Simplicius: On Aristotle Physics 1–8 Volume General Introduction to the 12 Volumes of Translations: General Introduction to the 12 Volumes of Translations 9781350286627, 9781350286658, 9781350286634

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Simplicius On Aristotle Physics 1–8

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Ancient Commentators on Aristotle GENERAL EDITORS: Richard Sorabji, Honorary Fellow, Wolfson College, University of Oxford, and Emeritus Professor, King’s College London, UK; and Michael Griffin, Associate Professor, Departments of Philosophy and Classics, University of British Columbia, Canada. This prestigious series translates the extant ancient Greek philosophical commentaries on Aristotle. Written mostly between 200 and 600 ad, the works represent the classroom teaching of the Aristotelian and Neoplatonic schools in a crucial period during which pagan and Christian thought were reacting to each other. The translation in each volume is accompanied by an introduction, comprehensive commentary notes, bibliography, glossary of translated terms and a subject index. Making these key philosophical works accessible to the modern scholar, this series fills an important gap in the history of European thought. A webpage for the Ancient Commentators Project is maintained at ancientcommentators.org.uk and readers are encouraged to consult the site for details about the series as well as for addenda and corrigenda to published volumes.

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Simplicius On Aristotle Physics 1–8 General Introduction to the 12 Volumes of Translations

Stephen Menn

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BLOOMSBURY ACADEMIC Bloomsbury Publishing Plc 50 Bedford Square, London, WC1B 3DP, UK 1385 Broadway, New York, NY 10018, USA 29 Earlsfort Terrace, Dublin 2, Ireland BLOOMSBURY, BLOOMSBURY ACADEMIC and the Diana logo are trademarks of Bloomsbury Publishing Plc First published in Great Britain 2022 Copyright © Stephen Menn, 2022 Stephen Menn has asserted his right under the Copyright, Designs and Patents Act, 1988, to be identified as Author of this work. For legal purposes the Acknowledgements on p. ix constitute an extension of this copyright page. Cover design: Terry Woodley All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage or retrieval system, without prior permission in writing from the publishers. Bloomsbury Publishing Plc does not have any control over, or responsibility for, any third-party websites referred to or in this book. All internet addresses given in this book were correct at the time of going to press. The author and publisher regret any inconvenience caused if addresses have changed or sites have ceased to exist, but can accept no responsibility for any such changes. A catalogue record for this book is available from the British Library. A catalog record for this book is available from the Library of Congress. ISBN: HB: 978-1-3502-8662-7 ePDF: 978-1-3502-8663-4 eBook: 978-1-3502-8664-1 Series: Ancient Commentators on Aristotle Typeset by RefineCatch Limited, Bungay, Suffolk To find out more about our authors and books visit www.bloomsbury.com and sign up for our newsletters.

Acknowledgements The present translations have been made possible by generous and imaginative funding from the following sources: the National Endowment for the Humanities, Divison of Research Programs, an independent federal agency of the USA; the Leverhulme Trust; the British Academy; the Jowett Copyright Trustees; the Royal Society (UK); Centro Internazionale A. Beltrame di Storia dello Spazio e del Tempo (Padua); Mario Mignucci; Liverpool University; the Leventis Foundation; the Arts and Humanities Research Council; Gresham College; the Esmée Fairbairn Charitable Trust; the Henry Brown Trust; Mr and Mrs N. Egon; the Netherlands Organisation for Scientific Research (NOW/ GW); the Ashdown Trust; the Lorne Thyssen Research Fund for Ancient World Topics at Wolfson College, Oxford; Dr Victoria Solomonides, the Cultural Attaché of the Greek Embassy in London; and the Social Sciences and Humanities Research Council of Canada. The editors wish to thank Dawn Sellars for preparing the volume for press, and Alice Wright, Commissioning Editor at Bloomsbury Academic for her diligence in seeing each volume of the series to press.

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Contents Editors’ Preface Abbreviations Acknowledgements Principal Philosophers and Mathematicians Discussed

General Introduction 1. Simplicius and his Physics commentary 2. Simplicius’ philosophical aims in his commentaries on Aristotle’s On the Heaven and Physics 3. Simplicius’ commentary-methods and his use of earlier commentators 4. Themes of Simplicius’ commentary on Physics 1.1–2 5. The text of Simplicius and our translation Appendix: Hippocrates’ constructions Notes Bibliography Index of Names Index of Subjects

vi viii ix x 1 1 4 9 32 100 109 119 149 155 159

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Editors’ Preface Michael Griffin and Richard Sorabji With Stephen Menn’s translation of Simplicius On Aristotle Physics 1.1–2, the Ancient Commentators on Aristotle series has published a complete English version of Simplicius’ commentary on Aristotle’s Physics in twelve volumes (a complete list is appended below). We do not know how long Simplicius took to write his commentary, which occupies more than half a million words in Greek; but its English counterpart has involved more than fifteen translators working across three decades, with the international collaboration of dozens of scholars and students. We want to take this opportunity to reiterate our gratitude to every colleague who has contributed to this enterprise. We are also grateful to our generous funders, listed in the Acknowledgements to this volume, who have made the project possible, and to our publishers, first at Duckworth and now at Bloomsbury, who have seen each translation to press with diligence and patience. Simplicius’ comments on the first two chapters of Aristotle’s Physics are the last to be rendered into English. They are also among the most complex, because they lay the methodological and philosophical foundations for the entire work. In introducing them, Professor Menn has surveyed the complete translation by many hands. He explains Simplicius’ interpretation of Aristotelian natural science, his motives and methods in writing Aristotelian commentaries, and his reasons for copying extensive verbal quotations from otherwise lost sources, such as the Presocratic philosophers. Menn also engages in a novel way with the commentary’s many exegetical, philosophical, and mathematical difficulties, and offers new textual readings, based on an autopsy of manuscripts, including a witness unknown to Diels, the editor of the currently standard text. Menn’s book-length introduction amounts to a significant new monograph on Simplicius’ commentary as a whole, including a close study of 1.1–2 in particular. In light of its length and scope, we have agreed with Bloomsbury’s proposal to print this text separately as a General Introduction, preceding the final instalment of the translation itself. In addition, we have offered a shorter overview of the work and Menn’s central conclusions as a Preface to the second volume. We note to the reader that § 4 of Menn’s Introduction focuses specifically on the content of Simplicius’ discussion of Physics 1.1–2. The mathematical stretch vi

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of the translation (53,30–69,34) is annotated to support the reader, who is especially encouraged to consult the endnotes in this section. Consultation of Menn’s detailed discussion in the Introduction (§ 4.5) will be helpful for deeper study (see below, pp. 80–92). Simplicius, On Aristotle Physics 1. 2. 3.

On Aristotle Physics 1.1–2, tr. S. Menn, 2021 On Aristotle Physics 1.3–4, tr. P. Huby & C. C. W. Taylor, 2011 On Aristotle Physics 1.5–9, tr. H. Baltussen, M. Atkinson, M. Share & I. Mueller, 2012 4. On Aristotle Physics 2, tr. B. Fleet, 1997 5. On Aristotle Physics 3, tr. J. O. Urmson with P. Lautner, 2001 6. On Aristotle Physics 4.1–5 and 10–14, tr. J. O. Urmson, 1992 7. Corollaries on Place and Time, tr. J. O. Urmson with L. Siorvanes, 1992 8. On Aristotle Physics 5, tr. J. O. Urmson, 1997 9. On Aristotle Physics 6, tr. D. Konstan, 1989 10. On Aristotle Physics 7, tr. C. Hagen, 1994 11. On Aristotle Physics 8.1–5, tr. I. Bodnar, M. Chase & M. Share, 2012 12. On Aristotle Physics 8.6–10, tr. R. McKirahan, 2001

Abbreviations References beginning with ‘A’ or ‘B’ (e.g. A15, B12) are to texts in the relevant chapter of DK. Bekker CAG Diels DK FHS&G

LSJ OCT Ross

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Immanuel Bekker, Aristoteles Graece, 2 vols (Berlin: Reimer, 1831) Commentaria in Aristotelem Graeca Hermann Diels, ed., Simplicii in Aristotelis Physicorum Libros Quattuor Priores Commentaria, CAG 9 (Berlin: Reimer, 1882) Hermann Diels and Walther Kranz, eds, Die Fragmente der Vorsokratiker, 6th edn, 3 vols (Berlin: Weidmann, 1952) W. W. Fortenbaugh, Pamela Huby, Robert Sharples, and Dimitri Gutas, eds, Theophrastus of Eresus: Sources for his Life, Writings, Thought, and Influence, 2 vols (Leiden: Brill, 1992-3) H. G. Liddell, R. Scott and H. S. Jones, Greek-English Lexicon, 9th edn (Oxford: Oxford University Press, 1940) Oxford Classical Text W. D. Ross, Aristotle’s Physics: A Revised Text with Introduction and Commentary (Oxford: Clarendon Press, 1936)

Acknowledgements For their comments on all or parts of the Introduction I would like to thank Rachel Barney, Andrea Falcon, Pantelis Golitsis, Christoph Helmig, Inna Kupreeva, the graduate student participants (and specifically Nicholas Aubin, Argyro Lithari, Robert Roreitner) in a workshop in Berlin in July 2017 on commentaries from the school of Ammonius, and Richard Sorabji. I thank the Berlin Graduiertenkolleg ‘Philosophy, Science and the Sciences’, based at the Humboldt-Universität Berlin, for supporting the July 2017 workshop. Support from the Alexander-von-Humboldt Stiftung, the Graduiertenkolleg ‘Philosophy, Science and the Sciences’, and a James McGill Professorship at McGill University, gave me some time free from teaching and the opportunity to work in an ideal research environment in Berlin. I would also like to thank Henry Mendell who generously supplied the mathematical diagrams in the Appendix to this volume. Finally, I thank Michael Griffin and Dawn Sellars for their help in preparing the manuscript and advising on editorial issues.

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Principal Philosophers and Mathematicians Discussed

Early Greek philosophers Thales of Miletus, 6th century bce Anaximander of Miletus, 6th century bce Anaximenes of Miletus, 6th century bce Xenophanes of Colophon, 6th century bce Hippasus of Metapontum, 6th–5th century bce , Pythagorean Heraclitus of Ephesus, 6th–5th century bce Parmenides of Elea, 6th–5th century bce Melissus of Samos, 5th century bce Zeno of Elea, 5th century bce , student of Parmenides Anaxagoras of Clazomenae, 5th century bce Empedocles of Acragas, 5th century bce Leucippus of Abdera, 5th century bce Democritus of Abdera, 5th century bce , student of Leucippus Diogenes of Apollonia, 5th century bce Hippo, 5th century bce Archelaus of Athens, 5th century bce , student of Anaxagoras and teacher of Socrates Antiphon of Athens, 5th century bce Gorgias of Leontini, 5th–early-4th century bce Lycophron, 5th–4th century bce Socrates of Athens, 5th century bce Menedemus of Eretria, 5th–4th century bce , student of Socrates Archytas of Tarentum, 5th–4th century bce , Pythagorean (some genuine, some spurious texts) Timaeus of Locri, fictional 5th century bce Pythagorean Plato of Athens, 5th–4th century bce , student of Socrates, founder of Academy in Athens

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Principal Philosophers and Mathematicians Discussed

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Speusippus of Athens, 4th century bce , nephew, student, and successor of Plato Xenocrates of Chalcedon, 4th century bce , successor of Speusippus as head of the Academy Aristotle of Stagira, 4th century bce , student of Plato, founder of Peripatetic School in Athens Theophrastus of Eresus, 4th–3rd century bce , Peripatetic, student and successor of Aristotle Eudemus of Rhodes, 4th–3rd century bce , Peripatetic, student of Aristotle

Mathematicians Hippocrates of Chios, late-5th century bce Euclid, early-3rd century bce Archimedes of Syracuse, 3rd century bce Nicomedes, 3rd century bce Apollonius of Perga, late-3rd century bce Nicomachus of Gerasa, 1st–2nd century ce , mathematician and neoPythagorean philosopher Eutocius, 6th century ce , commentator on mathematical texts, active in Alexandria

Later Greek philosophers and commentators Andronicus of Rhodes, 1st century bce , Peripatetic Nicolaus of Damascus, 1st century bce , Peripatetic Plutarch of Chaironeia, 1st–2nd century ce , Platonist Atticus, 2nd century ce , Platonist Adrastus of Aphrodisias, 1st–2nd century ce , Peripatetic Aspasius, 2nd century ce , Peripatetic Alexander of Aphrodisias, 2nd–3rd century ce , Peripatetic, chairholder in Athens Ammonius Saccas, early-3rd century ce , Platonist, teacher of Plotinus in Alexandria Plotinus of Lycopolis, mid-3rd century ce , Platonist, taught in Rome

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Principal Philosophers and Mathematicians Discussed

Longinus, mid-3rd century ce , Platonist, taught in Athens, adviser to Zenobia of Palmyra Porphyry of Tyre, late-3rd century ce , Platonist, student of Longinus and then of Plotinus Iamblichus of Chalcis, 3rd–4th century ce , Platonist, rebellious student of Porphyry Themistius, 4th century ce , Peripatetic, active in Constantinople

The Athenian and Alexandrian Platonist schools of the 5th–6th centuries ce Syrianus, 4th–5th century ce , Platonist, chairholder in Athens Proclus of Lycia, 5th century ce , Platonist, student of Syrianus, chairholder in Athens Hermias, 5th century ce , Platonist, student of Syrianus, taught in Alexandria Ammonius, 5th–6th century ce , Platonist, son of Hermias, student of Proclus, chairholder in Alexandria Olympiodorus, 6th century ce , Platonist, student and second successor of Ammonius Damascius, 6th century ce , Platonist, last chairholder in Athens Simplicius of Cilicia, 6th century ce , Platonist, student of Ammonius and Damascius Priscian of Lydia, 6th century ce , Platonist, active in Athens John Philoponus, 6th century ce , Christian, active in Alexandria

General Introduction

1. Simplicius and his Physics commentary In translating Simplicius’ commentary on the first two chapters of Aristotle’s Physics, more than 100 large pages in the Commentaria in AristotelemGraeca on four much smaller pages in a modern edition of the Physics, we are completing the translation, by many hands, of Simplicius’ commentary as a whole.1 So I am taking the opportunity in this introduction, published together with the translation volume, to introduce not only Simplicius’ commentary on Physics 1.1–2, and our translation of it, but also Simplicius’ commentary on the Physics as a whole. Some points made in the introduction will also bear on Simplicius’ commentaries on other texts of Aristotle, the Categories and On the Heaven, since they are methodologically similar and form parts of a single great project; the commentary on the Physics is especially closely tied to the commentary on On the Heaven. Simplicius’ commentary on the Physics, written some time around 540 ce , is at more than half a million words the longest surviving single-authored text from Greek antiquity: it is exceeded only by Eustathius’ commentaries on the Iliad and Odyssey, and they are from the twelfth century ce , which is not ‘antiquity’. Simplicius’ commentary on On the Heaven, almost 270,000 words, is also enormous; each is about nine times as long as the text it is commenting on. These commentaries combine philosophy and scholarship. Simplicius wants not only to elucidate Aristotle’s claims and arguments but also to defend them; since he is a committed Platonist, he must therefore undertake to defend the harmony of Plato and Aristotle on points of apparent disagreement. In defence of Aristotle he also undertakes the last great pagan-Christian polemic of Greek antiquity, an attack on the Christian philosopher John Philoponus’ denial of the eternity of the world and his denial of an incorruptible element making up the heavenly bodies: Simplicius argues that Philoponus is wrong philosophically, and he

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defends Aristotle’s arguments, and he also argues that Philoponus is wrong to claim Plato’s Timaeus as supporting his own side of these issues. Simplicius also engages in questions of textual scholarship on Aristotle, and he is also led to preserve, by quoting or closely paraphrasing, sometimes lengthy texts of earlier philosophers and mathematicians that would otherwise be lost. Most famously, he cites many texts of the pre-Socratic philosophers; but also, for instance, of the fifth-century bce mathematician Hippocrates of Chios (through an intermediate source); of the early Peripatetics, especially Aristotle’s immediate students Theophrastus and Eudemus; the commentaries of the second-third-century ce Peripatetic (neo-Aristotelian) Alexander of Aphrodisias on the Physics and On the Heaven, the commentary of the late-third-century ce neo-Platonist Porphyry on the Physics, and many earlier commentaries on the Categories (some cited directly and others at second hand); and the series of (mostly neoPlatonic) writers on place and time, culminating in Simplicius’ own teacher Damascius, that he cites in the Corollaries on Place and Time embedded in his commentary on Physics 4. Even when Simplicius is not our only source for some text, he is an important witness to its early history, often giving a slightly different version of the text than other sources: since Diels’ classic article, Simplicius has been used as a witness to the history of the text of Aristotle, earlier than any of our extant manuscripts.2 Simplicius’ aim in quoting is often not just to preserve an earlier thinker or to cite him as a witness, but to rehabilitate him against criticism, or to correct what he sees as a common misinterpretation of a past thinker. It is usually an interest in these accomplishments of Simplicius – preserving earlier texts, harmonizing Aristotle or other thinkers with Plato, arguing against other philosophers and scholars including Philoponus – that leads modern readers to Simplicius. But while it is easy to find interesting passages in Simplicius on all these things, without the larger context we cannot judge when he is quoting verbatim or paraphrasing, when he knows a text at first hand and when only through later sources, or what biases might influence his selection and interpretation of the particular passages he cites. We cannot evaluate his testimony on particular points without understanding the larger programme that leads him to write vast commentaries on Aristotle, to discuss the views of earlier thinkers, and sometimes to cite their writings. The three Aristotle commentaries, and especially the commentaries on the Physics and On the Heaven, are parts of a single programme, and can be dated relative to each other and placed within the larger frame of Simplicius’ career. In the Physics commentary 1117,15–1118,11 and in several later passages,3

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Simplicius refers back to what he has done in commenting on On the Heaven, so he wrote the On the Heaven commentary first. As we will see, the On the Heaven commentary helped to motivate the Physics commentary, and many themes touched on in the On the Heaven commentary are further developed in the Physics commentary, although Simplicius also changed his mind on some issues between the two works. In his Categories commentary, 435,20–4, he refers back to his Physics commentary, so the Categories commentary was the last of the three great commentaries. Simplicius’ only other extant work is a commentary on Epictetus’ Encheiridion. It was established by Bossier and Steel that the extant commentary on Aristotle’s On the Soul attributed to Simplicius is not really by him, and is probably by his Athenian colleague Priscian of Lydia.4 Two passages in this commentary on On the Soul, 28,19–20 and 217,23–8, refer back to a commentary on the Metaphysics by the same author, but if the commentary on On the Soul is not by Simplicius, there is not much evidence that he wrote a commentary on the Metaphysics.5 We have references from Byzantine and Arabic sources to lost works of his, notably a monograph on the principles (definitions, postulates, and common notions) in Euclid’s Elements, from which we have a few extracts in Arabic, and a commentary on Aristotle’s Meteorology. The Meteorology commentary may well have had thematic connections with the On the Heaven and Physics commentaries, but the other works (unless there was a Metaphysics commentary) probably would not add much towards understanding them.6 Simplicius first studied in Alexandria under Ammonius the son of Hermias, the author of an extant commentary on Aristotle’s On Interpretation and of lectures which shaped the next generation’s commentaries on other texts, including the Physics; Ammonius had studied under Proclus in Athens but was heavily influenced by Porphyry and committed to harmonizing Plato and Aristotle. Simplicius was, next, a student or junior colleague (hetairos)7 in Athens of Damascius, the last Platonic scholarch and the last great independent philosopher of pagan antiquity. Damascius, a more radical and experimental follower of lines of thought from Proclus and especially from Iamblichus, looks down on Porphyry and Ammonius as superficial thinkers; Simplicius, while impressed by Damascius, retains his respect for Ammonius and manages to balance both loyalties. Simplicius was one of the seven philosophers led by Damascius, who, according to Agathias’ Histories 2.30–31, emigrated to the court of the Persian king Chosroes I because ‘it was forbidden by the laws for them to take part in public life here without fear (adeôs)’ since ‘they did not agree with the opinion prevailing among the Romans about the divine’ (i.e. presumably, after Justinian’s ban on pagan teaching in 529), and who were then disappointed

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in the Persian court, and returned to Roman territory (or its border-zones) after Chosroes insisted on inserting in a peace treaty a clause guaranteeing toleration for them.8 Where exactly they returned to, whether they settled somewhere as a group, and whether they went back to teaching, are unclear and disputed; but Simplicius’ commentaries are too long to be written versions of lectures in the usual way, and he refers to future readers rather than to auditors.9 The first book of Simplicius’ commentary on the On the Heaven, the earliest of his three surviving Aristotelian commentaries, is credited in the oldest manuscripts to Damascius, and while no one doubts that in its present form it is by Simplicius, he may well have started it under Damascius’ tutelage.10 By contrast, the Physics commentary (775,31–4) refers back to Damascius as having died.

2. Simplicius’ philosophical aims in his commentaries on Aristotle’s On the Heaven and Physics The motivations of the commentary on On the Heaven are the clearest, and help us to see why Simplicius was also driven to write a commentary on the Physics. The first thing to say is that Simplicius was motivated in his commentary on On the Heaven to defend the harmony of Aristotle with Plato, or specifically of Aristotle’s On the Heaven with Plato’s Timaeus. But to see why that was important to him we need to say more concretely what needed to be harmonized.11 Here are some issues on which there is tension between the Timaeus and On the Heaven. The Timaeus clearly maintains that some god, the ‘demiurge’ or craftsman of the ordered physical world, who is apparently nous (reason or intelligence) personified, is the efficient cause of the physical world, and it seems to say that this god created the world (not out of nothing but out of a chaos) finitely many years ago.12 The Timaeus also says that the heavenly bodies are made of fire, or mainly of fire with some admixture of air, water, and earth, and it seems to say that they move in circles because they are pushed by a world-soul which moves in circles when it thinks. By contrast, On the Heaven clearly maintains that the physical world has always existed, and will always exist, in its current overall structure, a series of heavenly spheres surrounding domains of (partially intermixed) fire, air, water, and earth. On the Heaven has no clear assertion of any incorporeal divine efficient cause of the world, and although Physics 8 does posit incorporeal efficient causes of the motions of the heavens, it does not seem to make them causes of the existence of the heavens; and while

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Metaphysics 12 posits incorporeal final causes of the heavenly motions, and describes at least the first of these causes as nous, it is not clear that they are also efficient causes even of the heavenly motions, let alone of the existence of the heavenly bodies. Finally, On the Heaven says that the heavenly spheres are made not of fire or air, which naturally move away from the centre of the world, nor of water or earth, which naturally move towards the centre of the world, but of a fifth simple body, sometimes called aether, which naturally moves around the centre of the world. This seems to leave little room for incorporeal movers of the heavens: On the Heaven 1.9 does posit one or more incorporeal gods beyond the heavenly bodies (and this is even clearer in the Physics and Metaphysics), but they do not seem to be the creating and providential god of the Timaeus. Different Platonists react in different ways to Aristotle’s On the Heaven. Some, like Atticus in the second century ce , defend the straightforward meaning of the Timaeus and reject Aristotle’s doctrines of the eternity of the world and of the ‘fifth body,’ distinct from earth, water, air, and fire, as the substance of the heavens. But other Platonists welcome the challenge of On the Heaven as a means of distinguishing what is merely mythical in the Timaeus from the intellectual content of the myth. Aristotle does not want a god to begin to act at an arbitrary moment in time, without any change in circumstances that would give him a new reason for acting; he also does not want the heavenly bodies to move ‘violently,’ i.e. contrary to their natural motion, partly because he thinks it is absurd for a divine being to do or suffer violence, and partly because he thinks that nothing contrary to nature can endure eternally, and that what does not endure eternally cannot be the object of scientific knowledge. Many Platonists share these concerns with Aristotle and are willing to accept the Aristotelian theses of the eternity of the world and of the fifth body as part of a demythologized version of the Timaeus, as long as they do not have to sacrifice the Platonic doctrines of creation and providence. This yields a spectrum of possible positions on the harmony or disharmony of the Timaeus and On the Heaven. There are extreme Platonists, like Plutarch of Chaeroneia and Atticus, who hold that Plato is right in the Timaeus in positing a divine efficient cause of the world, and that Aristotle is wrong in On the Heaven in positing the fifth body and the eternity of the world. On the opposite side, there are extreme Aristotelians, like Alexander of Aphrodisias, who think that On the Heaven is right in positing the fifth body and the eternity of the world and that the Timaeus is wrong is positing a divine efficient cause of the world. Between these extremes are people who are simultaneously moderate Platonists and moderate Aristotelians. Such people hold that the Timaeus and On the Heaven are both right in their distinctive

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theses, and that Aristotle was criticizing not the Timaeus but only ‘extremist’ interpretations of the Timaeus – interpretations that make the demiurge the kind of efficient cause that begins to act at a certain moment of time, and make the heavenly bodies out of the kind of fire that naturally moves away from the centre of the world. Thus Porphyry, in his lost commentary on the Timaeus, argued against Atticus’ ‘extremist’ Platonism, and argued for an interpretation of the Timaeus consistent with Aristotle. Proclus, in his (largely extant) commentary on the Timaeus, followed Porphyry in saving Plato for the ‘moderate’ Platonist position, according to which the divine nous eternally gives being to the heavens, and eternally gives them circular motion, not by overriding their natural motion but by eternally giving them a nature that disposes them to move in circles. But Proclus declines to save Aristotle for the moderate position.13 Perhaps Proclus thinks that Aristotle thought God was only a final and not an efficient cause, or perhaps he just thinks that it is not his job as a Platonic commentator to save Aristotle, and that if someone with more affection for Aristotle wants to do it, it is up to them.14 Proclus’ student Ammonius took up that challenge: ‘my teacher Ammonius wrote a whole book giving many arguments that Aristotle thought that God was the efficient cause of the whole world’ (Simplicius, in Physica 1363,8–10, similarly in de Caelo 271,19–21). Ammonius’ (now lost) book was a monograph, not a commentary; one thing Simplicius is doing in his On the Heaven commentary is applying the basic insight of Ammonius’ monograph to particular contested passages of On the Heaven, and thus saving Aristotle as well as Plato for the ‘moderate’ position. Simplicius is particularly provoked to do this because a Christian former student of Ammonius, John Philoponus, in his On the Eternity of the World against Aristotle, had defended an ‘extreme’ Platonist view, maintaining against Aristotle that the world was created a finite time ago and that the heavens are made of ordinary fire.15 So Simplicius will defend Aristotle against Philoponus’ arguments, will show (following Proclus) that Plato did not really hold the ‘extremist’ positions that Aristotle attacks, and will show (following Ammonius) that Aristotle did not hold the ‘extremist’ positions that Alexander attributes to him, but rather agrees with Plato’s real position. Simplicius and others often express this interpretation of Aristotle’s attitude towards the Timaeus by saying that Aristotle is arguing, not against Plato’s real views but against to phainomenon (literally ‘the apparent’ or ‘what appears’), i.e. against the merely apparent sense of the Timaeus.16 According to Simplicius, Aristotle’s motive for rejecting certain predications – e.g. for refusing to say that the divine nous made the world, or that the heavens are generated or are made of

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fire, or that there is an eternal horse-itself – and his motive for arguing against Plato’s apparent sense when Plato says these things, would be that Plato is applying to divine realities (to intelligible things, or to sensible but eternal things) predicates that, taken in their proper sense, are applicable only to lower things.17 According to Simplicius, Aristotle knows that Plato does not mean these predicates in their ‘low’ sense, but Aristotle wants, by refuting the lower sense, to force Plato’s sympathetic readers to seek a ‘higher’ sense in which these things can be true. Aristotle himself, according to Simplicius, prefers to avoid metaphorical language which risks assimilating higher things to lower things. But this leaves Aristotle with very few predicates left to apply to divine realities, and so he exposes himself to the opposite danger of being interpreted as an ‘extreme’ Aristotelian, e.g. as denying that the divine nous is an efficient cause of the physical world, or that it contains intelligible paradigms of sublunary animal species. As Simplicius puts it: If I may state my own opinion, it seems to me that in these matters [the question of whether the heavens are composed of a fifth body, of fire, or of a mixture of fire and the other standard elements] Aristotle had the same experience as in the case of the Ideas. For in that case too it is clear that he grants that the causes of all things exist in God, and furthermore that they are distinguished [from each other: i.e. it is not just a single undifferentiated divine cause of all lower things], since he says that there is a twofold order, one here and the other in the demiurge, with the order here arising from the order there, in the same way that there is a twofold order, one in the general and the other in the army, with one order arising from the other.18 And where there is order, there must certainly also be distinction. But he scrupled to call these causes by the same names as the things here, man or horse or any other of the things here, since most people’s imaginations are easily carried away by names. So too in this case he too would say that [the heavenly bodies] are composed of luminous and tangible substance and that the luminous predominates, but he would not say that they are [composed] of the things here that are such [i.e. fire, which is the luminous substance down here, and earth, which is the tangible substance down here], but rather of their ‘summits’ [akrotêtes: i.e. of the highest luminosity and tangibility, which Plato is willing to call ‘fire’ and ‘earth,’ but Aristotle is not], as he makes clear by calling it divine and first, when he says ‘so if there is something divine, as indeed there is, then the things that we have now said about the first [= highest] bodily substance have been said rightly’ (On the Heaven 1.3, 270b10– 11). And for this reason he saw fit also to call it a fifth substance, in order that we should put forth conceptions of it as of something entirely transcending the things here. (Simplicius, in de Caelo 87,1–17)

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As this passage shows, Simplicius is as aware as anyone that Aristotle criticizes what Plato appears to be saying, and that Aristotle himself prefers to speak differently from Plato. But Simplicius diagnoses the difference by saying that Aristotle’s criticisms are effective only against a ‘low’ interpretation of the predicates that Plato attributes to divine realities. Simplicius offers a ‘high’ interpretation of Plato’s attributions, and, making heavy use of a principle of charity, he argues (often against Philoponus) that Plato must have meant them in the ‘high’ sense. Then, again using a principle of charity, he argues (often against Alexander) that Aristotle too would have no reason to reject these attributions in their high sense. A similar procedure is available whenever Aristotle seems to criticize anyone else that Simplicius wants to save, typically pre-Socratic forebears of Plato such as Parmenides or Empedocles. This helps to explain Simplicius’ motives for writing a commentary on On the Heaven. But it is also natural that, having shown how to harmonize On the Heaven with the Timaeus, he would then turn back to the more foundational investigations of Aristotle’s Physics. This is in part because Physics 8 gives Aristotle’s basic argument that motion is eternal (in the sense not just that at every time there is some motion, but that there is at least one motion which persists throughout all time), and thus that the world itself is eternal, and also his argument that there is an eternally unmoved cause of this eternal motion. At in de Caelo 201,3–10 Simplicius says that since Philoponus has tried to refute, among other arguments for the eternity of the world, also the arguments that Aristotle has given in Physics 8, he will defer the consideration of these arguments until then. So Simplicius is looking forward from the commentary on On the Heaven to the commentary on the Physics, rather than looking backward from On the Heaven to the Physics in accordance with the normal pedagogical order. And indeed in his commentary on Physics 8 he is concerned to reply to Philoponus’ criticisms (by contrast, he never mentions Philoponus in his commentary on Physics 1–7). But Simplicius is also very interested in the earlier books of the Physics, in part because they lay the foundations for Aristotle’s argument in Physics 8. Physics 8 is a tour de force, which (unlike On the Heaven) tries to establish the eternity of motion without any ‘cosmological’ assumptions, and in particular without any empirical premises about the motions of the heavenly bodies. So it relies heavily on the earlier books of the Physics, which investigate basic concepts presupposed by all of natural philosophy, such as nature itself, form, matter, causality, motion, and the really or allegedly necessary conditions of motion such as place, void, time, continuity, and infinity. As Simplicius puts it, the aim of the Physics is ‘to teach concerning the things which

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belong in general to all natural things inasmuch as they are natural, that is to say, bodily’: that is, to teach concerning the ‘principles’ common to all natural things, such as form and matter and the other kinds of causes, and their ‘concomitants’ such as place and time and continuity (3,13–4,7).19 Aristotle investigates each of these things in depth in the Physics before describing the cosmos in On the Heaven and subsequent treatises, and Simplicius, remarkably for a neo-Platonist, sees this as a methodological improvement over all of Aristotle’s predecessors, even Plato: Aristotle also surpassed both Plato and all those before Plato alike: while they either discussed natural subjects as if discussing all of the things that are (as some of those before Plato did), or raised the questions that are treated here as if they were questions about the cosmos and its parts and did so in writings on the cosmos (as Plato himself and some of those before him did), Aristotle both distinguished what rank natural things have among the things that are and also teaches, as if there were no cosmos, about natural body itself in its own right. (7,27–34)20

For Simplicius this explains why we can better study the foundations of natural philosophy by working through Aristotle’s Physics and raising and solving the problems that arise in it, rather than by studying any earlier writing, even the Timaeus. But Aristotle surpasses Plato only methodologically, not doctrinally: here too Simplicius will try to show that Plato, and other earlier philosophers that Simplicius approves of, at least implicitly agree with Aristotle’s views about the common principles of natural things and their concomitants, even if they do not spell out their views on foundational questions in as much precise detail as Aristotle.

3. Simplicius’ commentary-methods and his use of earlier commentators; from Alexander to other sources I turn now from Simplicius’ larger purposes in writing commentaries on these texts to the methods by which he did so. Here I mean not specifically methods for harmonizing Aristotle with Plato, but his methods for dealing with each ‘lemma’ (each chunk of the text taken as a unit for commenting)21 as he comes to it, since he is very thorough, and treats every text and every problem in the text, whether any great ideological issue hangs on it or not. Not all of the Physics commentary consists of commentaries on particular lemmas: there is also the

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introduction to the whole text, and introductions and sometimes epilogues to particular books, and ‘digressions’, including the lengthy Corollaries on Place and Time, that stand back from interpreting or defending particular passages. But the vast majority of the commentary is interpreting some particular lemma.22 In commenting on a given lemma, Simplicius will typically first summarize the overall thought of the text; then raise problems (he often speaks of ‘investigating’ (zêtein)) about details of the text;23 then cite the solutions that earlier commentators had offered for these problems, and then any supplementary material from authors other than the commentators that he thinks would help; then make various ‘observations’ (epistaseis), often critical of earlier commentators and in any case noting details of the text, overlooked by earlier commentators, that might have pointed them towards a more adequate solution; and then, finally, introduce his own proposed solution to the difficulties, typically introduced by the word mêpote, ‘perhaps’. Some discussion of each of these stages of Simplicius’ exegetical procedure should make it easier for the reader to follow Simplicius’ treatment of each lemma, distinguishing what Simplicius is repeating from earlier sources (with or without endorsing them) and what is his original contribution, and seeing where Simplicius wants the emphases to fall. And for those readers who are chiefly concerned with Simplicius’ use of earlier sources, it will be important to understand how Simplicius proceeds in invoking various types of earlier sources (cited by name or not) to help him understand each lemma, and what sources he is looking at and why. There are two crucial points to bear in mind. First, Simplicius, like all commentators of his time, always starts from the earlier commentators on the same text (in the Physics commentary primarily Alexander, and in the second place Porphyry), disagreeing with them or going beyond them only where he has some particular stimulus to do so. In particular, Simplicius’ initial summary of the overall thought of the lemma will typically follow an earlier commentator (in the Physics usually Alexander). Second, in going beyond the overall summary and beyond what earlier commentators had said, he is driven by problems. A problem may be simply a question raised by the lemma, but is typically a prima facie objection against what the lemma seems to be saying, and in solving the problem Simplicius is typically led to go beyond what earlier commentators had said, and often to interpret the lemma in different ways than they had done: sometimes an objection to Aristotle would be correct if Aristotle had meant what Alexander took him to mean, and solving the problem depends on interpreting Aristotle differently from Alexander. And, as we will see, when Simplicius cites sources other than the commentators,

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including the pre-Socratics, he is often doing so as a means towards solving some problem that he has raised.

3.1 Simplicius’ use of earlier commentaries The neo-Platonic philosophers of the fifth and sixth centuries ce standardly wrote their commentaries on texts of Plato and Aristotle by ‘wrapping’ their commentaries around earlier commentaries on the same texts, incorporating much of the substance of the earlier commentaries, including their references to earlier sources. They are, in effect, writing meta-commentaries on these earlier commentaries. This does not mean that the late neo-Platonists’ work is unoriginal, but it can be hard to determine what is original in it, and more generally to understand what they are doing, until we know what belongs to this ‘middle stratum’ between the primary text and the final commentary: naturally this is difficult in cases where the earlier commentary is lost. (In some cases the earlier commentary may be lost precisely because its content had been incorporated in the later commentary, and Byzantine scribes saw no need to transcribe both of them.) Simplicius is not trying to fool anyone into thinking that points he has taken from (e.g.) Alexander are his own discovery – he has no idea that he will have readers who will not know Alexander’s text and will not be able to look it up. But he takes over information from earlier commentators, without feeling a need to name them unless he wants to call attention to a disagreement between two earlier commentators, or unless he wants to say that an earlier commentator needs to be corrected or supplemented. Simplicius’ Categories commentary, like Proclus’ commentaries on Plato’s Timaeus and Parmenides, is responding mainly to earlier neo-Platonic commentaries by Porphyry and Iamblichus (and Iamblichus in turn is responding to Porphyry, and Porphyry to Peripatetic or middle-Platonist commentators). This was a common pattern. But in writing commentaries on Aristotle’s physical works, Peripatetic commentaries are more important, especially Alexander’s.24 It seems clear that, on the Physics, the only commentaries that Simplicius consults regularly are Alexander and Porphyry and the paraphrase by the later (fourth century ce ) Peripatetic Themistius:25 notably at 43,28, where Simplicius says that ‘all the commentators’ agree in attributing a certain view to Aristotle (but disagree on questions of detail), his only evidence is that Alexander and Porphyry and Themistius agree on this. Simplicius mentions Syrianus nine times in the Physics commentary, and five of these are probably references to a now lost Physics commentary by Syrianus.26 (The only other commentator on the Physics

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that he sometimes mentions is the earlier Peripatetic Aspasius, a teacher of a teacher of Alexander, but he seems to know him only through Alexander.)27 In addition to these written commentaries, Simplicius also makes use of the lectures of his teacher Ammonius: notably, on the mathematical reference Physics 1.2, 185a16–17, Simplicius mentions something that ‘our teacher Ammonius said’ (59,23), then what ‘I said to the teacher’ (59,30–1), then what Ammonius said in response. This is evidently something Ammonius said in a lecture-course on the Physics, which led Simplicius, as a student in the class, to ask a question and get an answer; presumably Simplicius either took notes on Ammonius’ lectures and answers to questions, or else relied on an official note-taker for the course.28 For On the Heaven Simplicius seems to know only Alexander’s commentary and Themistius’ paraphrase, although on the first page he discusses Iamblichus’ and Syrianus’ views about the object or aim (skopos) of the treatise.29 Themistius’ paraphrases of the Physics and On the Heaven are extant, so we can see how Simplicius used them, but they were too abridged to be much help to him or to us (Physics 1.1–2, 102 pages in Simplicius, are seven pages in Themistius): in most cases all we can say is that Themistius’ paraphrase is implicitly construing the text with Alexander or with Porphyry as the case may be.30 Thus, in the Physics, Alexander and Porphyry are the most important authorities that Simplicius uses to locate his own position. The situation is different in Physics 1–4 and in 5–8, since Porphyry wrote commentaries only on Books 1–4, which he regarded as a separate treatise and which he wanted to use in interpreting the Timaeus, although he also wrote short ‘synopses’ at least of Book 5 and perhaps of 5–8. Simplicius names Porphyry fiftynine times on Books 1–4 but only five times in Book 5 and never in 6–8,31 although, if Porphyry did write synopses of all these books, then Simplicius’ epilogues to Books 5, 6, 7, and 8, summarizing the arguments of those books (920,4–922,19; 1031,31–1035,12; 1111,29–1116,14; 1363,25–1366,32), may well be heavily indebted to Porphyry’s synopses. But even in Books 1–4, Simplicius seems to wrap his commentary much more around Alexander’s commentary than around Porphyry’s. He is indebted to Porphyry, directly and through Ammonius, for the project of harmonizing the Physics with the Timaeus, and he is grateful to Porphyry for preserving information from sources to which Simplicius (like us) does not have direct access: notably, in the Physics commentary, his information about Andronicus of Rhodes, Nicolaus of Damascus, Moderatus, and Dercyllides seems to come exclusively through Porphyry, and in the Categories commentary he calls Porphyry ‘the source to us of all fine things’ (in Categorias 2,5–9). But, although he is ideologically much closer to Porphyry than to

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Alexander, he does not often agree with Porphyry against Alexander where he cites them as disagreeing in their interpretations of particular lemmas; and he calls Alexander ‘the most genuine of Aristotle’s interpreters’ (80,15–16; 258,16– 17), which seems to praise him above Porphyry among others. While Simplicius’ citations-by-name are an imperfect guide to his use of earlier writers, he names Alexander in the Physics commentary overwhelmingly more often than Porphyry, indeed overwhelmingly more than any earlier author except Aristotle. Indeed, he names Alexander forty per cent more often even than Plato, and fully ten times as often as Porphyry (‘Aristotle’ 995 times, ‘Alexander’ 652, of which 4 are Alexander the Great, ‘Plato’ 468, ‘Eudemus’ 153, ‘Porphyry’ 64, ‘Themistius’ 38, ‘Theophrastus’ 37).32 Still, while Alexander is clearly Simplicius’ main point of departure, and while he does not often follow Porphyry against Alexander on particular lemmas, Porphyry remains important for him: where Porphyry disagrees with Alexander it is at least a sign that there is a problem in the lemma that warrants further investigation. (And thus the commentator is in a better position on Physics 1–4 than on Physics 5–8 and On the Heaven, where he does not have Porphyry to counterbalance Alexander.) And Simplicius, despite his high praise for Alexander, routinely complains about Alexander, not only that he represents Aristotle as really disagreeing with Plato (and with Parmenides and so on), but also that he represents Aristotle as agreeing with Alexander’s own opinion, notably that the human rational soul is inseparable and thus mortal, and that the divine nous is not an efficient cause of the existence of the heavens but only a (final or efficient) cause of their motions.33 Where the ‘standard’ interpretation of the text, Alexander’s, imputes such views to Aristotle, there is always a need for further investigation. As noted above, Simplicius usually starts with a summary of the lemma following Alexander (but commenting at 71,17 ff. on Physics 1.2, 185a20-b5, he is clearly following Porphyry, see 73,2–4), not bothering to name Alexander unless he has a specific reason for contrasting Alexander either with Simplicius himself or with another interpreter (Porphyry, Themistius, also Eudemus). Sometimes Simplicius does this because he thinks Alexander has gone wrong on some issue and wants to correct him; sometimes he wants to call attention to a disagreement among the commentators (whether Simplicius ultimately sides with Alexander or not); sometimes, without contradicting Alexander, he thinks that Alexander needs to be supplemented, and wants to contrast him with some other source of information. In a notorious passage at 13,16–21, Simplicius says something in his own voice which on the next page, at 14,13–19, he repeats almost verbatim as part of

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a quotation from Alexander. At 13,16–21 Simplicius is not intending to take issue with anything Alexander says in this passage, and feels no need to name him; by contrast, immediately after this passage, at 13,21–7, he does cite an extended passage of Alexander by name, and adds that ‘Alexander says these things in these very words’ (13,28), precisely because it is this second text that he here wants to challenge Alexander about.34 Only on the following page, where Simplicius goes back to contest something that Alexander said in the first passage (the passage quoted at 13,16–21), and tries to motivate his own solution to the same problem by contrast with Alexander’s, does he cite the earlier passage explicitly as Alexander’s.35 Ever since Diels’ introduction to his edition of Simplicius’ Physics commentary in the Commentaria in Aristotelem Graeca, this text has been taken as a clue that Simplicius is taking far more from Alexander than he admits, or even that most of Simplicius’ commentary is taken from Alexander, that it is an ‘expurgated edition’ of Alexander’s commentary, purged of anything that would contradict Platonism or that would represent Aristotle as contradicting Platonism.36 But, if nothing else, it seems clear that Simplicius’ commentary is much longer than Alexander’s was: Simplicius’ Physics commentary is almost ten times as long as the original text (measured by numbers of words), whereas in Alexander’s extant commentaries on the Meteorology, Topics, Metaphysics 1–5, and On Sensation the ratios are about 2½:1, 4:1, 6:1, and 6½:1.37 And while Simplicius’ disagreements with Alexander are often to defend Plato or some precursor figure (Parmenides, Empedocles, etc.) and to show that Aristotle is not really criticizing him, not all of Simplicius’ interventions can be motivated in this way.38 Notably, there seems to be no motive other than desire for historical accuracy behind Simplicius’ (entirely justified) correction of Alexander’s reconstruction of Hippocrates of Chios’ squaring of the lunes, which takes up fourteen pages of Simplicius’ commentary on Physics 1.2 (55,25–69,34). It is better to say that, while Simplicius takes Alexander’s commentary as giving the default interpretation of Aristotle’s text, which he follows unless there is some reason to question it, his own commentary is devoted to raising and solving problems about the text, and specifically problems which motivate deviating from Alexander’s interpretation.

3.2 Commentaries, problems and monographs: From grammatical to philosophical commentaries Simplicius speaks in several places about the relation between explicating a text and raising and solving problems or objections to it. Notably, at the beginning of

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his Categories commentary (1,3–2,29), he reviews what earlier writers on the Categories have done. Some, he says, have merely rewritten Aristotle’s expressions (lexis) for greater clarity; others have also tried to unpack its thought-content (ennoiai); and others – who Simplicius clearly prefers – have also dealt with problems (zêtêmata). These problems are, in the first instance, prima facie objections to what Aristotle has said (some largely verbal, like Lucius’ and Nicostratus’, some more substantive, like Plotinus’), which require solution: we will come to a deeper understanding of Aristotle’s thought in the process of solving these problems than we would if we tried to explicate it without facing the objections. Thus, as Simplicius says, we should be grateful even to those who only raised aporiai (difficulties or problems or objections against the text), since ‘they have given occasions for the solution of the aporiai and for many other beautiful theorems to those who have come after them’ (2,1–2); but Porphyry who ‘has diligently given a complete exegesis of the book and solutions of all the objections (enstaseis)’ in his now-lost great commentary in seven books (2,5–9), deserves the most gratitude and will be Simplicius’ model for integrating explanation of the argument and of lexical details with problems and their solutions. Commentaries, problems (problêmata, zêtêmata, aporiai), and monographic treatises had been closely connected at least as far back as the Hellenistic ‘grammarians’ (grammatikoi – that is, scholars of ancient poetic texts and especially of Homer), and Simplicius is drawing on their tradition of commentary writing as well as on a more specific tradition of philosophical commentary. Scholarship on Homer and other poets originates in the game of Homeric (or other poetic) ‘problems’ and ‘solutions’, which goes back at least as far as Protagoras (and is practised, on a poem by Simonides, at Plato, Protagoras 338E6–347B2). A Homeric problem might be just a question (‘what song did the Sirens sing?’), but is more typically a challenge against something Homer says that appears to be inappropriate, e.g. because it involves a grammatical or lexical error, or represents a hero as speaking or acting nonsensically or out of character, or contradicts something that Homer says elsewhere, or contradicts known facts, or pointlessly repeats information, or speaks unworthily of a god. The interlocutor’s task is to rescue Homer from the accusation, which he might do in many ways, e.g. by supplying the motivation for something that Homer or a character says, or giving the full grammatical construction (by supplying words that Homer has omitted for brevity, or changing the order of the words), or explaining the dialect meaning of a word, or explaining a metaphorical meaning, or repunctuating, or emending a line by the authority of a manuscript or of some

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earlier writer who cites the line, or emending a line even without external authority, or deleting a line because it is repeated elsewhere in Homer, or deleting a line as spurious, or allegorizing. This might be done purely orally, as a test of wits at a symposium; or it might be written up as a Question (zêtêma, problêma) or a set of such Questions, like Porphyry’s Homeric Questions. A single such Question, if long and important enough, can become a monograph in its own right. But one could also assemble a whole commentary on an ancient poem, which might have many such individual investigations embedded in it and might be largely constituted by them. One can also proceed in a similar way with a sufficiently important prose author, notably with the founder of one’s philosophical school, where it is important to defend the author against any objections, made for instance by members of other schools. Plutarch wrote an extant short collection of Platonic Questions, modelled in some way on poetic questions. And in philosophical as well as grammatical-critical texts, there is continual back-and-forth between commentaries and monographs, both of which can be largely driven by problems of various sorts. A commentary may be the written transposition of lectures on a text, or it may be an elaborated version of notes from the lectures, filled out by use of other written sources, but a lecture, where it goes beyond straightforward paraphrase of the authoritative text, is likely to be driven by problems. It may help to compare Simplicius-style commentaries with Plotinus’ treatises. Plotinus notoriously did not write commentaries, but he too taught out of texts of Plato and Aristotle, and Porphyry says that he would have someone read from one of the Platonist or Peripatetic commentators in the meetings, but that Plotinus ‘did not simply select something for himself out of these [commentaries]; rather, he was his own man and specially distinguished in consideration (theôria), and he brought the insight (nous) of Ammonius [Saccas] to bear in examining [questions]’ (Life of Plotinus 14.10–16). So a text of Plato or Aristotle would be read aloud, perhaps Plotinus would summarize what it was saying, and at least when a difficulty arose someone would check what a commentator had to say; but then Plotinus would give his own judgement on the problem, and if he did not find the commentator’s solution satisfactory he would raise objections to it and propose a better solution. So, as his opponent Longinus says in qualified praise of him, Plotinus and his student Amelius ‘show their seriousness in writing by the multitude of problems which they address, and apply a distinctive manner of consideration’ (Longinus quoted by Porphyry, Life of Plotinus 20.68–71). Doctrinal novelty is not in itself praiseworthy, and Longinus does not think that Plotinus’ distinctive manner of consideration always leads him aright, but it is

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important that Plotinus does not simply accept inherited solutions: he addresses new problems which earlier philosophers had ignored, and even with problems which earlier philosophers had treated, he criticizes their too-easy solutions, and proposes something of his own to meet a stricter standard.39 The treatises that Plotinus bothered to write up are not commentaries, but they are often provoked by problems that might come up in teaching one of the founding texts, e.g. by a dispute about how some assertion in Plato should be interpreted, or by an objection that needs to be resolved against something Plato says, or by a series of questions and objections (many of them taken from earlier commentators) against Aristotle’s Categories. If a fuller written record were made of this kind of teaching, including the initial paraphrase of the text and maybe checking more than one commentator, and perhaps naming them, before giving the teacher’s objections and own solution, then it would be a commentary, instead of what we actually have from Plotinus, namely a series of monographs on particular issues.40 As this example shows, one possible relation between commentaries and monographs is that a commentary can contain embedded within it a series of monographs on particular problems, problems which arise in reading the text but may well involve larger philosophical issues. This is the case most famously with the lengthy so-called Corollaries on Place and Time which Simplicius inserts in his commentary on Physics 4, but he also has many smaller embedded essays, e.g. on matter, on nature, and on chance.41 Alternatively, a commentary might work out the core insight from a monograph, applying it to all the problems that come up in a text and trying to show that the whole text can be made consistent with this interpretive proposal. Simplicius is doing this in applying the insights of his teacher Ammonius’ monograph arguing that Aristotle’s god is an efficient cause to a full commentary on On the Heaven (and perhaps Plotinus was doing something like this in applying the ‘insight’ (nous) of his teacher Ammonius Saccas, although Ammonius Saccas never wrote down his ideas). As we have seen, Simplicius at the beginning of his Categories commentary praises Porphyry’s integration of problems and solutions into his commentary. He makes similar programmatic remarks in his commentary on On the Heaven, and there he makes it clear that this programme also involves vindicating On the Heaven and the ‘pious conception of the universe’ in the face of Philoponus’ objections against the eternity of the world and against a fifth body naturally moving in circles: ‘it seemed to me [appropriate] to set forth [Philoponus’] objections too [sc. as well as the earlier objections of Xenarchus, to which Alexander had already responded], and to solve them to the best of my ability:

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for it seemed more appropriate to coordinate the objections and their solutions with the comments on the treatise’ (in de Caelo 26,13–17). Xenarchus’ objections to On the Heaven, like Lucius’ and Nicostratus’ and Plotinus’ objections to the Categories, had helped to fuel earlier commentaries, and Simplicius decides to include Philoponus as part of the same series of objections and solutions, even though Philoponus is motivated by a much more fundamental hostility to ‘the pious conception of the universe’: as Simplicius says, Philoponus has taken it as his aim ‘to demonstrate that the cosmos is corruptible, as if he were going to get a big prize from the demiurge for demonstrating that he is the demiurge only of corruptible things and not of anything incorruptible’ (25,26–8). Philoponus’ objections against Physics 8 similarly help to fuel Simplicius’ commentary on that book.42 On the Physics outside of Book 8, although Simplicius does not feel the need to rescue Aristotle from attack by a diehard ideological enemy, there are nonetheless many problems to solve. Some of these problems are just local issues in understanding a particular passage, unrelated to any grand conflict. But while it is a problem in Aristotle (as it would be in Homer) if he seems to contradict himself, Simplicius also takes it as a problem in need of solution if Aristotle in some passage seems to contradict Plato. (Proclus would take all such passages as grounds for suspicion against Aristotle.) This might happen, in particular, if Aristotle seems to raise an objection against Plato: where this happens, one of Simplicius’ tasks is to solve the objection against Plato, typically by showing that Plato did not hold the doctrine that Aristotle seems to attribute to him. But if Aristotle seems to raise an objection against Plato which misfires, that is not only a problem against Plato which must be solved, but also a problem against Aristotle which must be solved, by showing that Aristotle was not attributing a false and un-Platonic view to Plato (but rather was criticizing, perhaps people who misinterpreted Plato and so were led into error, or perhaps, e.g. some preSocratic), and also by showing that Aristotle himself agrees with the genuinely Platonic view on the question. It is likewise a problem, even when Aristotle is not raising objections against anyone, if he says something that seems to commit him to some objectionably un-Platonic doctrine, e.g. that the soul is the form of the body and that souls of mortal animals are therefore mortal, or that the divine nous is only a final and not an efficient cause to the physical world, or that the divine nous contains no distinctions and therefore no paradigms of the different natural things. Alexander often attributes such doctrines to Aristotle, and every time he does so there is a problem. Furthermore, Platonists like Proclus are often willing to accept

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Alexander’s attribution of such doctrines to Aristotle, and to take them as grounds for objecting to Aristotle from a Platonist point of view. Every such apparent divergence between Plato and Aristotle is a problem, because it is an apparent fault in Aristotle, and the commentator has the task of rescuing Aristotle from the charge, just as the grammarian has the task of rescuing Homer from any apparent fault. Furthermore, at least some of these charges against Aristotle would be correct if he thought what Alexander thinks he thought. Alexander’s interpretation of Aristotle is the vulgate, the default reading of Aristotle, comparable to the vulgate text of Homer; and just as solutions to Homeric problems may require challenging the vulgate text, punctuation, and construal of Homer, so solutions to Aristotelian problems may require challenging Alexander’s interpretation of Aristotle, and indeed sometimes his text and punctuation.43

3.3 Simplicius’ sequence of sources Simplicius, in explicating Aristotle’s text and raising and solving problems about it, makes heavy use of earlier written sources, other than the text of Aristotle that he is commenting on. There are some sources that he always consults on each lemma, and other sources that he consults when there is some special occasion in the lemma that calls for it. Simplicius also has remote sources, i.e. sources that he does not have direct access to, but knows only from intermediate sources, although the way he cites the remote sources can make it look as if he has direct access to them. (He also, as noted above, has oral sources, namely the lectures of his teachers, Ammonius and/or Damascius, on the texts he is commenting on.) That Simplicius draws heavily on earlier sources does not mean that he has nothing original to contribute, but his usual procedure is to begin with things taken from earlier sources and to motivate his own original contributions as solutions to problems not adequately solved by those earlier sources. He has different reasons for consulting his different kinds of source, and a typical sequence in which he cites them. The sources that Simplicius always looks at on each lemma are the earlier commentators, which on the Physics means Alexander and Porphyry and Themistius; and also probably always the Physics of Aristotle’s student Eudemus, which was not a commentary on Aristotle but closely followed Aristotle’s order of exposition. (More precisely, Simplicius always looks at Porphyry on Physics 1–4, and at Eudemus except on Book 7; he knows Aspasius’ commentary only indirectly.) As Diels had already noticed, Simplicius’ initial summary of each

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lemma follows some earlier commentator, usually Alexander but occasionally Porphyry. But he does not remain content with Alexander. Where there are problems, and Alexander’s interpretation is insufficient, Simplicius’ first impulse is to turn to Porphyry and Themistius, to see if they have an interpretation that would solve the problem. Indeed, he always looks at them, noting any significant differences between their interpretations, because any of them might have valuable contributions and because their disagreements are themselves problems in need of solution. Where there are no interesting contrasts between the earlier interpreters, Simplicius does not usually mention their names; where there are, he does. After he had drawn on the commentators and noted their difficulties or divergences, Simplicius’ next recourse is, systematically, to turn to early Peripatetic texts which, while not being commentaries on Aristotle, give parallels which may elucidate Aristotle’s meaning, and which often go into more detail than Aristotle does. Notably, these parallels sometimes name earlier authors that Aristotle may allude to without naming them, and the parallels may say in more detail than Aristotle what the earlier authors said. In the Physics commentary, the most important such early Peripatetic source (although by no means the only one) is Eudemus’ own Physics, which closely followed the order of Aristotle’s Physics except for Book 7. So, after looking up a passage in Alexander and the other commentators, it was easy for Simplicius to look up the corresponding passage in Eudemus and to compare his interpretation to the commentators’, in the first instance to Alexander’s. Simplicius calls Eudemus ‘the most genuine [gnêsios – literally the most legitimate offspring, thus the most authentically Aristotelian] of Aristotle’s students’ (411,15–16), as he has called Alexander ‘the most genuine (gnêsios) of Aristotle’s commentators’ (80,15–16 and 258,16–17, cited above),44 and he typically uses Eudemus to trump Alexander. If Alexander agrees with Eudemus on some issue, then Simplicius can say that Alexander got it from Eudemus, and then, whether Eudemus is right or wrong, we can deal with him as the more authoritative source and dismiss Alexander as derivative. Where, by contrast, Alexander disagrees with Eudemus, Simplicius almost always prefers Eudemus; and on some texts where Alexander thinks he is following Eudemus, Simplicius argues that Alexander is misinterpreting Eudemus, and so tries to chop Alexander’s support out from under him.45 Simplicius also draws on Eudemus’ works on the history of the different sciences. Notably, in the Physics commentary, in trying to explain what Aristotle means by ‘the squaring by means of segments’ which it belongs to the geometer to solve (185a16–17), Simplicius first cites at length Alexander’s account of this

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squaring of curvilinear figures, by Hippocrates of Chios (55,25–58,24 and 60,18–21),46 mentioning only at the very end that he has been taking all this from Alexander, and then he trumps Alexander by turning to Eudemus’ History of Geometry (60,22, 60,30–1). He then transcribes Eudemus’ account of Hippocrates’ squaring for a remarkable eight pages, 60,22–68,32, occasionally adding his own comments or filling in references to propositions in Euclid, finally concluding (rightly) that ‘for what concerns Hippocrates of Chios, we should rather trust Eudemus to know [sc. than Alexander], being closer to the times, and a student of Aristotle’ (68,30–31).47 He makes similar use of Eudemus’ History of Astronomy in the commentary on On the Heaven to explain the theories of planetary motion that Aristotle draws on in On the Heaven 2.12.48 Simplicius also draws freely on Theophrastus (thirty-seven citations by name in the Physics commentary, against 153 for Eudemus).49 In his introductory survey of the place of the Physics among other treatises he consciously cites treatises of Theophrastus as well as of Aristotle,50 and at 9,7–10, in commenting on the argument in the first sentence of Aristotle’s Physics, he notes that Theophrastus in the parallel argument at the beginning of his own Physics explicitly establishes a premise that Aristotle takes for granted. So Simplicius seems to assume that Aristotle and Theophrastus are engaged in a joint enterprise, and that what Theophrastus says is also evidence for how Aristotle is thinking, although Theophrastus sometimes makes more things explicit. He cites Theophrastus’ Physics by title six times, and also five times his On Motion, which may also have been part of his Physics, since Simplicius tells us that Theophrastus’ On the Heaven is the third book of his Physics (1236,1).51 The reason that Simplicius cites Eudemus’ Physics so much more often than Theophrastus’ is, presumably, that Eudemus follows Aristotle’s order much more closely than Theophrastus, so that on any given lemma Simplicius could easily locate the corresponding passage in Eudemus and find something directly comparable, from which he could infer how Eudemus was interpreting Aristotle. Simplicius’ main use of Theophrastus, however, is for his reports on the opinions of earlier thinkers. Simplicius does not usually give the title of the work he is citing in these passages, but most of the references seem to be drawn from a comprehensive treatise by Theophrastus (a few are from monographs about some individual thinker), and in three places he cites its title as Phusikê Historia (115,12; 154,17; just Historia at 149,32). This phrase might mean just Natural History, but here in context it means specifically History of Physics, exactly parallel to the titles that Simplicius cites from Eudemus, History of Geometry (Geômetrikê Historia) and History of Astronomy (Astrologikê Historia).52 He

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turns to Theophrastus, above all, to fill in Aristotle’s compressed division of all possible views about the principles, The principle must necessarily be either one or several, and if one, either unmoved, as Parmenides and Melissus say, or moved, as the natural scientists say, some of whom said that air and others of whom said that water is the first principle; and if several, either finitely or infinitely many, and if finite, but more than one, either two or three or four or some other number, and if infinite, either, as Democritus [thought], one in genus but differing in shape or form, or even contrary. (Physics 1.2, 184b15–22)

Or perhaps Simplicius turns to Theophrastus to fill in just the first clause, ‘the principle must necessarily be either one or several’, for, at least as Diels prints it, Simplicius cites just that clause as a lemma by itself, and then, after raising and solving some preliminary problems about the division, he says ‘but it is presumably better first to encompass all the opinions through a more complete division, and then having done so to go back to the text of Aristotle’ (22,20–1).53 Then for the next six pages (through to 28,31) he gives a grand map placing everyone before Aristotle’s time in the space of possible views about the principles, which clearly relies on Theophrastus as its major source, occasionally supplemented by later Peripatetics, Nicolaus of Damascus and Alexander.54 This same passage also helps to bring out the ways in which Simplicius thought the Peripatetic sources (both the commentators and older Peripatetics like Theophrastus and Eudemus) were inadequate, and his motivations for going beyond them. Simplicius ties the Peripatetics very closely with historia and the cognate verb historein, which we have translated as ‘report’ or ‘recount’.55 At the end of the grand map, following Theophrastus and other Peripatetics, he says, ‘This is a concise overview of the things which are reported (historêmena) about the principles, written up (anagrapheisa) not in chronological order, but according to which doctrines are akin’ (28,30–1). But he immediately refuses to leave it at that: ‘But, hearing of such great variation (diaphora), one must not think that these are contrary accounts on the part of those who have philosophized, a thing which some people, who encounter only reports and write-ups (historikai anagraphai) and understand nothing of the things said, try to criticize’ (28,32–29,1). As the immediately following lines (29,1–3) make clear, Simplicius is thinking of Christian polemicists who, drawing on Theophrastus’ or similar accounts of the ancient philosophers, use them to argue for the futility of philosophy by showing that the philosophers contradict each other. No doubt these ‘reports and write-ups’ could be similarly abused by Pyrrhonists or

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Epicureans, and could also be used more innocuously. But, as Simplicius sees it, Peripatetic superficiality, by noting the differences in the philosophers’ expressions (this person called two things ‘principles’, this person four, etc.) without probing into the insights behind them, has made these abuses possible. To overcome the Christian opponents, we have to investigate more deeply. As Simplicius says, ‘perhaps it’s not a bad idea, digressing briefly, to display for those more desirous of learning how the ancients, although appearing to disagree in their doctrines about the principles, nonetheless come together in harmony’ (29,3–5), and this ‘brief digression’ takes another eight pages (29,5–37,8). And the deeper investigation here provoked by the Christian opponents is also valuable in its own right.56 It is really only here that Simplicius tries to go beyond the Peripatetics to other sources, whereas earlier, in the grand doxographical map of 22,22–28,31, he had quoted only two short bits of Plato and of each of three pre-Socratics (Xenophanes, Anaxagoras, and Empedocles), and was otherwise content to follow his Peripatetic sources. In aiming at a deeper interpretation than (say) Theophrastus of some early thinker, it might be possible simply to start with Theophrastus’ report and secondguess him, without any independent testimony to the early thinker’s views; and where one Peripatetic is unsatisfactory we can try supplementing him with another. But obviously it is best if we can turn to the words of the thinker himself, and look for clues to the deeper meaning by attending closely to the precise words. Most obviously, this is something that Simplicius does with Plato, when he thinks that either Alexander or an early Peripatetic (Theophrastus or Eudemus) is misrepresenting him. Thus at 26,5–25, where Theophrastus says that Plato (at least in his physics) uses two kinds of principles, the efficient and the material (26,11–13), Simplicius corrects him, not in the first instance by citing Plato, but by citing Alexander, who says that Plato uses three kinds of principles, the material and the efficient and the paradigmatic (26,13–15: meaning the three things Plato posits in the Timaeus as existing from eternity, namely the Receptacle and the demiurge and the separate Forms);57 only then does Simplicius give two quotes directly from the Timaeus (26,15–18 and 26,18–25) which are supposed to show that Plato also used the final cause and an immanent formal cause.58 And when at 99,29–31 Alexander suggests that Plato is the person Aristotle criticized at Physics 1.2, 185b28–32, who restricted the use of ‘is’ in order to avoid problems of the same thing’s being both one and many, Simplicius cites from Plato’s Sophist and Parmenides to show that Plato was just as scornful as Aristotle of those who worried about ‘easy’ one-many problems, and that Plato himself solved one-many problems in an entirely different way (99,32–101,24).59

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But if Simplicius can use the texts of Plato to trump Peripatetic misrepresentations, he can do the same with pre-Socratic texts, in those cases where he can find the original text, or something that he thinks is the original text. He seems to make direct use, notably, of texts by (or supposed to be by) Parmenides, Melissus, Zeno, Empedocles, Anaxagoras, Diogenes of Apollonia, and Timaeus.60 Strikingly, on Physics 1.4, 187a21–6, Aristotle’s discussion of Anaxagoras and Empedocles on how things are both one and many, and how the many come-to-be by separation from the mixture, Simplicius first discusses the issues on the basis of Alexander and Theophrastus (153,27–155,20), and only then turns to draw directly on Anaxagoras (155,21–157,24) and Empedocles (157,25–161,20). It does not occur to Simplicius to go immediately to the preSocratic texts, but he turns to them in order to trump later writers, to resolve their disputes or to show how we can go beyond their interpretations. Simplicius does not seem to cite the views of earlier philosophers much more than, say, Proclus in his commentary on the Timaeus: the difference is that generally Proclus is happy to treat a philosopher to the extent that he is represented (notably) in Plato, while Simplicius, although he starts from the same places as Proclus, wants to go beyond the representations in even the most highly respected philosophical sources, and look for clues in the original wording. (Here Simplicius is perhaps modelling himself especially on Porphyry, who – guided by his philological studies with Longinus, and apparently with access to a remarkable library – has a strong interest in verbatim quotation, and who in many cases seems to have been the last ancient writer with direct access to a particular text.) As Alexander gives the ‘vulgate’ text and interpretation of Aristotle, so the Peripatetics give the ‘vulgate’ interpretation of the pre-Socratics (and at least a widespread interpretation even of Plato), and sometimes their interpretation needs to be challenged, ideally by a close examination of the original wording, in order to solve problems. Simplicius first turns to pre-Socratic texts and their interpretation in his commentary on On the Heaven, mainly in Book 3, where Aristotle examines the views of earlier thinkers on weight and lightness and more generally on the elements out of which bodies are composed and through which they can be transformed into each other.61 Many of the same earlier thinkers resurface in the more general investigation of the principles of natural things in Physics 1, and Simplicius takes them up again, sometimes citing the same passages, sometimes different passages, and in some cases revising his interpretations. One motive for reinterpreting the pre-Socratics against the ‘vulgate’ Peripatetic interpretation is, of course, to save people who were important precursor figures for the Platonists,

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notably Parmenides and Anaxagoras and Empedocles; but Simplicius seems relatively uninterested in the Pythagoreans, who are the most obvious ‘precursors’ of Plato, and it is not obvious why solicitude for Platonist precursors would require saving Melissus or Zeno. ‘Saving’ earlier thinkers very often turns on deciding what level of being (among the options available for a late neo-Platonist) they were referring to in particular passages of their texts – in many cases, on showing that some passages, which would be objectionable if they referred to the sensible world, really refer to some higher level of being, and describe it metaphorically in language that would apply literally only to sensible things. This general approach is by no means an innovation with Simplicius: Platonists had been ‘saving’ Parmenides this way at least since Plutarch’s Against Colotes, arguing that Parmenides distinguishes between an intelligible and a sensible/ opinable world and that his One Being is not an extended physical reality, even if his descriptions make it sound like a finite sphere. And it was natural for neoPlatonists to try to interpret Parmenides’ first principle by determining how far up the Platonist hierarchy it is, how far up Parmenides was able to see: his One Being is not the first One, which is ‘beyond being’, but it is the first and highest thing that participates in that One. Simplicius is also certainly not the first to extend this approach to other pre-Socratics. Notably, he seems to assume that the default interpretation of Empedocles, among his Platonist readers, will be that the domain of Love is the intelligible world and the domain of Strife is the sensible (or at least the sublunar) world. When Simplicius proposes that although Love dominates in the intelligible world, Strife is also present there, and that although Strife dominates in the sublunar world, Love is present here too, he is refining this default Platonist interpretation, not radically innovating.62 Simplicius is much more interested in saving the Eleatics and Anaxagoras and Empedocles than he is in saving other pre-Socratics. Nonetheless, at 29,3–5 (quoted above) he promises to show how all the earlier philosophers described by Theophrastus ‘come together in harmony’ on the principles, not in the sense that they were all saying the same thing about the principles, but in that each of them has grasped some genuine principle, i.e. something that genuinely exists somewhere in the hierarchy of beings and is a cause of sensible phenomena. As Simplicius says in summing up his presentation, some looked to an intelligible and others to a sensible world-arrangement; some sought the proximate elements of bodies and some the more fundamental ones; some laid hold of the elemental nature in a more particular way and others did so more universally; some sought the elements alone [i.e. the immanent causes,

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Simplicius: On Aristotle Physics 1–8 which are really only auxiliary causes] and others sought all the causes and auxiliary causes. [Thus] they say different things when they give an account of nature, but not contrary things, for someone who is able to judge correctly. (36,15–20)

So, for instance, the ‘homoeomerous’ things that Anaxagoras posited as principles (qualitatively uniform flesh divisible into more flesh, bone divisible into more bone and so on) really exist, but earth and water and air and fire as posited by Empedocles are more fundamental; but these in turn are composed of physical indivisibles as posited by Democritus and Timaeus (indivisible bodies for Democritus, indivisible surfaces for Plato and his alleged source Timaeus), and there are further principles even more basic than these. And while early philosophers either investigated only the elemental principles or spoke only briefly and cryptically about immaterial causes, later philosophers culminating in Plato and Aristotle speak more fully and explicitly about these, and carefully distinguish the different kinds of principles.63 Simplicius sees himself as justified here by Aristotle’s remark in Physics 1.5 that the earlier philosophers who posited pairs of contrary principles ‘differ from each other in that some took prior and others posterior things [as their principles], and some took things that were better known by reason, others by sensation . . . so that in a way they are saying the same things as each other, and in a way different things, different as indeed it seems to most people, but the same by analogy . . . since one of the [pair of] contraries contains and the other is contained’ (188b30-a9, partly quoted by Simplicius 36,20–24). Aristotle is arguing here only that the philosophers all implicitly agree that there are a pair of contrary principles related roughly as matter and form, so that Aristotle can rely on a consensus in asserting this. He is not saying that the philosophers were right in the things they assert about the principles. But Simplicius, building on Aristotle, is trying to show that each philosopher saw some way up the hierarchy of being, and described more or less clearly what he saw, although Anaxagoras and Empedocles and the Eleatics and Pythagoreans saw further and described more precisely than the ‘physicists’, and Plato and Aristotle more precisely than they.64

3.4 Simplicius’ introduction of original material: epistasis and mêpote So far we have seen some typical reasons why Simplicius feels the need to supplement Alexander, first by later commentators (Porphyry and, where useful,

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Themistius), then by older Peripatetic sources (known either through the commentators or directly), and then in many cases by direct use of texts older than Aristotle. But, while Simplicius wants to be sure to gather all the information that he needs to solve problems in the text, simply quoting earlier texts will very often not be enough to solve the problems, and Simplicius will then introduce his own distinctive proposals. When he feels that none of the earlier writers has offered a satisfactory solution to a problem that arises from the text, he needs to show the reader why their solutions are inadequate, so as to motivate the search for a new solution, and he needs to give the reader a criterion by which to recognize Simplicius’ own solution as preferable to the ones he has rejected; otherwise it will seem as if Simplicius is proposing a new interpretation merely from desire for novelty. While Simplicius does not have an entirely fixed terminology, he does have some typical ways of introducing material for which he has no older authority. Very often, after setting out the views of earlier commentators, Simplicius will give a series of ‘remarks’ or ‘observations’ or call our ‘attention’ to something or ask us to ‘notice’ something or ‘stop and wonder’ at something. Typically he uses forms of the verb ephistêmi or its later Greek variant ephistanô, which we have translated as far as possible with forms of ‘remark’ or ‘observe’, saying that we must remark or observe something or that something is worthy of remark (the cognate noun epistasis); sometimes instead he says ‘I remark’ (episêmainomai), or says that we should ‘attend’ (prosekhein) to something.65 Simplicius uses the transitive tenses (present and weak aorist) of ephistêmi or ephistanô, which would literally mean ‘to stop something’ or ‘to set something up’ or ‘to set something over something’. But since Aristotle the transitive tenses of ephistêmi had been used, either with an explicit direct object ‘thought’ or ‘investigation’ or ‘oneself,’ or elliptically without an explicit direct object, to mean ‘attend to,’ ‘pay attention’ (with ‘about’ (peri) or with a dative, or with a question ‘how . . .’ or ‘what . . .’ or ‘why . . .’).66 Behind these uses of epistasis and its cognates lies Plato’s etymology of epistêmê (knowledge), which ‘stops (histêsin) our soul at (epi) the objects’ (Cratylus 437A2–5); Aristotle takes this up, saying that ‘our intellectual cognition resembles a coming-to-rest and epistasis rather than a motion’ (De Anima 1.3, 407a32–3).67 Thus stopping to notice the salient point is supposed to bring the soul’s fluctuations to a stop. In one passage Aristotle says, as Simplicius often does, that something is ‘worthy of epistasis’: he says it would be remarkable if (as Democritus thinks), animals and plants come-to-be not by chance but by some determinate cause, but the more divine and orderly heaven comes-to-be spontaneously, ‘but if it is

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so, this is itself worthy of epistasis, and it would be good to have said something about it’ (Physics 2.4, 196a35-b1). Aristotle does not intend this exactly as a refutation of Democritus, but certainly as a criticism. So too when Simplicius says that something is ‘worthy of epistasis’, or equivalent expressions, this is at least implicitly critical of earlier interpreters. He is pointing out details of the passage that we ought to attend to, and that, if we attend to them, may allow us to solve the problems; these are things that (he implies) the earlier commentators did not notice, and that might have helped decide their disputes if they had. It is often directly critical, especially when ‘ephistanein’ takes a person in the dative: ‘we must ephistanein to him’ can be translated ‘we must point out to him’, but can equally be translated ‘we must object to him’.68 So in Simplicius’ commentary on the first lemma of the Physics, the epistaseis at 13,28–14,9 are criticisms of the view of Alexander quoted at 13,21–7, and in the third lemma the epistasis introduced at 21,5–6 is an objection against the view he has attributed to ‘the commentators’ in general at 20,31–21,5, and the epistasis introduced at 22,9 is an objection against Alexander. Rather differently, on the fifteenth lemma, Physics 1.2, 185a20-b5, after going through the interpretations of Alexander and Porphyry and the parallel in Eudemus, he says ‘let us add some things worth remarking (epistaseôs axia) as regards the text’ (74,30 – we count seven such epistaseis in our translation, although he does not use ‘epistasis’ in introducing each of them). In this case the epistaseis are not directly criticisms of Alexander or Porphyry or Eudemus, but they help Simplicius to motivate interpretations of points in the lemma, and solutions of problems, that the earlier commentators had not given, because they had not stopped to remark on these points.69 After raising problems, citing the views of earlier writers, and calling our attention to points which may cause difficulty for earlier solutions and may point us towards a better solution, Simplicius also has distinctive ways of introducing his own new solutions. Like earlier writers, he uses the words ‘ê (or)’ and ‘isôs (perhaps, presumably)’ to introduce more or less tentative solutions to problems: these can be his own new proposals, or he can copy the ‘ê’ and ‘isôs’ from Alexander or some other earlier commentator. But Simplicius’ most characteristic way of introducing his own solutions is with the word ‘mêpote’. Liddell-ScottJones give the primary meaning of ‘mêpote’ as ‘never’, also noting a later meaning ‘perhaps’, but in Simplicius’ characteristic use it does not mean ‘never’, and if it means ‘perhaps’ it is a very distinctive, almost technical, sense of ‘perhaps’. Simplicius’ usage here was noted by Diels in his preface to the Physics commentary:

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the summary of the main points is almost always from Alexander, although usually his name does not appear, except where Simplicius sees fit to disagree with him. Often he signals that things he has previously taken from elsewhere, i.e. from Alexander, are such [i.e. were taken from a source], [not when he first states them but] in order to set out his own interpretation starting from that mêpote. Sometimes, although less often, he uses Themistius in the same way.70

When Diels says ‘that mêpote’, he is noting a stylistic feature which, while not unique to Simplicius, is very characteristic of him. While Simplicius has often long before the ‘mêpote’ given criticisms of Alexander or Porphyry, and named them in criticizing their views or comparing their views with each others’, Diels is right that he uses the ‘mêpote’ to flag that he is introducing his own distinctive interpretation. While ‘mêpote’ is (like ‘ê’ and ‘isôs’, which Simplicius also uses) officially a modest ‘perhaps’, in fact Simplicius seems always to endorse the interpretation that he introduces with the ‘mêpote’ – he apparently never gives a series of alternative interpretations after the ‘mêpote’ for the reader to choose among.71 But ‘mêpote’ is genuinely epistemically modest in the sense that Simplicius is recognizing that he has no direct proof for the interpretation he is about to offer: the reasons for accepting it are that it seems to offer a better solution to the problems than the other solutions he has considered, that it is immune to the epistaseis he has raised against the other solutions, and perhaps that it does more justice to features of the text that these epistaseis have brought out. (‘Mêpote’ does not normally introduce a first solution to a problem, but rather a new solution after at least one proposed solution has been rejected.) Where the evidence is indirect in this way, Simplicius cannot introduce his interpretation directly, but must motivate it through an exposition and critique of earlier interpretations. While the transition from ‘mêpote’ meaning ‘never’ to meaning ‘perhaps’ to introducing a commentator’s positive proposals is a bit obscure, it probably comes from an ellipsed conditional, ei mê pote, ‘unless perhaps’: all the solutions here have objections, and there are difficulties however we read this passage, ‘unless perhaps . . .?’. At 59,16 Simplicius uses a conditional ei mê ara, ‘unless perhaps’ in precisely this way, where he would usually use ‘mêpote’, and this phrase may well be at the source of the commentarial, problem-solving use of ‘mêpote’.72 Just looking at the number of occurrences of ‘mêpote’ (without distinguishing its different meanings) is enough to show that the word is overwhelmingly late ancient, and overwhelmingly in commentaries. According to a search of the Thesaurus Linguae Graecae, the word occurs only seventeen times in the Platonic corpus, and only twice in authentic Aristotle (one of which

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is in a quote from Parmenides), and only twenty-five times in Alexander of Aphrodisias, sixteen in Plutarch and ten in Galen, all scholarly authors of many surviving words (Galen the most surviving words of any Greek author).73 By contrast, among later ancient commentators on the Bible, the word occurs thirtyfour times in Philo in the first century ce , and then 371 times in Origen (mostly in his commentaries), 241 times in John Chrysostom, 171 in Ephraem Syrus, 116 in Eusebius and 113 in Basil; and, among later ancient commentators on philosophical texts, 108 times in Proclus, 188 in Philoponus, a remarkable 274 in Damascius (from whom we have only about a quarter as many words as from Philoponus), and an astonishing 555 times in Simplicius’ three authentic Aristotle commentaries. Damascius is the problem-posing and -solving commentator par excellence, and he would be Simplicius’ most immediate model; but, as these statistics suggest, the usage is widespread among the neo-Platonic commentators, just taken further by Damascius and Simplicius.74 The word is already used in the ancient grammarians’ scholia on Homer (forty-nine times in the Scholia vetera on the Iliad), often as in Simplicius to introduce a new solution to a problem after raising objections to earlier solutions, and it is likely that the commentators on philosophical texts are borrowing this usage from the grammarians. Thus, for instance, a scholium from Nicanor on Iliad 1.211–12, after raising a problem and noting and criticizing earlier solutions, says ‘so perhaps it is better (mêpote oun ameinon) to punctuate (stizein) at the end of the verse [Iliad 1.211]’:75 Simplicius too uses the phrase ‘mêpote oun ameinon’, ‘so perhaps it is better’, many times in introducing a preferred solution. Simplicius’ ‘mêpote’ does not always introduce a climactic interpretation of the lemma as a whole. His commentary on a single lemma can include several small mêpotes. Once he has finished summarizing the overall thought of the lemma, and begun the detailed investigation, he may note several problems with ‘it is worth investigating’ (axion zêtein), and raise difficulties against earlier too superficial interpretations and solutions with ‘it is worth remarking’ (axion epistêsai) or ‘one might wonder’ (thaumaseien an tis), then introduce his own solution with ‘mêpote’, before going on to a new problem. As we have seen, Simplicius says that aporiai against the text, even those raised by malevolent critics, are valuable because ‘they have given occasions for the solution of the aporiai and for many other beautiful theorems (theôrêmata, literally “objects of contemplation”)’ (in Cat. 2,1–2). If the commentator takes the opportunities that the text and its earlier commentators give him for raising aporiai, these in turn give him occasion for introducing ‘beautiful theorems’, often presented as solutions introduced by ‘mêpote’. The epistaseis, observations

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occasioned by the text and pointing us away from superficial solutions and towards deeper ones, may also count as ‘beautiful theorems’. And often, even when it is not strictly necessitated by an aporia, Simplicius will take the occasion to introduce some material helpful for a deeper understanding: if not something original to himself such as would by introduced by ‘mêpote’, then at any rate borrowed or anticipated from some kindred study.76 He will say ‘perhaps (isôs) it is better’, or ‘perhaps (isôs) it is no worse’77 to add the additional considerations, or he will apologize that he is ‘compelled to extend this at length’: the ultimate excuse is Simplicius’ ‘passion’ (erôs) for the subject matter (so 90,20–22), which for a Platonist is the appropriate response to beautiful objects of contemplation. This is Simplicius’ motivation particularly when the theorem is something ‘deeper’ or more advanced. Thus when he says ‘perhaps it would not be a bad idea, for the sake of preliminary preparation in Plato’s thought, to cite what he says in the Sophist’ (89,4–5), and does in fact cite the Sophist for more than a page, ‘preliminary preparation’ means that the imagined reader will study Plato after first mastering Aristotle: but Aristotle helps us understand Plato because of the affinity of their doctrines, and where there is particularly close kinship Simplicius takes the opportunity to look ahead to Plato. When, in the first ‘mêpote’ of the Physics commentary, Simplicius explains Aristotle’s distinction between principles and causes and elements by saying ‘perhaps (mêpote) Aristotle, having taken “principle” as the common term, divided it into causes in the strict sense, such as the efficient and the final, and into what some people call “auxiliary causes” (sunaitia), such as the elements [i.e. matter and form]’ (11,29– 32), the ‘some people’ are Proclus. Simplicius is ‘looking ahead’ here to Proclus, solving a problem in Aristotle by attributing to him Proclus’ way of distinguishing between causes in the strict sense and auxiliary causes, with the implausible result that Aristotle will be saying that the immanent form is not really a cause; at the same time, he is implicitly answering Proclus’ accusation that Aristotle pursued only auxiliary causes and not the true causes. On a grander scale, in the Corollaries on Place and Time inserted in the commentary on Physics 4, Simplicius consciously goes beyond the duties of a commentator (601,1–13) to discuss, not only later objections to Aristotle’s theories, but later theories of place and time, which Aristotle would have discussed had he known about them. These give Simplicius an occasion to ‘look ahead’ to Damascius’ treatise on the three kinds of measure, namely number and place and time, and to the neo-Platonic theories that Damascius considers there, culminating in Damascius’ own. Simplicius knows that he is not a great original metaphysician like Damascius, although he probably also knows that he has more critical common sense than

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Damascius. The subjects of his extant works (and of his other well-attested works) suggest that he had a preference for working on things relatively low on the scale of being, and for engaging with Peripatetic and even Stoic sources, and with mathematical details where appropriate. He wants to explicate and defend Aristotelian scientific physics, against Philoponus’ Christian ‘extreme Platonism’, but also against Proclus’ claim that Aristotelian physics is not a real science and does not grasp real causes. His main concerns in the commentaries on the Physics and On the Heaven are to show how Aristotelian scientific arguments work, to defend the ‘pious conception of the universe’ (and thus the right conception of the relations between the demiurgic nous, the heavens and the sublunar world), and to harmonize Aristotle with Plato (and with the Eleatics and Pythagoreans and Anaxagoras and Empedocles, and everyone else while he is at it). But he also wants to take every occasion for investigation (zêtêsis), and to show how thinking through problems and objections to the text can lead us to glimpses of higher theorems, so that someone who turns to Simplicius’ commentaries to help him understand Aristotle (and perhaps as an aid in teaching) might be inspired with a love for the higher Platonic mysteries.

4. Themes of Simplicius’ commentary on Physics 1.1–2 In this section I will try to bring out the structure and main themes specifically of the portion of text that we have translated, namely Simplicius’ proem describing the Physics as a whole and of his commentary on Physics 1.1–2. He goes into so much detail on this short text (102 CAG pages on about one and a half Bekker pages of Aristotle) that there is a risk of getting lost in detail. Following the standard conventions for commentaries, Simplicius gives an introduction to the Physics as a whole before turning to comment on individual lemmas. Simplicius describes precisely the chunk of text that we call Physics 1.1 (although he splits it into two lemmas) as Aristotle’s own proem to the Physics, and he tries not only to make sense of details of this difficult text, but to show how it gives a programme for the Physics, more specifically for the study of principles of natural things, and in particular for the study of the elements of natural things, which is what he thinks Physics 1 is about. But Physics 1.2 does not leap immediately into Aristotle’s own account of the principles or elements of natural things; rather, as Simplicius says, ‘he thinks it reasonable not to express his own opinion about the principles before he has examined the opinions of the more ancient thinkers’ (22,23–5), and Simplicius is concerned both to show how

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Aristotle’s approach to the principles represents an advance over earlier thinkers, and also to show that the earlier accounts of the principles remain correct and consistent with each other despite Aristotle’s critical examination. Physics 1.2 is the beginning of a critical survey of pre-Socratic accounts of the principles, roughly Physics 1.2–4 (pre-Socratic rather than pre-Aristotelian in general: although Plato is briefly mentioned, he does not get a proper examination until Physics 1.9). Physics 1.2 is also more specifically the beginning of a critical examination of the Eleatics, more precisely of Parmenides and Melissus – Aristotle does not mention Zeno here, apparently because he does not regard him as having a positive theory of principles or of being. But before Aristotle gets down to refuting the Eleatics’ theses in Physics 1.2, and exposing the faults in their arguments in 1.3, he first surveys the full range of views about the principles, not as a diachronic narrative, but by dividing up the logical space of possible views (the principles must be either one or many, either moved or unmoved and so on), and either naming earlier philosophers who fit into each niche, or leaving the reader to fill in the identifications. Also before Aristotle gets down to dealing with the Eleatics, he discusses whether the physicist should respond to theses and arguments that are not themselves physical: this involves issues about whether the Eleatics are doing physics or something else, about how a science can speak about its own principles, and about the relations between physics and metaphysics. Simplicius’ commentary on Physics 1.2 is at first sight very oddly structured. He spends a grossly disproportionate amount of time (disproportionate in terms of how many lines of text get how many pages of commentary) on the overall doxographical division, on the discussion of what theses and arguments a scientist should respond to, and specifically on Aristotle’s example of whether a geometer should respond to fallacious circle-squarings. He does, of course, also discuss Aristotle’s arguments against the Eleatics, and against the Eleatic-influenced thinkers who Aristotle calls ‘the later ancients’. But here his main concerns are to rescue the Eleatics, to show that Aristotle is not criticizing Plato, and to show that Plato is Aristotle’s model in critically examining the Eleatics.

4.1 Simplicius’ proem and the object, structure and value of Aristotle’s Physics Most of Simplicius’ proem (i.e. of the part before he takes up Aristotle’s first lemma, 1,3–8,30) is structured by what was for sixth-century neo-Platonists a fairly standard list of six topics to be discussed in the proem to any commentary:

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the object (skopos) of the text being commented on, its title and the reasons for the title, the utility of the text or of the discipline it teaches, its order or appropriate place in the sequence of texts and disciplines to be studied, its authenticity, and its division into parts which might have their own titles and objects.78 Simplicius adds at the end two somewhat less standardized topics, first summing up the history of natural philosophy up to Aristotle and bringing out what is distinctive about Aristotle’s contribution, and then discussing the division of Aristotle’s works into ‘exoteric’ and ‘acroamatic’ (sparked by the word akroasis in the traditional title of the Physics, Phusikê akroasis, ‘Lectures on Natural Science’).79 These added discussions seem intended mainly to praise Aristotle’s text, to motivate the reader to study it, while also stressing its difficulty and so the need for Simplicius’ commentary. Some of Simplicius’ discussion of the six standard topics is perfunctory and pro forma (no one doubted the authenticity of the Physics, and there was no serious dispute about its place in the teaching order). But he also introduces here some important themes of his commentary, and he takes the occasion to sketch a broader picture of the teaching of philosophy, especially Peripatetic philosophy as handed down in the treatises of Aristotle and Theophrastus: while Simplicius is too polite to say so, the Peripatetics themselves are now extinct, and Simplicius as a Platonist feels the responsibility of keeping the study of the Peripatetic disciplines alive. The most important of the introductory topics was the object (skopos) of the text: this means something technical in the neo-Platonic context. A skopos is, etymologically, something you look towards, and it means ‘aim’ in archery; while we standardly translate ‘skopos’ as ‘object’, readers should add ‘aim’ under their breath as a supplementary translation. Metaphorically from archery, Aristotle says that we should choose a skopos of life and perform all the actions of life with reference to it (Eudemian Ethics 1.2, 1214b6–11; Nicomachean Ethics 1.2, 1094a22–4). Each particular art or science also has a skopos: thus Galen at the beginning of On the Sects for Beginners says that the skopos of medicine is health (and the end (telos) of medicine is to acquire health), because although medicine also talks, e.g. about bodily organs and diseases and drugs, it studies these things only because they have some relation to health and must be studied in order to have a scientific knowledge of health. And if a virtue is something like an art of living, it too will aim at some skopos. Some writers, like Galen, follow the Stoics in distinguishing between the skopos of an art as some being (like health) that the art aims at, and the telos of the art as some activity (like acquiring health) directed towards that being, but the neo-Platonists generally ignore this

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distinction, and go back and forth between the two kinds of formulation of what the skopos of some art is. It may be easier in English to call health the ‘object’ of medicine and acquiring health its ‘aim’, although we can use both words in both ways. If an art has a skopos, then a text that teaches that art will also have that same skopos. If a text is worth including in the curriculum, it is because it teaches some art or virtue, and so it should have some skopos. When a teacher says what the skopos of a text is, he is saying why the text is worth teaching and studying, and what you should attend to in studying it; and he is implicitly claiming that the text functions well in giving knowledge of this skopos, and promising to explain how each part that he goes on to discuss is related to the skopos. It was important for the neo-Platonists (more than for earlier commentators) to determine a single skopos for each text, which will guide the overall interpretation, and also show how it relates to the other texts in the curriculum; individual parts of the text may also have skopoi, but they must be somehow related to the skopos of the whole. Commentators sometimes criticize earlier commentators’ views of the skopos of the text (Simplicius does this with the Categories and On the Heaven but not the Physics), and in the process they give criteria which a skoposascription should meet. It is a fault if a proposed skopos fails to cover all parts of the text (for instance, according to the Anonymous Prolegomena to Platonic Philosophy, it is wrong to say that the skopos of the Phaedo is the immortality of the soul, since that leaves out the prohibition of suicide at the beginning and the myth of the true earth at the end).80 It is also a fault to give plural skopoi without subordinating them to a single skopos, as when Alexander said that the skopos of On the Heaven was the cosmos and the five simple bodies (so Simplicius, in de Caelo 3,12–16). Iamblichus and Syrianus say that the skopos of On the Heaven is just the divine heavenly substance, and that it treats the cosmos and the four sublunar simple bodies only insofar as they are related to the heavenly body; these people are presumably Simplicius’ models in criticizing Alexander for positing plural skopoi, but as Simplicius rightly observes, Iamblichus’ proposal cannot be made to fit what the text actually does, and Simplicius proposes instead that the skopos is just the simple bodies.81 Aristotelian ‘physics’ or natural science is about natural things, but different kinds of natural things – the simple bodies and non-living composites and living things – are the objects of different specific treatises. But the present treatise, the Phusikê akroasis or ‘Lectures on Natural Science’, comes before these specific treatises in the intended order of study, and contrasts with them in being about all natural things universally. As Simplicius says,

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Simplicius: On Aristotle Physics 1–8 The object (skopos) of the treatise at hand is to teach concerning the things which belong in general to all natural things inasmuch as they are natural – that is to say, bodily. And what belongs in general to all are the principles, and the concomitants of the principles. And the principles are the causes strictly speaking and the auxiliary causes (sunaitia); and the causes, according to [the Peripatetics], are the efficient and the final, and the auxiliary causes the form and matter and the elements generally. (3,13–18)

It may not be quite right to identify ‘natural’ with ‘bodily’ things – artifacts are bodies but can be contrasted with natural things – but among bodies, artifacts will be posterior to natural things, and so the principles of all natural things will also be principles of all bodily things. Simplicius, following earlier interpreters, is here picking up on programmatic things Aristotle says about starting by examining what is common to all natural things and proceeding to what is peculiar to some class of natural things: notably Physics 3.1 says that, after discussing nature, we should next investigate motion, continuity, infinity, place, void and time, ‘because they are common to all [sc. natural and thus mobile] things and universal . . . for the consideration of particular things (idia) is posterior to the [consideration] of common things’ (200b21–5).82 Simplicius thinks that Aristotle has made an important methodological advance in giving such a discussion of what is common to all natural things as such before giving his account of the cosmos and its constituents. We have already seen him praising the Physics above even the Timaeus: ‘Aristotle also surpassed both Plato and all those before Plato alike: while they either discussed natural subjects as if discussing all of the things that are (as some of those before Plato did), or raised the questions that are treated here as if they were questions about the cosmos and its parts and did so in writings on the cosmos (as Plato himself and some of those before him did), Aristotle both distinguished what rank natural things have among the things that are and also teaches, as if there were no cosmos, about natural body itself in its own right’ (7,27–34). Aristotle is praised here, first for distinguishing the disciplines of physics and first philosophy (i.e. of metaphysics, conceived as a science of things superior to the physical world and existing separately from it), but then also for making a separate study of the fundamental concepts presupposed by cosmology rather than treating them incidentally as they come up in cosmology itself. The study of what is common to all natural things will not be just a series of theorems ‘all natural things are P’ for some predicate P. Rather, what belongs to all natural things as such will include their principles, under universal descriptions: ‘to every natural thing belongs a matter, a form, and so on’. The Physics will prove

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that there is a matter, form, etc. of natural things, and then investigate what these are; and the matter, form, etc. of natural things as such will be more basic principles than the matter or form of some particular class of natural things. In the passage cited above, 3,13–18, Simplicius draws two important distinctions. First, while some things that belong universally to all natural things are principles, others are concomitants of the principles. So Simplicius does not have to say that, for instance, place and time, studied in Physics 4, are principles of natural things as form and matter are: rather, they are consequences of natural form and matter, which belong to natural things because natural form and matter belong to them. Second, Simplicius distinguishes between two kinds of principles, the ‘auxiliary causes’ which include especially the elements or constituent principles of things (their matter and immanent form), and the causes proper, the efficient and final (and, unfortunately omitted by Aristotle, the paradigmatic). He is drawing this distinction from Proclus (against, especially, Alexander and Eudemus who say that only matter is an element), precisely in order to vindicate Aristotelian physics against Proclus’ insinuation that it considers only auxiliary causes and not true causes. For Simplicius, Physics 1 treats matter and form as elements, Physics 2 treats nature as the proximate efficient cause and the final cause for which it acts, and Physics 3–4 treat concomitants such as motion, place, and time, as well as discussing things that other philosophers have wrongly regarded as belonging to all natural things, such as infinity and void. Simplicius is ultimately drawing much of this from Aristotle’s programmatic remarks, especially at the beginning of Physics 3 where Aristotle is introducing and justifying the topics of Physics 3–4 as what are common to all natural things; and the programme of Physics 3–4 can easily be seen as continuing Physics 2’s discussion of what nature and natural things are, and what kinds of causes physics should therefore investigate. And all of these discussions can be seen as continuing Physics 1 on what the principles of natural things (or of all changeable things) are, which does indeed focus on matter and form rather than on efficient and final causes, and which (like the beginning of Physics 3) says that we must first consider what belongs universally to all natural or changeable things as such. So it seems that Simplicius’ account here works better as an account of the skopos of Physics 1–4 than of the Physics as a whole, and indeed it seems to have begun as an account of something like Physics 1–4, and then been extended to the Physics as a whole. The Peripatetics Andronicus and Adrastus, in treatises known to Simplicius via Porphyry, had tried to determine the ‘true’ titles and extents and order of Aristotle’s works, basing themselves partly on the contents but also on how Aristotle and his students refer to Aristotle’s texts. In particular, Aristotle

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sometimes refers back to parts of the Physics as ‘in the On Principles’, and sometimes refers back to parts of the Physics as ‘in the On Motion’, and the Peripatetics tried to figure out what texts the titles On Principles, On Motion, and Physics covered.83 As Simplicius says, ‘The treatise as a whole being primarily divided into two, Adrastus says that the first five books are about all the natural principles and the things following from them, and the things that get caught up in the investigation.84 And, taking up the discussion of motion from the sixth book on, in the last three books he [Aristotle] relates all manner of naturalscientific findings concerning motion. Hence Aristotle was accustomed to call the first five books On Principles and the succeeding ones On Motion’ (6,4–10).85 Adrastus thinks that Physics 5 treats motion and rest as concomitants of the principles, as Physics 4 does with place and time; but it is hard to justify splitting Physics 5 from Physics 6, and Simplicius at 802,7–13 tells us that Porphyry, against these Peripatetic scholars, made Physics 5–8 the On Motion, so that Physics 1–4 would be the On Principles (in a sense of ‘principles’ broad enough to include place and time) or the Physics in the narrower sense. Simplicius in fact accepts this division of the Physics, presumably following Porphyry, in his earlier commentary on On the Heaven (226,19–23), and Philoponus in his Physics commentary accepts it without mentioning any dispute (2,13–21; 3,1–10). But Simplicius in the Physics commentary changes his mind and endorses Porphyry’s Peripatetic sources in preference to Porphyry (most clearly at 802,7–13, with some indignation at Porphyry). It is not clear why exactly Simplicius does this, but it fits with his general sense that Porphyry is a relatively superficial interpreter, and with his impulse to outbid more recent writers by going back to older sources. In any case Simplicius takes what was originally Adrastus’ description of Physics 3–5 as treating the concomitants of the principles of natural things, in which Physics 5 treats specifically motion (and rest), and he stretches the treatment of motion as a concomitant to cover Physics 6–8 as well.86 Besides the object of the Physics, its place in the Peripatetic teaching of philosophy, and its internal division into books or sub-treatises with their specific objects, Simplicius also says some interesting things about the utility of natural science and about the significance of the traditional title ‘Lectures on Natural Science (Phusikê akroasis)’. At 4,25–5,26 Simplicius gives a surprisingly eloquent encomium of natural science: the knowledge of nature is useful for more practical sciences (medicine and mechanics), and it theoretically perfects the part of the rational soul that is not elevated enough to grasp divine things, but, beyond this, understanding the greatness of the cosmos and the smallness of our body and lifespan will lead us to higher, rationally perfected versions of all

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the moral virtues, courage and temperance and so on. These seem like especially Platonic themes, but Simplicius is happy to accept Aristotelian natural science as a way of acquiring these virtues; and if natural science contributes in this way to our perfection, then so does the Physics proper as securing the foundations for scientific knowledge of nature (so 5,21–6). And, finally, Simplicius stresses that both for Plato in Laws 10 and for Aristotle in Physics 8, the study of natural motion is ‘the finest path to the knowledge of the substance of the soul and the study of the separate and divine forms’ (5,10–16).87 Although he had briefly treated the traditional title at 4,8–16, glossing Akroasis, literally ‘hearing’, as meaning that the text has been ‘worked out with enough precision as to be put forward for the hearing of others’ (4,10–11), Simplicius returns to the Physics as an ‘acroamatic’ work at 8,16–30, at the very end of his proem, right after his praise of the Physics as surpassing both the preSocratics and Plato (7,19–8,15). Here Simplicius is drawing on a division of Aristotle’s works into ‘exoteric’ and ‘acroamatic’ and ‘hypomnematic’, such as is worked out in Ammonius, in Categorias 3,20–5,20.88 A ‘hypomnematic’ work is an author’s series of notes on a given subject (drawn from his reading or conversations or observations or just thoughts that occur to him), intended mainly for the author’s own use including future writing projects; an ‘exoteric’ work is something polished for publication to a wide audience, but perhaps lacking technical precision. Simplicius’ point here is that acroamatic works aim at a high degree of precision (Simplicius has been stressing ‘precision’ and ‘working out’ the details as ways in which Aristotle surpassed earlier writers on physics, 8,9–15), but that they are correspondingly ‘obscure’, i.e. difficult to read and interpret. Simplicius cites some obviously forged letters between Aristotle and Alexander the Great, which we know to have been cited by Andronicus, where ‘Alexander’ complains that Aristotle has published his acroamatic discourses, thus making available to everyone the knowledge that had previously been reserved for Alexander’s private lessons. ‘Aristotle’ reassures Alexander that he has not lost his monopoly, since the texts are written in so difficult a way that they will not be comprehensible without Aristotle’s oral instruction. Presumably Andronicus had cited these letters in order to raise the value of the acroamatic texts: ‘you, the reader, will have access to what only kings had seen; and don’t be surprised if it’s difficult’. Simplicius too is capping his praise of Aristotle’s physical works and of the Physics as the necessary condition for scientific knowledge of nature, urging the reader to read on and not to be discouraged by the difficulty. But he is also explaining why you need his commentary, which is the closest thing now available to Aristotle’s own oral instruction.

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4.2 Simplicius on Aristotle’s proem to the Physics Simplicius turns from his proem to commenting on what he describes as Aristotle’s own proem to the Physics (compare 8,32 and 17,32), which corresponds exactly to what we call Physics 1.1. The Physics as Simplicius has described it is about the principles of all natural things, and what follows for them from these principles, and Aristotle starts (i) by arguing that we should determine the principles of natural things before we go on to the detailed parts of natural science, and (ii) by investigating how we should determine the principles. So Simplicius divides Physics 1.1 into two lemmas, the short 184a10–16 devoted to (i) and the longer 184a16-b14 devoted to (ii). In the first lemma, Aristotle’s overall meaning is fairly clear, and what he is saying also seems clearly true and does not need much defence, although there are some interesting problems in the details. In the second lemma, however, what Aristotle says does not seem entirely plausible, and seems to contradict things he says elsewhere; and so different ancient commentators – and different modern commentators as well – are led to interpret what Aristotle says here in quite different ways in order to resolve the apparent contradiction. Simplicius works out an overall story here which draws both on Proclus’ metaphysics and on a reading of epistemological texts in Plato and Aristotle; and he develops an interesting disagreement with Alexander about the methodology that Aristotle will follow in the Physics, and specifically in Physics 1, in determining what the principles are. Aristotle’s argument in the first lemma, 184a10–16, is straightforward enough: in every discipline which has principles (or every discipline about things which have principles), we have scientific knowledge of the things derived from the principles only through first knowing the principles; so, in order to gain scientific knowledge of natural things, which is what we are aiming at here, we should first try to determine about the principles. This doesn’t mean that we have to start our investigation from a cognition of the principles rather than of the things manifest to our senses which are derived from the principles: we have to begin from cognition of the things manifest to our senses, but that cognition cannot be scientific knowledge until it is derived from a cognition of the principles. And the cognition of the principles that we need in order to derive scientific knowledge of natural things cannot itself be scientific knowledge, or it would depend on yet prior principles. All of this is standard enough in an Aristotelian context, and Simplicius does not worry too much about it: he explains it, but probably there was no real disagreement among the commentators on these questions. Aristotle’s argument has a missing premise, namely that natural things

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have principles: perhaps Aristotle simply thought that was obvious, or was anticipating the arguments he would give later in Physics 1, but Simplicius (and Philoponus) point out that Theophrastus in his own Physics supplied an explicit argument for this premise.89 A more interesting issue is whether the physicist can argue about the principles of his own science, or more generally whether each science can establish its own principles. Aristotle has shown that in order to have scientific knowledge of physics it is necessary to determine the principles of natural things, but that does not yet show that we, in doing physics, must first determine the principles of natural things – perhaps these principles are determined, not by physics, but by a higher science such as metaphysics (‘first philosophy’), or by dialectic. Simplicius cites both Eudemus and Porphyry as raising an issue here. ‘Eudemus at the beginning of his Physics . . . [says]: “One might raise the puzzle whether each science discovers and passes judgement on its own principles, or a different one in each individual case, or whether there is a single one which does this for all”’ (48,6–10); and if it is not up to each science to discover its own principles, and if on pain of infinite regress some science must discover its own principles, what makes some sciences capable of this and others not? Simplicius says that Eudemus does not himself answer this question (at least not in his Physics), but Porphyry seems clear that the physicist does not himself determine whether natural things have principles (let alone what these are), but rather takes his principles from the first philosopher, just as the doctor takes his principles from the physicist (9,10–15). In Aristotelian terms, this means that he thinks that physics is a ‘subalternate science’ to first philosophy, in the way that for Aristotle mathematical music theory is ‘subalternate’ to arithmetic and optics to geometry, presupposing and using the results of these more fundamental sciences. Simplicius agrees with Porphyry that physics, and ultimately all the sciences, are subalternate to first philosophy: ‘first philosophy will demonstrate the principles of all [the sciences]’ (47,30, cf. 15,29–16,2). This identifies Aristotelian first philosophy with dialectic as Plato describes it in Republic 6–7, which establishes the first unhypothetical principle of all things and so converts the other sciences from hypothetical into unhypothetical knowledge (this identification explicit 49,3–11). Indeed, as Simplicius points out, Aristotle admits in Posterior Analytics 1.10 that while the common notions (universal truths applicable to all domains and presupposed by all sciences) and the definitions proper to each science are self-evident, other assumptions such as the existence of the subject-genus (or of its simple constituents, like points in geometry) are ‘hypotheses’ (48,29–49,8). Aristotle would probably be surprised to hear that he had thus admitted that physics is subalternate to first philosophy and not a fully

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independent science. But, Simplicius says, this does not mean that the physicist must simply wait on the first philosopher, and cannot do anything to determine the principles of his own science. Rather, it belongs to the natural scientist to demonstrate that natural things have principles, and have these principles, in the same way that it belongs to the doctor to demonstrate that the human body is composed out of the four elements . . . . But what power each of the elements has, belongs to the more elevated [scientist] . . . in the case of the human body, the natural scientist; in the case of the natural principles, the first philosopher. (9,16–22)

The physicist demonstrates that natural things have these principles, not by a ‘demonstration’ in the strict Aristotelian sense from the causes, but rather arguing ‘from what follows from the principles and is composed of them’ (16,2–5), which will not give us scientific knowledge of the principles, but only the familiarity with the principles for which Simplicius borrows Aristotle’s word gnôrizein (from the first sentence of the Physics, 184a10–16).90 Talk of starting from ‘what is composed from the principles’ is particularly appropriate to Physics 1, since Aristotle says in the second lemma that ‘at first it’s rather things which are confused which are manifest and clear to us; later on, starting from these things, the elements and principles become knowable as we divide them’ (184a21–3), and compares our starting points to ‘wholes’ (184a24– 5). And, in conformity with this, Simplicius understands Physics 1 as concerned not with all principles, but with the elements or constituent principles of natural things, matter and form. And Simplicius can point out that Aristotle in Physics 1 defers some things to higher enquiries: ‘hence Aristotle too, having shown that matter and form are principles of natural things, says that matter is known by analogy,91 even though the first philosopher also shows it from the causes; and he says, “concerning the formal principle, whether it is one or many, and what it is or what they are, it is the task of first philosophy to determine with precision. So let it be put off until that occasion” ’ (Physics 1.9, 192a34-b1) (9,22–7). Simplicius apparently takes this to mean that Platonic first philosophy will show that the highest form in the intelligible world is one, or is both-one-and-many, which is very unlikely to be what Aristotle means. And when Simplicius says that the first philosopher shows matter ‘from the causes’ – not from the material cause, which is only an ‘auxiliary cause (sunaition)’ – he is apparently referring to Proclus’ view that although the matter of the sensible world is independent of the demiurgic nous, it is produced directly by the One and then given to the demiurge to work on. And this is even less likely to be the result that Aristotle wants.

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The issue about the subalternation of physics to first philosophy as a science of separate intelligible realities is also connected with the question, prominent in Physics 1.2, whether in doing physics we should reply to the Eleatics. As Aristotle says there, ‘to examine whether what is is one and unmoved is not to examine about nature’ (Physics 1.2, 184b25–185a1), and he spends some time there explaining why the physicist does not need to reply to Parmenides and Melissus, before saying that we may as well do so anyway and spending the rest of 1.2 and 1.3 doing so. Simplicius takes him to mean that Parmenides and Melissus are doing first philosophy, and indeed Aristotle does say elsewhere that Parmenides and Melissus ‘even if they speak rightly in other respects, shouldn’t be counted as speaking physically: for that some beings are ungenerated and otherwise unmoved belongs rather to another and higher investigation than physics’ (On the Heaven 3.1, 298b17–20). Aristotle does not mean that what Parmenides and Melissus say in first philosophy is right (there is an eternally unmoved being, but not only one eternally unmoved being, much less only one being), but Simplicius will try to show that Parmenides and Melissus (and Xenophanes) were each expressing some truth about an intelligible first principle – each describing a different attribute of the principle, or describing different levels of intelligible reality. He thinks that Aristotle in arguing in the Physics against their monist thesis is arguing only against their apparent meaning, i.e. against what they would be saying if they meant it in a straightforward physical sense. Presumably this is valuable for the same reason that refuting the apparent meaning of Plato on Forms or the demiurge generating the cosmos or rotating souls is valuable, namely to lead anyone sympathetic to these philosophers to clarify the ‘higher’ concepts of generation, rotation, etc. on which the theses would be defensible. And, although in Physics 1 (and On the Heaven 3) it is only Parmenides and Melissus who Aristotle suggests may be doing something higher than physics, Simplicius extends the point to Anaxagoras and Empedocles: ‘those who philosophized about the principles were investigating them as principles of things that are: some did so without distinction, not distinguishing natural things from the things that are above nature; others did so distinguish, like the Pythagoreans and Xenophanes and Parmenides and Empedocles and Anaxagoras, but through their obscurity this escaped most people’s notice. For this reason Aristotle argues against [them], as against the apparent sense, in order to come to the help of those who took [them] superficially’ (21,15–20). All of these people were investigating principles of physical things, but not merely physical principles of physical things: examining the deeper meaning of Parmenides on the One Being or Anaxagoras on nous (and so on), by examining

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their original texts and investigating what they must have meant in order to survive Aristotle’s objections, will lead us up from physics to first philosophy. If Aristotle does not do this explicitly himself, then Simplicius will do it for him. As we have already seen, Simplicius thinks that the distinction between constituent principles of physical things (their matter and form), which do not lead beyond the physical domain, and non-constituent principles of physical things (their efficient and final and paradigmatic causes), which lead up to soul and ultimately to the intelligible world, lies behind Aristotle’s distinction between ‘principles, causes, and elements’ in the first sentence of the Physics (184a11 and 184a13–14). While he thinks that the general sense of the first lemma is clear enough, problems arise in the details from Aristotle’s speaking of ‘knowing (eidenai) and scientifically knowing (epistasthai)’ (184a10, Simplicius 12,14– 13,13) and ‘principles and causes and elements’. If Aristotle is using ‘knowing’ (eidenai) here for a genus of which ‘scientifically knowing’ (epistasthai) is a species, then why would we know something only ‘when we recognize (gnôrizein) its first causes and first principles and as far as the elements’? Presumably we could either know something sub-scientifically without recognizing its causes, or know supra-scientifically something which is itself a first cause. So Simplicius proposes that ‘knowing’ is not simply a genus, but an equivocal term, and that ‘and scientifically knowing’ fixes it here in its primary sense; and he cites the precedent of Plato’s Republic, where mathematicians do not know (eidenai) until their principles have been deduced from the unhypothetical first principle reached by dialectic. But if when Aristotle says ‘knowing and scientific knowing’, he means knowledge in the primary sense, scientific knowledge by deduction from first principles as described in the Posterior Analytics, then why does he say that ‘knowing and scientific knowing result, in all the disciplines of which there are principles or causes or elements, from recognizing these [sc. principles or causes or elements]’? Surely all scientific knowledge is of things that have principles or causes or elements – so why does Aristotle add the apparently restrictive relative clause? This had already worried Alexander, who proposed that while all sciences have principles or causes or elements, not all sciences have principles and causes and elements, since (according to Alexander) ‘element’ means especially matter, and ‘principle’ means especially the efficient cause: so only the science of generated material beings will have principles and causes and elements (13,21–8). As we have seen, Simplicius contests Alexander’s (and Eudemus’) interpretation of ‘element’, saying with Proclus that both matter and form are elements, and that ‘principle’ is the generic term covering both causes in the

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strict sense (non-constituent causes) and elements. But he adapts and develops Alexander’s idea of solving the problem by distinguishing between principles and causes and elements: he proposes to understand Aristotle’s phrase ‘hôn eisin archai ê aitia ê stoikheia’, not as ‘of which there are principles or causes or elements’ but as ‘of which the principles are either causes or elements’, or perhaps ‘of which there are principles, either causes or elements’. This also leads Simplicius to another revisionist reading of the syntax of Aristotle’s first sentence. When Aristotle says that we know each thing ‘when we recognize its first causes and first principles and as far as the elements (mekhri tôn stoikheiôn)’, the straightforward (and certainly correct) reading is that he means ‘when we recognize its first causes and first principles, i.e. as far as the elements’. On this straightforward reading, Aristotle would be using the Greek word for ‘element’, ‘stoikheion’, which literally means ‘letter of the alphabet’, metaphorically for ‘first cause’, so that he would mean ‘when we analyse a complex not merely into its asit-were syllables, but going as far as the letters’. But Simplicius proposes to read this clause instead as ‘when we go both as far up as the highest causes and principles, and also as far down as the lowest, most proximate principles, namely the elements’ (all this 11,29–36 and 14,25–8). And since the higher causes are also causes of the lower causes, you will not have scientific knowledge even of the elements until you have knowledge of the first causes (11,36–12,5). Since the true causes, i.e. the efficient, final, and paradigmatic causes of beings at each level, lead us in each case up to the next-higher level of being, this means that we will not properly have scientific knowledge of physics until we have knowledge of the highest intelligible levels of being through first philosophy. We have already seen Simplicius’ interpretation of the overall sense of the second lemma, where Aristotle turns from arguing that we must enquire into the principles to investigating how we can do that, especially given aporiai against the possibility of coming to know principles if we do not already know them. In cases where the principles of a science are not self-evident, as the common notions and (at least some) definitions are, we must either deduce them from their causes which are known in a higher science, or, as here, infer from effects which are ‘better known to us’ to the causes which are ‘better known by nature’: such an argument will not give us scientific knowledge of the principles we infer, but knowledge in a looser sense. But here, even more than in the first lemma, we get into difficulties with the details of the text, which has been a source of major trouble to modern as well as to ancient interpreters. Aristotle gives a number of examples to illustrate how we should proceed in coming to know the principles – or perhaps some of them are less than examples, merely analogies; or perhaps

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some of them are more than examples, general directives which apply to all enquiry into principles; and it is not clear how many independent examples he means to be giving. Aristotle says that ‘at first it’s rather things which are confused which are manifest and clear to us. Later on, starting from these things, the elements and principles become knowable as we divide them.’ To call the things better known to us ‘confused’ (sunkekhumena) suggests, not just that they are not clear in themselves, but that they are unclear because they are mixed, so that we will arrive at clearer things by dividing these mixtures into their simple constituents. This works well for principles understood as constituent elements, less well for other kinds of principles. Building on this conception, Aristotle says that we must start with wholes and proceed to their parts, and that we must start with universals (where ‘the universal is a kind of whole’) and proceed to individuals. Then he gives two examples or analogies: the way we proceed in enquiring into the principles is like the way we proceed from a name to its definition (or to each of the items mentioned in the definition, as we clarify the initially confused concept by breaking it down into simpler concepts); or it is like the way that ‘little children initially address all men as fathers and all women as mothers, while later on they distinguish each of these’. Simplicius at one point says that the name-and-definition and the little children are both ‘examples’ (paradeigmata) for the universal and the whole (‘this example [sc. name and definition] is appropriate to the compound and whole . . . but it is not appropriate to the universal . . . . This is why he adduced the second example, the observation from progress in growing up’, 17,5–14), which suggests that Aristotle’s main claims are that, in enquiring into the principles of natural things, we are proceeding from wholes to parts and from universals to individuals. But further down he describes the whole and the universal themselves as mere examples, and the whole as a more suitable example: ‘the example of the whole and the compound is proper to the present topic, but not the example of the universal’ (17,33–4). So it seems that, on Simplicius’ considered opinion, Aristotle is not saying either that the enquiry into the principles of natural things proceeds from universals to individuals or that it proceeds from wholes to parts, but only that it is analogous to a procession from universals to individuals and to a procession from wholes to parts, and it is more analogous to a procession from wholes to parts, inasmuch as the parts are ‘elements’ (constituent principles) of the whole, and at least some of the principles of natural things are elements. When Aristotle says ‘it’s necessary to progress from the universal to the individuals. For the whole is better known by sensation and the universal is a kind of whole,’ he seems to be using a premise about wholes to establish a

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conclusion about universals: so we might think that his main stress is on the thesis about universals. Unfortunately, the claim that universals are better known to us and particulars are better known by nature seems to contradict things Aristotle says elsewhere, notably in Posterior Analytics 1.2, 71b33–72a5 (and cf. Metaphysics 1.2, 982a23–5), which to all appearances says the exact opposite. All commentators, ancient and medieval and modern, have been troubled by this, and give different solutions. Alexander proposes that by ‘universals’ here Aristotle means, above all, topic-neutral axioms such as the principles of non-contradiction and excluded middle (17,25–31). This might seem remote from what Aristotle is supposed to be talking about, the enquiry into the principles (in the sense of ‘first causes’) of natural things, but as Alexander points out, when Aristotle proceeds in Physics 1 to determine what the principles are, he starts by saying that ‘the principle must necessarily be either one or several’ (Physics 1.2, 184b15), where ‘that the principle must be either one or several is equivalent to its being either one or not one, and this is subordinated to [the axiom that] of each thing either the assertion or the negation ought to be predicated’ (Simplicius perhaps paraphrasing Alexander, 19,31–3). And, starting from this extremely general disjunctive description of the principle(s), Aristotle in the course of Physics 1 will progressively specify how many they must be and what they must be like: he will show first that the principles are several, and neither one nor infinitely many, then that there must be both a contrariety in them and something that underlies the contrariety; then, making a transition from these [assertions], which are common, he will show what they [the principles] are: for the person who knows these [general characterizations of the principles] does not yet know what the principles are. (19,21–5)

Alexander apparently takes Aristotle to be mainly asserting that we must start from universals, mentioning wholes merely as a premise or an illustration. And Aristotle does indeed say as the Physics proceeds that we must consider common or universal things before particular things, for instance in Physics 1.7 in saying why we should consider coming-to-be in general before its particular types (189b30–32), and in 3.1 in justifying studying motion, continuity, infinity, place, void, and time ‘because they are common to all [sc. natural and thus mobile] things and universal . . . for the consideration of particular things is posterior to the [consideration] of common things’ (200b21–5). So we might think that Aristotle’s point is that we should start from universal principles of all natural things before narrowing to particular principles of particular classes of things, or that we should start from general descriptions of the principles (perhaps even as

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general as ‘either one or many’) before narrowing to more precise descriptions of the principles. Simplicius shares the view that it is important for Aristotle to begin from the principles of all natural things universally and the concomitants of those principles, but he thinks that cannot be what Aristotle is talking about here: Aristotle must be saying that we should begin from what is better known by sensation, and the axiom of excluded middle, or ‘neither one nor infinitely many, with a contrariety and something that underlies the contrariety’ are not things that are known by sensation. And if these axioms and the like ‘are said about the principles themselves and not about the things that are composed out of them, how will this procedure send us up from the compounds to the principles?’ (19,27–9). The sort of ‘universal’ or ‘whole’ that Aristotle wants us to start from must be something compounded out of the principles, not a truth about the principles (19,33–20,2). Simplicius thinks that what Aristotle is recommending here, and what he actually does in Physics 1, is to reason from manifest effects to their causes, not to reason beginning with general truths about the causes; and it seems that for Simplicius, reasoning from effects to causes is more like passing from whole to part than it is like passing from a universal to its particulars. Nonetheless, he tries to give an interpretation which will fit both the example of whole-and-part and the example of universal-and-particulars, and indeed name-and-definition as well, and will bring out the structure, common to all cases, which gives us a model for the enquiry into principles. If Aristotle says in Physics 1.1 that universals are better known to us but less well known by nature than particulars, and in Posterior Analytics 1.2 that particulars are better known to us but less well known by nature than universals, Simplicius proposes that the two texts are talking about different kinds of universals. The problem here fits into a larger ontological problem, since Aristotle says in different places that more universal things are prior to the less universal things that fall under them, and also that they are posterior. (The issue is not just about ‘universals’ and ‘particulars’ as two types of beings, but about more and less universal things, e.g. genera and species.) Notably the Categories makes universals posterior to and dependent on particulars. For the Platonists, of course, it is important to save a sense in which some universals, such as Platonic Forms, are prior to the particulars that participate in them; but even apart from any commitment to Plato, Aristotle gives it as a test of ontological priority that X is prior to Y if X can exist without Y but Y cannot exist without X, and by this test animal is prior to human and human to Socrates. Indeed, Aristotle himself applies this test in Categories 13 to show that genera are prior to their species

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(15a4–7); and Simplicius says here – oversimplifying a complicated situation – that ‘even Alexander of Aphrodisias agrees that the common and universal is prior by nature to the things under it, e.g. animal is prior by nature to man in destroying it when it is destroyed and not vice versa’ (19,5–7).92 An obvious strategy is to distinguish different kinds of universals: there are some kinds of universals, the ‘secondary substances’ of the Categories, which are dependent on particulars and to which Aristotle’s critique applies, but there are other kinds of universals which are ontologically and causally prior to particulars. Simplicius follows a version of this view which was worked out by Proclus: he gives a full statement of the view in his Categories commentary (82,35–83,16), but here in the Physics commentary he brings out only the aspects of it he needs to solve the immediate problem. What is universal or ‘common’ to many can be either (1) a one F before the many F’s, existing separately from them and causing them to be F, ‘common’ to them as being a cause to them in common, not in the sense of being present in them or predicated of them in common; or (2) a one F in the many F’s, so the F-ness that is the effect of the common cause, present in the many F things; or (3) a one F after the many F’s, a concept of F present in a rational soul which abstracts it from many F things. (The animal-itself, the paradigm of the sensible world in Plato’s Timaeus 30C2–31A1, is supposed to be a universal animal in the first sense: it exists by itself, causes other animals to be animals, and also somehow contains within itself the differentiae of animals – terrestrial and aquatic and so on – rather than simply abstracting from them. The animality in the many animals is said to exist differently in the different kinds of animal – notably, it must be different in immortal and mortal animals – while the animality formed by abstraction in the soul abstracts away from these differences.)93 Thus Simplicius proposes that the universal that is said to be better known to us but less well known by nature is the ‘one after the many’, the concept produced by abstraction (19,12–17): since this does not ‘comprehend the particulars’, its destruction does not entail the destruction of the particulars so it need not be prior to them (19,15–17), while its generation depends on the soul’s experience of many particulars. Simplicius seems not to need to call on the ‘one in the many’ here, but the ‘one after the many’ and the ‘one before the many’ have opposite ontological priorityrelations with the many, and they are also objects of contrasting cognitive states. ‘There is a twofold cognition of the whole and of the universal, just as there is of the name, one kind of cognition being crude and confused and arising from a bare notion of the thing known’ (17,38–18,1). If we start from this confused conception of F abstracted from the many instances, and enquire into the causes

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of the many things’ being F, we will first reach a plurality, just as if we begin from a crude impression of a whole and attempt to discern its constituent parts, or if we begin from a name and try to discern the terms that will have to go in its definition. But the ultimate aim of causal research is to reach a knowledge of the one before the many, ‘[a cognition] which is synthesized and united and comprehends the particulars . . . [and is] intellectual and simple’ (18,2–3). To say that this higher cognition of the universal is ‘intellectual’ (noera), i.e. that it belongs to nous, is to say that it is not only above sensation and imagination and opinion, but also above ‘discursive thought (dianoia)’, i.e. following a step-by-step sequence of thoughts. Simplicius develops the analogy with the case of definition: grasping each of the components of the definition is better than remaining with the initial unclarified conception associated with the name, ‘but the philosopher synthesizes the definition in a single simplicity, so that he thinks the multiplicity of the definition united, and grasps simultaneously the multiplicity and the one’ (18,11–13). He is here picking up Aristotle’s claim in Metaphysics 7.12 and 8.6 that to grasp a scientific definition of something we must grasp the cause of the unity of the many components of the definition, and he suggests that Plato also ‘hints’ in the Theaetetus that ‘this is proper to scientific knowledge’ (18,13–14): presumably Plato is hinting that the people who have true opinion with an account by spelling a thing out into its letters or elements (stoikheia) – where this might be a metaphorical description of the components of the definition – fall short of scientific knowledge because they do not grasp the unity of the many stoikheia. By contrast, ‘the cognition according to the definition and through the elements is intermediate’ between the imaginative conception associated with the name and the intellectual grasp of the definition as a unity, ‘being, rather, discursive (dianoêtikê) or else opinionative (doxastikê), surpassing the inferior kind of cognition in its precision, but falling short of the superior kind of cognition through being divided and also through being more or less lacunose’ (18,14–16). Presumably whether this intermediate cognition is discursive thought (dianoia) or mere opinion (doxa) depends on whether it is ‘lacunose’: if in ‘spelling out’ the object I leave some of its syllables unanalysed and not do not go back all the way to the letters, or if I omit some of the letters altogether, I will have mere opinion. Simplicius is evidently harmonizing Aristotle’s text here with not one but two Platonic dialogues, which had probably already been harmonized with each other by earlier neo-Platonic interpreters: not only with the Theaetetus, but also with the hierarchy of cognitive states from the ‘Divided Line’ of Republic 6–7.94 An advantage of this way of thinking is that it brings out the analogy between Aristotle’s examples of name-and-definition and of whole-and-parts, and that it

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explains the sense in which the whole (or the overall concept of F) is what we should start from, better known to us and less well known by nature than the parts (or the conceptual constituents of F), and also the sense in which the whole (or the overall concept) is what we should aim at, better known by nature and less well known to us. It is less clear how it applies to universals. Simplicius says that we start from a concept of F-ness that abstracts away from the differences in the F-nesses in things, and end up with a concept of F-ness that comprehends the particulars and their differences (18.5–10): this would be illustrated by the example of the Timaeus’ animal-itself, which contains within itself the differentiae of animals according to Simplicius’ discussion in his Categories commentary cited above. In more Aristotelian terms, we might think of a scientific concept of animal that allowed us to understand the different possible ways of realizing vital activities such as locomotion, and so allowed us to grasp differentiae of animal such as winged, four-footed, or two-footed, just as a scientific grasp of number allows us to grasp such differentiae as even and odd, prime and composite. But Simplicius does not work this out here. All he needs in the context of Physics 1.1 are the kinds of universals that we start out from; and, unlike Alexander, he thinks that the example of the whole gives a closer model for the enquiry into physical principles than the example of the universal. It is interesting that while both Simplicius and Philoponus give the example that ‘it is easier to discern that what is approaching from a distance is an animal than that it is a human being’ (16,18–19, cf. Philoponus 19,16–17 – the Philoponus passage is almost verbatim identical with Themistius on the same text, 2,8–9),95 Philoponus denies that what we start by knowing here is properly a universal. Philoponus says that it should properly be called an ‘indeterminate particular’, although Aristotle here loosely calls it a universal (10,28–11,3), and he rejects an interpretation, akin to Simplicius’ but different in detail, which uses the theory of the three kinds of universals to say that the universal that is better known to us than the particulars is the one in the many (distinguished both from the one before the many and from the one after the many, 11,24–12,2). Simplicius and Philoponus and Philoponus’ unnamed opponents (Ammonius?) are all drawing on a broad way of interpreting the universals that Aristotle is speaking of here, which is older than Proclus’ technical theory of the three kinds of universals (it goes back at least to Themistius, but quite possibly to Porphyry and/or Alexander), but they are making different choices about whether and how to use Proclus’ theory to solve problems in the older interpretation and make it more precise. Simplicius (but not Philoponus or Themistius) adds that, because the example of name-and-definition fits well with the example of whole-and-parts but not so

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well with the example of universal-and-particular, Aristotle supplements it with the example of the young children who call all men ‘father’ and all women ‘mother’, ‘but as time progresses they articulate what is crude into what is proper to the particular, and in this way they acquire a precise knowledge of their parents’ (17,16–18). This gives a better model for how someone can start by using a word so broadly that it applies to all women universally, and refine it conceptually until it picks out what is distinctive to their real mother. ‘So we too, as long as we discern things by following what is crude and confused in sensory cognitions, are in no way unlike young children who call all the men they meet fathers’ (17,18–21). This means, notably, that we do not discern what is different about ordinary sensible objects, their constituent principles, and their nonconstituent principles, but apply the same language and concepts indiscriminately to all of them. As we have seen, Simplicius thinks that of philosophers before Aristotle who investigated the principles of things that are, ‘some did so without distinction, not distinguishing natural things from the things that are above nature’, while ‘others did so distinguish . . . but through their obscurity this escaped most people’s notice’ (21,15–19). Whether the pre-Socratics, and their readers, are lacking in concepts or only in the precise assignment of words to concepts, in either case they, and we, have work to do, and Aristotle and Simplicius will help us do it.96

4.3 Views about the principles: Division and harmonization After discussing Aristotle’s proem (Physics 1.1), Simplicius gives a very extended treatment (from 20,19 to 45,12 or even 46,8) of Aristotle’s division (diairesis), at the beginning of Physics 1.2 (184b15–25), of possible opinions about the principles. (Simplicius speaks of ‘sections’ (tmêmata), as if Aristotle were dividing a straight line into smaller segments, where we might have imagined a branching tree.) Specifically, I am interested in Simplicius’ understanding of Aristotle’s programme in laying out this division and then in critically examining the different possible opinions, as Aristotle does at least through to Physics 1.6, more broadly throughout Physics 1: this also informs Simplicius’ own programme, in his commentary on these chapters, in making explicit what Aristotle has not. Aristotle’s purpose in these chapters is of course not mainly to determine what past thinkers had said, but to determine what the principles are; the discussion of past thinkers is supposed to help in this. Recall that Alexander had interpreted Aristotle’s injunction to start from universals as meaning that we will start from universal axioms like the principle of excluded middle, and thus from general

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disjunctive descriptions like ‘the principles are either one or not one, either one or many, either moved or unmoved.’ Simplicius does not accept this explanation of what Aristotle means by starting from universals, and thinks we should rather be starting from sensible effects and working back to their causes (including their constituent elements), but he agrees with Alexander that division or disjunction is an important tool in determining how many the principles are and what they are like. But he does not see Aristotle simply as setting out all the prima facie possibilities and then excluding the false ones in order to isolate the correct description of the principles. It is important that a given view of the principles has actually been maintained by someone, and it is important what they meant by it. As Simplicius says, ‘having shown [in the first lemma 184a10– 16], given that there are principles, that knowledge about the principles is necessary, and having conveyed [in the second lemma 184a16-b14] the manner of approaching them, he thinks it reasonable not to express his own opinion about the principles before he has examined the opinions of the more ancient thinkers’ (21,22–5); and Aristotle skips some theoretically possible divisions, because he is not interested in sections that no one has inhabited (so 22,16–18). In giving the division in 184b15–25 Aristotle does not usually bother to attach names to the sections (he names only Parmenides, Melissus, and Democritus) and he does not say what these people thought, beyond putting them in the right section of the line. (Aristotle will in many cases fill in more details in the course of Physics 1.) So, Simplicius says, ‘it is presumably better first to encompass all the opinions through a more complete division, and then having done so to go back to the text of Aristotle’ (22,20–1), filling in the names and details of their views. He draws the information for the ‘more complete division’ from the Peripatetics, above all from Theophrastus, although he also mentions Nicolaus of Damascus and Alexander where they diverge from Theophrastus. He calls this, summing up at the end, ‘a concise overview of the things which are reported about the principles, written up not in chronological order, but according to which doctrines are akin’ (28,30–1) – where ‘reported’ (historêmenon) means ‘reported by the Peripatetics’. But because the doctrines so ‘reported’ seem to show the ancients contradicting each other on every possible issue (are the principles one or many, finite or infinite, moved or unmoved, etc.), Simplicius adds a deeper investigation of these people’s meanings, in order to show ‘how the ancients, although appearing to disagree in their doctrines about the principles, nonetheless come together in harmony’ (29.4–5). Simplicius thinks that this deeper investigation is important, not merely in order to do historical justice to past thinkers or to block Christian arguments from the disagreement of ancient

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authorities, but in order to assist the enquiry into the principles. I have spoken above about Simplicius’ attempts to go back beyond the Peripatetics to the original sources, and his hope that a close examination of the original wording (where available) will give clues to deeper meanings than the superficial Peripatetic ‘reports and write-ups’ (historikai anagraphai, 28,33–4) had observed. Here I want to look briefly at Simplicius’ views of the different kinds of principles and different past views of the principles, and of how he sees Aristotle’s engagement with past views of the principles (and what he, Simplicius, can do in filling in what Aristotle leaves implicit) as helping us to get clear about the principles. On Simplicius’ reading, Aristotle is not simply refuting all possible false views about the principles in order to leave only the true view remaining. Rather, by refuting the apparent meaning of earlier philosophers’ views, he helps us to understand what kind of principles they really meant (sensible or intelligible principles, elemental or non-constituent principles, etc.) and what attributes they really meant to assert of these principles; and this helps us to distinguish the many different kinds of principles that exist in reality, and to see how they all fit together. There are two issues, important to Simplicius, which arise from things Aristotle says, or fails to say, outside the division itself. First, when Aristotle says ‘the principle must necessarily be either one or several’ (184b15), he seems to be assuming without argument that there is some principle. As we have seen, Theophrastus supplied an argument that natural things have principles; but Porphyry, apparently displeased with Theophrastus, asked why Aristotle did not investigate here whether there are principles of natural things, and answered that physics cannot establish the existence of its own principles, that it must receive them from a higher science, namely first philosophy. Simplicius objects that if physics could not establish the existence of its principles, it also could not solve the harder problems of what and how many they are, problems which Aristotle in fact addresses in Physics 1; so Simplicius concludes that Aristotle omits demonstrating that natural things have principles, not because this is beyond the domain of physics, but because it is too obvious to need proof. Nonetheless (as we saw above) Simplicius grants to Porphyry that physics is subalternate to first philosophy and that a fully scientific proof that natural things have principles, and what and how many principles, would have to draw on first philosophy. This is important for the present enquiry because not all the views on the principles that Aristotle goes on to encompass in the division are physical views. As we have seen, Aristotle himself says (putting Physics 1.2 together with On the Heaven 3.1) that Parmenides and Melissus were doing first philosophy rather than physics.

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Simplicius goes further, saying that Aristotle calls only ‘those who say that the principle is one and moved’ natural philosophers or physicists (phusikoi) in the proper sense (23,21–2), presumably because Anaxagoras and Empedocles posited both natural elements and also above-natural causes (nous or Love and Strife). And although Aristotle’s main interest here is in physical principles, and in Physics 1 mainly in elemental principles, Simplicius thinks that the investigation of principles in Physics 1.2 is not limited to physical principles, much less to elements, and that a scientific understanding even of the elements depends on understanding how they are related to higher causes. Another issue, outside the division itself, comes from what Aristotle says about how the investigation of principles relates to the investigation of being. Aristotle says that philosophers have had various views about how many principles there are and what they are like, ‘and the people who investigate how many the beings are investigate in the same way: for they investigate first concerning the things out of which the beings are, whether these are one or many, and if many, [whether they are] finite or infinite, so that they are investigating whether the principle and the element are one or many’ (184b22– 5). A common modern interpretation is that in Aristotle’s time there was a standard way of dividing up philosophers by how many beings they posited, and that Aristotle wants to adapt this to divide up philosophers by how many principles they posited, and tries to show that both divisions come to the same thing.97 But this is not how either Alexander or Simplicius read the passage. Alexander needs to distinguish the investigation of the principles from the investigation of being, since he follows Aristotle in saying that Parmenides, who thought there was only one being, must have thought there were no principles, since a principle must be a principle of something else and there is nothing else for Parmenides’ being to be a principle of. So Alexander says that ‘the natural scientists, although setting out to investigate about the beings, how many they are, were compelled first to investigate about the principles of the beings, since the knowledge of the beings depends on these’ (45,17–19), for the same reason that Aristotle has given in the first sentence of the Physics for why we must investigate the principles. Alexander also says that, when Aristotle examines the thesis that the principle is one and motionless, he is not examining Parmenides’ view (since Parmenides thought there were no principles), but rather a view that no one ever held; and that Aristotle mentions Parmenides’ view in order to motivate the study of the thesis that the principle is one and motionless, on the ground that, if the bizarre view that being is one and motionless (and there are therefore no principles) could be maintained by a famous philosopher, then the

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less bizarre view that the principle is one and motionless is even more worth examining (37,22–38,1). Simplicius rejects all this: Aristotle is examining real people’s claims (sometimes in their apparent meaning, but with a view to clarifying their real meaning), and Parmenides did indeed maintain that the principle is one and motionless, since he did not maintain the absurd view that there is only one thing: only one thing is strictly a being, but it is a principle of the many things that come-to-be and are objects of sensation and opinion. Indeed, Simplicius says, when Parmenides says ‘being is F’ (one, motionless, limited, etc.), we should charitably interpret him to mean ‘the principle is F’; and this is what Aristotle means when he says that investigating the being(s) and investigating the principle(s) come to the same thing (38,3–18; 45,26–9; 46,16–27). Thus Simplicius thinks that when Parmenides says ‘being’ (in the strict sense), he means ‘the principle of beings’ (beings in a looser sense), principle ‘not as elemental but as having brought them forth’ (38,12–13). Indeed, since Aristotle says that for everyone the investigation of being and the investigation of the principles come to the same thing, Simplicius concludes that all the philosophers, when they said ‘being(s)’, meant ‘the principle(s) of beings’. But the study of the principles of beings as beings is first philosophy – we expect Simplicius to say that Parmenides and Melissus were doing first philosophy, but is he going to say that of everyone else too? This is the context in which Simplicius says that ‘[Aristotle] says that also those who investigated what is were investigating the principle of what is. For those who philosophized about the principles were investigating them as principles of things that are: some did so without distinction, not distinguishing natural things from the things that are above nature; others did so distinguish, like the Pythagoreans and Xenophanes and Parmenides and Empedocles and Anaxagoras, but through their obscurity this escaped most people’s notice’ (21,14–19). So in a sense even Anaximenes was doing first philosophy, but indeterminately, without distinguishing it properly from physics; not only Parmenides but also Empedocles and Anaxagoras were doing both first philosophy and physics, and distinguishing them. Aristotle, ‘being concerned for those who listen more superficially, refuted the apparent absurdity in their accounts, since the ancients were accustomed to express their doctrines in riddles’ (36,28–31, cf. 21,19–20): so by refuting, e.g. the thesis that there is only one thing, or that the sensible cosmos or its material substrate is motionless, he forces us to make the distinctions explicit, and to recognize that Parmenides is talking about an intelligible non-constituent principle. (Simplicius points out that Plato, and Parmenides before that, and Xenophanes even before that, were Aristotle’s models in refuting earlier thinkers; since Plato professes his

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admiration for Parmenides, his aim cannot have been to refute Parmenides’ real meaning, and Simplicius suggests hopefully that this goes for Aristotle too, 36,5– 37,2.) ‘So these people [sc. Aristotle, Plato, Parmenides, Xenophanes] seem to be refuting, when sometimes they are supplying what was left out, sometimes making clear what was said unclearly, sometimes marking off what has been said about the intelligibles, since it cannot apply to natural things (as in the case of those who said that what is is one and unmoved), sometimes forestalling the easy interpretations of more superficial people. And we ourselves will try to remark on these in [discussing] Aristotle’s arguments against each of them’ (37,2–8). And drawing these distinctions, between the different levels of being (sensible, intellectual, intelligible, etc.) and between the different kinds of principle (constituent and non-constituent, etc.), will help us understand not only the higher principles but also the lower ones, because we get clearer about the lower principles by distinguishing them from the higher ones and because the lower principles themselves depend on the higher principles. Against this background, it is easy enough to understand who Simplicius ‘saves’ in 28,32–37,9, and in what sequence and why and how. Naturally Simplicius will stress the people who, as he says, ‘distinguish[ed] natural things from the things that are above nature . . . like the Pythagoreans and Xenophanes and Parmenides and Empedocles and Anaxagoras’ (21,17–19), although in fact he says almost nothing here about the Pythagoreans except for ‘Timaeus’. But even within this group there is a definite sequence and ranking. The first order of business is to save and harmonize the Eleatics (Parmenides and Melissus, mentioned in Aristotle’s text, plus Xenophanes but not Zeno), who are speaking in the first instance about an intelligible non-constituent principle of physical things, and who speak as if there were only one such principle.98 The Eleatics disagree with sense-experience if they are taken to be speaking about the sensible world, and they also seem to disagree with each other, if Parmenides says that being is finite while Melissus says that it is infinite; worse, the Pseudo-Xenophanes says that it is neither finite nor infinite, and also that it is neither at motion nor at rest, whereas Parmenides and Melissus seem to make it simply at rest. Aristotle describes Parmenides as saying that ‘there is no being besides being itself (auto to on)’ (Physics 1.3, 187a5–6, paraphrasing Parmenides B8.36–7), and to a Platonist like Simplicius this means that Parmenides is talking about the Form of being. Following Proclus, Simplicius takes this to be not the very first principle (which is a One beyond being), but the first participant in the One-itself, the summit of the intelligible world and the cause of being to all other beings. If this is what the Eleatics were talking about, then it is not too hard to find legitimate

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senses in which Parmenides could call it finite or limited, Melissus could call it infinite or unlimited, and Xenophanes could exalt it above both limit and unlimited. Furthermore, Proclus makes limit and unlimited the highest principles after the One, and analyses each intelligible being (including beingitself) as a triad of limit, the unlimited, and their mixture; so we can say either that Parmenides and Melissus each fastened on one attribute of being-itself, or that they each contemplated a different principle, a different member of the first intelligible triad.99 (For Proclus the infinite or unlimited in intelligible beings is infinite productive power, and Simplicius tries to show that when Melissus said that being was infinite he meant not that it was infinitely spatially extended, nor even just that it was eternal, but that it was eternal because of its inexhaustible power, 29,19–22.) So neither Parmenides nor Melissus saw all the way up to the first principle, but they both came very close; perhaps Xenophanes, in exalting his principle above both limit and unlimited, saw all the way to the One-itself. Parmenides, more than the other Eleatics, is also important for Simplicius here because he also gives an account of sensible things, and thus provides a bridge to connect the Eleatics with those physicists who also talked about intelligible principles (although obscurely, so that they have been misread as just doing physics). Most immediately, Simplicius’ understanding of how the ‘Truth’ and ‘Doxa’ parts of Parmenides’ poem fit together gives him a model for understanding the relation between Empedocles’ descriptions of the world unified by Love (the ‘Sphairos’) and of the world separated into distinct components by Strife; and Empedocles in turn gives him a model for understanding Anaxagoras. At Parmenides B8.50–2 the goddess tells Parmenides that she will cease the reliable account of truth which she has so far been giving him, and will now give him an account of mortal doxa – of the opinions of mortals, or of the world as it appears to mortals; and such fragments as we have of this second, ‘Doxa’, part of the poem describe a world composed of light and night (and living beings mixed out of them), whose relations with the world of uniform being described in the ‘Truth’ part are unclear. Alexander assumes that Parmenides is describing only one world throughout, that in the Truth Parmenides is describing this world as he thinks it really is, and that in the Doxa he is simply reporting opinions that he disagrees with about this world. Simplicius of course rejects this, and thinks that the Truth is Parmenides’ account of the intelligible world and the Doxa is his account of the sensible world. He cites Parmenides’ transition passage from the Truth to the Doxa (30,14–31,2, and again 38,24–39,12 specifically against Alexander) in order to show that ‘Parmenides passes from the intelligibles to the sensibles, or as he himself says

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from truth to seeming (doxa)’ (30,14–16); ‘so he calls this account opinable (doxaston) and deceptive, not as being simply false, but as having fallen off from intelligible truth into what is apparent and seeming, the sensible [world]’ (39,10– 12). Simplicius’ aim here is partly to show that Parmenides wasn’t contradicting the evidence of the senses, and partly to show that his being-in-the-strict-sense was indeed a principle (of sensible things). But he also wants to show that Parmenides is doing both physics and first philosophy, and distinguishing the two. As Aristotle says, Parmenides ‘when he was forced to follow the appearances’ posited two contrary principles, hot and cold or fire and earth (Metaphysics 1.5, 986b31–987a2; cf. 1.3, 984b1–8 and Physics 1.5, 188a20–22). Against Alexander, who lazily says that Parmenides ‘hypothesized . . . earth as matter and fire as efficient cause’ (38,22–3 – Alexander is probably following Metaphysics 1.3, 984b1–8 rather than anything in Parmenides), Simplicius cites textual evidence that Parmenides posited fire and night (not earth) as elemental (constituent) causes of generated things, and also a distinct efficient cause, the goddess who presides over generation, and who is a cause not only to bodies but also to souls, causing them to descend into the world of generation and to ascend from it again.100 Simplicius is doing all this (and complaining about ‘the current widespread ignorance of ancient writings’, i.e. the uncritical reliance on doxographies, 39,20– 21), not just in order to show that Parmenides distinguished different levels of being and constituent and non-constituent principles, but to give himself a model for interpreting Empedocles. Empedocles does not give separate accounts of Truth and Doxa, but, like Parmenides, he gives descriptions of two different worlds. On the obvious straightforward interpretation, Empedocles narrates a repeating cycle of transitions between the Sphairos the world unified by Love, and a world like the one we now live in, with domains of earth, water, air, and fire separated by the action of Strife, and living beings formed within it by Love trying to reunify the different elements into a whole. Alexander, naturally, thinks that Empedocles’ Sphairos and his world governed (partly) by Strife are two different states of the sensible world succeeding each other in a temporal cycle. Simplicius wants to show, against Alexander, that the Sphairos is a description of the intelligible world, and is therefore eternal. Simplicius’ interpretation of Parmenides’ Being (also described as spherical) gives him a model for interpreting Empedocles’ Sphairos; his interpretation of Parmenides’ goddess, responsible for the mixture of the elements and for the incarnation of souls, gives him a model for interpreting Empedocles’ Love and Strife; and his interpretation of Parmenides’ light and night gives him a model for Empedocles’ four elemental

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principles. As Simplicius says, against Alexander’s interpretation of two worlds succeeding each other in time, ‘Empedocles too [sc. as well as Parmenides], teaching both about the intelligible and about the sensible world, and positing the former as the archetypal paradigm of the latter, posited in each as principles and elements these four – fire, air, water and earth – and Love and Strife as efficient cause’ (31,18–21). So Empedocles must have used the same names, ‘fire’ and so on, for principles in the sensible and intelligible worlds: he must mean these words equivocally, but naive readers who take ‘fire’ in its everyday sense will have difficulty in understanding how the Sphairos can be the intelligible world, and so will take it instead to be perishable, and to be just another temporal phase of our sensible world. But, of course, Plato (and ‘Timaeus’ before him) also speak of earth, water, air, and fire, and the kinds of animals that inhabit each of those elements, in the intelligible paradigm (so Simplicius 31,23– 8): so the same techniques that we use in interpreting Plato’s descriptions of the animal-itself can be applied to Empedocles’ descriptions of the Sphairos, and indeed Simplicius says that Timaeus and Plato were following Empedocles (31,23–4). In maintaining against Alexander that Empedocles’ Sphairos is the intelligible world, Simplicius is following a standard neo-Platonic interpretation; but he also sees himself as correcting this standard interpretation, giving a more subtle version of it.‘It is not the case, as most people think, that according to Empedocles Love alone produced the intelligible world, and Strife alone the sensible, but rather that he considers both of them everywhere in the appropriate manner [i.e. the manner appropriate to each level]’ (31,31–32,1). It is surprising to be told that ‘most people’ give such a Platonizing interpretation of Empedocles, but this is pretty much Philoponus’ interpretation (in Physica 24,3–9), and it must go back at least to Ammonius’ lectures, very likely to Porphyry’s commentary on the Physics.101 To support his correction of this view, Simplicius cites texts of Empedocles proving that Love is ‘the cause of the demiurgic blending down here too’ (32,2–3), so that the sublunar world is not entirely controlled by Strife – which is certainly true, but does not support Simplicius’ claim that Strife is also active in the intelligible world. But what Simplicius thinks is that when Empedocles describes different phases of the cosmic cycle, each characterized by different relative strengths of the powers of Love and Strife, he is describing not a temporal succession, but higher (more unified) and lower (more differentiated) levels of reality: ‘perhaps (mêpote) he is conveying a certain progression of the unification and differentiation of beings, speaking riddlingly of several varieties of the intelligible world above this sensible world [distinguished] according to

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the greater or lesser dominance of Love, and in the sensible world he displays varieties of the domination of Strife’ (34,8–12). In speaking of ‘several varieties of the intelligible world’, Simplicius is making the typical late neo-Platonic move of adding ‘subtlety’ to the simple Porphyrian account of a single intelligible level of being, by distinguishing with Iamblichus a higher ‘intelligible’ (noêton) level, the level of the objects of nous, from a lower ‘intellectual’ (noeron) level, the level of nous itself. Following Proclus and Damascius, Simplicius distinguishes the ‘intelligible unification (noêtê henôsis)’, the greater unity of the intelligible Forms, from the ‘intellectual differentiation (noera diakrisis)’, the greater differentiation of Forms within nous itself102 – which Empedocles might poetically express by saying that Love is relatively stronger at the higher levels, and Strife is relatively stronger at the lower levels. This ‘subtle’ interpretation of Empedocles also gives Simplicius a model for interpreting Anaxagoras. Aristotle often groups Anaxagoras and Empedocles together, treating them as variants on the same fundamental ideas (they agree that change arises from combination and separation of permanent underlying substances under the influence of a moving and ordering principle; they differ in that Anaxagoras posits one moving principle and Empedocles two, Anaxagoras posits infinitely and Empedocles finitely many material principles, Anaxagoras posits a single cosmogony, Empedocles repeated cosmogonies). Once Simplicius has assimilated Empedocles to Parmenides, he can extend the same treatment to Anaxagoras. On the obvious straightforward interpretation, Anaxagoras narrates a transition from an inactive divine nous and a static mixture of ‘all things together’ to the ordered world which emerges when nous begins to act on the mixture. But if Parmenides’ transition from Truth to Doxa, and Empedocles’ transition from the Sphairos to the differentiated world, can be interpreted as merely a shift of attention from the intelligible to the sensible world, then so can Anaxagoras’ transition from nous and ‘all things together’ to the differentiated world. And if the ‘earth, water, air, and fire’ present in a unified way in the Sphairos can be interpreted as intelligible paradigms of earth, water, air, and fire here, then so can the ingredients or ‘things’ (khrêmata) in Anaxagoras’ pre-cosmic mixture. Anaxagoras does say, in a passage Simplicius cites, that ‘before these things were separated, all [of them] being together’ (34,21–2), their union with each other prevented them from manifesting any sensible qualities. So heat or fire in that mixture is not sensibly hot, but is rather a paradigm of heat or fire that is inseparably united with the paradigms of all other sensible things. Simplicius may have read Anaxagoras as saying here that ‘all things are one in the totality’ (34,25–6),103 and he will have taken Anaxagoras’ ‘all together (homou panta)’

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(34,20) or ‘all being together (pantôn homou eontôn)’ (34,21), as a restatement of Parmenides’ ‘it is all together (estin homou pan)’ which he had cited a few pages before (30,3). So, Simplicius concludes ‘this “totality” would be the One-which-is of Parmenides’ (34,26–7) – except that presumably Anaxagoras brought out, more than Parmenides had, its containing inseparably the paradigms of the plurality of natural things. So Anaxagoras’ ‘things (khrêmata)’, present both in the original mixture and in the present sensible world, must be forms, present at different levels in the modes of being appropriate to those levels. Anaxagoras describes the transition from the original mixture to the present sensible world as a ‘separation’ or ‘distinction’ (apokrisis or diakrisis) of these ‘things’, and Simplicius can easily take this as the contrast between intelligible unification and sensible differentiation (diakrisis). And if nous’ act of producing the sensible world in the image of the intelligible can be taken as an eternal act in the Timaeus, it is no harder to take it as eternal in Anaxagoras. This seems to give us forms at two levels, intelligible and sensible, and nous as the cause producing the sensible world in the image of the intelligible. And indeed this seems to be what Simplicius attributes to Anaxagoras in some passages.104 Here, however, he tries to push it a step further, saying that Anaxagoras ‘seems to have considered there to be a threefold variety of all forms’ (34,18–19), which become progressively more differentiated at the intelligible, intellectual, and then sensible levels. In other words, Simplicius tries to argue that the forms also exist in nous itself. This is not easy to maintain, since Anaxagoras insists that nous is separate and unmixed with any of the ‘things’; but, of course, so does Aristotle, and Simplicius has argued that Aristotle’s nous must contain a structured plurality of paradigms if it is to impose rational order on the sensible world. (And there is indeed a notorious difficulty about how Anaxagoras’ nous can know the ‘things’, as Anaxagoras says it does, if it has nothing in common with them.) Simplicius tries to support this interpretation of Anaxagoras by citing texts where Anaxagoras speaks of a separation occurring ‘as it does among us’: he might be talking about other places and times within the sensible world, or he might just mean ‘in this thought-experiment things would come about as you now see them doing, so you should believe me that this is how it happened’, but Simplicius insists that he must be talking about another, intellectual, diakrisis. It helps that Anaxagoras innocently uses the word ‘idea’ (all this 34,27–35,21). Thus there is a single coherent strategy for saving and harmonizing Parmenides and Empedocles and Anaxagoras, in that determinate order, modelled on strategies developed for interpreting and harmonizing Plato and

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Aristotle. By contrast, Democritus and the material monists were not doing first philosophy (or at least were not conscious of doing so), and this strategy does not apply to them. Still, while Simplicius has only the most perfunctory interest in the material monists, he is more seriously interested in Democritus, because of the points of contact between his physics and Timaeus’ – while his discussion of Democritus here is fairly short, he has more to say elsewhere, especially in commenting on On the Heaven. Indeed, Aristotle in On the Heaven 3 had grouped Democritus and the Timaeus together, as making bodies out of indivisible elements (indivisible bodies for Democritus, indivisible surfaces for Plato), and explaining the apparent sensible qualities of bodies by the shapes of their elements. Simplicius shows no interest in Democritus’ account of the causes of motion, which would not lead to anything like Love or Strife or nous; he is not even interested here in the void, which he might have compared with the Receptacle of the Timaeus. He is interested in saving and harmonizing Democritus only on the atoms as elemental principles, which he assimilates to the indivisibles of the Timaeus. Indeed, rather than distorting Democritus, Simplicius seems to distort the Timaeus, by claiming that its indivisible surfaces ‘have some depth’ (35,29), i.e. are thin bodies, so that Aristotle’s contrast between Democritus (solids) and the Timaeus (surfaces) collapses. On the face of it, this is a surprising thing for Simplicius to do. He unsurprisingly harmonizes Anaxagoras and Empedocles on the material principles by fitting them into different levels of the composition of bodies that Aristotle recognizes: Anaxagoras rightly recognizes that homoeomerous things like flesh and blood and bone are material constituents of (especially) living bodies, but Empedocles, also rightly, recognizes that these in turn are composed of earth, water, air, and fire, which are more fundamental. But, more surprisingly, Simplicius also reads Democritus and ‘Timaeus’ as taking yet a further step – as recognizing, also rightly, that these four in turn are composed out of more fundamental indivisible constituent shapes. And to this extent he does distort Democritus, assimilating him to the Timaeus when he says that ‘Leucippus and Democritus and the Pythagorean Timaeus and their followers did not contradict [the thesis that] the four elements are principles of compound bodies’ (35,22–4), but only looked for more fundamental principles underlying the four. (There is no reason to think that the historical Democritus gave earth, water, air, and fire any status as principles.) Simplicius is here again adding ‘subtlety’ beyond the ‘standard’ interpretation represented by Porphyry.105 Everyone seems to agree that Aristotle has shown that bodies cannot be composed of two-dimensional figures as material constituents, and so the Timaeus must not have meant that. The usual response is to take the

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triangles ‘symbolically’ (attributed to Iamblichus among others, Simplicius, in de Caelo 564,10–13), and to interpret the Timaeus in a way that brings it closer to Aristotle’s theory of the four sublunar simple bodies, which would differ mainly by the contrarieties of hot and cold and moist and dry. But Simplicius (following Proclus) wants to get something more than this out of the Timaeus, and so is led to resurrect its Democritean background. He says here that a series of philosophers going back to Democritus ‘looked for causes that would be more principial and simpler than [earth, water, air, and fire], by means of which they could also give an account of the qualitative differences among these elements. And in this way Timaeus, and Plato following him, posited surfaces which have some depth and differences of shape as first elements of these four elements, judging that the nature of body [i.e. three-dimensional extension], together with bodily shapes, is more principial than, and is a cause of, qualitative difference’ (35,26–36,1). And earlier, in his commentary on On the Heaven, he had cited from Theophrastus (Simplicius has no direct access to Democritus’ writings) that Democritus ‘ascended to atoms, on the ground that those who give causal explanations in terms of the hot and the cold and so on are explaining amateurishly (idiôtikôs)’ (in de Caelo 564,24–6, and again 576,13–16); or as he says more fully, perhaps himself expanding on Theophrastus, ‘explanations in terms of the hot and the cold and so on were said by Democritus before [sc. before the Timaeus] to have been given amateurishly, as Theophrastus reports, the soul desiring to hear another principle more appropriate to the nature of body [sc. as three-dimensionally extended being] than such an activity of the hot’ (641,5–9). Whatever the faults or limits of Democritus’ explanations, this will have led him deeper into the elemental principles than Anaxagoras or Empedocles, and Timaeus and Plato, picking up from Democritus, will go still deeper in this direction. And Plato will integrate this mathematical (and to that extent ‘intelligible’ rather than sensible) theory of the elemental principles with Empedocles’ and Anaxagoras’ account of something like nous or Love as an intellectual efficient principle, and with something like the Sphairos or ‘all things together’ as an intelligible paradigm of the sensible world; and with the principles of the Eleatics, who saw all the way, or almost all the way, to the One as the first principle of all things.

4.4 Arguing against the Eleatics, the puzzle about whole and parts, and the ‘later ancients’ After the division of different opinions on the principles, Aristotle devotes most of Physics 1.2, and Physics 1.3 as well, to a critical discussion of the Eleatics – that

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is, of Parmenides and Melissus, since he does not take Zeno to have given a positive account of the principle. Aristotle first explains why we do not need to respond to Parmenides and Melissus – ‘to examine whether what is is one and unmoved is not to examine about nature’ (184b25–185a1), and it does not belong to the science of nature to argue against someone who abolishes the principles of nature – and then he relents and does it anyway. Physics 1.2, 185a20–186a3 examines the different things that the Eleatics might mean by their thesis that ‘what is is one’ (or that ‘all is one’ or ‘all things are one’), and shows that on each interpretation the thesis is either false or else harmless (and indeed implies that there are many beings); then Physics 1.3 examines Parmenides’ and Melissus’ arguments for their thesis, or their aporiai against there being many beings, and shows how to resolve each argument. The Greek commentators take up the issue of whether the Eleatics are doing physics or something else and what the Eleatics meant by saying that what is is one (and how this relates to saying that the principle is one), and the issue of who should respond to someone who denies the principles of a science and how; they also, of course, examine Aristotle’s arguments in Physics 1.2 against different interpretations of the Eleatic thesis, and his responses in Physics 1.3 to Eleatic aporiai against plurality. In commenting on these parts of Physics 1.2 (I will leave Physics 1.3 aside) Simplicius is engaged in, at least, a three-cornered debate with Alexander and Porphyry. While Simplicius sometimes agrees and sometimes disagrees with Porphyry in these sections, Porphyry does seem to be playing a larger role here than he does in most other parts of the commentary. As we know, a fundamental disagreement between Alexander and Simplicius is that Alexander thinks the Eleatics think that there is only one thing, while Simplicius thinks the Eleatics think that only one thing is in the strict sense, but that there are also many sensible things, which fall short of being in the strict sense. So Alexander finds it puzzling that Aristotle, in the midst of a discussion of how many principles natural things have, should bother refuting the thesis that there is only one being, since if there is only one thing, there is nothing for it to be a principle of – as Aristotle says, ‘there is no longer a principle if there is only one thing, and one in this way. For the principle is of something or of some things’ (Physics 1.2, 185a3–5). Alexander’s solution is that Aristotle is not arguing here against the thesis, mentioned in the doxographic division, that the principle is one and unmoved; rather, since the Eleatics would have thought there were no principles, Aristotle must here be taking up the question he had apparently set aside, whether there are principles of natural things at all (46,10–16). For Simplicius, by contrast, to say that there is only one being-in-the-strict-sense is

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precisely to say that there is only one principle; it is a principle of things that are in looser senses. So, rather than trying to prove against the Eleatics that there are principles of natural things, Aristotle would be taking this premise as agreed, and using it to infer, against the apparent meaning of the Eleatic thesis, that natural things also exist (46,16–47,3). But why does Aristotle decide to do this in a work on physics, and how can the physicist, while doing physics, argue against someone who denies his principles? As Aristotle says, ‘to examine whether what is is one and unmoved is not to examine about nature. For as for the geometer too there is no arguing against someone who abolishes the principles, but [such arguing belongs] either to another science or to one common to all, so too [such arguing does not belong] to one who [investigates] the principles’ (Physics 1.2, 184b25–185a3). For Simplicius, when the Eleatics say that being is one they are doing first philosophy, not physics (Parmenides also does physics, in the Doxa), but they do raise aporiai about nature:106 it is up to the physicist to reply to these aporiai, and presumably that will help him understand more clearly the principles of his science. These aporiai would be, in the first instance, the Eleatic arguments that Aristotle examines in Physics 1.3; they might also include Zeno’s aporia against place, discussed in Physics 4, and his aporiai against motion, discussed in Physics 6. But, as Simplicius says, it is important to reply both to an opponent’s arguments (as in 1.3) and to his thesis (as in 1.2): if you only refute the thesis, you ‘leave behind aporiai’, and if you only resolve the arguments, you leave open the possibility that the thesis could be supported by other stronger arguments (71,19–26). While the physicist can presumably resolve the aporiai, he cannot scientifically refute a thesis of someone who denies the principles of physics. That could be done by a higher science (either the person who denies the principles of each science can be refuted by the next science up, or they can all be refuted by the very highest science, first philosophy or Platonic dialectic). Or the opponent could be refuted by Aristotelian dialectic, which is not a science. But, Simplicius proposes, the physicist can also refute someone who denies the principles of natural things, not refuting him scientifically, i.e. by cause-to-effect inference, which here would mean arguing ‘from the principles of the principles’, but rather refuting him ‘from the principles of demonstration’ (49,23–50,4). Here Simplicius seems to mean, not just that (trivially) the argument against the opponent proceeds from the principles of that argument, but that it proceeds from things presupposed by demonstration in general. And among these principles Simplicius includes not just, e.g. the principle of non-contradiction (which Aristotle does call a principle of demonstration), but also sensation and

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induction (which Aristotle probably would not have called principles of demonstration). As Simplicius points out, Aristotle says ‘let us hypothesize that some or all of the things which are by nature are moved: it is clear from induction’ (Physics 1.2, 185a12–14); and Simplicius suggests that Aristotle can assume on similar grounds that there are substance and quantity and quality, and use this to argue against the Eleatic thesis in its apparent meaning, that there is only one thing (all this 49,23–50,4). When Aristotle examines the Eleatic thesis in Physics 1.2 (before turning to the Eleatic arguments in 1.3), he lists different possible interpretations of ‘what is is one’. At 185a20-b5 he considers different interpretations of ‘being’ or ‘what is’, namely the senses of being corresponding to the different categories, and at 185b5–25 he considers different interpretations of ‘one’, namely ‘either the continuous or the indivisible or things the formula of whose essence is one and the same’ (185b7–9). We could see this as a formula for an oral dialectical refutation: if your opponent asserts ‘what is is one’, ask him whether he means this or that sense of ‘what is’, and depending on his answer pursue this or that line of argument; alternatively, ask him whether he means this or that sense of ‘one’, and depending on his answer pursue the appropriate line of argument. Different Greek commentators understood these lists of senses of being and unity in different ways; in particular, they had different understandings of how the two lists, for being and for unity, fit together. Simplicius, basing himself largely on Porphyry, is rightly critical of Alexander, who thinks that Aristotle is giving, not first a list of senses of being and then a list of senses of unity, but a single overarching list of senses of unity, from which the Eleatic opponent must choose the kind of unity he means to assert. When Aristotle, starting at 185a20, asks in what sense of being the Eleatics assert that what is is one – does ‘being’ here mean substance, so that everything would be one substance, or does ‘being’ mean quality or quantity, so that everything would be one quality or one quantity, or do all of these exist, so that there would be substance and quantity and quality? – Alexander takes him to be asking whether ‘what is is one . . . on account of the name, since the one name [sc. “being”] is predicated of all the things that are, or [whether it is one] in reality’ (73,5–7). Alexander’s thought is that, if there are beings in different categories (say a substance and a quantity), then, since ‘being’ or ‘is’ is not predicated univocally of things in different categories, all things would be one only ‘on account of the name’, i.e. because they all have the name ‘being’ predicated of them in different senses, but there would be no real essence that would apply to them all. If, on the other hand, all beings fall under the same category, then they

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are one in reality, since a single real essence, a single sense of being, would apply to them all. But if so, then either they are one in genus but many in species, or they are one in species but numerically many, or they are numerically one; and if they are numerically one, this means either that they are continuous, or that they are indivisible, or that the formula of their essence is one and the same (so Alexander as cited by Simplicius 73,4–13). Aristotle would then take up each of these options in turn, and argue in each case either that the thesis is absurd or that it entails that there are many beings. This seems like a rather artificial interpretation of Aristotle’s text; certainly it needs to add many things to the text. As Simplicius points out, Aristotle says nothing here about the options of saying that things are one in genus or in species, and at 185b5–7 (picking up 185a20–2) he passes from the many senses of being to the many senses of unity, so it would be strange if he had been describing senses of unity since 185a20 (73,13–17). Perhaps surprisingly, Porphyry and Simplicius accept Alexander’s view that Aristotle would say that, if there are beings in different categories, then being would be one in name but not in reality. This is not in Aristotle’s text, and it makes Aristotle rest his argument against the Eleatics, unnecessarily, on his controversial claim that being cannot be said univocally of things in different categories: all Aristotle needs to say is that if there are (say) both a substance and its quantity, then there are two beings and the Eleatic thesis is falsified. But Porphyry’s interpretation seems to be significantly different from Alexander’s. For Alexander, Aristotle’s main question is whether being is a single real essence predicated of all beings, or whether being is only a shared name, said in different senses and thus standing for different real essences when predicated of different things; only in the former case do we ask whether that real essence has many instantiations, differing in species or number. For Porphyry, it seems, Aristotle’s main question is whether there is just one individual being, or whether there is more than one individual being, so that being would be one only in name (so, apparently, 74,5–12). On Porphyry’s reading, apparently, Aristotle in claiming that being is said in many ways would not be arguing against monist opponents who say that being is said univocally of things in different categories (this is an obviously self-defeating kind of monism and does not need to be argued against), but against monist opponents who have not noticed that non-substances are beings at all. A would-be monist will not say that both Socrates and Plato exist, but he might say that what is is infinite, without noticing that not only the underlying substance but also its infinite quantity would then have to exist. Aristotle would still be relying on a controversial claim of his, namely that quantities and qualities are real things distinct from substance,

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against the view that these different predicates are just different names for the underlying substance. But he would have a clear motive for using this claim, whereas on Alexander’s reading he seems to have no good motive for making his argument depend on the equivocity of being. And, as we will see below, on Porphyry’s reading Aristotle goes on to give a supporting argument for his claim that quantities and so on are real beings, in the passage on the ‘later ancients’. Simplicius very reasonably thinks that at 185b5–25 Aristotle turns from a division of senses of being to a division of senses of unity, and that he is interested here only in senses of numerical unity, since if what is were only generically or specifically one, it would be numerically many and the opponent’s monist thesis would collapse without needing any argument. There is not much controversy about Aristotle’s overall strategy in refuting the thesis that what is is numerically one: the numerically one here would be ‘either the continuous or the indivisible or things the formula of whose essence is one and the same’ (185b7–9). If everything has the same essential formula, then this would be a Heraclitean unity of opposites (on the usual caricature of Heraclitus) – to-be-good and tobe-bad would be the same, indeed to-be-good and not-to-be-good would be the same. If the opponent means that all of what is is continuous, he may be right, but what is continuous is infinitely divisible, so that what is (the so-called one) would be many and indeed infinitely many. If what is is one in the sense of ‘indivisible’, it may not follow that it is many, and while it is certainly ‘counterintuitive’ (our translation for Simplicius’ word ‘apemphainon’) to say that what is is indivisible in the way that a point is, the Eleatics do not much care whether something is counter-intuitive. Aristotle says that if what is is indivisible, then it cannot be a quantum and therefore cannot be either finite nor infinite (185b16– 19). As Simplicius understands it, Aristotle is not arguing either against the thesis that what is is a point (which Zeno does seem to have argued against), or against the thesis that what is is a non-spatially-located intelligible (which is what Simplicius thinks Parmenides and Melissus really meant), but rather against the apparent meaning of Parmenides and Melissus, that what is is spatially extended, with either a finite or an infinite extension: if it is extended, then it is not indivisible but continuous and therefore infinitely many, and if it is indivisible then it is not extended and does not have the attributes that Parmenides and Melissus gave it. The main difficulty here is in how Aristotle infers from ‘continuous and thus infinitely divisible’ to ‘many and indeed infinitely many’. This difficulty may be connected with an oddity of the lemma 185b5–25, that besides listing and refuting the three senses in which what is might be numerically one, Aristotle

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also includes a parenthetical reference to an aporia about whether the part and the whole are one or more than one (185b11–16), and an even more parenthetical sub-reference to an aporia about ‘non-continuous parts’ (185b14). The ancient commentators think that, although Aristotle officially only raises the aporia without solving it, his aim in raising it is to show that the part is not one with (or the same as) the whole, since if it were then, absurdly, each part would be one with (or the same as) each other part. (The commentators, following Eudemus, think the argument on the other side, that the part is the same as the whole, is that if each part were other than the whole, the parts collectively would be other than the whole; but the commentators all think that this argument is sophistical and the argument for non-identity is correct.) And Aristotle’s aim in showing that the part is not the same as the whole would be to show that if something is continuous and therefore divisible, it and its parts are many, and therefore what is would be many. But what is the aporia about non-continuous parts, and why does Aristotle mention it, if he is trying to make an argument about what continuity would imply? Here the commentators split many ways, and they cannot agree even on what Aristotle means by ‘non-continuous parts’. Alexander suggests that they are simply detached parts, i.e. former parts that have been separated from the wholes they formerly belonged to. Eudemus thinks that they are parts of continuous wholes which are not continuous with each other, because there is some other part between them (say the leftmost third and the rightmost third of a finite line), and Alexander also mentions this as a possibility. Simplicius apparently follows Porphyry in thinking that they are parts which are intrinsically discrete, and so cannot be continuous with each other whether there is another part between them or not, like units in a number or bricks in a house.107 But everyone agrees that these are parts which are obviously not one with each other, and therefore also cannot be one with the whole, whereas continuous parts might more plausibly be thought to be one with each other and with the whole. So perhaps Aristotle mentions non-continuous parts, the clearest cases of nonidentity, as part of a strategy for persuading the reader that continuous parts too are not one with their wholes. If Eudemus’ interpretation of ‘non-continuous parts’ is right, then perhaps Aristotle is arguing against an Eleatic monist who says that being is uniform and continuous, and that its parts, being qualitatively indistinguishable and continuous with each other, are one with each other and with the whole; Aristotle would reply that (say) the leftmost third and the rightmost third are not continuous with each other and so cannot be one with each other, and so cannot be one with the whole even though they are each

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continuous with the whole. Simplicius, who thinks that ‘non-continuous parts’ must be a different kind of parts than ordinary continuous parts, proposes that Aristotle raises the case of non-continuous parts in order to resolve the aporia about whether (continuous) parts are one with their wholes, by showing that the argument against parts being other than their wholes does not work. It is obvious that non-continuous parts, like bricks in a house or units in a number, are not one with each other and therefore not one with the whole; but even these noncontinuous parts are collectively the whole, just as continuous parts are; so the fact that the continuous parts are collectively the whole gives no ground for concluding that each continuous part is one with the whole. For Simplicius, all this is a refutation only of the apparent meaning of Parmenides and Melissus. Simplicius produces something of a flourish in showing that especially Parmenides, rightly understood, is immune to these arguments. What would Parmenides say if asked whether he means that the all is one as ‘the continuous or the indivisible or things the formula of whose essence is one and the same’? Simplicius rightly says, and shows by direct quotation, that Parmenides says explicitly both that what is is continuous and that it is indivisible, and indeed also that it is whole (another sense of unity according to Aristotle). Simplicius adds that Parmenides also accepts Aristotle’s third and supposedly most absurd option, that all beings are one in the sense of sharing a single essence, namely the essence of being: this captures the uniformity that Parmenides attributes to the world of being, and Simplicius says that it is not absurd if restricted to true or intelligible being. More generally, Simplicius tries to show that the absurdities that Aristotle tries to derive from each possible interpretation of Parmenides’ thesis are not absurd if interpreted appropriately. Parmenides accepts Aristotle’s inference that, since being is indivisible, it is neither finite nor infinite in the senses in which bodies could be called finite or infinite (even if it has a limit in a deeper metaphysical sense, and is also in another sense unlimited). And since Parmenides does not mean that everything is one in this way, but only that what is in the strictest sense, namely the principle, is one in this way, Aristotle can hardly object, since his own principle, the nous of Metaphysics 12, is a one which is neither finite nor infinite in the bodily sense (all this 86,19–87,18). More adventurously, Simplicius says that Parmenides accepts Aristotle’s inference that, since being is whole and continuous, it has parts and indeed infinitely many parts, although not in the way that bodies have parts (the parts of being are not spatially extended parts, and it is not possible for one part to perish while another remains, or for two parts to both exist but be separated from each other). Simplicius has unfortunately no textual evidence that Parmenides accepts these

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conclusions. But, as Simplicius has already argued, what Parmenides is talking about is the intelligible One-which-is (not the One-itself beyond being), which is also the subject of the second Hypothesis of Plato’s Parmenides. Plato argues at 142C7–143A3 that the One-which-is has infinitely many parts each of which possesses both unity and being; and since Plato’s arguments proceed validly from Parmenides’ (true) hypothesis, why would Parmenides not have accepted their conclusions (87,18–88,8)? More adventurously yet, Simplicius says that Aristotle himself would accept these conclusions about his own principle, the nous of Metaphysics 12, since as we have seen above Simplicius reads Metaphysics 12.10, 1075a11–15 as saying that the order exists both in the army and in the general, i.e. in nous: since nous thus contains an ordered plurality of paradigms, it is a whole of parts, one and many, and the conclusions of the second Hypothesis of the Parmenides will apply to it (88,8–11). But if Aristotle’s arguments do not apply against Parmenides’ real meaning, or if Parmenides would simply accept their apparently absurd conclusions, and especially if Aristotle himself has to accept the same apparently absurd conclusions, then why is Aristotle arguing this way – is it from malice, or from ignorance of Parmenides’ real meaning? But, Simplicius says, Aristotle is right to conclude that finitude, infinity, continuity, and wholeness, in the senses in which they apply to sensible things, cannot apply to the intelligible first principle, and so Aristotle’s arguments here, like his arguments against Platonic Forms or against nous’ generation of the world in the Timaeus, are correct refutations of inappropriate assimilations of divine to lower things, and cautions against accepting Parmenides’ descriptions literally. And, as Simplicius notes, Aristotle is following Plato’s model in the Parmenides and in Sophist 244B6–245E5 (which Simplicius cites in full to make this point) in arguing that Parmenides’ One-which-is is a complex whole of parts; and Sophist 244E3–5 cites Parmenides’ description of being as a sphere as if it were not merely a metaphor but a precisely intended statement and so a fair target for refutation. Since Plato cannot have been motivated by ‘contentiousness’, we can acquit Aristotle of that too: he is doing whatever Plato was doing. Thus on Simplicius’ reading both Plato and Aristotle are arguing that what the Eleatics posit as one, if anything positive can be said of it (for instance that it is finite or infinite), must also be many, so that the Eleatic attempt to find a pure one-being that is not also many is self-defeating. In the last lemma of Physics 1.2, 185b25–186a3, on the mysterious ‘later ancients’, Aristotle argues that the same difficulty arises not only for the Eleatics, but also for people who did not say that all is one, but who posited something as one and tried to avoid its being many. (Simplicius says they ‘posit[ed] that each of the sensibles, such as Socrates, is one’,

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but he is probably just guessing from Aristotle’s example of a human being who walks and has gone white, 185b29–30.) Aristotle mentions various solutions that these people tried in order to avoid admitting that a one is also many, argues (or at least tries to make plausible) that they fail, and uses this to motivate his own solution to the problem that troubled both the Eleatics and the later ancients – his solution being that, given the many senses of ‘being’ and of ‘one’, something can be both one and many without contradiction. While there is some obscurity here that might attract commentators – who were these people (Aristotle names only Lycophron), what did they say exactly, how can we fill in the details of Aristotle’s argument against their solutions? – they seem to be only a parenthesis in Aristotle’s response to Parmenides and Melissus, and we might not expect the passage to be a source of much excitement or controversy among the commentators. In fact there was both excitement and controversy, and Simplicius spends twelve pages on these twelve lines, chiefly because of two other philosophers who Aristotle does not mention here by name, but who had been inserted into the discussion as far back as Eudemus, namely Zeno and Plato. Simplicius first (90,24–92,26) gives an overview of the passage; he may be largely following Porphyry, but he is sceptical of Porphyry’s claim that Aristotle is giving a reductio ad absurdum argument that being must be said in different ways of things in different categories, and in general he seems to suspect Porphyry of overreading the passage. So he gives extended extracts from Porphyry (92,26–95,30) and indicates his doubts (95,31–96,21). But the issues are relatively minor and do not involve much excitement. So far Simplicius has not mentioned either Zeno or Plato – indeed, Zeno has not yet been mentioned in the Physics commentary in any context. The excitement starts when Simplicius turns to Alexander at 96,21, and then, since Alexander is relying on Eudemus, starts citing Eudemus at 97,9. Originally he turns to Alexander to illustrate Alexander’s disagreement with Porphyry on a relatively minor point. But Alexander’s commentary on this lemma, and Eudemus’ parallel to this lemma in his own Physics, turn out to involve a story on which the ‘later ancients’ are responding to Zeno, and on which Plato either was one of the ‘later ancients’ or at least was developing their response to Zeno; and this generates excitement and controversy. For the basic points: Aristotle tells us the ‘later ancients’ wanted to avoid saying that anything they posited as one was also many, and they thought that any non-tautologous application of the copula, like ‘Socrates is white’, would entail that something is both one and many. (Perhaps the worry was that ‘Socrates is white’ and ‘Socrates is musical’ would entail that one thing, Socrates, is two

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things, white and musical, or that ‘Socrates is human’ and ‘Plato is human’ would entail that one thing, human, is two things, Socrates and Plato. Or perhaps they just thought that ‘Socrates is white’ would entail that two things, Socrates and white, are one and the same thing.) At least some of them thought that the problem arose from the copula ‘is’, and tried to rephrase the predications without ‘is’, either by saying ‘Socrates white’ (which is grammatically possible in Greek although not in English) or by replacing the adjective with a verb, roughly ‘Socrates has gone white’. Porphyry and Simplicius do not seem to have more information about these people than they can get from Aristotle’s text. Porphyry and Simplicius suggest that some more radical philosophers – they say ‘the Eretrians’, which probably means just one person, Socrates’ eccentric disciple Menedemus of Eretria – rejected all non-tautologous predication, with or without a copula, and would only assert ‘Socrates is Socrates’, ‘white is white’. However, Porphyry and Simplicius may be influenced here less by primary sources than by Plato’s description, in the Sophist, of some opponents of his who (allegedly) say ‘that it is impossible for the many to be one, and the one many’, and who therefore ‘do not allow us to call [a] human good, but [only to call] the good good and the human human’ (251B6-C2): it may be that nobody actually held the more radical view that Porphyry and Simplicius attribute to the Eretrians. In any case Porphyry thinks that Aristotle uses the discussion of the different varieties of ‘later ancients’ to support his claim that being is said in many ways, both as said of things in different categories and as said of what is actually and what is potentially. Aristotle’s argument would be that since the copula-free paraphrases of predications either fail to produce propositions or else are liable to the same objections as regular predications, and since we cannot simply dispense with all non-tautologous predications like the Eretrians, the absurd conclusion that the same thing is both one and many in the same sense would follow unless being had different senses so that, e.g. Socrates could be one thing in the substance-sense and many things in the quality-sense, or one thing in the actuality sense and many things in the potentiality sense. However, as Simplicius points out against Porphyry, Aristotle does not explicitly say here that distinguishing different senses of being for things in different categories will solve the problem of a single thing’s being predicatively many (indeed, he doesn’t even explicitly say or argue that the later ancients’ solutions to this problem don’t work). Rather, Aristotle stresses that the later ancients could not solve the problem of a thing’s being extensionally one whole and many parts, and that the distinction between being in actuality and being in potentiality allows us to solve this problem. Perhaps he wants us to infer that it is in general pointless to try to

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avoid one-many problems by avoiding the copula, and perhaps he wants us to see that there is a solution by distinguishing senses of being in the predicative as well as the extensional one-many problem; but he does not say so here, and it is not obvious how the solution would work. Simplicius agrees with Alexander against Porphyry that Aristotle does not solve the predicative one-many problem here, and this is his initial reason for citing Alexander. But then new issues arise about Zeno and Plato. First Zeno: Alexander, following Eudemus, suggests that if the later ancients ‘were disturbed lest the same thing should turn out for them to be at the same time one and many’, then it was Zeno’s arguments that had disturbed them, and that their reworkings of language were intended as solutions to Zeno’s arguments. This raises interpretive issues about Zeno, which Simplicius finds more interesting than the later ancients themselves. It is not hard to see why someone could be troubled, as a result of reading Zeno, about a thing’s being extensionally one and many (i.e. one whole and many parts); but why would they be troubled about a thing’s being predicatively one and many (i.e. one subject and many attributes)? As Alexander says, ‘as Eudemus reports, Zeno the companion of Parmenides tried to show that it is not possible for the beings to be many, on the ground that there is no one among beings, and that the many are a plurality of units’ (Simplicius quoting Alexander, 99,13–16). But how did Zeno try to show this, and to what end? As Eudemus himself puts it, ‘Is it the case that this is not one, but that there is some one? For this was an aporia. And they say that Zeno said that if someone could give him an account of what the one is, he would be able to say the [many] things that are. And he [sc. Zeno] was in aporia, as it seems, because each of the sensibles is called many both predicatively and by partition, and because he posited the point as not even one: for what neither makes something larger when it is added, nor makes it smaller when it is taken away, he thought was not something that is’ (Simplicius quoting Eudemus 97,11–16). These texts attribute to Zeno a general strategy for arguing against some domain of entities X that other philosophers, or ordinary people, believe in. Namely: if an X exists, it must be either one or many; but if it is many, it must be composed of ones; but everything among the X’s that is claimed to be one can be shown to be many (or else to be nothing at all); but if something is many, it cannot be one; therefore there is no one among the X’s; therefore no X exists. (The ‘later ancients’ would have been following Zeno in assuming that if something is many it cannot be one, and Aristotle would be showing how to avoid this assumption, by distinguishing different senses of ‘is’, and/or different senses of ‘one’.) Two issues immediately arise: what domains of entities does

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Zeno claim to abolish by this argument-strategy, and what grounds does he admit for concluding that an alleged one is really many and therefore not one? Eudemus claims that Zeno accepted both extensional grounds (having many parts) and predicative grounds (having many attributes) for concluding that a thing is really many. Eudemus may be wrong about this: our verbatim fragments of Zeno’s book show him interested in extensional plurality but apparently not in predicative plurality. But Eudemus might be right: he could read Zeno’s whole book and we cannot, and if Zeno said something like this it would help to explain what the ‘later ancients’ were disturbed about. In any case both Alexander and Simplicius seem to accept that Zeno gave both kinds of grounds for concluding that something is many. But they disagree about what domains of entities Zeno claims to abolish by these means. A Platonist who accepts Plato’s testimony in the Parmenides that Zeno was trying to support Parmenides’ monism (or who simply wants to ‘save’ Zeno) will say either that Zeno was trying to refute the claims of sensible things to be in the strict sense, or else that he was trying to refute the claims of any kind of many whether sensible or not, and that he therefore also had to refute the existence of any kind of one that could be a part of a many. But Eudemus and Alexander, in the texts cited above, seem to say that Zeno tried to show that there is no one, and that therefore there are also no many. Both on this Zeno issue and on the issue whether Plato was one of the ‘later ancients’ whom Aristotle criticized, Simplicius not only criticizes Alexander but tries to reclaim Eudemus for himself against Alexander. This is an instance of Simplicius’ favoured strategy of trumping Alexander with Eudemus or other early Peripatetics: Simplicius insinuates that Alexander’s only reason for saying X was that Alexander was following Eudemus’ authority and read Eudemus as saying X, and then Simplicius argues that Eudemus in fact thought not-X, so that there will be no remaining reason to support Alexander’s saying X. On the Zeno issue, Simplicius says that Alexander was wrong to read Eudemus as saying that Zeno, in the argument that Eudemus describes, was arguing against the many. As we have seen, Alexander says that ‘as Eudemus reports, Zeno the companion of Parmenides tried to show that it is not possible for the beings to be many, on the ground that there is no one among beings, and that the many are a plurality of units’ (99,13–16). But Simplicius says that ‘Zeno’s argument here [sc. as reported by Eudemus] seems to be a different one from the one contained in the book which Plato also mentions in the Parmenides. For there he shows that there are not many, [arguing] from the opposite to come to the aid of Parmenides who says that there is one; whereas here, as Eudemus says, he even abolished the one

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(for he speaks of the point as the one), and he concedes that there are many’ (99,7–12). While Alexander thinks that Zeno argued against the one and against the many as successive stages in the same argument (there can be no many because there is no one), Simplicius thinks that Zeno here only argued against the one and ‘conceded’ that there are many. Simplicius of course accepts on Plato’s authority that Zeno wrote a book in which he defended Parmenides’ monism by deriving absurdities from the hypothesis that there are many, and since he cannot accuse Eudemus of simply making it up, he assumes that Eudemus was reporting something that Zeno did on a different occasion: Simplicius says in a parallel passage of his commentary on Physics 1.3 that Zeno probably raised aporiai against the one as part of a dialectical exercise of arguing on both sides (139,3–5), so that he would not have been committed to his conclusions there, whereas he would have been committed to the conclusion of his treatise that there cannot be many. So Simplicius, without denying Eudemus’ report, blocks it from having any influence on the interpretation of the serious Zeno, the book, which would argue against the many, and argue against any kind of one that could be part of a many (for instance, against ones that could touch each other and must therefore have middles and ends and must therefore be each many), but not against Parmenides’ one rightly interpreted as non-extended. It seems clear that Simplicius has no direct evidence that Zeno’s book did not argue against the one (he says ‘I think that neither in Zeno’s book was there contained such an argument as Alexander says’, 99,17–18).108 Rather, Simplicius says, ‘that Eudemus is not now mentioning Zeno as abolishing the many is clear from his [Eudemus’] own words’ (99,16–17), so that Zeno did not argue against the one in order to establish a premise in his argument against the many, but rather in some separate (and less serious) context: for ‘here, as Eudemus says, he even abolished the one (for he speaks of the point as the one), and he concedes that there are many’ (99,7–12). But in fact it seems clear, from Simplicius’ own citation of Eudemus, that Eudemus thought Zeno in raising aporiai against the one was also raising aporiai against the many: ‘Is it the case that this is not one, but that there is some one? For this was an aporia. And they say that Zeno said that if someone could give him an account of what the one is, he would be able to say the [many] things that are’ (97,11–13). Zeno ‘conceded’ that there are many in the sense that he took it as a premise for a reductio ad absurdum, but we have nothing from Eudemus, or from any other source, to suggest that he conceded the premise in any stronger sense than that. When Simplicius says that Eudemus’ own words show that Zeno conceded the many, it looks as if Simplicius is simply inferring from the fact that Eudemus says that Zeno was arguing against the one.

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Simplicius seems to assume that ‘there is one’ and ‘there are many’ are contradictory propositions, so that whoever argues against one of these propositions is automatically arguing for the other; so that if Zeno argued against the one, and argued against the many, he must have been doing so as parts of two opposite arguments. But it is perfectly possible that, as Alexander says, Zeno first argued that there is no one, and then inferred that there are no many: the theses ‘there is one’ and ‘there are many’ are not contradictories, since there might be nothing at all, and so someone who argues against ‘there is [only] one’ or ‘there is [some] one’ is not automatically arguing for ‘there are many’. It seems likely that Eudemus thought that Zeno was arguing, much as Gorgias did, for nihilism, and that Alexander understood Eudemus correctly. Whether Eudemus’ and Alexander’s Gorgianic nihilist interpretation, or Simplicius’ Parmenidean monist interpretation, is truer to the historical Zeno, is much harder to say.109 Simplicius also argues against Alexander, and tries to reclaim Eudemus against Alexander, on whether Plato was one of the ‘later ancients’ that Aristotle is criticizing, and naturally this is closer to Simplicius’ heart than whether Zeno can be saved for Parmenidean monism. ‘Alexander says that Plato is the person who refashioned the manner of speaking regarding the accidents [i.e. nonessential attributes like “white”], perhaps because Eudemus mentioned this opinion after those who abolished “is” ’ (99,29–31). Aristotle has distinguished between Lycophron, who abolishes ‘is’ and just says ‘Socrates white’, and unnamed ‘others’ who replace ‘is white’ with a verb and says ‘Socrates has gone white’ (where ‘has gone white’ is a single word, a verb in the perfect tense). Eudemus in the parallel passage in his Physics (recorded in Simplicius 97,21–9, with what follows) distinguishes between Lycophron, who abolished ‘is’, and Plato, who thought that ‘is’ followed by a non-substance term does not signify what something is, but rather ‘as “is prudent” signifies being-prudent [the infinitive verb phronein, with no word for “being”] and “is seated” signifies being-seated [the infinitive verb kathêsthai, with no word for “being”], so too in the other cases, even if the names are not available [i.e. even if there is no corresponding verb]’ (97,26–8). So Plato in Eudemus’ account seems to correspond to the ‘others’ in Aristotle’s account who say ‘Socrates has gone white.’ Indeed, Eudemus might reasonably think that Plato was motivated by at least some of the same worries as Lycophron and his friends: notably in the Timaeus Plato thinks that we should avoid saying of a sensible thing that it is fire, since we would then also have to say of the same thing (if not at the same time, then at a later time) that it is air or water. In the Timaeus Plato prefers to call the sensible thing ‘inflamed’ (51B4, using a perfect passive participle reminiscent of the perfect passive verb

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‘has gone white’); elsewhere Plato is willing to say of a body that it is fire, or of a soul that it is prudent, but distinguishes the weaker sense of being fire or being prudent that applies to bodies or souls from the stronger sense that applies only to the Forms. So it is not too surprising that Eudemus substitutes Plato’s name in his parallel to the Aristotle passage, or that Alexander (and Themistius, 7,3–4) thinks that Plato was the person that Aristotle was referring to. But Eudemus says that Plato ‘by introducing the “twofold” [sc. by distinguishing two senses of a term], solved many aporiai’, meaning that Plato distinguished two meanings of ‘is’, or perhaps two meanings of ‘is F’ for some values of F: so apparently for Eudemus Plato would not reject ordinary predications of the type ‘S is F’, but would merely reinterpret them as holding in a weak sense of ‘is’ (or a weak sense of ‘is F’). Simplicius uses this difference to denounce Alexander as misinterpreting Eudemus to fit his own anti-Platonic agenda. Simplicius thinks that it is entirely reasonable to distinguish senses of being here, but that rejecting ordinary predications ‘S is F’ is an extreme and unsuccessful solution to a problem that was elementary for Plato, and he thinks that attributing such a solution to Plato is slanderous. As Simplicius points out (starting at 99,32), Plato in parallel passages of the Philebus, Sophist, and Parmenides makes fun of people, whom he describes as ‘young, and late-learners among the elderly’, who say ‘that it is impossible for the many to be one, and the one many’ and therefore prohibit any non-tautologous predication (these passages are from Sophist 251A8-C6, which Simplicius cites in full at 100,3–15). These seem to be the same people, Lycophron and his friends (and perhaps the Eretrians that Porphyry mentions), whom Aristotle is talking about at the end of Physics 1.2. As Simplicius says, Plato ‘says that the aporia that asks how the same thing among sensibles is both one and many involves nothing serious’ (100,26–7), and Plato solves it by saying that the same sensible thing participates in many Forms: Forms and participation give him the correct solution to the problems that troubled Lycophron and his friends, including Zeno’s problems about extensional plurality. But Simplicius also wants to emphasize that this was not Plato’s more serious contribution: ‘you see that [Plato in Parmenides 129C4-E4, which Simplicius has just cited in full] says that there is nothing surprising in the same thing among sensibles being both one and many, just as [it is nothing surprising if they are] both like and unlike, but that to display such a mixture and blending in the intellectual paradigms of these things – as he himself has done in the Sophist, saying that this is proper to the philosopher – that would be very noteworthy’ (101,10–14). These ‘hard one-many problems’, as modern Plato scholars often call them, concerned with the ways that the paradigms of

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sensible things in nous are themselves one and many, go beyond the domain of physics. But Simplicius takes the opportunity, not just to defend Plato from Alexander’s accusations, but to point to the higher mysteries that the student will learn when he goes on to study Plato, and he quotes large parts of the Sophist and Parmenides in order to whet the student’s appetite. Simplicius does not take these ‘hard one-many’ problems to be simply challenges which the theory of Forms must repel. Rather, they are positive opportunities for discovering the complex internal structure of the world of nous; and, just because they show us that nous is a complex whole of parts, it too must be one by participation, so that we must seek the highest principle, not in nous, but in something entirely simple which must be beyond nous. Studying Aristotle’s Physics will also lead you beyond the bodily world to nous, but most readers think that Aristotle’s nous is entirely simple and is itself the first principle. Simplicius tries to point to hints in Aristotle that there is complexity in nous (that it contains paradigmatically the order of the physical world) and therefore that there must be something even beyond it. But even if Aristotle hints at something beyond, only studying Plato can lead you to knowledge of it.

4.5 Antiphon and Hippocrates of Chios A long section of Simplicius’ commentary on Physics 1.2, 53,30–69,34, is sparked by the lemma 185a14–17, ‘At the same time it is also not appropriate to solve all [eristic arguments], but only the ones someone uses to argue falsely from the principles, and not the others. For instance, it belongs to the geometer to solve the squaring [of the circle] by means of segments, but [to solve] Antiphon’s [squaring] doesn’t belong to the geometer.’ As we have seen, there is an important issue about whether and how to respond to arguments that deny the principles of a science, but the vast majority of Simplicius’ commentary on the lemma is devoted to explaining what Antiphon’s squaring and the squaring by means of segments were, in what sense they did or didn’t proceed from the principles of geometry, and in what sense they were or weren’t fallacious. Indeed, since Simplicius goes through Antiphon very quickly, the vast majority of the commentary is devoted just to explaining the squaring by means of segments, which he attributes to Hippocrates of Chios (as did Alexander, and as does Philoponus). He cites what Alexander says about this squaring, and then he turns to Eudemus’ History of Geometry for what he rightly thinks will be a more accurate account; he does not have a text by Hippocrates himself.

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While Aristotle in Physics 1.2 does not name the person who tried to square the circle by means of segments, in a parallel passage of On Sophistical Refutations 11 he speaks of a pseudographêma (a geometrical fallacy, typically turning on something inappropriate in the diagram,‘diagrammatic fallacy’ in our translation) ‘like that of Hippocrates or (ê) the squaring by means of lunes’ (171b14–16): a lune is the area bounded by two circular arcs, a convex ‘outer circumference’ and a concave‘inner circumference’.110 Modern scholars have tried three interpretations of this passage: perhaps Aristotle is distinguishing Hippocrates’ fallacy (whatever it was) from the squaring by means of lunes; perhaps ‘or (ê)’ is explicative, so that he would be identifying Hippocrates’ fallacy as the squaring by means of lunes; or perhaps, as often happens, ‘or (ê)’ introduces some ancient reader’s gloss which has been wrongly incorporated into the text, so that not Aristotle but this ancient reader would be identifying Hippocrates’ fallacy as the squaring by means of lunes – in which case the gloss might be either right or wrong, and the gloss might already have been in the text by the time Simplicius read the Sophistical Refutations, or it might not have been.111 One motive for reading the Sophistical Refutations passage as doing something other than attributing a fallacious circlesquaring to Hippocrates is that, as is clear from the passages of Eudemus that Simplicius gives us, Hippocrates was an excellent geometer who reasoned carefully and correctly in his squarings of lunes. It is very hard to believe that he also committed a fallacious circle-squaring, and people have tried not only to acquit him of doing such a thing, but also to acquit Aristotle of saying that he did. But on any reading the Sophistical Refutations is attributing some diagrammatic fallacy to Hippocrates; and, since we know from Eudemus that Hippocrates squared three different kinds of lune, and showed that if another kind of lune could be squared then the circle could also be squared, it is beyond belief that ‘the diagrammatic fallacy of Hippocrates’ could have been another fallacy beside ‘the squaring by means of lunes’. It is also, given the close parallel between the Sophistical Refutations and Physics passages, very hard to believe that ‘the squaring by means of segments’ of Physics 1.2, 185a14–17 is not the same as ‘the squaring by means of lunes’ or ‘the diagrammatic fallacy of Hippocrates’.112 Simplicius raises a difficulty, because properly speaking a segment of a circle is the area between a circular arc and a straight line, while a lune is the area between two circular arcs; but Aristotle may be using ‘segment’ loosely, and it is also true that Hippocrates’ arguments (as reported by Eudemus and also by Alexander) make crucial use of segments in the strict sense. The ‘squaring by means of lunes’ would be the diagrammatically fallacious result of putting together Hippocrates’ argument that a lune (one lune) can be squared with his argument that a circle

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plus a lune (another lune) can be squared, which implies that, if that lune can be squared, a circle can also be squared. If we assume that the two lunes are the same, or that the squaring of the first lune will also work for the second, then we have a diagrammatically fallacious squaring of the circle. I think there is no real doubt that this is what Aristotle calls ‘the diagrammatic fallacy of Hippocrates’, and that he is also referring to it at Physics 1.2, 185a14–17. What might be doubted, however, is how strictly Aristotle attributes ‘the diagrammatic fallacy of Hippocrates’ to Hippocrates. In Prior Analytics 2.25 Aristotle tries to explain in terms of his syllogistic what it is to ‘reduce’ a proposition we are trying to prove to another proposition that might be easier to prove: if we are trying to prove that A holds of all C, then it might be useful to prove that A holds of all B, if it is more immediately plausible that B holds of all C than that A does, or if there are fewer middle terms between B and C than between A and C: we can thus reduce the problem of proving that A holds of all C to what might be the easier problem of proving that B holds of all C. Aristotle gives an example: ‘if D is squaring, and E is rectilineal, and Z is circle: if there is only one middle term between E and Z, namely that a circle plus lunes (meta mêniskôn) becomes equal to something rectilineal, that would be close to knowing’ (69a30–34). The thought is: we want to show that the circle can be squared (‘squaring belongs to circle’). We first show that every rectilineal figure can be squared; this reduces the problem of squaring the circle to the problem of finding a rectilineal figure equal to the circle. We then further reduce this problem by showing that there is a rectilineal figure equal to a circle-plus-lunes (probably meaning a circle plus some number of congruent and thus equal lunes – see below for how Hippocrates may have done this). This leaves only the gap between ‘circle’ and ‘circle plus lunes’: if a circle could be shown equal to the circle-plus-lunes (or if a circle plus a rectilineal figure could be shown equal to the circle-plus-lunes, as would happen notably if the lunes themselves were shown equal to a rectilineal figure), then we would know that squaring belongs to circle. It is clear that Aristotle is here thinking precisely of what Hippocrates did to a circle-plus-lunes (in the fourth construction reported by Eudemus or the second reported by Alexander, see below), and that he very reasonably interprets Hippocrates as reducing the problem of squaring the circle, not as pretending to have solved it.113 Hippocrates’ diagrammatic squaring of a lune and his diagrammatic squaring of a circle-plus-lunes do indeed combine to yield a diagrammatically fallacious squaring of the circle, but given that Aristotle in Prior Analytics 2.25 seems to recognize Hippocrates’ careful correct step-bystep reduction of the problem, I think it is likely that he did not think that Hippocrates either was himself deceived by this fallacy or deliberately deceived

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anyone else, although people may have been deceived nonetheless. Aristotle may be using ‘the diagrammatic fallacy of Hippocrates’ as he uses ‘the logos of Heraclitus’, ‘the logos of Parmenides’, or ‘the logos of Protagoras’. These are famous tags associated with each person and arising from something they are supposed to have said (and in Hippocrates’ case to have drawn), but for the purpose of analysing or refuting or discussing different possible interpretations of these logoi it no longer matters whether this person actually said it, whether they were the first to say it, what they meant by it, or whether they believed it or merely said it as part of a dialectical or rhetorical exercise. They have become the common intellectual property of the philosophical school, detached from any necessary connection with the person who, perhaps inadvertently, has given rise to them and whose name has wound up attached to them. Simplicius, in any case, accepts that it is Hippocrates that Aristotle is talking about in Physics 1.2, 185a14–17 with ‘the squaring by means of segments’,114 and in order to fill out what Hippocrates did and so to explain what Aristotle was referring to, he turns first to Alexander and then to Eudemus – not, as elsewhere, to Eudemus’ Physics but to his History of Geometry, where Eudemus apparently described what Hippocrates did within a larger account of the ‘first discoverers’ of different theorems or procedures.115 Rather than objecting piecemeal to things Alexander says, and comparing and contrasting him with Eudemus, Simplicius gives Alexander’s full account of Hippocrates almost without interruptions or criticisms, and then turns to give Eudemus’ full account of Hippocrates, which he rightly thinks is more accurate than Alexander’s. More precisely, the overall structure of Simplicius’ commentary on the lemma 185a14–17 is as follows. First, Simplicius paraphrases (perhaps following Alexander) Aristotle’s text on what kinds of arguments we should or should not reply to (53,27–54,19). Then, since Aristotle mentions Antiphon’s squaring (presumably of the circle) as an argument that contradicts the principles of geometry and which it is not the geometer’s business to respond to, Simplicius explains, following Alexander, what Antiphon’s squaring was (he constructed a square inside the circle, then showed how to expand the square to an octagon, a 16-gon, a 32-gon, etc. all inscribed in the circle and taking up progressively more of the circle’s area; then he assumed that eventually the polygon would coincide with the circle; so, since by elementary geometry any polygon can be squared, he inferred that the circle can be squared), and then Simplicius adds a comment, dissenting from Alexander and following Eudemus, on which principle of geometry Antiphon was contradicting (54,20–55,24). Then Simplicius gives a first account of Hippocrates’ fallacious attempt to square the circle by means of

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lunes, following Alexander, with an evaluative comment on Hippocrates also apparently following Alexander (55,25–57,29). Then Simplicius gives an account of two extremely silly attempts to square the circle, one from decomposing the circle into an infinite sum of lunes (58,1–24; this has no advantages over Antiphon’s decomposing the circle into an infinite sum of polygons, and is apparently just a random guess as to what Aristotle might have meant by the ‘squaring by means of segments’ or ‘squaring by means of lunes’), the other from the fact that ‘circular numbers’ are square numbers (58,25–59,22). At least the second (perhaps also the first) of these reports comes from Alexander, with Simplicius’ added comments, and it is hard to imagine why Simplicius would have thought either of them worth discussing if they were not in Alexander or some similar source who Simplicius thought might have some historical information about what Aristotle was talking about. But the discussion of the silly (alleged) attempt at circle-squaring through ‘circular numbers’ leads to an interesting report of a discussion between Simplicius and his teacher Ammonius on whether the circle has been, or can be, squared (59,23–60,18). And then Simplicius says that since Eudemus says something that disagrees with Alexander’s report of what Hippocrates did, ‘I will set out verbatim what Eudemus says, adding a few things for clarity by reference to Euclid’s Elements, on account of Eudemus’ hypomnematic [i.e. series-of-notes] manner, since in the ancient manner he sets out his results concisely’ (60,27–30). And so, for the remainder of his commentary on this lemma, Simplicius reproduces Eudemus’ text (and, presumably, Eudemus’ diagrams), filling in the steps that he thinks need to be added for the clarity of the argument, often as he says supplying references to Euclid’s Elements, a text written later than Eudemus and a fortiori than Hippocrates and which they certainly did not cite. At the end (68,32–69,34) Simplicius adds a comment on why Eudemus’ report should be preferred to Alexander’s (‘so for what concerns Hippocrates of Chios, we should rather trust Eudemus to know [sc. than Alexander], being closer to the times, and a student of Aristotle’), and on whether Hippocrates committed a fallacy and if so what it was. This text is our single most important document for the history of Greek geometry before 400 bce , and has been intensively studied by historians of mathematics, although naturally they have mainly been interested in the oldest layers, trying to distinguish what parts are Simplicius and what are Eudemus in order to discard Simplicius and get to Eudemus, and then if possible to see through Eudemus’ text (and diagrams) to Hippocrates himself. I will refer the reader to specialist studies, and will not take sides on their disagreements, but will try to give, here and in my endnotes and supplements to the translation, the

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basic mathematical background for understanding what Hippocrates was doing and the philosophical context for why Eudemus and Alexander and Simplicius were interested in it. Simplicius’ treatment of Hippocrates here, besides being a witness to the early history of Greek mathematics and a point of comparison for Simplicius’ treatments of other earlier thinkers, is also a nice example of the mathematical side of fifth-sixth-century Platonic teaching at Athens and Alexandria. All the philosophers of the fifth and sixth centuries ce , following Plato, thought that mathematics was important for philosophers, and helped and encouraged their students to learn it. Thus Proclus in mid-fifth-century Athens wrote an extant commentary on the first book of Euclid’s Elements and an extant outline of the main astronomical hypotheses; Proclus’ successor Marinus wrote an extant introduction to Euclid’s Data; Eutocius, a fellow student with Simplicius of Ammonius in Alexandria (and perhaps Ammonius’ successor as head of the school)116 wrote extant commentaries on much more difficult mathematical texts by Archimedes and Apollonius; and Simplicius himself wrote a now lost monograph on the principles (definitions, postulates, common notions) in Euclid’s Elements. But it is clear that not everyone in these schools was equally excited about mathematics, or equally good at it, and it is striking that manuscript F gives up at 64,19 and skips to the end of the mathematical section at 69,34. The most basic mathematical background information here is why squaring was important in Greek geometry and why someone would be interested in particular in squaring circles and lunes. To square a given figure in the plane is to construct a square equal to the given figure, and to prove that it is indeed equal. Euclid in Elements 1.45 taken together with 2.14 shows how to square any given rectilineal figure – i.e. any plane figure bounded by some number of straight lines, in modern terms a polygon. This is in turn a special case of Elements 6.25, which shows how to construct a figure equal to any given rectilineal figure and similar to any other given rectilineal figure, i.e. having the same size as the former and the same shape as the latter: if the second figure is a square, this is just the problem of squaring the first figure. This is important because the most basic problem of Greek geometry is to measure how big something is. Greek mathematicians do not think you can answer how big some length or area or volume is by giving a number (numbers are discrete quantities, in modern terms positive integers, so multiples of an indivisible unit, while lengths and areas and volumes are continuous quantities, so divisible ad infinitum and without any fixed unit). The only way to determine how big some figure is is to transform it into some other figure whose area is known. That is, we determine the size of figure X by finding a figure Y, of some desired shape, which is equal to

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X. In this sense Elements 6.25 shows how big all rectilineal plane figures are, by showing how to transform any given rectilineal figure into a rectilineal figure of any other given shape. But the standard way to exhibit how large some area is is to transform it into a square; if you can construct a square equal to any given rectilineal figure, you know how big any given rectilineal figure is. It is then natural to try to extend this knowledge, to determine how big nonrectilineal figures are by trying to square them. The most basic non-rectilineal figure in Greek plane geometry is the circle, but already the programme seems to hit a dead end here. Aristotle in the Categories, talking about correlative terms such as knowledge and the knowable, mentions the squaring of the circle as an example of something that is perhaps knowable, but of which there is no knowledge, although perhaps there will be (Categories 7b31–33, quoted by Simplicius here at 69,20–1): evidently he assume that his audience will be familiar with circle-squaring as an example of something that is being sought but has not yet been found, and indeed might not be findable. Simplicius quotes Ammonius as saying that ‘it is nothing surprising that no rectilineal figure has been discovered equal to a circle . . . even though it has been sought by such famous men down to the present’ since ‘the straight line and the circumference are magnitudes of unlike kinds’ (59,23–30); Aristotle himself seems to say in Physics 7.4 that no straight line can be equal to the circumference of a circle (so esp. 248b4–6), which if true would imply that no rectilineal figure can be equal to the area of a circle. Iamblichus, in a piece of neo-Pythagorean one-upmanship, had said that the Pythagoreans had discovered the squaring of the circle (cited by Simplicius at 60,7–11), apparently implying that they had discovered it before Aristotle’s time, so that if Aristotle did not know about it, that was because he had not been initiated into Pythagorean secrets. And, as Iamblichus rightly says, after Aristotle’s time Archimedes and others gave constructions to square the circle (60,11–16).117 But it depends on what you are willing to accept as a circlesquaring. Mêpote, as Simplicius says in response to Iamblichus, ‘all of these [people] used a mechanical construction of the theorem’ (60,17–18) – Archimedes’ construction, for instance, involves a spiral curve generated by uniformly moving a point along a straight line while simultaneously uniformly rotating the line around one endpoint. We might feel that we have really solved the problem only when we have solved it by more elementary methods. Euclid carries out his squaring of a given rectilineal figure using only very elementary methods – what modern writers often describe as ‘straightedge and compass’ (or ‘ruler and compass’) constructions, although no Greek mathematical text has any such phrase and Euclid never mentions either straightedges or compasses.

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And Euclid also uses only very elementary methods in proving that the square he constructs is equal to the original figure – in proving the proposition in Elements 1–2, he deliberately avoids using the theory of proportions and similar triangles, which he introduces only in Elements 5–6. While Hippocrates does not restrict himself to anything like straightedge and compass, and does not try to avoid proportionalities, he does square his lunes using relatively elementary methods (and in fact all the figures that Hippocrates constructs can be constructed by straightedge and compass, although Hippocrates does not seem to have been interested in doing that). As Simplicius rightly sees, this raises the hope that the circle too can be squared by relatively elementary methods: ‘but I said to the teacher’ – i.e. to Ammonius, in response to his suggestion that the circle is unsquarable because straight lines and circumferences are magnitudes of unlike kinds – ‘that if indeed the lune on the side of the square is squared (for this much has been concluded without error), and the lune, being composed out of circumferences, is of the same kind with the circle, what prevents the circle too, as far as this goes, from being squared?’ (59,30–60,1). It is likely that something like this was Hippocrates’ thought too: that if he could square (some) lunes, that would show that there was no in-principle objection to the possibility of squaring the circle. It is clear from Eudemus’ account (and would also follow from Alexander’s account, if Alexander were right) that Hippocrates did indeed square some particular types of lunes, and this would give him some hope for thinking that the same kind of construction would ultimately lead to squaring the circle. There is a dispute about whether Hippocrates falsely thought that he had in fact achieved this goal. It is clear that he showed both that some lunes are squarable, and that if all lunes are squarable, then circles are also squarable. Alexander and Eudemus give disturbingly different accounts of what are supposed to be the same constructions. It seems clear that Simplicius is right that Eudemus’ account is closer to the source, and closer to being historically correct, than Alexander’s. Alexander’s account is probably a simplifying rational reconstruction of what Hippocrates might have done, starting from some basic information about Hippocrates’ squarings (probably all of it derived originally from Eudemus) but without ever going back to check the details against historical evidence. But for all their differences in detail, both Eudemus’ and Alexander’s constructions turn on the same fundamental idea to show why some lunes are equal to rectilineal figures, and are thus squarable since all rectilineal figures are squarable. And a variation of this same idea shows, on both Eudemus’ and Alexander’s accounts, why it can happen that some number of equal lunes plus a

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circle will be equal to a rectilineal figure; and then, if this lune is squarable, it will follow that the circle is equal to the difference between two rectilineal figures, and is thus itself equal to a rectilineal figure, and thus squarable. The basic idea behind Hippocrates’ proofs can be seen as an extension of the way that Greek geometers prove equalities of rectilineal areas, for instance that parallelograms of the same height on the same base are equal even if they have different shapes. The optimal way to show that two plane figures are equal is to show that they are congruent, i.e. that you can pick one up and put it on top of the other in such a way that they will exactly coincide. When the figures F and G have different shapes, a second-best way to show that F and G are equal is to show something like ‘F+A is congruent to G+B, where A and B are congruent and thus equal’ or ‘F-B is congruent to G-A, where A and B are congruent and thus equal’ or ‘F+A-B is congruent to G, where A and B are congruent and thus equal’. Alexander’s reports on Hippocrates’ proofs work this way, where F is a lune (or in one argument a lune plus a circle) and G is a rectilineal figure, but Alexander is probably ‘improving’ on the historical record, and making Hippocrates’ arguments more ‘elementary’ than they actually were. Eudemus’ probably more accurate reports have Hippocrates using a kind of generalization of this argument-strategy, which is less ‘elementary’ but easier to apply to the case of lunes. As I’ve said, Hippocrates does not try, as Euclid does in Elements 1–4, to avoid assumptions about proportionalities. He uses, in particular, the rule that if A and B are similar figures, so that every length in A is to the corresponding length in B in the same ratio r:s, then area A is to area B in the ratio r2:s2. Thus Simplicius, following Eudemus, says that Hippocrates asserted, or even showed, ‘that diameters have the same ratio in power that the circles have’, i.e. that if A is a circle of diameter r and B is a circle of diameter s then A:B::r2:s2, and that Hippocrates then somehow deduced from this that ‘similar circle-segments have the same ratio to each other that their bases have in power’ (61,5–9): circlesegments (figures bounded by a circular arc and by a straight line, the ‘base’) are similar if their circular arcs are the same proportion of the whole circular circumference (both are semicircles, or both are quadrants, etc.).118 So if circlesegment A is similar to circle-segment B and the base of segment A is √m times as long as the base of segment B (or, as a Greek mathematician would say, the base of segment A is m times the base of segment B ‘in power’), then area A is m times area B. So if figure F+A-m·B is congruent to figure G, then areas F and G are equal.119 So if we can convert a lune F into a rectilineal figure G by adding a circle-segment A and subtracting m smaller circle-segments, B1 though Bm, which are congruent to each other and similar to A, where the base of A is √m

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times as long as the base of the Bi, then the lune F will be equal to the rectilineal figure G, and so we can square the lune F. Any lune is a larger circle-segment minus a smaller circle-segment on the same base, which we can call the ‘base of the lune’. The lune has a convex ‘outer circumference’, the circumference of the larger circle-segment, and a concave ‘inner circumference’, the circumference of the smaller circle-segment. The basic idea is to transform a lune into a rectilineal figure of the same area by filling in the concavity – adding back the missing smaller circle-segment – while simultaneously removing several smaller circle-segments inside the outer circumference which will add up to the same area. So the concave inner circumference will be replaced by a straight line inside the circumference (thus beyond the concave boundary of the lune), and the convex outer circumference will be replaced by a polygon inside the circumference (thus inside the convex boundary of the lune). The area added to the lune inside the inner circumference will be equal to the area subtracted from inside the outer circumference if there are m little segments subtracted from inside the outer circumference, and each of them is similar to the segment that will fill in the inner circumference, and the base of the segment that will fill in the inner circumference is √m times as long as the bases of each of the little segments inside the outer circumference. Two of Hippocrates’ arguments as Eudemus reports them follow this strategy exactly, and the other two are more complicated variations on the same basic strategy. I give a sketch of the more particular strategies of Eudemus’ four constructions, and of Alexander’s two constructions, in the Appendix. Alexander’s constructions are generally simpler than Eudemus’ but harder to motivate. That is, while his arguments are easy to follow, and presuppose fewer geometrical propositions and construction techniques than Eudemus’, it is harder to see how anyone would come up with these diagrams in the first place, unless he was starting with something more like Eudemus’ diagrams and working to simplify them. I give details in the Appendix. Alexander entirely omits the particularly complicated arguments of Eudemus’ second and especially third constructions. In Alexander’s arguments the equality between a curvilineal and a rectilineal figure is readily visible: one and the same plane region, added to both figures, will produce figures that can be readily seen to be equal, using only the assumption that a circle with √2 times the diameter has double the area, or that a circle with twice the diameter has four times the area (both cases of Euclid 12.2). Although Alexander does not explicitly tell you how to construct his figures, they can be very easily constructed by straightedge and compass. The preference for ‘elementary’ constructions and proof methods contrasts especially sharply with

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the so-called ‘neusis’ construction in Eudemus’ third lune-squaring, described in the Appendix. Much of the progress of Greek geometry between Hippocrates’ time and Euclid’s involved learning how to avoid such construction techniques where they could be avoided, and to reduce as many proofs and constructions as possible to the most elementary steps. Alexander is presenting an ‘elementarized’ version of Hippocrates’ arguments, avoiding unnecessarily complicated steps, and this is a real advantage. But it falsifies how mathematics worked in the fifth century bce , and so it falsifies the starting point of the historical development of Greek mathematics, and makes it much harder to see which direction this development moved in and why. Alexander does not care. He is not giving a history of mathematics, but trying to explain what Aristotle means about the kinds of diagrammatic fallacies which it belongs to the geometer to solve, like the squaring of the circle by means of segments, and the kinds of diagrammatic fallacies which the geometer cannot and need not reply to, like Antiphon’s circlesquaring. The geometer can see, as someone without at least passive knowledge of geometry could not, that Hippocrates’ squaring of the lune in the first construction depends on particular features of the shape of that lune, which would not apply to the lune that Hippocrates needs to square in order for his final construction to succeed in squaring the circle. In this sense, according to Alexander, Hippocrates has fallaciously assumed that he has proved for all lunes what he has proved only for a particular kind of lune. That illustrates what Aristotle meant about this kind of fallacy, and there Alexander’s interest ends. Simplicius, as usual, trumps Alexander by going back to the old Peripatetics (where he cannot go back to the original source behind them) in the hope of doing more justice to a thinker’s original meaning than the standard handbook treatments do. In so doing, he preserves for us not only Hippocrates’ original constructions, but also an archaic style of geometry that otherwise tends to be eclipsed by the later Euclidean ‘elementarization’. Simplicius does not seem to want to preserve this archaic style. He is aware of it, although he may think of it as a feature of Eudemus’ style rather than (or as well as) Hippocrates’: as he says, ‘I will set out verbatim what Eudemus says, adding a few things for clarity by reference to Euclid’s Elements, on account of Eudemus’ hypomnematic manner, since in the ancient manner he sets out his results concisely’ (60,27–30). Eudemus’ old-fashioned ‘hypomnematic manner’ seems to mean, at least, that he writes as if taking notes for himself, and does not sufficiently flesh out his notes to make them intelligible to others by filling in the missing steps, notably the sequence of inferential steps and their justifications; so Simplicius will do it for him, particularly, as he says here, by showing how Hippocrates’ claims or constructions

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as Eudemus reports them can be justified using Euclid’s repertory of elementary constructions and inferences. Simplicius probably knows that Eudemus was a generation or two older than Euclid, and he certainly knows that Hippocrates wrote long before Euclid, so he knows that even if they might have filled out their arguments, they would certainly not have done so by citing Euclid. But Simplicius is not trying primarily to be faithful to the text of Eudemus, or to the text of Hippocrates (which he does not have), but rather, using Eudemus as a witness, to explain to his readers what Hippocrates accomplished mathematically, and what a geometer would do to show how Hippocrates failed to square the circle. So he cites Eudemus, but also fills in his gaps. Sometimes it is clear in this text what is Eudemus and what is Simplicius, but sometimes it is not. A considerable amount of scholarly effort has gone into sorting out the different layers of the text, yielding some areas of agreement but also some unresolved controversies: I have noted the main issues in endnotes to the translation. Naturally, the modern scholarship on the mathematical passage 53,30–69,34 has been overwhelmingly concerned with reconstructing what Hippocrates was thinking, not what Eudemus or Alexander or Simplicius was thinking; and since probably Alexander and Simplicius do not have any genuine information about Hippocrates that is independent of Eudemus, scholars have mainly been concerned to distinguish Eudemus’ words from Simplicius’ supplements and then to work back (to the extent that they think it is possible) from Eudemus to Hippocrates himself. Even if anyone had been interested in what Alexander was thinking, there is not much problem in distinguishing Alexander’s words from Simplicius’: it is only in citing Eudemus that Simplicius is tempted to supplement, both because Eudemus’ account seems to leap over intermediate steps and because Simplicius is trying to use it (appropriately interpreted) to give a better picture than Alexander’s of what Hippocrates did. Distinguishing Eudemus’ text from Simplicius’ contribution is difficult in some cases, but even once we have done that, distinguishing what is Eudemus’ contribution and what is Hippocrates himself would have to be highly speculative. But these decisions may have important consequences for reconstructing the archaic pre-Euclidean style of geometry that Simplicius preserved by citing Eudemus gagainst Alexander, but which Simplicius’ supplements tend to efface; and we have little control over how much Eudemus may already have ‘modernized’ Hippocrates. Reviel Netz has made a plausible case that Eudemus’ text contains an older stratum, closer to Hippocrates’ original, which does not use letter labels (points called A, B, and so on), and a more ‘modernized’ stratum which does; Netz suggests that this goes with an older way of doing geometry where points

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were less important, and regions of the plane more so, than in most extant Greek geometrical texts. But large parts of the argument, especially in the third lunesquaring (not the squaring itself but the construction of this lune and the argument that its outer circumference is less than a semicircle) would be extremely difficult to carry out without being able to name particular points and the lines between them. So, if Netz is right, it is likely that much of the text is not so much Hippocrates showing something as Eudemus showing what Hippocrates had done (‘I will prove that Hippocrates squared lunes with outer circumferences equal to, greater than, and less than, a semicircle’).120 We have annotated this section of the translation more fully than usual, to help readers follow the mathematical argument. We thank Henry Mendell for supplying the diagrams. We have endnotes noting some scholarly controversies, particularly on how far Simplicius’ quotations from Eudemus extend. For those who wish to pursue the mathematics and the problems of its historical reconstruction further, we note a vigorous scholarly literature.121

4.6 Simplicius and Philoponus on Physics 1.1–2 Philoponus’ commentary on these chapters,122 half the length of Simplicius’ (proem 1,3–3,10; commentary 3,14–50,21), contains many points of contact with Simplicius’. In trying to understand what Simplicius is doing in his commentary on some passage, it is always worth checking Philoponus to see where they agree, where they disagree, where Simplicius adds something on which Philoponus is silent. It seems clear that neither knew the other’s commentary. Where they agree, or where they both cite the same possible solution to some problem even though one of them then accepts that solution and the other rejects it, it is because they are drawing on the same sources. That might be an oral source, namely Ammonius’ lectures on the Physics, which they will both have heard at different times (Ammonius may of course have changed his mind on some issues in between), or it could be a written source, Alexander or Porphyry or Themistius. Or, if X is in both Simplicius and Philoponus, it is also possible that Simplicius read X in some older commentary, and Ammonius also read X in some older commentary and used it in his lectures, and Philoponus took it down from Ammonius. In general, Philoponus consulted far fewer sources than Simplicius, and he is also less inclined to name those that he does consult. Notoriously he includes a great many extracts or close paraphrases from Themistius (his editor Vitelli, in his index, estimates that there are 600 such passages), but he names Themistius only seventeen times. While some parts of

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the Physics commentary are marked by Philoponus’ strong and idiosyncratic opinions, there is not much sign of that in our chapters. Except for a few possible personal contributions (perhaps the theory of indeterminate particulars [10,28– 14,20], the bizarre idea that ‘better known by nature’ means better known to nature itself as a cognizer [12,17–22 and 13,17–14,20],123 the discussion of the relation between body and quantity [38,19–39,29]), Philoponus in these chapters is probably mainly recording Ammonius’ lectures and supplementing them where appropriate from Themistius.124 In general in these chapters Philoponus is presenting one or more of the interpretive options that Simplicius will have been familiar with, and that he may well have heard in Ammonius’ lectures. Comparing the two commentaries on a given passage may shed light on both commentators’ methods of composition, and where Simplicius agrees with Philoponus it shows that he is not making an original contribution, and can lead us to investigate the common source (is it Ammonius, Alexander, Porphyry, Themistius?). Where Simplicius disagrees with Philoponus, or adds something that is not in Philoponus, he may simply be choosing from a pre-existing menu of options, but he may well be adding something distinctive, at least in going back to much older sources (e.g. Eudemus or a pre-Socratic text) where Philoponus and probably most contemporary teachers and commentators were content to repeat information at second (or third, fourth, . . .) hand. Philoponus’ proem is less than a third the size of Simplicius’. He says similar things to Simplicius about the skopos of the Physics, its place within Aristotle’s philosophical teaching, its title (except that Philoponus says nothing about the ‘lecture (akroasis)’ in the title), and its internal division. He does not discuss its (uncontested) authenticity or its utility (on which Simplicius had waxed poetic), and he does not add Simplicius’ appendices on the precision and obscurity of Aristotle’s acroamatic works and the superiority of Aristotle’s physics to the contributions of earlier philosophers. In sum, Philoponus does not make Simplicius’ protreptic-rhetorical effort to convince the reader that the text is very much worth studying and that it needs a commentary. There are some interesting minor divergences on the skopos and division of the Physics and on the other Aristotelian treatises that it is compared to, notably On the Heaven and On the Soul.125 Philoponus apparently follows Porphyry (as Simplicius had in his commentary on On the Heaven) in making the last four books of the Physics the On Motion, where Simplicius’ Physics commentary goes back to the older Peripatetic view on which the On Motion is just Physics 6–8. Simplicius and Philoponus both say that the Physics treats the things that belong to all natural things, but where Simplicius divides these into ‘the principles, and the

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concomitants of the principles’ (3,15–16), Philoponus describes them all as ‘the general concomitants of all natural things’ (2,13–14). Still, they seem to have similar understandings of what these are and of where in the Physics Aristotle treats them; one difference is that while Simplicius describes the transition from Physics 1 to 2 as a transition from the constituent elements of natural things (their matter and form) to their non-constituent causes, Philoponus describes it more simply as a transition from matter to form. In explaining the first lemma of Physics 1.1, both Philoponus and Simplicius introduce Proclus’ distinction between three true causes and three auxiliary causes, both explain the different kinds of causes through the ‘metaphysics of prepositions’, and both explain why Aristotle’s physics uses only four of the six. Both describe both matter and form as elements, so that the elements are auxiliary causes, and both make the same ingenious but unlikely suggestion to read ‘when we recognize its first causes and first principles and as far as the elements’ as ‘when we go both as far up as the highest causes and principles, and also as far down as the lowest, most proximate principles, namely the elements’. Since all this draws on Proclus’ distinctive theory of the six principles, it cannot come from earlier authors like Alexander or Porphyry (although it incorporates Porphyry’s metaphysics of prepositions):126 it must come to our commentators from their teacher Ammonius, who was after all a student of Proclus. But, although the content of their views is similar, Philoponus’ presentation is much less scholarly. He does not cite Porphyry for the metaphysics of prepositions. And while Simplicius cites Eudemus’ and Alexander’s explanations of principle, cause, and element, and attacks them especially for saying that only matter and not form is an element, Philoponus simply takes it as uncontroversial that both matter and form are elements. Philoponus suggests that only sensible things have elements, a view that Simplicius cites from Alexander and attacks. Both Simplicius and Philoponus cite Theophrastus’ argument, filling in a gap in Aristotle, that natural things have principles. Philoponus does not seem to be concerned, as Simplicius is, with Porphyry’s argument that the physicist cannot establish the existence of the principles of his own science. Philoponus does later say, like Simplicius, that if an opponent denies the principles of physics it is up to either dialectic or first philosophy, not physics, to refute him, but Philoponus seems to be thinking of propositional principles (e.g. ‘some things are in motion’) rather than entities. Philoponus cites no one by name in this section except Aristotle and Plato and (once) Theophrastus: in particular, not Eudemus, Alexander, or Porphyry. As we have seen, Philoponus and Simplicius take different paths in the second lemma, in dealing with the apparent conflict between what Aristotle says about

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universals here (they are better known to us but less well known by nature) and what he says about them in Posterior Analytics 1.2 (the reverse). Where Simplicius draws on Proclus’ theory of the three kinds of universals and of wholes (at least, he uses the one-before-the-many and the one-after-the-many, not explicitly the one-in-the-many), Philoponus shows no interest in this and instead develops a theory of indeterminate particulars, and he criticizes an interpretation which resembles Simplicius’ (although differing in making the one-in-the-many, not the one-after-the-many, the universal that is better known to us; the interpretation stated 11,24–12,2, criticized 12,2–13,4): it seems likely that this was something Ammonius had suggested in his lectures on the Physics. Philoponus does not mention Alexander’s proposal, which Simplicius is at pains to refute, that the universals from which we start are universal axioms like the principle of excluded middle. Where Simplicius suggests that ‘the example of the whole and the compound is proper to the present topic [i.e. to coming to know the principles of natural things], but not the example of the universal’ (17,33–4, discussed above), Philoponus is much more interested in universals and particulars, and says almost nothing about wholes in his overall discussion of the second lemma (9,6–19,2). Philoponus does have a paragraph on wholes when he comes to the detailed discussion of problems raised by the wording (19,15–31), but he copies most of this directly from Themistius (2,6–17), and like Themistius he takes Aristotle’s point to be an analogy: as the whole is better known to sensation, so the universal is better known to reason, so the present rational enquiry will start with universals (i.e. for Philoponus, with indeterminate particulars) – there is no further interest in compounds and their analysis into elements. So Philoponus does not, like Simplicius, try to integrate what Aristotle says here with the Theaetetus on elements and complexes and the different kinds of cognition that we can have of them. Instead of resolving the conflict with the Posterior Analytics by distinguishing different kinds of universals and wholes and different kinds of cognition of them, Philoponus interprets ‘better known by nature’ as ‘better known to nature’, and develops a theory of what objects nature (either universal nature or a particular nature) produces, and what nature must know in order to produce them. Both here and in the theory of indeterminate particulars it looks as if he is starting from an incidental remark in Themistius.127 On Aristotle’s division of possible views about the principles (1.2, 184b15– 25), Philoponus gives us something far less comprehensive and far less scholarly than Simplicius’ grand division and harmonization (Philoponus 20,21–25,11 is the overall account, corresponding to Simplicius 20,29–37,9, followed by explanations of details of Aristotle’s wording, Philoponus 25,14–26,20

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corresponding to Simplicius 37,12–46,8). Philoponus does, of course, give a division of possible views about the principles, and supplies names for those who held the different positions (Aristotle here names only Parmenides and Melissus and Xenophanes). He does not tell us how he knows that these people held these views about the principles. He cites a line and a half of Empedocles at 24,20–21 (B115.13–14) – calling it ‘much bandied about’ (poluthrulêton), which does not suggest that he has looked it up in a manuscript of Empedocles, and indeed he misquotes it – and he cites Anaxagoras’ tag ‘all things were together’ (25,1), and that is all. He does not cite Theophrastus, or any of the other Peripatetic authorities that Simplicius brings in, although he must be dependent on them directly or indirectly – indeed, he might be an example of what Simplicius means by ‘people who encounter only reports and write-ups’ (28,33– 4). Philoponus, like Alexander and Themistius, thinks that the Eleatics cannot have thought that their One Being was a principle (since, as Aristotle says, there would be nothing else for it to be a principle of), so that in refuting the view that the principle is one and motionless, Aristotle must have been refuting not the Eleatics but a view that no one actually held (22,23–33). Nonetheless, Philoponus too does a bit of saving and harmonizing. Like Simplicius, he says that Parmenides and Melissus and Xenophanes were doing not physics but first philosophy, i.e. that they were talking about intelligible rather than sensible being, and like Simplicius he harmonizes Melissus with the others by saying that Melissus was talking about infinite power: but of course Philoponus does not supply any quotations as evidence, and he simply identifies Xenophanes’ view with Parmenides’ (all this 22,12–23). He also, like Simplicius, says that Parmenides’ Doxa is Parmenides’ own account of sensible things; and, like Simplicius, he assimilates Empedocles to Parmenides by identifying the Sphairos with the intelligible world, so that there would be two worlds always coexisting, a sensible and an intelligible, rather than cyclical alternation between them. Unlike Simplicius, he explains why there would appear (perhaps even to Empedocles) to be cyclical alternation between the two worlds, namely because each rational soul goes back and forth and so experiences them in succession. His view seems to be that Empedocles’ Love and Strife are not metaphysical causes responsible for the unity of the intelligible world and the disunity of the sensible world, but are simply the forces within the individual soul (identified with the Timaeus’ circles of same and different) which are responsible for the soul’s ascent and descent and so for its encountering the two worlds in succession (24,7–22). Except possibly for this last twist, this must be close to the vulgate Platonic interpretation of Empedocles, probably going back to Porphyry and

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probably transmitted by Ammonius, that Simplicius is trying to improve on (what ‘most people think’, 31,31).128 Philoponus gives only the brief quote about the soul’s exile, and has nothing about a distinction between intelligible and intellectual levels, and so no bridge to Anaxagoras: astonishingly, Philoponus’ account of Anaxagoras here does not mention nous, or the distinction between the pre-cosmic mixture and the cosmos, but only the material ingredients. He attempts no harmonization of the different philosophers’ material principles, and no saving of Democritean atoms. On detailed problems of the division of views about the principles (e.g. why doesn’t Aristotle mention many unmoved principles, is it Democritus or Anaxagoras who said their infinitely many principles included contraries?), and on whether and how to reply to someone who denies the principles of a science, it is often possible to locate Philoponus on the map of views of earlier commentators that Simplicius discusses: Philoponus usually agrees with Themistius, and usually does not help give us a better picture of the available spectrum of opinion than we would have had just from reading Simplicius. On the circle-squarings of Antiphon (who denied the principles of geometry) and Hippocrates (who did not), Philoponus fills in the missing name ‘Hippocrates’, tells an anecdote about Hippocrates, and gives the standard description of what Antiphon did, but his account of what Hippocrates did is very brief and general: Hippocrates squared some lune (i.e. a figure bounded by two circular arcs) but wrongly inferred that he could also square a circle (31,24–7). By contrast, Simplicius gives first a full account from Alexander, and then a more accurate account from Eudemus, of Hippocrates’ constructions: on either account we see that Hippocrates successfully squared at least one type of lune, and also correctly argued that if he could square another kind of lune then he could square a circle. Perhaps Hippocrates wrongly inferred that if he could square one kind of lune then he could square another, or perhaps this was merely something he hoped he would be able to do with more work, rather than something he thought he had already done. But while Simplicius’ account tells us far more about the history of Greek mathematics than Philoponus’, and allows us to see how Hippocrates reasoned, and also perhaps how he went wrong if indeed he did, Philoponus might reasonably reply that none of this helps us understand better the point that Aristotle is making here in the Physics. Although the discussion of circle-squaring is one of very few places where Simplicius explicitly refers to Ammonius’ lectures (59,23–30), Philoponus does not bother to preserve that side of Ammonius’ teaching, if indeed Ammonius discussed the mathematics in the Physics lectures that Philoponus heard (it may instead have been in lectures on the Categories).

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Philoponus and Simplicius disagree about the structure of Aristotle’s arguments against the Eleatics in Physics 1.2, where Philoponus broadly follows Alexander and Simplicius follows Porphyry instead. In Physics 1.3 Aristotle responds to Parmenides’ and Melissus’ arguments, but in 1.2 he just argues against their theses without considering their arguments. Aristotle seems to take the Eleatics to say that ‘all things are one’ or that ‘all is one’: in 185a20-b5 he asks what they mean by ‘are’ or ‘is’ or ‘being’, and argues against their thesis on any answer, and in the remainder, 185b5–186a3, he does the same for ‘one’. Or so Simplicius takes it. Philoponus, however, takes the whole argument to turn on a classification of senses of ‘one’ rather than of ‘being’. If there are beings in different categories, then they can be one only in name; if they all fall into a single category, whether substance or some other category, then they can be one in reality, either universally (as one genus or species) or as a particular one; and if they are one as a particular, then either as continuous, as indivisible, or as one in essence (i.e. as all having the same definition). Where Simplicius sees 185b5 as passing from senses of being to senses of unity, Philoponus (40,11–24) sees it as passing from non-individual to individual senses of unity. Simplicius at 73,2–13 cites this interpretation as Alexander’s, and goes on to criticize it, following Porphyry. (Simplicius says, reasonably enough, that Aristotle would not have bothered considering and criticizing the thesis that all things are only nominally or universally one, since this would immediately imply that they are many.)129 Although Aristotle never mentions Zeno in Physics 1, both Simplicius and Philoponus introduce him into the discussion of the final lemma of Physics 1.2, 185b25–186a3, on the mysterious ‘later ancients’ including Lycophron, who ‘were disturbed lest the same thing should turn out for them to be at the same time one and many’, either because a single subject is also many predicates (Socrates is white and musical) or because a single whole is also many parts. Philoponus takes these people to have been responding to Zeno (43,6–23). As Simplicius makes clear, Alexander had proposed this, following the parallel passage in Eudemus’ Physics. (Simplicius cites Alexander 96,21–30, then trumps him by citing Eudemus, 97,9–99,6, and arguing that he has misinterpreted Eudemus.) Our commentators, starting from Alexander, give their versions of this story, which can be compared in detail. (Themistius does not mention Zeno here and is not Philoponus’ source.) Alexander and Eudemus take Zeno to have been trying to disqualify most of the things that other philosophers claim to exist, by claiming that no such thing can be one, and also that no such thing can be many, because it cannot be composed of genuine ones. They take Zeno to have argued both from pluralities of predicates and from pluralities of parts, so

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that the ‘later ancients’ would have been trying to respond to him on both issues, and both Philoponus and Simplicius seem to accept this interpretation. Both Eudemus and Alexander say or suggest that Zeno argued not only against the many, but also against the one, i.e. that he would have argued not only against the beings alleged by Parmenides’ opponents but also against the being alleged by Parmenides himself. Simplicius gets very exercised about this and tries to respond, presumably because he wants to defend Plato’s report in the Parmenides that Zeno’s aim was to defend Parmenides against his opponents, and perhaps also because he wants to ‘save’ Zeno along with the rest of the Eleatics.130 Philoponus seems unaware of the problem, and takes for granted that Zeno was defending Parmenides (42,9–17), but he also has no compunction in describing Zeno as arguing sophistically against the obvious (42,17–22). Both Alexander (see Simplicius 99,25–31) and Themistius (7,3–4) say that Plato was the ‘later ancient’ whom Aristotle describes as ‘refashion[ing] [his] manner of expression, [saying] not that the human being “is white” but that he “has been whitened” ’. Perhaps Alexander’s thought is that for Plato, when we say of a sensible object X (or perhaps of the Receptacle of the Timaeus) that it is fire, we should instead say, or instead mean, that it is fiery or inflamed by participating in the Form of fire, and that only this Form straightforwardly is fire. But both Philoponus and Simplicius seem to assume that this is a slur on Plato, and they try to show that Aristotle is instead criticizing the same people that Plato himself criticized, notably in the Sophist (Simplicius also cites the Philebus and Parmenides), who do not understand how a single thing can have many predicates (Philoponus 49,20–53; Simplicius 99,25–101,24). Plato thus emerges, not as someone ‘disturbed’ by sophistical arguments, but as Aristotle’s source for a theory of the senses of unity; or, on Simplicius’ account, as someone who solved not just the ‘easy’ problems about how sensible things can be both one and many, but also the ‘hard’ problems about how the intelligibles can be both one and many, so plumbing metaphysical depths that perhaps Aristotle himself did not. These concerns lead Simplicius to a complex and sophisticated discussion of texts of Eudemus, Alexander, Porphyry, and Plato himself, as well as Aristotle, and of the issues they raise about the one and the many. Philoponus does not quote these texts or argue about their interpretation, and his treatment is certainly less sophisticated than Simplicius’. But Philoponus is probably a fair representative of the vulgate Platonist understanding of the early history of the one-many problem which Simplicius is presupposing. Simplicius seeks to defend this understanding against its Peripatetic rival, support it by textual analyses, and add further Platonic metaphysical depth.

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5. The text of Simplicius and our translation In translating Simplicius’ commentary on the Physics, we have started from the only modern edition, that by Hermann Diels in the Commentaria in Aristotelem Graeca published by what was at that time the Royal Prussian Academy of Sciences in Berlin (volume 9, prolegomena and Physics 1–4, 1882; volume 10, Physics 5–8 and indices, 1895). The CAG was one of the Academy’s prestige series of critical editions of historical sources: it came out of a recognition that the Greek commentators were authors deserving of critical editions in their own right, not merely to be culled for ‘scholia’ as they had been in Volume 4 of Bekker’s complete Aristotle (Scholia in Aristotelem, edited by C. A. Brandis, 1836). But the main interest was still to use them as sources for the interpretation of Aristotle, for the history of his texts, and for other Greek writers, especially those no longer extant. The committee in charge of the CAG included Adolf Torstrik as chief editor, and Torstrik did much to seek out manuscripts of the commentators and to collate them himself. Torstrik had apparently chosen Simplicius’ Physics commentary, with its wealth of information about earlier writers, to edit himself as the first flagship volume of the series, but Torstrik died suddenly in 1877, at the age of only 56, and Diels inherited the editorship of the CAG and in particular of Simplicius on the Physics. He also inherited Torstrik’s collations of manuscripts and many proposed emendations, which Diels reports, often but not always accepting them himself.131 Diels was, of course, very interested in critically assessing the sources for the history of early Greek philosophy and science. His Doxographi Graeci of 1879 already drew on his work on Simplicius, and this work would be an important source for his later projects, Parmenides’ Lehrgedicht (1897), the Poetarum Philosophorum Fragmenta (1901), and the Fragmente der Vorsokratiker (first edition 1903). Diels had great sympathy with Simplicius as a scholar devoted to preserving ancient learning as the lights went out around him. By contrast, he had little patience with neo-Platonism, and seems to prefer to think of Simplicius, not as a neo-Platonist, but as someone who merely had the poor judgement to transmit some neo-Platonic sources as well as many other more valuable ones. In the commentary on the first four books of the Physics, Diels reports the Florence manuscript D (Laurentianus 85,2), the Venice manuscripts E (Marcianus Graecus 229) and F (Marcianus Graecus 227), and the Aldine edition a.132 (The manuscript tradition for the commentary on Physics 5–8 is completely different; only codex F and some later copies give [almost] the complete commentary on Physics 1–8.) Diels also gives separate reports on two aberrant parts of Codex E, which he calls Ea and Eb, which I will return to below. He also draws on Torstrik’s

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notes; on earlier scholarship on pre-Socratic texts, which included some emendations to Simplicius; and on Hermann Usener’s and especially Paul Tannery’s notes on Simplicius’ report on the mathematician Hippocrates of Chios, which Diels prints as the ‘Appendix Hippocratea’ to his preface (pp. xxiiixxxi). The work of David Sider and A. L. Coxon on the tradition of some preSocratics, and of Leonardo Tarán and Dieter Harlfinger on Simplicius’ Physics commentary in general, have brought out significant deficiencies in Diels’ editing, including in his reports of the manuscripts, and his edition must be used with caution.133 But there has been no new edition to replace Diels, except for fragments of some pre-Socratics and Hippocrates of Chios, and the forthcoming edition by Pantelis Golitsis and Philippe Hoffmann of the Corollaries on Place and Time from Book 4.134 Golitsis and Lutz Koch have begun work on a new edition of the commentary on Book 1 (and we have sent them our suggested corrections to Diels), but for the moment we have only Diels and the manuscripts. A user of Diels’ edition should be aware of six kinds of problems. There are three kinds of problems in Diels’ reports of the manuscripts in his apparatus: (1) Diels was unaware of another primary witness to the first four books, the Moscow manuscript (State Historical Museum, codex 3649) which, following Harlfinger, we refer to as Mo, written by the Byzantine princess Theodora Rhaulaina or Raoulaina (a niece of Michael VIII Palaeologus, who had reconquered Constantinople from the Crusaders in 1261). Mo often agrees with F, and with E when it is no longer following D, but she often has distinctive readings of her own, which often seem to be right. (2) Because Diels relied on other people’s collations of the codices and did not have the opportunity to check their reports against the codices themselves or photographs of them, he sometimes misinterpreted their reports, and in particular sometimes interpreted silences in their reports as implying that the manuscript agreed with a standard edition. This leads to some cases where he reports the reading of a manuscript in places where it is in fact illegible or missing. Leonardo Tarán in ‘The Text of Simplicius’ Commentary on Aristotle’s Physics’135 describes and discusses these errors. (Such errors in reporting are all too common in critical editions before the mid-twentieth century.) Tarán has also called attention to a particularly unfortunate mistake, where Diels must have misinterpreted his own notes, at 86,27. Here Simplicius is quoting the first half of the first line of Parmenides B6 (for which this passage in Simplicius is the only witness): Diels prints ‘khrê to legein te noein t’ eon emmenai’, and reports that

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the manuscripts of Simplicius have ‘te noein’ but that Simon Karsten in his edition of Parmenides’ fragments emends to ‘to noein’; in fact, however, all collated manuscripts of Simplicius have ‘to noein’ and Karsten emends to ‘te noein’.136 Also at 80,2, quoting Parmenides B8 line 28, Diels reports all manuscripts as having the first word ‘têde’, when in fact both Mo (which Diels did not know) and E have ‘têle’. Diels and all modern editors think that Parmenides actually wrote ‘têle’, but Diels describes this as Scaliger’s emendation, when in fact it has manuscript authority.137 (3) Diels regards codex E as an independent witness, but it is clear that E switches exemplars at 52,18, and it is quite possible that E is a copy of D up to that point; after that it is an independent witness, but belongs to the same family as F and Mo (although F is probably contaminated from a source in the D family; certainly E and Mo are closer to each other than to F). Dieter Harlfinger in his article ‘Einige Aspekte der handschriftlichen Überlieferung des Physikkommentars des Simplikios’138 gives an excellent discussion of the state of codex E and some potentially misleading aspects of Diels’ reports. At some point in codex E’s lifetime, its leaves corresponding to CAG 52,18–72,11 (in the commentary on Physics 1.2) were removed from their natural place near the beginning and were reattached at (almost) the end of the codex; Diels cites this section of codex E in his apparatus to 52,18–72,11 under the siglum Eb, but it has exactly the same status as any other section of E, specifically of the second part of E, after it switches exemplars from D (or a close relative) to the second family. Further complicating the situation, according to Harlfinger’s diagnosis, the exemplar of the second part of E (i.e. the now lost manuscript from which the scribe of E copied the leaves corresponding to CAG 52,18–795,35) had previously suffered a similar dislocation, perhaps in some accident which also led to the loss of the first part of this manuscript and thereby forced the scribe of E to look to another manuscript for 8,32–52,18.139 Two sections of the otherwise lost first part of this exemplar before 52,18, corresponding to CAG 20,1–30,16 and 35,30– 44,19, had been removed and reattached at the end of the exemplar (perhaps they had been rescued from whatever happened to the rest of 1,3–52,18 in this manuscript), and are therefore copied along with everything else into codex E. Of course the first part of E also includes the passages 20,1–30,16 and 35,30– 44,19, copied from a first family exemplar (D or a close relative), so these passages occur twice in codex E, and Diels cites both versions in his apparatus for these passages, citing the first family text from near the beginning of codex E as ‘E’ and the second family text from near the end of codex E as ‘Ea’. (Weirdly, when section 52,18–72,11, ‘Eb’, was reattached near the end of codex E, it was reattached in the

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middle of Ea, specifically in the middle of the second of the two sections that constitute Ea, yielding a bizarre sequence of texts.)140 Thus Ea and Eb are not, as Diels apparently thought, further manuscript sources with their own positions on the stemma of manuscripts: rather, they are both parts of E copied from the same second family exemplar as E’s text of 72,11–795,35.141 In addition to these problems in Diels’ reports of the manuscripts, (4) Diels, and Torstrik before him, were probably too ready to follow the Aldine against the manuscripts, and also too quick to posit lacunae and especially to emend the text, sometimes due to a lack of understanding of neo-Platonism. A lack of understanding of the philosophical issues as Simplicius saw them led Diels in particular to a catastrophic emendation at 18,4 and a false positing of a lacuna and false bracketing of a correct transmitted text at 18,14–15, which managed to make nonsense of a perfectly reasonable paragraph of Simplicius. There are many smaller but similar issues, and a reader or translator should be cautious before accepting one of Diels’ or Torstrik’s emendations. They were careful readers and are generally responding to real difficulties in the text, and their solutions deserve a respectful hearing, but progress often consists in finding gentler solutions. There is also a specific issue in Simplicius’ quotations from earlier authors, especially the pre-Socratics. Diels in principle distinguishes between the question of what some pre-Socratic really wrote and the question of what Simplicius wrote in citing him. (Simplicius will be using a manuscript close to a millennium after the autograph, and he may also misread, quote from memory, or paraphrase.) Diels aims to print what Simplicius wrote, and, if he thinks that the pre-Socratic’s original wording differed from Simplicius’ quotation, to comment on that in the apparatus rather than changing Simplicius’ text. But Diels does not observe this consistently, and in some cases, perhaps from excessive charity to Simplicius, he will print in Simplicius’ quotation a text that is probably right for the pre-Socratic but probably wrong for Simplicius. (5) Diels, like editors of classical texts generally, decides what punctuation to print based on his own judgement of what would make sense. The manuscripts of Simplicius do sometimes contain punctuation, but it is hard to say whether the punctuation goes back to Simplicius’ autograph or was added by later scribes or annotators. And in any case the people who made the collations that Diels used almost certainly did not report the punctuation, so Diels would not have known about it. Diels’ judgement on such matters deserves respectful consideration, but it has no authority, and major interpretive issues may hang on correct punctuation. Simplicius himself explicitly discusses issues of how to

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punctuate Aristotle’s text, notably at 70,3–71,16 on the lemma Physics 1.2, 185a17–20. There is a special issue about quotation marks: it is obviously important to know what Simplicius is saying in his own voice and what he is attributing to someone else, and what he is quoting verbatim and what he is paraphrasing. These are often difficult questions, and Diels’ judgements cannot be taken for granted. It is a bit disconcerting that Diels often includes words like ‘says’ within his quotation marks, when they are clearly Simplicius’ interruptions of the quotation. It is more disconcerting that sometimes Diels prints a left quotation mark with no corresponding right quotation mark, apparently because he is suspending judgement about how far the quotation extends. Christian Wildberg in an important article has described the quotation marks in the Simplicius manuscripts, has argued that in at least some cases they go back to Simplicius himself, and has shown at least one clear case where we can restore sense if we follow the quotation marks in codex A of Simplicius’ commentary on Physics 5–8 and realize that a passage that Diels had printed as if it were in Simplicius’ own voice is in fact a quotation from his adversary Philoponus.142 (6) The lemmas, i.e. the excerpts from the text of Aristotle being commented on, presented above the corresponding commentary, are given more fully in some manuscripts and more sparsely in others. Some manuscripts include the complete text of Aristotle, either in specially demarcated regions of the page or incorporated into the commentary; others apparently assume that you are looking at a separate text of the Physics at the same time. Diels says in his preface (pp. x-xi) that he thinks (he doesn’t say why) that Simplicius himself just wrote the first and last words of each lemma, connecting them with ‘heôs tou’, ‘up to’, the equivalent of the modern ellipsis ‘. . .’, and that later scribes copied in more of the lemma from whatever manuscript of the Physics they had to hand. Diels does not report what the different manuscripts have in the lemmas, presumably because he thinks it would be useless in establishing the text of Simplicius. Perhaps Diels’ general policy is to follow codex E in Books 1–4 and codex A in Books 5–8. But his edition cannot be used as a guide either to what the manuscripts have or to what Simplicius himself wrote (or, rather, directed his secretary to write). It is a serious mistake to speak of ‘Simplicius’ lemmas’ to mean ‘the portion of each lemma that Diels decided to print’: what Diels prints in the lemmas has no authority and is not evidence of Simplicius’ intentions. Simplicius’ commentary could never have been used without the text of the Physics, and it is unlikely that Simplicius intended his readers to be juggling two books at the same time: most likely he expected his secretary to copy out the full text of Aristotle’s lemma, if not in the moment of dictation then in a later fair copy, whether or not the

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secretary actually got around to doing this.143 Later scribes do whatever they find most convenient. We have not pretended to produce a new critical edition of the part of Simplicius’ commentary that we translated. But we have had to translate something, and in each case we have used our best judgement, in the absence of a proper critical edition, on what Simplicius said. In each case where this differs from Diels’ text (and sometimes also where we follow him on points of uncertainty) we have signalled this in the endnotes. We have systematically checked codex Mo (which Diels did not know), and we report the reading of Mo in any case where we differ from Diels. We have in some cases checked Diels’ reports of codices D, E, and F, but not systematically. Sometimes we accept Diels’ or Torstrik’s emendations, sometimes we reject them and go back to a text attested in (some) manuscripts, and sometimes we propose a new emendation. There are places where Diels’ text does not seem to make good sense, and places where he adopts what we find an adventurous emendation to get it to make sense. There are places where he suspends judgement and obelizes, and there are places, not always the same ones, where we would probably do that if we were editing the text. But since we are not editing but translating, and since we cannot translate an untranslatable text and are unwilling to put obeli in a translation,144 we in some cases translate an emendation of Diels or Torstrik, or one of our own, even if we have no great confidence in it. In some cases where we would print something different from Diels if we were editing, we accept his text for the purposes of translation, if the change would make no significant difference to the meaning or translation. Since Diels’ text in the lemmas has no authority, and is generally too short to help the reader make sense of Simplicius’ commentary, which often depends heavily on textual details of the lemma, we always translate the full text of each lemma. Since there is no good reason to think that the lemmas found in any of the diverging manuscripts reflect what Simplicius thought Aristotle said, we have simply imposed a modern standard, Ross’ editio maior of the Physics.145 We note the cases where it emerges from Simplicius’ commentary that he is reading something different, or where he discusses several possible readings. Since Diels’ punctuation has no textual authority, we have (like Diels) repunctuated, and also in particular reparagraphed, as we thought the sense required. We have often preferred shorter paragraphs than Diels, and sometimes we have found that his paragraph breaks are in odd places. We have added short headings in brackets in front of each paragraph, in the hope that this will help

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the reader follow Simplicius’ argument; it helped us. We have paid special attention to the issue of what to put in quotation marks, and how far each quotation extends. We have often disagreed with Diels on this, or followed a more conservative policy on how much to put in quotation marks even if the quotation may extend further. Where we diverge from Diels’ quotation marks we have noted the divergence. We have sometimes been tempted to imitate Diels’ practice of printing a left quotation mark without a corresponding right quotation mark, but we have never actually done so. One thing that we have not done, but perhaps should have, is to follow Wildberg’s lead and study the manuscripts for their punctuation including quotation marks. But Byzantine manuscripts never have enough punctuation for a modern reader, and it is very hard to be sure that a given punctuation mark goes back to Simplicius: a scribe, or simply a Byzantine or Renaissance reader, could easily add such marks, and would have no inhibition about doing so. Where Simplicius quotes, our aim is to determine and translate the text of Simplicius, not the text of the authors he is quoting. Simplicius often cites what seems to be the same passage, e.g. of Parmenides or Empedocles, several times in the Physics commentary (sometimes also in the commentary on On the Heaven), and often he seems to quote it in slightly different ways in the different contexts. When Simplicius in our section of the Physics commentary cites a lost text (typically of a pre-Socratic) that he also cites elsewhere, we flag the other places (whether in our section or not) where he cites what is apparently the same passage. If he seems to quote it in different ways in different places, we have generally not imposed uniformity, i.e. we have not presumed that the differences are due to later scribes rather than to Simplicius himself. This is especially delicate because in some cases there is a question whether it is really the same passage that he is quoting: this is especially an issue with Empedocles, who often repeats the same line or part of a line either verbatim or with deliberate variations in different passages. We leave these judgements to the editors of the preSocratics. While Simplicius is, by ancient standards, very accurate in his citations, he is not perfect, and our strong impression is that he is much more accurate (to the manuscript he was using) in his longer citations, where he is not tempted to rely on memory. We have not found it possible to translate in a way that precisely mirrors the structure of Simplicius’ Greek while also yielding readable and easily intelligible English. We have had to make some compromises. There is no point in publishing a translation if readers can only guess its meaning by trying to reconstruct the underlying Greek. We have sometimes broken long Greek sentences into shorter

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English sentences. We have also sometimes had to translate the same Greek term in different contexts by different English words in order to remain intelligible. The Greek-English Index and English-Greek Glossary will allow the interested reader to trace what we have done. We sometimes add a note when the translation issue seems especially important. I collect the most important issues here. We translate ‘mêpote’ by ‘perhaps’, but we add the Greek word in parentheses to flag it as a technical term, marking Simplicius’ original proposal for solving some problem that he has raised. We usually translate ‘skopos’ by ‘object’, but sometimes ‘aim’ where it means not the object that an art or science or text is about, but the activity that it aims at performing: the reader should bear both meanings in mind.‘Ephistanai’/‘ephistanein’ (with the connected noun ‘epistasis’), marking Simplicius’ observations on the text at hand, which serve to criticize previous interpretations and to give a basis for his own, is usually ‘remark’, ‘observe’, or ‘note’, but it has the overtone of ‘objecting’ against earlier more superficial interpreters. It would be simplest to translate ‘on’ by ‘being’, but because ‘being’ in English is ambiguous between what is and that it is, whereas ‘on’ always means ‘what is’, we cannot always make this translation work. Especially when ‘on’ is the subject of a sentence, we have often translated it by ‘what is’ (‘Parmenides said that what is is one’, but ‘being is said in many ways’); we have often translated the plural ‘ta onta’ by ‘the things that are’. ‘Nous’ is ‘intellect’ only when it means the rational part or power of the soul; when it is the separately existing reason-itself in which souls participate we translate it by ‘reason’ or ‘Reason’, and once ‘intelligence’ to keep a connection with ‘intelligible’ for ‘noêtos’. (It is also once ‘intellectual intuition’ as opposed to deductive knowledge, and ‘attention’ in the phrase ‘prosekhein ton noun’, ‘pay attention’; it can also mean the ‘sense’ or thought or argument of a passage under discussion.) But ‘noein’ has to be ‘think’ or ‘understand’, since the verb ‘reason’ has the wrong meaning and ‘intelligize’ is barbarous, so in some passages we must go back and forth between English words from different roots translating different Greek words derived from ‘noein’. We have tried to flag this where it is important and non-obvious. Similarly, we normally translate ‘apeiros’ as ‘infinite’, since this is what it means, and its opposite ‘peperasmenos’ as ‘finite’, but ‘peras’ has to be ‘limit’; ‘end’ is ‘telos’ or ‘teleutê’, but ‘telikos’ is ‘final’. We prefer to translate ‘hupokeimenon’ as ‘underlying’, but in some contexts there is no choice but to speak of subject and predicate. There is a particular difficulty in translating Greek verbs of knowing: Greek has many verbs of knowing, the distinctions between them do not map neatly onto

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distinctions between different English verbs, and each of these verbs can have stricter and looser senses. The most important point is that ‘epistasthai’, although it can be used for knowing in general, is very often used technically, contrasting with other knowledge verbs, to mean knowing in the strictest and strongest sense. We have translated ‘epistasthai’ by ‘scientifically know’, and the connected noun ‘epistêmê’ by ‘scientific knowledge’ or ‘science’. For a more general sense of ‘know’, Simplicius standardly says ‘gignôskein’, and we have usually translated this by ‘know’ or ‘come to know’. But when, in his discussion of the first lemma of the Physics, Physics 1.1, 184a10–16 (from 11,36 and especially 12,14–13,13), Simplicius discusses the relation between the meanings of epistasthai and eidenai in Aristotle, there is no reasonable alternative to translating eidenai as ‘know’, and so in this passage we translate ‘gignôskein’ as ‘cognize’, or, where ‘know’ is inescapable, have put the Greek in parentheses to flag that ‘know’ here translates ‘gignôskein’ rather than ‘eidenai’. (Since ‘eidenai’ means ‘know’ only in the perfect tense, ‘gignôskein’ is sometimes used to fill in the other tenses, to describe the process whose result is knowledge: the translations ‘cognize’ and ‘come to know’ reflect that meaning.) We normally translate the adjective ‘gnôrimos’, derived from ‘gignôskein’, by ‘known’ or ‘knowable’ according to the context, and the verb ‘gnôrizein’, derived from ‘gnôrimos’, by ‘recognize’: in Aristotle’s commentators, as in Aristotle, ‘gnôrizein’ often seems to be equivalent to ‘gignôskein’ (‘recognize’ to ‘cognize’), but it may sometimes mean to make something gnôrimon (typically, make it gnôrimon to oneself). The word ‘phusis’ and its cognates also cause difficulty: ‘phusis’ can only be ‘nature’, but it is hard to avoid translating ‘phusikê’ as ‘physics’, and this threatens to obscure the connection with ‘nature’. We have preferred to translate all phusis words by nature words: thus ‘phusikê’ is ‘natural science’. We have translated ‘ta phusika’ by ‘Physics’ when Simplicius uses it as the title of a book, by Empedocles or Theophrastus or Eudemus, and ‘ta meta ta phusika’ by ‘metaphysics’ as a discipline and ‘Metaphysics’ as a book title; but the title of the Aristotelian treatise that Simplicius is here commenting on, ‘Phusikê akroasis’, is ‘Lectures on Natural Science’ when we are translating Simplicius (when we speak in our own voice we call it ‘Physics’). We prefer to translate ‘diakrinein’ (with the connected noun ‘diakrisis’) by ‘differentiate’, but have sometimes used ‘distinguish’ or ‘separate’; sometimes diakrinein is a cognitive act, sometimes ‘sunkrisis’ means combining things and ‘diakrisis’ means separating them out into their constituents, and sometimes ‘diakrisis’ means a level of being at which things are differentiated, by contrast with a higher level of being at which everything is unified. ‘Diaphora’ can mean ‘difference’, or ‘differentia’ as opposed to genus, and we have used both of these translations, but sometimes ‘variety’ or ‘variation’: Simplicius says that

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Anaxagoras recognized ‘a threefold variety [diaphora] of all forms’ (34,18–19), meaning that forms exist at three different levels of being. Like most translators of Greek texts, we have given up on finding a single English equivalent of ‘logos’: we have preferred ‘account’, and ‘argument’ when it means ‘argument’, but have resorted to a range of translations as the context seemed to demand. We give references in the endnotes to standard modern editions of the preSocratics and of other authors whom Simplicius cites (e.g. FHS&G for Theophrastus, Wehrli for Eudemus, Smith’s Teubner for Porphyry, the Oxford Classical Text for Plato), and we refer the reader to those editors’ discussions of the problems of establishing and interpreting the text, and of the other ancient witnesses to the text besides Simplicius, where there are any. For the pre-Socratics we always cite DK, but often also more recent editors for a fuller and more upto-date discussion. Some of these editors, notably Coxon for Parmenides and Sider for Anaxagoras, have themselves done good work on the manuscripts of Simplicius, and we are particularly grateful to them. André Laks’ and Glenn Most’s Loeb Classical Library edition of the fragments of early Greek philosophy came out too late for us to use.

Appendix: Hippocrates’ constructions Hippocrates’ first argument, as Eudemus reports it, concerns a lune with a semicircular outer circumference and a quarter-circle inner circumference. He draws three lines: the base of the lune, and the two lines connecting the two ends of the base with the midpoint of the semicircular outer circumference. These three lines form an isosceles triangle, and because any angle in a semicircle is a right angle it is an isosceles right triangle, so that the base of the lune, which is the hypotenuse of the triangle, is √2 times as long as the other sides of the triangle. But the segments which the two short sides cut off from the outer circumference are segments in a quarter-circle arc (each is half of the semicircular outer circumference), so they are similar to the segment cut off by the base and the inner circumference, which is also in a quarter-circle arc. So the segment cut off by the base and the inner circumference, being similar to each of the segments cut off by the short sides, and on a base √2 times as long, will be twice as big in area as each of the segments cut off by the short sides. So if we subtract from the lune the segments cut off by the shorter lines and the outer circumference, and add to the lune the segment cut off by the base and the inner circumference, the area will remain the same. So the lune will be equal in area to the isosceles right triangle.146

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Probably this argument of Hippocrates (which is the simplest, and also the only one that is reported by both Eudemus and Alexander in even loosely related versions) was his original and basic argument, and the others are variations, trying to see how much else he can prove by adapting the same strategy. The second argument in Eudemus, while more complicated, is very close in strategy to the first argument. Here, instead of drawing two equal lines cutting segments from the outer circumference, we draw three equal lines and cut three equal segments from the outer circumference; and we set up the lune so that, instead of the base of the lune being √2 times as long as the lines we draw in the outer circumference, it is √3 times as long as them. And once more we set up the lune so that the segment that fills in its inner circumference will be similar to the segments we are cutting off from the outer circumference. So if we subtract from the lune the segments cut off by the shorter lines and the outer circumference (segments AG, GD, and DB in the diagram), and add to the lune the segment cut off by the base and the inner circumference (segment AB), the area will again remain the same. So the lune will again be equal in area to a rectilineal figure, which this time is a trapezoid (AGDB), bounded by the base of the lune and by the three lines we have drawn in the outer circumference.

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The third argument in Eudemus, which is even more complicated, uses a variation of the same strategy. Once again we divide the outer circumference into three equal arcs and draw three lines cutting off equal segments from the outer circumference (segments EK, KB, and BH in the diagram). But instead of filling in the whole inner circumference with a single segment, we divide the inner circumference into two equal arcs and fill them in with two equal segments (EZ and ZH). We set up the lune so that the two segments that fill in the two halves of the inner circumference (EZ and ZH) will be similar to the three segments we are cutting off from the outer circumference (EK, KB, and BH), and so that the bases of the segments in the inner circumference will be to the bases of the segments in the outer circumference in the ratio of √3:√2, so that each of the two segments in the inner circumference will be one-and-a-half times as big in area as each of the three segments in the inner circumference. So if we subtract from the lune the three segments in the outer circumference (EK, KB, and BH), and add to the lune the two segments in the inner circumference (EZ and ZH), the area will again remain the same. So the lune will again be equal in area to a rectilineal figure, which this time is a complicated concave figure with five sides (KEZHB).

To make each of these constructions work, we need to choose a very specific type of lune. Simplicius, following Eudemus, shows that the outer circumference of the lune is a semicircle in the first case, more than a semicircle in the second case, and less than a semicircle in the third case. Simplicius thinks this is an important correction to Alexander, because Alexander suggests that Hippocrates squared only one kind of lune, and that Hippocrates then argued that if another kind of lune could be squared, we could square the circle. In the two constructions that Alexander attributes to Hippocrates, the outer circumference is always a semicircle. Simplicius objects that ‘Eudemus in his History of Geometry says that Hippocrates showed the squaring of the lune not in the case of the side of the square, but rather, one might say, universally. For if every lune has its outer

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circumference either equal to a semicircle or greater or less, and if Hippocrates squares both the [kind] that has [its outer circumference] equal to a semicircle and the [kinds where it is] greater or less, then, as it seems, he would have shown it universally’ (60,22–7). This suggests that Hippocrates did indeed square the circle; but, as Simplicius ultimately admits, ‘perhaps (mêpote) not every lune universally was squared by Hippocrates’, since even if Hippocrates had given squarings for lunes with every outer circumference (which of course he did not), there would still be infinitely many possible choices of inner circumference; ‘he, however, assumed that the inner circumference was determined: for he assumed that it cuts off a segment similar to the segments constructed on the outer circumference . . . . So not every lune has been squared’ (69,23–34). Eudemus reports a complicated construction which implies that, if one particular type of lune can be squared, a circle can also be squared. It implies this, but this is not what it explicitly asserts: ‘rather’, as Simplicius says against Alexander, ‘he squared both a lune and a circle [taken] together’ (67,11–13), i.e. he showed, without any hypothesis, how to construct a rectilineal figure (and thus a square) equal to a certain lune plus a certain circle. But if a lune plus a circle is equal to a rectilineal figure, then if the lune is also equal to a (smaller) rectilineal figure, then the circle will be equal to the difference between the two rectilineal figures, and it is straightforward to square any such area. While the squaring of the circle plus the lune is complicated (Alexander gives a simpler construction which accomplishes something ultimately equivalent), it too is a variation on the same strategy used in the three lune-squarings as Eudemus reports them. Here is the basic idea: Start from a regular hexagon inscribed in a circle. Take three successive vertices of the hexagon, HQI, and draw the line HI so that we have a triangle. The line HI cuts off a segment from the circle, and the sides HQ and QI cut off two smaller segments, congruent to each other. Construct a lune by taking the segment cut off by HI and subtracting from it a smaller circle-segment on the same base HI, constructed so as to be similar to the little segments cut off from the original circle by the sides HQ and QI. By some elementary geometry the line HI is √3 times as long as the sides of the hexagon, HQ and QI, which are equal to the radius of the circle. We can compare this situation with the first two lune-squarings that Eudemus reports. In the first lune-squaring we had an isosceles right triangle, with two short equal sides and a hypotenuse √2 times as long as the short sides: because of the ratio √2:1, this triangle was equal in area to a lune which adds circle-segments on the two short sides and subtracts a similar circle-segment on the hypotenuse. In the second lune-squaring, we had a

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trapezoid, with three short equal sides and a base √3 times as long as the short sides: because of the ratio √3:1, the trapezoid was equal in area to a lune which adds circle-segments on the three short sides and subtracts a similar circlesegment on the base. In the present case we have instead an isosceles triangle (120°-30°-30°) with two short equal sides and a base √3 times as long as the short sides. In this case, if we turn the triangle HQI into a lune HI by adding circlesegments on the two short sides and subtracting a similar circle-segment on the base HI, then because the segment on the base will be three times as big in area as each of the two segments on the short sides, the lune HI will not be equal to the triangle HQI: rather, the lune will be less than the triangle by an area equal to one of the segments HQ or QI. We can describe this difference in another way: the excess of the circle over the hexagon inscribed in it will be precisely the segments cut off of the circle by the six sides of the hexagon, so the circle will be greater than the hexagon by six times the area of the segment HQ. It follows that the lune HI will be less than the triangle HQI by an area equal to one sixth of the excess of the circle over the hexagon.

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This would be enough to demonstrate Hippocrates’ claim that, if the lune HI can be squared, a circle can also be squared, since the triangle minus the lune plus one sixth of the hexagon is equal to one sixth of the circle. If we can construct a rectilineal figure equal to the lune, then we can also construct a rectilineal figure equal to the triangle minus the lune plus one sixth of the hexagon, and this figure will also be equal to one sixth of a circle; so six such rectilineal figures together will be equal to the circle. But Hippocrates (or Eudemus) finds a more elegant way of displaying the result. He constructs a smaller circle and inscribed hexagon ABGDEZ, with a radius 1/√6 of the original circle and hexagon,147 so that one sixth of the excess of the big circle over the hexagon inscribed in it will be equal to the total excess of the small circle over the hexagon inscribed in it. It follows that the lune HI will be less than the triangle HQI by an area equal to the excess of the small circle over the small hexagon. So the lune HI plus the small circle minus the small hexagon is equal to the triangle HQI, or the lune HI plus the small circle is equal to the triangle HQI plus the small hexagon. Since the triangle plus the hexagon is a rectilineal figure, it follows that the lune HI together with the small circle can be squared, which is the form in which Hippocrates states his result. Again, it follows straightforwardly that if the lune can be squared, the circle can also be squared. Alexander’s constructions are generally simpler than Eudemus’ but harder to motivate. That is, while his arguments are easy to follow, and presuppose fewer geometrical propositions and construction techniques than Eudemus’, it is harder to see how anyone would come up with these diagrams in the first place, unless he was starting with something more like Eudemus’ diagrams and working to simplify them. Alexander entirely omits some complicated arguments in Eudemus’ second and especially in his third construction. Although Alexander does not explicitly tell you how to construct his figures, they can be very easily constructed by straightedge and compass; this preference for ‘elementary’ constructions and proof methods contrasts especially sharply with the ‘neusis’ construction in Eudemus’ third lune-squaring.148 In both of his constructions, Alexander takes a curvilineal figure (a lune, or in his second construction, three congruent lunes plus a semicircle) and shows that it is equal in area to some rectilineal figure by showing that if you add the same figure to both of them, the resulting figures will be equal. By contrast, Eudemus’ proofs that two given figures are equal do not add the same figure to both of them, but rather add equal figures to both of them: for instance, adding to one figure two small congruent segments, and adding to the other figure a larger segment, similar to the small segments but on a base √2 times as long as the bases of the smaller segments. The

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arguments in Eudemus thus depend on the proposition that ‘similar circlesegments have the same ratio to each other that their bases have in power’ (61,6– 7, cited above), which Eudemus says that Hippocrates not only stated but proved. Alexander’s arguments do not need this proposition. (He does still, like Eudemus, need the proposition that ‘diameters have the same ratio in power that the circles have’ (61,8–9), which is only trivially different from Euclid 12.2.) As we have seen Simplicius pointing out, Alexander’s lunes always have a semicircular outer circumference, whereas Eudemus seems to think it is important that Hippocrates squared lunes with outer circumferences greater, equal, and less than a semicircle. In Alexander’s first construction, Hippocrates squares a lune whose outer circumference is a semicircle (arc AEG in the diagram) and whose inner circumference is a 90° arc (arc AG of semicircle AGB) – the same lune as in Eudemus’ first construction. Assuming the lune has been given, we can describe Alexander’s construction as follows: draw in the quadrant of the circle, AGD, bounded by the 90° arc AG. The semicircle AEG and the quadrant AGD overlap in a region, namely the circle-segment cut off by the line AG from the circle AG centred at D (this is a segment on a 90° arc). The quadrant AGD is half of a semicircle AGB whose diameter ADB is √2 times as long as the diameter AG of the semicircle AEG. So semicircle AGB is twice as big as semicircle AEG; so quadrant AGD, since it is half of semicircle AGB, is equal to semicircle AEG. So we subtract both from semicircle AEG and from quadrant AGD the common area, the circle-segment cut off by the line AG from circle AG, the remainders are equal. The remainder from semicircle AEG is the lune AEG, and the remainder from quadrant AGD is the triangle AGD, so the lune is equal to the triangle.

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If we compare this construction with Eudemus’ first construction, we can see where Alexander’s construction might have come from. In Eudemus’ construction we can start with an isosceles right triangle inscribed in a semicircle, its hypotenuse being the diameter of the semicircle: we can take this to be triangle AGB in the diagram from Alexander. In Eudemus’ construction, if we add to the triangle two circle-segments on the short sides, namely the segments cut off by the sides AG and GB from the circle AGB, which are segments on 90° arcs, and subtract a similar circle-segment on the hypotenuse ADB, we will get a lune, whose outer circumference is the semicircular arc AGB and whose inner circumference is a 90° arc on the line ADB. Because the hypotenuse ADB is √2 times as long as the short sides AG and GB, the 90° segment on ADB will be twice as big as the 90° segments on each of the short sides; so the lune we get from the triangle by adding the two small circle-segments and subtracting the big circlesegment will be equal to the triangle. To get Alexander’s construction, start with the same triangle AGB, and add on the short sides, not segments in 90° arcs, but semicircles, the semicircle AEG on side AG and an equal semicircle on side GB; and subtract from inside the hypotenuse ADB, not a segment in a 90° arc, but a semicircle, namely the semicircle AGB. For exactly the same reason as in Eudemus’ construction, the curvilineal figure that we get from the triangle AGB by adding the two small semicircles and subtracting the big semicircle will be equal to the triangle AGB. But now the segment we are subtracting, the semicircle AGB, will not be a part of triangle AGB, but will include all of triangle AGB and extend beyond it to include the 90° segments on the short sides AG and GB. The resulting curvilineal figure will not be a lune; rather, it will be two congruent lunes, one on line AG and one on line GB, each having as its outer circumference a semicircle and as its inner circumference a 90° arc. So these two lunes together will be equal to the triangle AGB; so one of these lunes, say the lune on AG, will be equal to half of the triangle AGB, i.e. to triangle AGD. And this gives us Alexander’s diagram. Alexander’s second construction, like Eudemus’ fourth, is designed to show that, if a particular kind of lune can be squared, a circle can also be squared. Unlike Eudemus’ conclusion, it is not framed to show that a lune plus a circle can be squared, but it could in fact have been reframed in this way, by a device like the one in Eudemus’ construction. We can motivate Alexander’s second construction by seeing it as a variation on his first construction; or we can say that, like his first construction, his second construction too is a variation on, and simplification of, some ideas in Eudemus’ constructions. In Alexander’s first construction, as we have just described it, we start with an isosceles right triangle inscribed in a semicircle – we can think of it as the upper

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half of a square that would be inscribed in the whole circle – and we add semicircles on the two short sides and subtract the semicircle on the hypotenuse. Because the hypotenuse is √2 times as long as the short sides, the semicircle on the hypotenuse is twice as big in area as the semicircles on the two short sides: so the curvilineal figure, consisting of two congruent lunes, that we get by adding the two small semicircles and subtracting the big semicircle, is equal to the original isosceles right triangle. In Alexander’s second construction we can start from a trapezoid inscribed in a semicircle (GEZD in the diagram), which we can think of the upper half of a hexagon that would be inscribed in the whole circle, and we add semicircles on the three short sides GE, EZ, and ZD, and subtract the semicircle on the base GD. Because the base GD is a diameter of the circle, and the short sides are sides of an inscribed regular hexagon and these are equal to the radius, the base is twice as long as the short sides. So the semicircle on the base is four times as big in area as the semicircles on the three short sides, and so the curvilineal figure, consisting of three congruent lunes GE, EZ, and ZD each having as its outer circumference a semicircle and as its inner circumference a 60° arc, that we get by adding to the trapezoid or half-hexagon GEZD the three small semicircles and then subtracting the big semicircle, is not equal to the original trapezoid, but rather is less than the original trapezoid by an area equal to one of the three small semicircles. So the three equal lunes plus the small semicircle AB are equal to the trapezoid; or, equivalently, six equal lunes plus a

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small circle are equal to a hexagon. So if this lune is squarable, the circle is also squarable. If we like we could put this by saying, as Eudemus does, that the lune together with one sixth of the circle, or the lune together with a circle of 1/√6 the radius, can be squared. While this has obvious features in common with Eudemus’ fourth construction, it is also a variation on Eudemus’ second construction, rewritten in the same way that Eudemus’ first construction is rewritten in Alexander’s first construction. In Eudemus’ second construction, we had an trapezoid with three short equal sides and a base √3 times as long as the short sides: because of the ratio √3:1, the trapezoid was equal in area to a lune which adds circle-segments on the three short sides and subtracts a similar circle-segment on the base. In Alexander’s second construction we also have a trapezoid, the half-hexagon, with three short equal sides and a base twice as long as the short sides. What Eudemus’ Hippocrates would do at this point would be to construct a lune by adding to the trapezoid three circle-segments on the short sides, namely the segments cut off from the circle by those three sides of the hexagon, and subtracting from the trapezoid a circle-segment on the base similar to the segments on the three short sides. Because the base is twice as long as the short sides, the segment on the base will be four times as big in area as each of the three segments on the short sides, and so the lune will not be equal to the trapezoid: rather, the lune will be less than the trapezoid by an area equal to the segment on one of the short sides, i.e. to a segment cut off of the circle by one of the sides of the hexagon, or one sixth of the excess of the circle over the inscribed hexagon. (This would give a result very much like Eudemus’ fourth construction, where again a lune – not the same lune! – is less than a rectilineal figure by an area equal to one sixth of the excess of the circle over the inscribed hexagon.) But Alexander gives us a variation on this construction in the same way that his first construction is a variation on Eudemus’ first construction. He adds on the three short sides, not the segments that these sides cut off from the semicircle around the trapezoid (which will be segments in 60° arcs), but semicircles, and he subtracts the semicircle on the base of the trapezoid. As we have seen, the resulting curvilineal figure will consist of three congruent lunes, and it will be less than the trapezoid by an area equal to the semicircle on one of the short sides. The conclusion that if the lune is squarable the circle is also squarable, or that the lune together with an appropriately chosen circle is squarable, follows in a very similar way on either construction.

Notes 1 In this Introduction, ‘I’ means Stephen Menn, and ‘we’ means Stephen Menn and Rachel Barney, except where it includes the reader. 2 Hermann Diels, ‘Zur Textgeschichte der aristotelischen Physik’, Abhandlungen der Königlichen Akademie der Wissenschaften in Berlin, Philosophische-Historische Klasse, 1882, pp. 1–42 (available on the website of the Berlin-Brandenburg Akademie der Wissenschaften). 3 Besides 1117,15–1118,11, the passages are 1146,24–8; 1169,5–9; 1175,26–32; 1178,33–7; 1326,38–1327,11; 1329,38–1330,3; 1330,18–1332,2 and 1334,40–1335,2. All are references to Simplicius’ arguments against Philoponus in his commentary on On the Heaven 1. 4 The best and most accessible statement of the case that the commentary on On the Soul is not by Simplicius, and is instead by Priscian of Lydia, is Carlos Steel’s Introduction, pp. 105–40, in Priscian, On Theophrastus on Sense-Perception, tr. Pamela Huby, with ‘Simplicius’, On Aristotle’s On the Soul 2.5–12, tr. Carlos Steel, in the present series (Ithaca: Cornell University Press, 1997). The case for the attribution of the commentary to Simplicius has been made by Ilsetraut Hadot, most recently in Le néoplatonicien Simplicius à la lumière des recherches contemporaines: un bilan critique (Sankt Augustin: Academia Verlag, 2014), reviewed by Pantelis Golitsis, ‘On Simplicius’ Life and Works: A Response to Hadot’, Aestimatio 12 (2015), 56–82. The controversies between Hadot and her opponents often turn on her claiming that an apparent disagreement between two late ancient philosophical texts can be explained by their playing different and complementary roles within the same overall curriculum. 5 Ilsetraut Hadot, in ‘Recherches sur les fragments du commentaire de Simplicius sur la Métaphysique d’Aristote’, in her Simplicius: sa vie, son oeuvre, sa survie (Berlin: De Gruyter, 1987), pp. 225–45, shows that Michael of Ephesus believed that Simplicius wrote a commentary on the Metaphysics, and that a scholiast (the so-called E3) in the Paris Codex E of the Metaphysics cites, directly or indirectly, a passage which he believes to come from Simplicius’ commentary on Metaphysics 1. The references in Michael of Ephesus may mean nothing more than that he knew the references in the commentary on On the Soul which he thought was by Simplicius, as pointed out by Marwan Rashed, ‘Traces d’un commentaire de Simplicius sur la Métaphysique à Byzance?’, Revue des sciences philosophiques et théologiques 84 (2000), 275–84, reprinted in his L’héritage aristotélicien (Paris: Les Belles Lettres, 2007). The E3

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scholium, although the passage it cites is not very interesting, may point to a real commentary, whether by Simplicius or by the author of the commentary on On the Soul. The references in the commentary on On the Soul are to an interpretation of the Metaphysics more influenced by Iamblichus than would be likely for the genuine Simplicius. For a survey of what we know about these lost works, see the article ‘Simplicius de Cilicie’ (by Richard Goulet and Elisa Coda) in Goulet, ed., Dictionnaire des philosophes antiques VI (Paris: CNRS Éditions, 2016), pp. 341–94 at 361–4 and 390–4. See Edward J. Watts, City and School in Late Antique Athens and Alexandria (Berkeley: University of California Press, 2006), for what we know about the organization of the schools, and for the distinction between junior colleagues or ‘fellows’ (hetairoi) and ordinary students. I think adeôs, here translated literally as ‘without fear’, really means something like ‘with immunity, legal protection’ (LSJ cite uses in this sense). Agathias uses the word ‘adeôs’ twice in this passage, in 2.30.4 (quoted above) for the philosophers being forbidden by the laws to ‘take part in public life (empoliteuesthai)’ adeôs, and at 2.31.4, where the treaty guarantees that the philosophers can return es ta sphetera êthê (to their previous way of life? to their own abodes?) and thenceforth live eph’ heautois (as they wish? as a group? by themselves rather than publicly?) adeôs. Presumably teaching, at least teaching in an institution with as important a civic role as the Platonic school at Athens, would count as empoliteuesthai, perhaps especially insofar as it involved collective worship at the school. There is an English translation by J. D. Frendo, Agathias: The Histories (Berlin: De Gruyter, 1975). The usual view, based on taking eph’ heautois in Agathias 2.31.4 (see the previous note) as ‘by themselves rather than publicly’, is that the treaty guaranteed toleration for the philosophers only as long as they did not return to teaching, but it is not clear that the text means that. Alan Cameron proposed that they went back to Athens and resumed teaching (‘The Last Days of the Academy at Athens’, Proceedings of the Cambridge Philological Society, n.s. 15 (1969), 7–29); Michel Tardieu and Ilsetraut Hadot that they went to Harran, the home of the later ‘Sabaeans’, a tolerated polytheistic minority under Islamic rule (Hadot, ‘La vie et l’oeuvre de Simplicius d’après des sources grecques et arabes’, in Hadot, ed., Simplicius, sa vie, son oeuvre, sa survie, pp. 3–39, English translation in Richard Sorabji, ed., Aristotle Transformed, Ithaca: Cornell University Press, 1990, pp. 275–304); and Golitsis that they each went back to their home cities (‘On Simplicius’ Life and Works’, pp. 62–3). On Simplicius’ reference to future readers (he uses forms of the verb ‘entunchanô’), see Golitsis, Les Commentaires de Simplicius et de Jean Philopon à la Physique d’Aristote (Berlin: De Gruyter, 2008), p. 18, with references n. 36. Golitsis helpfully suggests that Simplicius is writing not, e.g. for hypothetical post-Christians a thousand years in the future,

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but for teachers at Alexandria who might be able to draw on his commentaries in their lectures, as indeed Olympiodorus and Philoponus do draw on Damascius’ commentaries. See Philippe Hoffmann’s discussion of the manuscript attributions in his article ‘Damascius’, in Richard Goulet, ed., Dictionnaire des Philosophes Antiques II (Paris: CNRS Éditions, 1994), pp. 541–93, at 577–9. On Simplicius on harmony see Rachel Barney, ‘Simplicius: Commentary, Harmony, and Authority’, Antiquorum Philosophia 3 (2009), 101–20: as she notes, texts of Aristotle (notably Metaphysics 1, and Physics 1.5) give Simplicius a model for doing the history of philosophy, starting by surveying the views of the ancients and seeing their points of agreement. For some useful skepticism about the attribution to most late ancient philosophers of a harmonizing project, and some useful clarifications about in what senses various projects were ‘harmonizing’, see Golitsis, ‘Syrianus, Simplicius, and the Harmony of Ancient Philosophers’, in Benedikt Strobel, ed., Die Kunst der Philosophischen Exegese bei den Spätantiken Platon- und AristotelesKommentatoren (Berlin: De Gruyter, 2018), pp. 69–99. While Golitsis is right that Ammonius, and following him Simplicius, made stronger claims about the harmony of the ancient philosophers, and especially of Plato and Aristotle, than most other late ancient philosophers had, probably all late ancient philosophers were committed to some programme of harmonization, although they differed about who was to be included and with what reservations. Even Syrianus in his hostile commentary on Aristotle’s Metaphysics 13–14 works hard to harmonize Plato, Speusippus, Xenocrates, and the Pythagoreans, although not Aristotle. Even Proclus, despite his criticisms of Aristotle in his Timaeus commentary, gives a long argument that it can be truly said both with Plato that there are four bodily elements and with Aristotle that there are five (2,42,3–51,1), concluding ‘let so much be said about the harmony (sumphônia) of the philosophers on this [issue].’ On the interpretation defended by the neo-Platonists, the nous which is the demiurge of the Timaeus (and the nous which is the first mover of the heavens in Metaphysics 12) is not a reason or intelligence in the sense of being something like a mind or rational soul, but rather the reason-itself or intelligence-itself in which rational souls participate. The usual English translation ‘intellect’ is dangerously misleading, as it seems to presuppose that this nous is a rational soul, or the rational part or power of a soul. But it is common in speaking of Anaxagoras’ divine cause of order to the world simply to transliterate it as ‘nous’ or ‘Nous’, and in the Introduction I will do that also in speaking about Plato and Aristotle and their interpreters. In the translation we usually say ‘reason’, using ‘intellect’ only when it means a rational soul or rational part or power of a soul. See especially Proclus, in Timaeum 2,92,10–95,11, arguing that if the heavens are moved by nous then they are moved by nature and vice versa. He speaks of Plato

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avoiding both extremes (2,92,24–6) and as anticipating Aristotelian theses (2,93,30– 32); he does not say that Aristotle avoided both extremes or held on to Plato’s doctrine. 14 In many of the passages where it is likely that Proclus is criticizing Aristotle, he does not name his targets, or calls them ‘the Peripatetics’, which allows some ambiguity (Proclus may think that Theophrastus is the founder of the Peripatos, and that the Peripatetics develop Aristotle’s thoughts in an anti-Platonist direction). At in Timaeum 1,2,15–29 he says that ‘the leaders of the school after Plato, not all, but the most exact of them, thought that the physicist should study the form together with the matter, and reduced the principles of bodies to matter and form’: he admits that they ‘mention an efficient cause when they say that nature is a principle of motion,’ but says that they made it not really an efficient cause (but merely a formal or instrumental cause) by denying that it contains within itself a rational plan for the things it will produce, and that they denied that there was any efficient cause for eternal things such as the whole heaven or cosmos. This certainly sounds like Aristotle and allows Proclus to argue that Plato’s criticism of other physicists for citing not true causes but only ‘auxiliary causes (sunaitia)’ applies not only against the pre-Socratics but also against Aristotle. (See below for discussion of Proclus’, and Simplicius’, view that not only the material but also the formal constituents of a thing are merely auxiliary causes, and that only the efficient, final, and ‘paradigmatic’ causes are true causes.) At in Timaeum 1,7,9–16 Proclus explicitly names Aristotle, saying that where Plato considered both the true causes and the auxiliary causes of living things, Aristotle ‘scarcely and in a few cases’ considered the form, and otherwise explained things in terms of the matter. In Timaeum 1,390,3–6, again naming Aristotle, says that because Aristotle does not admit any complex structure in the divine nous, it cannot be an efficient cause to the world (presumably because it cannot contain a rational plan for the world to guide its action) but is only a final cause; similarly in Timaeum 1,266,28–267,1 against the ‘Peripatetics’. On Proclus’ criticisms of Aristotle, see Carlos Steel, ‘Why should we prefer Plato’s Timaeus to Aristotle’s Physics? Proclus’ critique of Aristotle’s causal explanation of the physical world’, Bulletin of the Institute of Classical Studies, Supplement 78 (2003), 175–87, and ‘Proclus’ Defence of the Timaeus against Aristotle: A Reconstruction of a Lost Polemical Treatise’, in Richard Sorabji, ed., Aristotle Re-Interpreted (London: Bloomsbury, 2016), pp. 327–52. 15 See Simplicius, in de Caelo 25–6, discussed below, on the importance of responding to Philoponus’ objections. 16 Syrianus, in Metaphysica 171,9–20 speaks of Plato’s criticism of Parmenides’ monism being directed only towards to phainomenon, the apparent sense. Syrianus says that Parmenides was talking about the intelligible world, and that Plato’s criticisms would indeed refute the apparent sense of Parmenides’ assertions, which would deny

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plurality even in the sensible world. If we can say this about Plato’s criticisms of Parmenides, then, if we decide we want to, we can also say similar things about Aristotle’s criticisms of Parmenides, or about his criticisms of Plato. There is a useful Arabic word, tashbîh, for the error of assimilating divine things to lower things. For some thoughts on the sense in which Aristotle and many Platonists are concerned to avoid tashbîh, while also avoiding the opposite error of taʿ․t îl, i.e. of so restricting what we can say about divine things that there is no content left to our description of them, see Stephen Menn, ‘Self-Motion and Reflection: Hermias and Proclus on the Harmony of Plato and Aristotle on the Soul’, in James Wilberding and Christoph Horn, eds, Neoplatonism and the Philosophy of Nature (Oxford: Oxford University Press, 2012), pp. 44–67. Simplicius is thinking of Metaphysics 12.10, 1075a11–15, where Aristotle says that the good both is in the (immanent) order of the army, comparable to the immanent order of the cosmos, and is the general, comparable to the divine nous, and that the order exists (or is good) on account of the general and not vice versa, so that the general (the divine nous) is the good in the primary sense. But Simplicius construes the passage as saying that the order both is in the army and is in the general, and primarily in the general, in the battle-plan which he communicates to his troops; and this ‘order in the general’, i.e. the providential paradigm in the divine nous for the order in the sensible world, would be what Plato meant by the world of separate forms. As Golitsis notes, the same ingenious misconstrual of this text is in Philoponus, in de Anima 37,20–26 and 63,7–9, apparently following Ammonius, who would be Simplicius’ source as well (see his ‘John Philoponus on the third book of Aristotle’s De anima, wrongly attributed to Stephanus’, in Richard Sorabji, ed., Aristotle Re-Interpreted, pp. 393–412, at 402–3). Proclus, in Timaeum 1,390,3–6 gives the straightforward reading of Metaphysics 12.10, 1075a11–15, and says that Aristotle did not recognize the order in the demiurge, but only the order in the cosmos and the goodness in both; Ammonius would have re- (and mis-)construed the text in order to defend Aristotle against Proclus’ objections. See below for Simplicius on the skopos of the Physics; Philoponus’ formulation is similar. As Golitsis notes (in ‘Simplicius and Philoponus on the authority of Aristotle’, in Andrea Falcon, ed., Brill’s Companion to the Reception of Aristotle in Antiquity, Leiden: Brill, 2016, pp. 419–38, at 430), Simplicius is apparently the only neoPlatonist to call Aristotle ‘divine (theios)’, the epithet given to Plato and Plotinus and Iamblichus, rather than merely ‘daemonic (daimonios)’. Simplicius does this twice, at in Physica 611,8 and in de Caelo 87,26–8. By ‘lemma’ I mean the section of the original text being commented on. I do not mean the parts of that section (sometimes just the beginning, or the beginning and the end) that are present in different manuscripts, or different printed editions, of the

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commentary. Different manuscripts include more or less of each lemma (some consistently including the full text, either in a separate part of the page or just incorporated into the commentary). These cannot all go back to the commentator’s autograph, and it is possible that none of them do. See discussion in Section 5. 22 I will say something below about Simplicius’ introduction to the whole text, and a bit about the function of the digressions. 23 In the first two lemmas of the Physics Simplicius makes an explicit transition from the overall sense of the lemma to particular observations or investigations (10,7–9; 17,31–3). This structure (sometimes called a theôria-lexis structure) is typical of sixth-century ce commentaries arising from lecture-notes (see Karl Praechter’s review of the CAG, translated by Victor Caston in Richard Sorabji, ed., Aristotle Transformed, Ithaca: Cornell University Press, 1990, pp. 31–54 at 47–9, with Praechter’s and Sorabji’s footnotes). But Simplicius is not usually so explicit about this structure. (See note 53 for an issue about whether he uses this structure further on.) The idea behind this structure is to first give an overview of the thought-content of the text at hand, and then discuss particular problems raised by its wording: this takes up both the very old distinction between the thoughtcontent (dianoia or ennoia) and the wording (lexis) of a text, and the Alexandrian grammarians’ practice of raising and solving problems in the texts of the poets. See below for the grammarians’ Homer-scholarship as a methodological model for Simplicius. Simplicius uses the phrase ‘it is worth investigating (axion zêtein)’, verbatim or with trivial variants, at 10,8; 19,1; 19,20; 285,14; 333,21; 358,30; 408,15, etc.; he uses the phrase ‘whether these things are so or otherwise is worth investigating (tauta men eite houtôs eite allôs echei, zêtein axion)’ at 99,24–5 and, verbatim, at 157,24. 24 While Alexander’s commentary on the Physics is lost, significant extracts from it are preserved in scholia to the Physics which Marwan Rashed has edited with a very substantial introduction in Alexandre d’Aphrodise, Commentaire perdu à la Physique d’Aristote (Livres IV-VIII): Les scholies byzantines (Berlin: De Gruyter, 2011). There is often overlap between the scholia and Simplicius, sometimes but not always in what Simplicius explicitly cites as Alexander; Rashed argues, convincingly in my opinion, that the scholia are extracted directly from Alexander’s commentary, not from Simplicius. So the scholia help give us evidence for Simplicius’ methods in using Alexander – what we learn in this way is generally not very surprising given what we can tell just by studying Simplicius’ commentary, but it gives welcome external confirmation. Unfortunately, the scholia draw on Alexander only on Physics 4–8, and most of the individual scholia are fairly short, but Rashed has done excellent work in bringing out their implications. For Alexander’s commentary on On the Heaven we have no such independent source (except for a few pieces quoted by Philoponus), but Andrea Rescigno has given a reconstruction of the commentary to the extent that it is preserved in Simplicius’ commentary, Alessandro di Afrodisia, Commentario al De Caelo di Aristotele, 2 vols (Amsterdam: Hakkert, 2004–8).

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25 Themistius’ works, on the Physics and other Aristotelian texts, are ‘paraphrases’ rather than commentaries (and that is what our manuscripts of Themistius call them) because with rare exceptions he does not talk about Aristotle and his texts, but rather himself speaks as if he were Aristotle, following Aristotle’s text closely and restating his theses and arguments in a more readily comprehensible and less circuitous form for contemporary readers. Unlike Alexander or Simplicius, Themistius does not raise challenges against Aristotle and then offer a solution, or assess different ways of interpreting Aristotle’s text, but it is often possible to see how he must be interpreting Aristotle. 26 The references apparently to Syrianus’ Physics commentary are at 192,29–193,1; 193,16 (to the same passage of Syrianus); 213,24–25; 241,22–27 and 269,10–17. The first of these is immediately followed by a reference to Ammonius, which suggests that at least here Simplicius is following Ammonius’ lectures in referring to Syrianus. The other four references to Syrianus are in the Corollary on Place, 618,25–619,2; 628,25–34; 635,11–14 and 637,25–30: the first of these is cited as coming from Syrianus’ commentary on Laws 10, and that may be the source of the others as well. 27 Aspasius is never cited on Physics 1.1–2: first 131,13–14; then 422,19–26; 436,13–22, more often after this (twenty-nine times in all). In many of these passages (including these first three) it is clear that Simplicius knows what Aspasius said because Alexander cited him in order to disagree (probably in most cases where Alexander agreed with Aspasius he didn’t mention his name). At 559,16–18 Simplicius says that ‘all the commentators I have encountered’ agree on a certain interpretation, but unfortunately he does not list who these are. Simplicius also, of course, cites Philoponus in his commentary on Physics 8, and in his commentary on On the Heaven, but the work he is citing there is Philoponus’ On the Eternity of the World Against Aristotle, not a commentary; Simplicius does not seem to know Philoponus’ commentary on the Physics. 28 Golitsis has argued, in ‘μετά τινων ἰδίων ἐπιστάσεων: John Philoponus as an editor of Ammonius’ lectures’, in Pantelis Golitsis and Katerina Ierodiakonou, eds, Aristotle and His Commentators: Studies in Memory of Paraskevi Kotzia (Berlin: De Gruyter, 2019), pp. 167–94, that some of the commentaries transmitted under Philoponus’ name, including the commentary on Physics 1–2, are Philoponus’ write-ups of his notes from Ammonius’ lectures, with only occasional critical remarks (epistaseis) by Philoponus himself. (See below for a discussion of the meaning of ‘epistasis’.) Thus some parallels between Simplicius’ and Philoponus’ Physics commentaries are probably to be explained by a common source in Ammonius’ lectures rather than by a common written source, although Philoponus is likely to be much more dependent on Ammonius’ lectures, and to make much less independent use of written sources, than Simplicius. Naturally Ammonius in his lectures will himself have made use of earlier commentaries, so it is possible that Simplicius has taken something from

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Alexander’s or Porphyry’s commentary, and that Philoponus has taken it from Ammonius’ lectures which drew on that same commentary. See below for a comparison of Simplicius and Philoponus on Physics 1.1–2. On the neo-Platonic notion of the skopos of a treatise see discussion below. Simplicius at the beginning of his Categories commentary, reviewing the work of earlier commentators, says dismissively that Themistius merely paraphrased to make the diction or expression clearer, whereas the other commentators also cared about the thought-content (in Categorias 1,8–18). He would probably not be much more charitable towards Themistius on the Physics or On the Heaven. And of these five, one is a reference to Porphyry’s breaking up the Physics into Physics 1–4 and 5–8, which Simplicius had already complained about in his proem, and one is to say that Porphyry did not mention something in his synopsis. This is leaving out pre-Socratics, several of whom score over 100, although none score higher than Eudemus. When Simplicius says ‘Alexander says’, ‘Porphyry says’, ‘Themistius says’, there is a very strong presumption that he means ‘he says this in his commentary on the present lemma’. The case is more complicated with Eudemus and Theophrastus, since Simplicius cites more than one of their writings. Still, ‘Eudemus says’ should mean that Eudemus says it in the passage of his Physics corresponding to the present lemma in Aristotle, unless there is some indicator otherwise. Simplicius does not cite Eudemus in Book 7, except at 1036,13–15 to say that Eudemus had nothing corresponding to this book in his Physics. At almost the beginning of his commentary, 2,2–6, Simplicius claims that Alexander is misinterpreting Aristotle in denying that the ‘active nous’ (which Aristotle describes in On the Soul 3.5 as separable and immortal) is part of the human soul, and therefore in denying that any part of the human soul is separable from matter and thus immortal. At almost the end, 1362,11–1363,24, he argues, following his teacher Ammonius, against ‘Alexander and some other Peripatetics’ who ‘think that Aristotle believes in a final and moving, but not an efficient, cause of the heaven’. But there is a twist on this at 258,14–25 where, instead of rescuing Aristotle from Alexander and other Peripatetics who attribute this impious and anti-Platonic opinion to him, Simplicius rescues Alexander himself from those who ‘think that Aristotle did not assert an efficient cause of the universe but only a final cause, and think that this was also Alexander’s view’: and he cites there a passage from Alexander which (assuming it’s authentic) does indeed show that Alexander was willing at least in some contexts to call Aristotle’s God an efficient cause. But this is certainly not the usual representation of Alexander, and Simplicius seems to have forgotten it by the end of the commentary. Simplicius often says that someone says something ‘in these very words’: this is almost always someone he is now about to criticize for saying this. The phrase ‘in these very words’ attests that Simplicius is reporting the passage fairly, not distorting

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for polemical purposes; it may also carry a note of sarcasm (‘he actually said this outrageous thing’). 35 There is also a less striking duplication between 3,16–19, where Simplicius says in his own voice that in Aristotle’s and Theophrastus’ physics ‘the principles are the causes strictly speaking and the auxiliary causes (sunaitia); and the causes, according to them, are the efficient and the final, and the auxiliary causes the form and matter and the elements generally. But Plato adds the paradigmatic to the causes, and the instrumental to the auxiliary causes’, and 10,32–5, where in an extended quote from Porphyry about the kinds of principles and causes according to Plato and Aristotle, ‘Aristotle, having considered only the form which is in matter, said that this was a principle, while Plato, having recognized in addition to this also the separate form, introduced in addition the paradigmatic principle.’ The two passages have important differences: Porphyry does not say that the immanent form (and the matter and instrument) is only an auxiliary cause, which seems to be an innovation of Iamblichus (at Simplicius, in Categorias 327,6–17) later taken up and systematized by Proclus; and Porphyry is embedding all this in a ‘metaphysics of prepositions’, which is not mentioned in the passage at 3,16–19. But the strange picture of Plato starting with Aristotle’s four causes and then adding to them, reversing the historical order, is in both passages, and it very much looks as if Simplicius at 3,16–19 is drawing on the same passage of Porphyry that he quotes at 10,32–5. 36 Diels says (CAG 9, p. v, n. 1) that Alexander’s commentary on the Physics is lost because the Byzantines would not have kept both his commentary and Simplicius’, particularly since ‘[Simplicius’] summary of the main points is almost always from Alexander, although usually his name does not appear, except where Simplicius sees fit to disagree with him. Often he signals that things he has previously taken from elsewhere, i.e. from Alexander, are such [i.e. were taken from a source], [not when he first states them but] in order to set out his own interpretation starting from that mêpote [“perhaps”]. Sometimes, although less often, he uses Themistius in the same way’ (‘cum praesertim Simplicius optima quaeque ex Alexandro iure tralaticio transcripsisset. nam observandum est summam capitum fere ubique esse Alexandream, cuius plerumque nomen, nisi ubi dissentire placebat Simplicio, non apparet. haud raro aliena, i.e. Alexandrea antea repetita esse ita significavit, ut suam interpretationem a μήποτε illo exorsus contra poneret. eadem ratione quamvis minus frequenter Themistio abutitur’). I don’t know why Diels mentions Themistius but not Porphyry, whom Simplicius uses more often. Diels is making an important point about ‘that mêpote’, for which see discussion below. Rashed says of Simplicius that ‘his commentary on the Physics is an edition ad usum Delphini of Alexander’s [commentary], on principles dictated by the creed of Syrianus, Proclus and Damascius’ (‘son commentaire à la Physique est une édition ad usum Delphini de celui d’Alexandre, aux principes dictés par le credo de Syrianus, Proclus et

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Damascius’, Alexandre d’Aphrodise, Commentaire perdu à la Physique d’Aristote, p. 29). ‘Ad usum Delphini’ means something like ‘bowdlerized, purged of offensive or corrupting passages’, from a series of editions of classical texts ‘for the use of the Dauphin’. Only Alexander’s commentary on Prior Analytics 1, about 9:1, rivals Simplicius. The On Sensation and Prior Analytics 1 are fairly short texts. Very few people could carry out that scale of commentary for a work as long as the Physics; and, if the commentary was given as lectures, very few students could endure it. To repeat, Simplicius’ Physics commentary is the single longest extant text of Greek antiquity and was not given as lectures. But Simplicius’ commentaries are much longer on Physics 1, 4, and 8 than on the other books. On this see Barney, ‘Simplicius: Commentary, Harmony, and Authority’. This is particularly important since Plotinus had been accused of copying Numenius: Longinus had at one point been sympathetic to that charge, and Porphyry is citing this passage partly to show that Longinus had by this point dismissed it. There are other texts praising someone for the multitude of problems they consider, and for their not resting content with easy solutions: this is the sort of originality that late ancient philosophers value. Simplicius praises Damascius in this way at in Physica 624,37–625,3 and 795,11–17 (which notes Damascius’ raising problems against Proclus). Besides Damascius’ Aporiai and Solutions on the First Principles, his commentaries on the Philebus and Parmenides are largely considerations of problems raised against Proclus’ commentaries on those texts. On the relation of Plotinus’ treatises to his teaching, see Paul Kalligas, The Enneads of Plotinus: A Commentary, vol.1 (Princeton: Princeton University Press, 2014), pp. viii-ix. See Golitsis, Les Commentaires de Simplicius et Jean Philopon à la Physique d’Aristote, for a list and detailed analyses of such embedded essays. The word ‘Corollary’ here is apparently Diels’ innovation, not in the sense of a corollary of a theorem, but something like a ‘crown’ of the previous discussion – ‘corollary’ was standardly used this way notably in earlier German academic dissertations. Earlier writers refer to these parts of Simplicius’ text simply as digressions. On Simplicius’ motives in replying to Philoponus in defence of the ‘pious conception of the universe’ see especially Philippe Hoffmann, ‘Simplicius’ Polemics: Some aspects of Simplicius’ polemical writings against John Philoponus: From invective to a reaffirmation of the transcendency of the Heavens’, in Richard Sorabji, ed., Philoponus and the Rejection of Aristotelian Science (London: Duckworth, 1987), pp. 57–83. I am taking the word ‘vulgate’ from discussions of ancient Homer scholarship, where it means the text of Homer in common use, which individual Homer scholars either accept or modify in particular passages (by deleting a line, by repunctuating, by

Notes to pp. 19–21

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following a minority report of the text or proposing an emendation); where they change the vulgate text, they note and defend their changes. Simplicius takes up all the grammarians’ techniques of problem-solving, including repunctuating: see, in the section we translate, his discussion of different possible punctuations of Physics 1.2, 185a17–20 (70,5–32), and similarly, beyond our section, on 2.7, 198b4–5 (368,13–17) and 3.1, 200b26–8 (399,19–400,8). But he calls Theophrastus, not Eudemus, ‘the leader among Aristotle’s students’ (964,29–30): but perhaps this is praising Theophrastus as a philosopher rather than for his fidelity to Aristotle. In separate texts Simplicius calls both Aristotle (in de Caelo 378,20–21) and Xenocrates (1165,34 and in de Caelo 12,22) Plato’s most gnêsios student. Notably at 99,7–31 Simplicius argues that Eudemus does not say what Alexander says he says about Zeno and Plato; Simplicius insinuates that Eudemus was Alexander’s only source here, and that Alexander’s interpretations of Zeno and Plato are due entirely to his misreadings of Eudemus. With some material from other sources, and Simplicius’ comments on it, at 58,25– 60,18. I don’t mean that Simplicius merely cites authorities: he adds his own reflections on Aristotle’s probable meaning and on what Hippocrates probably did and didn’t accomplish, 68,34–69,34. There is a similar comment on Eudemus knowing Aristotle’s thought better than the commentators, 991,27–9. In de Caelo 488,18–24. Simplicius also cites a later source here, Sosigenes, and it is possible that his knowledge of Eudemus’ History of Astronomy comes entirely through Sosigenes. Simplicius’ other references to Eudemus in this commentary are probably also to the History of Astronomy. Proclus in his introduction to his commentary on Euclid’s Elements I makes heavy use of Eudemus’ History of Geometry (alongside Iamblichus); Damascius in On First Principles makes similar use of Eudemus’ History of Theology. On Eudemus’ histories of the sciences see Leonid Zhmud, The Origin of the History of Science in Classical Antiquity (Berlin: De Gruyter, 2006). Eudemus seems to have been a pioneer as a historian of science; he seems to have been particularly interested in deciding who was the ‘first discoverer’ of this or that. Strato fifteen, Nicolaus five, Andronicus and Adrastus each four, Boethus three, Aristoxenus only twice and only as an example of ‘musician’, Dicaearchus never; Damas, if he’s a Peripatetic, once. At 3,4–5 Simplicius switches from saying what ‘he’ (Aristotle) has done in various treatises to saying what ‘they teach . . . in the treatises On Minerals’, where ‘they’ must mean ‘Aristotle and Theophrastus’ (see our note in the translation): he keeps the plural at least through 3,10, speaking of what ‘they’ have taught about animals and about plants.

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51 Likewise Themistius says that Book 2 of Theophrastus’ On the Soul is Book 5 of his Physics (Themistius, in de Anima 108,11). The issue is presumably similar to the issue about Aristotle’s Physics and On Motion, and was presumably also discussed by Andronicus. 52 For issues about the titles of Theophrastus’ physical and doxographical works see Robert Sharples, Theophrastus of Eresus: Sources for his Life, Witings, Thought and Influence, Commentary Volume 3.1 (Leiden: Brill, 1998), pp. 1–13. The book that Simplicius is citing here may well be the book cited by other people as ‘Physical Opinions (Phusikai Doxai)’ or ‘Opinions of the Physicists (Phusikôn Doxai)’, but Simplicius thinks the title is Phusikê Historia, and the parallels with Eudemus show that this does not mean simply ‘natural history’ = ‘physics’ but rather ‘history of physics’; when Simplicius wants to cite Theophrastus’ Physics, he does. Simplicius’ reference at 115,12 to Theophrastus’ Phusikê Historia seems to be taken from Alexander, but Simplicius often tries to check up on Alexander’s references to the early Peripatetics: in the same passage he says that he can’t confirm Alexander’s reference to Eudemus, and that Eudemus says something different elsewhere. At 166,17 he cites Book 2 of Theophrastus’ On Anaxagoras. At in de Caelo 294,33–295,1 he says that he will cite from Aristotle’s On Democritus: this is otherwise unattested, but Diogenes Laertius 5.49 lists a book of Theophrastus with that title, so perhaps it is the same treatise which has been differently attributed. At 22,26–23,14, where Simplicius apparently claims to be following Theophrastus on Xenophanes, the interpretation presented seems to be very close to that in the Pseudo-Aristotle On Melissus Xenophanes Gorgias (which most modern scholars think is badly at variance with the historical Xenophanes), and it may be that that is Simplicius’ source and that he thinks it is by Theophrastus. At in de Caelo 266,25–6 he says that ‘some people’ attribute the (Pseudo-Aristotelian) On Indivisible Lines to Theophrastus. On Simplicius’ use of Theophrastus, particularly at in Physica 28,4–31, see also Malcolm Schofield, ‘Leucippus, Democritus and the οὐ μᾶλλον Principle: An Examination of Theophrastus Phys. Op. Fr. 8’, Phronesis 47 (2002), 253–63. 53 But see our note in the translation at lemma 184b15. It is probably better to take what Diels prints as an extremely long commentary (20,29–37,9) on a very short lemma 184b15 (which would be the third lemma of the Physics as a whole) to be rather Simplicius’ discussion of the overall sense of a longer lemma 184b15–22 (or possibly even 184b15–25). What Diels prints as commentaries on the fourth, fifth, sixth, and seventh lemmas of the Physics (and possibly also on the eighth) would then be Simplicius’ investigations of particular problems arising from details of the wording in different parts of this longer lemma. Simplicius would thus be following the so-called theôria-lexis structure which he also follows in his commentary on the first two lemmas: see note 23. In the transition to what Diels prints as the fourth lemma (184b15–16 – which would include Diels’ whole third lemma as a part!),

Notes to pp. 22–3

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Simplicius says ‘but now we must take up Aristotle’s text (lexis) again and articulate the things that are said in it’ (37,8–9, picking up the promise at 22,20–1, cited above). This suggests, not that we are proceeding to a new lemma, but that we are going back to consider the details of the lemma whose overall sense we have already been discussing. And most of 22,22–28,31, divided into pieces, appears as fragments of Theophrastus in DG and in the now standard collection of Theophrastus’ fragments, FHS&G. Simplicius very parenthetically inserts Aristotle himself and the Stoics into the classification. The only work of Nicolaus that Simplicius knows is On the Gods (which he cites for the views of Xenophanes and Diogenes of Apollonia), and he seems to know him only through Porphyry (see 149,11–18 and 151,20–4), who may have cited him as a Peripatetic counterweight to Alexander. Nicolaus wrote a Universal History in 144 books, and perhaps he, like the somewhat earlier Diodorus Siculus in his Library of History, began with an account of the gods. If so, Nicolaus would have reported there the different philosophers’ opinions about the gods, and connected them with the first formation of the universe. Simplicius applies the verb historein to many Peripatetics: Adrastus 4,12–13, Eudemus 7,14 and 99,13–14, Theophrastus 25,6 and 26,7 (with a verbal prefix, prohistorein), Nicolaus 25,8–9 and 151,21–2, Alexander 67,7–8 and 115,11, besides the mentions of the Histories of the different sciences by Eudemus and Theophrastus. The verb apomnêmoneuein, which we have translated ‘record’ (said of Nicolaus 23,14–16, Alexander 26,13–14 and 43,3–4, and Aristotle himself 44,13–14 and 116,18–20), seems to be synonymous with historein. With either verb, some philosopher is reporting the opinions or arguments or writings of some earlier thinker. The reporter is usually a Peripatetic, but once each Porphyry (247,31) and the neo-Pythagoreans Moderatus (230,26) and Dercyllides (256,34), all reporting Pythagorean teachings or Plato’s unwritten doctrines, and once Plato himself in Laws 10 reporting the views of the pre-Socratic physicists (358,12–16); Simplicius also describes some of his own activity this way. Simplicius also says that Aristotle proceeds ‘historically (historikôs)’ in the History of Animals but ‘causally’ in the Parts and Generation and so on (3,6–9), which may give some help on what he means by historia, and what it contrasts with. Thus Simplicius says that we should be grateful even to people who only raised objections against the Categories, like Lucius and Nicostratus, even if they did so maliciously, because some of their aporiai have real content and because they have given those who have come later occasion for solving the aporiai and discovering ‘many other beautiful theorems’ (in Categorias 1,18–2,2). Late ancient authors distinguish what might loosely be called ‘formal causes’ into the ‘formal cause’ properly speaking, the form immanent within the thing that comes-tobe, and the ‘paradigmatic cause’, a separately existing model in imitation of which the

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thing comes-to-be. Platonic Forms, if there are any, would be paradigmatic causes of sensible things. I will generally follow the usage of the late ancient authors and say ‘formal cause’ to mean the immanent form. Modern interpreters disagree about whether the ‘Receptacle of becoming’ which Plato posits at Timaeus 48E2–49A6 as existing before the sensible world is an empty space in which the demiurge places sensible things, or the matter out of which he makes sensible things in imitation of the Forms, or shares aspects of both space and matter, but late ancient authors take it to be straightforwardly a material cause. At 43,3–23, when he comes to the same passage in Alexander’s commentary, Simplicius repeats the citations of Plato, to the same effect, at somewhat greater length. Here Simplicius is showing, not just that Plato is not the person Aristotle is criticizing, but also that Plato’s criticisms of earlier thinkers are the source of Aristotle’s criticisms of the same thinkers. Naturally Simplicius in general likes finding Platonic anticipations for things in Aristotle. He also argues that Plato’s criticisms of Parmenides are the model for Aristotle’s criticisms of Parmenides: this is the reason for his long citation from the Sophist at 89,5–90,20 (see 88,30–89,5). Simplicius would also presumably say that Aristotle’s criticisms of the Forms are derived from Plato’s criticisms of the Forms in the Parmenides, and that, like Plato’s criticisms, they are meant to be resolved by giving an appropriate ‘higher’ conception of the Forms. See below for discussion of the issues at Physics 1.2, 185b28–32, and of ‘easy’ and ‘hard’ one-many problems in Plato. He also cites verses of Xenophanes, perhaps at first hand. What is sometimes described as Simplicius’ quotation from Anaximander at 24,16–21 (esp. 24,19–21) is in indirect discourse, so certainly not a verbatim quotation, and is probably from Theophrastus. He has no first-hand knowledge of Anaximenes or Heraclitus or Democritus (or, of course, Thales, from whom even Aristotle had no texts). The text of the Pythagorean ‘Timaeus’ that he cites is a forgery, as is the text of ‘Archytas’ that he cites, perhaps only from Iamblichus, in his Categories commentary. In some Eleatic cases (Melissus 103,13–104,15, a bit of Parmenides in prose 31,3–7, a dialogue between Zeno and Protagoras 1108,18–28) he seems to have mistaken a later reconstruction for the original. But generally, Simplicius’ judgement about these things is pretty good. He cites very little of the Pseudo-Pythagorean texts, and his main source for Zeno is authentic, unlike the ‘Forty Logoi of Zeno’ which Proclus cites and seems to have been influenced by. Simplicius does cite, at second hand, some fake letters between Aristotle and Alexander the Great, 8,20–30. Some of these texts come up earlier in Simplicius’ commentary on On the Heaven, notably on 1.3 on different pre-Aristotelian views on whether the world has come-to-be, and on 2.2 on Aristotle’s criticisms of Pythagorean cosmology. See discussion below: as we will see, Philoponus gives this default interpretation, probably following Ammonius.

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63 Simplicius at 6,31–8,15 tells the whole story of the development of philosophy in Greece up to the time of Aristotle. ‘People like Thales and Anaximander and their followers . . . searched for the causes of things which arise by nature, and, since they began from below, studied the material and elemental principles and brought them to light without distinction, as if they were bringing to light the principles of all existing things.’ The Eleatics and Pythagoreans ‘passed on a most complete philosophy of their own as regards both the natural things and the things above nature, albeit in a riddling way.’ Anaxagoras introduced nous as an efficient (nonelemental, non-natural) cause of natural things; and then Plato and Aristotle clearly set out separate accounts of natural and higher things, distinguished the different elemental principles (matter and form) from each other and from the non-elemental causes (efficient, final, and paradigmatic), and explained the higher things without the Pythagorean ‘riddles’. Simplicius’ story bears some relation to the story in Proclus, Platonic Theology 1, contrasting Plato with earlier philosophers, notably the Pythagoreans, who spoke in symbols or riddles. But Simplicius is modifying the story to take in more of the early philosophers, and to make it culminate in Plato and Aristotle rather than just Plato: see 7,27–34, cited and discussed above, for how Aristotle surpasses even Plato. 64 Simplicius, peculiarly, thinks that ‘physicists’ in the strict sense means something like ‘material monists’ (23,21–2 [see our note on that passage] and 153,27–154,1 and in de Caelo 561,1–5), perhaps because he thinks that the pluralists all had to posit non-physical causes of the combination of their many elements. 65 Golitsis (personal communication) suggests that the original meaning of episêmainomai is ‘comment in the margins of someone’s text’. 66 Aristotle uses forms of ephistêmi with a direct object (‘thought’ or the like) at Metaphysics 1.6, 987b3 and 14.2, 1090a2, On Youth and Old Age 6, 470b5, Topics 5.5, 135a26; without a direct object at On Generation and Corruption 1.2, 315b18, History of Animals 1.1, 487a13, Nicomachean Ethics 6.12, 1144a22–3, Politics 7.16, 1335b3–4. Where Aristotle uses the verb without a direct object it is in very stereotyped contexts, typically ‘we must, having stopped and noticed, say . . .’. The verb can also be used with a person as object, ‘to call someone’s attention’ to something (apparently not in Aristotle, but e.g. at Polybius, Histories 2.61.11 and 4.34.9). 67 Aristotle in this passage doesn’t use epistêmê (knowledge) or epistamai (know) (the word translated ‘intellectual cognition’ above is noêsis), but the point of ‘coming-torest and epistasis’ is that you are supposed to recognize that knowledge (epistêmê) resembles a coming-to-rest rather than a motion when you realize that coming-torest is epistasis. Similarly, but using the actual words epistêmê and epistamai, Physics 7.3 says that the acquisition of epistêmê is not a motion, since ‘we say that epistasis and intelligence is through thought’s coming-to-rest and stênai (standing still)’ (247b9–12) and since there is no motion from motion to rest, on pain of an infinite

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regress. Modern scholars generally agree that epistamai ‘know’ does somehow come from the preposition epi plus a middle voice of histêmi ‘to stand’, and is therefore cognate with epistasis (but it’s not obvious why the form would be epistamai rather than ephistamai). Here the implicit direct object of the verb would be not ‘our thought’ but ‘his thought’. Golitsis in ‘μετά τινων ἰδίων ἐπιστάσεων: John Philoponus as an editor of Ammonius’ lectures’, interprets epistaseis in general as objections or critical remarks. Similarly, Simplicius’ three epistaseis on the second lemma at 17,33–18,34 are not objections to earlier interpreters (at least not explicitly or obviously so), although what he says after that, beginning 19,1, is critical of Alexander. Cited in note 36. But the paragraph 19,12–18 begins with a mêpote and ends ‘So if someone can give a yet more persuasive account of this, let him do so.’ So likewise in Categorias 83,19–20. Denniston on ei ara says ‘ara in a conditional protasis denotes that the hypothesis is one of which the possibility has only just been realized: “If, after all” ’ (J. D. Denniston, The Greek Particles, 2nd edn, revised by K. J. Dover, London: Duckworth, 1996, p. 37). LSJ under ara, meaning B5, give ei mê ara = ‘unless perhaps’: so used at Plato, Apology 38B3–4, unless perhaps the jury would like to fine me the amount I can afford. In an autograph manuscript of John Scotus Eriugena’s On the Division of Nature (Latin, ninth century ce ) there are remarks added by a second writer, apparently a student of Eriugena, whose name is unknown, but who, since his habit is to begin with ‘nisi forte’ = ‘unless perhaps . . .’, is now commonly referred to as ‘Nisifortinus’ (see Édouard Jeauneau, ‘Nisifortinus: le disciple qui corrige le maître’, in John Marenbon, ed., Poetry and Philosophy in the Middle Ages, Leiden: Brill, 2001, pp. 113–29 – I thank Carlos Steel for calling my attention to Nisifortinus). Aristotle uses mêpote or mê pote at Categories 14, 15a18– 20: ‘there is an aporia about alteration, whether perhaps it is necessary for what is altered to be altered according to one of the other kinds of motion’: perhaps this is ancestral to the later commentarial use. Similarly Proclus, in Rem Publicam 1,21,8 ‘one might raise the aporia whether perhaps . . .’, and 1,276,6–7 ‘I think we should investigate whether perhaps . . .’. It is an editor’s choice whether to print ‘mêpote’ as one word or ‘mê pote’ as two, but the online Thesaurus Linguae Graecae gives only fifteen further uses of ‘mê pote’ in Galen, of which only four might possibly be Simplicius’ usage. Because earlier commentators sometimes use the word mêpote (though far less often than Simplicius), it can happen that Simplicius includes a mêpote as part of a quotation from an earlier commentator, in which case it would not signal a new proposal of his own and may not carry his endorsement. This does not happen often: in the portion we have translated, it may happen once, at 84,29, where he may be taking the word from Alexander (see our note there). Rachel Barney in ‘Simplicius:

Notes to pp. 30–6

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Commentary, Harmony, and Authority’, p. 110, n. 2, lists as other places where Simplicius has apparently quoted the word from an earlier commentator in Categorias 373,18 (from Boethus), 144,7, 144,18, 395,2, 415,31 and 426,9 (all from Iamblichus); in Physica 173,8, 340,30–31 and 1093,27 (all from Alexander) and 192,29 (from Syrianus); and in de Caelo 311,5 and 429,17 (from Alexander). Hartmut Erbse, ed., Scholia Graeca in Homeri Iliadem, 7 vols (Berlin: De Gruyter, 1969–1988), vol. 1, p. 67. For instance, Simplicius in his Categories commentary says that Porphyry in his (now lost) greater commentary on the Categories introduced Stoic doctrines ‘on account of what the [Stoic and Aristotelian] theories have in common’ (in Categorias 2,5–9), and Simplicius too gives us such Stoic material, presumably borrowing it from Porphyry. Likewise he says (2,9–25) that Iamblichus in his (equally lost) commentary introduced material from Archytas on the categories and the application of the categories to suprasensible things (the ‘noera theôria’, giving the reader a taste of something higher), and Simplicius too gives us such material, presumably borrowing it from Iamblichus. We have translated the former expression as ‘presumably it is better’ to avoid confusion with mêpote; we have translated the latter fixed expression more idiomatically as ‘perhaps it’s not a bad idea’. See Jaap Mansfeld, Prolegomena: Questions to be Settled before the Study of an Author or a Text (Leiden: Brill, 1994) and Ilsetraut Hadot, ed. and tr., Simplicius, Commentaire sur les Catégories, Fascicule I (Leiden: Brill, 1990). On these classifications see Simplicius 4,8–11 and 8,16–20; I give a brief discussion, and references to other sources, below. This is part of a thorough discussion in Chapter 9 of the Anonymous Prolegomena (an Alexandrian teaching text contemporary with Simplicius) of the rules for assigning the skopos of a Platonic dialogue: see the text and translation of this chapter in L. G. Westerink, ed. and tr., Anonymous Prolegomena to Platonic Philosophy, 2nd edn, (Westbury: Prometheus Trust, 2011), and Westerink’s discussion in his introduction of the issues about the skopos. Probably most writers before Iamblichus, including Alexander, were less insistent on finding a single skopos to fit everything in a text, and they may not have used the technical term skopos (sometimes they say prothesis in roughly the same sense), so attributions to them of views about the skopos of a text may involve some anachronism. Aristotle also says that we should first speak ‘about all coming-to-be: for it is according to nature after first speaking of what is common to then consider what is proper to each thing’ (Physics 1.7, 189b30–32). And Physics 1.1, 184a22–6 says that we should start with what is universal and proceed to what is particular, although Aristotle’s meaning here is in dispute among the commentators: see discussion below.

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83 The references are collected and discussed by W. D. Ross, Aristotle’s Physics: A Revised Text with Introduction and Commentary (Oxford: Oxford University Press, 1936), pp. 1–6. 84 The things that ‘get caught up [parempiptein]’ in the investigation would be things like infinity and void, which some earlier philosophers have wrongly regarded as principles of natural things or as belonging to all natural things, and which, for this accidental historical reason, the natural philosopher needs to investigate. 85 This is part of a fuller summary of Adrastus on the first five books, 6,4–30; Simplicius similarly cites what must be the same treatise of Adrastus, the On the Order of Aristotle’s Writings, at 4,11–16. At 802,7–13 Simplicius cites Porphyry and says that Porphyry cites earlier writers on how the Physics should be divided: Porphyry himself says that the last four books are the On Motion, but he cites ‘everyone’ as dividing it into a five-book Physics in a narrower sense and a threebook On Motion. At 923,7–925,2 Simplicius cites Andronicus as calling the first five books Physics and the remaining three On Motion, and ‘Damas who wrote the life of Eudemus’ (otherwise unknown but most likely a Rhodian like Eudemus and Andronicus, and cited by Andronicus) as calling the last three books On Motion. It seems clear that Simplicius knows Andronicus and Damas and Adrastus only through Porphyry, and that they are the ‘everyone’ who Porphyry cited as dividing the Physics into a five-book and a three-book treatise. 86 See below for a comparison with Philoponus on the structure of the Physics. 87 In describing on how the study of nature supports the moral virtues, Simplicius is drawing partly on Alexander’s commentary on the Physics, but also on a tradition going back to Aristotle’s Protrepticus and to texts in Plato’s Theaetetus and Laws: see in particular Marwan Rashed, ‘Alexandre d’Aphrodise, lecteur du Protreptique’, in his L’héritage aristotélicien (Paris: Les Belles Lettres, 2007), pp. 179–215. See also the end of Simplicius’ commentary on On the Heaven, 731,25–9, where Simplicius offers up the whole study as a hymn to the demiurge. Philippe Hoffmann in a number of studies, starting with his fundamental ‘Simplicius’ Polemics: Some aspects of Simplicius’ polemical writings against John Philoponus: From invective to a reaffirmation of the transcendency of the Heavens’, has stressed Simplicius’ ‘cosmic piety’ and his defence of a tradition of cosmic piety against Philoponus. 88 Ammonius also notes ‘personal’ works, e.g. Aristotle’s letters and his will, and ‘historical’ works. There is a similar classification at Simplicius, in Categorias 4,10–5,2, but without the term ‘acroamatic’. For discussion of the ancient classifications of Aristotle’s works see Paul Moraux, Les listes anciennes des ouvrages d’Aristote (Louvain: Éditions Universitaires, 1951); for discussion of the stages of composition involved in notions of ‘hypomnematic’ and ‘acroamatic’ writings, see Tiziano Dorandi, Le stylet et la tablette (Paris: Les Belles Lettres, 2000) and Nell’ officina dei classici (Rome: Carocci, 2007).

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89 While Simplicius cites Theophrastus a fair amount (although not as much as Eudemus, and mainly his History of Physics), this is one of only three places that the much less scholarly Philoponus mentions him in his Physics commentary; and one of Philoponus’ two later citations (108,25) is a reference back to the present passage. 90 See 18,24–34, where Simplicius approvingly cites Plato as saying that our accounts of nature must be probable rather than demonstrative, and thus not strictly science; what is surprising is that Simplicius manages to represent Aristotle as agreeing with this. 91 As Aristotle says at Physics 1.7, 191a7–8. The thought is that we grasp what matter is by an analogy or proportion: as bronze is to a statue, or as wood is to a bed, so matter is to a substance. 92 X ‘destroys Y it when it is destroyed’ if Y cannot exist without X, so that when X perishes, Y must perish with it. Simplicius actually uses a single word here, saying that X sunanairei Y, literally X ‘co-destroys’ Y, i.e. X destroys Y along with itself. Simplicius’ account of Alexander’s view on universals needs some qualification. Alexander thinks that the thing which is a universal or a genus is prior to the thing which is an individual or a species falling under it, but not that the universal is prior to the individual or the genus to the species. Thus animal, which is a genus, is prior to human, but the genus animal is not prior to human, since the genus animal could be destroyed without humans being destroyed: for if all non-human animals perished, animal would no longer be a genus, since it would no longer be predicated of things differing in species. For Alexander on common and universal things and their priority relations, see his Quaestiones 1.3 and 1.11. Simplicius, in Categorias 82,22–8, says baldly that Alexander makes the particular prior to the universal. 93 Beside the cited passage in Simplicius on the Categories, see Proclus’ Commentary on Euclid’s Elements 1 50,16–51,9. See also Proclus’ Elements of Theology 67–9 on the three kinds of wholes, which Simplicius is also drawing on to give parallel accounts of universals and wholes, and see the passages cited by Dodds in his commentary on this text, E. R. Dodds, ed., tr. and comm., Proclus: Elements of Theology, 2nd edn (Oxford: Oxford University Press, 1963), pp. 236–7. 94 Caution: Diels emended the text at 18,4, posited a lacuna at 18,14, and bracketed a passage at 18,14–15, in ways that are not only unnecessary but also destroy or radically change the sense of the paragraph 17,38–18,23, whose transmitted text has no serious problems. See our notes to the passage in the translation, and my ‘Simplicius on the Theaetetus (in Physica 17,38–18,23 Diels)’, Phronesis 55 [2010], 255–70. 95 There are some permutations in the word order. The whole sentence Philoponus 19,15–19 is quasi-identical with Themistius 2,6–10; Philoponus’ commentary on this lemma follows Themistius very closely. 96 Calcidius in his Latin commentary on the Timaeus cites Aristotle as saying that young children regard all men as fathers and all women as mothers, then learn to

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distinguish, but sometimes still make mistakes (208), and that Aristotle calls grownups who are unaware of their own ignorance and assent to false impressions in place of the true ones ‘aged children, since their mind scarcely surpasses a child’s’ (209). It is a plausible guess that Calcidius is here drawing on Porphyry’s Timaeus commentary (which made heavy use of the Physics) and that Simplicius is drawing on a parallel passage in Porphyry’s Physics commentary. This would be part of the older heritage that does not depend on Proclus’ technical theory of universals. For Calcidius, in the Latin and in English translation, see John Magee, ed. and tr., Calcidius: On Plato’s Timaeus (Cambridge: Harvard University Press, 2016): these texts are on pp. 444–7. Because Calcidius reports things that Aristotle doesn’t actually say in Physics 1.1, it’s sometimes thought that he is referring to an exoteric work of Aristotle, but he is unlikely to have read either the acroamatic or the exoteric works himself: he may simply be relying on Porphyry’s interpretation of Physics 1.1, or perhaps Porphyry himself has used an exoteric work to expand on Physics 1.1. For difficulties in the passage of Physics 1.1 about the children (184b12–14), see my ‘Physics I 1: The path to the principles’, in Katerina Ierodiakonou, Paul Kalligas, and Vassilis Karasmanis, eds, Aristotle’s Physics I (Oxford: Oxford University Press, 2019), pp. 19–52. There is a dispute, turning in part on a textual issue, about whether the children call all women ‘mother’ or merely think that all women are mothers. 97 On early ways of dividing up philosophers by how many beings they posit, perhaps going back to the sophist Hippias in the late-fifth century bce , see Jaap Mansfeld’s ‘Aristotle, Plato, and the Preplatonic Doxography and Chronology,’ in his Studies in the Historiography of Greek Philosophy (Assen: Van Gorcum, 1990), pp. 22–83. 98 Simplicius does not use the modern label ‘Eleatics’. To Parmenides and Melissus (who was not, of course, from Elea), he adds Xenophanes, or, as we would say, the Pseudo-Xenophanes who is summarized in the Pseudo-Aristotle treatise On Melissus, Xenophanes, Gorgias. (He seems to follow the On Melissus, Xenophanes, Gorgias closely, although he says he is following Theophrastus; the easiest explanation is that he thinks the On Melissus, Xenophanes, Gorgias is by Theophrastus.) He does not include Zeno here, presumably because he has no texts from Zeno giving a positive account of a principle, but later he discusses Zeno and defends Plato’s report that Zeno was defending Parmenides, against Eudemus’ view that Zeno argued against the one as well as against the many. 99 Proclus gives a brief ‘deductive’ statement on limit and the unlimited or infinite in Elements of Theology, propositions 89–96, and a much fuller exposition, with references to Plato, in Platonic Theology 3, Chapters 8–10. Proclus’ ‘limit’ and ‘unlimited’ or ‘infinite’ are close to what Proclus’ teacher Syrianus, in his commentary on Aristotle’s Metaphysics 13–14, calls ‘monad’ and ‘dyad’ respectively. Syrianus and Proclus are partly trying to systematize what Plato says in Philebus 16C-19A and 23C-27C about ‘limit’, ‘unlimited’, ‘mixed’, and ‘cause’ as four kinds of beings;

Notes to pp. 58–63

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they are also trying to make sense of sayings attributed to the Pythagoreans about ‘the one’ and ‘the dyad’ (or ‘monad’ and ‘dyad’) or ‘limit’ and ‘the unlimited’ as principles of beings. Aristotle in Metaphysics 13–14 (and Metaphysics 1.6) says that Plato used the One and the ‘indefinite dyad’ as respectively the formal and material principles of the intelligible world, and Aristotle criticizes this theory. For the neo-Platonists, the One is a self-sufficient principle, not needing to combine with any opposite principle such as a Dyad; and at least the later neo-Platonists deny that there is matter in the intelligible world. So Syrianus (followed by Proclus) tries to show that the Monad which is coordinated with the Dyad is not the first One-itself: rather, the Monad and Dyad, or limit and unlimited, are a pair of opposed principles which are inferior to the One, but are preconditions for the production of any further beings from the One. And they try to show that the Dyad or unlimited is not, as Aristotle suggests, a material principle, but is rather the infinite productive power of the One, responsible for the eternity and stability of the things that proceed from the One. Simplicius does not refer to this theory very often, but he accepts it, and draws on it where he finds it useful to solve some particular problem. Specifically on the goddess as an efficient cause, see 31,10–17 and 39,12–20. Simplicius stresses that Parmenides posits two opposite elemental causes (which therefore need an efficient cause for their mixture), and when Parmenides says ‘For they set down two shapes for naming in their judgements/ Of which one it is not right – in which they have wandered astray’ (B8.53–4, Simplicius 30,23–4), Simplicius (like a few modern interpreters) takes Parmenides to mean that it is those who do not recognize two opposite elements who have gone astray. See below on Philoponus on Empedocles on the realms of Love and Strife, and an individual soul’s oscillation between them; he agrees with the position that Simplicius is criticizing. Philoponus however adds an interpretation of what Love and Strife themselves are which Simplicius does not seem to be aware of here. The target of Simplicius’ criticism here is not Philoponus himself but an earlier source or sources. See for instance Proclus, Platonic Theology 4,88,21–2 and 5,11,15–23. The issue turns on whether we read hen einai, ‘are (or were) one’, with the manuscripts, or eneinai, ‘are (or were) present’, with Diels, at 34,26 and 35,1. Anaxagoras certainly meant eneinai, but Simplicius probably read it as hen einai; see our note at 34,26. This is how it looks at in Physica 461,10–16 and in de Caelo 608,31–609,12. Simplicius’ account of Anaxagoras in the present passage is a shorter version of what he does later on Physics 1.4. Simplicius develops this much more fully in his commentary on On the Heaven, pp. 642–71, starting from things in Proclus’s Timaeus commentary and in Proclus’

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Notes to pp. 63–81 lost reply to Aristotle’s objections against the Timaeus. See for discussion Ian Mueller, ‘Aristotelian objections and post-Aristotelian responses to Plato’s elemental theory’, in James Wilberding and Christoph Horn, eds, Neoplatonism and the Philosophy of Nature (Oxford: Oxford University Press, 2012), pp. 129–46; Jan Opsomer, ‘In defence of geometric atomism’, ibid., pp. 147–73; and Carlos Steel, ‘Proclus’ Defence of the Timaeus against Aristotle: A Reconstruction of a Lost Polemical Treatise’. , in Richard Sorabji, ed., Aristotle Re-Interpreted, pp. 327–52. This is Simplicius’ construal of the disputed passage 185a17–20, which, depending on where a comma is placed, says either that the Eleatics ‘are not speaking about nature but are stating natural aporiai’ or that they ‘are speaking about nature but not stating natural aporiai’: see Simplicius’ discussion 70,3–71,10. Since it is important for Simplicius that Parmenides in the Way of Truth is talking about an immaterial principle, not about the natural world, he will favour the former construal. But Simplicius disagrees with Porphyry’s view that Aristotle is here responding to a monist opponent who says that while Aristotle has successfully refuted the theses that what is is one as continuous, indivisible, or having the same essence, he has not yet refuted the view that it has a fourth weaker kind of unity, namely the unity of a whole with its non-continuous parts. See 83,9–19 and 86,10–13. Simplicius does seem to cite directly from Zeno’s book, but this passage shows that he is not sure whether he has a complete text. It is also not out of the question that he is citing from a collection of excerpts. On Eudemus’ interpretation of Zeno, see now also David Sedley, ‘Zenonian Strategies’, in Oxford Studies in Ancient Philosophy 53 (2017), 1–32. We and Sedley were working on Eudemus on Zeno at the same time and completely unaware of each other’s work. I mainly agree with Sedley’s reconstruction of Eudemus’ nihilist interpretation of Zeno, but he is sure that Eudemus was wrong, and I am not. I am also much less sure than Sedley is that Aristotle’s interpretation of Zeno was monist rather than nihilist. With SE 11, 171b14–16 or more broadly 171b12–17, compare SE 11, 172a2–4 and more broadly 171b34–172a7. In both passages (as in the Physics 1.2 passage) Aristotle contrasts diagrammatic fallacies, which are errors proper to geometry, with sophistical or eristic arguments. Bryson is mentioned as an eristic circlesquarer in both passages of the Sophistical Refutations. On lunes, see the diagrams below and in the translation. The usual view is that Aristotle here identifies Hippocrates’ fallacy with the squaring by means of lunes. But Ian Mueller, ‘Aristotle and the Quadrature of the Circle’, in Norman Kretzmann, ed., Infinity and Continuity in Ancient and Medieval Thought (Ithaca: Cornell University Press, 1982), pp. 146–64 at 150–1, takes Aristotle as distinguishing Hippocrates’ fallacy from the squaring by means of lunes. Diels bracketed ‘or the squaring by means of lunes’ as a gloss: see DK 42A3 and

Notes to pp. 81–3

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Kranz’ apparatus there. Curiously, Michael of Ephesus’ commentary (the PseudoAlexander, CAG vol. 2.3) attributes the squaring by means of lunes to Antiphon and not to Hippocrates (90,8–9). In both passages Aristotle’s aim is to distinguish between fallacies belonging to some particular art (which it belongs to the practitioner of that art to solve) and sophistic or eristic fallacies (which it belongs to the dialectician to solve). In both passages Aristotle illustrates the distinction by citing a fallacious but geometrical squaring (presumably of the circle) and a non-geometrical squaring, attributed to Bryson in the Sophistical Refutations and to Antiphon in the Physics (Antiphon is mentioned alongside Bryson in the second Sophistical Refutations passage, SE 11, 172a7). It is not clear how far Simplicius, in substituting a ‘squaring by means of lunes’ for the ‘squaring by means of segments’ in the text of the Physics, is following the Sophistical Refutations passage or Eudemus or both: there is no clear proof that the phrase was in the version of the Sophistical Refutations that Simplicius read. If the phrase in the Sophistical Refutations is a gloss, then the glossator may just be taking the phrase from the parallel at SE 11, 172a2–4 (reasoning, rightly or wrongly, that if Hippocrates’ squaring is contrasted with Bryson’s at 171b15–17, and the squaring by means of lunes is contrasted with Bryson’s at 172a2–4, then Hippocrates’ squaring must be the squaring by means of lunes). But it is also possible that the glossator is following Eudemus, or following some commentator on the Physics who would in turn be following Eudemus. As has often been noted, this fits well with the only other thing we know about Hippocrates, his reduction of the problem of doubling the cube to the problem of finding two mean proportionals. The only sense in which Simplicius, or Alexander, express a reservation about this at 68,34–69,6, is that they are leaving open the possibility that Aristotle might have been talking about the silly proof attempt by showing that ‘circular numbers’ are squares, or the attempt to exhaust the circle with infinitely many lunes (see below). But in the unlikely event that anyone did put one of these forward as a circlesquaring, it would be the kind of fallacy that a geometer does not have to respond to, so the opposite of what Aristotle is trying to illustrate here. For Eudemus’ work and methodology as a historian of science see Zhmud, The Origin of the History of Science in Classical Antiquity, which is mainly about Eudemus. As noted above, Proclus in his introduction to his commentary on Euclid’s Elements 1 makes heavy use of Eudemus’ History of Geometry. Also Eutocius, who was a student of Ammonius like Simplicius, uses Eudemus as Simplicius does, as a historical source for geometry in his commentaries on Archimdes’ Measurement of the Circle (on circle-squarings) and On the Sphere and the Cylinder (on cube-doublings). Eutocius says ‘it is clear that this [a circlesquaring] was the thing-sought (zêtoumenon), attentively seeking which

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Notes to pp. 83–92 Hippocrates of Chios and Antiphon discovered for us those paralogisms which I think those who examine Eudemus’ History of Geometry and those who partake in the Aristotelian honeycombs will understand precisely’ (in Archimedis dimensionem circuli 228,14–19). (‘Aristotelian honeycombs’ [Aristotelika kêria] was apparently the title of a book by Sporus of Nicaea, see Wilbur R. Knorr, Textual Studies in Ancient and Medieval Geometry (Boston: Birkhäuser, 1989), p. 93 with the attached notes (and also n.124)). So Eutocius seems to report Eudemus as saying that Hippocrates, like Antiphon, committed a fallacy. There is no direct evidence that Eutocius held the chair, but there was a head of the school between Ammonius and Olympiodorus, whose name we are not told; we have two references to Eutocius’ commentary on Porphyry’s Isagoge (which was taught as an introduction to Aristotle’s logical works), so he taught philosophy and not just mathematics; and Eutocius’ commentary on Archimedes’ On the Sphere and the Cylinder is addressed to ‘Ammonius, mightiest of philosophers’, which suggests that he was a student of Ammonius. The evidence (except this last item) is collected in L. G. Westerink, ed., Prolégomènes à la Philosophie de Platon, 2nd edn (Paris: Les Belles Lettres, 2003), pp. xv-xvi. Archimedes in On Spirals 18 shows how, using spirals, to construct a line and a circle whose circumference will be equal to the line; and in Measurement of the Circle 1 he shows how, given a line equal to the circumference of a circle, to construct a rectilineal figure (a triangle) equal to the area of the circle. On the history of ancient attempts to square the circle, and what they did and did not accomplish, see Wilbur R. Knorr, The Ancient Tradition of Geometrical Problems (Boston: Birkhäuser, 1986), pp. 25–39 (on Hippocrates and Antiphon and Bryson), 76–86 and 153–70. The proposition about similar segments can be proved rigorously using Eudoxus’ method of exhaustion, but not using methods that were available in Hippocrates’ time. Hippocrates may have assumed, or given an intuitive but not rigorous argument, that similar sectors of circles are in the same ratio as the squares of their radii (a sector is like a slice of pie, the portion of a circle cut off by two radii from the centre to different points on the circumference), and then deduced from this (which is not hard to do) that similar segments of circles are in the same ratio as the squares of their bases (a segment is a portion of a circle cut off by a chord). More generally, if circle-segment A is similar to circle-segment B and the base of segment A is to the base of segment B in the ratio √m:√n (‘the base of segment A is to the base of segment B in power as m:n’), then area A is to area B as m:n. So if figure F+n·A-m·B is congruent to figure G, then areas F and G are equal. One of Hippocrates’ arguments uses this more general principle. See Reviel Netz, ‘Eudemus of Rhodes, Hippocrates of Chios and the Earliest Form of a Greek Mathematical Text’, Centaurus 46 (2004), 243–86. Netz argues against

Notes to pp. 92–3

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Oskar Becker, who had noticed the difference between a lettered and a letterless stratum within Eudemus’ report but thought that the lettered stratum was earlier. There are far more letters in Eudemus’ third and fourth constructions than in the first two. Note that even the lettered stratum refers to points and lines in a relatively old-fashioned way, often saying, as Aristotle also sometimes does, ‘the [line] on which AB,’ where Euclid would say simply ‘the [line] AB’. In the way of thinking that this old-fashioned style of reference reflects, ‘A’ and ‘B’ are not in the first instance names of points, but names of the letters themselves which are written in the diagram. Note in particular Netz, ‘Eudemus of Rhodes, Hippocrates of Chios and the Earliest Form of a Greek Mathematical Text’; G. E. R. Lloyd, ‘The Alleged Fallacy of Hippocrates of Chios’, Apeiron 20 (1987), 103–28; Knorr, The Ancient Tradition of Geometrical Problems, pp. 29–39; Ian Mueller, ‘Aristotle and the Quadrature of the Circle’, pp. 146–64; Wilbur R. Knorr, ‘Infinity and Continuity: The Interaction of Mathematics and Philosophy in Antiquity’, ibid., pp. 112–45 (esp. pp. 123–35); Fabio Acerbi in the introduction to his Euclide: Tutte le Opere (Milan: Bompiani, 2007), pp. 28–71; Oskar Becker, ‘Zur Textgestaltung des eudemischen Berichts uber die Quadratur der Mondchen durch Hippokrates von Chios’, Quellen und Studien zur Geschichte der Mathematik, Astronomie und Physik B3 (1936), 411–19, and the even older literature (notably by Paul Tannery and Ferdinand Rudio) cited by these sources. There is much to be learned from all of this literature, including a sense of what issues are still in dispute. But some cautions: these writers are mostly interested in getting back to the oldest layers in Simplicius’ report and discarding the rest; in most cases they are not starting from any great acquaintance with Simplicius’ methods elsewhere; and in some cases they are unreasonably hostile to Simplicius or unduly suspicious about who had access to what sources or who is representing their sources accurately. In vol. 16 in the CAG; translated in the present series by Catherine Rowett, Philoponus: On Aristotle Physics 1.1–3 (London: Duckworth, 2006). In both of these cases Philoponus seems to be running with something mentioned in passing by Themistius: see note 127. Golitsis in ‘μετά τινων ἰδίων ἐπιστάσεων: John Philoponus as an editor of Ammonius’ lectures’, maintains that Philoponus’ commentary on Physics 1–2 (but not his commentary on Physics 3–4 or his lost commentary on Physics 8) is Philoponus’ edition of Ammonius’ lectures, with only occasional objections added by Philoponus himself. Golitsis thinks that the extracts from Themistius were already in Ammonius’ lectures (or that Ammonius asked someone in the class to read them out), whereas I tend to think that they are Philoponus’ additions, and that at least sometimes he intends them as a criticism or positive alternative to Ammonius’ interpretation. There is a similar issue about Asclepius’ commentary on

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Notes to pp. 93–7 the Metaphysics, which is mainly reporting Ammonius’ lectures but includes numerous extracts (verbatim or closely paraphrased) from Alexander’s commentary: are these passages of Alexander that Ammonius himself incorporated into his lectures (or asked someone in the class to read out), or is Asclepius using them to supplement Ammonius? Philoponus treats On the Soul as part of the physical treatises, when for Simplicius it is apparently midway between physics and first philosophy. But Philoponus lists On the Soul last, after the biological treatises and Parva Naturalia, which may reflect the same underlying thought, even though he classifies it as a physical treatise. Philoponus says that On the Heaven is about eternal natural things; it becomes clear from the parallel in the proem to his commentary on On Generation and Corruption (probably reflecting Ammonius’ lectures) that this means not just the heavenly bodies but also the totalities of the four sublunar elements, each of which is eternal as a whole although perishable in its parts, and that it also includes a discussion of the world as a whole. Simplicius in the proem to his commentary on On the Heaven criticizes both Alexander, who says that the skopos of On the Heaven is ‘the world and the five simple bodies’ (rejected because there needs to be a single skopos), and the view of Iamblichus and Syrianus that the skopos is just the heavenly body and that the treatise discusses sublunar things only insofar as they are related to the heavenly body (rejected because On the Heaven 3–4 are talking about the four corruptible simple bodies for their own sake). Simplicius thinks that the skopos is all five simple bodies, and that Aristotle has no treatise which would, like the Timaeus, be talking about the world as such: Aristotle’s account of the world as a whole can only be found in all his physical treatises taken together. Simplicius criticizes Porphyry for making cause and principle coextensive (11,23–9), so that he can clear the way for Proclus’ distinction whereby all causes are principles but not vice versa; and he sharply attacks Eudemus and Alexander for the way they distinguish ‘cause’ and ‘principle’ and ‘element’ (10,23–4; 11,16–23; 13,28–33). Philoponus’ theory of indeterminate particulars seems to be starting from Themistius’ example (2,6–9) of the thing approaching, of which one recognizes, e.g. first that it is an animal and only later that it is a human (this example is also in Simplicius 16,18–20, whether he is taking it from Themistius or both from a common source). For nature producing compounds from simples, so that simples must be prior for nature although they are posterior for us, see Themistius 1,18–20: but while Themistius is taking ‘nature’ in Aristotle’s text as a producer, he may not be taking it as also a cognizer, in the way that Philoponus does. In at least some of these passages Philoponus seems to be using Themistius against Ammonius. In other cases he would just be using him to supplement Ammonius. Probably whoever came up with this interpretation was troubled by the difficulty of finding a real extra-psychic principle that does what Empedocles’ Strife is supposed

Notes to pp. 97–101

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to, without positing a bad demiurge: and the problem is even more serious if Strife is also active in the intelligible world. But Iamblichus and Syrianus and Proclus and Damascius will not be troubled by this, since they think there is a real principle of diversification (the dyad or the infinite or the divine power (dunamis)) operating even in the intelligible world. Conversely, a post-Iamblichean neo-Platonist might be troubled by the idea that the soul ever enters the intelligible world, so that it could now be exiled from it. Porphyry is a likely source for Philoponus’ interpretation – perhaps even for the psychologizing interpretation of Love and Strife, in order to avoid positing Strife within the intelligible world. See above for Simplicius’ criticisms of Alexander here. Philoponus here does not seem to be following Themistius (the directly comparable passage would be Themistius 5,9–14). Probably Philoponus is following Ammonius who in turn followed Alexander, and Simplicius is deviating from Ammonius in preferring Porphyry to Alexander. See above for Simplicius’ ‘defence’ of Zeno. For the story of how the Academy, and specifically Diels, came to edit the CAG in general, and Simplicius on the Physics in particular, see Karl Praechter’s review of the CAG, in Sorabji, ed., Aristotle Transformed, pp. 31–54. Diels’ edition of Simplicius on Physics 1–4 and Hayduck’s edition of [Ps.-]Simplicius on On the Soul were the two first volumes in the series, both in 1882; I don’t know which was published first, although Hayduck’s preface is dated two months before Diels’. Simplicius had long been seen as the best source of scholarly information (Alexander was of course also highly valued), and had already been heavily used by editors of pre-Socratic fragments, especially C. A. Brandis and Simon Karsten. This had already led Karsten to edit Simplicius on On the Heaven (Utrecht: Kemink, 1865), of which there had been no earlier edition except the fake Aldine of 1526 (a Greek retranslation of a Latin translation, passed off as the Greek original); in other cases, before the CAG, people had relied on Renaissance editions or Latin translations. D stops p. 347 in the middle of Book 2. E starts after the proem, 8,32, and stops just short of the end of Book 4. See David Sider, The Fragments of Anaxagoras, 2nd edn (Sankt Augustin: Academia Verlag, 2005); A. H. Coxon, The Fragments of Parmenides, 2nd edn (Las Vegas: Parmenides Publishing, 2009); Leonardo Tarán, ‘The Text of Simplicius’ Commentary on Aristotle’s Physics’, in Ilsetraut Hadot, ed., Simplicius, sa vie, son oeuvre, sa survie (Berlin: De Gruyter, 1987), pp. 246–66; and Dieter Harlfinger, ‘Einige Aspekte der handschriftlichen Überlieferung des Physikkommentars des Simplikios’, in ibid., pp. 267–94. We follow Harlfinger on the relations between the different manuscripts. See Pantelis Golitsis and Philippe Hoffmann, ‘Simplicius et le “lieu”: À propos d’une nouvelle édition du Corollarium de loco’, Revue des Études Grecques 127/1 (2014), 119–75.

146

Notes to pp. 101–4

135 In Hadot, ed., Simplicius, sa vie, son oeuvre, sa survie, pp. 246–66. 136 See Simon Karsten, Parmenidis Eleatae Carminis Reliquiae (Amsterdam: Müller, 1835; a series title page describes this as Philosophorum Graecorum veterum, praesertim qui ante Platonem floruerunt, Operum Reliquiae, vol. 1, pt. 2), p. 32, for the text he prints (it’s his line 43), and p. 77 for his explanation of how he is emending the text we read in Simplicius. (Karsten may be proposing this only as the correct text of Parmenides and not also of Simplicius.) Diels’ mistake here had particularly unfortunate consequences: in later work, relying on his own edition of Simplicius, Diels drops the reference to Karsten’s alleged emendation to noein and keeps only the reference to the alleged manuscript reading te noein, which is in fact Karsten’s emendation and has no manuscript support. This is unfortunately propagated at DK 28B61. 137 See our note to the translation at 40,1, Simplicius’ first citation of this verse. The correct reading of E here had been noted before us by Coxon, The Fragments of Parmenides, in his apparatus to B8 line 28, and the reading of Mo by David Sider, ‘Textual Notes on Parmenides’ Poem’, Hermes 113 (1985), 362–6, at 366. 138 In Hadot, ed., Simplicius, sa vie, son oeuvre, sa survie, pp. 267–94. 139 Why he did not copy the proem 1,3–8,30 is unclear, although there are also some other manuscripts of Greek commentaries which skip their proems. It is also possible that it was his exemplar for 8,32–52,18 that was damaged, forcing him to change exemplars at 52,18. If so, then the fact that the second exemplar was also damaged is just a coincidence. 140 Eb is folios 408–415. Ea begins in the middle of folio 402, continues through to the end of folio 407, and resumes after Eb with folios 416 to some way down 418. Then the text of the commentary on Physics 4 resumes, 787,31–795,35, at which point it finally breaks off shortly before the end of Physics 4. The jump between the two disjoined sections of Ea, 20,1–30,16 and 35,30–44,19, happens within folio 407, i.e. before the mechanical interruption by Eb, and passes from 30,16 to 35,30 as if there were nothing missing. Presumably 20,1–30,16 and 35,30–44,19 were on different folios in E’s exemplar, but the scribe of E copied them together without noticing that there was anything missing between them, just as he seems not to have noticed that these texts did not belong inside a commentary on Physics 4. 141 A. H. Coxon, ‘The Manuscript Tradition of Simplicius’ Commentary on Aristotle’s Physics i-iv’, Classical Quarterly 18 (1968), 70–75, has some useful observations on particular passages but should be used with great caution. Coxon does not understand the difference between the relations of E to D in different parts of the text, or the relation between E and Ea, and this vitiates many of his conclusions. For some other cautions see Tarán, ‘The Text of Simplicius’ Commentary on Aristotle’s Physics’. 142 See Christian Wildberg, ‘Simplicius und das Zitat: zur Überlieferung des Anführungszeichens’, in Friederike Berger et al. eds, Symbolae Berolinenses: Für Dieter Harlfinger (Amsterdam: Hakkert, 1993), pp. 187–99.

Notes to pp. 105–14

147

143 But see Mirjam E. Kotwick, Alexander of Aphrodisias and the Text of Aristotle’s Metaphysics (Berkeley: California Classical Studies, 2016), pp. 38–45, for an argument that Alexander inserted a ‘lemma’ containing only the first sentence of each passage selected for commenting into the text of his Metaphysics commentary, and that these original ‘lemmas’ are sometimes reflected in our extant manuscripts. 144 But we actually do so once, at 33,9, in a fragment of Empedocles (B21, line 4). 145 Listed as ‘Ross’ in the Abbreviations; the text and apparatus are reproduced apparently unchanged in Ross’ Oxford Classical Text of 1950. 146 The diagrams given here are diagrams that will be given in the translation of Simplicius on Physics 1.1–2, in the translation of 55,25–68,32: look there for explanation of the details of the diagrams. 147 Actually, according to Eudemus-Simplicius, he does the reverse, starting with the small circle and hexagon, and then constructing the big circle, and the hexagon inscribed in it (or at least two of the sides of this hexagon), with radius and sides √6 times as long as in the small circle, and then constructs the lune inside the big circle. That makes the thought unnecessarily difficult to follow. 148 Given a point B on a circle, and given a line GD, we are asked to find a line from some point on the circle to some point on the line GD which ‘points’ or ‘inclines’ (neuei) towards B (i.e. which, if prolonged further in the same direction, will reach B) and which is equal to √(3/2) times the radius of the circle. Presumably you would do this by laying down a straightedge with one end at B: start with it lying on line BG and rotate it around the fixed end at B until it reaches line BD. As you move the straightedge, the distance along the straightedge between where it intersects the line GD and where it intersects the circle again (on the opposite side of line GD from point B) will vary in a continuous manner. In the diagram that Hippocrates (according to Eudemus) is considering, the distance at the beginning will be 3/2 times the radius and at the end it will be zero, so somewhere in between it will be equal to √(3/2) times the radius. Move the straightedge until this equality is reached, stop there, and mark the points where the straightedge now intersects the line GD and the circle.

148

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Index of Names Adrastus 37–8, 129 n.49, 131 n.55, 136 n.85 Agathias 3, 120 n.8, 120 n.9 Alexander of Aphrodisias 2, 5–6, 8, 10–14, 17–24, 26, 28–30, 35, 37, 39–40, 44–5, 47, 49, 51–3, 55, 58–60, 65–70, 73, 75–80, 92–9, 124 n.24, 125 n.25, 125 n.27, 126 n.28, 126 nn.32–3, 127 n.36, 128 n.37, 129 n.45, 130 n.52, 131 nn.54–5, 132 n.58, 134 n.69, 134–5 n.74, 135 n.81, 136 n.87, 137 n.92, 144 nn.124–6, 145 n.129, 145 n.131, 147 n.143 on Hippocrates’ circle-squaring 80–5, 87–91, 110, 112–13, 115–18, 141 n.114 Alexander the Great 13, 39, 132 n.60 Ammonius, son of Hermias (6th century ce) 3, 6, 12, 17, 19, 39, 51, 60, 84–7, 92–7, 121 n.11, 123 n.18, 125 n.26, 125–6 n.28, 126 n.33, 132 n.62, 134 n.68, 136 n.88, 141 n.115, 142 n.116, 143–4 n.124, 144 n.125, 144 n.127, 145 n.129 Ammonius Saccas (3rd century ce) 16–17 Anaxagoras 23–6, 32, 43, 55–8, 61–4, 96–7, 109, 121 n.12, 130 n.52, 133 n.63, 139 nn.103–4 Anaximander 132 n.60, 133 n.63 Anaximenes 56, 132 n.60 Andronicus 12, 37, 39, 129 n.49, 130 n.51, 136 n.85 Anonymous Prolegomena to Platonic Philosophy 35, 135 n.80 Antiphon 80, 83–4, 90, 97, 141 n.111, 141 n.112, 142 n.115, 142 n.117 Apollonius of Perga 85 Archimedes 85, 86 On the Sphere and the Cylinder 114 n.116 On Spirals, Measurement of the Circle 114 n.117

Archytas 132 n.60, 135 n.76 Aristotelians, see also Peripatetics extreme and moderate Aristotelians 5–6 Aristotle passim biological works and Parva Naturalia 131 n.55, 133 n.66, 144 n.125 Categories 48–9, 86, 134 n.72 ethical and political works 34, 133 n.66 Metaphysics 5, 47, 50, 59, 71–2, 108, 121 nn.11–12, 123 n.18, 133 n.66, 138–9 n.99 On Democritus 130 n.52 On Generation and Corruption 133 n.66, 144 n.125 On the Heaven 9, 21, 24, 35, 43, 54, 63 On the Soul 27, 126 n.33, 144 n.125 Physics passim Posterior Analytics 41, 44, 47, 48, 95 Prior Analytics 82 Protrepticus 136 n.87 pseudo-Aristotle, On Melissus Xenophanes Gorgias 130 n.52, 138 n.98 Topics and On Sophistical Refutations 80–1, 133 n.66, 140 n.110, 141 n.112 Aspasius 12, 19, 125 n.27 Atticus 5–6 Calcidius 137–8 n.96 Damascius 2–4, 19, 30–2, 61, 121 nn.9–10, 127–8 n.36, 128 n.39, 129 n.48, 145 n.128 Democritus 22, 26, 27–8, 53, 63–4, 97, 130 n.52, 132 n.60 Dercyllides 12, 131 n.55 Diels, Hermann 2, 14, 19, 22, 28–9, 100–6, 119 n.2, 127 n.36, 128 n.41, 130–1 n.53, 137 n.94, 139 n.103, 140–1 n.111, 145 n.131, 146 n.136 Diogenes of Apollonia 24, 131 n.54 Diogenes Laertius 130 n.52

155

156

Index of Names

Empedocles 8, 14, 23–6, 32, 43, 55–64, 96, 106, 108, 139 n.101, 144–5 n.128, 147 n.144 Epictetus 3 Euclid 21, 84–91, 115, 142–3 n.120, 143 n.121 Eudemus 2, 13, 19–23, 28, 37, 41, 44, 70, 93–4, 108–9, 126 n.32, 129 nn.44–8, 130 n.52, 131 n.55, 136 n.85, 137 n.89, 138 n.98, 144 n.126 on Hippocrates 80–92, 97, 109–18, 141 n.112, 141–2 n.115, 142– 3 n.120, 147 nn.147–8 History of Astronomy 21, 129 n.48 History of Geometry 21, 80, 83, 120, 141–2 n.115 History of Theology 129 n.48 Physics 19–21, 41, 83, 98, 108, 126 n.32 on Zeno and the ‘later ancients’ 73–9, 98–9, 140 n.109 Eutocius 85, 141–2 n.115, 142 n.116 Galen 30, 34, 134 n.73 Gorgias 78 Heraclitus 69, 83, 132 n.60 Hippocrates of Chios 2, 14, 20–21, 80–92, 97, 101, 109–18, 129 n.47, 140– 1 n.111, 141 nn.112–13, 141– 2 n.115, 142 nn.117–19, 142– 3 n.120, 143 n.121 Iamblichus 3, 11–12, 35, 61, 64, 86, 120 n.5, 123 n.20, 127 n.35, 129 n.48, 132 n.60, 135 n.74, 135 n.76, 135 n.81, 144 n.125, 145 n.128 Karsten, Simon 102, 145 n.131, 146 n.136 Leucippus 63 Longinus 16, 24, 128 n.39 Lucius and Nicostratus 15, 18, 131 n.56 Lycophron 73, 78–9, 98 Melissus 22, 24, 25, 33, 36, 43, 53–4, 56–8, 65, 69, 71, 73, 96, 98, 138 n.98 Menedemus 74 Moderatus 12, 131 n.55

Nicolaus of Damascus 12, 22, 53, 127 n.49, 131 nn.54–5 Numenius 128 n.39 Olympiodorus 121 n.9, 142 n.116 Parmenides 8, 13–14, 22, 24–5, 30, 33, 43, 53–8, 62, 65–6, 69, 71–3, 75–7, 83, 96, 98–9, 101–2, 106, 107, 109, 122–3 n.16, 132 n.59, 138 n.98, 139 n.100, 146 nn.136–7 alleged prose text 132 n.60 Way of Truth 58–9, 61, 140 n.106 Way of Doxa 58–9, 61, 66, 96 Peripatetics 2, 11–12, 16, 20, 22–4, 27, 32, 34, 36–8, 53–4, 76, 90, 93, 96, 99, 122 n.14, 126 n.33, 129 n.49, 130 n.52, 131 nn.54–5 see also Theophrastus, Eudemus, Alexander, Themistius Philoponus, John 1–2, 6, 8, 17–18, 30, 32, 38, 41, 51, 60, 80, 104, 119 n.3, 121 n.9, 122 n.15, 123 nn.18–19, 124 n.24, 125 n.27, 125–6 n.28, 128 n.42, 132 n.62, 136 nn.86–7, 137 n.89, 137 n.95, 139 n.101, 143 nn.122–4, 144 n.125, 144 n.127, 145 nn.128–9 Philoponus and Simplicius on Physics 1.1–2, 92–9 Plato 1–9, 11, 13–14, 16–19, 23–6, 27, 29, 31–3, 36, 39–41, 43, 48, 56–7, 62, 66, 72–80, 85, 94, 99, 109, 121–2 nn.11– 14, 122–3 n.16, 123 n.18, 123 n.20, 127 n.35, 129 nn.44–5, 131 n.55, 132 nn.58–9, 133 n.63, 138–9 n.99 Apology 134 n.72 Laws 39, 125 n.26, 131 n.55, 136 n.87 Parmenides 11, 23, 72, 76–7, 79–80, 99, 128 n.39, 132 n.59, 138 n.98 Philebus 79, 99, 128 n.39, 138 n.99 Protagoras 15 Republic 41, 44, 50 Sophist 23, 31, 72, 74, 79–80, 99, 132 n.59 Theaetetus 50, 95, 136 n.87 Timaeus 2, 4–6, 8–9, 11–12, 23–4, 26, 36, 49, 51, 60, 62–4, 72, 78, 96, 99, 121 nn.11–12, 132 n.57, 137 n.90, 137–8 n.96, 139–40 n.105, 144 n.125

Index of Names Platonists, Platonic school passim extreme and moderate Platonists 5–6 Plotinus 15, 16–17, 18, 123 n.20, 128 nn.39–40 Plutarch of Chaironeia (1st–2nd century ce) 5, 16, 25, 30 Porphyry 2–3, 6, 10–13, 15–17, 19–20, 24, 16, 28–9, 37–8, 41, 51, 54, 60, 63, 65, 67–70, 73–5, 79, 92–4, 96, 98–9, 109, 125 n.28, 125 nn.31–2, 127 nn.35–6, 128 n.39, 131 nn.54–5, 135 n.76, 136 n.85, 138 n.96, 140 n.107, 142 n.116, 144 n.126, 145 nn.128–9 Priscian of Lydia 3, 119 n.4 Proclus 3, 6, 11, 18, 24, 30, 31–2, 37, 40, 42, 44, 49, 51, 57–8, 61, 64, 85, 94–5, 122 n.14, 127 n.35, 127–8 n.36, 128 n.39, 132 n.60, 138 n.96, 138–9 n.99, 144 n.126, 145 n.128 Commentary on Euclid’s Elements I, 85, 129 n.48, 137 n.93, 141 n.115 Commentary on Plato’s Republic 134 n.72 Commentary on Plato’s Timaeus 24, 121 n.11, 121–2 n.13, 122 n.14, 123 n.18, 139–40 n.105 Elements of Theology 137 n.93, 138 n.99 Platonic Theology 133 n.63, 138 n.99, 139 n.102 Protagoras 15, 83, 132 n.60 Simplicius passim Commentary on Aristotle’s Categories 1, 3, 11–12, 15, 17–18, 35, 49, 51, 126 n.30, 127 n.35, 131 n.56, 132 n.60, 134 n.72, 135 n.74, 135 n.76, 136 n.88, 137 n.92 Commentary on Epictetus’ Enchiridion 3 Commentary on Aristotle’s Metaphysics (lost and possibly spurious) 3, 119–20 n.5 Commentary on Aristotle’s Meteorology (lost) 3 Commentary on Aristotle’s On the Heaven 1–8, 12–13, 17–18, 21, 24, 32, 35, 38, 63–4, 93, 106, 119 n.3, 122 n.15, 123 n.20, 124 n.24, 125 n.27, 129 n.44, 129 n.48, 130 n.52, 132 n.61, 133 n.64,

157

135 n.74, 136 n.87, 139 n.104, 139–40 n.105, 144 n.125, 145 n.131 Commentary on Aristotle’s On the Soul (spurious) 3, 119 n.4, 119–20 n.5, 145 n.131 Commentary on Aristotle’s Physics passim work on the principles in Euclid (lost, some fragments preserved in Arabic) 3 Speusippus 121 n.11 Stoics 32, 34, 131 n.54, 135 n.76 see also Epictetus Syrianus 11, 12, 35, 121 n.11, 122 n.16, 125 n.26, 127 n.36, 135 n.74, 138–9 n.99, 144 n.125, 145 n.128 Thales 132 n.60, 133 n.63 Themistius 11–13, 19–20, 27, 29, 51, 79, 92–3, 95–9, 125 n.25, 126 n.30, 126 n.32, 127 n.36, 130 n.51, 137 n.95, 143 nn.23–4, 144 n.127, 145 n.129 Theophrastus 2, 13, 21–5, 34, 41, 53–4, 64, 94, 96, 108–9, 122 n.14, 126 n.32, 127 n.35, 129 n.44, 129 n.50, 130 nn.51–2, 131 nn.54–5, 132 n.60, 137 n.89, 138 n.98 History of Physics (= Physical Opinions, Opinions of the Physicists?) 21, 130 n.52, 137 n.89 On Anaxagoras 130 n.52 On the Heaven 21 On Minerals 129 n.50 On Motion 21 On the Soul, 130 n.51 Physics 21, 41, 108, 130 nn.51–2 Timaeus of Locri (fictional author) 24, 26, 57, 60, 63–4, 132 n.60 Torstrik, Adolf 100–1, 103, 105 Xenocrates 121 n.11 Xenophanes 23, 43, 56–8, 96, 130 n.52, 131 n.54, 132 n.60, 138 n.98 Zeno of Elea (5th century bce) 24, 25, 33, 57, 65, 66, 69, 73, 75–8, 79, 98–9, 129 n.45, 132 n.60, 138 n.98, 140 nn.108–9, 145 n.130

158

Index of Subjects aether, fifth body, fifth substance 1, 5, 7, 17, 121 n.11, 144 n.125 aporiai, problems, solutions 9–11, 13–20, 22–4, 27–32, 40, 44–5, 48–9, 51, 54, 65–6, 70–1, 73–5, 77, 79–80, 82, 85–6, 95, 97, 99, 107, 124 n.23, 128 n.39, 128–9 n.43, 130–1 n.53, 131 n.56, 140 n.106, 141 n.113 see also one-many problems arts 34–5, 107, 141 n.112 artifacts 36 atoms, indivisibles (Democritean and Timaean) 26, 63–4, 97 see also one as indivisible bodies 9, 24–6, 35–6, 59, 63–4, 71, 79, 93, 122 n.14, 144 n.125 human or animal bodies 18, 38, 42 see also simple bodies, fifth body, heavenly bodies categories 67–9, 73–4, 98, 135 n.76 causes 4–9, 13, 17–18, 23, 25–7, 31–2, 36–7, 42, 44–5, 47–50, 53, 55, 57, 59–60, 62, 64, 66, 94, 96, 122 n.14, 126 n.33, 127 n.35, 131–2 n.57, 133 n.63, 139 n.100, 144 n.126 cause vs. auxiliary cause (sunaition) 25–6, 31, 36–7, 42, 94, 122 n.14, 127 n.35 efficient cause 4–7, 13, 17–18, 23, 31, 36–7, 44–5, 59–61, 64, 122 n.14, 126 n.33, 127 n.35, 133 n.63, 139 n.100 end, final cause 5–6, 13, 18, 23, 31, 34, 36–7, 44–5, 107, 122 n.14, 126 n.33, 127 n.35, 133 n.63 form, formal cause 8–9, 18, 23, 26, 31, 36–7, 42, 44, 62, 94, 122 n.14, 127 n.35, 131–2 n.57, 133 n.63, 139 n.99 instrument, instrumental cause 127 n.35

matter, material cause 8–9, 17, 23, 26, 31, 36–7, 42, 44, 59, 61, 63, 94, 97, 122 n.14, 126 n.33, 127 n.35, 132 n.57, 133 n.63, 137 n.91, 139 n.99 paradigm, paradigmatic cause 7, 18, 23, 37, 44–5, 46, 49, 60–2, 64, 72, 79–80, 122 n.14, 123 n.18, 127 n.35, 131–2 n.57, 133 n.63 continuity 8–9, 36, 47, 69–70, 72 continuous and discrete quantities 85 continuous and non-continuous parts and wholes 70–1, 140 n.107 see also one as continuous demiurge 4, 6–7, 18, 23, 32, 42–3, 60, 121 n.12, 123 n.18, 131–2 n.57, 136 n.87, 144–5 n.128 differentiation, degrees of differentiation or unification 60–2, 108–9 dyad 138–9 n.99, 144–5 n.128 epistasis, ephistanai, observations, remarks, objections, calling attention 10, 27–31, 44, 107–8, 125 n.28, 133 n.66, 133–4 n.67, 134 nn.68–9 fifth body, fifth substance, see aether fire 4–7, 59, 61, 99 see also simple bodies generation, coming-to-be, corruption, perishing 1, 6, 18, 24, 27, 43–4, 47, 49, 56, 59–60, 72, 132 n.61, 135 n.82, 144 n.125 genus, see species and genus God, gods, divine things 3–8, 13, 15, 17–18, 27, 35, 38–9, 58–9, 61, 72, 121 n.12, 122 n.14, 123 nn.17–20, 126 n.33, 131 n.54, 139 n.100, 144–5 n.128 grammarians, grammatikoi 15–16, 19, 30, 124 n.23, 128–9 n.43

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heavens, heavenly bodies 1, 4–8, 13, 27, 32, 35, 121 nn.12–13, 122 n.14, 126 n.33, 144 n.125 infinity 8, 22, 26–7, 47–8, 53, 55, 57–8, 61, 68–9, 71–2, 84, 96–7, 107, 136 n.84, 138–9 n.99, 141 n.114, 145 n.128 intellectual (noeron) vs. intelligible (noêton) 57, 60–2, 79, 97 knowledge: terms for knowledge 27, 107–8, 133–4 n.67 confused and scientific knowledge 49–52 knowledge of principles and of things derived from the principles 40–5, 53–4 lunes 14, 80–92, 97, 109–18, 140 n.110, 140–1 nn.110–11, 141 n.112, 141 n.114, 147 n.147 mathematics 2, 12, 32, 41, 44, 64, 80–92, 97, 101, 109–18 mêpote, ‘perhaps’ 10, 28–31, 60, 86, 107, 112, 127 n.36, 134 nn.71–3, 134–5 n.74, 135 n.77 metaphysics, first philosophy 33, 36, 40–5, 54, 56, 59, 66, 96, 108, 144 n.125 metaphysics of prepositions 94, 127 n.35 see also Aristotle, Metaphysics mixture 4, 24, 46, 58, 61–2, 79, 97, 138–9 n.99, 139 n.100 motion 4–6, 8, 13, 21, 27, 36–9, 47, 51, 63, 66, 94, 122 n.14, 133 n.67 motionlessness, 55–7, 96 nature, natural things, natural science 5–6, 8–9, 17–18, 21–2, 24–6, 32, 34–44, 46–8, 52, 54–7, 62, 64–7, 93–5, 108, 121–2 n.13, 122 n.14, 130 n.52, 133 n.63, 136 n.84, 136 n.87, 137 n.90, 140 n.106, 144 n.125, 144 n.127 better known by nature 45, 47–9, 51–2, 93, 95 neusis constructions in geometry 90, 114, 147 n.148

nous (Reason, intelligence, intellect: discussion of meanings and translations of nous, 107) 4–7, 13, 18, 32, 42–3, 50, 55, 61–4, 71–2, 80, 97, 107, 121 n.12, 121–2 n.13, 122 n.14, 123 n.18, 126 n.33 the nous (insight) of Ammonius, 16–17 number 31, 51, 70–1, 84–5 one in number, numerically one 68–9 One as first principle 42, 57–8, 64, 72, 138–9 n.99 One Being, one-that/which-is 25, 43, 57–8, 62, 72, 96 one as indivisible 67–9, 71, 98, 140 n.107; see also atoms, indivisibles one as continuous, 67, 71, 98, 140 n.107; see also continuous one as whole, see whole and parts one-many problems 23, 67–80, 98–9, 132 n.59 one before many, in many, after many 49–51, 95 ‘perhaps’, see mêpote place 2, 8–10, 17, 31, 36–8, 47, 66 planets 21 see also heavens, heavenly bodies Platonic Forms 23, 39, 42–3, 48, 57, 61–2, 72, 79–80, 99, 123 n.18, 127 n.35, 131–2 n.57, 132 n.59 see also (under ‘cause’) paradigm, paradigmatic cause potentiality and actuality 74 principles, 9, 22–6, 32–3, 36–8, 40–6, 48, 51–60, 63–7, 71–2, 80, 83, 85, 93–7, 122 n.14, 127 n.35, 133 n.63, 136 n.84, 139 n.99, 144–5 n.128 principle, cause, element 25–6, 31, 32, 36–7, 42, 44–6, 50, 53–6, 59–60, 63–4, 94–5, 127 n.35, 133 n.63, 139 n.100, 144 n.126 simple bodies (earth, water, air, fire, aether) 4–5, 7, 24, 26, 35, 59–61, 63–4, 78–9, 121 n.11, 144 n.125

Index of Subjects skopos, aim, object 8–9, 12, 33–8, 93–4, 107, 123 n.19, 126 n.29, 135 nn.80–1, 144 n.125 soul 4–5, 18, 27, 35, 38–9, 43–4, 49, 59, 64, 96–7, 107, 121 n.12, 126 n.33, 139 n.101, 144–5 n.128 species and genus 6, 41, 44, 48–9, 137 n.92, 108 one in species or genus 68–9, 98 squaring, defined 85–6 14, 20–1, 33, 80–92, 97, 109–18, 140 n.110, 143 n.121

161

theôria and lexis 124 n.23, 130–1 n.53 time 2, 8–10, 17, 31, 36–8, 47 creation in time, 5–6 universals, things said universally 25, 35–7, 41, 46–53, 94–5, 98, 135 n.82, 137 nn.92–3, 137–8 n.96 void, emptiness 8, 36–7, 47, 63, 132 n.57, 136 n.84 wholes and parts, one as whole 42, 46–51, 70–2, 74–6, 80, 95, 98, 137 n.93, 140 n.107

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