Vaticana, lat. 3049 339 Cordoba, Biblioteca del del Excellentissimo Cabildo, 52 259n180, 262n189 Eton, Eton College Library, 129 302n92 Firenze, Biblioteca Medicea Laurenziana, S. Marco 310 145n32 Firenze, Biblioteca Nazionale Centrale, Conventi Soppressi E.I.252  317nn146–149, 424–427 Firenze, Biblioteca Nazionale Centrale, Conventi Soppressi J.v.51 217n62 Klosterneuburg, Stiftsbibliothek, CCI 274 259n180, 260nn181–184, 261nn185–187 Lubbock, Texas Tech University, ms. 0894 339 Milano, Biblioteca Ambrosiana, C.161. Inf. 421–424 Milano, Biblioteca Ambrosiana, F.56 305 München, Bayerische Staatsbibliothek, clm 6726 306, 309nn117-118, 310nn119– 120, 348n264, 349–350n269 München, Bayerische Staatsbibliothek, clm 14246 329nn191–192, 330n194, 428–434

München, Bayerische Staatsbibliothek, clm 14460 259n180, 279n1, 336n217, 337nn218–219, 338n221 München, Bayerische Staatsbibliothek, clm 14697 305, 306n104, 307nn106 and 108, 412–421 München, Bayerische Staatsbibliothek, clm 14763 326nn183–184, 327n185 Oxford, Bodleian Library, Laud. lat. 67 145n34 Oxford, Bodleian Library, Canon. misc. 403 280n3 Oxford, Merton College 292 421–424 Padova, Biblioteca Antoniana, 429 305, 306n104 and 106, 307nn106 and 108, 346n259, 412–421 Paris, Bibliothèque de l’Arsénal 910  320n160 Paris, Bibliothèque de la Sorbonne, 120 300n82, 404–411 Paris, Bibliothèque Nationale de France, lat. 6433 305n98 Paris, Bibliothèque Nationale de France, lat. 6576 216n57 Paris, Bibliothèque Nationale de France, lat. 11412 338n220 Paris, Bibliothèque Nationale de France, lat. 14705 401–404 Paris, Bibliothèque Nationale de France, lat. 15130 145nn33 and 35, 146nn36-37 Paris, Bibliothèque Nationale de France, lat. 16126 305, 307nn106 and 108, 412-421 Paris, Bibliothèque Nationale de France, lat. 16170 259n180, 262n189 Paris, Bibliothèque Nationale de France, lat. 16583 302n92 Paris, Bibliothèque Nationale de France, lat. 16609 401–404

478

Index of Manuscripts

Paris, Bibliothèque Nationale de France, lat. 16619 434–440 Paris, Bibliothèque Nationale de France, lat. 16681 300n82, 404–411

Toledo, Biblioteca del Capitolo 47.10  302n92

Salamanca, Biblioteca Universitaria, 2350 441–444

Wolfenbüttel. Bibl. ducale, ms. 488 302n92

Todi, Biblioteca Comunale, 54 280n3, 339

Venezia, Bibl. Marciana, Z.L.240 216n57

York, Minster Library, XVI.M.7 140nn10–12, 141n13

37mm

IMP 20

Costantino Marmo, Ph.D. (University of Bologna, 1992), is Full Professor of Semiotics and History of Semiotics at the University of Bologna. He has published articles, editions of texts, and books, including Semiotica e linguaggio nella Scolastica. La semiotica dei Modisti (Rome, 1994), and La semiotica del xiii secolo (Milan, 2010). Francesco Bellucci, Ph.D. (University of Siena, 2012), is Associate Professor of Semiotics at the University of Bologna. He has published in The Journal of the History of Philosophy, Archiv für Geschichte der Philosophie, The British Journal for the History of Philosophy, and The Journal of the History of Ideas.

ISBN: 978-90-04-54315-7

ISSN 187 brill.com/imp Costantino

Marmo and Francesco Belluc Downloaded from Brill.com09/08/2023 04:33:46PM via Western University

Costantino Marmo and Francesco Bellucci

This book reconstructs the history of the notion of “demonstration through signs” from roughly the third through the thirteenth century. It examines the work of Aristotle’s Greek, Arabic, and Latin commentators, both within and outside the tradition of the Posterior Analytics.

Signs and Demonstrations from Aristotle to Radulphus Brito

In the Posterior Analytics Aristotle contrasts demonstrations with syllogisms through signs. In the Prior Analytics he defines a sign as a demonstrative premise. One is thus led to ask: is a sign a demonstration?

INVEST IGATING MEDIEVAL PHILOSOPHY • 20

Signs and Demonstrations from Aristotle to Radulphus Brito Costantino Marmo Francesco Bellucci