John Philoponus on Physical Place (Ancient and Medieval Philosophy–Series 1, 60) 9789462702745, 9789461663856, 9462702748

Table of contents :
9789462702745_frontcover
9789461663856
Contents
Acknowledgments
Preface
Chapter 1. Form, Method and Structure of the Physics Commentary
1.1 The form of the Physics commentary
1.2 A note on Vitelli’s edition
1.3 The form of the commentary and Philoponus’ philosophical contributions
1.4 Levels of interpretation
1.5 Dividing Aristotle’s Physics into lectures
1.6 Introduction to the digressions
1.7 The argument of the digressions
1.8 A note on Philoponus’ sources and targets in the digressions
Chapter 2. Place as Extension: Problems and Solutions
2.1 Aristotle’s rejection of place as extension
2.2 Themistius’ exegesis of Aristotle’s argument
2.3 Philoponus’ exegesis of Aristotle’s argument
2.4 Philoponus refuting the infinity of places
2.5 Philoponus refuting changing and coinciding places
Chapter 3. The Ontology of Place According to Philoponus
3.1 Three-dimensionality of place
3.2 Place as measure
3.3 Place and the ‘violation’ of nature
3.4 The empty universe
3.5 Place, substance, qualities and quantity
Chapter 4. Philoponus on Void as Place
4.1 The concept of plērōsis
4.2 The void is place
4.3 Motion through void and motion through a corporeal medium
4.4 Motion of bodies in Philoponus’ cosmological system
4.5 Philoponus on physical place
Chapter 5. Philoponus against Aristotle and the Peripatetic Tradition
5.1 Aristotle’s definition of place
5.2 The equality between place and the bodies in it
5.3 The immobility of place
5.4 Motion through surfaces
5.5 The place of the heavens
Epilogue
Bibliography
Texts
Translations
Secondary literature
Index Locorum
Index Nominum

Citation preview

.

AM P�

S.1

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ancient and medieval philosophy · series 1

Ioannis Papachristou holds a PhD in Philosophy from Humboldt-Universität zu Berlin. He is a post-doctorate researcher in the Project ‘Sourcebook of Byzantine Philosophy’ at the National and Kapodistrian University of Athens.

AM P1

John Philoponus on Physical Place Ioannis Papachristou

This book examines the place of physical bodies, a major topic of natural philosophy that has occupied philosophers since antiquity. Aristotle’s conceptions of place (topos) and the void (kenon), as expounded in the Physics, were systematically repudiated by John Philoponus (ca. 485-570) in his philosophical commentary on that work. The primary philosophical concern of the present study is the in-depth investigation of the concept of place established by Philoponus, putting forward the claim that the latter offers satisfactory solutions to problems raised by Aristotle and the Aristotelian tradition regarding the nature of place. ­Philoponus’ account proposes a specific physical model of how physical bodies exist and move in place, and regards place as an intrinsic reality of the physical cosmos. Due to exactly this model, his account may be considered as strictly pertaining to the study of physics, thereby constituting a remarkable episode in the history of philosophy and science.

John Philoponus on Physical Place Ioannis Papachristou

Leuven University Press

9789462702745-Case.indd 1

27-05-21 13:12

JOHN PHILOPONUS ON PHYSICAL PLACE

ANCIENT AND MEDIEVAL PHILOSOPHY

DE WULF-MANSION CENTRE Series I

LX

Editorial Coordinator Russell Friedman

Editorial Board Pieter d’Hoine Jan Opsomer Andrea Robiglio Carlos Steel Gerd Van Riel

Advisory Board Brad Inwood, Yale University, USA Jill Kraye, The Warburg Institute, London, United Kingdom John Marenbon, University of Cambridge, United Kingdom Lodi Nauta, University of Groningen, The Netherlands Timothy Noone, The Catholic University of America, USA Robert Pasnau, University of Colorado at Boulder, USA Martin Pickavé, University of Toronto, Canada Pasquale Porro, Università di Torino, Italy Geert Roskam, KU Leuven, Belgium

The “De Wulf-Mansion Centre” is a research centre for Ancient, Medieval, and Renaissance ­philosophy at the Institute of Philosophy of the ku Leuven, Kardinaal Mercierplein, 2, b-3000 Leuven (Belgium). It hosts the international project “Aristoteles latinus” and publishes the “Opera omnia” of Henry of Ghent and the “Opera Philosophica et Theologica” of Francis of Marchia.

JOHN PHILOPONUS ON PHYSICAL PLACE

Ioannis Papachristou

LEUVEN UNIVERSITY PRESS

© 2021 by the De Wulf-Mansioncentrum – De Wulf-Mansion Centre Leuven University Press / Presses Universitaires de Louvain/ Universitaire Pers Leuven Minderbroedersstraat 4, B-3000 Leuven / Louvain (Belgium) All rights reserved. Except in those cases expressly determined by law, no part of this publication may be multiplied, saved in an automated data file or made public in any way whatsoever without the express prior written consent of the publishers. ISBN 978 94 6270 274 5 eISBN 978 94 6166 385 6 https://doi.org/10.11116/9789461663856 D/2021/1869/13 NUR: 732 Cover: Geert de Koning

Στους γονείς μου, Στέργιο και Βασιλική

Contents Acknowledgments

IX

Preface

XI

Chapter 1. Form, Method and Structure of the Physics Commentary 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

1

The form of the Physics commentary 1 A note on Vitelli’s edition 5 The form of the commentary and Philoponus’ philosophical contributions 7 Levels of interpretation 13 Dividing Aristotle’s Physics into lectures 17 Introduction to the digressions 23 The argument of the digressions 26 A note on Philoponus’ sources and targets in the digressions 30

Chapter 2. Place as Extension: Problems and Solutions 2.1 Aristotle’s rejection of place as extension 2.2 Themistius’ exegesis of Aristotle’s argument 2.3 Philoponus’ exegesis of Aristotle’s argument 2.4 Philoponus refuting the infinity of places 2.5 Philoponus refuting changing and coinciding places Chapter 3. The Ontology of Place According to Philoponus

33 33 37 40 43 49 55

3.1 Three-dimensionality of place 3.2 Place as measure 3.3 Place and the ‘violation’ of nature 3.4 The empty universe 3.5 Place, substance, qualities and quantity

55 61 69 79 84

Chapter 4. Philoponus on Void as Place

91

4.1 The concept of plērōsis 4.2 The void is place 4.3 Motion through void and motion through a corporeal medium 4.4 Motion of bodies in Philoponus’ cosmological system 4.5 Philoponus on physical place

91 94 98 108 115

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Chapter 5. Philoponus against Aristotle and the Peripatetic Tradition

123

5.1 Aristotle’s definition of place 5.2 The equality between place and the bodies in it 5.3 The immobility of place 5.4 Motion through surfaces 5.5 The place of the heavens

124 127 131 136 138

Epilogue

147

Bibliography

151

Texts Translations Secondary literature

151 152 153

Index Locorum

161

Index Nominum

171

Acknowledgments The doctoral dissertation of which this book is a revised version was written within the framework of the Excellence Cluster Topoi ‘The Formation and Transformation of Space and Knowledge in Ancient Civilizations’ during the period when I was a Doctoral Fellow of Topoi at Humboldt-Universität zu Berlin (2009-2012). I owe much to Topoi and the Graduate School of Ancient Philosophy (Humboldt-Universität zu Berlin) for their generous funding during my studies. I am grateful to the supervisors of this dissertation, namely Prof. Dr. Christoph Helmig (Universität zu Köln) and Prof. Dr. Christian Wildberg (University of Pittsburgh), for their assistance and advice throughout all those years. It has been a great pleasure to work under their supervision, since they repeatedly forced me to develop my thoughts with fresh insights. I also wish to thank Prof. Wildberg for the period I spent at Princeton University as a Visiting Student Research Collaborator (2011-2012) under his supervision. In addition, I would like to thank my colleagues of the Topoi Research Group D-II-2 ‘Place, Space and Motion’; their work along with the lively academic atmosphere of our seminars always inspired me. I am indebted to Prof. Dr. Frans A. J. de Haas for hosting me at Leiden University (July 2012); I have greatly benefited from our conversations on final stages of my dissertation. I would like to express my gratitude to Prof. Dr. Keimpe Algra, who trusted me with the translation of Philoponus’ commentary on the Physics, IV.1-5 before its publication. I would also like to thank the director of Aristoteles Archiv (Berlin), Prof. Dr. Dieter Harlfinger, for giving me permission to work on the microfilms of Philoponus’ manuscripts; Prof. Dr. Jan Opsomer, from the editorial board of the Ancient and Medieval Philosophy Series 1 (Leuven University Press), for his thorough and insightful comments and the two anonymous reviewers for their careful reading of the manuscript; their critical suggestions helped me to proceed to substantial improvements. Τhis dissertation could not have been completed without the constant encouragement, the spiritual generosity and the friendship of Katerina Ierodiakonou and Anna Ntinti. Finally, I could not forget Michael Frede, whose stimulating personality motivated me to exercise my mind thoroughly on ancient philosophical thought. I owe him much, but above all, in respect of this book, for the fact that he mentored me to study Iōannēs Philoponus’ work.

Preface This is a philosophical study on the concept of τόπος (place) in late antiquity (sixth century C.E.).1 The book centres on the theory of place held by a Christian2 theologian and commentator on Aristotle known as Ἰωάννης γραμματικός, φιλόπονος, Ἀλεξανδρεύς (ca. 485-570).3 His birth name, Iōannēs, indicates that the commentator was a Christian and that he was given the last epithet most likely becauce he lived in Egyptian Alexandria.4 The epithet ‘grammatikos’ shows his early devotion to grammar and his intense interest in the field, as attested to in his surviving grammatical works.5 Finally, the epithet ‘philoponos’ testifies to his character as a scholar, for it signifies that Iōannēs was a lover of (spiritual) labour or toil.6 Iōannēs Philoponus was a member of the Platonic school of Alexandria when Ammonius (ca. 435/445–517/526)7, the son of Hermeias (ca. 410–450), held its chair.8 We have one clue concerning the date of Philoponus’ arrival at Alexandria’s philosophical school. Simplicius, who first attended the Alexandrian school under Ammonius and then left to join the Platonic school at Athens, reports that he never met Philoponus in the Alexandrian school; therefore we can assume that Philoponus joined the school shortly after Simplicius left Alexandria in ca. 510.9 Whether or not Philoponus succeeded Ammonius as head of the school is uncertain, but Philoponus’ philosophical association with the Platonic school may have lasted until his death. His surviving philosophical works show that he edited the lectures of 1

2

All dates, unless otherwise stated, are C.E. Supporting monophysitism as indicated by his theological treatise Arbiter. See Lang 2001: 40;

41-60. 3 Golitsis (2008: 7) places Philoponus’ birth around 485; Wildberg (2008a) believes that Philoponus was born around 490. See also Verrycken 2010: 733. 4 We have no evidence of Philoponus’ birthplace and it is unclear what the oldest reference to the epithet ‘Ἀλεξανδρεύς’ is. The use of the epithet in the given titles of the manuscripts containing Philoponus’ works cannot lead us to safe conclusions. Souda’s lemma which is dedicated to Philoponus includes the epithet (464.1-6). 5 For instance, the De vocabulis quae diversum significatum exhibent secundum differentiam accentus. In addition, Simplicius attests that Philoponus signed himself as ‘grammarian’ (in De caelo, 119.7). 6 An alternative interpretation, that modern scholarship rejects, connects Iōannēs to a group of Christian labourers called ‘philoponoi’ (Saffrey 1954: 403-405). The philoponoi were groups of Christians offering different kinds of assistance to the Church, such as helping the sick and the poor, constructing or repairing churches, following pagan rituals in order to destroy sanctuaries and idols, and being chanters in churches. For more details on the activities of the philoponoi of Alexandria read Trombley 1995, vol. II: 1-51 (The philoponoi of Alexandria and Hellenic religion). 7 For more on Ammonius’ life see Blank 2010: 654-666 and Blank 2012. 8 Philoponus, in Meteor., 106.9-10: καὶ ὁ ἡμέτερος δὲ διδάσκαλος Ἀμμώνιος Ἑρμείου οὕτως ἐξείληφε. 9 On this I follow Saffrey’s (1954: 403) and Golitsis’ view (2008: 7, n. 2); see also Simplicius, in De caelo, 26.17-19, where he notes that he never met Iōannēs in Alexandria.

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his master Ammonius into the form of commentaries. Despite these duties that we assume he had, Philoponus later continued working on Aristotle’s and Plato’s works, producing his own commentaries, which were partially prepared as lectures addressed to pupils of the school.10 Later in his career Philoponus abandoned the production of philosophical commentaries and focused on theological debates of Christianity supporting monophysitism and tritheism.11 Philoponus wrote his commentary on Aristotle’s Physics in 517.12 The chronology stems from the commentary itself, since the commentator says in his first lecture on Physics IV.10, ‘For we say now the present year and month and day, year 233 of Diocletian’s reign, month pachōn, the tenth day’—that is 10 May 517.13 The commentary consists of four sharply distinguished parts which comprise an organic whole: the proem, the running commentary (i.e., the lectures),14 and two digressions (παρεκβάσεις), which concentrate respectively on the concepts of place and void. Although Philoponus’ text is a commentary sensu stricto—i.e., an exegesis of the Aristotelian work—he also bequeathed to us a corpus of arguments against Aristotle. The structure of the commentary makes it exceptional among the commentaries of late antiquity.15 The lectures on the fourth book of the Physics are interrupted by two long digressions; additionally, comments are often completed by short critical observations (ἐπιστάσεις) expressing Philoponus’ arguments on different topics. Two digressions devoted to the concepts of place and void respectively and an 10 From Philoponus’ surviving commentaries the following are supposed to be editions from Ammonius’ courses: on Aristotle’s Prior Analytics, on the Posterior Analytics, on the On Generation and Corruption and on the On the Soul. The manuscript tradition indicates in the titles of the last three commentaries that they also contain personal observations by Philoponus (μετὰ τινων ἰδίων ἐπιστάσεων). The remaining preserved commentaries belong to Philoponus’ own commentaries— namely, on the Categories, on the Physics, and on the Meteorology. Philoponus also refers to one of his commentaries, now lost, on Plato’s Phaedo (in Anal. Post., 215.3-5). 11 His theological works did not survive in Greek, apart from the commentary on the book of Genesis, known as the De opificio mundi. The monophysitic and tritheistic corpus survives in Syriac translations edited and translated by Šanda 1930 and A. van Roey 1982. On Philoponus’ theological works see Papachristou 2020 and 2021. 12 Verrycken’s claim (2010: 733-734; 736-738) that Philoponus revised his commentary on the Physics after 529 might have had some plausibility if the whole argument had not relied on his view that we can distinguish between two different periods of Philoponus’ intellectual course (‘Philoponus 1’ and ‘Philoponus 2’; see also Verrycken 1990: 236-254). Golitsis (2008: 27-37) convincingly rejects Verrycken’s assumption and Algra—Ophuijsen (2012: 5-11) has reinforced Golitsis’ rejection. I also disagree with Verrycken’s assumption, following the aforementioned scholars. A remarkable view on Philoponus’ thought development in both its philosophical and theological context is proposed by Wildberg (1999: 115-120), who explains Philoponus’ scientific method based on his monophysitic convictions. 13 φαμὲν γὰρ ἐνεστηκέναι νῦν καὶ ἐνιαυτὸν καὶ μῆνα καὶ ἡμέραν, ἐνιαυτὸν Διοκλητιανοῦ ἔτος σλγ΄, μῆνα παχών, ἡμέραν δεκάτην, in Phys., 701.16-17. 14 We know from Philoponus that the commentary on the Physics was a text directly related to the school: περὶ δὲ τούτου ἐν τοῖς εἰς τὸ τέταρτον τῆς Φυσικῆς ἀκροάσεως σχολικοῖς ἡμῶν συγγράμμασιν αὐτάρκως εἴρηται, in Meteor., 35.18-19. 15 Simplicius’ commentary on Aristotle’s Physics does not have the same form as Philoponus’ commentary, but it also contains two large texts known as ‘Corollarium de loco’ (in Phys., 601.1-645.19) and ‘Corollarium de tempore’ (in Phys., 773.8-800.25).

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epistasis on the motion of projectiles (impetus) notoriously disagree with Aristotle in various respects.16 However, it is not the refutations alone that catch the attention of the reader; more importantly, Philoponus substitutes Aristotle’s theories and provides alternative accounts of place and void. My research focuses on Philoponus’ definition of place and aspires to demonstrate that Philoponus provides a coherent theory which includes a complete study of place, void, and motion through void. To state the status quaestionis, I will proceed with the following remarks. The study of Philoponus’ philosophical work has flourished since the twentieth century mainly because of the publication of his commentaries on Aristotle in the series Commentaria in Aristotelem Graeca in the late nineteenth century.17 Since the 1950s especially, Philoponus’ commentaries have gradually begun to gain the attention of scholars. In the last sixty-five years many publications have provided new insights into the study of Philoponus, opening discussions on both his philosophical and theological texts which, in parallel, shed light on his career.18 For Philoponus’ commentary on the Physics the secondary literature derives from different disciplines. On the one hand, historians of science are interested in Philoponus’ commentary on the Physics because it contains his contributions to puzzling physical issues—for example, the motion of projectiles (impetus theory), the existence of the void and motion through void—which have been tackled by physicists from the medieval era to the present day.19 On the other hand, philoso16 Philoponus is opposed to Aristotle’s definition of place (among other Aristotelian views), to his statements on the void and the motion of bodies through it, as well as to his explanations of forced motions such as the motion of projectiles. 17 For this bibliographical survey (which is not meant to be exhaustive) I rely mainly on the following four bibliographical sources: Sorabji 1990: 497-499; Sellars 2004: 239-268; Golitsis 2008: 281-291; Gerson 2010: 1143-1147. 18 For instance, the collections of articles edited by R. Sorabji, Philoponus and the Rejection of the Aristotelian Science (1987, 2nd revised edition 2010) and Aristotle Transformed. The Commentators and their Influence (1990) and Aristotle re-interpreted. New findings on seven hundred years of the Ancient Commentators (2016), which contain studies on various of Philoponus’ theories related to psychology, physics, dynamics, logic, and theology. Apart from collections of articles, there are other significant contributions to the secondary literature, for instance: Böhm, W. (1967), Johannes Philoponos, ausgewählte Schriften, Ferdinand Schöningh: München; Évrard, E. (1957), L’école d’Olympiodore et la composition du commentaire à la Physique de Jean Philopon, Liège (unpublished); Haas, F. A. J. de (1997), John Philoponus’ New Definition of Prime Matter: Aspects of its Background in Neoplatonism and the Ancient Commentary Tradition, Philosophia Antiqua 69, Brill: Leiden; Tempelis, E. (1998), The School of Ammonius, Son of Hermeias, on Knowledge of the Divine, Parnassos Literary Society: Athens; Lang, U. M. (2001), Philoponus and the Controversies over Chalcedon in the Sixth Century. A Study and Translation of the Arbiter, Spicilegium Sacrum Lovaniense, Peeters: Leuven; Wildberg, C. (1987), Philoponus. Against Aristotle, On the Eternity of the World, Duckworth: London; Wildberg, C. (1988), John Philoponus’ Criticism of Aristotle’s Theory of Aether, Peripatoi 16, W. de Gruyter: Berlin; Verrycken, K. (2010), ‘John Philoponus’, in Gerson (ed.), The Cambridge History of Philosophy in Late Antiquity, vol. II, Cambridge University Press: Cambridge: 733-755. 19 Some works dealing with Philoponus’ commentary on the Physics from a scientific point of view are: Clagett, M. (1959), Science of Mechanics in the Middle Ages, The University of Wisconsin Press: Madison/Wisconsin; Duhem, P. L. (1954), Le système du monde, I-II, Hermann: Paris (Index: Jean d’Alexandrie); Grant, E. (1964), ‘Motion in the Void and the Principle of Inertia in the Middle

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phers and historians of philosophy have found in Philoponus’ commentary a criti­ cism of the Aristotelian tradition’s definition of place. Although the concept of τόπος figures prominently in philosophical discussions of cosmology and physics from classical antiquity (Plato, Aristotle) up to late antiquity (Philoponus, Damascius, Simplicius), the study of Philoponus’ theory of place has only recently attracted the attention of scholars.20 Philoponus’ theory of place as an extension, i.e., as an empty bodiless interval in which natural bodies are, has occasionally been discussed in the secondary literature. Yet only four essays are entirely devoted to it. David Furley in his translation of Philoponus’ digressions on place and the void offers short comments on Philoponus’ thoughts, comments that by no means are aimed at being analytical or exhaustive.21 David Sedley dedicates a paper to Philoponus’ views about place and touches upon the difficulty of defining place as void. His remarks on the use of the ‘force’ of void and the analogy between matter deprived of form and place deprived of bodies are of great importance in understanding some basic features of Philoponus’ theory.22 Pantelis Golitsis’ monograph (which is the most recent book on Philoponus’ commentary on the Physics) attempts a parallel reading of Simplicius’ and Philoponus’ commentaries. Golitsis successfully fills many gaps in our knowledge of the history of Philoponus’ commentary: he examines several issues such as Philoponus’ philosophical career and the form of the commentary, and he presents the argument of the digressions, offering French translations of important texts of the commentary.23 Nonetheless, Golitsis’ philosophical focus is mainly on Ages’, Isis 55: 265-292; Grant, E. (1965), ‘Aristotle, Philoponus, Avempace and Galileo’s Pisan Dynamics’, Centaurus 11: 79-95; Grant, E. (1981), Much Ado about Nothing. Theories of Space and Vacuum from the Middle Ages to the Scientific Revolution, Cambridge University Press: Cambridge. 20 Secondary literature related to Philoponus’ commentary on the Physics: Évrard, E. (1957), L’école d’Olympiodore et la composition du commentaire à la Physique de Jean Philopon, Liège (unpublished); Haas, F. A. J. de (1997), John Philoponus’ New Definition of Prime Matter: Aspects of its Background in Neoplatonism and the Ancient Commentary Tradition, Philosophia Antiqua 69, Brill: Leiden; Golitsis, P. (2008), Les commentaires de Simplicius et de Jean Philopon à la Physique d’Aristote, Commentaria in Aristotelem Graeca et Byzantina 3, W. de Gruyter: Berlin-New York; Lang, H. S. (2001), ‘Philoponus’ Aristotle: The Extension of Place’, in Sharples (ed.), Whose Aristotle? Whose Aristotelianism?, Ashgate: Aldershot: 11-27; Macierowski, E. M., Hassing, R. F. (1988), ‘John Philoponus on Aristotle’s Definition of Nature’, Ancient Philosophy 8/1: 73-100; Martin, C. J. (1999), ‘Non-Reductive Arguments from Impossible Hypotheses in Boethius and Philoponus’, Oxford Studies in Ancient Philosophy 17: 279-302; McGuire, J. E. (1985), ‘Philoponus on Physics II.1: Physis, Hormē Emphytos and the Motion of Simple Bodies’, Ancient Philosophy 5: 241-267; Sedley, D. (1987), ‘Philoponus’ Conception of Space’, in Sorabji (ed.), Philoponus and the Rejection of Aristotelian Science, Duckworth: London: 140-153; Todd, R. B. (1980), ‘Some Concepts in Physical Theory in John Philoponus’ Aristotelian Commentaries’, Archiv für Begriffsgeschichte 24: 151-170; Wildberg, C. (1999), ‘Impetus Theory and the Hermeneutics of Science in Simplicius and Philoponus’, Hyperboreus 5: 107-124. 21 Furley 1991. Elsewhere, he paraphrases Philoponus’ arguments of the digressions on place and the void without offering any philosophical comment (see Furley 1987:130-139). 22 See Sedley (1987), ‘Philoponus’ Conception of Space’. The article examines several arguments of Philoponus’ theory of place, especially those related to the definition of place as void. 23 See Golitsis 2008: 22-37; 55-64.

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Simplicius. Philoponus’ theory of place, his reflections on the void, and his theory of the motion of the projectiles (impetus) are presented, but not examined in detail.24 Finally, the introduction to the translation of Philoponus’ commentary on the Physics IV.1-5 by Algra and Ophuijsen is a useful guide to the running commentary; it sheds lights on the relationship between running commentary and the digressions and points out passages of philosophical interest concerning Philoponus’ theory of place appearing in the running commentary. In other words, there are still many aspects of this theory that need to be studied. When I started working on Philoponus’ theory of place, many questions arose: general questions about the form of the commentary or particular issues related to Philoponus’ account of place. But the secondary literature did not cover all those questions, nor did it have solutions to some crucial problems appearing in Philoponus’ commentary. As a result, the present study encountered many profound difficulties. The absence of a substantial bibliography on Philoponus’ theory of place and the lack of a translation of the running commentary on the Physics IV.1-9 were further obstacles. At that time, only the digressions on place and on the void had been translated into English (Furley 1991). The running commentary on the Physics IV.1-5 and 6-9 was translated into English by Algra—Ophuijsen (2012) and Huby (2012) respectively shortly before the completion of my dissertation.25 The present study aims to be an exegetical commentary, with a compounding character, on Philoponus’ critique of the theory of place and discussion on the void that Aristotle expounded in Physics IV.1-9. I say exegetical, in the sense that it attempts to present a comprehensive explanation of Philoponus’ complex theory of place and the void and to exhibit his contributions to the discussion of the concept of τόπος in antiquity and beyond. The compounding character of this work lies in the systematic collection and connection of all the passages which relate to the concept of place throughout the proem, the exegesis and the digressions of the commentary. One of the concerns of this study is to read Philoponus’ theory of place in accordance with the running commentary and, whenever necessary, in accordance with the proem.26 There are two reasons for this: first, we may be able to obtain a better understanding of the commentary’s form and structure and, second, we can shape a more precise idea of Philoponus’ theory of place by following his reflections on the concept of topos from the introduction to the com24 To be more precise, Golitsis (2008: 174-195) presents Philoponus’ digressions on place and on void and the short excursus on the motion of the projectiles in 21 pages. 25 The English translations of Philoponus’ commentary on the Physics appear in the series Ancient Commentators on Aristotle, edited by R. Sorabji: Osborne (2006), Philoponus, On Aristotle Physics 1.1-3; Lacey (1993), Philoponus, On Aristotle Physics 2; Edwards (1994), Philoponus, On Aristotle Physics 3; Algra—Ophuijsen (2012), Philoponus, On Aristotle Physics 4.1-5; Huby (2012), Philoponus, On Aristotle Physics 4.6-9; Furley (1991), Philoponus, Corollaries on place and void; Broadie (2011), Philoponus, On Aristotle Physics 4.10-14; Lettinck (1994), Philoponus, On Aristotle Physics 5-8. 26 Algra—Ophuijsen correctly note the need to study the running commentary (2012: 1-2; 7-10).

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mentary (proem) and the exegesis up to the theory of place itself (digressions of the commentary). The primary philosophical concern of this book, however, is the in-depth investigation of the concept of place established by Philoponus. Apart from a commentary on his account of place, we aim to clarify the meaning of τόπος, i.e., of physical place. Aristotle and his faithful commentators propose a concept of relative place, namely the place of a body defined by its surrounder or that which contains it. Philoponus finds that this definition of place is insufficient and does not totally reflect the nature of place and the way motion of bodies occurs. He suggests a concept of absolute space, a reality in which physical bodies are located and move, offering a substantialist treatment of space. We will look at two main questions. First, what is Philoponus’ ontology of place? Philoponus argues for the necessary ontological difference (ἑτερότης) of place from bodies. We will go through Philoponus’ method of demonstration from common observations, such as measurement, vessels and clepsydras (proofs of the so-called ‘force’ of void), as well as his use of thought experiments. We shall see how the entire point of these demonstrations is to show that place subsists as such and that it differs ontologically from bodies. Second, what does the void mean within Philoponus’ theory of place? In other words, in what sense does Philoponus define place as void and what does it mean to be in place and to be in the void? We shall examine a series of arguments proving that motion of bodies through void is possible, against the Aristotelian assumption of the impossibility of motion through void. Thus, the study wishes to offer an overall reading of Philoponus’ commentary on the Physics IV.1-9 through the philosophical examination of his theory of place. The book consists of five chapters. The first (Form, Method and Structure of the Physics Commentary) briefly introduces the reader to the form of the commentary, then presents Philoponus’ methodological approach to the Physics and, finally, exposes the overall structure of the digressions on place and void, which are the central texts under examination in this book. Philosophical theories are not independent of the texts in which they are contained. In a sense, the text is the topos where a theory resides. Therefore this study has to revisit issues relating to the form of the commentary (called θεωρία-λέξις form), though aspects of it have already been discussed in the secondary literature, as noted earlier. The special interest of this chapter focuses on simple exegesis, critical observations (ἐπιστάσεις) and digressions (παρεκβάσεις), discussing their relation and function in Philoponus’ commentary. The chapter also distinguishes between certain levels of interpretation appearing in the commentary to show the method with which Philoponus works and divides Aristotle’s Physics. Finally, the chapter presents in detail the structure and argument of the digressions, mapping Philoponus’ concerns in rejecting the Aristotelian account and defending his own theory against various targets such as Alexander of Aphrodisias, Themistius, the Stoics and the atomists.

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The second chapter (Place as Extension: Problems and Solutions) opens the philosophical discussion on Philoponus’ theory of place. The starting point of this chapter is Aristotle’s critique of the view that place is a kind of extension (διάστημα). In a nutshell, Aristotle argues that place cannot be an extension over and above the bodies for there will be an infinity of coincident places and changing places. As a follow up, we turn to Themistius’ reception of Aristotle’s objection and the additional criticisms against the topology of the atomists and the Stoics that triggered, as we claim, Philoponus’ objections. In this chapter we follow Philoponus’ defence of his extension theory, which does not imply infinity or change of places, as Aristotle suggests. In addition, the chapter investigates the way his theory overcomes difficulties posed by other extension theories in antiquity (those of the atomists and the Stoics) by defining place as the three-dimensional, incorporeal, unaffected and immobile extension that is always filled with bodies. The third chapter (The Ontology of Place According to Philoponus) offers a systematic commentary on the core of Philoponus’ digression on place. His theory suggests that place must be three-dimensional, since it is the physical place of three-dimensional physical bodies. On the ground of the different kind of three-dimensional extensionality of place and of body Philoponus builds his ontology of place. To establish the ontological difference between place and body Philoponus draws on three types of arguments: first, he proceeds to observations pertaining to our common experiences employing examples with clepsydras, vessels with pipes and measurements; second, he uses thought experiments hypothesising something impossible in order to grasp the concept of absolute space and the way it exists in nature; and, third, he attempts to clarify the way place differs from substance, quality and quantity. In this context, place is conceived as an existing reality in the universe, and thus Philoponus’ theory in a sense supports a substantialist view of space. The chapter concludes that Philoponus asserts a special notion of absolute space that, although ontologically different in its own right from the bodies in it, it is the physical place always filled with physical bodies. The ontology of place, as Philoponus sets it, also has consequences on his cosmological views, since he considers the cosmic extension of place (that is three-dimensional, immobile, unchangeable and equal to the whole cosmos) to be a reality that guarantees the arrangement of the bodies in the cosmos given by the demiurge. The fourth chapter (Philoponus on Void as Place) deals with Philoponus’ definition of void as the place of physical bodies. The digression on the void of the commentary establishes the subsistence of the void in nature as a place always filled with bodies and as a necessary condition for locomotion of bodies. The chapter opens with two sections on Philoponus’ conception of empty space (void), examining (a) the fundamental concept of ‘filling up’ (πλήρωσις) which is a prerequisite for our understanding of the way bodies occupy place, and (b) the definition of the absolute empty space. The next two sections of the chapter are concerned with Philoponus’

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arguments for the body’s motion through the void. More precisely, the attention of these sections centres around the way such a theory of place applies to all types of motion (natural and forced) and the arguments demonstrating that the void does not affect the motion of bodies which is entirely related to the natural impulses of bodies. The aim is to show that Philoponus presents a cosmological model of how bodies are in place and move within it, comprehending locomotion as a mutual replacement of bodies caused by the natural impulses of bodies. The chapter concludes with a section relevant to Philoponus’ account of place discussing the dispute that Philoponus had with his teacher, Ammonius Hermeiou, on the nature of the extension of place (τὸ τοπικὸν διάστημα), i.e., place. The study argues that Philoponus proposes a purely physical conception of place of the physical bodies. The final chapter (Philoponus against Aristotle and the Peripatetic Tradition) presents Philoponus’ repudiation of Aristotle’s own doctrine of place. This chapter closely follows Aristotle’s definition of place, namely place as the first immobile limit of the surrounding body that can be characterised as a relativist theory of space, since it implies that the place of a body is relative to the body whose place it is. We present Philoponus’ arguments against the main points of the definition of place found in the Physics, namely place as a limit, the equality between place and the body contained in it, and the immobility of place. The last two sections of the chapter focus on other problems deriving from the Aristotelian definition concerning the motion of bodies and the place of the heavens, a problem with which the Peripatetic tradition up to Themistius was much concerned. Philoponus’ critique of Aristotle and the Peripatetic tradition is a very cautious attack aiming at deconstructing fundamental assumptions regarding the conception of place. Philoponus explicitly intends to dispute the cogency of the arguments that are supposed to support the Aristotelian view. The chapter draws attention to the way a type of substantialist theory of place, such as Philoponus’, attempts to solve problems arising from Aristotle’s sort of relationalist theory of place. The study claims that Philoponus offers satisfactory solutions to problems raised by Aristotle and the Aristotelian tradition regarding the nature of topos. Philoponus’ account proposes a specific physical model of how physical bodies are and move in place, namely that of an existent, absolute, incorporeal extension of place, substituting Aristotle’s rather relativist model. Philoponus regards topos, i.e., the extension of place that is, as an intrinsic reality of the physical cosmos. Due to exactly this model his account may be considered as strictly pertaining to the study of physics, thereby constituting a remarkable episode in the history of philosophy and science.

Chapter 1

Form, Method and Structure of the Physics Commentary This chapter focuses on the form, method and structure of Philoponus’ commentary on the Physics. The first section briefly presents the form of the commentary, recapitulating, so to speak, the secondary literature on this topic, so that the reader will more easily follow the subsequent discussion about the digressions of the commentary which are the main texts under consideration in this study. In relation to its form, the chapter focuses on a philological issue touching on the edition of the commentary by G. Vitelli in the series Commentaria in Aristotelem Graeca and points out changes based on the manuscript tradition that could be useful for a future new edition of Philoponus’ text. Then, the chapter is intended to provide a reading map of the commentary on Physics IV.1-9. First, we examine the relationship between the running commentary and the digressions in the light of Philoponus’ philosophical contributions to the topic. The issue under discussion is how we should conceive of the function of critical observations (ἐπιστάσεις) within the running commentary and digressions (παρεκβάσεις) that deviate from the form of the commentary. Second, the presentation of Philoponus’ method, namely the way he works on Aristotle’s Physics, will allow us to comprehend the boundaries between exegesis and the theory of place established by Philoponus. Finally, the exposition of the structure will elucidate the philosophical content and the sources of Philoponus’ theory of place before moving on to further analyses.

1.1 The form of the Physics commentary Only one commentary on Aristotle’s Physics from the late Platonic school of Ale­ xandria (fifth-sixth centuries) is preserved—that is, Philoponus’ commentary.27 Unfortunately, the comments on the first four books of the Physics are the only ones which have been preserved in their entirety since the comments on the last four books are fragmentary. Based on the results of the existing literature, Philoponus’ commentary on the Physics belongs to a category of commentaries written in a specific form.28 The 27 Simplicius’ commentary on the Physics is not a product of the school of Alexandria, the commentaries of which are my main interest here. 28 The study takes into consideration questions and solutions concerning the form of Philoponus’ commentary that have been raised by other scholars. Golitsis (2008: 55-64; 83-88), for instance, discusses the form of the commentary and attempts to shape a coherent view about the role of the digressions in the commentary. Different types of philosophical commentaries were developed in late antiquity.

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commentary, as we have it, is constructed according to the form called ‘θεωρίαλέξις’ which is actually the form of exegesis Ammonius Hermeiou was using in the school of Alexandria.29 Two different kinds of exegetical comments run through the commentary. First, there are extended comments, which are called ‘θεωρίαι’.30 A theōria is a presentation of the arguments found in a particular passage of the Aristotelian text; usually, these arguments are also analysed and explained. The theōria also contains signs of the methodological approach followed by the commentator. The methodological issues are connected to the way in which Philoponus structures Aristotle’s text and to the way he conceives of, and explains, the Aristotelian arguments. This kind of comment can easily be recognised by the reader, for it is a more systematic and, thus, extended text. It can be thought of as an overview of the structure and the content of Aristotle’s Physics.31 Second, there are shorter comments on the ‘ λέξις’, the term indicating the ‘words’ of someone, as for instance the words of Aristotle.32 This particular kind of comment usually lacks descriptions and generally does not contain analyses of arguments. Thus, the comments on lexis consist of explanatory notes containing textual, grammatical and syntactical clarifications of a single word or a short sentence.33 The structure of a commentary based on the theōria-lexis form appears as follows. First we observe a lemma (i.e., a passage of one or more sentences) taken from Aristotle’s text.34 This lemma can refer to many lines of the Aristotelian text, though we have been given only a few lines of it.35 The following theōria often deals with a larger text than the one given in the lemma. First, Philoponus constructs the theōria of a passage. The theōria is followed by its lexis, always placed after the theōria, in which Philoponus usually comments on several phrases of the whole passage

For instance, a widely used type is the continuous commentary on the whole text, like Alexander of Aphrodisias’, some of Proclus’ and Simplicius’ commentaries. On forms of commentaries and exegesis in late antiquity see Baltussen 2007: 261-273 and Falcon 2017. 29 This structure of commentary seems to be the preferred one of Ammonius’ school in Alexandria and it is attached to the teaching method of the philosopher. 30 This is also Philoponus’ terminology. See in Phys., 552.10-13; 591.23-24. Note that alternatively he uses the expression ‘διάνοια-λέξις’ (in Phys., 125.27-28). 31 See Philoponus, in Phys., 630.6-634.2. 32 Philoponus, in Phys., 548.30-549.1; 591.23-25. 33 The use of lexis has its origins in the ancient literary tradition in order to explain a word, as for instance in Homer’s works, and it is not an invention of the commentators of late antiquity. 34 The expression ‘τὸ πρῶτον τῶν λημμάτων’ (in Phys., 102.13) appears once in Philoponus’ commentary on the Physics. 35 Lemmas should not be considered parts of commentary’s form. It seems that the lemmas are added either by editors of such commentaries or at some point in the manuscript tradition. We should not forget that commentaries used to be written in the margins of the page, around the text that they comment on. Thus commentaries are linked to specific lines of the commented text; lemmas help us to identify what the comments refer to. For a discussion about lemmas in philosophical commentaries see Wittwer 1999: 51-58.

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discussed in the theōria. Afterwards, we find a lemma of the next bit of Aristotle’s text, followed by its theōria and its lexis in turn, and so forth.36 It is important to note that the form of the commentary is a matter of conscious choice: we have evidence from at least two segments of the commentary that Philoponus deliberately chose to use this form of commenting on Aristotle’s Physics. The first, and stronger, piece of evidence derives from a passage where Philoponus refers to things already mentioned in the previous theōria, namely in the third theōria of chapter IV.4. This remark shows the form in which the commentary is constructed; there always is a theōria presenting and analysing the arguments followed by its lexis, which briefly clarifies some terms and sentences.37 The second piece of evidence appears at the end of the second theōria of chapter IV.4. This is a significant passage because, as we shall see, it announces the digression on place. The last sentence of this passage reads: μετὰ τὸ ἐπεξελθεῖν τὸ ῥητὸν ἐροῦμεν, in Phys., 552.13. According to the proposed interpretation, ‘τὸ ῥητὸν’ refers to the immediately following section of comments on the lexis of Aristotle and the verb ‘ἐροῦμεν’ to the digression on place that comes afterwards. In other words, Philoponus, in finishing this theōria, announces that he will run through the lexis, and that after that he will return to examine some arguments.38 During the fifth and sixth centuries commentators had already developed characteristic forms of articulating their commentaries: even the commentators of different schools and times constructed commentaries in similar ways (see, for example, Alexander and Philoponus’ commentaries on the Meteorology). The theōria-lexis form relates to the lectures given in the philosophical school. One pair of theōria-lexis corresponds to a lecture or a lesson in the school.39 Among the 36 This exegetical method has been called ‘double exegesis’. Golitsis (2008: 23) makes use, as he points out, of Évrard’s terminology (1957) according to which the commentator offers a first exegesis (theōria) of a passage and then returns to comment on phrases (lexis) of that passage. 37 Philoponus says in Phys., 591.23-24, ‘This is how some people have explained these passages, as we have already said before in the theoretical introduction to the lecture.’ Transl. Algra—Ophuijsen 2012: 77. 38 Algra—Ophuijsen (2012: 67) translate the sentence as ‘we will expound after having gone through the text’, following the same interpretative line. 39 Later, in Olympiodorus, it appears that lessons were mainly called θεωρία and, at least in one case, πρᾶξις. Sometimes Olympiodorus starts a lesson by referring to what was said the day before in the school (Olymp., in Meteor., 16.25-17.1; 31.3-4). Also see Olymp., in Cat., 70.11; in Meteor., 69.26; 89.12-13; 94.17-18 and in Gorg., 48.10.1-3. The terms ‘θεωρία’ and ‘πρᾶξις’ also occur in Elias, David and Stephanus’ works. See Elias, Proleg., 2.31-32; 29.2; in Isagōgē, 38.25-26; 42.10; 79.6-7; 90.28; 94.30. David, in Categ., 108.14; 117.13-14; 123.11; 124.24; 190.23; Proleg., 2.24; 6.21; in Isag., 83.6; 107.19. Stephanus, in De interpr., 2.9-10; 6.32; 8.28; 37.29; 65.26. In some cases these terms do not appear within the text; however, we can assume that this is the terminology used by teachers and students in the school of Alexandria during the fifth and sixth centuries. But the issue seems to be more complicated. I only wish to make a few remarks on the subject. It seems that both terms, i.e., θεωρία and πρᾶξις, are used to mean the same thing, namely a lecture or lesson. Yet the fact that we have titles like πρᾶξις α΄ at the beginning of a lecture cannot mean that the commentator separates his lectures that way. It could be the case that these titles are not parts of the commentary itself, but rather a matter of editing the commentary. I also often doubt that even the standard expression ‘ἐν οἷς ἡ πρᾶξις/θεωρία’ (which is found at the end

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commentaries by Philoponus preserved for us, only the commentary on the Physics is constructed according to the theōria-lexis form. This form of commentary seems to follow a tradition which derives from the head of the school of Alexandria, i.e., Ammonius Hermeiou. As evidence for this hypothesis, a similar form to that among the commentaries of the school of Alexandria seems to be found in the commentary on the Metaphysics by Asclepius, which seems to be earlier than Philoponus’ commentary on the Physics. This commentary, transmitted as ἀπό φωνῆς Ἀμμωνίου Ἑρμείου, appears to have been constructed according to the theōria-lexis form.40 This evidence suggests that Asclepius’ commentary used Ammonius’ form of constructing his lectures, since it reflects the teachings of Ammonius. Certainly, Philoponus and Asclepius both followed the paradigm of Ammonius’ teachings in some of their commentaries. To conclude, the θεωρία-λέξις form of Philoponus’ commentary allows us to decipher the way in which the commentators of the philosophical school of Alexandria taught philosophy, since a commentary was usually either a text which derived from teachings or a text destined to be taught to pupils. The theōria-lexis form clearly indicates the educational function of the commentary. The theōria section collected Aristotle’s arguments, analysing the syllogisms and sometimes providing historical background on how an Aristotelian passage had been treated prior to Philoponus. The section of comments on lexis clarified the meanings of some words and phrases and, in addition, gave a brief exegesis of a lemma. The distinction between the theōria section and the lexis section is meant to imply not that the lexis is a dinstict structural unit of the commentary but rather a section or a part of the pair theōria-lexis that constitutes an inseparable unit, as the interpretation of the ‘double exegesis’ suggests by admitting two ways of commenting on the Aristotelian text that are not identical, namely the analytical comments on the Aristotelian argument (theōria) and the shorter comments on Aristotle’s phrases (lexis). Thus, a commentary structured according to this form provided the pupil with a line by line overview and analysis of an Aristotelian work by bringing forward Aristotle’s accounts and discussing the problems that had been raised during a long philosophical tradition dealing with Aristotle’s text.

of many sections of the commentaries) derives from the hand or words of the commentators and not from the hands of copyists. My doubts are based on differences found in different manuscripts of the same text. There is a case where the expression occurs in margine (David, in Categ., 178.12). In two cases there are manuscripts where one gives θεωρία and the other πρᾶξις in the same line of the text (David, Proleg., 8.19-20; and in Isag., 99.28). Another example is a sentence which contains both terms: ταῦτα ἔχει ἡ θεωρία καὶ ἡ παροῦσα πρᾶξις, David, in Isag., 113.8-9. In general, it is safer to trust the terms found within the body of the exegesis than those found in the beginning or the end of a comment section. 40 For example, a θεωρία-λέξις pair in Asclepius’ commentary on the Metaphysics is the following: in Metaph., 63.25-65.28 and 65.29-35.

Form, Method and Structure of the Physics Commentary

5

1.2 A note on Vitelli’s edition Having discussed the form of Philoponus’ commentary, I will now consider the standard scholarly edition of that text. The series Commentaria in Aristotelem Greaca (henceforth CAG), published in the nineteenth century by the Academia Litterarum Regia Borussica, has been commonly accepted as the most significant work on the commentary tradition of late antiquity since the first printed editions appeared in Venice from the mid-sixteenth century onwards. With its publication the modern critical editions of the texts of the Aristotelian commentators were finally accessible for study. The publication of the CAG editions prompted the study of the ancient commentators which has now flourished for approximately 100 years.41 This current flourishing has, however, also revealed the need to revise some of these monumental editions—or perhaps to re-edit some of the texts.42 Girolamo Vitelli edited Philoponus’ commentary on Aristotle’s Physics and published it in two volumes in the CAG series (CAG, vol. XVI, published in 1887 and CAG, vol. XVII, published a year later, in 1888). Vitelli’s edition has a disadvantage: it fails to render the form of the commentary accurately. If we look carefully at Vitelli’s edition we see that the theōria-lexis form, according to which the commentary is structured, is not properly presented.43 A closer reading of the text in the CAG edition shows that many of the theōriai end in a paragraph which starts with a lemma from Aristotle’s text. But this is misleading: these paragraphs do not belong to the theōria and should be separate from it in the text. The reason I believe that these final paragraphs really belong to the section of the comments on lexis is that they are short comments on phrases of Aristotle, which is the typical form of commenting on lexis.44 It is easy to recognise them in the CAG edition because Vitelli starts a new paragraph at the end of the lecture (theōria) and types the first sentence(s) of these comments, leaving one space between each letter, just as he does with lemmas; in every case he repeats the lemma of the theōria. The point is that Philoponus, after the presentation and analysis of the arguments in a segment of Aristotelian text, often then comments on the first sentence of that segment. But this indicates the start of the section commenting on the lexis. In other words, Philoponus’ commentary often comments twice on

41 On the importance of the CAG series in the philosophical and philological studies see Praechter 1990. 42 For instance, see P. Hoffmann and P. Golitsis’ new edition of the Greek text of Simplicius’ Corollarium de loco, published online in Teuchos, viewed 18 October 2020: . See also P. Golitsis and P. Hoffmann (2014), ‘Simplicius et le « lieu ». À propos d’une nouvelle édition du Corollarium de loco’, Revue des études grecques 127/1: 119-175. 43 The problem has already been noted. See Golitsis 2008: 57, n. 70; Osborne 2006: 7-8. 44 Some characteristic examples of the long list of these paragraphs are: in Phys., 501.13-20; 518.26-519.8; 589.19-26; 699.21-26.

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one phrase—i.e., on the same lemma from Aristotle’s text—first in the theōria and then in comments on its lexis. The question is: why did Vitelli present the form of the commentary in this way? I argue that the source of this mistake is the way lemmas are presented in the manuscripts. Lemmas were not always chosen by the commentators, but by copyists or by whoever edited the commentary. The role of a lemma is to indicate what the comments refer to. Different manuscripts, even those belonging to the same family, present lemmas differently. Vitelli’s edition is mainly based on three manuscripts: the Laur. Plut. 87, 6 (G), the Marc. gr. 220 (K), and the Marc. gr. 230 (M). Moreover, Vitelli relied heavily on Trincavelli’s first printed edition of the text.45 The oldest manuscript, the Laur. Plut. 87, 6 (twelfth century, henceforth Ms. G), articulates the Aristotelian text and Philoponus’ comments in an intricate way. Ms. G provides the whole text of Aristotle that is examined in each theōria, not merely its first lines. The same applies to the lemmas of the lexis section. Moreover, these lemmas are presented as distinct paragraphs, indicated by paragraph marks and by numbers in margine. Each lemma from the Aristotelian text and the subsequent comment by Philoponus have corresponding numbers. The crucial passages, which Vitelli kept as the last paragraph of the theōria, appear in Ms. G as separate paragraphs (indicated by signs) at the end of the theōria, without a lemma quotation from the Aristotelian text. The codex Marc. gr. 230 (Ms. M), dated, according to Vitelli, to the fourteenth century, has quotation marks in margine for the lemmas of Aristotle’s text, and rather than long sections of the text, just one or two sentences are given. The quotation marks in margine clearly separate the theōria sections from the lexis ones. So the comments that Vitelli includes in the theōria are not presented as parts of the theōria in Ms. M. Finally, in the codex Marc. gr. 220 (Ms. K), dated to the fifteenth century, marks (double dots) separate the lemmas from Philoponus’ comments. The lemmas usually consist of a few Aristotelian words. The comments that Vitelli includes in the theōriai are clearly separated from the theōriai with lemmas in Ms. K. Vitelli’s edition partly follows Ms. G, in that it articulates these comments as a paragraph of the theōriai, and partly follows Mss. M, K, in that these comments appear after their lemmas. I assume that Vitelli thought this was the best way to stay close to the manuscript tradition. According to this view, the reason Ms. G does not indicate the first comment of some lexeis with a lemma and a number, but only with paragraph marks, is that the lemma of this very first comment of the lexis section has already been given in the lemma introducing the theōria. But this does not mean that it should be considered part of the theōria section: it is clearly separated 45 Victor Trincavelli, Ioannis Grammatici in primos quatuor Aristotelis de naturalia auscultatione libros commentaria, Venice, 1535.

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from the theōria by the paragraph marks. What Mss. M and K do is to repeat some words of the lemma of the theōria in order to show that these comments are lexeis. The theōria-lexis form of the commentary is inaccurately presented if these passages appear as the last paragraph of the theōriai. Philoponus considers it necessary to comment briefly on the lemma which heads the previous theōria, whether he has said something about it in the theōria or not. This is not a rule of the theōria-lexis form, but rather a matter of exegesis: if the lemma needs a word by word explanation, then Philoponus includes this second exegesis. What Vitelli seems to have missed is that these paragraphs should clearly open the lexis section. His confusion is also indicated in the way he uses lemmas above a theōria or a lexis section in his edition: wherever he thinks that a lexis section starts, he clearly separates it from the theōria section with lemmas, though he does not do so in the cases discussed here. But the manuscript tradition, either by separating the comments as paragraphs without a lemma or by separating them with a lemma, suggests that these are comments belonging to the lexis section, not to the theōria. Moreover, the form and content of these comments show where they belong. The correct way to present the theōria-lexis form is to place the lemmas above these paragraphs to and to separate them from the theōriai. Although Vitelli’s edition is faithful to the transmission of the text in the manuscripts, he, nevertheless, partly misinterprets the form of the commentary.

1.3 The form of the commentary and Philoponus’ philosophical contributions Philoponus’ commentary on the Physics has become famous since antiquity for two main reasons: the critique of Aristotle’s theory of place and his views on the void found in the so-called Corollarium de loco and the Corollarium de inani respectively, and the theory of the forced motion of projectiles (impetus).46 But before considering in more depth how Philoponus rejects Aristotle’s account, I would like to make a few remarks about the meaning and the use of the word ‘corollarium’ in the case of Philoponus’ texts on place and the void. In standard Latin the word ‘corollarium’ means ‘money paid for a garland, a gift, a present, a gratuity’; in logic it means ‘deduction’. The word ‘corollary’ in English, which comes from the Latin ‘corollarium’, means, as a noun, ‘a logical proposition that follows from one already proved, a direct consequence, a result’ or, as an adjective, ‘supplementary, something which comes to complete, an accomplishment’. In scholarship on Philoponus’ commentary, the word ‘corollary’ is used to mean those parts of the commentary which complete the comments. Vitelli, the editor of Philoponus’ commentary on the Physics, called ‘corollaries’ Philoponus’ excursuses 46 Corollarium de loco, in Phys., IV.4, 557.8-585.4, Corollarium de inani, in Phys., IV.9, 675.12695.8, and the impetus theory in Phys., 639.3-642.26.

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on place and the void, following H. Diels who used the same word to describe Simplicius’ excursuses on place and time. The term ‘corollary’, for Diels and Vitelli, most probably means ‘the crowning’ of the commentary, recognising that these texts are inserted as supplements. However, scholars pointed out that the way Philoponus’ excursuses on place and the void are inserted in the commentary leads to the adoption of a more technical term related to the style and the philosophical content of these texts. The question has been examined by Golitsis, who establishes the term ‘digression’ in his book, though, in French, he seems to use the terms ‘digression’ and ‘corollaire’ interchangeably.47 Based on Golitsis’ idea, I would like to elaborate more on this subject because, as I will argue, the digressions of the commentary are not just a matter of differentiation of style and content with respect to the running commentary, but also may have a connotation relating to the form of the commentary that helps us comprehend better how Philoponus integrated these texts in his commentary on the Physics. We do have one piece of evidence for what some parts of the commentary were called in Greek: the word ‘παρέκβασις’ written in margine of the manuscript Marc. gr. 230 (Ms. M2) by an unknown hand at the point where the texts on place, on the motion of projectiles (impetus) and on the void respectively start.48 The Greek word ‘παρέκβασις’, i.e., digression,49 literally means in English ‘going aside from’ or ‘a deviation from constitutional forms’. ‘Digression’ is the term used by V. Trincavelli in his edition of the commentary and by Dorotheo in the Latin translation of the commentary in which he indicates the relevant texts with the heading ‘digressio’, clearly separating them from the running commentary.50 Unfortunately, Philoponus himself does not use any term to describe these two parts of his commentary.51 Philoponus refers to the part dealing with place—I leave aside the section on the impetus theory for the moment—with the expression ‘ἐν τοῖς περὶ τοῦ τόπου λόγοις’.52 When we reach the point in the commentary where these parts—i.e., the sections on place and the void—start, it is obvious that the continuity of the comments has been interrupted. Two passages, one before the section on 47

Golitsis 2008: 124. Cod. Marc. gr. 230, f. 128v: παρέκβασις, f. 143v: παρέκβασις περὶ τῶν ῥιπτουμένων, f. 150r: παρέκβασις. 49 The term ‘παρέκβασις’ (in Latin ‘digressio’) has a long tradition in rhetoric as a technical term; Quintilian and Cicero were considered masters of digression which was an excursus at first glance irrelevant to the main subject but finally leading to it. See, for instance, the digressions in Cicero’s Brutus and the digressions cited by Canter 1931. 50 Α s Vitelli points out in his Conspectus librorum manu scriptorium et impressorum (CAG, vol. XVI: xv). Also see Dorotheo (1542), Liber quartus, f. 11r and f. 30r. 51 The term ‘παρέκβασις’ occurs twice (in Phys., 393.15-16 and in Phys., 458.15-16) in Philoponus. Of these, only the second occurrence is worth noting: δυνατὸν μὲν οὖν ἦν ἐπὶ πλεῖον τὸ ἀνόητον τῶν τοιούτων λόγων ἐλέγξαι, ἀλλ’ ὡς ἐν παρεκβάσει ἱκανὰ καὶ ταῦτα. The term appears in Contra Proclum, XI.1, 407.18-21: εὔλογον ἡγοῦμαι πρὸ τῆς τοῦ προκειμένου ἐπιχειρήματος ἐξετάσεως μικρόν τι παρεκβάντας διασκοπῆσαι […]. 52 Philoponus, in Phys., 675.21; 687.15-16; 688.33; 694.17. 48

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place and one before the section on the void, announce that the comments will cease for the moment and that a discussion of Aristotle’s accounts will begin.53 But what do we mean by interruption here? In my view, interruption should be understood as deviation from the θεωρία-λέξις form of the commentary—i.e., a παρέκβασις. This is announced, first, by the introductory comments to the digressions. Second, the first sentence of each digression shows that we have now left the exegesis aside.54 These parts of Philoponus’ commentary are closely related to his exegetical comments on Aristotle’s accounts of place and the void; in that sense, these texts are not digressions—they are not true interruptions in that they do continue to develop the commentary’s conceptual concerns. Nevertheless, these texts can be considered as παρεκβάσεις in the sense that they break up the main form of the commentary, since they interrupt the continuity of the theōria-lexis-theōria-lexis schema. Although we do not know if Philoponus would have called these two parts (on place and the void) ‘digressions’, it seems to be a reasonable speculation. The word ‘corollary’ (which was traditionally used for these texts by Diels and Vitelli in nineteenth century) does not sufficiently describe what the excursuses on place and the void are. For to say that these texts just complete, or are ‘crownings’ of, the exegetical comments on place and the void (i.e., are corollaries) and to say that these texts diverge from the exegetical comments or interrupt the course of the commentary (παρεκβάσεις) are different things. For this reason, I will refer to the two texts on place and the void as παρέκβασις, translated as ‘digression’, not as ‘corollary’, since the latter term fails to convey the idea that the form of the commentary has been interrupted. Since there is no strong evidence provided by Philoponus himself, the most reliable solution is to follow the later tradition (anonymous comment in Ms Marc. gr. 230, V. Trincavelli, Dorotheo) that conceives of these texts as digressions of the commentary. To protect the reader from confusion, I should say here that the term ‘digression’ is utilised to clarify the differences between the running commentary and Philoponus’ excursuses on place and the void. In fact, this clarification leads to a further remark regarding other passages in Philoponus’ running commentary. Philoponus often expresses his own arguments and appears to criticise Aristotle but does so in order to complete the topic under examination without interrupting the theōria-lexis form of the commentary. In other words, he proceeds to express his own argument on a specific topic within the exegetical framework—action that is known in late antiquity as ἐπίστασις. The term ‘epistasis’ is attested to in the late commentary tradition to describe further reflections of the commentators that 53

in Phys., 552.10-13; 651.1-4. The opening sentence of the digression on place says: καιρὸς δὴ λοιπὸν καὶ τὰ παρ’ ἡμῶν προστεθῆναι τῷ λόγῳ, in Phys., 557.8. The digression on the void begins: μέχρι μὲν οὖν τῶν ἐνταῦθα πέρας ἔχουσι τῷ Ἀριστοτέλει οἱ περὶ τοῦ κενοῦ λόγοι, δεῖ δὲ ἡμᾶς ἄνωθεν ἀναλαβόντας τὸν λόγον ἕκαστον τῶν ἐπιχειρημάτων ἐπισκέψασθαι, in Phys., 675.12-14. 54

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in many cases are critical observations.55 Philoponus’ commentary on the Physics contains several epistaseis that are all, in my view, critical. Some of these critical observations appear in the theōria section of a lecture and some, surprisingly enough, in the section of comments on the lexis of Aristotle. Here is a list of the epistaseis found in the commentary: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.

14. 15.

On the generation of being (54.8-55.26). On matter (191.9-192.2). On ideas/forms (225.4-226.11). On a possible objection to Aristotle concerning motion (384.3-385.11). On the infinity of matter (401.1-403.31). Against the eternity of time (456.17-458.31). Defending Plato against Aristotle (524.1-22). Place is not the limit of the containing body (592.15-32). Rejecting the suggestion that the place of bodies has a power or quality (632.4-634.2). On the forced motion of projectiles: the impetus theory (639.3-642.26). On the fact that nothing moves against nature through void (644.15-22). Against Themistius on the explanation of the ‘into an equal amount’ (εἰς ἴσον) in Physics, 216b26 (671.7-672.17). Against those who state that the reason that two bodies cannot be in the same place and that heaven does not rise in waves (κυμαίνει ὁ οὐρανός) is the condensation (πύκνωσις) and rarefaction (μάνωσις) of bodies (697.25699.20). On time and corruption (748.7-33). On being in motion with regard to the whole and to the parts, because of being in place with regard to the whole and to the parts (774.6-775.5).

The digressions, on the other hand, are systematic arguments which interrupt the continuity of the theōria-lexis form and attack the whole Aristotelian theory of place and the Aristotelian argument that motion in void cannot occur. Here are the digressions found in the commentary: 1. Digression on place (557.8-585.4). 2. Digression on the void (675.12-695.8).

55 The manuscript tradition of Philoponus’ commentaries attests that some of them (namely, the commentaries on the De anima, on the De generatione et corruptione and on the Anlytica Posteriora) contain his own critical observations on various topics. See also Philoponus, in Anal. Post., 322.14-19. I agree with Golitsis who establishes the meaning of ‘epistasis’ as ‘criticism’ in the context of philosophical commentaries of late antiquity (see, Golitsis 2019: 169-172).

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What allows us to identify an internal boundary in Philoponus’ commentary, and thus distinguish critical observations and digressions from the remaining exegetical comments? In general, there are three characteristics which critical observations and digressions have in common. First, both digressions and critical observations make use of the first person singular or plural of verbs and of the personal pronoun (ἐγώ, ἡμεῖς). The commentator frequently, and explicitly, uses these forms, which indicate that this section of the commentary is a critical observation or a digression, in order to separate his position from Aristotle’s account. Second, the critical observation and the digressions are not just exegetical comments, even though the critical observations are placed within the exegetical framework. Philoponus seems to care about the cogency of Aristotle’s arguments,56 and he seems to care about the truth.57 He often aims to clear up the misconceptions and fallacies58 that arose from Aristotle’s views of place and void by demonstrating that there is no necessity in some of Aristotle’s arguments; it turns out that Philoponus tries to re-establish the truth about natural phenomena in these sections. In more or less every critical observation and digression we find this intention, which goes beyond a simple clarification—it provides a new argument. Third, the method used in the critical observations and the digressions is similar in every case. That is to say, most of the comments are just explanations and presentations of arguments, but when a critical observation or a digression is introduced, Philoponus usually quotes Aristotle’s arguments and then proceeds to reject them by developing his own arguments during the discussion. These shared characteristics are found in both critical observations and digressions and differentiate them from the exegetical comments. Nevertheless, there is a crucial difference in the way Philoponus introduces critical observation and digressions: in the case of the two digressions on place and the void Philoponus announces the interruption of the comments (in Phys., 552.10-13; and 651.1-4), whereas critical observations appear in the exegesis without any previous indication—this is because critical observations are considered to be (ad hoc) criticisms, closely related to the exegesis. The remark that I wish to make about critical observations and digressions and their relation to the general form of Philoponus’ commentary, the θεωρία-λέξις form, affects the picture that modern scholarship has had of the whole commentary on the Physics. This distinction between critical observations and digressions is not entirely compatible with the most recent presentation of Philoponus’ commentary, namely that of Golitsis. Golitsis argues that Philoponus’ commentary contains three digressions: one on place, one on the void and one against the eternity of time 56 See

in Phys., 557.9; 632.7; 639.4-5; 676.1-2; 680.24-26. Ibid., 651.1-4; 687.23-24. 58 σύγχυσις, ibid., 567.5; παραλογισμός, ibid., 685.23. 57

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(i.e., the sixth critical observation of my list).59 Golitsis calls the first two digressions, according to his division, ‘scientific digressions’, and the third a ‘polemical digression’. He argues that the digression, as he calls it, against the eternity of time belongs to a category of digressions concerned with points to the exegesis.60 I do agree that the passage on the eternity of time closely relates to points of the exegesis since it follows the exegesis of Aristotle’s argument on the eternity of time (Phys., 206a25 ff.). And I do agree that this critical observation is polemical, though I would not call it a digression. What seems inconsistent to me in Golitsis’ definition of a digression is this: he says that he will also examine another section of the commentary, that in which Philoponus expounds the impetus theory, but he states that this section does not belong to any of the categories of digressions he has already mentioned.61 In addition to this, Golitsis argues that the passage on the eternity of time is the only part of Philoponus’ commentary that qualifies as a digression (apart from the digressions on place and the void).62 But, seen side by side, the section against the eternity of time and the section on the impetus theory share the same characteristics: for example, both sections are related to points in the exegesis and both texts are polemical. So, if the section on the impetus theory is not a digression, according to Golitsis’ categorisation, then the section against the eternity of time too should not be considered a digression. An attentive reading of the commentary shows that Philoponus quite often added arguments at the end of theōriai (or the sections of comments on Aristotle’s lexis), i.e., critical observations, when he thought it necessary. Sometimes these additions have a critical character; the case of the critical observation on the motion of projectiles is one of them. Although I do not consider this section a digression in the sense of a deviation from the form of the commentary, it has, as I pointed out earlier, been called a παρέκβασις (codex Marc. gr. 230, f. 143v).63 But the use of 59

Golitsis 2008: 87-88. ‘Digressions portant plutôt sur des points d’exégèse; […] ainsi que la brève digression de Philopon consacrée à l’éternité du temps.’ Golitsis 2008: 87. The fact that Philoponus refers to this section as a παρέκβασις (in Phys., 458.16) is not evidence of a strict distinction between different parts of the commentary. 61 ‘Enfin, nous étudierons les digressions scientifiques des deux commentateurs, auxquelles nous ajouterons le bref excursus de Philopon consacré à la question du mouvement contre nature (In Phys., 693.3-642.26), où il développe sa célèbre théorie de l’impetus. Cette partie du Commentaire ne constitue pas une digression selon les critères formels que nous avons adoptés plus haut; elle se situe néanmoins dans la même perspective que les deux Corollaires sur le lieu et le vide et mérite d’être étudiée avec eux.’ Golitsis 2008: 88. 62 ‘Outre ses Corollaires sur le lieu et le vide qui contredisent ouvertement Aristote, la seule autre partie de son Commentaire qui puisse être qualifiée de digression présente, elle aussi, un caractère polémique.’ Golitsis 2008: 124. 63 Indeed, when we read the critical observation on projectiles (in Phys., 639.2-642.26) the introductory sentence reminds us of the digression on place, in which Philoponus claims the cogency of Aristotle’s arguments (in Phys., 639.3-5): ‘So, in this way, Aristotle showed that motion that is forced 60

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the term—the reader of the codex Marc. gr. 230 noted in margine: παρέκβασις περὶ τῶν ῥιπτουμένων—cannot be explained as an attempt to present the form of the commentary, in the way modern scholars do. Although the reader of this manuscript and his notes on these significant sections of the commentary inspired my interpretation of the digressions, I do not agree with his annotations in every respect. So Philoponus’ attack on Aristotle’s view of the motion of projectiles should not be considered a deviation from the theōria-lexis form of the commentary. The innovative content of the critical observation—the attack actually introduces a new theory of the motion of projectiles (impetus)—makes it tempting to see it as a digression. Nonetheless, formally speaking, this text is a critical observation ad hoc and not a digression: it belongs to the second lecture on Physics IV.8, as a part of the exegetical comments. Therefore, the fact that a critical observation includes original insights is irrelevant to the structure and form of this commentary. The picture of the commentary, in Golitsis’ presentation, is of three digressions and a section (on impetus theory), which is closely related to the digressions on place and the void (2008: 87-88). However, I propose to read the excursuses on place and void as the only digressions of the commentary and the rest of the philosophical contributions of Philoponus as epistaseis (which run to a total of fifteen) in which he adds to the discussion something more than a simple explanation of the Aristotelian arguments. The distinction between critical observations, which appear in the θεωρία-λέξις form, and digressions, which deviate from this form, provides, I think, sufficient guidelines for reading Philoponus’ commentary. The advantage of this reading is that it explains why the digressions are placed as they are and shows the function of all the critical observations found in the running commentary. This brief discussion about the form of the commentary aims at providing a way of reading Philoponus’ commentary on the Physics. Let us now move on to another question, namely how Philoponus works as an exegete, but also as a reader, of Aristotle’s Physics. So, before focusing on the digressions of the commentary and their argument, we will proceed to some remarks concerning Philoponus’ methodological approach to the Physics.

1.4 Levels of interpretation The exegesis conveys different levels of interpretation, starting from simple aporiai (questions) up to the production of new philosophical theories (digressions). When we read a late antique commentary we immediately realise that there is a writer (or a teacher) working on and thinking about the text of a philosopher.64 Commentaries and contrary to nature would be impossible if the void existed; but it seems to me this argument is not at all cogent.’ 64 E.g., in sentences such as this one: ταῦτα δὲ ἐκ στοχασμῶν φαμέν· οὐ γὰρ ἔχομεν εἰπεῖν σαφῶς τί βουλόμενος ὁ Ζήνων τοῦτο ἠπόρει. ἴσως δὲ καὶ τὸ ἄπειρον εἰσαγαγεῖν βουλόμενος. Philoponus, in Phys., 513.11-13.

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were mostly produced in philosophical schools and, if not, they are still lively and intellectually stimulating texts. Philoponus’ commentary has all the characteristics of a typical (Alexandrian) philosophical commentary of the sixth century and, at the same time, its content is philosophically innovative. Often questions emerged that needed to be answered either in the lessons of the schools or in private while reading the text of a philosopher. The basic task of all commentaries is to explain difficulties and answer questions. The methods of the commentators, their interpetations and the form of their commentaries also depend on the level of difficulties to be resolved. The first and simplest level of interpretation in commentaries is often signalled, for instance, by the expression ‘ἀκουστέον’. This technical term is common in the commentary tradition. In the case of Philoponus’ commentary on the Physics the expression occurs when Aristotle’s text is not straightforward and easily comprehensible. The term signifies how Aristotelian arguments or words should be interpreted, either according to the Aristotelian doctrines or according to Philoponus’ exegesis.65 The commentator clarifies for the pupils how the text should be understood, giving an alternative reading, explanation or word. This is the simplest and most basic way for the commentator to give an interpretation. The second level of exegesis appears in the form of questions: these questions may really have been asked, or they may be raised in the commentary in order to object to a hypothetical opponent.66 These questions (or objections) serve to confirm the proper understanding (ἀκουστέον) of Aristotle’s words. Within the running commentary two types of questions occur: (1) questions solved within the Aristotelian framework, in the sense that Philoponus uses Aristotle to answer these questions;67 (2) questions deriving from Aristotle’s discussion but going beyond Aristotle’s worries.68 Neither type of question is supposed to be Aristotle’s: these are questions (or objections) set up by the commentator throughout the discussion of Aristotle’s views, and they are either addressed to hypothetical opponents of Aristotle or related to interpretations held by other commentators, or, rarely, addressed to Aristotle. The second type, in particular, often appears as a general question by someone—this could be Philoponus—and the answer given may represent Philoponus’ answer to

Ιn Phys., 530.2; 532.12; 601.25; 651.19. The term ‘ἀπορία’ is usually employed by Philoponus. It is important to note that one reads in margine of f. 18r (counting from the page that starts the commentary on the fourth book in Ms. G, Laur. Plut. 87, 6) the abbreviation of the word ‘ἀπορία’ where the question starts (in Phys., 509.15), and the abbreviation of the word ‘ λύσις’ where Philoponus’ answer starts (in Phys., 509.22). This is the text in which Philoponus raises the question whether or not place is the efficient cause of natural motions (in Phys., 509.15-510.2). 67 See, for instance, in Phys., 588.20-27; 670.26-671.2. 68 Ιn Phys., 509.15-510.2. 65

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the question (or objection), or it may be a standard response from the commentary tradition.69 The habit of posing hypothetical questions and objections through the exegesis cultivates the ground for more profound thoughts that constitute what was called ‘critical observation’ (epistasis) in section 1.3. The manuscript tradition of the commentaries attributed to Philoponus emphasises his attitude to adding his own thoughts on specific philosophical problems in the titles of the commentaries. Three of his early commentaries, which are largely reportationes of Ammonius’ teachings, contain a few epistaseis, namely the commentaries on Aristotle’s De anima, Analytica posteriora, and De generatione et corruptione. The commentary on the Physics is based on Ammonius’ teaching, but Philoponus seems to be less attached to the views of his teacher. Thus the reader finds many and lengthy critical observations in this commentary. The critical observations constitute the third level of interpretation; their starting point can be thought of as an intention to solve a serious difficulty. But there is a difference. An observation of this kind is a critical comment which offers a new insight into the discussion. Philoponus certainly praises Aristotle’s ability to present sound arguments.70 But sometimes he believes that Aristotle’s arguments lack cogency; they are proved to be invalid. Philoponus questions Aristotle or other commentators and he repudiates unsatisfactory arguments. The critical observations belong to the running commentary because they complete the comments on a section of the exegesis. Philoponus puts a lot of effort into providing a meaningful exegesis of Aristotle’s text—this involves sometimes radical criticisms of arguments. For example, the epistasis on the forced motion of projectiles (impetus theory) is one of the most characteristic polemical passages of the commentary. The aim of this critical observation is to offer a sound explanation of the projectile’s motion against Aristotle’s vague view. Critical observations provide a link to the fourth level of interpretation found in Philoponus’ commentary on the Physics. Critical observations, I think, are a 69 Α s, for instance, in the passage in Phys., 509.15-510.2: ‘With respect to this (last argument) one might raise the following difficulty. If what is striving for the good wants to be in a good state, and if what is striving for health wants to be in health, and if similarly what is striving for a particular place wants to be in that place, why is it not the case that, just as the good and health are the end of the things that strive for them, so also place is the end of the things that want to be in it? For certainly everything is at rest and stops striving as soon as it has reached that which was the object of its striving, just as things in locomotion also stop moving once they have reached their natural place, which is indeed what they are striving for. So how come, then, that their place is not a final cause? I reply, first as has already been said, that things striving for something when they have obtained it, in so far as is possible for them become that which is the object of their striving, and are named after it …’, trans. Algra—Ophuijsen 2012: 28-29. 70 In several passages Philoponus approves of Aristotle. For instance, we read (in Phys., 599.11-12), ‘The following, too, reasonably applies to things that are in a place: that each tends to move to its proper place and remains in it. And this he establishes very elegantly.’ Trans. Algra—Ophuijsen 2012: 84; see also in Phys., 620.4-5.

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necessary step to creating the form of text used in the digressions on place and the void. These digressions, however, are not parts of the running commentary: they interrupt the course of the comments, i.e., the sequence of the theōria and lexis sections. The digressions are fairly long texts in which Philoponus methodically gathers Aristotelian arguments from the accounts on place and the void that are not true according to logical necessity. As will be shown, in the digressions Philoponus repudiates Aristotle’s theory of place and his opinion on the void. At this level the text is not just interpretative. In contrast to the running commentary, which is mainly exegetical, Philoponus uses digressions to establish alternative theories. But, although the digressions are relatively self-standing treatises that could be read without the commentary, there is no evidence of their separate circulation. The digressions are interpretations inasmuch as they start from Philoponus’ understanding of specific Aristotelian arguments, but they exceed the exegesis in the sense that they include new theories, new arguments. It is worth pointing out that, after the digression on place, there are signs of Philoponus’ own views within the exegetical comments.71 A shift can be seen from exegesis to the investigation of how far Aristotle’s views of place and the void are applicable to nature. The levels of interpretation help us to distinguish ‘Philoponus as a working exegete of Aristotle’ from ‘Philoponus as a philosopher of his own right’. To recapitulate, we first looked at two levels of interpretation: one regarding how Aristotle’s words should be understood (ἀκουστέον) and another based on questions (or difficulties) concerning the exegesis, usually supporting Aristotle. The third level of interpretation contains Philoponus’ own philosophical contributions (epistaseis). A critical observation starts from a difficulty, but challenges Aristotle’s arguments. At this level of interpretation Philoponus takes a position against Aristotle (or others) and provides an opposing argument. The critical observations complete the discussion of a passage, providing new insights within the exegesis. Finally, the digressions on place and the void complete the picture of Philoponus’ interpretative style in his commentary on the Physics. His style in the digressions differs from the reader’s expectations for the exegesis of the running commentary: the digressions are continuous texts, uninterrupted by lemmas, and Philoponus uses verbal forms showing his own contributions to the discussion of the problems. The content and structure of the commentary introduce some innovations to the commentary tradition (of course, Simplicius’ commentary on the Physics is a parallel example).72 The critical observations and the digressions introduce a kind 71 For instance, see in Phys., 587.26-588.27; 592.29-32; 598.3-30; 632.4-8. However, an earlier sign of Philoponus’ own theory of place in the running commentary is this (in Phys., 408.7-9): τὶς ἡ ἀποκλήρωσις ἐν ἑνὶ μὲν μέρει τοῦ κενοῦ εἶναι σῶμα, μὴ καὶ πανταχοῦ δὲ εἶναι, εἴπερ τὸ κενόν τόπος ἐστίν ἐστερημένος σώματος; 72 Golitsis (2008) offers a parallel reading of Simplicius’ and Philoponus’ commentaries on the Physics.

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of dialectic between the commentator and the text. It is not—or, at least, it is not only—the dialectic between the authority (Aristotle) and the commentator (Philo­ ponus); it is, further, the dialectic between the philosopher Aristotle and the philo­ sopher Philoponus that opens the ground for philosophical debates.73 It would not be excessive to say that Philoponus, in many cases, stands up to Aristotle, equal to equal. This kind of dialectic reconfigures the relationship between authority and commentator. But, despite these innovations, Philoponus relies much on the commentary tradition, as every commentator does. The refutations found in the digressions on place and the void and in the critical observation Philoponus made on projectiles (impetus theory), especially, introduce a different model of physics, a different image of nature; in this sense Philoponus stands shoulder to shoulder with Aristotle, as his equal. Philoponus contests Aristotle’s views on place and the void by proposing a new theory. As a follow up to the discussion about the levels of interpretation in the Physics commentary let us turn to the method with which Philoponus approaches the text of the Physics.

1.5 Dividing Aristotle’s Physics into lectures Philoponus develops a double methodological approach within the theoretical part of the lectures (θεωρίαι): (a) his own method of articulating Aristotle’s text and (b) his method of presenting Aristotle’s approach to his subjects of inquiry. The latter also relates to the methods of explanation that Philoponus elaborates. His commentary is not supposed to be just a compilation of comments. Another aspect of the commentary’s form is that it offers a structured reading of the Physics. The commentator establishes his personal articulation of Aristotle’s arguments and text, just as generally happens in the commentary tradition. In what follows the starting point of the discussion is the question: what does the division of Aristotle’s text into lectures mean? To put it differently, how did Philoponus structure his courses and divide Aristotle’s Physics? In addition, one may ask: how does Philoponus introduce and explain Aristotle’s arguments? The investigation of Philoponus’ approach to the Physics will focus on the chapters which deal with place and the void (Philop., in Phys., IV.1-9). Before we examine Philoponus’ approach in more depth it is useful to present the division of Aristotle’s Physics IV.1-9 and the corresponding lectures in Philoponus’ commentary, as in Table 1:

73 Christian Wildberg (2008a) argues that: ‘… it seems certain that what essentially enabled Philoponus to operate both as a critic of Aristotelianism and as a constructive thinker in his own right was somehow tied up with new understanding of what one ought to do when one is reading and interpreting the philosophical texts of Plato or Aristotle.’ On Philoponus’ critical stance towards Aristotle’s authority also see Golitsis 2016: 431-436.

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Chapter 1 TABLE 1: Philoponus’ division of Aristotle’s Physics IV.1-9 into lectures

Aristotle’s Physics IV.1-9

Philoponus’ commentary on Physics IV.1-9

Introduction. Questions on the nature of place: IV.1 (208a27-209a2) IV.1 (209a2-30)

IV.1 (496.5-501.20) IV.1 (504.8-510.26)

Place is neither form nor matter: IV.2 (209a31-210a13)

IV.2 (514.7-519.8)

Ways of being in something and being in place: IV.3 (210a14-b8) IV.3 (210b8-31)

IV.3 (526.10-528.22) IV.3 (533.20-536.20)

Definition of place and arguments against other optional definitions: IV.4 (210b32-211b5) IV.4 (211b5-212a7) IV.4 (212a7-30)

IV.4 (539.17-543.4) IV.4 (546.25-552.13) Digression on place (557.8-585.7) IV.4 (585.5-589.26)

Further considerations about bodies in place and the place of the universe: IV.5 (212a31-213a11)

IV.5 (593.11-600.24)

Introduction. Questions on the nature of the void: IV.6 (213a12-b29)

IV.6 (606.25-610.23)

Arguments against those who posit the void: IV.7 (213b30-214a26) IV.7 (214a26-b11)

IV.7 (616.9-619.22) IV.7 (623.19-628.24)

Against the view that the motion is possible in the void and that the void exists as separate: IV.8 (214b12-28) IV.8 (214b28-215a24) IV.8 (215a24-216a11) IV.8 (216a11-b21)

IV.8 (630.6-634.2) IV.8 (636.23-642.26) IV.8 (645.27-651.4) IV.8 (660.7-662.27)

Against those who posit the void through the conception of the dense and the rare: IV.9 (216b22-217a21) IV.9 (217a21-b28)

IV.9 (667.6-675.12) Digression on the void (675.13-695.8) IV.9 (695.9-699.26)

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Let us begin with the question: how does Philoponus present Aristotle’s arguments of Physics IV.1-9? Philoponus often prepares more than one lecture for each chapter of the Physics (as indicated in Table 1). In the commentary on IV.1-9 we find three cases where Philoponus has just one lecture that covers the whole chapter: these are chapters IV.2, IV.5, and IV.6. The remaining comments on the chapters of book IV (chapters 1, 3, 4, 7, 8, 9) are divided into two, three, or even four lectures, such as, for instance, section IV.8. Every lecture divides each chapter into parts according to the way in which Philoponus decides to present Aristotle’s text. Sometimes Philoponus follows Aristotle’s divisions: for example, when Aristotle examines the question ‘what is place?’ (Phys. 209a2-30), Philoponus prepares a single lecture (in Phys., 504.8-510.26) containing all Aristotle’s arguments on this question. However, there are cases where Philoponus divides the text according to his own priorities. A striking example is the second lecture of chapter IV.9 (in Phys., 695.9-699.26), where he cuts off Aristotle’s sentence in the middle (Phys., 217a21), places his digression on the void in between the two halves, and then starts a new unit with a new lecture. In this way, Philoponus offers his own understanding of how the text should be read and how it should be separated into units. In addition, he carefully distinguishes units within the chapters of the Physics. It is also worth pointing out that Philoponus systematically lists Aristotle’s arguments. But as we have seen, the θεωρία section is not just a list of arguments. Philoponus often tries to analyse an argument which Aristotle sketched in rough outline. He also tries to reconstruct arguments by revealing hidden premises. The obscurity of Aristotle’s words (ἀσάφεια), notorious among the commentators of late antiquity, sometimes forces Philoponus to analyse these arguments. A commentator’s duty, roughly speaking, is to unveil the hidden meaning of Aristotle’s sayings.74 In the context of clarifying the Aristotelian word, Philoponus in his lectures provides examples and raises questions of his own, as we shall immediately see. A lecture always begins with the description of Aristotle’s method of approaching the subjects of inquiry.75 Philoponus recapitulates in a few lines what Aristotle has previously said and what he is planning to say. This methodological approach does not occur solely at the beginning of the lecture but also within it, when a unit is completed, and a new issue is raised. One reason that Philoponus includes this methodological element in the theoretical part of the lecture is to make the exegesis comprehensible to the audience. It is helpful for students to have a clear, concise reminder of what Aristotle said and of what Philoponus is intending to 74 Philop.,

in Categ., 1.12-13. A characteristic example appears in this passage (in Phys., 636.25-28): ‘Having shown that the void is not a cause of motion either as efficient or as final, he wants finally to show that neither can the void be a cause of motion as through which, like the instrumental, but before that he takes up the things that have been said and shows what follows from these for their hypotheses.’ Trans. Huby 2014: 37-38. Algra—Ophuijsen (2012: 2) argue that Philoponus was influenced by Alexander of Aphrodisias’ style of structuring Aristotle’s arguments. 75

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say in the following section.76 Another reason is Philoponus’ concern, as a commentator, to introduce Aristotle’s method of approaching the issues in the Physics. Commentators follow a general structure according to which they comment on the philosophical works of Aristotle and Plato. The exegesis attempts in various ways to make the arguments of these works comprehensible. Here I will present some basic methodological features taken from Philoponus’ commentary. First, Aristotle’s arguments are categorised: the commentator distinguishes the arguments, so that pupils can understand the sequence of the arguments more easily.77 Second, Philoponus uses other texts of Aristotle to clarify particular notions or phrases. Parallel texts are mainly used to show that Aristotle has coherent views, though sometimes they set up a new discussion in order to further explain an Aristotelian argument.78 For us today, parallel texts are valuable from a philosophical point of view but also because they inform us about those of Aristotle’s books that Philoponus was using when he commented on the Physics. Parallel texts are also employed to quote from other commentators when either a different interpretation or support for the Aristotelian view is needed. Philoponus sometimes names other commentators; generally, however, he does not name his source and uses the indefinite expression ‘the exegetes’ (οἱ ἐξηγηταί).79 Third, Philoponus changes his manner of speaking, as though making an oral presentation (which, of course, may be the case if this commentary derives from teachings). 80 Fourth, in the running commentary Philoponus praises the utility of some Aristotelian ideas, examples and views.81 The background for praising Aristotle’s wellconstructed arguments and examples connects to Aristotle’s (and Plato’s) authority. Aristotle stands as the philosopher who teaches (διδάσκει); the commentators and their students are those who learn (μανθάνομεν, γινώσκομεν).

76

For example, see in Phys., 496.5-9; 514.10-18. The following text is a characteristic example of this categorisation (in Phys., 500.26-30): ‘These arguments are based on actual facts. The remaining two, however, are based on received opinions and on the testimony of earlier thinkers. The fourth one comes from those who introduce the void … The fifth one is that Hesiod …’. Trans. Algra—Ophuijsen 2012: 21. 78 For instance, see in Phys., 500.6; 598.17; 609.16; 616.11. 79 See in Phys., 526.29-30; 528.2; 541.7; 594.14; 701.1-5. 80 Verbs in either the first or second person singular are an example of this, as, for instance, in the following quotation (in Phys., 518.10-11): ‘You can reduce the argument to a syllogism of the first figure as follows …’. Trans. Algra—Ophuijsen 2012: 36. These changes of style relate to explanations of dense and elliptical texts of Aristotle. We find such changes also when Philoponus adds his own examples while explaining Aristotle’s argument (in Phys., 500.19-20): ‘Hence if I turn the triangle around, I thereby create another top, and another base, and I switch the position of the sides.’ Trans. Algra—Ophuijsen 2012: 20. 81 See in Phys., 531.19-20; 543.13-25. 77

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Fifth, Philoponus appears to worry about the philosophical correctness of Aristotle’s arguments. 82 The explanation of the argument is sometimes its reconstruction. The exegesis does not aim to fill possible gaps or to clarify obscure points, but it attempts to save the philosophical coherence of Aristotle’s statements. In other words, the reconstruction of Aristotle’s arguments assures students of their philosophical exactness. Moreover, in some cases arguments are first presented and then presented again according to a different logical method, for instance, the method Philoponus calls ‘ἐκ διαιρέσεως’. 83 In other cases Philoponus points out that the argument under examination does not derive from the previous one but should rather be examined together with another argument. 84 Sixth, the exegesis includes also textual comments. The commentator sometimes had different manuscripts of the same text. 85 Philoponus discusses alternative phrases or words in Aristotle’s text. Further, he makes grammatical comments and proposes alternative words in order to explain Aristotle’s meaning. 86

The six aforementioned methods of explaining Aristotle’s arguments relate to the task of the exegete. Aristotle’s text must not have obscure parts; everything must be illuminated. Arguments should be sound, eloquent and comprehensible. In fact, obscurity (ἀσάφεια) often troubles the commentator.87 It is well-known that Aristotle’s commentators discussed obscurity as one of the ten introductory issues in the proems of their commentaries on the Categories—‘the reasons why Aristotle tends to be obscure’.88 Aristotle, according to the commentators, tends to be obscure, and he has a reason for this. The reason relates to a concern that Aristotle may plausibly have had: to make his pupils cleverer and to deter the careless ones.89 Furthermore, 82 Evidence of this is, for example, the passage in Phys, 535.15-20: ‘And no one should demand that the explanation we have given of the incidental fits directly the case of the jar … We have yet to find out how we can accommodate the incidental in this case as well, given the fact that there is no other way the concept of the incidental can possibly be saved than in the way we have explained.’ Trans. Algra—Ophuijsen 2012: 52. 83 In Phys., 547.20-22; 672.7-12. The ἐκ διαιρέσεως method, a terminus technicus, clarifies a concept in reference to a scheme of logical distinctions. 84 In Phys., 645.19-26. 85 Philoponus’ comments on textual variants are evidence that, in the school of Alexandria, Aristotle’s texts were available in many manuscripts and that Philoponus used at least two versions of the Physics. 86 Grammatical and textual problems are some of the matters the exegesis deals with. See in Phys., 540.22-30; 653.17-22; 701.1-5. 87 See, for example, Philoponus, in Phys., 635.24-25; 672.7-12; 696.17. 88 I quote the explanation given by Philoponus of Aristotle’s obscurity in the proem on the Categories (in Categ., 6.22-28): ‘He (i.e., Aristotle) deliberately used this obscurity because of the students, in order to make them cleverer at listening to the ordered character of what has been said, and in order to deter careless disciples from the beginning; for the true disciples will struggle to understand and to reach the depths even more if what is being said is said obscurely. He used obscurity just as a cover for the uninitiated people, clothing the noble in obscurity.’ 89 Aristotle’s obscurity according to the commentators has been described by Jonathan Barnes (1992: 269) with the following words: ‘Philosophers are secretive beasts: only initiates may read their works.’

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his obscurity forces the real student of philosophy to fight and struggle in order to reach the philosophical depths. Obscurity hides the noble and modest thoughts that one may discover in philosophy. Such was Aristotle’s authority that the commentators could not think of his obscurity as a bad argument or misstated view. Thus the commentators take it to be a choice to strengthen the strong minds and prevent the lazy ones. This seems to be the general opinion concerning Aristotle’s obscurity: it is a planned obscurity. Nonetheless, we should be mindful of a distinction that often appears in Philoponus: Aristotle’s obscurity is at times treated as the sign of a real philosophical problem. Philoponus sometimes emphasises the need for a re-examination of Aristotle’s statements and sometimes takes the obscurity as opportunity for mental exercise. In several instances obscurity occurs together with the term ‘γυμνάζειν’,90 especially in the main body of Philoponus’ exegesis of the Physics. The meaning of the term is ‘to train’, ‘to exercise’.91 The exegesis points out the obscurities but also stresses the mental exercise that derives from solving these obscurities. In Philoponus, the term ‘γυμνάζειν’ occurs within the framework of ‘σαφηνίζειν’, of making clear Aristotle’s views. The exegesis aims to achieve exact knowledge of how philosophical inquiries are constructed and of the debates on these inquiries. The mental exercise results from the greater effort needed to comprehend the argument because it involves a certain level of mental difficulty. In this sense, the expression ‘γυμνάζειν τὸν λόγον’ is used to note either that Aristotle works through an argument or that the commentator himself will mentally work through an argument, or an example.92 In both cases, the relationship between eliminating the obscurity and working through the argument is significant for the task of explaining Aristotle’s statements to the pupils. Everything considered, the explanation of an obscure argument can be extremely challenging for the commentator.93 Up to this point we have presented the form of the commentary and the methods Philoponus deploys to build his exegesis on the Physics—that is to say, the part where he explains Aristotle’s text. Now we may proceed to the introduction to the digressions of the commentary and their argument to complete our discussion about the form, the methods and the structure of the Physics commentary.

90 The term reminds of Aristotle’s Topics, where he explicitly states that the usefulness of this work is the exercise: πρὸς γυμνασίαν χρήσιμος (see Topics, 101a28-30). 91 Usually, it appears in a similar context to the following (in Phys., 504.14-17): ‘The arguments on both sides of the question are such as to exercise the mind and to provide an exact understanding of the subject matter, not only in so far as the problem itself gets clearly delineated, but also in so far as the accounts try to destroy it {i.e. place} are being refuted.’ Trans. Algra—Ophuijsen 2012: 24. 92 For example, in Phys., 55.24-26; 65.3-6; 119.26-27; 502.15; 507.17; 549.28-29; 589.29; 667.28-31. 93 The struggle to resolve such difficulties can be seen, for instance, in the following passage: ἀσαφής δὲ πάνυ ὁ τῶν λέξεων νοῦς, καὶ εἰ μὴ αὐτός ἐν τοῖς τοῦ κενοῦ λόγοις ἡρμήνευσεν ἑαυτόν, ἔμεινεν ἄν ἀνερμήνευτος, in Phys., 548.16-18.

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1.6 Introduction to the digressions Philoponus divides the fourth chapter of Physics IV into three lectures. As noted in section 1.5 (Table 1), the digression on place interrupts the transition from the second lecture to the third. The first lecture (on the section of the Physics, 210b32211b5) covers Aristotle’s definition of place, the second (on Physics, 211b5-212a7) contains the exegesis of the arguments against the view that place is extension, and the third deals with the last part of Physics IV.4 (212a7-30) where Aristotle expounds the full version of the definition of place. From the last lines of the second lecture we learn that it discussed the refutations of the view that place is an extension (τὸ διάστημα), as they arose from the exegetical tradition of Aristotle’s words. Philoponus also announces that he will examine all the refutations added to the discussion by the commentators and the arguments of those who support the thesis that place is extension after he has gone through Aristotle’s lexis.94 The passage is extremely important for our understanding of the position of the digression on place within the running commentary:

αἱ μὲν οὖν ἀνασκευαὶ τοῦ μὴ εἶναι διάστημα τὸν τόπον, αἱ ἐκ τῶν ἐξηγήσεων τῶν Ἀριστοτελικῶν ῥητῶν ἀναφανεῖσαι, αὗταί εἰσιν, ὅσας δὲ ἔξωθεν προστεθείκασιν οἱ ἐξηγηταί, καὶ ὅσα εἴποιεν ἂν οἱ προϊστάμενοι τοῦ διάστημα εἶναι τὸν τόπον, μετὰ τὸ ἐπεξελθεῖν τὸ ῥητὸν ἐροῦμεν. (in Phys., 552.10-13) These are the attempts culled from the exegetical tradition devoted to the Aristotelian text that are intended to establish that place is not an extension. The external arguments that the commentators have added, and whatever the proponents of the view that place is an extension could say, we will expound after having gone through the text. (trans. Algra—Ophuijsen 2012: 67)

First, this text is evidence of the commentator’s methodology in recapitulating for his students what has been explained so far. In addition, Philoponus clearly announces in the text what his next step will be. He says that later on he will move on to something different, an exposé of the refutations expressed by the commentators. Indeed, after the lexis section (in Phys., 552.14-557.7) of the second lecture on IV.4, Philoponus interrupts the exegesis with quite a large amount of text (the digression on place covers 28 pages in the CAG edition), placed between the second and third lectures on IV.4. Philoponus leaves aside the comments on the text and returns to some Aristotelian arguments presented in the previous theōria (in Phys, 546.2594 The expression ‘τὸ ῥητὸν’ (in Phys., 552.13) refers to the comments on Aristotle’s lexis of the relevant theōria that immediately follows (in Phys., 552.14-557.7); the reason is that the digression on place starts exactly after the lexis section of the second lecture on the Physics IV.4. Algra—Ophuijsen’s translation (2012: 67) as ‘the text’ is pointing out the same thing: first he will complete the exegesis of the text (that is the short comments found in the lexis section of this lecture) and then expound the different opinions.

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552.13), adding his own views to the previous discussion (τῷ λόγῳ). The digression on place examines the cogence of Aristotle’s arguments, which posit that place cannot be a kind of three-dimensional extension (τὸ τριχῇ διαστατόν διάστημα).95 The digression on the void is announced and starts in a similar way to that on place. The digression on the void (in Phys., 675.12-695.8) is placed almost at the end of the running commentary on the Physics IV.9, the last chapter in which Aristotle discusses the concept of void. More precisely, the digression on the void comes in between Philoponus’ two lectures on the Physics, IV.9 (on Physics, 216b22-217a21 and 217a21-b28). But the announcement of the digression comes several pages before it itself appears, at the end of the third lecture (of four) on the Physics IV.8. All four lectures comment on Aristotle’s arguments against the possibility of motion through the void and against the existence of a separate void. The announcement of the digression on the void goes as follows:

τῷ μὲν οὖν Ἀριστοτέλει μέχρι τῶν ἐνταῦθα πρόεισιν ὁ λόγος ἐκ τῆς ἀνισότητος τῶν κινουμένων τῆς παρὰ τὸ δι’ οὗ ἡ κίνησις γινομένης, κατασκευάζοντι ὡς οὐκ ἂν ἐνδέχοιτο, εἰ κενὸν ἦν, κίνησιν δι’ αὐτοῦ γενέσθαι, ὅτῳ δὲ σκοπὸς τῆς ἀληθείας πανταχοῦ τυχεῖν, περιαθρείτω ὅση δύναμις μή που τῇ δεινότητι καὶ τῷ δυσθεωρήτῳ τῶν ἐπιχειρημάτων τοῦ σκοποῦ διαμάρτοι. κάλλιον δὲ ἴσως πρῶτον τὸν πάντα διελθεῖν περὶ τοῦ κενοῦ λόγον, εἶτα οὕτως ἀναλαβόντας ἐξ ἀρχῆς ἕκαστον ἐπισκέψασθαι τῶν ἐπιχειρημάτων, ὅπῃ ἀληθείας ἔχει ἢ ψεύδους, μηδὲν αἰδεσθέντας, μηδὲ τῆς ἀληθείας τὸ τοῦ ἀνδρὸς ὑπειλημμένον ἐπίπροσθεν θέντας. (in Phys., 650.27-651.4) Up to this point Aristotle’s argument proceeds from the inequality of the speed of moving things compared with that through which their movement occurs, arguing that it would not be possible, if there were a void, for motion to occur through it, but anyone who has the goal of arriving at the truth from all sides, let him look round at how great the power [of these arguments] is, lest through the harshness and obscurity of the arguments he misses his goal. It is better perhaps first to go through the whole argument about the void, and then to take up each of the arguments from the beginning and enquire what the truth or falsity is in it, respecting nothing, and not putting the reputation of the man before the truth. (trans. Huby 2012: 52)

The announcement, like the announcement of the digression on place, describes Philoponus’ methodology in examining Aristotle’s arguments on the void. Philoponus points out that some problematic issues arise from the Aristotelian doctrine against the existence of the void. However, he first wants to go through the whole account on the void and then to examine the arguments. Cross-examining Aristotle’s arguments is, again, an attempt to get at the truth. Philoponus will scrutinise the 95 The digression on place starts with the following words (in Phys., 557.8-10): ‘It is time, then, that our own contributions be added to the discussion, and, in the meantime, that we examine if there is any cogency in the Aristotelian arguments showing that it is impossible for place to be a three-dimensional extension.’

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cogence of the Aristotelian arguments and then their truth value. As will be shown later, Philoponus’ main difficulty with Aristotle’s account is to accept the view that, even if void existed, motion of bodies would be impossible.96 Undoubtedly, there is a structural connection between the running commentary and the digressions. The difference between παρεκβάσεις and θεωρίαι is that the latter have an exegetical purpose, whereas the former do not. That is the main reason that digressions, in a sense, stand ‘outside’ the running commentary and the theōria-lexis form (the lectures proper). Nonetheless, the digressions are organic parts of the commentary on the Physics. The digressions cannot be detached from the running commentary: all the arguments discussed in the digressions are connected to the lectures in the commentary’s exegetical part. In some cases, as we shall see, Philoponus’ argument in the digressions relies on his interpretation of Aristotle’s text as expressed in the main body of the exegesis. Without paying attention to the discussion of Aristotle’s arguments in the lectures, the reader of the digressions will be unable to comprehend the strategies behind some of Philoponus’ critiques. Digressions and running commentary share the same ground—the exegesis of Aristotle’s Physics—though they differ in that they serve distinct purposes.97 Philoponus regards his digressions as additional thoughts, related to the discussion of the Aristotelian arguments on place and the void.98 Both digressions should therefore be read along with the corresponding exegesis of the arguments in the running commentary, not as separate, autonomous texts. This view allows us to elucidate Philoponus’ steps entirely before introducing his criticisms and to give a better explanation of his criticisms of the Aristotelian tradition on the concept of place. Because of their content the digressions are quite dense texts: the arguments succeed each other, both systematically attacking (mainly, but not only) the Aristotelian account of place and expressing Philoponus’ own account of place. Philoponus picks up specific arguments which, according to his view, lack cogency and whose truth is disputable. Thus both digressions are specialised texts, dealing with the problems and difficulties which had arisen within the Aristotelian tradition on 96 Philoponus says at the beginning of the digression on the void (in Phys., 675.12-14; 675.26676.2), ‘Up to this point the Aristotelian account of the void is complete, but we must anew take up the account, examining each of the arguments. … My objection is to Aristotle’s arguments which tried to show that if void existed, nothing would move through it, and that, even if there is no void in any way separated from bodies, instead there is the void that is filled, which is also the place of bodies, as we proved in the previous arguments.’ 97 The digressions on place and void play the role of completing the study of physics; they are considered to be accounts of place and void that are closer to the nature of place than Aristotle’s account. Therefore, we cannot separate them from the body of the commentary on the Physics. The innovative character of these texts forced Philoponus to incorporate them as deviations from the theōria-lexis form. 98 προστεθῆναι τῷ λόγῳ, in Phys., 557.8; and εἶτα οὕτως ἀναλαβόντας ἐξ ἀρχῆς ἕκαστον ἐπισκέψασθαι τῶν ἐπιχειρημάτων, in Phys., 651.2-3.

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place and the void, as the argument of the digressions will show in the following detailed presentation.

1.7 The argument of the digressions As both digressions are long sequences of arguments, before we move on to the analysis of the arguments it is necessary to provide an overall preview of their subject-matter and to sketch out their structure. The grounds of the division are based on the internal structure of Philoponus’ discussion about place and the void. The digression on place can be divided into five parts: 1. Against Aristotle and Themistius’ view that place cannot be a (three-dimensional) extension (in Phys., 557.10-563.25). 2. Against Aristotle and Themistius’ view that place is the limit of the surrounding body (in Phys., 563.26-567.28). 3. Defending the thesis that place is a three-dimensional extension, different from the bodies that come to be in it (in Phys., 567.29-579.18). 4. Place as a three-dimensional extension neither has any power nor is infinite (in Phys., 579.19-583.12). 5. A conversation between Ammonius Hermeiou and Iōannēs Philoponus (in Phys., 583.13-585.4). This division attempts to develop Furley’s and Golitsis’ division. Furley divides the digression on place into three parts (the last part of Furley’s division corresponds to parts 3, 4 and 5 of mine).99 Golitsis divides the digression into four parts (I split the third part of his division into two: parts 3 and 4 of the proposed division).100 Philoponus’ text contains clear points suggesting the division of the digression into five parts. The reason for the addition of the fourth part above is the clear change of subject in the passage in Phys., 579.19-583.12. This section is not an additional argument to the difference of place from bodies (part 3); Philoponus clearly changes the subject to argue first against the objection that the proposed theory of place fails to explain the distinction between up and down; second, against the view that place has a power; and, third, the impossibility of an infinite, extra-cosmic void. Although the third and fourth parts of the digression on place are supposed to be the main sections in which Philoponus introduces his account of what place is, the two first parts of the digression, in a sense, provide us with a positive definition of place as well: the criticisms either of Aristotle or of Themistius and others also give Philoponus space to argue for his alternative theory of place. Apart from the fifth part, where Philoponus presents a discussion with his teacher Ammonius 99

100

Furley 1991: 14. Scholten (2015: 152) follows the tripartite division too. Golitsis 2008: 175.

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Hermeiou, the remaining parts of the digression have a dual character: they criticise (mainly) Aristotle and the Peripatetic tradition, and they establish a different definition of place. Philoponus himself says that all his criticisms fall into the framework of the truth about the definition of place and aim to re-establish the real picture of nature.101 A brief overview of the contents of each part of the digression will be helpful before we examine Philoponus’ text in detail.102 Philoponus (in part 1 of the digression, in Phys., 557.10-563.25) focuses his attack on Aristotle’s denial of the thesis that place can be an extension in between the limits because of a subsequent infinity of places (Physics, 211b7-8). Philoponus’ critique is systematic: he constructs different arguments to refute an Aristotelian or a Themistian thesis. In some cases he even applies to the Aristotelian doctrine the problems that Aristotle and Themistius ascribe to the proponents of the extension view. Sometimes he uses Aristotle in order to reject Themistius’ interpretations. Philoponus claims that place as extension must be natural, three-dimensional, bodiless, immaterial and unaffected in any sense; place cannot divide the body that comes to be in it nor is it divided by body. Philoponus goes on to repudiate the Aristotelian definition of place as the limit of the surrounding body (part 2, in Phys., 563.26-567.28). Place as three-dimensional cannot be a surface—i.e., just the limit of the surrounding body. Philoponus attacks the Aristotelian definition of place with four arguments (listed in the next paragraph) showing how the definition militates against crucial considerations about place, as, for instance, place’s equality to bodies and place’s immobility. In the third part of the digression (in Phys., 567.29-579.18) Philoponus is interested in various matters related to the nature of the extension of place (τὸ τοπικὸν διάστημα) he supports and offers solutions to different objections. The core of his theory is based on his claim that the three-dimensional extension of place should be conceived of as an extension different (ἕτερον τι διάστημα) from the bodies that come to be in it. In the first two parts of the digression this kind of differentiation was expressed: (a) in terms of a body that comes to be into something else, namely a three-dimensional extension, a place; (b) in terms of bodiless extensions which can fit on to each other, not necessarily linked with bodies; (c) in terms of a place being deprived of any body, being empty. In the third part Philoponus argues in favour of the idea that place is a real extension different in any way from the bodies that come to be in it. He uses four arguments to prove this differentiation: (a) the mutual replacement of bodies in a place that is equal to their three dimensions; (b) the ‘force’ of void (ἡ τοῦ κενοῦ βία); (c) that place, i.e., void, is not a non-being but an extension in which there is no body; and (d) thought experiments such as the 101 See 102

153-156.

in Phys., 578.11-14; 30-31; 581.8; 650.30-651.1; 687.19-29. For a detailed description of the contents of the digression on place see also Scholten 2015:

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universe empty of bodies and the half empty spheres and jars the boundaries of which collapse. Philoponus claims in the fourth part (in Phys., 579.19-583.12) that place relates to the order of nature given by the demiurge. Place is not the object of desire which forces bodies to be in their proper place; thus it has no power. In addition, he points out that because of the equality between place and the body in it, place cannot be an infinite extension extending outside the cosmos. Finally, the fifth part (in Phys., 583.13-585.4) presents a discussion between Ammonius Hermeiou and Philoponus about the kind of extension Philoponus is introducing. According to Philoponus’ testimony, Ammonius criticises Philoponus’ view for the extension it suggests exceeds the limits of natural philosophy and, therefore, it goes beyond Aristotelian physics. Philoponus appears to defend his thesis in front of his master, Ammonius, by claiming that this kind of extension is totally compatible with physics since it is the natural place of natural bodies. Let us turn now to the digression on the void (in Phys., 675.12-695.8). This may reasonably be divided into six parts: 1. Introduction: setting up the criticism (in Phys., 675.12-676.3). 2. Rejection in three arguments of Aristotle’s view that motion is impossible through the void because the void does not exist (in Phys., 676.4-686.29):103 i. It is not necessary for bodies moving through the void to move at equal speed (in Phys., 677.9-680.23). ii. The mediums through which motion happens are not the causes of unequal motion, even when the motion happens in the void (in Phys., 680.24-684.10). iii. The void has no proportional relationship to the full, τὸ πλῆρες (in Phys., 684.10-686.29). 3. Against the Aristotelian assumption that the void does not fill the need of bodies for a place (in Phys., 686.30-689.25). 4. Motion is possible through the void, even if the void were separated from and deprived of bodies (in Phys., 689.26-693.27). Three examples: i. Circular motion (in Phys., 690.3-691.8). ii. Motions of choice, προαιρετικαὶ κινήσεις (in Phys., 691.9-692.26). iii. Motions forced and contrary to nature (in Phys., 692.27-693.27). 5. The occurrence of motion is totally impossible without the void (in Phys., 693.28-694.27). 6. For what reason do bodies of different shape move differently in void? (in Phys., 694.28-695.8). 103 The second part starts with a recapitulation of Aristotle’s arguments (in Phys., 676.4-677.8). I do not read this section as a different part of the digression.

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Furley roughly divides the digression on the void into two parts.104 The first part of his division includes the first three parts of my proposed division. The second part includes parts 4-6 above. It seems that Furley’s intention in both digressions was to give a very general guide to their structure, so he just points out where Philoponus defends his own theory and where he criticises Aristotle. Golitsis divides the digression into three parts, the third being subdivided into two.105 The second part of Golitsis’ division corresponds to the second and third parts of my division, and his third part corresponds to the last three parts of the list above that is intended to present in detail the content of the digression on the void. With the digression on the void Philoponus wants to reconsider the validity of some arguments introduced in the Physics IV.6-9. He says that he will not return to all the arguments concerning the void. He aims to prove that Aristotle wrongly assumes the impossibility of motion through the void, if it existed, and the impossibility of a void extension (place) filled with bodies, although it would never occur without body. The examination (part 2, in Phys., 676.4-686.29) starts from the causes of unequal motions. Different bodies moving through the same medium, i.e., void, will have unequal motions because their heaviness (ἡ βαρύτης) produces different impulses (ῥοπαὶ). If the void were the medium through which different bodies move, then the void would not make the bodies move at equal speeds. Philoponus points out that in the case of equal and similar bodies that move through different mediums we should consider that the motion through void occurs in time and that the ratio of the times of the moving things does not follow the ratio of their weights. He claims that if we drop two bodies of different bulk from the same height at the same time, they will reach the ground in equal times or, if there is a difference, it will be almost imperceptible by senses. Philoponus agrees with the Aristotelian idea that the void (τὸ κενὸν) cannot have the same ratio to the full (τὸ πλῆρες), but he gives a different reason for it. The commentator, once again, rejects Aristotle’s argument that there could be many overlapping extensions and that there would be an infinite regress (part 3, in Phys., 686.30-689.25). The extension theory proposed by Philoponus distinguishes between bodily and non-bodily extension; therefore it escapes many problems that Aristotle raised against the atomists in the Physics (213a12 ff.). Philoponus reverses the Aristotelian statement that there would not be motion if void existed by claiming that locomotion would be impossible without the existence of an empty extension. According to Philoponus’ theory, even if the separate void existed nothing would prevent locomotion from happening. Locomotion through a separate void can happen, Philoponus argues, in time (part 4, in Phys., 689.26-693.27). To reinforce his 104 105

Furley 1991: 49 ff. Golitsis 2008: 191.

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thesis Philoponus introduces three examples: circular motion (the motion of the fixed sphere), motions of choice (a man walking from Athens to Thebes), and forced motions or motions contrary to nature (one who throws a rock, or an archer). In the last two parts of the digression (part 5, in Phys., 693.28-694.27 and part 6, in Phys., 694.28-695.8), Philoponus defends the thesis that without the void it is impossible for motion to occur, based on the equality between place and what is in place. In addition, he explains the reason that bodies of different shapes have different motions, such as, for instance, a spherical and a flat body might have when they move through the void. Having seen the contents of the digressions of Philoponus’ commentary on the Physics and before we move on to the philosophical debate on the nature of place and the void, it is necessary to present Philoponus’ sources and targets in the digressions.

1.8 A note on Philoponus’ sources and targets in the digressions In this final section of Chapter 1, I would like to draw attention to a crucial point regarding the criticisms that Philoponus expounds in the digressions. The digressions are traditionally interpreted as an attack on Aristotle’s account of place and the void.106 Indeed, Aristotle is Philoponus’ principal target. But, sometimes it looks as if Philoponus does not successfully refute the Aristotelian account. Some of Philoponus’ arguments against Aristotle do not correspond to Aristotle’s views, giving the impression that Philoponus is not directly answering Aristotle’s arguments. Reading Philoponus’ digression on place, we take it for granted that the problems he discusses have their background in Aristotle’s Physics, but, I argue, some of the thoughts that Philoponus attacks may be Aristotelian in origin but not Aristotle’s own thoughts. To begin with, it should be noted that Ammonius Hermeiou is the basic source of Philoponus. In fact, Philoponus’ commentary plausibly incorporates parts of Ammonius’ lectures on the Physics, though the text we possess must be a commentary created by Philoponus. We know from the digression on place that Ammonius was aware of and against Philoponus’ objections to Aristotle’s concept of place. A fact showing, among other things (see section 4.5), that Philoponus certainly attended Ammonius’ lectures on the Physics before writing his own commentary. In parallel, Philoponus was well acquainted via Ammonius with the long exegetical tradition of the Aristotelian text and the questions raised by other philosophers. The most important source in both digressions is Themistius’ In Physica Paraphrasis.107 The role that Themistius played in the composition of Philoponus’ commentary on the 106

See, for instance, Furley 1987: 130-139; Sedley 1987: 141; Lang 2001: 19.

107 See CAG V/2, 1900. A guide to Themistius’ life (ca. 317-388) and work can be found in Kupreeva’s

article (2010: 397-416).

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Physics is easily recognised, for the paraphrase was the handbook Philoponus used when he was commenting on Aristotle’s Physics.108 Philoponus quotes Themistius by name many times in his commentary.109 There are, however, as will be shown in the following chapters, many cases in which Philoponus does not refer to Themistius by name but still appears to have him in mind. So it is often Themistius’ interpretation of Aristotle’s account of place and void that Philoponus tackles in the digressions. Themistius’ paraphrase of the Physics contains, for Philoponus, many problema­ tic assumptions. Philoponus believes that the Aristotelian doctrines on place and the void lead Themistius’ interpretations to deal with the same problems as ­Aristotle. He disproves Themistius’ interpretation, partly because he thinks that Aristotle left room for such fallacies, but also because he thinks Themistius himself is responsible for further controversial assumptions. But this is not the whole picture regarding Philoponus’ sources and targets in the digressions. I attempt to clarify throughout my study when Philoponus is dealing with Aristotle and when he is alluding either to Themistius or to some other, unnamed source, for instance, Strato of Lampsacus, the Stoics, the early atomists and Epicurus. Philoponus deals with the Stoics and the atomists, both because Themistius is unfairly opposed to some Stoic and atomist points of view (place is for all of them a kind of bodiless extension) and because Philoponus himself differentiates his positions from their view (like, for instance, in rejecting the Stoic view of extra-cosmic space). Occasionally, it is possible accurately to identify the theories lurking behind Philoponus’ arguments, but in other cases we can only speculate or simply remain silent. It is certainly the case that Philoponus’ criticisms attack theories of place other than Aristotle’s, as it is beyond doubt that they attack the Peripatetic tradition endorsing Aristotle’s views. Philoponus refers to the commentary of Alexander of Aphrodisias on the Physics—we know this because Philoponus names him when referring to some of his interpretations.110 We cannot draw any secure conclusion from this, apart from the fact that Philoponus knew indirectly Alexander’s, now lost, commentary. Philoponus certainly used Alexander’s exegesis, as his teacher, Ammonius Hermeiou, must have done extensively. However, Alexander’s presence in the digressions often remains a mystery. It is reasonable to assume that some of the criticisms in the digressions on place and the void may have been directed against Alexander. Philoponus could easily rely on Alexander’s exegesis and criticise his views, as he often does with Themistius and others. After all, Alexander was the orthodox interpreter 108

Golitsis 2008: 65. According to the Index Nominum of Vitelli’s edition (see CAG XVII: 992) Themistius’ name appears in the commentary 16 times. 110 Vitelli’s Index Nominum testifies that the name of Alexander of Aphrodisias appears 10 times in Philoponus’ commentary (in Phys., 81.25; 349.5; 356.8; 492.3; 528.12; 738.24; 745.20; 756.9; 854.14; 891.1). Rashed (2011) tries to follow Philoponus’ readings of Alexander in his reconstruction of Alexander’s lost commentary on the Physics IV.1-9. 109

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of Aristotle’s words in late antiquity and Themistius relies heavily on Alexander’s exegesis.111 Thus Philoponus’ critique, via Themistius and Alexander of Aphrodisias, attacks a long Aristotelian tradition. At the same time Philoponus keeps a certain distance from other extension theories of place of antiquity like those of the atomists and the Stoics. Chapter 1 stresses some main issues on the form, method and structure of Philoponus’ commentary on the Physics in order to clarify the position and the content of the digressions dedicated to the concept of place and the concept of the void respectively. In the following study we concentrate on some of the most decisive aspects of Philoponus’ theory of place and void. Generally, I follow the structure of the digressions, since they have a coherence which should not be broken up; sometimes I move back and forth within the digressions and the running commentary in order to complete and explain arguments in the light of the running commentary. Chapters 2 and 3 are devoted to the digression on place, generally following its structure. I focus on the kind of extension that Philoponus claims is the place of bodies and how this extension differs from the one that Aristotle refutes in the Physics. Chapter 4 centres around the principal issues raised in the digression on the void, such as Philoponus’ definition of void as the place of bodies and his conception of void as the necessary condition for the motion of natural bodies. The interpretative line according to which these chapters are constructed has two main interests: first, to show that Philoponus introduces a theory of place that escapes the problems Aristotle ascribes to other theories of place; second, to reveal Philoponus’ conception of topos: the existence of a physical extension that is the place of physical bodies; in other words, to inquire into Philoponus’ ontology of place. Finally, Chapter 5 examines Philoponus’ objections to Aristotle’s definition of place, as presented in the digression on place, and Philoponus’ reaction to some of Aristotle’s assumptions that triggered philosophical puzzles within the Peripatetic tradition.

111 Especially in his paraphrase of the Physics IV.1-9, apart from one reference by name (in Phys. Paraphr., 104.20), we can identify, according to the apparatus criticus of Schenkl’s edition (CAG), the following references based on Simplicius’ quotations: in Phys. Paraphr., 106.6; 107.13; 108.4; 112.18; 117.3-4; 118.11; 119.22; 130.9; 133.10; 135.25; 140.1.

Chapter 2

Place as Extension: Problems and Solutions Philoponus’ criticisms of Aristotle and the Peripatetic tradition, as well as the theory that he himself proposes, are driven by an interest in reconciling our explanations to nature’s facts. Philoponus’ underlying worry is to stay close to the facts, such as the motion of bodies and its relation to place. Philoponus opts for a definition of place as extension (τὸ τοπικὸν διάστημα). Is it possible, however, to theorise a kind of extension compatible with the nature of bodies? This is the starting question of Philoponus’ theory of place. Philoponus proposes a definition of place that falls under the general category of theories considering place as an extension, as an interval in which bodies are located and move. But his theory differs in some fundamental respects from other extension theories of antiquity (i.e., early atomists’, Epicurus’ and Stoics’), as we shall explain later. Apart from criticising his obvious opponents, namely Aristotle, Themistius and perhaps Alexander of Aphrodisias, Philoponus criticises or brushes aside all the unsatisfactory elements of other extension theories that might produce further complications. This chapter concentrates on Philoponus’ reaction to Aristotle’s rejection of the dimensionality of place, as followed by Themistius. I shall first present Aristotle’s objections to the view that place is an extension (διάστημα); next I will examine Themistius’ and Philoponus’ interpretations of the Aristotelian objections. Finally, this chapter focuses on Philoponus’ arguments against Aristotle’s objections. Philoponus takes up the task of demonstrating the logical weaknesses of the charges which Aristotle makes against the proponents of the extension theory of place. He examines the cogence and the truth value of Aristotle’s arguments in order to show that there is a kind of extension which avoids the problems Aristotle ascribes to the concept of extension. The central interpretative line of the chapter is that Philoponus, in attacking Aristotle and Themistius at the same time, defends a kind of natural extension which is not disputable in the sense that Aristotle and Themistius thought it to be.

2.1 Aristotle’s rejection of place as extension Aristotle in Physics IV.1-5 examines the concept of τόπος. He considers the examination of place to be one of the major tasks of the physicist (Phys., 208a27-29). For this reason, the principal question of these chapters of the Physics is how to define the place of natural bodies.112 Aristotle takes four possible answers into account: place can be (a) form, (b) matter, (c) the extension between the limits of bodies, and 112

Aristotle’s reply to this question comes in Phys., 211b5-212a7.

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(d) the limit of the surrounding body. He refutes the first three answers and defends the fourth by defining place as the first and immobile limit of the surrounding body (at which it is in contact with the surrounded body).113 Here, I am interested in Aristotle’s refutation of the position that there cannot be an extension that is the place of bodies which is over and above the bodies that come to be in it because it is particularly relevant for the discussion of Philoponus, since he adopts a version of it.114 So, for the moment, I leave aside Philoponus’ critique of Aristotle’s own definition of place which is discussed point by point in Chapter 5. The most useful way to approach Aristotle’s argument against the view that place is a kind of extension is to start from lines 211b14-19 of the Physics: [A1] διὰ δὲ τὸ μεταβάλλειν πολλάκις μένοντος τοῦ περιέχοντος τὸ περιεχόμενον καὶ διῃρημένον, οἷον ἐξ ἀγγείου ὕδωρ, τὸ μεταξὺ εἶναι τι δοκεῖ διάστημα, ὡς ὄν τι παρὰ τὸ σῶμα τὸ μεθιστάμενον. τὸ δ’ οὐκ ἔστιν, ἀλλὰ τὸ τυχὸν ἐμπίπτει σῶμα τῶν μεθισταμένων καὶ ἅπτεσθαι πεφυκότων.

The extension between the extremities is thought to be something, because what is contained and separate may often be changed while the container remains the same (as water may be poured from a vessel)—the assumption being that the extension is something over and above the body displaced. But there is no such extension. One of the bodies which change places and are naturally capable of being in contact with the container falls in—whichever it may chance to be. (trans. Barnes 1991, vol. I: 56)

To begin with, it is crucial to note that the case Aristotle constantly has in mind in the whole passage (Physics, 211b14-29) is a vessel containing water or air. He argues that some might think that there is an extension in between (the limits of) the vessel and the body in it; something over and above the vessel and, let us say, the water that changes place, because what is contained and separate (i.e., the water) often changes while the container (vessel) remains the same—by ‘change’ we need to understand an increase or decrease in the body’s quantity or the mutual replacement of bodies. For example, when water is poured from the vessel some people think that a separate extension exists over and above the displaced body, as if these two bodies are not in contact.115 But, according to Aristotle, such extension does not exist; what happens is that any chance body of those capable of changing places falls into the container. In other words, it is impossible for a separate extension to exist in addition to the water and the vessel when the water changes place, for another body will occupy the place occupied by the water. The reason for rejecting the existence 113 See

Physics, 212a5-6; 212a20-21. In Aristotle’s words: παρὰ τὸ τοῦ ἐγγιγνομένου σώματος μέγεθος, Phys., 211b9; and ὡς ὄν τι παρὰ τὸ σῶμα τὸ μεθιστάμενον, Phys., 211b17. 115 Simplicius takes it that Aristotle has in mind the case of a vessel containing water which one tips to and fro (ἐν τῷ κλυδασμῷ, in Phys., 575.1-2). 114

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of such an extension is, according to King and Morison, that Aristotle conceives the physical world as a plenum, as a network of continuous physical bodies without gaps.116 To reinforce his statement in text [A1] Aristotle constructs a refutation characterised by Philoponus as quite obscure and difficult, since the text may be partially corrupt.117 Τhe objection to the thesis that place is an extension runs as follows (Phys., 211b19-29): [A2] εἰ δ’ ἦν τι [τὸ] διάστημα τὸ πεφυκὸς καὶ μένον, ἐν τῷ αὐτῷ ἄπειροι ἂν ἦσαν τόποι (μεθισταμένου γὰρ τοῦ ὕδατος καὶ τοῦ ἀέρος ταὐτὸ ποιήσει τὰ μόρια πάντα ἐν τῷ ὅλῳ ὅπερ ἅπαν τὸ ὕδωρ ἐν τῷ ἀγγείῳ)· ἅμα δὲ καὶ ὁ τόπος ἔσται μεταβάλλων· ὥστ ’ ἔσται τοῦ τόπου τ ’ ἄλλος τόπος, καὶ πολλοὶ τόποι ἅμα ἔσονται. οὐκ ἔστι δὲ ἄλλος ὁ τόπος τοῦ μορίου, ἐν ᾧ κινεῖται, ὅταν ὅλον τὸ ἀγγεῖον μεθίστηται, ἀλλ’ ὁ αὐτός· ἐν ᾧ γὰρ ἔστιν, ἀντιμεθίσταται ὁ ἀὴρ καὶ τὸ ὕδωρ ἢ τὰ μόρια τοῦ ὕδατος, ἀλλ’ οὐκ ἐν ᾧ γίγνονται τόπῳ, ὃς μέρος ἐστὶ τοῦ τόπου ὅς ἐστι τόπος ὅλου τοῦ οὐρανοῦ.

But if there were some extension which was natural and stayed still, there would be infinite places coinciding (for as the water and air change position, all the parts will do the same thing in the whole, as the whole of water in the vessel); and at the same time the place will be changing; therefore there will both be some other place of the place and many places will be coinciding. But the place of the part in which it moves, whenever the whole vessel moves, is not some other, but the same; for air and water or the parts of the water replace each other in the thing in which they are, but not in the place in which they come to be, which is part of the place that is the place of the whole universe.118

Aristotle believes that if there were a natural extension that stayed still, some serious complications would occur. Let us suppose that water goes out of the vessel and that the water is replaced by air. Just as all of the water leaves the vessel, so each part of the water also leaves the vessel, replaced by each part of the air coming into the vessel, as the water is leaving. According to Aristotle, if this is true and this extension exists over and above the body which comes to be in the vessel, then there are infinite places coinciding. The contrast is between a natural extension that stays still and moving bodies. Yet, the consequence of producing an infinity of coincident places appears to be obscure. Aristotle says nothing about that kind of infinity and he does not explain the reason for the occurrence of the infinity. 116

King 1950: 87 and Morison 2002: 23. in Phys., 548.16. Themistius too finds it obscure (in Phys. paraphr., 116.11-12; see below section 2.2). See also Simplicius, in Phys., 574.19-21; 576.28-29. Morison argues that the text is corrupt (2002: 122, 129) and Hussey (1983: 116) treats lines 211b25-29 as an ‘appended note’. 118 The text quoted is taken from Ross’ edition (Oxford, 1950). I do not translate the τὸ; instead, I read the article τὸ (Phys., 211b20). I read the although I am not convinced whether it should be in the text or not. I ignore the [τὸ] in line 211b19. See Ross’ comprehension of the passage (1936: 53-58; 375-376; 572-574). 117 Philoponus,

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The parenthesis in lines 211b21-23 of text [A2] may be a hint that helps to explain the term ‘infinite’. All the parts of water change position with the parts of air as the whole volume of water goes out of the vessel and the air replaces it. So, we could create an infinite number of parts of water or air, occupying their own extensions, since bodies are infinitely divisible. A further puzzling fact about Aristotle’s argument is the meaning of the ‘ἐν τῷ αὐτῷ’ (Phys., 211b20). Does it mean ‘at the same spot’ in the sense that x and y coincide with each other? Does it mean the vessel? For it is one thing to say that there will be infinite places overlapping with each other, and another to say that there will be infinite places in the same place, i.e., in the vessel. I prefer the first option, although I believe that, for Aristotle’s argument, it makes no difference which of the two is correct, since the problem is the infinity of places. Moreover, in lines 211b23-25 of [A2] Aristotle seems to state that place will change at the same time, so that there will both be another place of the place and many places will coincide. It is hard to see how this idea relates to the earlier concept of infinite places. An initial point is that Aristotle refers to many places this time, not to infinite places. Once again, the case Aristotle has in mind is unclear. One could ask, for example, why would there be many places coinciding because of an independent natural extension. Although ancient commentators and modern scholars have suggested various interpretations to explain Aristotle’s attack against the extension view (text [A2]), I still believe that the answer is a matter of guesswork.119 As we shall see, Themistius seems to understand infinity in the sense that we can infinitely divide bodies (and therefore place too). According to Simplicius, the infinity of places derives from the infinity of magnitudes and their motions (in Phys., 575.21-26). Mendell, to turn to the modern scholarship, maintains that the case which Aristotle has in mind is that of an extension occupied by moving liquids that eventually leads him to the argument that dividing up extensions implies plurality of places. Morison argues that ‘since the motions of the water as it leaves the vessel and of the air as it replaces the water are infinitely divisible, there will be an infinity of overlapping or coincident places’, he too emphasising the infinite divisibility of the motions of bodies.120 So, at the moment, I will just state the obvious, based on the vessel example. Place will change either when the vessel stays still and the water moves, exchanging position with air, or when the whole vessel moves along with the contained water. That something must move in order to have a change of place derives from the sentence that clearly refers to the case where the whole vessel changes place (ὅταν ὅλον τὸ ἀγγεῖον μεθίστηται, Phys., 211b26). It seems that the argument implies that 119 Of the ancient commentators Themistius, Philoponus and Simplicius should be mentioned (see Simplicius, in Phys., 574.19-578.13). Unfortunately, we do not possess Alexander of Aphrodisias’ full exegesis, but only fragments of it (edited by Rashed 2012). Of the modern scholars dealing with the text we should mention King (1950), Mendell (1987), Lang (1998), Morison (2002) and Bostock (2006). 120 See Mendell 1987: 223; Morison 2002: 124-125.

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when the vessel moves—i.e., when the place changes and the independent extension remains still—then the very same extension, i.e., place, would have another place: it comes to be in another extension, another place. Then we can assume that there can be places of places coinciding with each other, i.e., extensions that come to be in different extensions, coincident extensions. This is the main body of Aristotle’s objection(s) to the thesis that place can be an extension in between limits, over and above bodies. To reject the result of infinite or many coincident places, Aristotle points out in the end of [A2] that when the whole vessel changes place, the place in which the part of water moves is not different, but remains the same. For air and water, or the parts of water, change places in the place they are in, namely the vessel, but not in the place in which they come to be, which is part of the place that is the place of the whole universe. In this case there cannot be a change of place in the sense that the vessel, at any rate, happens to be the place of the water or the air. Hence, we have only one body at a time in the vessel, not many, and accordingly we have only one place, neither many nor infinite. Anyone reading Aristotle’s Physics 211b14-29 (namely texts [A1] and [A2]) cannot ignore two things: first, that we cannot be entirely certain what Aristotle really meant; second, that his arguments, as we have them, raise many objections. The issue becomes more and more complicated because of the different possible ways of interpreting these lines of the Physics and the possible objections to those interpretations. Philoponus disagrees with Aristotle on whether ‘extension’ introduces an infinite regress of places, and he takes up several positions put forward in the Physics, doubting their validity. But let us first illuminate Themistius’ and Philoponus’ interpretations of Aristotle’s objection(s).

2.2 Themistius’ exegesis of Aristotle’s argument Themistius in his paraphrase of the Physics devotes a long section to discussing the view that τόπος is a kind of diastēma (in Phys. paraphr., 113.7-119.2). He ascribes the δόξα first of all to those whom Aristotle himself had in mind, that is to say to those claiming that place is extension, namely the early atomists Leucippus and Democritus. The assumption that it is the theory of place held by the atomists that Aristotle criticises (Physics, 211b14 ff.) derives from the fact that Aristotle explicitly says that the proponents of the void represent it as a place and a kind of vessel (Phys., 213a15-16).121 Themistius additionally ascribes an extension theory to the circle of Chrysippus and to Epicurus. He notes that some people falsely attributed the doctrine that place is extension even to Plato and he attacks Galen’s approach, which 121 Simplicius testifies that Aristotle says that Democritus also describes place as ‘void’, ‘nothing’ and ‘infinite’ (in De caelo, 295.1-5). Mendell (1987: 213-219; 226) argues that Aristotle may have been rejecting—apart from the atomists—a (Platonic?) theory, and that this may have led him to his statements about place in the Categories. For further reading on the subject see Algra 1995: 123-153.

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might be of Platonic origin, that there is some kind of extension of place (while openly defending Aristotle’s definition that place is the limit of the surrounding body).122 Before providing an explanation of Aristotle’s text in Physics 211b19-29, Themistius attempts to compare the concepts of τόπος and διάστημα. He builds up a schema of four propositions contrasting place and extension, and he further points out five difficulties resulting from the extension view (in Phys. paraphr., 115.13-116.9). That place is not the extension in between the limits of the surrounding body can be shown, according to Themistius, merely by determining the common conceptions about place and staying close to them. Themistius contrasts place and extension as follows: (1) place contains, but extension is contained, (2) place is separated from bodies, but extension comes and goes along with bodies, (3) the quantity of extension remains the same, but extension in its own right does not, (4) place does not belong to a body, but extension is almost the body itself.123 For his comparison Themistius uses four of Aristotle’s claims: that place is a container; that place is not part of a body; that place is not smaller or bigger (than the thing that comes to be in it); and that place is separated from things and not perishable (Physics, 210b34211a3). The contrast between place and extension serves Themistius in developing the following line of thought: Aristotle gave us a definition of place; the concept of extension does not satisfy the same requirements which Aristotle determined for place; therefore, place cannot be an extension.124 According to Themistius, those who claim that place is the extension between the limits are challenged by many problems to which they cannot give any proper reply (in Phys. paraphr., 115.22-116.9). He observes five principal difficulties. First, let us assume that we accept place to be extension: is the body in place or is place, rather, in the body? For the extension is in the body rather than the body in the extension, given that the extension is an accident (because it is a quantity), and body is a substance (because it is sensible). Second, when a body comes to be in place, is it the case that it is in place while keeping its own extension (for all bodies are in the extension) or does it throw off its own extension and come to be only in the extension of place? If the proponents of the extension view will endorse the second case, then, according to Themistius, they teach us how the extension perishes, although the body does not. But how is it possible that the body’s own extension perishes and yet the foreign extension accrues? Third, if they affirm that these two extensions exist (that of the body and that of place), then how can the extensions both exist together, and which one will be in the other? Which is the contained and which is 122 Themistius,

in Phys. paraphr., 113.7-13; 114.7-115.12. Ibid., 115.21-22: τὸ διάστημα δὲ ἐστιν μικροῦ δεῖν αὐτὸ τὸ σῶμα. 124 Themistius takes for granted the common assumptions about place that Aristotle set out in the Physics and he conceives of extension as Aristotle describes it without attempting to develop a more viable and competitive concept, as Philoponus does. 123

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the one that contains? Fourth, Themistius questions, how can two extensions exist together and in the same magnitude (i.e., in the same body)125 in which the other was, but two bodies not do so? For instance, heat, cold, whiteness, blackness and other accidentals do not provoke any increase in bulk, but extensions can.126 Finally, fifth, when the body increases, then does the extension of the body increase too, or does the one extension increase, but the other not? Themistius finds Aristotle’s text [A2], that is Phys., 211b19-29, vague, and he tries to unveil the meaning of Aristotle’s words.127 He interprets the example of the vessel that contains water as a case of a moving vessel. In this respect, he states, whenever the vessel moves, what will happen is that, just as all of the water occupies its proper extension and moves along with the moving vessel, in the same way each part of the water occupies its proper extension and will move along with the vessel. When the vessel happens to be in another place, it will occupy an extension between the limits of the surrounding air, of which (i.e., the air) the extensions and water are parts; and, at the same time, the parts of the water will occupy an extension. This will result in the occupation of multiple coincident extensions (i.e., where the vessel is located): one occupied by the whole vessel, another occupied by this part of the water, another by each part of the water, another by the whole water, another which is in between the curved surfaces of the vessel, and so forth. Themistius, following the Aristotelian argument, points out that the extension theory falls into the para­ dox of multiple overlapping places. Themistius points out a further absurdity—a significant one for Philoponus, as we shall see next—as far as the parts of the bodies are concerned. Each part will be both in its own proper extension and in the extension of the whole (of the water). And as the division goes on ad infinitum, the addition of places too will go on ad infinitum.128 For, according to Themistius, if place is extension, it is not absurd that each of the parts in its own right is in place and, therefore, each part in its own right is in the extension, which is part of the whole place. The problem, as Themistius sees 125 I have chosen to translate the expression ἐν τῷ αὐτῷ μέτρῳ (in Phys. paraphr., 115.34) as ‘in the same magnitude’, for, I take it, Themistius means ‘it is impossible to have two extensions in the same body’. For the problem here is how two distinct dimensions can have the same measure. The dimensions seem to be treated as quantitative, so their measures should add up. Hence the contrast with the qualities which are purely qualitative and thus can coexist in the same measure. The only parallel I have found expressing something close enough to my suggestion is in Simplicius’ Corollary on place, 622.16-17: εἰ δὲ δύο, πῶς οἷόν τε ἐν τῷ αὐτῷ ὄγκῳ δύο ὕλας εἶναι τὴν τε τοῦ τόπου καὶ τὴν τοῦ σώματος; The context in which this phrase occurs in Simplicius is very similar to Themistius’ set of ἀπορίαι. 126 This may be taken from Alexander of Aphrodisias’ similar argument (see De mixtione, 219.918). Generally, Themistius’ critique against the Stoics relies heavily on Alexander’s treatise. Themistius declares that he has read Alexander’s De mixtione in the beginning of his paraphrase of Physics book IV (in Phys. paraphr., 104.9-22). 127 ἀσαφέστερον μὲν ἔχει , πειρατέον δὲ , ὅπως ἐνδέχεται , κἀκεῖνα , ὡς ἐξ ἀρχῆς προυθέμεθα , ἐκκαλύπτειν, in Phys. paraphr., 116.11-12. 128 γινομένης δὲ εἰς ἄπειρον τῆς τομῆς εἰς ἄπειρον καὶ ἡ τῶν τόπων πρόσθεσις προελεύσεται , in Phys. paraphr., 116.29-30.

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it, is that in nature the infinite regress of places is impossible, for place is not a divisible magnitude. The target of that argument might be Chrysippus who, according to Stobaeus, said that ‘bodies are divided to infinity and likewise things comparable to bodies, i.e., subsisting in a sense, such as surfaces, place, void, and time.’129 Themistius’ explanation of Aristotle’s argument plays a crucial role in our understanding of Philoponus’ reaction to the Aristotelian tradition in the first part of his digression on place. For it is Themistius’ view of an infinite divisibility of the extension and the idea of multiple overlapping places that trigger Philoponus’ attack. But, before going more deeply into Philoponus’ objections, let us first present Philoponus’ exegesis of the Physics, 211b19-29.

2.3 Philoponus’ exegesis of Aristotle’s argument Philoponus divides Aristotle’s argument found in text [A2] into two parts. He clearly reads an argument in lines 211b19-23 of the Physics, and another argument in lines 211b23-29. The latter argument seems to be twofold, its second section being that found in lines in Phys., 551.20-28. This is also supported by the way Philoponus structures his attack in the first part of the digression on place: he clearly distinguishes between two arguments, the second being twofold, in this way resulting in three consequences (infinity of places, change of place, and plurality of places), as we shall see later.130 The first part of the exegesis (in Phys., 548.30-549.4) deals with the assumption that there will be infinite places coinciding (see Physics, 211b19-23). Aristotle, explains Philoponus, implies that place, as the extension in between limits, would go through (χωρήσει) the bodily extension in the case of a body that came to be in it, so that place would receive the body in each of its own dimensions. Just as the whole extension of place goes through the whole extension of the body, in the same way the parts of place go through the parts of the body. The parenthetical phrase in Physics 211b21-23131 appears to describe a sine qua non of the extension view in 129 Wachsmuth/Hense 1884 (repr. 1958), Eclogae, I. 14.1e. 2-7 (=SVF, II.482). Sextus too reports (Adv. Math., X. 142) that the Stoics argue for the infinite division of place: πρὸς μὲν οὖν τοὺς εἰς ἄπειρον τέμνεσθαι λέγοντας τὰ τε σώματα καὶ τοὺς τόπους καὶ τοὺς χρόνους (οὗτοι δὲ εἰσιν οἱ ἀπὸ τῆς Στοᾶς) ταῦθ’ ἥρμοζε λέγειν. Similar criticisms are expressed by Galen in the short treatise against the Stoics entitled Quod qualitates incorporeae sint: εἴ τε καὶ συμβεβηκότα σώματά ἐστι, πᾶν δὲ σῶμα ἐπ ’ ἄπειρον τέμνεται ἕκαστον τῶν ἀπείρων τούτων σωμάτων πᾶσι τοῖς ἄλλοις συμβεβηκόσι σωματικοῖς οὖσι καὶ αὐτοῖς συμβέβηκεν, σκόπει τὸ πλῆθος τῶν ἀτόπων, Kühn 1821, 19.469.10-13; 474.2-10. Rashed (2009: 348-350) argues, on the basis of his reconstruction of a corrupted Stoic fragment, that Chrysippus did not accept that the cut (ἡ τομή) is infinite but rather incessant (ἀκατάληκτος). 130 Simplicius too explicitly explains the text of the Physics, 211b19-29, by distinguishing three consequences which argue against the extension theory (Simplicius, in Phys., 574.23-26). It is worth noting that Philoponus in his exegesis (in Phys., 551.20-28) incorporates Alexander of Aphrodisias’ exegesis. My claim is based on the evidence of Simplicius’ quotation of Alexander’s exegesis (in Phys., 576.30-577.1). 131 I quote the phrase again: ‘(for as the water and air change position, all the parts will do the same thing in the whole, as the whole of water in the vessel)’.

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Philoponus’ exegesis: if the part does not go through the part, neither does the whole go through the whole. Moreover, given the infinite divisibility of bodies and of every magnitude, both body and place will be infinitely divisible too. For instance, in the case of the water which comes into the vessel and the air which, at the same time, goes out, each part of the water will be in place, by having its own place. Hence there will be infinite places coinciding with each other in actuality.132 This argument reminds us precisely of the theory that Alexander attributes to Chrysippus (De mixtione, 213.6-13). Further, we might see a clear parallel to Stobaeus, who, as we noted earlier (see n. 129), ascribes to Chrysippus infinite divisibility of body and place. Although it is tempting to say that the Stoic view influenced Philoponus’ exegesis of Aristotle’s words, we should not be confused, since Philoponus will reject the divisibility of place. Philoponus’ exegesis suggests that the argument presupposes that the extension is a magnitude like a body and hence the infinite divisibility should be understood as infinity in actuality. In this way Aristotle arrives at the implausible consequence of infinite overlapping places. The second, twofold part of Philoponus’ exegesis aims to explain the passage of the Physics, 211b23-29, in which Aristotle states that during the motion of the vessel there will be another place of the place and many places coinciding with each other. The explanation runs as follows: let us suppose that the place of the water is not the concave surface (ἡ κοίλη ἐπιφάνεια) of the vessel, but a different extension, over and above the extension of the water contained within the concave surface of the vessel that receives the water. When the vessel moves, it is clear that the whole vessel will occupy a different place (which is three-dimensional as well),133 therefore, the extension of place will go through the whole vessel and, thus, through the water in the vessel and through the extension that receives the water. As a result, there 132 The surviving fragment of Alexander’s comment on Phys., 211b19-29, is not of much help in concluding whether or not Philoponus also has Alexander in mind (Rashed 2011: 208, fr. 54). The fragment deals with the explanation of lines Phys., 211b21-23, where Aristotle says, ‘For, as the water and air change position, all the parts will do the same thing in the whole as the whole of water in the vessel.’ Alexander seems to explain Aristotle’s phrase as follows: the case which Aristotle considers suggests that there is a moving vessel that contains water. When the vessel moves, its content (water) is still in the same place or, as Alexander says, ‘As all the parts are in the whole, in the same way the whole water is in the vessel.’ That ‘the whole will remain in the same place during the motion of the vessel’ means that ‘the parts will remain in the same place when the whole moves.’ According to Rashed: ‘Quelle conclusion Alexandre tirait-il de ces réflexions excessivement subtiles? Sans doute, que pour les partisans du lieu-intervalle, tout n’est jamais qu’une partie, que donc il n’y a pas de suprématie absolue, comme chez Aristote, de la « partie » la plus englobante sur les parties englobées. Toutes les parties sont autant « subsistantes » les unes que les autres. Or, les corps étant infiniment divisibles, les parties sont en nombre infini; comme par hypothèse elles existent en acte, on aura une infinité actuelle de lieux.’ Two remarks: first, it seems that Alexander interprets Aristotle’s argument in such a way that it can object to the Stoics (see also fr. 47: 205-206). Second, if Alexander truly presupposed an infinite number of parts of the extension of place, which is not obvious at all, then surely Philoponus is also attached to Alexander’s exegesis regarding the actuality of infinite places. 133 For the way in which Philoponus introduces the concept of three-dimensionality, see section 3.1.

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will be three coincident extensions, namely the extension of place in the vessel, the water which is in the vessel, and the part of the place of the whole vessel towards which the vessel moves. What will happen, first, is that the place changes in place, for while the vessel changes (place) and in its entirety comes to be in a different (three-dimensional) extension of place of its own, the extension in the vessel that receives the water will be in place; second, if it is possible for two and three extensions to overlap with each other, then many extensions can coincide with each other, and nothing would prevent infinite overlapping extensions.134 The second section of this argument again concludes with the possibility of having a plurality of coincident places, for a place will be in another place. The plurality of places follows as an inevitable consequence (in Phys., 551.20-29).135 Having seen Philoponus’ exegesis of Aristotle’s objection to the extension view, we can make two remarks, one methodological and one philosophical. First, the exegesis already contains some important elements of Philoponus’ theory of place, for instance the three-dimensionality of the extension of place that is not part of Aristotle’s argument. The reference to the three-dimensionality of place is an important indication of Philoponus’ revisions of the running commentary with respect to his theory of place developed in the digression. Second, Philoponus focuses on the actual infinity of places that the extension theory supposedly implies. The importance of the latter point relates to Philoponus’ objections to the Peripatetic rejection of the extension theory. In what follows we shall show that Aristotle’s and Themistius’ claims against the extension view do not necessarily harm Philoponus’ theory. The proponents of Philoponus’ view do not have to be committed to the absurdities that Themistius ascribes to other extension theories. Consequently, Philoponus’ theory differs from the theories of the atomists and the Stoics in several aspects.

134 For the sake of the exegesis, Philoponus tries to clarify the argument by demonstrating it with the following example (in Phys., 549.28-550.8). Suppose that we have a cup (ξέστης), that is to say a measure of liquid. If the extension of the inner limits was different from the body in the cup—for instance, water—and if we put the whole cup into a bigger utensil, it is obvious that the (three-dimensional) extension of place in the utensil would go through the whole cup, and therefore through its depth as well. Thus it would go through both the water in it and the extension that receives the water; therefore, there would be three extensions overlapping with each other at the same spot. Again, if the utensil were put into a pot, the same would happen, and the extension in the pot would go through every extension of the utensil. Now, if we put the ceramic into a jar, the same would happen again and so on ad infinitum. 135 Philoponus gives the example of a moving amphora which comes to be in a place (extension). The amphora will be equal to itself (in regard to its three dimensions, Philoponus adds), so that the place that the water occupies in the amphora will occupy a part of the place that the amphora occupies. So that place will be in place. From this we can infer that more than two places might come to be in the same place and, consequently, that many places can be in the same place.

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2.4 Philoponus refuting the infinity of places As we saw previously, Philoponus points out that the Aristotelian tradition detects three unacceptable consequences deriving from the extension view: that the extension passes through the body, that the divisibility of bodies into parts produces infinity (or plurality) of places, and that the extension will be moving along with the moving bodies. What triggers Philoponus’ attack is the lack of cogence in the claim regarding the consequences of an extension theory: [P1] τὸ μὲν οὖν οἴεσθαι, εἰ διάστημα εἴη ὁ τόπος, χωρεῖν τοῦτο δι’ ὅλου τοῦ ἐγγινομένου ἐν αὐτῷ σώματος, ἔπειτα καὶ διαιρεῖν αὐτὸ οὕτως ὡς ἐνεργείᾳ ἄπειρα ποιεῖν τὰ μόρια, αὐτόν τε τὸν τόπον ἐνεργείᾳ ἐπ’ ἄπειρον διῃρῆσθαι, παντάπασιν εὔηθές τε καὶ οὐδὲ τὸ πιθανὸν ἔχον εἶναί μοι δοκεῖ. (in Phys., 557.10-14)

To believe that if place is extension, then the extension goes through the whole body that comes to be in it, and, thereafter, it (i.e. the extension) also divides the body in such a way as to make an actual infinity of parts, and that the place itself is actually divided to infinity—this seems to me quite foolish and not even plausible. (trans. Furley 1991: 15, modified)

In the quoted passage Philoponus is not disagreeing with Aristotle’s text. The citation refers to Themistius’ interpretation of Aristotle’s argument (Physics, 211b19-29) and his attack on a source of Stoic inspiration, as we shall see. Against Themistius’ attack, which departs from the Aristotelian text [A2], Philoponus raises two objections (the second of which is twofold) in the first part of the digression on place. He rejects the assumptions that: 1) if place is extension, then there will be infinite places (in Phys., 557.10-560.17); and 2) if place is extension, then many extensions will coincide with each other (in Phys., 560.17-562.1), and, in addition, the assumption that place comes to be in place or moves along with the bodies (in Phys., 562.1-563.25). Philoponus discards both the infinity suggested by Aristotle and the actual infinity implied by Themistius. To begin with, a few remarks regarding Aristotle’s concept of the infinite are needed. In Physics III.4-8 (202b30-208a23), Aristotle examines the concept of the ‘infinite’ (τὸ ἄπειρον). He argues that either the infinite cannot exist at all in actuality or we should accept it as potential (it may accidentally exist as, for instance, a quantity is accidental to substance). It is remarkable that in the context of Physics III Aristotle uses the concept of place in order to show that no natural body can be infinite in actuality.136 Aristotle would never accept infinity of places in actuality, since he uses the impossibility of having infinite places, either of wholes or of parts, as an argument against the possibility of having infinite bodies in actuality. In this context, the infinity of places is not only numerical but also extensional because a place is always attached to a three-dimensional extension, 136

Phys., 205a8-205b1.

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namely body. Both sorts of infinity are impossible when we are dealing with natural bodies. For Aristotle, the infinite divisibility of magnitudes does not imply infinite divisibility of place, given that the place of the parts of a whole is the same as the place of the whole.137 Moreover, Aristotle claims that the division of a magnitude should be thought of as potentially infinite, not actually infinite.138 We should keep in mind that Aristotle’s assertion of potential infinity in Physics IV remains problematic in the light of his views on potential infinity in Physics III, and it makes no sense with regard to his objection to extension theory, as we shall see. But for the moment let us say that Aristotle, in Physics IV.4, claims a potential infinity of place139 that is in accordance with Physics III.4-8. So, he is using the concept of a potential infinity counterfactually in a reductio ad absurdum against the extension theory. Philoponus does not comment in his running commentary on the kind of infinity Aristotle ascribes to the proponents of extension theory. However, he must have thought that potential infinity is permitted as the only way we can think of the infinite in nature and that the acceptance of a potential infinity is not equivalent to the actual infinity that bothers both Aristotle and Philoponus. Thus the problem must be Themistius’ interpretation: [Τ1] ἐν140 μὲν τοῖς μορίοις καὶ ἕτερον ἔγωγε ἀτοπώτερον ὑφορῶμαι. ἕκαστον γὰρ ἔν τε

τῷ οἰκείῳ διαστήματι ἔσται καὶ ἐν τῷ μείζονος μέρους· γινομένης δὲ εἰς ἄπειρον τῆς τομῆς εἰς ἄπειρον καὶ ἡ τῶν τόπων πρόσθεσις προελεύσεται. ὅλως γὰρ εἰ διάστημα ὁ τόπος, οὐδὲν ἄτοπον καὶ τῶν μορίων ἕκαστον ἐν τόπῳ εἶναι καθ’ αὑτό· καὶ γὰρ ἐν διαστήματι καθ’ αὑτό ἐστιν ἕκαστον, ὃ διάστημα μόριον ὅλου τοῦ τόπου. (in Phys., paraphr., 116.27-32)



And I also suspect another even more absurd consequence concerning the parts. For each part will be both in its proper extension and in the extension of the greater part (i.e., of place); because of the infinite regress of the partition, the addition of places will process to infinity too. For generally, if place is extension, it would not be absurd that each of the parts is in place in its own right; and each part is in its own right in the extension, which extension is part of the whole place.

137 There are a few assumptions, according to Aristotle, from which we infer the belief that the infinite exists (Phys., 203b15-30); one of these assumptions is the division of magnitudes. 138 Phys., 206b3-20; 207b10-12; 207b19. Much has been said about Aristotle’s conception of the infinite. Hintikka (1966: 199) holds that the infinite is neither actual nor potential with respect to individual things (for example, women or horses) but it is an attribute of ‘certain sequences of individual things or individual events’ that though it is said to be potential it can be actualised in a sense. Lear (1979-1980: 191-208) argues that Aristotle wishes ‘to remove the infinite from its position of majesty’. He claims that the infinite in every case Aristotle examines, namely magnitudes, numbers and time, can exist only potentially, as matter does. Finally, Bostock (2006: 116-118) discusses in what sense Aristotle posits potential infinity. 139 Aristotle says: ἄπειροι ἂν ἦσαν τόποι , 211b19-21. 140 In line 116.27, I read ἐν instead of ἕν, following the Latin translation of Hermolaus Barbarus (1542: 127): ‘Ego absurdius quiddam in partibus video.’

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Themistius holds that the actual infinity of places is possible because each part of the extension exists in its own right and so each part of the body occupies a different extension.141 The passage [T1] expresses what will happen if place is the extension, not what could happen. The reason is presumably that the view attributed to the Stoic Chrysippus, whom most likely Themistius is attacking, allows divisibility of both body and place, as we saw in section 2.2. Especially in a Stoic context, as Sextus and Stobaeus testify,142 the infinite partition (ἡ τομή) of a body would result in an infinite partition of places. Since bodies are three-dimensional extensions with resistance, they are infinitely divisible and each part of a continuum can have its own place.143 If so, then place should also be infinitely divisible or, in Themistius’ words, there will be an increase of places in number such that they will process to infinity. Themistius’ way of explaining Aristotle’s text reinforced Philoponus’ suspicions that actual infinity is the problem at hand, because verbally Themistius does not make any mention of potential infinity. Let us consider in what follows Philoponus’ objection to Themistius’ argument. The assumption that Philoponus has Themistius in mind is also evident from the following passage from the digression on place: ‘For when the bodiless goes through body it neither causes any division nor any partition (τομή).’144 Philoponus opposes Aristotle’s view to Themistius’ hypothesis that the extension of place either divides or can be divided by bodies in actuality. Philoponus takes into account the hypothetical assumption that place is a body. Even in the event that place goes through that which is in place or the body goes through the place, there is no necessity implying that the same absurdity will occur—namely, that they will divide each other ad infinitum in actuality. What could follow from this presupposition is either that a body can go through a body, which is impossible, or that one of the bodies is empty so that it can go through the other. Philoponus explicitly states that Aristotle would never claim that bodies would actually be divided to infinity.145 At the same time, Themistius’ claim does not harm a Stoic or Epicurus, who could also reply to Themistius that place, as an incorporeal, cannot act or be acted upon by a body and therefore place would be indivisible.146 Philoponus gives the incorporeality of place 141 Simplicius clearly interprets the Aristotelian tradition as implying that the parts of the water are infinite in actuality: ὥστε τὸ διάστημα τόπος ὑποτεθὲν αἴτιον γέγονε τοῦ τὰ μόρια καθ’ αὑτὸ κινεῖσθαι κατὰ τόπον καὶ ἐν τόπῳ εἶναι, τοῦτο δὲ τοῦ διωρίσθαι τὰ μόρια καὶ τοὺς τόπους, τοῦτο δὲ τοῦ καὶ τὰ μόρια ἄπειρα εἶναι ἐνεργείᾳ καὶ τοὺς τόπους, in Phys., 575.16-19. 142 Sextus, Adv. Math., X. 142 and Stobaeus, Eclogae, I. 14.1e. 2-7=SVF, II.482. 143 Rashed (2011: 206) comments that the Stoic account permits the localisation also of parts of a continuum: ‘La théorie stoïcienne permet de tout localiser, en particulier les parties du continu (puisque tout, précisément, pour les Stoïciens, est une partie du continu).’ 144 τὸ γὰρ ἀσώματον χωροῦν διὰ σώματος οὐδεμίαν διαίρεσιν οὐδὲ τομὴν ἀπεργάζεται, in Phys., 557.2324, (my italics). 145 See Philoponus, in Phys., 559.19-27. 146 That Philoponus, via Themistius, may have had in mind the Stoics is also attested to by the use of the Stoic term ‘ἀντιτυπία’, ‘resistance’ (in Phys., 558.1-2), which is part of body’s definition (see

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as one of place’s main characteristics; a view that is straightforwardly maintained by Aristotle, the Stoics and Epicurus, for if place were a body, two bodies would be at the same spot, which is absurd. But to define place simply as bodiless is not enough, according to Philoponus. He further claims that place should be void, an empty space or extension.147 What happens when the body goes through void is that the body fills it. So there is no necessity to assume that the bodiless causes an actual partition (τομή) of the body. The example given by Philoponus is that of qualities, for instance, whiteness and heat.148 Qualities are bodiless, and they cannot divide the body. For it is not in the nature of body to be divided by the bodiless. Philoponus thinks that it is impossible for something which is unaffected in any way (and which has no bodily quality) to divide a body.149 He argues that, just as a surface (or even ten thousand surfaces) fitted on (ἐφαρμόζειν) to a surface causes neither any increase nor any division to it,150 in the same way a bodiless, three-dimensional (extension) fitted on to a three-dimensional extension causes neither any division nor any other effect to it. By ‘fitted on’ (ἐφαρμόζειν) Philoponus means a kind of mental application of lines, surfaces and incorporeal extensions that the one passes into the other. Based on this example, Philoponus turns to Themistius’ assumption that there will be an actual division of place against Aristotle (in Phys., 558.10-19). Aristotle thought that place is equal to what is in place and that the limit of the container is at the same location as the limit of the contained, so that, if both limits are in the same location, then, just as the whole is in the whole, in the same way the part is in the part.151 The existence of a bodiless three-dimensional extension, which goes through and divides the body, necessarily leads to the conclusion that the parts of the limits (of the surfaces) too are actually infinite (given the divisibility of every continuum ad SVF, II.381 and II.501; Falcon (2005: 51-54) discusses the concept of antitypia in the Hellenistic period). According to a Stoic view, the bodiless (τὸ ἀσώματον) that has no resistance neither acts on anything nor is affected in any way (Sextus, Adv. Math., VIII. 263 (=SVF, II.363): τὸ ἀσώματον κατ ’ αὐτοὺς οὔτε ποεῖν τι πέφυκεν οὔτε πάσχειν). The impassivity of the void is also attested to by Cleomedes, the Stoic astronomer: ‘[Void] is neither acted on in any way nor acts, but is without qualification capable of receiving body.’ Caelestia, I.1.62, trans. Bowen—Todd 2004: 25. Epicurus’ position that the void cannot act on or be acted on by bodies is expressed in the following passage: τὸ δὲ κενὸν οὔτε ποιῆσαι οὔτε παθεῖν δύναται, ἀλλὰ κίνησιν μόνον δι’ ἑαυτοῦ τοῖς σώμασι παρέχεται, Epist. Herod., 67. 147 κενὸν γὰρ εἶναι τῷ ἰδίῳ λόγῳ, in Phys., 557.18-19 and χώρα κενή, in Phys., 557.31. At the moment, I will not go into the details of Philoponus’ definition of place as void or empty space (which I discuss in section 4.2). 148 See Philoponus, in Phys., 557.24-28. The example echoes Themistius (in Phys. paraphr., 115.36). 149 Philoponus’ claim also goes against the Stoic view that qualities are bodies, as attested to in Plutarch, De comm. not. cp. 50, p. 1085e (=SVF, II.380): τὰς δὲ ποιότητας αὖ πάλιν οὐσίας καὶ σώματα ποιοῦσι· ταῦτα δὲ πολλὴν ἔχει ταραχήν. 150 Themistius implies elsewhere that extensions cause bulk increase (in Phys. paraphr., 115.33116.1; also see Alexander of Aphrodisias, De mixtione, 219.9-18). 151 Philoponus presupposes for this argument Aristotle’s claims that place is equal to what is in place and that the limits of the container are together with, or coincident with (ἅμα), the limits of the contained (Physics, 211a1-2; 212a29-30).

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infinitum). In other words, to the extent that the surfaces (or the limits, in Aristotle’s terminology)152 are fitted on to each other and go through each other, they should divide each other in actuality—a conclusion which Aristotle could not accept. So the case of a bodiless three-dimensional extension fitted on to a three-dimensional bodily extension perfectly agrees with Aristotle’s assumption about the incorporeality of place. Thus there is no reason to claim that there will be partition when a line is fitted on to another line or a three-dimensional bodiless extension to a three-dimensional extension, as Themistius suggests. Philoponus stresses the non-bodily determination of place and emphasises that all three dimensions are not separated from body, their existence appears in nature through the body, and they can fit on to those that have the same nature, i.e., to those being bodiless. The extension of place (τὸ τοπικὸν διάστημα) can be thought of as separated from body, bodiless, and as self-subsistent; without its existence being dependent on a substrate, that is to say dependent on a body which is the compound of matter and form (meaning again a physical body): [P2] καίτοι τὸ μὲν μῆκος καὶ τὸ πλάτος οὐκ ἄνευ σώματος, ἀλλ’ ἐν σώματι τὸ εἶναι ἔχει, ἀλλ’ ὅμως ἐφαρμόζουσι τοῖς ὁμοίοις ἀσώματά γε αὐτὰ ὄντα, τὸ δὲ διάστημα τὸ τοπικὸν ἀσώματόν ἐστι καὶ χωριστὸν σώματος καὶ καθ’ αὑτὸ ὑφεστηκός, οὐκ ἐν ὑποκειμένῳ τινὶ τὸ εἶναι ἔχον. πολλῷ οὖν μᾶλλον ἐφαρμόσαι δυνήσεται τῷ σώματι, ἀπαθὲς φυλάττον αὑτό. […] οὐκοῦν οὐ τὸ διάστημα ἁπλῶς ὁποῖον ἂν ᾖ διαιρέσεώς ἐστιν αἴτιον, ἀλλὰ τὸ μετὰ ὕλης, τοῦτο δέ ἐστι τὸ σῶμα· ἡ γὰρ ὕλη τοῦ ποιεῖν καὶ πάσχειν αἰτία τοῖς εἴδεσι, τοῖς ὅλως ποιεῖν καὶ πάσχειν πεφυκόσιν. (in Phys., 558.27-31; 559.9-12)

Yet length and breadth are not without body but have their being in body; all the same, they are fitted on to their likes because they themselves are bodiless. The extension of place is bodiless and separable from body and self-subsistent, not having its being in a substrate. All the more, then, will it be able to be fitted on to the body and preserve its unaffectedness. … Surely then it is not the extension simpliciter, whatever it may be like, that is the cause of division, but the extension with matter, that is, the body; for matter is the cause of acting and being acted on for the forms, those that generally are of such a nature as to act and be acted on.

Text [P2] highlights two of the most important features of the extension of place that, so to speak, belong to the core of Philoponus’ theory of place. The extension of place is self-subsistent and not subject to affection. Extension qua extension cannot 152 Aristotle considers a two-dimensional limit to be a surface: μεγέθους δὲ τὸ μὲν ἐφ’ ἓν συνεχὲς μῆκος τὸ δ’ ἐπὶ δύο πλάτος τὸ δ’ ἐπὶ τρία βάθος. τούτων δὲ πλῆθος μὲν τὸ πεπερασμένον ἀριθμὸς μῆκος δὲ γραμμὴ πλάτος δὲ ἐπιφάνεια βάθος δὲ σῶμα, Metaphysics, 1020a11-14 (and 1022a4-5). See also Alexander

of Aphrodisias, fr. 64 (Rashed 2011: 213). Philoponus calls the limits of the bodies ‘surfaces’ in a comment: πέρατα δὲ τῶν σωμάτων ἐπιφάνειαι, in Phys., 546.2.

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partake of matter; it shares no common substrate with the corporeal extensions; thus the diastēma is separable from body and not subject to any kind of affection. The self-subsistence of the extension is not explicitly stated by Aristotle in the Physics, though he characterises place as being no part of the thing and separable (Phys., 211a1-3). Place appears to be self-subsistent in the doctrines of the atomists and the Stoics, as both schools consider place (void) as a bodiless extension that either exists or subsists without being totally independent of bodies.153 Philoponus in [P2] aims to distinguish between incorporeal and corporeal extensions. The infinity of places and the (infinite) division of place implied by Aristotle and Themistius bother Philoponus because they presuppose a confusion concerning the nature of the extension of place. Division amounts to affection of corporeal extensions. Matter, as the substrate of bodies, is the cause of division.154 For instance, we can divide a human body into parts because it is material, but not a bodiless, immaterial (and thus not subject to affection) extension, such as place. A body, compounded by matter and form, is different from the extension of place. This claim will lead, as we shall see in Chapter 3, to the crucial ontological distinction that Philoponus establishes between the extension of place and bodily extension. To conclude, we need to point out that Philoponus’ account of place escapes Themistius’ objection exactly because (incorporeal) extensions qua extensions, when simply fitted on (τὸ ἁπλῶς ἐφαρμόζον) to one another, do not divide each other. The contrast is between ‘to divide an extension’ and ‘to fit on an extension’. Division requires a cut, a partition of a body but, according to Philoponus, this is not the proper way to think of the extension of place. A body is a compound of matter and form capable by its nature (τοῖς πεφυκόσιν) of acting (ποιεῖν) and being affected by (πάσχειν) other bodies of this kind. The extension simpliciter (τὸ διάστημα ἁπλῶς) fits on other incorporeal (or corporeal) extensions without being subject to division. It is unclear whether Philoponus relies on earlier extension theories to build his own; he offers no evidence that he is directly influenced by an extension theory, though there are similarities with the atomists (Democritus and Epicurus) and the Stoics, such as the subsistence of the void extension of place, its incorporeality and thus its not being subject to affection. We could say that Philoponus attempts to protect these theories from Themistius’ critique. Yet, we need to stress the crucial differentiation between Philoponus’ theory and Chrysippus’ view on the divisibility of place from which one can infer infinite places. The extension of place suggested by Philoponus is bodiless, self-subsistent, immaterial and, thus, not subject to affection extension, by its nature incapable of causing any physical and corporeal 153 The Stoic theory (SVF, I.95, II.331) which considers place and void as two of the four bodiless entities that subsist (ὑφίστανται) is used by Philoponus against Themistius. On the atomists see, for instance, DK, 54.1, 55.40; Epicurus, Epistula ad Herodotum, 40. 154 I am here in total agreement with F. de Haas (1997: 33), who points out that the issue in this passage is that place does not share a common substrate with body.

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affection (πάθος). Thus, Aristotle’s claim of (even a potential) infinity of places and Themistius’ argument that extension should divide (or be divided by) a body are not necessarily valid.

2.5 Philoponus refuting changing and coinciding places Aristotle holds that taking place to be an extension implies that there will be another place of the place and many places will be coinciding, as we saw in text [A2].155 Philoponus was puzzled by Aristotle’s objection, that ‘has a certain plausibility, baffling refutation by its denseness, but it too is not altogether true’.156 Philoponus constructs a twofold objection: first, he refutes the thesis that if place is extension, then many places will be coinciding (in Phys., 560.17-562.1) and, second, he refutes the claim that place moves along with bodies or that place comes to be in place (in Phys., 562.1-563.25). Philoponus’ first refutation repeats the example of lines and surfaces being fitted on to each other which he had previously used in a slightly different context.157 Given the possibility of lines fitted on to lines, surfaces to surfaces, and of finding many qualities in a body—e.g., honey is sweet, yellow, sticky, heavy and moist—what prevents a three-dimensional extension from being fitted on to another three-dimensional extension, as for instance the void being applied to a body? According to Philoponus, nothing prevents something bodiless from being fitted on to a body. The comparison between lines, surfaces, qualities and the extension of place aims at pointing out the bodiless nature of the latter: several bodiless extensions can overlap with each other just like many lines fit on to other lines and qualities are found in a body without any absurd consequences. Aristotle’s conclusion of the reductio ad absurdum that place comes to be in place or moves when, for example, a vessel is moving attracts more of Philoponus’ attention. His refutation aims to show, first, that place does not necessarily move; second, that place will not be in place;158 and, third, that there are not many overlapping extensions. Philoponus examines two cases, namely a continuous body 155 Aristotle concludes ὥστ ’ ἔσται τοῦ τόπου τ ’ ἄλλος τόπος, καὶ πολλοὶ τόποι ἅμα ἔσονται , Physics, 211b24-25. The same problem is pointed out by Themistius too: ‘If they say that they save both extensions, namely the bodily and that of place, how will these two be coincident? And which one will be in the other? … How then is it possible that two extensions can coincide and in the same magnitude in which the other was, but two bodies cannot?’, in Phys. paraphr., 115.31-35. 156 Philop., in Phys., 560.17-19; trans. by Furley 1991: 19. 157 This refutation seems to be redundant (see in Phys., 558.3-10; 558.21-26). In his objection to the first part of Aristotle’s argument (Physics, 211b19-23) the problem was already the infinity of coincident places, a problem similar to that introduced in the second part of the argument, which claims that there will be many overlapping places. 158 We can read that as an attack on Zeno of Elea’s paradox, which says that place will be in another place and that this place will be in another place, creating an infinite regress of places being in places—this is discussed by Aristotle in the Physics (209a23-25; 210b22-27). For a compelling treatment of Zeno’s paradox see Rashed (2011: 38-39).

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(a solid sphere) and a case of bodies in contact (a vessel containing water). A solid sphere will fill just so much place as its own size; if you move it, then you will not move along with it any of the void that received the sphere, nor the void which the depth of the sphere filled; but now the sphere will fill this, and then it will fill the other portion of the extension of place, as it moves. In the same way, the moving vessel does not move the internal extension of place that receives the water along with it, but rather the whole vessel changes its whole position. The vessel traverses, one might say, the extension when it moves, and thus the whole vessel changes its whole position in place. But the extension itself will remain at rest, for the void cannot move. This argument implies that, when a body moves, it does not possess the extension which is left behind, and the extension is not moved along with the body. Philoponus also examined a third case, that is a divided body. Let us suppose that the solid sphere is divided and that the external part of the sphere is the container and the internal the contained. When it moves, the divided sphere does not occupy the previous part of the extension but leaves behind the whole extension which it had occupied. The sphere even in this case—i.e., being divided—will fill the whole place it occupies right now. The sphere (either divided or not) fills the place in the same way. The extension of place is neither divided nor moved, but the places turn out to be different (ἕτεροι) from the portions.159 They are different in the sense that each body, when moving, is neither standing nor occupying the same portion—i.e., position—of the extension; its position within the extension of place is determined differently right now in relation to the other bodies than it was before. Bodies, for Philoponus, do not carry their places; they rather fill now this, then that position within the extension of place. Each part of the sphere is not transferring its own place at the same time, but the whole moves, and each of the parts leaves the place it occupied before, and because of this each part comes to be in another, different place. A body is always in place. When a body moves, it always leaves behind the former extension of place it was occupying and comes to be in another, different place. Only corporeal extensions can come to be in the extension of place, so two extensions can be fitted the one to the other; a third corporeal extension cannot be fitted because two bodies cannot be in the same place. Aristotle’s attack on the extension view (as well as Themistius’ and Simplicius’ interpretations) implies that the water as a whole and each part of the water, when it is poured from the vessel, has occupied its own extension, thus many places will be coinciding.160 Here, however, Philoponus refutes this idea by arguing that there is a way to understand the extension of place without falling into the trap of having many coincident places. He argues that there is neither possession of place nor a ἀλλ’ οἱ μὲν τόποι ἕτεροι γεγόνασι τῶν μορίων, in Phys., 562.25. Simplicius reads Aristotle’s text (Phys., 211b19-29) in terms of having parts of the extension occupied by each part of the water: ἔσται ἕκαστον μόριον ἐν μέρει τοῦ διαστήματος, τουτέστιν ἐν τόπῳ καθ’ αὑτό, in Phys., 575.2-3. 159

160

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dependence of place on (corporeal) substances. According to Philoponus’ doctrine in the digression on place, body and place do not share the same substratum, so place’s existence is independent of the body (in Phys., 558.29-30). Applying this interpretation to Aristotle’s example of the water poured from the vessel, the argument is as follows: the part of the water leaving the vessel does not occupy different extensions at the same time, contrary to Aristotle’s argument when he insists that its place is the same as the place of the whole (Physics, 211b25-26). Philoponus would reply that, if we are about to create parts of the water, which in his view is not necessary, then the part of the water fills another place at another time, since it is moving. The example of the solid sphere, presented by Philoponus, shows exactly how a body moves or traverses the extension of place. When the vessel moves, whether it contains water or not, it is not moving the place it previously occupied, but while it moves, it occupies other places—i.e., other positions within the extension. The extension theory that Philoponus defends does not presuppose that the water has parts as it leaves the vessel. All the water moves towards the exit of the vessel, and it all occupies different positions within the extension at different times, avoiding many places coinciding with each other at the same spot. In my view, Philoponus is in complete agreement here with Aristotle’s argument in Physics 211a29-b1, where he says that the parts of a whole (i.e., a continuous body), when they move, are not related to their immediate surroundings as something which is in place but as parts in a whole. So, the parts do not move in their surroundings (i.e., in place) but rather with them. There is no reason—this is also the case for Philoponus—to think of parts of water leaving the vessel instead of a whole and continuous body (water) occupying the extension of place. As Philoponus explicitly points out in the digression on place, because bodies fill out (πλήρωσις) the place and do not go through each other (χώρησις δι’ ἀλλήλων), the parts cannot have a place in their own right.161 The fact that Philoponus defends a bodiless extension, deprived of matter and, thus, of the capacity to divide or be divided, ensures that there is no reason to admit 161 Philoponus says (in Phys., 577.30-578.4), ‘For this reason also the part will not in itself be in place; for if the body that passed inside the place were actually divided by the extension, it would necessarily follow that, because each part is individually outlined, each part is individually in place; but if the body is not divided by the extension and the extension does not pass through the body, why should it necessarily follow that the part is in place in itself?’ (trans. Furley 1991: 40). Simplicius suggests a similar solution for the proponents of extension theory (in Phys., 577.32-37; 578.2-5): ‘If someone suggests place to be the extension that passes through all the parts, nothing prevents the parts to be in place in their own right, though it is not necessary that they are divided. But, since we call them parts, although they are not divided (for when they are divided, they are not parts anymore), in the same way we say that the parts of the continuum are in place in their own right, without being forced to divide them. … But, according to this assumption, it is neither necessary that place will be in place nor that there will be many places together nor that place is changing, if indeed the extension that passes through all of them is one and receives at one time another (part of body) in a different part of itself and (at a different time) another body.’

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that parts of bodies, when individually determined, have their own place. The extension of place is filled by continuous bodies. We could say, paraphrasing Aristotle, that the parts of the continuous bodies are not in place individually, but as parts of a whole—i.e., each time their place is the place of the whole body.162 Moreover, the key to comprehending Philoponus’ response to the objection that place comes to be in place is, I think, to be found in the consequence of what it means for place to be immobile. Place is filled with bodies (πληροῦται), and not vice versa, because it is immobile; then again, because of place’s immobility, it is impossible for the void to come to be in the body. This suggests that only two extensions can coincide at a time, namely the corporeal extension and the extension of place in which it comes to be. Furthermore, Philoponus adds, as a follow-up to the previous thought, an argument to avoid the problem of having infinite or many coincident places. Three (or more) bodies cannot be in contact at the same spot. Philoponus claims that there can be multiple surfaces in the same place but that it is impossible that more than two surfaces can be fitted on to each other in actuality (in Phys., 563.6-12). What happens in actuality—i.e., in nature (and not in mathematics)—is that only two extensions are fitted on to each other, namely a body and place. Places neither overlap nor coincide with each other, for that would imply that two bodies are in the same place, which is impossible—this is the objection Aristotle makes to the extension view. Since this is the only significant case of many places overlapping with each other, two or more bodies could never be in the same place in actuality. Moreover, if we accept that the void can come to be in the void, the right way to approach the issue, for Philoponus, is to consider lines fitted on to lines and surfaces fitted on to surfaces. To put it another way, even if ten thousand bodiless extensions, just as lines fitted on to lines, were fitted on to each other, there is no increase of the whole, for it still remains one, and only one, extension. This demonstrates that the proponents of Philoponus’ theory of place need not conclude that more than two extensions come to be in the same place, nor that place comes to be in place (as Zeno’s paradox suggests, Phys., 209a23-25), nor that place moves at all. The outcome of Philoponus’ argument is that place in its own definition is a voided, three-dimensional, unaffected, immaterial and immobile extension, always filled with bodies. The danger of having coincident or overlapping places was discussed by Morison in his analysis of Aristotle’s relevant argument. I quote his interpretation (2002: 124-125): The diastēma theory entails that at every moment t between t1 and t2 (where t1 is the time at which the vessel starts to empty and t2 is the time at which it has just become empty), there is a different interval—or place, according to this theory—occupied by the water left in the vessel. But the interval occupied by the water in the vessel at 162

Philoponus refers to this argument in the running commentary; see in Phys., 598.20-21.

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any point between t1 and t2 is also occupied at t1 by some water, namely a part of the total water in the vessel at that time, and since the motions of the water as it leaves the vessel and of the air as it replaces the water are infinitely divisible, there will be an infinity of overlapping or coincident places occupied by water at t1. … In effect, this argument suggests that the water in a vessel occupies a particular interval, but that there are infinitely many other intervals within this interval, each of which will be occupied at some point during the water’s departure from the vessel by some incoming air.

I disagree with Morison insofar as he believes that every extension theory (Philoponus’ theory included) should admit the problems that Aristotle may have—possibly—pointed out. First, Morison’s interpretation presupposes that the extension theory—he does not specify whose extension theory he means—implies different intervals causing an infinity of coincident places, which actually reflects Simplicius’ interpretation (in Phys., 575.1-12). Philoponus’ theory, of course, states that there are different places filled with bodies. What is different, according to Philoponus, is the position that bodies of the universe occupy each time in the extension of place in relation to each other. When the water leaves the vessel there is no reason to determine different actual parts of the extension that in t1 were occupied by the front part of the water and now at t2 are occupied by the back part of the water as it leaves the vessel. Between t1 and t2 the water occupies a different position as a whole; we determine the position the water now occupies from the previous one in relation to the vessel and the air around the water. Bodies just fill the extension of place. The extension, seen in its own right, cannot be characterised as ‘same’ or ‘different’. Such characterisations would imply that we are dealing with something that undergoes physical changes; yet the extension of place, seen in its own right, does not have a material substratum, nor does it undergo physical changes in the same way as bodies do. The three-dimensional extension does not essentially change in any physical way, as Philoponus argues in the De aeternitate mundi contra Proclum (XI.4). The differentia of place are the up, down, right and left, and these are determined by the position bodies fill each time, or when they traverse the extension of place. Therefore, place is not ‘different’ in the sense that you can actually divide the entity called ‘place’ and so create different parts of it. Second, Morison claims—again reflecting, I believe, Simplicius’ argument (in Phys., 575.12-19)—that motions are infinitely divisible and that this is how the infinity of overlapping places occurs. Philoponus’ answer is clear: Aristotle or Themistius should either prove that there can be infinite places in actuality or they should admit that potential infinity of places is a harmless mental construction, since in nature it is never possible to create infinite places coinciding with each other. The nature of bodies allows only two coincident extensions, namely the bodily extension and the extension of place. Philoponus’ extension theory does not suggest in any

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way that there are ‘infinitely many other intervals within this interval’, as Morison concludes about the extension theory. If we can create different parts of water, then each part as a different whole this time fills the extension of place and thus occupies a different position within the extension. The actual, or even the potential, partition of bodies and places is not necessary, and it is certainly not implied by Philoponus’ theory of place, as he explicitly denies that parts of continuous bodies have their own place, as if place were body’s possession. The first part of the digression on place (in Phys., 557.8-563.25) concludes by claiming that it has demonstrated how the problems Aristotle ascribes to the extension theory can be avoided. The central line of my interpretation suggests that Aristotle may have been rejecting an extension theory that was known in his era (the diastēma theory and the void theory of Leucippus and Democritus). But we cannot infer from Physics IV.1-9 that all possible extension theories of place will have the same weaknesses as the theories with which Aristotle struggled. The same goes, as we have seen in this chapter, for Themistius’ critique of certain views of the Stoics. Philoponus relentlessly tries to verify the cogence of Aristotle’s and Themistius’ arguments providing solutions related to the nature of the extension of place. After refuting Aristotle’s arguments against place as a sort of extension, he methodically offers a replacement of the Aristotelian doctrine on place with a theory of place which is new, at least in its details.

Chapter 3

The Ontology of Place According to Philoponus Having examined Philoponus’ objections to the Peripatetic tradition, with which he defends the definition of place as extension, we may now turn to Philoponus’ account of place. In what follows I deal mainly with the third part of the digression on place, which contains some of the most important aspects of Philoponus’ theory of place (in Phys., 567.29-579.18). The whole section aims to elucidate the nature of place that Philoponus often calls τὸ τοπικὸν διάστημα, meaning the extension of place. To that end, Philoponus provides us with several syllogisms showing that place differs from the bodies that come to be in it. He relies on ordinary observations, such as the measurement of a three-dimensional body or the inspection of clepsydras, which demonstrates the so-called ‘force’ of void (ἡ βία τοῦ κενοῦ). Furthermore, Philoponus’ attempt to establish the absolute space that is the extension of place in its own right relies on thought experiments such as the possibility of an empty universe. This theory entails that place can be conceived of as an absolute physical extension that is ontologically present in nature and different (ἕτερον) from physical bodies. The ontology of place, according to Philoponus, presents a conception of a subsisting space in nature but as such differs from some theories of antiquity supporting a substantialist view of space. To make this clear, our efforts now focus on determining the kind of ‘ἑτερότης’ Philoponus attributes to place. We shall see that he defends a certain kind of intra-cosmic void extension that differs from the conception of the atomists and, moreover, we will focus on how he rejects the extra-cosmic void extension supported by the Stoics. But first I would like to draw attention to the three-dimensionality of place in Philoponus’ theory that carries considerable weight in the understanding of physical topos.

3.1 Three-dimensionality of place Broadly speaking, dimensionality is a concept concomitant to extensionality. Every aspect of extensionality (excluding the extensionality in logic) implies a dimensionality. In antiquity place has been defined as a kind of extension that is either separate from physical bodies or relevant to the materiality of physical bodies. Here our interest is in the concept of place that Philoponus determines as three-dimensional extension separate from physical bodies. In this section we will attempt to classify Philoponus’ conception of place among other theories of antiquity, especially drawing attention to how Philoponus conceives of the three-dimensional extension of place.

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Frans de Haas points out that the following aspects of three-dimensionality appear in ancient philosophical doctrines: extensionality (in relation to space/ place), extension (definiteness in terms of size), determination (three-dimensiona­ lity attached to that which possesses it) and limitation (related to mathematics).163 I take it that these aspects represent three more general categories of ascribing three-dimensionality to something, namely a) to place, b) to physical body, and c) to mathematical objects. But topos is not always considered as three-dimensional in antiquity. The receptacle or space (ὑποδοχή, χώρα), in Plato’s Timaeus, is not explicitly stated as three-dimensional, though in fact one can deduce the three-dimensiona­ lity of space because it is a kind of extension in which forms and physical bodies come to be.164 The three-dimensionality of place has been stated later on in the Platonic tradition by Syrianus, Iamblichus and Damascius, authors who clearly distinguish between the three-dimensional physical and intelligible space.165 Aristotle—and generally, everyone asserting that place is the relative location of a physical body—avoids ascribing three-dimensionality to place. Early atomists and Epicurus consider the void as a primary constituent of the cosmos, as that in and through which the atoms move. Aristotle characterises the void of the early atomists as a diastēma, but we cannot assume with certainty that this kind of extension is considered as three-dimensional because of the lack of textual evidence. The same goes for Epicurus, since the void, the intangible nature (ἀναφὴς φύσις) or chōra, is not explicitly stated as a three-dimensional extension in the texts we possess, but rather as an extension (since Epicurus also calls it χώρα) in and through which the atoms and the bodies move.166 The Stoics, by accepting that the reality consists of three-dimensional corporeal bodies that are, so to speak, accompanied by incorporeals—namely, lekta, time, place and void—are constrained to accept that topos too is three-dimensional; otherwise, it cannot be conceived as a subsistent entity in relation to three-dimensional bodies.167 Philoponus’ account of place presupposes its three-dimensionality without any explanation, as a self-evident fact about the extension of place. Right from the beginning of his digression on place, three-dimensionality appears as a correlate term to the extension of place.168 Aristotle, in contrast, denies the three-dimensionality 163

F. de Haas 1997: 47-49. Timaeus, 48E-52D. 165 Syrianus, in Metaphysics, 84.31-85.15 and 186.15-28; Iamblichus apud Simplicium, in Cat., 363.29-364.6; Damascius, De primis principiis, II.219.21-220.2. A survey of theories of place in late Platonism is offered by Sambursky 1977. 166 On the kind of void accepted by the early atomists and Epicurus see Epicurus, Epist. Her., 40; Lucretius, De rerum natura, I.426. See also Solmsen 1977: 267-268; Bailey 1964; Sedley 1982. 167 See the Stoic fragments SVF I.95, II.503, II.505. For further reading on the Stoic concept of place see Algra 1995: 261-336. 168 The first time three-dimensionality appears in the running commentary is in the second lecture on Physics IV.1 (in Phys., 504.29-505.11). The concept of three-dimensionality also appears in 164 Plato,

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of place because he thinks that it leads to absurd conclusions.169 The three dimensions—namely length, breadth and depth—define anything that is a body. If place is considered three-dimensional, then two bodies must be admitted to be present at the same place. Philoponus picks up Aristotle’s starting argument on the genus of place by saying that it intends to show that place is either a body or something bodiless.170 He presents an analysis of Aristotle’s argument which divides it into two parts: (a1) showing that place is a body, and (a2) claiming the absurdity of a bodily place.171 (a1) Place is three-dimensional. Everything that is three-dimensional is a body. Therefore, place is a body. (a2) Every body is in place. Every place is a body. Therefore, every body is in a body. In syllogism (a1) Philoponus establishes the premise that place is three-dimensional. But where does this premise come from? There is another syllogism lying behind this premise and it runs as follows. If a body is in place, then all of its dimensions must be in place; therefore if the body has three dimensions, then all of its dimensions are in (a) place and the place receiving them necessarily is three-dimensional too.172 Yet since three-dimensionality defines body, as Aristotle argues, then whatever is three-dimensional must be a body. Therefore, place is a body. The conclusion of (a1) appears as the second premise of the second argument (a2): if all bodies are in place and all place is a body (since place is three-dimensional), then all bodies are in body, which is absurd, since it is impossible to have two bodies at the following passages of the running commentary before the digression on place: in Phys., 526.20-23; 547.15-16; 549.16; 549.25; 549.33; 551.23-24. 169 Aristotle’s starting point of his discussion of the genus of place goes as follows (Phys., 209a4-6): ‘There are three dimensions, length, and breadth, and depth, according to which all body is defined. It is impossible that place is body; for two bodies would be at the same spot.’ Themistius follows Aristotle in attaching three-dimensionality to bodies, for he admits that ‘[t]hree-dimensionality is ascribed only to body’, in Phys. paraphr., 104.23-24. 170 See in Phys., 504.24-28. 171 As Simplicius testifies, Alexander of Aphrodisias distinguishes between two arguments. Philoponus’ argument (a1) is identical to Alexander’s—both are constructed as categorical syllogisms (κατηγορικός συλλογισμός). But Philoponus constructs a further categorical argument (a2), whereas, according to Simplicius, Alexander constructs his second argument according to the scheme of the second hypothetical syllogism called ‘ἀντιστροφὴ σὺν ἀντιθέσει’, ‘conversio per contrapositionem’, ‘conversion with opposition’ (see Simpl., in Phys., 529.34-530.3; Rashed 2011: 175-176, fr. 7). For a brief history of the term ‘ἀντιστροφὴ σὺν ἀντιθέσει’ see Shorey 1913: 228-229. 172 Philoponus, in Phys., 504.29-505.8. The argument infers the three-dimensionality of place from the fact that each dimension of a body needs to be in (a) place. Philoponus’ argument is flawed since what warrants that the place of a body is the place of its dimensions is that physical bodies are in place.

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the same spot. In this way Aristotle demonstrates, according to Philoponus, that place must be bodiless.173 Take note that Philoponus several times presents the three-dimensionality of place as if it were part of Aristotle’s worries. I quote, as an example, Philoponus’ text from his exegesis of Aristotle’s refutation of place as the extension in between the limits:174 [P3] ᾗ δὲ πάλιν χωριστὸς ὢν ὁ τόπος καὶ ἕτερος μένων εἷς καὶ ὁ αὐτὸς ἄλλοτε ἄλλα δέχεται σώματα, δοκεῖ διάστημά τι εἶναι ἕτερον τῶν ἐν αὐτῷ γινομένων σωμάτων· οὐδαμόθεν γὰρ ἄλλοθεν ἤλθομεν εἰς ἔννοιαν τοῦ εἶναί τι τὸν τόπον, εἰ μὴ ἐκ τῆς

ἀντιμεταστάσεως τῶν σωμάτων· εἰ τοίνυν εἷς καὶ ὁ αὐτὸς ὢν τὰ ἀντιμεθιστάμενα δέχεται σώματα, ἔστι δὲ τὰ μετεμπίπτοντα εἰς αὐτὸν σώματα τριχῇ διαστατά, ἀνάγκη καὶ τὴν δεχομένην αὐτὰ χώραν τοιαύτην εἶναι· ὥστε καὶ ὁ τόπος τριχῇ ἂν εἴη διαστατός. (in Phys., 547.9-16)



Again, in so far as place, being separate and different, receives ever-different bodies while remaining one and the same, it appears to be an extension that is different from the bodies that come to be in it. For we have not arrived at the conception that place is something from anything other than the mutual replacement of bodies. If, then, it receives these bodies that replace each other while itself remaining one and the same, and if the things which replace each other entering into it are three-dimensionally extended, then it is necessary that the space which receives them is so too; so that place too will be threedimensionally extended. (trans. Algra—Ophuijsen 2012: 63)

When reading [P3], attention should be given to the contrast with Aristotle’s argument denying the three-dimensionality of place. Aristotle argues that the three-dimensionality of place is impossible, for all three dimensions define all body. Otherwise, we would have to admit the existence of a bodily place and the simultaneous appearance of two bodies at the same spot. Surprisingly enough, Helen Lang argues that Aristotle does not deny the three-dimensionality of place: Place again contrasts sharply with surface. Because place is the first limit, it can have no limit. Because it has no limit, place must have every possible interval, length, breadth, and depth. Indeed, this point solves the problem raised at the outset: how can place be in the same genus as body, even though it is not a body. They are in the same genus because both have three intervals, although for different reasons: body has length, breadth, and depth because it is complete magnitude while place has them because, being the first limit, it can have no limit.175 173 Philoponus,

in Phys., 505.11-13. Physics, 211b14-19. Philoponus indirectly inserts the three-dimensionality of place when he discusses another ἀπορία of Aristotle’s, which considers the possibility that place is one of the intelligibles (νοητά, Physics, 209a16-18). Place cannot be a νοητόν, for intelligibles are not extended according to magnitude, whereas place is extended because it is capable of receiving extended bodies (i.e., three-dimensional bodies, in Phys., 508.9-20). 175 Lang 2001: 16-17. 174 See

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I do not see this argument anywhere in Aristotle’s theory of place. It is clear that Aristotle tries to avoid the identification of place with three-dimensionality because the latter implies that place has a corporeal characteristic. I also have difficulty in understanding the idea that ‘place is three-dimensional because it has no limit’. According to Lang, place has no limit because it is defined as the first limit of the surrounding body, and hence it is three-dimensional. Body is a ‘complete magnitude’, which obviously has a limit, and hence it is three-dimensional. But this argument is a fallacy: beings which have no limit and those which have limit are both three-dimensional. Again, it is awkward to claim that a limit is three-dimensional because it has no limit (for instance, an unlimited line does not have three dimensions). Aristotle does not argue in favour of place’s three-dimensionality in the Physics, though he insists on the equality of place and the body in it. In contrast, in text [P3] we see that Philoponus incorporates three-dimensionality in his exegesis as if the problem in Aristotle was constantly place conceived as a three-dimensional extension.176 Philoponus conceives of the absence of three-dimensionality as a major weakness of the Aristotelian tradition directly deriving from Aristotle (as we will show in Chapter 5). In this context, Lang’s claim that ‘Philoponus replaces the phrase “which is between limits” with the phrase “in three dimensions” and so attributes to Aristotle the view that it is impossible that place be an interval in three dimensions, i.e., extension’177 makes no sense. How does Philoponus conceive of the three-dimensionality of place? He insists three-dimensionality should not be considered as identical with body, for then, in the case of a body being in place, one would be obliged to admit the absurdity of having two bodies at the same spot. A three-dimensional extension cannot be a definition of what body is. Body is a substance, and quantity is accidental to substance: hence three-dimensionality is accidental to substance.178 Body is composed of matter and such-and-such a form, but because quantity is an inseparable accident (ἀχώριστον συμβεβηκός) of the body, it is in this sense that body is three-dimensional.179 Philoponus relies on Aristotle for this argument. He quotes a passage from the Physics where Aristotle criticises Melissus, who said that being is infinite and 176 Another instance of the same attitude is found in Philoponus’ exegesis of Physics, IV.1-2. There he concludes that all the difficulties of those who hold that place does not exist are solved, but chiefly the difficulties deriving from views that misconceive the nature of place, like those who hold that place is a three-dimensional extension (in Phys., 526.21-23). However, Aristotle is just rejecting the three-dimensionality of place in an attempt to define the genus of place. 177 Lang 2001: 20. 178 Philoponus attacks the position that three-dimensionality defines only bodies by saying (in Phys., 561.5-25), ‘For we will not accept either that the three-dimensional directly is a body or that it is a definition of body; for the body is three-dimensional in respect of being something else.’ 179 In line in Phys., 561.23 of the digression on place I read ἀλλ’ ἀχώριστον συμβεβηκός, following manuscript Laur. Plut. 87,6 (G) and Trincavelli’s edition (1535), instead of reading ἀλλὰ χωριστόν συμβεβηκός, as Vitelli does. Philoponus clearly says that quantity is an inseparable accident of body, and this is exactly the point that he wants to stress by quoting Aristotle’s objection to Melissus.

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further maintained that being is a quantity. There Aristotle objects that the infinite is a quantity and quantity is accidental to being.180 The point that Philoponus attempts to make, through Aristotle’s objection to Melissus, is that three-dimensionality belongs to quantity (κατὰ τὸ ποσόν): hence, three-dimensionality is accidental to substance. Since body is a substance, three-dimensionality belongs to bodily substance accidentally. Consequently, three-dimensionality cannot define what body is but must rather be something accidentally and yet inseparably attributed to it—inseparably in the sense that we cannot think of a physical body which does not have three dimensions. But this does not imply that whatever is three-dimensional is automatically a body. At this point, we may see clearly in what sense τόπος is a concomitant (παρακολούθημα) of all physical beings, as discussed in Philoponus’ preface to the commentary on the Physics: place is an incidental which is common to all physical bodies because it is one of their natural concomitants (παρακολουθήματα), though it is not inseparable as three-dimensional quantity is for bodies.181 A further remark is that Philoponus shows with his account of place that the three-dimensionality of a body is a different instance of three-dimensionality from that of the extension of place. He is disconnecting three-dimensionality from body to prove that place as a bodiless and immaterial extension is just another instance of three-dimensionality. Philoponus also considers the three-dimensionality of place to be different from another instance of three-dimensionality that relates to prime matter, i.e., the notion of three-dimensionality (τὸ τριχῇ διαστατόν) that is attached to what Philoponus calls ‘the indeterminate quantified matter’. The empty extension that is place is still a different instance of three-dimensionality that should not be confused with that of prime matter.182 However, place resembles matter with respect to separability: insofar as matter can be thought of as separated from qualities, so place can be thought of as separated from bodily extension.183 Philoponus, as we shall see, builds an account according to which place is a bodi­ less, three-dimensional, immaterial, impassive, void, immobile and unchangeable extension. Place must be bodiless, for otherwise we would have to deal with the problem of having two bodies at the same spot. Place must be extended in three dimensions because it is always the place of three-dimensional bodies. Place must be impassive for, if not, then it would be material. Place is necessarily immaterial, 180 See

Physics, 185a32-37. See Philop., in Phys., 2.13-16. 182 Philoponus calls it ‘ἡ ποσωθεῖσα ὕλη’ (in Phys., 520.19-25) or ‘ἡ ὀγκωθεῖσα ὕλη’ (in Phys., 687.3035); the term also appears in the running commentary (in Phys., 515.19). In addition, we must not identify the three-dimensionality of place with the three-dimensional unqualified body or second substrate (τὸ ἄποιον σῶμα, τὸ δεύτερον ὑποκείμενον); see in Phys., 579.3-13. 183 I will not go into the details of Philoponus’ view on three-dimensional prime matter here. The best guide on the issue is Frans de Haas 1997: 262-263; 280-290. See also the discussion of the concept of the three-dimensional prime matter by Scholten 2015: 158 ff. 181

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for otherwise it would be a cause affecting bodies. Place must be void, since a body cannot be in a body. Consequently, place must be immobile, since the void cannot move, but bodies move within place. Finally, place cannot undergo any kind of change because it is not a body. The last sentence of the first part of the digression on place states that Philoponus considers place to be different from the bodies that come to be in it (ἕτερον τῶν ἐγγινομένων σωμάτων, in Phys., 563.23-24). What Philoponus means by ‘different’, how place is different, from which things place is different, and how the differentiation of place fits Philoponus’ account of place will be shown after the examination of the third part of the digression on place, which now follows.

3.2 Place as measure In the first part of the digression on place Philoponus speaks of an extension of place as something other than corporeal in three ways: (a) in terms of a body which comes to be in something else, namely a three-dimensional extension, a place; (b) in terms of the kinship of the extension of place with other bodiless extensions, such as lines and surfaces; and (c) in terms of a place being deprived of any body, being empty. However, it is only in the third part of the digression that Philoponus explicitly argues in favour of an ontology of place in terms of an essential difference (ἑτερότης).184 He holds the view that topos is an absolute space, that is to say an extension void in itself and separate from any corporeal substance. I claim that the essential difference of place from physical bodies established by Philoponus aims at demonstrating a physical extension of place which is the underlying reality in which physical bodies are and move through. Philoponus conceives of topos as an extension always filled with bodies. In this sense, he avoids establishing place as a mere notion that would result in a mathematical conception of place. He argues, as we shall see, for the real existence of place, even though human beings have no direct experience of it as a voided place. In order to show how, on the one hand, we may conceptually claim the existence of an empty space, and, on the other hand, determine place as the physical extension in which physical bodies are, Philoponus employs experiments rooted in both common experience and thought. Let us begin with his observations about physical facts of which we have direct experience and see how he advances in designating place as the measure of a body that is in it. The mutual replacement of bodies (ἡ ἀντιμετάστασις τῶν σωμάτων), for Philoponus, proves that place is different in every way (ἕτερον πάντῃ) from the bodies that come to be in it (in Phys., 567.29-569.17). Consider a body moving through the air. According to Philoponus, if it is true that the moving body does not go through another body and that it is three-dimensional (not a surface), then when 184 The terms ‘ἕτερος’ and ‘ἑτερότης’ signify an essential difference; Philoponus does not refer to place in terms of ‘διαφορά’, which means a ‘specific difference’.

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it cuts the air it comes to be in the place where the air was. The air is replaced by the moving body in the same quantity as the moving body itself. If the air is ten solid cubits, then the space (χώρα) receiving it necessarily has the same quantity (I suppose it refers to the volume)—i.e., ten solid cubits. Place is what the air and the moving body fill; it is what they exchange with each other. Philoponus emphasises two things with this argument. First, place is something solid and, second, place is the measure of what comes to be in it.185 To begin with, we need to explain what is meant by ‘solid’ (στερεός). The term ‘solid’ has a mathematical and a physical sense.186 The adjective στερεός is used in mathematics to describe a three-dimensional object, namely a type of object which has length, breadth and depth, such as geometrical figures.187 Yet, solid is a state of matter and any given body is a physical solid in three dimensions that has resistance. Place is characterised as something solid (στερεόν τι), i.e., three-dimensional, but neither in the mathematical nor in the physical sense, for place is neither a mathematical object nor a physical body. The occupation of place by three-dimensional bodies leads to the observation that place must also be solid, that is to say three-dimensional in the sense we described in section 3.1, namely as extensionality of place. Place receives the body in its entirety, all its three dimensions together. The important feature of Philoponus’ example is its observation that three-dimensionality is a quantity (ποσόν) that determines the volume of a body. Therefore a body needs to fill a (dimensional) quantity of place equal to its own. This quantitative equality results from the (essential) three-dimensionality of place and body. The cause, according to Philoponus, of the equality between place and what comes to be in it is that place is a measure of what is in place.188 Equal (ἴσος) in this context means that place’s three-dimensionality must be exactly proportional to the three-dimensionality of the body.189 However, some difficulties with Philoponus’ position need consideration. Based on everyday observations, we might think that place cannot in any way be a measure of a body, for we think of place as something immaterial and undetermined (ἀόριστον). Another difficulty is how to conceive of the link between measure, measurement and the notion of place. What does Philoponus mean when he describes place as measure? The examination of place as measure appears only once in Philoponus’ commentary on the Physics (in Phys., 568.14-569.7). In order to clarify his thesis that ‘place, as The Greek expression translated here as ‘solid’ is στερεόν τι, in Phys., 568.13. Philoponus describes both senses in his commentary on Aristotle’s Meteorology (in Meteor., 41.25-29). 187 See Euclid, Elementa XI.1. For the use of the terms ‘σῶμα’ and ‘στερεόν’ in Plato and Aristotle see Falcon 2005: 45. On the use of either the mathematical or physical sense of the term stereos in Philoponus’ works see Scholten 2015: 297-308. 188 μέτρον δὲ καὶ ὁ τόπος τῶν ἐν τόπῳ, διό καὶ ἴσος, in Phys., 568.14. 189 Philoponus proposes an alternative understanding of the same principle established by Aristotle in the Physics (see section 5.2). 185

186

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the measure of what is in it, is considered to be the cause of its equality to bodies’, he looks at the case of the vessel.190 The vessel is the measure of what it contains—for instance, air. The air occupies the extension which extends between the concave surfaces of the vessel. If the vessel has a specific solid (three-dimensional) quantity, then the air in it should have the same solid quantity. When the water, which is a solid body, replaces air, it occupies as much place as the air occupied (i.e., the vessel is full of water). Now, if the water is measured by the vessel, the measure (vessel) is of equal quantity to what is measured (water) by it. The conclusion then is that the measure must necessarily be equal to what is measured.191 For, as Philoponus emphasises, the measure and the measured body must both be solids—i.e., three-dimensional—not two-dimensional surfaces. When we fill the vessel and measure the water, we say that the space of the vessel is equal to the space of the water. But what exactly are we measuring in this case? Is it the perimeter of the surface of the water? Are we measuring the air that was previously in the vessel? Is it the surface of the vessel that we are measuring? Philoponus excludes these three possibilities by answering that what we are measuring is the solid (στερεόν)—i.e., the three-dimensional quantity of the bodies: we measure neither the perimeters, nor the planes, nor the surfaces of either the vessel or the water; nor we are measuring something which previously was in the vessel—like the air—which exchanged its position with the water. We look only for the solid surfaces.192 This kind of measuring, i.e., the measuring of solids, measures the quantity of solids or, to put it differently, the three-dimensional quantity of bodies. Given that the vessel is a three-dimensional body, the water it contains must be three-dimensional, for the water is measured by the vessel. Philoponus further claims that when the water is contained in the vessel, we admit that the extension between the limits of the vessel, occupied by the water, is something. At first glance, the nature of place seems completely undetermined or, as Aristotle says, it is difficult to comprehend; if place is, then what exactly is it (Phys., 209a3-4). Philoponus’ effort to make the extension of place comprehensible falls into the field of geometrical measuring because he wants to avoid an explanation which exceeds the field of physics (as measuring the angles of a triangle is a subject 190 The same analogy between place and a vessel occurs in Aristotle’s Physics. See, for instance, 208b3; 209b28-30; 210a24; 210b10-16. 191 The same idea occurs in Simplicius’ Corollarium de loco (in Phys., 634.11-15). Simplicius also testifies that his teacher, Damascius, had a theory about place which involved the concept of measure and was propounded in a treatise probably called Περὶ ἀριθμοῦ καὶ τόπου καὶ χρόνου. Simplicius himself seems to endorse a view according to which place is measure (in Phys., 644.10-654.19). On Damascius’ influence on Simplicius see Golitsis-Hoffmann 2014: 162-172. 192 ‘Did we then measure the surface of the water, in order to see how much its perimeter is? Not at all, but we measured the solid; wherefore, we do not attach ourselves to what sort of shape the measure could have, but we look only at the solid surfaces’, in Phys., 568.26-29. By ‘solid surfaces’ I translate the term ‘τὰ στερεά ἐμβαδά’ (see Liddell-Scott 1882: 458); Furley suggests the term be translated as ‘solid contents’ (1991: 29).

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of geometry, so measuring solid surfaces (τὰ στερεὰ ἐμβαδά) is a subject of geometry).193 This kind of measuring—i.e., the procedure of measuring a certain kind of solid (στερεόν τι), the three-dimensionality of a body, and its place—is a matter that geometry deals with. However tempting it may be, I would not claim that we should think of Philoponus’ extension of place as an abstract geometrical scheme like, for instance, the ὀκτάεδρον, which is a solid figure. Place is the measure of something: it measures the three-dimensionality of bodies, and therefore, Philoponus claims, place is something different (ἕτερον τι) from the bodies filling it. Now if place is something different from the bodies that come to be in it, can we, then, assume that place is ontologically independent of anything that comes to be in it? Philoponus’ answer to this seems to be crucial not merely for his account of place but also for his conception of the void: [P4] ἔστιν ἄρα τι τὸ μεταξὺ διάστημα παρὰ τὰ ἐμπίπτοντα σώματα. καὶ οὐ δήπου τοῦτο λέγω, ὅτι τὸ διάστημα τοῦτο ἤ ἐστί ποτε ἢ δύναται εἶναι κενὸν παντὸς σώματος· οὐδαμῶς, ἀλλ’ εἶναι μέν φημι ἕτερον παρὰ τὰ ἐμπίπτοντα σώματα καὶ τῷ ἰδίῳ λόγῳ κενόν, μηδέποτε μέντοι χωρὶς σώματος, ὥσπερ ἀμέλει καὶ τὴν ὕλην φαμὲν τῶν μὲν εἰδῶν ἑτέραν εἶναι, μηδέποτε μέντοι χωρὶς εἴδους εἶναι δύνασθαι. οὕτως οὖν καὶ τὸ διάστημα ἕτερον μὲν εἶναι παντὸς σώματος καὶ κενὸν τῷ ἰδίῳ λόγῳ νοοῦμεν, ἀλλ’ ἀεὶ μετεμπίπτει εἰς αὐτὸ ἄλλοτε ἄλλα σώματα αὐτὸ ἀκίνητον μένον καὶ καθ’ ὅλον καὶ κατὰ μόρια, καθ’ ὅλον μὲν διότι τὸ κοσμικὸν διάστημα τὸ δεξάμενον τὸ τοῦ κόσμου παντὸς σῶμα οὐδέποτ ’ ἂν κινηθείη, κατὰ μόρια δὲ διότι κινεῖσθαι τὸ ἀσώματον διάστημα καὶ τῷ ἰδίῳ λόγῳ κενὸν ἀδύνατον. (in Phys., 569.7-17)

So the extension in between is something over and above the bodies that come to be in it. And I am not saying that this extension either ever is or ever can be empty of all body; this is in no way possible, but I say [the extension] is different from the bodies that come to be in it and in its own definition empty, although it never exists without body; just as we consider matter to be different from the forms, although it can never be without form. So we consider the extension to be different from all body and empty in its own definition, yet other bodies always fall into it, while it remains immobile both as a whole and as regards its parts; as a whole because the cosmic extension that receives the body of the whole cosmos could never move, and as regards to its parts because the extension that is incorporeal and empty by its own definition cannot be in motion.

I consider [P4] to be one of the most essential parts of Philoponus’ theory of extension. Aristotle, and later his commentators, already expressed a worry about the existence of a diastēma that exists over and above the bodies that come to be in it. Aristotle argues that such a substantialist view will conclude that the extension should be somewhere in the universe, which is absurd. Philoponus proposes a kind of extension that escapes the danger of such consequences and thus differs from 193 See

in Phys., 567.29-569.17 and especially lines 568.14-569.7.

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the atomist theory Aristotle had in mind. Philoponus’ answer is that, despite the fact that the absolute extension as such, i.e., deprived of bodies, is not experienced by human beings through their senses, it exists by itself exactly like the matter that can never be deprived of forms. Accordingly, this extension never in any way is or can be empty of all body, though it is void, empty by its own definition. It seems legitimate then to ask how this extension differs from bodily extension. Philoponus establishes a particular concept of an absolute topos. Place, i.e., void, is essentially different from the bodies that come to be in it and empty, but it does not exist in nature as an intra-cosmic extension without body, like the kind of void the atomists accept and Aristotle discusses in Physics IV.6-9, namely the separate void that is the place in which atoms and bodies are and move. The concept of a void always filled with bodies has been introduced, as Simplicius testifies, by many Platonists and Strato of Lampsacus (Simpl., in Phys., 618.20-25): [S1] οἱ δὲ ἰσόμετρον αὐτὸ τῷ κοσμικῷ σώματι ποιοῦσι, καὶ διὰ τοῦτο τῇ μὲν ἑαυτοῦ φύσει κενὸν εἶναι λέγουσι, πεπληρῶσθαι δὲ αὐτὸ σωμάτων ἀεί, καὶ μόνῃ γε τῇ ἐπινοίᾳ θεωρεῖσθαι ὡς καθ’ αὑτὸ ὑφεστώς, οἷοί τινες οἱ πολλοὶ τῶν Πλατωνικῶν

φιλοσόφων γεγόνασι· καὶ Στράτωνα δὲ οἶμαι τὸν Λαμψακηνὸν ταύτης γενέσθαι τῆς δόξης.



But others make it (e.g., place) equal in extent to the cosmic body and say that for that reason it is empty in its own nature, but is always filled with bodies and is only notionally seen as existing itself. Many of the Platonic philosophers were of this persuasion, and I think that Strato of Lampsacus held this view. (trans. Urmson 1992: 43)

It is uncertain who are the many Platonists—elsewhere they are characterised by Simplicius as renowned (kleinoi)—and whether truly Strato was supporting this view, since there is no further textual evidence to support it.194 Leaving aside the problem of Simplicius’ vague reference to Platonists, text [S1] gives evidence that the thesis of an extension of place equal to the cosmic body which is void in its own right but always filled with bodies was established before Philoponus. We cannot state whether Philoponus relies on that view or arrives at it by himself (which is less probable), but we should note that he plausibly can be listed among those who admit that place is the void always filled with bodies. We should also note that Philoponus is our only source for a complete and systematically presented version of that view in antiquity. The extension of place, for Philoponus, does not figure out among physical bodies or atoms but is always filled with the cosmic body (the total of physical bodies). To illustrate this determination of absolute place in text [P4] 194 Simplicius attributes this view to Strato of Lampsacus also in the passage in Phys., 601.22-24. About Strato’s view see Furley 1985: 594-597. The only reference that may shed some light on the theory of place supported by these Platonists is a passage in Syrianus (in Metaph., 84.31-85.15).

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he uses the example of matter, which is different from the forms, but nevertheless cannot exist without form. Matter exists and we conceive of its existence, though we do not have direct experience of it. In the same way the extension of place exists as such, though we always experience it filled with bodies. The example of matter seems to be Philoponus’ preferred way of describing his determination of place, for he almost always uses it whenever he attempts to explain his conception of place in both digressions of the commentary.195 The source of the analogy seems to be his interpretation of Aristotle’s opinion on why some people might think of place as analogous to matter (Phys., 209b6-17). In the first lecture on Physics IV.2 (in Phys., 515.14-24), Philoponus explains the analogy of matter in the same terms he will later use in the digressions. He explains that prime matter never remains without the different forms it receives, but prime matter is still an extension undetermined in its own definition, as Plato defines it in the Timaeus. Just as indefinite matter is different from magnitudes but always receives them, place too is different from the bodies that always come to be in it.196 An understanding of place in its own right emerges from the fact that the extension cannot act in any way upon the bodies and vice versa, for this kind of extension is immaterial and impassive (ἀπαθές). We should consider this as an ontological difference from bodies. Place ontologically—i.e., essentially—differs from bodies, for place can be considered per se in the special, absolute sense of emptiness described above but also because it is immaterial and thus impassive. The physical space of bodies is not identical to the physical bodies filling it. Bodies are the corporeal extensions that come to be in the physical extension of place and take positions within it. In this way Philoponus establishes the self-subsistent extension which is always filled with the body of the universe, as he points out in [P4]. At this point I shall add that text [P4] gives rise to some further reflections. For example, given that place as measure is equal to what is measured, namely a body, does place have a shape? And, further, does the extension change shape or extend infinitely beyond the cosmos? The theory of place proposed by Philoponus holds that the specific extension in a sense has an equal shape and equal dimensions to that of the specific body occupying it. The claim that place is measure (τὸ μέτρον) suggests that place and 195

See Philoponus, in Phys., 569.10-11; 574.28-575.2; 579.3-6; 694.19-23. A parallel argument, taken from Plato, appears in Alcinous’ Didaskalikos (§ 8.163.3-6) where we read, ‘It is likewise proper to all-receptive matter, if it is to receive the forms thoroughly, not to have subsistent in itself any of their nature, but to be without quality or form in order to be the receptacle of the forms.’ Trans. by Dillon 1993: 15-16. Alcinous here underlines the difference that matter needs to have from the forms for, otherwise, matter cannot be capable of receiving the forms. In addition, Giacomo Zabarella uses a similar analogy, which, as he says, derives from Plotinus: ‘si materiam mente contemplemur abiunctam a formis, nil aliud concipere possumus nisi corpus quoddam vastum, et indistinctum, et molem quandam vacuam, ut dicebat Plotinus.’ De rebus naturalibus libri XXX, col. 217. I copy Zabarella’s text from Grant 1978: 554-555, n. 15. 196

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body have at least one common characteristic. More precisely, their similarity in this respect is based on their capacity to have a quantity attributed to them—i.e., on their three-dimensionality. Philoponus’ theory leaves open the ground to attribute to the extension of place a shape: the shape of the body that fills it. As a result, it may also be argued that the three-dimensionality of the filled place is measurable too, since it has even a temporary or ostensible shape. But then, to come to the other question set out above, is it the case that the cosmic extension (τὸ κοσμικὸν διάστημα) receiving the body of the universe changes shape or that it grows or diminishes following the generation and corruption of the physical bodies or that it is infinitely extended outside the universe? Philoponus considers, according to text [P4], the cosmic extension to be immobile and extended as much as the whole universe. The several generations and corruptions of natural bodies within the universe seem to be entirely unproblematic. The generation and corruption or the growth and diminution of bodies do not affect place, for place is not attached to bodies. Each time a body is generated (or is corrupted, or grows, or diminishes) the remaining bodies in the universe rearrange their positions within the extension. Obviously, we should take into account that all natural bodies simultaneously undergo generation, corruption, growth and diminution, so there is no danger that, at some point, there will not be space equal to body’s dimensions to fill. An attempt to grasp Philoponus’ concept of ‘place totally deprived of body’ is necessarily linked to corporeality. It is true that Philoponus thinks of the three-dimensionality of place as it relates to a specific body. Philoponus invites his reader to think of the body of the whole cosmos and think of its place as having this particular quantity of three-dimensionality (and maybe a particular shape). This abstract and undetermined three-dimensional extension is conceivable per se only conceptually as a phyical extension that exists. What is observable in the sensible world is just the bodies which fill the extension of place. The tree in front of me fills an extension equal to its three dimensions; if we abstract the tree from the field, then we can think of the empty three-dimensional space remaining—that is to say empty place in its own right even if the tree is no longer there. Of course, in actuality these three dimensions are no longer the specific place (or three dimensions) of that tree, since air, for example, now fills the extension. Nonetheless, we can think of the specific extension occupied by that tree: a bodiless place, simply dimensions empty of bodies.197 What we would not be able to perceive is the place of nothing; we can only think of a place having such-and-such three dimensions as a conceptual operation. In text [P4] Philoponus claims that there is no extra-cosmic extension. The extension of place is not infinite but finite, equal to the corporeal extension of the universe. This presupposes the cosmological view of a finite cosmos that is compatible with both Platonic and Aristotelian philosophy. Since the sensible cosmos 197

Philoponus says: διαστάσεις μόναι κεναί σώματος, in Phys., 567.32.

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is limited, its physical extension of place cannot extend outside it. To the assumption of some philosophers who thought that if the empty extension exists then it must be infinite, Philoponus returns at another point in the digression on place.198 He represents their argument as an objection to his own extension theory in the following manner: if the extension is three-dimensional, then that extension must have a surface; furthermore, if the extension has no surface, and it extends up to the furthest surface of the heavens, then it might be possible that the extension can keep extending outside the universe ad infinitum. The reference is unclear, but the target may well be the Stoics, who considered the extra-cosmic void to be infinite since there is nothing further limiting it. For this claim I especially rely on the term ‘κεχύσθαι’ used by Philoponus (in Phys., 582.25) that plausibly is a direct reference to the Stoics, since the terms ‘χύσις’ and ‘ἀνάχυσις’ in relation to the void describe the extension of the void outside the cosmos.199 As Algra points out, the extra-cosmic void, according to some Stoics, surrounds the cosmos and it is ‘a necessary condition for the expansion of the cosmos at a conflagration.’200 Philoponus’ reply draws on the impossibility of an infinite extension, in the sense that there cannot in actuality be any extension not filled with body; therefore, the extension has to extend as far as the universe extends. Philoponus compares the cosmic extension to an empty jar (amphora).201 When different bodies that are in contact with each other take place in the jar, each part of the void they occupy must be coterminous (συμπερατοῦται) with the body received by it. Just as the hollow surface of the jar is limited, the whole void in the jar is limited too and, in the same way, all the bodies inside it are limited. The cosmic extension is coterminous with the whole universe, since all the spheres of the universe are coterminous with the void they fill. The surface of the outermost body is coterminous with the whole cosmic extension. To return to the discussion about place as measure, I argue that it is in this sense too that the subsisting cosmic place is the measure of the whole cosmos: the extension of place is coterminous with the cosmos. Given that the cosmic body is in place, then the measure—i.e., the place—must be equal to what is measured—i.e., the cosmic body. The universe occupies a limited extension (limited in accordance with its own three-dimensionality), and there is nothing to prevent us from thinking of the extension as having an equal surface to the surface of the universe, Philoponus 198

Ibid., 582.19-583.12. See, for instance, Stobaeus, Eclogae, I.161.8 (=SVF, II.503): τὸ μὲν οὖν κενὸν ἄπειρον εἶναι λέγεσθαι· τὸ γὰρ ἐκτός κόσμου τοιοῦτ ’ εἶναι, τὸν δὲ τόπον πεπερασμένον διὰ τὸ μηδὲν σῶμα ἄπειρον εἶναι. Other fragments implying the infinity of the void according to the Stoics are the following: Arius Didymus, fr. 25 (Diels, 1879); Simplicius, in De caelo, 284.28. See also Algra’s paper (1993) on the concept of extra-cosmic void in Posidonius. On the terms ‘χύσις’, ‘ἀνάχυσις’ see SVF, II.619. A reference to the atomists is also reasonable: see Epicurus, Epist. Herod. 41-42 and Simplicius in De caelo, 594.33-595.3. 200 Algra 1995: 318-320. 201 Philoponus, in Phys., 582.29-583.12. 199

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argues. The ontology of place, according to Philoponus, proposes a physical extension of place that can be thought of as an absolute space, essentially different from the physical bodies, though it can never be deprived of bodies. Philoponus establishes an extension theory according to which bodies necessarily are somewhere. Therefore, what they fill must be ontologically different from them; otherwise two or more bodies would fill the same place, which is absurd. This kind of extension is bodiless and equal to what comes to be in it; it is also immobile. Philoponus’ cosmology implies a subsisting extension of place filled with the cosmos. Bodies come to fill the cosmic place (the extension filled with the whole universe, in which natural bodies exists). In order to conceive their equality, Philoponus states that the place can be seen as a measure equal to what is measured (contained body).202 As we shall see next, Philoponus employs more examples taken from common observations that show the ontological difference between bodily extension and the extension of place.

3.3 Place and the ‘violation’ of nature We have said that Philoponus aims to illuminate, by a series of arguments, the sense in which place can be thought of as something different (ἕτερόν τι) from the bodies that come to be in it. The so-called ‘ἡ τοῦ κενοῦ βία’ (in Phys., 569.18-573.21), translated into English as ‘the force of the void’, is a cardinal argument brought by Philoponus to describe the ontological difference between place and body. The ‘force’ of void, according to Philoponus, convincingly illustrates two rather significant claims concerning the extension of place. First, that the extension of place essentially differs from the bodies and, second, that this extension never occurs without body.203 The Greek expression ‘ἡ τοῦ κενοῦ βία’ is known from medieval times onwards as ‘horror vacui’ (or fuga vacui). However, the ancient and the medieval concepts do not seem to convey absolutely the same idea. Horror vacui conveys the idea that nature fears the presence of the void; in order to avoid empty space in nature, bodies move even against their natural motion in order to fill a possible gap. Nature abhors the void, that is thought to have a magical connotation in medieval times.204 The ‘force’ of void in antiquity seems to relate with the peculiar case that bodies are forced to stay still, though they should naturally move towards a direction; in this sense it is the mysterious nature of the void (which should not appear as separate 202 There is a certain similarity between the ‘place-body’ and ‘time-motion’ schemes in Philoponus’ conception of the relationship between time and motion later in the commentary: time appears to be the measure of motion (in Phys., 741.21-742.28). 203 Philoponus, in Phys., 569.17-20: ‘Furthermore, to one who looks to the truth, the force of void will clearly bring forward both points, I mean, both that the extension is something different from the bodies that come to be in it and that it is never beyond body.’ 204 For the medieval adaptation of the ‘force’ of void read Duhem (1914), who also discusses the horror vacui in Arab and early medieval authors, and Grant 1981.

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from bodies) that forces the bodies to stay still. The origins of the term in antiquity are quite obscure, though Philoponus describes it as notorious,205 and it was used both by the holders of the view that void exists and those who deny its existence. In fact, arguably the few sources deriving from antiquity show that the ‘force’ of void was a concept with which physicists, doctors and engineers were so familiar that they had no reason to specify its origins. The concept of the ‘force’ of void in antiquity and the variety of texts in which it was used seem to have common ground in the existence of the void and the possibility (or impossibility) of bodies’ motion through it. Let us name a few examples of how ancient writers approach this concept. Aristotle’s long discussion of the void in the Physics criticises the atomists, but without making a straightforward reference to the ‘force’ of void. Aristotle’s attack relates to the atomist arguments of an existent and separate void necessary for the motion of bodies. Berryman suggests that Aristotle perhaps attributes the force of the void to the atomists in Physics, 215a22-24.206 There Aristotle seems to imply that some people believe that the bodies move into the void because it yields, thus implying the force of void. Yet, Aristotle himself makes no use of the ‘force’ of void as a cause for the fact that some bodies rest in certain cases, for bodies are continuous and no empty spaces occur while they move or rest.207 Strato of Lampsacus, the head of Aristotle’s school in Athens after Theophrastus, could be one of the ancient philosophers to involve the ‘force’ of void in their theories on the void, but there is no clear evidence of this.208 More likely, his theory of interspersed void in bodies could have included the discussion of the ‘force’ of void as well. In the work of writers such as Erasistratus, Hero of Alexandria and Galen we find descriptions of what they often call ‘the following into what is emptied’ (ἡ πρὸς τὸ κενούμενον ἀκολουθία), a procedure relevant to the motion of bodily fluids and air’s motion during respiration.209 The ‘following into what is emptied’ is not He calls it ‘πολυθρύλητος’ (in Phys., 570.17). Berryman 1997: 155. 207 See Aristotle’s Problemata, 16.8-9. The idea of an inward pressure on the world that prevents void within the cosmos also appears in Plato: σφίγγει πάντα καὶ κενὴν χώραν οὐδεμίαν ἐᾷ λείπεσθαι, Timaeus, 58A7. 208 See Hero of Alexandria, Pneumatics, I.16,20. The passage does not name Strato, but scholars tend to attribute the theory described there to him; these include Wehrli (1950: 21-22, fr. 64) in his collection of testimonia about Strato’s life and work. I will not go into the details of the question whether Strato really is behind the passage of Hero’s Pneumatics, but I only wish to stress that the ‘force’ of void could reasonably be a concept with which Strato dealt in his theory of void. One can read about the whole discussion on Strato’s theory of void and the origins of the concept in antiquity in the articles by Lehoux 1999, Furley 1985 and Algra 1995: 58-69. 209 Galen reports that Erasistratus refers to the ‘following into what is emptied’ in order to describe nature’s avoidance of the void: γίνεσθαι δέ φησιν ὁ Πλάτων τὴν περίωσιν ταύτην διὰ τοῦ κενοῦ, τουτέστι τοῦ μηδεμίαν χώραν γενέσθαι κενήν· καὶ διὰ τοῦτο κενουμένου τὸ συνεχὲς ἕπεται τὴν χώραν αὐτοῦ πληροῦν, ὅπερ Ἐρασίστρατος ὀνομάζειν εἴωθε τὴν πρὸς τὸ κενούμενον ἀκολουθίαν, in Platonis Timaeum commentarii fragmenta (cod. Paris. gr. 2838), fr. 17.35-39. From this 205

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identical with the concept of the ‘force’ of void but seems to be relevant to a process of filling empty space, as certain passages of Hero of Alexandria, Oribasius and Galen show.210 The question is: how does the ‘force’ of void appear in nature? What is it that indicates that nature is in a sense forced by the void? One of the standard practical experiments demonstrating the ‘force’ of void is the clepsydra (ἡ κλεψύδρα), which literally means the ‘water thief’.211 Clepsydras are narrow-mouthed vessels, which have a wide base with many small holes in it. The clepsydra was known to Aristotle and his predecessors.212 A detailed description of it is given by Simplicius in his commentary on the De caelo, and a simpler one by Philoponus in his commentary on the Physics.213 The experiment of the clepsydra, according to Philoponus, works in the following way. Assume that there is a vessel (clepsydra) which has a mouth at the top and many small holes in the bottom, and that it is filled with water. When we lift the vessel and at the same time cover the hole at the vessel’s mouth with our finger, we observe that the water does not go out through the small holes at the bottom of the vessel, despite its being heavy and having so many exits. The water rests, which is, in a sense, contrary to nature. When we unblock the hole at the vessel’s mouth we observe that the water is forced out through the holes in the base.214 This phenomenon, Philoponus claims, is caused by the ‘force’ of void. When the vessel’s mouth is covered by a finger the water does not go out through the small holes because the air cannot take the place of the water. The mutual replacement of bodies (here between water and air) is impossible: the air can neither fill the vessel from the upper mouth, because it is covered, nor come in through the thin, small text we also infer that Plato, according to Galen, recognises the concept of the ‘force’ of void in the Timaeus. 210 See Hero of Alexandria, Pneumatics, Ι.80-91; Galen, De naturalibus facultatibus, 64.4-10 and De instrumento odoratus, 5.12.1-13.1. Oribasius writes: φέρε γοῦν εἰ δυνηθείημεν αὐτῷ αἰτίαν εἰπεῖν.

διαστελλομένῳ δὴ τῷ θώρακι συγκινηθήσεται πάντως ὁ πνεύμων ὑπὸ τῆς πρὸς τὸ κενούμενον ἀκολουθίας ἑλκόμενος· ἕπεται γὰρ ἀεὶ τῷ κενουμένῳ τὸ πλησίον, ὡς ἐπὶ τῶν αὐλίσκων τῶν εἰς τὸ ὕδωρ καθιεμένων ἐστὶ δῆλον, ὧν ἐκμυζήσας τῷ στόματι τὸν ἀέρα τὸ ὕδωρ ἐπισπᾶται διὰ μακρᾶς πάνυ πολλάκις ὁδοῦ παρὰ φύσιν ἄνω φερόμενον. οὕτως ἔχει τι βίαιον ἡ πρὸς τὸ κενὸν ἀκολουθία, καὶ εἴ τί γε ἦν ἕτερον ἐπιτηδειότερον ἀναπληροῦν τὸ μεταξὺ τῶν ὀργάνων, κἂν ἀκίνητος ἔμενεν ὁ πνεύμων, ὅπερ ἐν ταῖς μεγάλαις τρώσεσι συμβαίνει, Collectiones medicae, 60.4.1-7.1. The term occurs in Ps.-Alexander’s Problemata, II.59 (Ideler,

Problem 59: 69). 211 Philoponus also reports its common name, i.e., ‘snatcher’ (τὸ ἁρπάγιον). 212 The clepsydras were already known in Empedocles’ era (fr. 100, DK), as Furley (1957: 265-274) notes. See also Aristotle, De caelo, 294b20-21. The figures in Guthrie’s translation (1960: 226-229) of the De caelo are extremely helpful in understanding the way a clepsydra works. Also see Aristotle’s Physics, 213a27; De respiratione, 473a15-b10; Problemata, 16.8 ff. 213 See Simplicius, in De caelo, 524.17-525.4; in Physics, 647.26-30. Philoponus, in Physics, 608.1-10; 612.15-19. 214 See Philoponus, in Phys., 569.20-28. In my childhood we did that with fresh eggs. I made holes in them with a needle (one in the upper part of the egg and three in the lower part). Then I covered the upper hole with my finger. The liquid part of the egg did not move downwards to its proper place, leaving the eggshell as it should, according to the law of gravity.

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holes in the bottom, because the water is there; furthermore, the air outside the vessel cannot press the water to find an entrance, nor is it possible for air to come in and for water to go out at the same time. Two more examples are given by Philoponus to demonstrate the ‘force’ of void (in Phys., 570.9-571.9). The first describes the perforated vessels containing wine: the wine flows out through the holes unhindered, for air presses the wine through the holes. The second example described is that of vessels that contain water where someone drops a pipe in them and sucks the water through the pipe out of the vessel. The water moves upwards contrary to nature. Although there would be a risk of creating a void when sucking out the air in the pipe, the ‘force’ of void moves the water in a direction contrary to nature, for the ‘force’ of void always comes to fill what is about to be emptied. All these examples, according to Philoponus, demonstrate that the ‘force’ or ‘suppression’ of the void is responsible for the phenomenon which occurs in the use of the clepsydra, perforated vessels and water pipes. To make it clearer on what it is meant to be the ‘force’ of void in this context we should say that it is a case of obscurum per obscurius: it explains (rather vaguely) why the water behaves contrary to its nature, when it does not move in its proper direction, but rather remains at rest. The ‘force’ of void is not the fact to be explained; it rather explains why nature prevents the danger of an actual void in the physical cosmos, of an extension being totally empty without being filled with body. The ‘force’ of void secures nature against empty space. We observe this behaviour in the exchange and motion of bodies. Philoponus seems to be positively in favour of the continuity of bodies within the extension—this can be seen especially in the example of the vessel with the pipes.215 The cosmos contains bodies in successive positions in the sense that there is a continuity of bodies, the one next to the other positioned in the extension of place. This kind of continuity of bodies in Philoponus’ theory comes within the scope of the concept of πλήρωσις (discussed in detail in section 4.1). Bodies fill the extension, creating a continuous universe with no gaps or empty spaces. In fact, the ‘force’ of void implies this continuity. For example, if the water could escape through the small holes when the clepsydra were lifted up and the upper mouth of the vessel covered, then what would replace the water except empty space? And what can remain in the vessel other than empty space if we suck the air from the pipe and the water does not move upwards at the same time? On the one hand, these experiments demonstrate the continuity of bodies in nature guaranteed by the ‘force’ of void, but, on the other hand, they show, according to Philoponus, that the extension of place is something different from the bodies in it.

215 κατὰ τὸ συνεχὲς γίνεται and κατὰ συνέχειαν σύνεισι , in Phys., 570.28-29; 571.8-9. The idea also occurs in Aristotle’s Categories, 5a8-14.

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Since the void must be something that nature avoids, then the void in some sense is ontologically different from the bodies. Philoponus seems to be allusively criticising the Peripatetic tradition when he asks whether the extension remaining in the clepsydra can be occupied because he excludes the case of a two-dimensional surface. If this extension is a surface, as the Aristotelian account of place suggests, then we cannot determine the quantity of the body in all of its dimensions when the body is in it (in Phys., 571.18-27).216 A critique that Philoponus turns against the Aristotelian definition of place elsewhere, as we shall see in Chapter 5. The point here is that the Aristotelian concept of place as limit fails to explain the remaining space in the clepsydra in case the water moves to its proper place rather than remaining still. For the problem here is again related to the three-dimensionality of place which Aristotle explicitly denies. As Philoponus puts it, to hold the view that the limit of the surrounding body can be either filled or emptied is absurd. And if some Aristotelian philo­ sophers insist that there is no need to explain what the remaining space would be, since after all we only observe the water in the vessel without caring about a hypothetical result, another complication occurs: the Aristotelian definition also fails to explain why the water behaves as it does. Aristotle’s theory of the motion of the four elements would force him to admit that this case is contrary to water’s nature. But he would need an explanation for the phenomenon of the non-replacement of bodies in this case; he would need to explain why the water remains still. However, we can only speculate about Aristotle’s position on the phenomenon of the ‘force’ of void.217 We can simply assume that the ‘force’ of void would be an awkward subject for him to deal with, as he states that void does not exist; there is no reason to assume that natural motion is forced by something that does not exist.218 There is, however, a serious difficulty with Philoponus’ argument. What if the fact that nature does not allow void does not imply that void exists, as Philoponus 216 It may be true that Philoponus is not able to do that, but that is only because he does not have the required mathematical knowledge. If you know the shape and size of the surfaces and their solid angles, there is no problem calculating the volume. 217 It is worth pointing out that Aristotle, at least in the Physics (213a24-27) and in the De caelo (294b20-21), is not using the clepsydra example in order to explain the ‘force’ of void. In the Physics, the clepsydra example appears where Aristotle describes in what ways Anaxagoras and others tried to show that air exists. Philoponus’ exegesis in the running commentary points out that, when Anaxagoras and others were using the clepsydra, they were doing so in order to show that air is something; they were not trying to refute the void’s existence (in Phys., 607.12-608.10; 612.15-613.6). 218 Themistius claims that those who use the clepsydra try to show that there is an empty extension in which bodies are coming to be. He accepts, with regard to the replacement of bodies, that when we put a stone into water the stone occupies a bulk equal to the bulk of the displaced water (in Phys. paraphr., 133.22-134.2). But what if we put a body in the void? Will it occupy a bulk of the void equal to itself? Philoponus does not take any position on that question. But, needless to say, Themistius’ objection does not threaten Philoponus’ position: void is bodiless—i.e., it cannot have any bulk itself—so bodies fill just as much empty extension as their three dimensions need.

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wishes to show, but rather signifies its non-existence? For exactly the same experiment, namely the clepsydra, could be used to show that void does not exist. Philoponus’ argument could be criticised as circular: it seems as if the ‘force’ of void consequently proves the existence of the void, but its existence is already presupposed in the definition of the ‘force’ of void phenomenon. We would expect that the ‘force’ of void results from void’s existence. But what is Philoponus attempting to prove with this argument? Philoponus’ manoeuvre does not aim to prove the existence of the void, but rather that there is an extension which ontologically differs from the bodies. The ‘force’ of void should not be considered as a term of the void’s definition. In fact, the definition of place is presupposed, but does not derive, from the definition of the ‘force’ of void. Still, that the void violates, puzzles us. Philoponus also describes the phenomenon as a power in nature that often constrains bodies to move contrary to nature and forces nature to behave differently from in its regular state (like a body being still, though we would expect that it needs to move).219 The term ‘power’ would be perfectly comprehensible if Philoponus did not elsewhere claim that place does not have any power at all. To begin with, Philoponus’ discussion on the power of place in the digression on place does not originally relate to the topic of place’s essential difference (ἑτερότης). However, it is tempting to discuss two passages from Philoponus’ commentary on the Physics in which he takes a clear position on the void and the attribution to it of power. So, in order to understand in what sense the void is a power which violates nature, I shall refer first to the fourth part of the digression on place and to the critical observation (epistasis) rejecting the suggestion that the place of bodies has any power or quality.220 Aristotle believes that place exists and ascribes to it a kind of power because the four elements move in their proper directions—i.e., light bodies naturally move upwards, and heavy bodies naturally move downwards (Phys. 208b8-11). Themistius, Philoponus’ constant interlocutor, does not take any clear position on the subject; when he paraphrases Aristotle’s relevant passage he emphasises that place has some differentiations which are, so to speak, powers.221 I cannot find a passage in which Themistius goes so far as to say that place has a power. Nevertheless, Philoponus, in his running commentary on the Physics IV.1, holds that Aristotle considers place as an object of striving (τὸ ὀρεκτὸν) and explains Aristotle’s thoughts on the idea that place has natural powers and differentiations (διαφοραὶ).222 Of course, we should 219 τίς ἐστιν ἡ ἐν τῇ φύσει δύναμις ἐπὶ τὸ παρὰ φύσιν κινοῦσα τὰ σώματα […]; in Phys., 572.3-4; and τί οὖν βιάζεται ἡ φύσις παρὰ φύσιν ἤ μένειν ἤ κινεῖσθαι τὸ ὕδωρ; δῆλον ὅτι ἵνα μὴ τὸ ἐντὸς κενὸν μείνῃ […],

in Phys., 573.17-19. 220 See in Phys., 581.18-31 and in Phys., 632.4-634.2 respectively. 221 Themistius says: οἷον δυνάμεις, in Phys. paraphr., 103.6-8. 222 See in Phys., 498.30-499.30. As evidence of this, note the difficulty raised after the argument on why place is not the efficient cause (τὸ τελικόν αἴτιον) in the passage in Phys., 509.15-510.2. Philoponus

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be careful in ascribing to Aristotle an argument that place has natural powers. Aristotle’s theory does not attest to an argument as such. It seems that he does think of the four elements as being in their proper natural places under specific circumstances, namely that heavy bodies move downwards and light bodies move upwards. We do not possess evidence of the sources for Philoponus’ exegesis. But his exegesis deals with the problem as if it were an Aristotelian one or as if it derived from the tradition of the Peripatetics.223 Philoponus says in the digression on place that some people ridiculously hold the view that because bodies desire place—namely the limit of the surrounding body—each moves to its proper place. He argues instead that bodies desire the arrangement that they have been given by the demiurge.224 [P5] τὸ δὲ λέγειν δύναμίν τινα ἔχειν αὐτὸν καθ’ αὑτὸν τὸν τόπον γελοῖον πάνυ· οὐ γὰρ ἐπιφανείας ἐφιέμενα φέρεται ἐπὶ τοὺς οἰκείους τόπους ἕκαστα, ἀλλὰ τῆς τάξεως ἐφιέμενα, ἧς παρὰ τοῦ δημιουργοῦ τετυχήκασιν. (in Phys., 581.18-21)

It is quite ridiculous to say that place has any power in its own right; it is not by desire for a surface that things move each to their proper place, but by desire for the order which they have been given by the demiurge.

As we have seen, Philoponus asserts that the extension cannot act upon bodies and vice versa (in Phys., 559.14-18). So, he cannot accept that place is the object of desire. Moreover, he states that the proper place of each body is only an instance of the universal order. The object of striving cannot be the extension, but rather the arrangement (τάξις) given by the demiurge. The order of the bodies in the universe means that each body fills its proper place.225 We need to understand the case of bodies that are forced (or suppressed) unnaturally to fill place within this framework. When the arrangement is disturbed, bodies try to move just as much as needed in order to achieve the arrangement they received from the demiurge; in other words, bodies try to reach the closest possible position with respect to this arrangement (in Phys., 581.23-26). But there is something more than this: the bodies moving to their proper place desire the order established by the demiurge, and ‘this wonders how it is possible to maintain, on the one hand, that place is not the efficient cause and, on the other hand, that place has a power which forces bodies to move towards their proper place. 223 Algra—Ophuijsen (2012: 9) point out that: ‘there is no suggestion that he [Philoponus] is straightforwardly attacking Aristotle himself here. … He does indeed repudiate such an ascription of power to places, but he does not repudiate it as a position that was in fact endorsed by Aristotle.’ 224 Scholars tend to interpret this passage as evidence of Philoponus’ Christian beliefs; see Verrycken 1990: 236-237, 264-274; Furley 1991: 44. But I would like to note that it is very difficult to decide with certainty whether Philoponus’ text refers to the Creator of Christianity or to Plato’s demiurge. 225 The idea of the arrangement and order of the beings given by the demiurge is strikingly paralleled in Plutarch’s De facie (927B-C): τῷ θεῷ δ’ ἡ τάξις τῶν ὄντων προσήκει καὶ διαιρεῖν, τί θαυμαστὸν οὕτως τετάχθαι καὶ διηρμόσθαι τὴν φύσιν, ὡς ἐνταῦθα μὲν πῦρ ἐκεῖ δ’ ἄστρα, καὶ πάλιν ἐνταῦθα μὲν γῆν ἄνω δὲ σελήνην ἱδρῦσθαι […]. See Opsomer 2017: 87-88.

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is when they have their being most fully and achieve their perfection.’226 To occupy your proper place means to achieve your perfection. To achieve your perfection is to be ordered according to the demiurge. Thus your perfection mirrors the perfection of the universe. Philoponus displaces the power from place to the demiurge or, to be more precise, to the order that the demiurge determined. It is not the case that place itself has the natural power to move the bodies to their proper position, but rather that bodies desire to preserve their own arrangement in the universe. Place, being totally impassive, cannot possess any power. The short excursus in which Philoponus deals with the issue of the power or quality of place closes his first lecture on Physics IV.8 (in Phys., 632.4-634.2). He begins with an objection addressed to the proponents of the void theory, who cannot explain why bodies move in this or that direction and are unable to determine when a body is up or down within the extension.227 He considers that this attack on the void theory actually maintains that place, as the limit of the containing body, can cause the motion of simple bodies; hence, place (which is not the undifferentiated void) has power because we can determine when a body is up or down. The argument is slightly different from that in the digression on place. For instance, the word ‘demiurge’ is absent. However, the short epistasis helps to clear up what Philoponus means by the term ‘τάξις’ in the digression on place. The order or the arrangement of bodies in the universe derives from the such-and-such relation of bodies. The proper relation bodies have to one another constitutes a continuous universe. Bodies, which complete the universe and have some natural impulse, desire this relation to other bodies; in other words, they desire to be in a position within the extension of place because they desire that relation to other bodies. That the demiurge is not mentioned as having established this order does not prevent us from assuming that the demiurge stands behind this arrangement of the universe. Nature contains bodies which are (naturally) capable of having such-and-such a relation to one another:228 226

227

τότε γὰρ μάλιστα τὸ εἶναι ἔχουσι, καὶ τὴν ἑαυτῶν τότε ἔχουσι τελειότητα, in Phys., 581.28-29.

At first glance, the short excursus appears as Philoponus’ response to Themistius because Philoponus copies right before the excursus (in Phys., 631.21-632.3) Themistius’ text almost word for word (in Phys. paraphr., 128.9-17). But Themistius states that the extension cannot be the cause of the natural motion of bodies because the void is undifferentiated (ἀδιάφορον) in every sense (in Phys. paraphr., 127.28-128.8), following Aristotle (Phys., 214b13-23). The primary source for both Themistius and Philoponus is Alexander of Aphrodisias: ‘Pour Aristote, qui dit que le lieu est la limite du corps englobant, il suit fort raisonnablement que chacun des corps est transporté vers son lieu propre. Car il est fondé en raison qu’ils soient transportés vers le corps de même genre, dont la limite constitue pour eux un lieu selon la nature et propre. En revanche, pour ceux selon qui le lieu est un intervalle, d’après quel principe diront-ils encore que se produit le mouvement naturel des corps vers leur lieu propre? L’intervalle est en effet indifférent, tel intervalle n’étant pas davantage propre à l’un des corps que tel autre.’ Rashed 2011: 224, fr. 81. 228 It is important to note that Philoponus believes that bodies are generated by nature to occupy this or that place which happens to be the proper place of each body (in Phys., 632.13-633.5).

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[P6] τοῦτο καὶ ἐπὶ τοῦ παντός φημι (καὶ γὰρ μέγα τι ζῷόν ἐστιν ὁ κόσμος), ἐπειδὴ

ἀγαθὸν ἦν πρὸς τὴν τοῦ ὅλου κόσμου σύστασιν τοιάνδε σχέσιν ἔχειν πρὸς ἄλληλα τὰ τὸν κόσμον συμπληροῦντα σώματα, εἰκότως ἕκαστον τῶν σωμάτων ὁρμήν τινα φυσικὴν ἔχον τὸ ἐφίεσθαι τῆς τοιᾶσδε πρὸς τὰ λοιπὰ σχέσεως, ἐπειδὴ τοῦτο συμβαίνει αὐτῷ τόδε τὸ μόριον τοῦ διαστήματος καταλαβόντι, εἰκότως ἐφίεται τούτου, οὐ διὰ τὸ ἐκεῖνο ἔχειν τινὰ δύναμιν, ἀλλ’ ὅτι καὶ τῷ παντὶ ἀγαθὸν καὶ ἑκάστῳ τό τε εἶναι καὶ τὸ εὖ περίεστιν, ὅταν ὑπείκῃ μὲν τῷδε, ὑπερανέχῃ δὲ τοῦδε. ἐφίεται οὖν τοῦ τοπικοῦ διαστήματος οὐ δι’ αὐτό, ἀλλὰ διὰ τὴν πρὸς τὰ λοιπὰ σχέσιν. (in Phys., 633.5-14)



And I say the same for the universe (for the cosmos is a kind of great living being); because it is good for the formation of the cosmos that the bodies completing the cosmos have such-and-such relation towards one another, it is reasonable that each of the bodies possesses some natural impulse, desiring to have such-and-such relation to the rest (of the bodies); it is because it [the body] happens to occupy this part of the extension, that [the body] reasonably desires the extension, not because it [the extension] has some power, but because it is good for the whole and for each of the bodies existing and being well ordered, when it [the body] is under this [body] and above the other [body]. It is not the case that it [the body] desires the extension of place for its own sake, but for the relation to the other bodies.

Bodies fill place and are in relation to other bodies, as stated in text [P6]. The network of bodies, namely their such-and-such relation to one another, constitutes the whole universe. Philoponus, however, excludes the possibility that place can be the object of bodies’ striving. The extension of place, seen as the cosmic, universal extension, has no differentiation in its own right—that is to say, we cannot attribute to it any differentia, as for instance up and down (in Phys., 633.22-28). From this perspective, place is different (ἕτερος) from bodies because the pure three-dimensional extensionality cannot be characterised by up and down. Differentia of place occur when place is seen as the positions of bodies: it is when the cosmic bodies take up their relations to one another that the differentiation of up and down emerges. Place in its own right, that is the void, has neither any power nor quality. And the motion of bodies towards their proper places is explained by Philoponus as the desire for the order of the cosmos, or, in other terms, for the specific relation (position) of the bodies. It would be reasonable to ask how it is possible for Philoponus, on the one hand, to accept that the void is a kind of violating condition for nature and, on the other hand, to deny that the void has a power of a particular sort. The inconsistency is only seeming because the so-called ‘force’ of void is an explanatory device for the forced position of bodies within the extension of place. Philoponus detects no inconsistency between the two propositions. Place has no power because bodies act in such a way as to avoid the existence of empty space. So, I take it that, for Philoponus, the

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‘force’ of void comes as a further explanation of a specific case of motion within the extension. The ‘force’ of void describes a rest (or a motion) contrary to nature and, as we have seen, the desire of bodies to move towards their proper place is nothing more than the actualisation of nature: bodies possess such-and-such relation to other bodies, filling such-and-such position within the extension of place. Returning to the question of how to explain the unnatural motion or the rest of bodies because of the ‘force’ of void, I would like to add a few remarks. Forced motion in the Aristotelian universe is, of course, acceptable, but only if a body is the cause of the forced motion of another body—the void cannot in any way be the cause of any motion. Aristotle explicitly rejects motion through the void.229 With regard to the experiment of the clepsydra, Aristotle would answer that the water remains at rest because it has nowhere else to go, that is to say he considers it as a case where we do not have mutual replacement of bodies—though, obviously, bodies should exchange place(s). Philoponus interprets the water being at rest as an action contra naturam. It is not enough to say that the water cannot move any­ where, as an Aristotelian would say; we should take a further step and ask what the cause of such action is. The ‘force’ of void, for Philoponus, explains the water’s rest contrary to nature. This power, so to speak, is not a natural one—i.e., it is not the same power that my hand transmits to the stone when I throw it. For example, a law prevents us from doing specific things that would violate the regular state of society. Laws in one sense stop us either from doing or from omitting certain actions. In that sense, sometimes a law can prevent someone from acting in a specific manner. This is how I think the term ‘βία’ should be understood. The void seems to prevent nature in the same way: it forces and presses physical bodies to fill places other than those in which they properly belong. But what is it that the actual presence of the void in nature violates? The universal order: if the void existed, it would violate nature’s order in the sense that there would be something empty among bodies. Sedley’s suggested interpretation of how we should comprehend the conception of ‘force’ in Philoponus’ philosophical context intends ‘… to take the force (bia) in question to be of only a very attenuated kind. This will be rather easier if we take it to be the purely notional force of a non-existent vacuum.’230 An existent void, in a strong sense like the atomist’s void, would be a serious transgression of nature. To avoid this violation bodies rest contrary to their natural motion in their proper direction so that the order does not collapse.231 Philoponus builds his account on a different sense of how the void exists, that is a void always filled with bodies, an extension

229

Physics, 214a26-32; 214b28-215a6. Sedley 1987: 145. 231 This definitely is a disturbance of the arrangement given by the demiurge, but it is a legitimate disturbance, necessary for maintaining the continuity of the cosmos. 230

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that exists because it is the place of bodies, though we can think of the absolute space as an existing, empty space. Philoponus’ argument regarding the ‘force’ of void saves the phenomena, for it explains the results observed in experiments such as the clepsydra and vessels with pipes. In addition, his belief that place has no power is an argument in favour of the preservation of the order of the whole universe. In all cases bodies tend to preserve their own arrangement in a particular state so that they are closer to the good they desire. It is in the nature of the universe to be well-ordered (εὖ περίεστιν) in accordance with the demiurge’s arrangement. Bodies, according to Philoponus, have their being fully and achieve their perfection when they are placed in the right order within the extension. The ‘force’ of void indicates the continuity of bodies in nature and the ontological difference of the extension of place from bodily extension. The ‘force’ of void turns out to be as important as the mutual replacement of bodies is in Philoponus’ theory. Philoponus holds that the mutual replacement of bodies and the ‘force’ of void are the most significant procedures in nature for preventing the actual presence of the empty extension, i.e., void in the strong sense.232 Hitherto, we have examined Philoponus’ employment of experiments and arguments rooted in common experience. The aim, to refresh our memory, is to establish the subsistence of the physical, bodiless, three-dimensional extension of place, which is void in its own right, as an ontologically different extension from corporeal extensions. In the cases we examined, namely the place as measure and the ‘force’ of void, Philoponus starts from cases that an average human being can directly experience, and then goes on to describe a whole cosmological model according to which topos plays a notable role by being the necessary entity in which physical bodies are ordered according to the demiurge. Now let us examine how Philoponus exploits the so-called ‘thought experiments’ to make clear every aspect of the ontology of place.

3.4 The empty universe Examples, demonstrations and experiments often accompany Philoponus’ arguments throughout the digressions on place and the void. Of course, physics could not be taught otherwise. A distinction can reasonably be made between experiments based on natural phenomena and the sort of experiment which scholars nowadays call ‘thought experiments’.233 Thought experiments are hard to define since they are used in different circumstances and different disciplines (for instance, philosophy, physics and mechanics) and therefore have different 232

See Philoponus, in Phys., 575.32-33; 577.7-9; 579.14-15. For a helpful survey of the history of the term (from the sixteenth to the twentieth centuries) see Roux 2011. 233

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characteristics. However, we can safely draw some conclusions from the thought experiments of antiquity. The present section discusses the role of the thought experiments which Philoponus uses throughout the digressions of the commentary to assert the ontological difference of place and show how the extension of place exists in nature. Some remarks on this subject are necessary before we enquire into the details of the argument. Philoponus does not call his examples either experiments or thought experiments. In order to introduce a thought experiment he uses the verbs νοῶ, ἐννοῶ and ἐπινοῶ, which literally mean in English ‘I think’, ‘I reflect’ and ‘I contrive’.234 The Greek verbs leave room for multiple interpretations. For example, ‘ἐννοῶ’ means to think of something or to reflect upon something, but the verb ‘ἐπινοῶ’ also describes the grasping of a hypothetical assumption—it implies mental constructions based on imagination. Products of the imagination can be plausible without always being possible. Thought experiments usually cannot be played out in reality. In general, we will not be far from the truth if we assume that we are dealing with mental examples and constructions that do not correspond to natural phenomena. Nonetheless, sometimes thought experiments may involve phenomena which occur in nature, as for instance in the second experiment discussed below (text [P8]). Furthermore, thought experiments tell a story. Often they contain a narrative or they describe something impossible.235 I mainly focus on the following two thought experiments with which Philoponus demonstrates the ontological difference (ἑτερότης) of place in the third part of the digression on place (in Phys., 567.29-579.18):236

234 Examples of the usage of these verbs taken from the digression on place are the following: in Phys., 562.17; 574.15; 575.23; 579.8; 580.24-30; 582.31; 583.1 and 583.9; κατ ’ ἐπίνοιαν, in Phys., 574.14; 575.18. A thought experiment can be introduced with the expression ‘δεδόσθω μοι τῷ λόγῳ’ or the verb ‘ὑποτίθημι’ as well (see in Phys., 574.20 ff.; 576.1; 688.24). The same terms are also sometimes used by Philoponus in the digression on the void to mark off simple hypothetical examples, which, I think, differ from thought experiments since they describe cases that may occur in reality (as in the following passages: in Phys., 681.24; 681.33; 682.17; 688.14; 688.21; 691.18). Of course, a thought experiment is introduced even without the use of the aforementioned verbs and expressions, as for instance: in Phys., 687.29 ff.; 689.26 ff.; 693.15 ff. 235 I rely greatly on the observations made by K. Ierodiakonou 2011: 47-49 and P. Lautner 2011: 52. See also Martin’s (1999: 279-287) introduction to impossible hypothesis. 236 Note that both thought experiments are also brought into the discussion by Philoponus to refute Themistius, who did not understand how it is possible to think of place as different from bodies, and against the criticism—unfair, according to Philoponus—that Themistius made of Galen. See Philoponus, in Phys., 575.27-578.4 and Themistius, in Phys. paraphr., 114.7-115.12.

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[P7] σκόπει δὲ καὶ ὧδε. εἰ μηδέν ἐστιν

ἕτερόν τι διάστημα παρὰ τὰ ἐγγινόμενα σώματα τὸ δεχόμενον αὐτά, ὑφέλωμεν κατ ’ ἐπίνοιαν τὰ μεταξὺ σώματα καὶ ἴδωμεν εἰ τῷ ὄντι οὕτως ἔχει. ἆρ’ οὖν εἰ ἐπινοήσωμεν τὰ ἐντὸς τοῦ οὐρανοῦ σώματα μὴ ὄντα, γῆν λέγω καὶ ὕδωρ καὶ ἀέρα καὶ πῦρ, τί λοιπὸν τὸ μεταξὺ κατελείπετο ἢ διάστημα κενόν; ἦν γὰρ δηλονότι εὐθείας ἀπὸ τοῦ κέντρου ἐπὶ τὴν περιφέρειαν πανταχόθεν ἐκβαλεῖν· τὸ οὖν δι’ οὗ τὰς εὐθείας ἐκβάλλομεν τί ἄλλο ἐστὶν ἢ διάστημα κενὸν τριχῇ διαστατόν; […] εἰ γὰρ μὴ ἦν τι μεταξὺ τῶν περάτων τῆς κοίλης τοῦ οὐρανοῦ ἐπιφανείας, τῶν ἐντὸς σωμάτων κατ ’ ἐπίνοιαν ἐξαιρεθέντων συνέπεσον ἂν τὰ τοῦ οὐρανοῦ πέρατα. τοῦτο δὲ ἀδύνατον· οὐ γὰρ διὰ τὰ ἐντὸς σώματα ὁ οὐρανὸς ἔχει ὡς ἔχει, ἀλλὰ κἂν μηδὲν ἦν, ὡσαύτως εἶχεν. (in Phys., 574.13-19; 575.17-20) [P8] γενέσθω γάρ μοι σφαῖρα χαλκῆ μὴ ναστή, ἀλλ’ ὑπόκενος· δῆλον δήπου ὡς τὸ ἐντὸς ἀπειλημμένον ἀὴρ ἦν. ἐὰν οὖν ἐπινοήσω τὸν ἐντὸς ἀέρα, οὐ λέγω εἰς τὸ μὴ ὂν φθαρέντα, ἀλλὰ εἰς γῆν μεταβάλλοντα ἢ εἰς ὕδωρ (οὐ γὰρ δήπου τοῦτο ἀδύνατον), ἐλάττονα τόπον

δηλονότι τοῦ ἀέρος κατεχούσης τῆς γενομένης γῆς ἢ τοῦ ὕδατος τὸ λοιπὸν ἐν ᾧ πρότερον μὲν ἀὴρ ἦν, νῦν δὲ οὐδέν, ἐξ ἀνάγκης κενὸν εἶναι. ἀλλά φησιν ὁ Θεμίστιος πρὸς τοῦτο ἐνιστάμενος, ὅτι θᾶττον ἂν συνέπεσεν ὁ χαλκὸς τῆς κοίλης σφαίρας, πρὶν ἢ ἐκρυῆναι τὸ ἐντὸς σῶμα ἢ μεταβαλεῖν εἰς γῆν. τοῦτο δὲ ἀληθῶς μὲν λέγεται, οὐκ εἰδότως δέ· διὰ τί γάρ, εἰπέ μοι, συνέπιπτεν ὁ χαλκός; […] πλὴν εἰ καὶ μὴ ἡ φύσις τοῦτο ἔχει, δεδόσθω μοι τῷ λόγῳ μὴ συμπεσεῖν τὸν χαλκόν, μεταβάλλειν δὲ τὸν ἐντὸς ἀέρα εἰς γῆν, καὶ ὄψει ὡς ἔστι τι μεταξὺ διάστημα ἕτερον παρὰ τὰ ἐν αὐτῷ σώματα. (in Phys., 575.21-30; 575.33-576.3)

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Examine it then in this way too. If there is not some different extension receiving them, over and above the bodies that come to be in it, let us remove in thought the bodies in between and see if it is really so. So, then, if we think of the bodies within the universe as not existing—that is to say earth and water and air and fire—will there remain anything in between other than an empty extension? For we could clearly produce straight lines from the centre to the circumference everywhere; so what else is it through which we produce the straight lines but threedimensional empty extension? … For if there were nothing in between the limits of universe’s hollow surface, the bodies in it being removed in thought, then the limits of the universe would collapse. But this is impossible; for it is not because of the bodies in it that the universe is as it is, but rather it would be the same, even if there were nothing there. So give me a bronze sphere, not full but partially hollowed out; it is obvious that what is trapped inside was air. So, if I think of the interior air, not corrupted into non-being, but changing either to earth or water (for of course this is not impossible), and the earth or water evidently occupies a smaller place than the air—namely the remaining place in which previously there was air, but now there is nothing— then void necessarily exists. But Themistius says against this that the bronze of the hollow sphere would collapse before either the body inside flows out or changes into earth. And that is truthfully said, but unwittingly. For why, tell me, would the bronze collapse? … Besides, and even if this cannot happen in nature, let me grant that in theory the bronze does not collapse and that the air inside changes into earth, and you will see that there is some extension in between different from the bodies in it.

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The first thought experiment [P7] comes as an alternative argument to show that the extension of place differs from bodily extension and that it exists. The narrative of the experiment is as follows. The universe contains bodies made of the four elements (earth, air, fire and water). If we remove (ὑφέλωμεν) bodies in thought, what happens?237 If we think of the bodies as non-existent, then what else would remain, if not empty extension? Our narrative even allows us to imagine producing straight lines in every direction from the centre of the universe to the circumference. That through which we produce straight lines must be something which is not a body, since we removed all body: it would be empty extension. In addition, if there were no such empty extension between the limits of the hollow surface of the universe, the limits of the universe would collapse. Philoponus asks us to imagine taking away the bodies of the universe and leaving behind only its boundaries. He is aware of the impossibility of such an action happening in reality. And because he is concerned that people might accuse him of talking nonsense, he explains why he has chosen to base his argument on an impossible hypothesis. In fact, he says, the impossibility of a hypothesis has no bearing on its validity as a demonstration. When something impossible follows from a hypothesis, we can then refute the hypothesis from the impossibility of the consequence; this does not mean that we cannot hypothesise the impossible for the sake of seeing the nature of the things (in Phys. 574.21-24). The impossible consequence that the limits of the universe would collapse if there were no such extension refutes the hypothesis that we can actually remove all bodies from the universe. At the same time, the thought experiment demonstrates that the extension of place exists. We can imagine an empty universe, or we can imagine an empty space equal to the universe and create a narrative explaining the impossible assumption that the limits of the universe collapse. In this way, the absolute space that is deprived of bodies is ontologically different from any corporeal extension. We can even imagine producing straight lines throughout this empty extension.238 In doing so, we experiment with impossibilities in order to understand the real nature of things: in this case the existence of the extension of place. It is worth noting that Philoponus provides a further explanation of this impossible consequence which, at first glance, seems odd. He says that the universe is as 237 Sextus describes the same thought experiment, which derives, it seems, from the Stoic tradition: κἄν κατ ’ ἐπίνοιαν δὲ ἅπαντα ἀνέλωμεν, ὁ τόπος οὐκ ἀναιρεθήσεται ἐν ᾧ ἦν τὰ πάντα, ἀλλ’ ὑπομένει, τὰς τρεῖς ἔχων διαστάσεις, μῆκος βάθος πλάτος, χωρὶς ἀντιτυπίας· τοῦτο γὰρ ἴδιον ἦν σώματος, Adv. Μath., Χ. 7= SVF, II.501. Yet, one cannot confirm with certainty that Sextus is Philoponus’ direct source. Grant (1964: 284-285) quotes a similar thought experiment found in Albert of Saxony (ca. 1316-1390) in his work Questions on the Physics (Quaest., 12, fol. 51r, c. 1-2, Paris 1518): ‘secundo conclusio. si esset vacuum inter celum et terram […].’ 238 Again, Philoponus plays with analogies from the geometrical field, in which we can draw figures and lines in thought, as in the case of place measuring solid surfaces. See Philoponus, in Phys., 568.14-569.6.

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it is not because of the bodies in it but rather because the absence of the bodies in theory does not disturb the universe at all: the universe would remain as it is (in Phys., 575.19-20). This suggests that there is a cosmic place filled with the universe. It seems that, for Philoponus, the extensionality of the universe and the extensionality of all bodies are not identical, though bodies constitute the universe. Therefore, the universe extends as much as it does independently of the existence of bodily extensions in it because there is an equal to it extension of place to fill. Furley asks the wrong question, I think, when he says (1991: 37, n. 36): This is a strange argument. The collapse of the heavens is of course as theoretical as the removal of the interior bodies. Why should the heavens not collapse in theory? It must be because their nature as a set of hollow spheres is essential to them, and not conceptually dependent on the fact that the hollow interior is filled. Philoponus would no doubt defend this by claiming that God made them so.

Philoponus defends the independent extensionality of the heavens. The limits of the heavens, of course, can collapse in thought, as Furley puts it. They collapse by removing the extension that bodies fill. But the thought experiment at hand opts to remove the bodies inside the universe, rather than the extension they fill. It seems that genuine thought experiments are counterfactuals. Text [P7] draws our attention to the absolute sense of place—that of pure extensionality deprived of bodies—which Philoponus earlier stated as conceptually possible. We can think of place without bodies in it, although that can never occur in reality. The second thought experiment [P8] draws our attention away from the universe and its limits. Let us think of a bronze sphere which is partially hollowed out and imagine that the body occupying that space in the sphere is air. Now, think of the amount of air contained in the sphere and imagine that the air can change into water or earth. If the air changes into earth in the sphere, the earth occupies a smaller place than the air previously occupied. Philoponus seems to imply that when the air changes into earth a part of the hollow sphere that was occupied by the air remains empty because the earth (or the water) is denser than the air. As a result, the bronze of the holllow surface of the sphere would collapse either before the air left the sphere or before the air changed into earth or water. Philoponus agrees with Themistius that the bronze of the sphere would collapse in reality, but he accuses Themistius of ignorance of the real cause of that phenomenon. Themistius states that the reason for the collapse is that nothing could prevent the bronze of the hollow surface from collapsing and make it remain there without body.239 Philoponus claims that it is the ‘force’ of the void (ἡ τοῦ κενοῦ βία) that prevents the actual presence of the void, as we saw in section 3.3. The thought experiment in 239

See Themistius, in Phys. paraphr., 114.19-20.

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text [P8] involves a hypothesis that can actually be proved, namely that air might change into water or earth. The experiment states the impossible hypothesis that the bronze of the sphere will not collapse against the natural, so to speak, rule of the ‘force’ of void, which prevents gaps in nature.240 The part of the extension inside the bronze sphere, which remains empty in thought, appears as something essentially different from the bodies occupying the hollow sphere. The two experiments, taken together, constitute an advantageous argument, for they show two ways of thinking about place. Place differs ontologically from bodies either with regard to what actually happens in nature or with regard to what we mentally construct about nature. The absurd consequences of both thought experiments, on the one hand, save the phenomenon (the limits of the heaven or the surface of a hollow sphere cannot collapse in actuality) and, on the other hand, provide a plausible explanation, showing the existence and difference of the extension of place from bodies. Though the thought experiments demonstrate the abstract (ontological) difference of place from bodies—or, to put it differently, they describe in what sense we should conceive of the physical absolute place—Philoponus also draws on everyday experience in order to make his argument more convincing and easily comprehensible, as we saw in the previous sections.

3.5 Place, substance, qualities and quantity There is a further issue regarding the ontology of place according to Philoponus that needs clarification in order for us to fully understand how the philosopher establishes the ἑτερότης of place (topos). Philoponus’ account of place involves references to substance, qualities and quantity. Any account of place that comes after Aristotle’s Categories could reasonably be expected to include a discussion of the substance (οὐσία) and its relationship to place, since all natural bodies are somewhere and, as Aristotle expresses it, we need to define where substances are (τὸ ποῦ).241 Aristotle’s discussion of the ten categories led his commentators into various interpretations, the category of ‘where’ being no exception. For instance, Simplicius reports that Andronicus and Archytas arrived at a category of place and a category of time in which they included the categories Aristotle called τὸ ποτέ and τὸ ποῦ.242 Ammonius Hermeiou explicitly claims that we have four main categories (substance, quantity, quality and relativity), from the combination of which the other six categories can 240 Martin (1999: 295-296) describes Philoponus’ thought: ‘If we suppose per impossibile that a body is removed from its place without replacement, we shall not be drawn into logical inconsistency; but no non-mental process can overcome the horror vacui to effect such a removal.’ 241 See Aristotle’s Categories, 1b25-27. Note, however, that we do not have a unified theory of place in Aristotle since, as Mendell (1987: 210 ff.) argued, the concept of place in the Categories contradicts the concept of place in the Physics. 242 Simplicius, in Categ., 134.5-11; 342.22-25. Simplicius, in his comments on the Categories, 11b10 ff., says that Aristotle considers time and place to belong to quantity (see in Categ., 342.21-22).

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be deduced. The category of where derives from the combination of substance and quantity.243 Philoponus’ commentary on the Physics, however, does not examine place in the context of Aristotle’s categories. In defending his theory Philoponus distinguishes place from substance; he questions the relationship between place and quantity; and he draws analogies between place and qualities. The digression on place contains most of Philoponus’ reflections on these issues. Here, I start with a few remarks on place and qualities. I will then continue by examining Philoponus’ way of dealing with place and quantity and, finally, I will conclude by discussing Philoponus’ thesis on the relationship between place and substance and how this relationship constitutes an additional argument supporting the ontological difference (ἑτερότης) between the extension of place and substances. At first glance, it seems that Philoponus is comparing place with qualities. He often illustrates the ontological state of place with the qualities of a body. Themistius, as we saw in section 2.2, suggests that the extension would divide the body or be divided by body. To refute this Philoponus argues that, just as different (incorporeal) qualities are in bodies without being responsible for any kind of division—exactly because they are incorporeal—in the same way an incorporeal extension, that is to say place, is possible: it is inappropriate to assume that the bodiless affects the body in any way. A three-dimensional bodiless extension (which is the place of bodies) obviously cannot either divide the body or be divided by the body. The analogy between place and qualities proves to be satisfactory, since both relate to body and are bodiless.244 But it would be misleading, as Philoponus argues, to infer from the fact that place can be compared with qualities either that place is a quality or that it has a quality. A quality of a body perishes along with it, but place does not undergo corruption. In addition, a bodiless extension that is empty by its own definition cannot have any quality or power, as we stated earlier.245 The same stands for the extension of place and quantity: we can only draw an analogy between them. A three-dimensional bodiless extension can certainly be fitted on to body; otherwise, one could not fit bodiless quantities such as length to bodies (in Phys., 558.27-31). But the extension of place cannot have or be a quantity. Length and breadth do not exist beyond body in actuality; the extension of place 243 Ammonius, in Categ., 92.6-12. The same idea occurs in Philoponus (in Categ., 163.4-164.5). For the opinions held by Ammonius, Philoponus and Simplicius see Algra 1995: 137-138, n. 39. 244 See Philoponus, in Phys., 557.24-31. There are many similarities between Philoponus’ treatment and a short treatise on the incorporeality of qualities attributed to Galen, namely the Quod qualitates incorporeae sint, which attacks the corporeal universe of the Stoics in different aspects, one of them being the notion of place. The writer examines the absurd consequences deriving from the case of corporeal qualities of bodies with respect to the three dimensions of bodies and their place (Kühn 1821, 19.471.16 ff.). 245 Philoponus clearly states that we should not think of place as having a quality (see in Phys., 632.7-8).

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which Philoponus establishes resembles these quantities (length, depth, breadth) in that they are bodiless and capable of fitting on body, but defined in its own right as bodiless empty dimensions alone, it subsists beyond body. Philoponus asserts that three-dimensionality cannot be a term which defines only body. It is an inseparable accident (ἀχώριστον συμβεβηκός) in the case of bodies, since it belongs to the category of quantity.246 Briefly to call to mind the argument discussed in section 3.1: body is substance; quantity is an inseparable accident of substance; three-dimensionality is a quantity; therefore, three-dimensionality is accidental to substance. Yet, even if we think of place as a quantity, because it is three-dimensional, we should note that place will be a separable accidental to physical bodies. This fits with the idea that place is one of the physical concomitants (παρακολούθημα) of all physical bodies.247 A difficulty, perhaps raised in Ammonius’ classroom, introduces, in the digression on place, the issue of a quantity separated from bodies.248 Given that the category of quantity (τὸ ποσόν) always appears to be connected to a substance (ἡ οὐσία) and that extensionality belongs to the category of quantity, then the separation of extensionality from bodies would imply the separation of quantity from substance, which is impossible. In fact, a separate, self-subsistent (καθ’ αὑτὸ ὑποστῆναι) quantity is impossible.249 The difficulty seems to focus on the particular extensionality of a particular substance, given that the extensionality of a tree cannot exist indepedently of that specific tree. The argument seems to be strong enough to refute the assumption of a separate extension. In reply, Philoponus draws our attention to the weakness of our senses and to the relative way in which we build our knowledge about nature. It is true from observation that we always see quantity attributed to a substance. We do not see anywhere in nature a quantity alone. But then we could also say that substance cannot subsist beyond quantity, quality and its other attributes, because we always see substance accompanied by a specific quantity, colour, taste, etc.250 Philoponus’ hypothesis partially reverses the scheme of Aristotle’s categories by hypothetically stating that the ‘bare’ substance cannot be self-subsistent. The idea lurking behind Philoponus’ hypothesis is that our observations of nature do not provide us with any secure reason for accepting the self-subsistence of substances. The Aristotelian scheme of the categories actually suggests com246

Ibid., 561.5-27. Ibid., 2.14-16. 248 This difficulty is raised in lines in Phys., 561.25-27, but discussed much later in lines in Phys., 578.5-579.18. 249 Ibid., 578.10; 31-32. 250 Philoponus characterises the assumption that quantity cannot be self-subsistent beyond substance as a belief we have a habit of endorsing (in Phys., 579.15-17): ‘[t]hus, then, we can also save what seems to have been agreed upon through our habit of continually saying it (διὰ τὸν συνεθισμὸν τοῦ συνεχῶς τοῦτο λέγεσθαι): I mean, that quantity cannot subsist without substance.’ Trans. by Furley 1991: 41. 247

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binations of categories with one another. We cannot, by observing any one of the categories alone, infer that a substance is self-subsistent. It could be claimed that every natural substance needs a determinate quantity for its being. For example, each form of flesh subsists only in a specific quantity. When the quantity perishes, then the form perishes along with it.251 In this way, for Philoponus, the natural forms may have their being in the quantity (as a substrate). Philoponus, by hypothesising that substance cannot be self-subsistent, wants to show that the nature of things cannot be refuted by the assumption that quantity cannot subsist in its own right (in Phys., 578.27-32). He recommends that we should either demonstrate that such extension does not exist or leave everything as it is. When we study nature, we always have to change our point of view in order to be consistent with nature and not insist on our assumptions, even if the nature of the things differs from what we are able to perceive at the time.252 To some extent we have already touched upon the relationship between place and substance. This relationship clearly connects to the differentiation of place from bodies. The extension of place is beyond matter and, as a result, beyond substance. Substances are composed of matter and form. Physical bodies are substances composed of matter and form—for instance, a human being. These substances have three dimensions—i.e., they are extended in length, breadth and depth. In Philoponus’ terminology, substances fill the extension of place. The fact that bodies fill the extension does not mean that we cannot grasp place existing in its own right (absolute place). If place is a three-dimensional extension and it belongs to the category of quantity, we still think of it as being different from the bodily extension that fills it. But to stand beyond substance does not contradict the assumption that place is never deprived of bodies. The essential difference between two kinds of extension, those of place and the bodily, remains the cornerstone of Philoponus’ account. Philoponus is aware of the fact that an extension independent in any way in nature would create serious complications. But the extension of place should be distinguished from substances, even though we cannot observe an empty bodiless extension.253 In that sense, place in its own right does not perish when a body does. The decay of a body does not affect the extension of place, for another body comes to fill its position within the extension. 251 Philoponus’ argument (in Phys., 578.18-23) may rely on Aristotle, who said in Physics I, 187b1321 that it is impossible for any form to subsist in any randomly given magnitude. 252 I quote Philoponus’ words: ‘So I say that what is most of all necessary is not for the nature of things to follow our own accounts, but for our own agreed assumptions to be consistent with the things. There is no necessity for the nature of things to be like this, just because we have determined that it is impossible for some quantity to subsist without substance.’, in Phys., 578.11-15. 253 The analogy is between place and matter, but also between place and the unqualified body: if and inasmuch as the unqualified body can be self-subsistent, in the same way we can think of the extension of place being self-subsistent (εἰ καὶ ὅσον ἐφ’ ἑαυτῷ ἠδύνατο ὑποστῆναι ἂν καθ’ αὑτό, in Phys., 579.3-7).

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To summarise, the analogy between place and qualities, the reflections on the extension of place and quantity, and the clear distinction between place and substance are all collected here in order to complete Philoponus’ views regarding place as ontologically different from body. According to Philoponus’ account, the extension of place (τὸ τοπικὸν διάστημα) exists as ontologically different from bodies, though we never take notice of it as a separate extension in nature. In this way the account introduces a real ontology of topos, understanding place as separated from bodies, contrary to our observations. Before closing this chapter I would like to draw attention to a text of the astro­ nomer Cleomedes that most likely reflects a mixed background of Epicurean and Stoic inspiration, which is relevant to the kind of difference Philoponus attributes to place. Cleomedes’ text runs as follows: [C1] ὅτι δὲ ἔστι κενόν, διὰ βραχέων ὑπομνήσομεν. πᾶν σῶμα ἔν τινι εἶναι ἀναγκαῖον. τοῦτο δὲ ἐν ᾧ ἐστι, τοῦ κατέχοντος αὐτὸ καὶ πεπληρωκότος ἕτερον εἶναι δεῖ, ἀσώματον ὂν καὶ οἷον ἀναφές. τὴν οὖν τοιαύτην ὑπόστασιν, οἵαν τε οὖσαν δέχεσθαι σῶμα καὶ κατέχεσθαι, κενὸν εἶναί φαμεν. (Caelestia, I.1.20-26)

We shall now briefly summarize [the argument] that there is a void: Every body is necessarily present in something; but the thing that a body is present in, given that it is incorporeal and as such without physical contact, must be distinct [ἕτερον] from what occupies and fills it; we therefore speak of such a state of subsistence—namely, a capacity to receive body and be occupied—as void. (trans. Bowen-Todd 2004: 22-23)

Cleomedes argues that the void, as the place of bodies, exists. At first glance, he seems to imply a separate (Bowen and Todd translate the ‘heteron’ as ‘distinct’) ‘thing’, as he calls the void, in which bodies are present and fill it. But I think that Cleomedes’ claim here does not state just a distinct incorporeal ‘thing’, that might be an extension. He claims that the void subsists and differs from the bodies because it is bodiless, intangible (using Epicurus’ wording), and capable of receiving and being occupied and filled. This kind of difference already suggests an ontology of place similar to that established by Philoponus. I would not go as far as to say that Philoponus alludes to Cleomedes’ text, since we have no textual evidence to support such a claim. Nevertheless, we should keep in mind that the conception of an existing separate void, as set in antiquity, seems to find an ultimate and profound representative in late antiquity, that is Philoponus and his theory of place defending a substantialist view of place. Having said that, the whole treatment of the subject in the digression on place clearly suggests that Philoponus establishes an ontology of place by defining place as a reality in nature. Place, i.e., the void, subsists despite the fact that human beings have no direct experience of it, since it is always filled with bodies. This

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whole chapter has examined the various arguments used by Philoponus to claim that place is ontologically different (ἕτερος) from bodies. Philoponus argued that the three-dimensionality of a bodiless extension cannot be conceptually identical with the three-dimensionality of a body, though he emphasises the equality of the three-dimensionality of a specific body to the three-dimensionality of the extension of place this body fills. In this sense, place is conceived as the measure of the three-dimensionality of a body. At the same time, Philoponus expands his theory of place to the cosmological level. The extension of place is always filled with the cosmic body and each body of the cosmos moves within it. Place as the underlying reality of the cosmic body makes its arrangement possible in the sense that bodies desire to take their proper position within the extension of place according to the cosmic order set by the demiurge. Bodies even occupy positions contrary to their natural motion to that effect. We have seen that Philoponus proposes an intra-cosmic space always filled with bodies and equal to the cosmos, a view that was expressed by certain Platonists and Strato of Lampsacus. This view, as pointed out, differs from the intra-cosmic space proposed by the atomist tradition in that it does not imply a separate void space existing as a gap in nature and it is opposed to the existence of an extra-cosmic space extended outside the cosmos. The physical, bodiless, impassive, immobile and void by its own definition extension of place does not undergo any change like bodies do and thus ontologically differs from substances. This kind of void, namely the special sense of an existing void filled with bodies, that Philoponus introduces in the digression of place is further explained in the digression on the void, where he explicitly claims that the motion of bodies through the void is possible and thus, in a sense, redefines locomotion with respect to his definition of place, as we shall now proceed to show in the next chapter.

Chapter 4

Philoponus on Void as Place The digression on the void, which Philoponus places within the running commentary on Physics IV.6-9, notoriously establishes an account that permits the subsistence of the void in nature. The digression on place, which we have just considered, deals with understanding the extension of place in its own right, as something different from the bodies within it, and at the same time as the place, i.e., the location, of those bodies. The very same interpretative line is also traced in the digression on the void, in which Philoponus additionally attempts to correct Aristotle’s theory of the motion of bodies, introducing a theory of empty place compatible with the motion of bodies. The general opinion nowadays regarding the digression on the void is that it undermines Aristotle’s denial of the void’s existence. I suggest, in addition to this, that the digression further exculpates, so to speak, the concept of the void: the void is seen as part of nature together with the mutual replacement of bodies. The present chapter centres on the question: how does Philoponus go about introducing a conception of void that is compatible with the nature of the universe that is filled with bodies? The digression on the void is congruent with his theory of place; so, while reading it, we should always be mindful of the principles set out in the digression on place. To put it differently, I read both digressions plus Philoponus’ observations on the motion of the projectiles (in Phys., 639.3-642.26) as a coherent theory of place and as a theory of the motion of physical bodies.254 The first subject discussed in this chapter is the fundamental concept of πλήρωσις (plērōsis), which is a prerequisite for our understanding of the way bodies occupy place. Next, the chapter examines Philoponus’ definition of the void as place. The following two sections of the chapter are devoted to Philoponus’ arguments in favour of the motion of bodies through the void and how he applies his theory to every kind of motion. The last section of the chapter claims that the kind of absolute topos introduced by Philoponus does not imply a conception of place that exceeds the study of physics.

4.1 The concept of plērōsis One of the essential features of Philoponus’ account of place is the concept of πλήρωσις—i.e., ‘filling up’. We have already touched upon this concept several times in the previous two chapters. At the beginning of the digression on place Philoponus focuses on the objections raised in the Peripatetic tradition against older extension 254 Some excerpts from Philoponus’ commentary support the view that the digression on the void connects with the digression on place and the excursus on the motion of projectiles: in Phys., 675.15-16; 675.29-676.1; 687.14-19; 688.31-34; 689.6-7; 689.14-16; 694.16-27. In these texts the arguments of all three sections of the commentary produce one single theory on place and motion.

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theories, as we have discussed. These theories seem to entail absurd consequences in their explanations of how a body comes to be in the extension (place), such as that the extension penetrates through the whole body that comes to be in it and that the extension divides the body in such a way as to make an actual infinity of parts.255 Philoponus therefore introduces the concept of ‘filling up’ in order to establish a sound theory of extension, i.e., a theory that does not entail absurdities like the ones described by the Peripatetic tradition. To do so he uses Aristotle to justify the introduction of such a concept. Philoponus introduces the concept of plērōsis through the example of nourishment, which appears in Aristotle’s Physics as well as in On generation and corruption.256 Aristotle attacks those (most likely Empedocles and the early atomists) who claimed that growth (ἡ αὔξησις) happens through the entry of food into the voids or pores contained in the bodies. From the supposition that food enters the body through the voids or pores it follows, Aristotle claims, either that there is no growth or that two bodies are at the same spot (which is impossible) or that the body is entirely void.257 Philoponus explains Aristotle’s thought that there is no growth in the following way: since the food enters into an empty pore, then the food is only filling up an empty pore, so that there is no actual growth of the nourishing body.258 Philoponus takes up this point to suggest that, in the same way, those who claim that place is an extension (should) endorse the position that when the body passes through the void it fills it, and therefore neither is the void divided by the body that comes to be in it nor does the void divide the body nor is the body entirely void nor are two bodies at the same spot.259 It is striking that Philoponus presents it as a claim of Aristotle, although the term ‘πλήρωσις’ does not appear in the context of the Aristotelian argument, at least not in the Physics.260 The transition from the ancient theory entailing that the explanation of growth is based on the existence of the void that Aristotle had in mind to a void theory accepted by Philoponus is unclear. The gist of Philoponus’ intention is to point out the way bodies (i.e., the corporeal extensions) are in the (incorporeal) extension of place. The ancient explanation of growth implying empty pores serves as a starting 255 Philoponus, 256

in Phys., 557.8-559.27.

Ηowever, there are several passages Philoponus could have in mind, for instance: De genera-

tione et corruptione, 321a5-9; 321a29-32; 321b10-16. 257 See Physics, 213b6-12; 213b18-20 and 214b5-9. 258 Philoponus says: ἢ ἀναπλήρωσιν εἶναι μόνον τῶν κενῶν, οὐκ αὔξησιν, in Phys., 560.1-2. 259 Philoponus, in Phys., 560.3-11. Other occurrences of the term ‘πλήρωσις’ may be found in several passages of the commentary: see in Phys., 557.21; 560.3-15; 562.6-563.2; 577.25-578.4; 592.29-32; 598.24-30; 624.26-625.9; 675.23-29; 681.15-17; 682.18-19; 684.13-685.23; 686.30-687.35; 689.14-20; 694.1927. 260 In fact, the term ‘πλήρωσις’ occurs in the De gen. et corr., 326b6-28, where Aristotle rejects a theory of pores in the body, since a body is a full body (πλῆρες) and, hence, the void pores are considered as contradicting the nature of the body. Νote that Plato describes a filling of extensions in the Timaeus (35A2-36B5).

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point for introducing (via Aristotle’s attack to it) a conception of the void that escapes the problems Aristotle and his commentators ascribed to it. The concept of πλήρωσις also substitutes, as it stems from Philoponus’ usage, for the Stoics’ troublesome concept of χώρησις δι’ ἀλλήλων (‘passing through each other’).261 The latter, according to Alexander of Aphrodisias, was a concept used by the Stoic philosopher Chrysippus and his circle; it describes the process by which bodies mix.262 According to Chrysippus, some bodies can entirely pass through other bodies and yet still keep their qualities and proper substance.263 Alexander points out that the χώρησις δι’ ἀλλήλων goes against every common observation, such as that a full body (τὸ πλῆρες) cannot pass through another full body. So, one of the bodies either must be void or must contain pores that are void. But then the question is: how do the pores receive another body? The only possible way for this to happen is if the entire body is an empty pore.264 Philoponus is aware that (three-dimensional) extensionality in the Peripatetic tradition remains attached to corporeality. For this reason, he shows that the relationship between place and the corporeal extension is not of the same kind as the one between different (three-dimensional) corporeal extensions. The proponents of the extension view could, Philoponus holds, just assert that the void is filled with the bodies. For the void does not occupy or come to be in bodies, but rather the other way round: namely, the body becomes the occupant of the void. The principle of πλήρωσις derives from the definition of the extension of place. Place is void by its own definition (τῷ ἰδίῳ λόγῳ). Since place is void, we cannot speak of bodies passing through each other (χώρησις δι’ ἀλλήλων), but of bodies filling (πλήρωσις) something empty. Furthermore, the void cannot undergo any motion. The immobility of place should be understood in accordance with the principle of plērōsis, for it is always place that is filled by moving bodies and not vice versa.265 Place is an extension which cannot undergo motion as bodily extensions do. These are some intrinsic differences between place and body which, according to Philoponus’ theory, determine the way we should conceive of bodies being in a place. Having discussed the concept of plērōsis, we can now turn to the details of Philoponus’ definition of void as place.

261 See

in Phys., 559.19-560.15. See Alexander of Aphrodisias, De mixtione, 213.6-13; Rashed 2011: 176, fr. 8; Simplicius, in Phys., 530.9-14. 263 Alexander provides an overview of Chrysippus’ account of mixture (De mixtione, 216.14218.10) and then rejects it (De mixtione, 218.10-221.25). 264 Philoponus wants to differentiate his position from the Stoic view of mixture, especially that attributed to Chrysippus. On the attack against the Stoic theory of interpenetrating extensions see also Alexander, De mixtione, 233.14 ff.; Themistius, in Phys. paraphr., 113.7-116.9. 265 Aristotle argues in favour of the immobility of place in the Physics, but Philoponus repudiates the Aristotelian doctrine of place’s immobility, precisely because Aristotle defines place as the limit of the surrounding body (see the criticism in sections 5.2 and 5.3). 262

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4.2 The void is place The word ‘τὸ κενὸν’ often means ‘empty’ in the sense that we use it in everyday life—for instance, a glass empty of water or any other body.266 Philoponus’ definition of place involves the concept of the void: place is a bodiless, three-dimensional, voided extension. Algra distinguishes between three basic conceptions of the term ‘τὸ κενὸν’ in the philosophical discussions of antiquity: 1) space, 2) empty space or empty place, 3) an empty thing or an empty part of a thing. According to Algra’s distinction, (2) and (3) do not necessarily correspond to two different conceptions of space.267 Philoponus uses the term to denote either space (1) or empty place, empty thing (2 and 3). Right from the beginning of the digression on place the concept of τὸ κενὸν appears to designate the same thing as ὁ τόπος.268 For Philoponus the word ‘void’ basically denotes the extension which is the place of bodies, a meaning of the void already set in ancient thought by the atomists and the Stoics, as we discussed in Chapter 2. Philoponus considers a conception of place to make necessary the notion of an empty space: χώρα κενὴ (in Phys., 557.31).269 The term ‘χώρα’ echoes, of course, the doctrine of the receptacle (χώρα, ὑποδοχὴ) of Plato’s Timaeus.270 Generally, there is a tendency in antiquity to use ‘χώρα’ and ‘τόπος’ in different contexts, which in English are often distinguished by the words ‘space’ and ‘place’ respectively. In the Hellenistic period of philosophy, the word ‘χώρα’ was already used interchangeably with ‘τόπος’. For instance, Epicurus and the Stoics used both terms to describe two different instances of the same condition, namely of ‘being somewhere’: a larger undetermined place (χώρα), the place of a specific body (τόπος)—using the term ‘τὸ κενὸν’ to describe the ‘nowhere’ that is a place empty of body.271 Philoponus tends to use all three interchangeably and coextensively as denoting ‘place’ and ‘space’, the only difference being that ‘void’ is several times used literally, to mean something empty. Within the framework of Philoponus’ account, ‘being nowhere’ is acquired only by mental operation, when thinking of place in its own right as void. Two requirements, it seems to me, are the keystones of Philoponus’ definition of place: (a) three-dimensionality and (b) voidness. The constituent role of the void 266 See, for instance, Philoponus, in Phys., 579.7-9; also Aristotle, Physics, 213b30-34; Themistius, in Phys. paraphr., 125.28-126.3. 267 Algra 1995: 39-40. See also Sedley (1982: 175-176) on the meaning of the term ‘void’. 268 ‘Because they assume that place is not a body (for to say “three-dimensional” is not the same thing as to say “body”) but bodiless (for it is void by its own definition) …’, Philoponus, in Phys., 557.1719. This passage refers to Themistius’ critique of the extension theory of the atomists and the Stoics (in Phys. paraphr., 113.7-11; 116.29-32; 123.15-22). Nonetheless, Philoponus uses the term ‘void’ to proclaim his definition of place. 269 See Algra 1995: 33-38. 270 Plato, Timaeus, 49A1-6; 50B5-D3; 52A8-B5. 271 For Epicurus see Epist. Herod., 39-40; Sextus Empiricus, Adv. Math., X.2; for the Stoics, see Aёtius, I. 20, 1 (Diels, 1879); Sextus Empiricus, Adv. Math., X.3-4.

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in the definition of place can be seen in the following two passages, taken from the digression on place. [P9] δῆλον δὲ ὅτι κἂν κενὸν εἴπω κἂν τοπικὸν διάστημα τριχῇ διαστατόν, τὸ αὐτὸ λέγω. (in Phys., 563.20-21)

It is obvious that whether I say ‘void’ or ‘three-dimensional extension of place’, I say the same thing.

[P10] […] ὅτι δὲ διάστημά τί ἐστι τριχῇ

… that there is a kind of extension that is three-dimensional, different from the bodies that come to be in it, bodiless in its own definition and extensions alone, emptied of bodies (for the void and the place are actually identical in substrate), will be shown by the refutation of the remaining arguments.

διαστατὸν ἕτερον τῶν σωμάτων τῶν ἐμπιπτόντων εἰς αὐτὸν ἀσώματον ὂν τῷ οἰκείῳ λόγῳ καὶ διαστάσεις μόναι κεναὶ σώματος (ταὐτὸν γὰρ τῷ ὄντι τὸ κενὸν καὶ ὁ τόπος κατὰ τὸ ὑποκείμενον), δειχθείη ἂν καὶ ἐκ τῆς τῶν λοιπῶν ἀναιρέσεως. (in Phys., 567.30-33)

Both texts emphatically express the identification of place with the void, consequently understood as empty space. Text [P9] conveys the idea of conceptually identifying the void with the place of bodies. The notion of place and that of the void are coextensive. Glancing at the digression on place, the identification of place with the void can be grasped through the conceptual aspect of the extension of place, namely that of being deprived of bodies. Text [P9] suggests that the terms ‘place’ and ‘void’ are coextensive. It asserts that saying ‘the lion fills the three-dimensional place’ is exactly the same as saying ‘the lion fills the void’. Text [P10] maintains that ‘the void and the place actually are identical in substrate’. On the one hand, it is the same thing to say ‘void’ and to say ‘place’ and, on the other hand, place and void actually are identical in substrate. The word ‘hypokeimenon’ has both a logical and a physical meaning. Logical in the sense of a subject and physical in the sense of a substrate, of an underlying physical entity. Here Philoponus is proposing the physical meaning—i.e., place and void ontologically are one and the same thing. Furley translates the Greek expression ‘κατὰ τὸ ὑποκείμενον’ as ‘in substance’, noting that the word ‘substance’ here does not mean that Philoponus believes that either place or void is a substance (οὐσία). Furley then adds that ‘they (i.e., place and void) differ only in their accidental properties’.272 Philoponus draws a connection between place and void: he wants to clarify the nature of this kind of extensionality. Text [P10] suggests that place and void are actually identical in substrate, that is they both share bodiless three-dimensionality. The three dimensions are what place has in common with the void, whether seen as a filled place or as an empty place (void). In that sense, place is characterised as ‘dimensions alone’, emptied of bodies; it actually is the void. 272

Furley 1991: 28, n. 22.

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So, the bodiless three-dimensionality of place is not accidental to place. But in what sense do place and void ‘differ only in their accidental properties’, as Furley pointed out? As a matter of fact, the presence or absence of the body, in this case the bottle of wine, in the extension is the accidental property. Place and void differ in that in one instance the bottle of wine is in the extension and in another instance there is no bottle and the extension is empty, an absolute void. In my view, this leads to a further conclusion. To give an example of what would be an accidental property of place: the specific three dimensions of the bottle of wine (that now is on the table) could be an accidental property of the extension of place filled with this bottle of wine. The extension must be equal to the dimensions of the bottle of wine filling it. But the fact that the place of the bottle necessarily has the specific three dimensions of this bottle of wine—i.e., the bottle’s place has the same extent that the bottle does—would be a further sense in which place could have an accidental property (namely, the three dimensions of the bottle, whatever they might be). The cosmic extension (τὸ κοσμικὸν διάστημα) itself is unified, but it is filled with different bodies each time.273 We pinpoint parts of that extension because of the bodies’ presence; we try to determine the specific position that a particular body fills right now in connection to other bodies around it within the extension. The position I fill within the extension certainly differs from the position filled by the bottle of wine with regard to the accidental property of our bodies’ extensionality. But place as dimensions alone, empty in its own definition, is an absolute void: place and void share the same hypokeimenon, namely bodiless three-dimensionality, but they differ in the accidental presence of physical bodies that come to fill the void (in its own definition) place. Philoponus often uses the words ‘void’ and ‘place’ interchangeably.274 Then why do we need the notion of the void, if ‘place’ sufficiently denotes that a body is somewhere and nowhere is only mentally grasped? In Aristotle’s words, the void cannot exist in nature exactly because place is always occupied by natural bodies. Aristotle further signals the impossibility of the void’s existence by arguing that the bodily extension would be identical to the empty extension of place, which implies the possibility of many coincident extensions at the same spot.275 Themistius takes up the last point, claiming that the existence of the void is unnecessary—he characterises it as pointless.276 Philoponus’ own statement that a separate extension cannot exist in actuality can also, in fact, be used against his definition of place. Why does he need to speak of the void? Or, as Sedley, who addressed the same question, says, 273

See Philoponus, in Phys., 569.13-17. Ibid., 559.17-18; 562.28; 563.5-15; 569.6-9; 577.4-9; 577.14-16; 579.6-10; 583.6-8. Note that Philoponus points out (in Phys., 573.11-13) the identification of place with void in Aristotle’s Physics (214b2324). 275 See Phys., 214a16-19; 216a26-b21. 276 Themistius calls the void ‘μάταιον’, in Phys. paraphr., 134.33-135.1; 137.16-23. 274

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‘[w]hat possible merit can there be in bracketing vacuum and space together with the single label “void”?’277 Philoponus attempted to reply to this objection in the third part of the digression on the void. Even though the above objection seems inescapable, still Philoponus thinks of the void as one of the necessary conditions for us to speak of the physical place of bodies. He devotes a long section of the digression on the void (the third part, in Phys., 686.30-689.25) to grounding his view in safe arguments. The objections expressed by Aristotle and Themistius depend on an assumption that identifies extensionality with body.278 We saw that Philoponus introduces a kind of extension of place that differs ontologically from the bodies. According to his doctrine, if you take away every quality a body has, you still do not get voided place; what remains is matter and unqualified body (which consists of matter and the form of quantity). But the void does not consist of matter and form: the void is formless and immaterial. Philoponus considers a plausible objection which says that if we take the bodiless matter away from the body, we see that the void is identical to the matter of that body.279 Ηe refuses to admit the identification between body and the void (place). For to take away the matter of a body means that the body no longer exists; nothing like a natural body that needs place remains. It makes no sense to identify the void with the bodiless matter of a non-existent body. In this way Philoponus establishes an absolute concept of the void: the void can still be something else in its own right, even if we take away a natural body in any sense. This kind of extension is a bodiless, immaterial and empty space. Attaching the concept of voided extension to body, as maintained by the Aristotelian tradition, suggests that the absolute void is unnecessary, since bodies always have a place. However, Philoponus makes clear the essential difference between bodily extension and the void. The absolute void serves to define place and explains, at the same time, how bodies come to fill the extension and how they exchange positions within it. The void, according to Philoponus, plays an important role in the mutual replacement of bodies and in their motion, as we shall see in the next two sections of the chapter. He considers it pointless to refute the nature of things, accusing the enemies of the extension theory of establishing theories incompatible with the true nature of the cosmos. It is perfectly legitimate, in Philoponus’ view, to refute the existence of something when we understand its causes or when we can go through the difficulties of the subject. Since we are unable to understand the nature of things, we must learn how to acquire knowledge of their nature.280 So, the 277

Sedley 1987: 141. in Phys., 687.29 ff. A similar argument was discussed in the digression on place (in Phys., 557.17-18; 559.9-14; 561.5-24). 279 Ibid., 688.2-5. It is not certain whom Philoponus had in mind, but the objection strongly resembles Physics, 214a13-16. 280 Philoponus challenges his opponents to refute his theory or otherwise remain silent: ‘So now too either they should refute the arguments with which we proved the existence of this extension or, 278 See

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definition of place as void cannot be pointless, because it has a role in locomotion, that is the mutual replacement of bodies. Although it is verbally odd, we assume the void’s subsistence in nature, in the sense that it is the extension which bodies fill. It would be impossible for a body to fill something already filled or to fill a body. Reasonably, according to Philoponus, we need the empty extension; otherwise, we have to deal with many absurdities (for example, two bodies at the same spot). Beyond doubt, Philoponus does not fail to distinguish between full and empty space. He is able with a mental operation to isolate the void as such, though he does not accept an absolute void, an extension not filled with bodies in the cosmos.281 He defines place as void in its own right, highlighting its nature as a bodiless three-dimensional extension, and distinguishes this sense of absolute void from place always filled with bodies. Philoponus’ insertion of the concept of void into the definition of place allows him to suggest a solution for several problems concerning the void, the most crucial being the motion of bodies through it, with which the next two sections deal.

4.3 Motion through void and motion through a corporeal medium Aristotle in Physics IV.8 criticises the position that the void is a separate extension and argues against the possibility of motion through void. It appears that Aristotle and the late Peripatetic tradition (for instance, Alexander of Aphrodisias and Themistius) treated the void as one of the most controversial concepts in physics, because its nature did not seem to fit in with their conception of natural cosmos. The mysterious void, for many philosophers in antiquity and later on, represents the fallacy that a non-being occurs in nature. Yet, some philosophers tend to believe that the void—perceivable or not—must be there and, strangely enough, this assumption presupposes our ability to perceive that a body is somewhere. According to these philosophers, if we can think of ‘somewhere’ then we can also think of ‘nowhere’. But ‘nowhere’, as the Aristotelian tradition points out, signifies a non-being, something that can never occur in actuality. It is true to say that some of the problems Aristotle discusses in Physics IV.6-9 start from such trivial observations, from which he builds some elaborate arguments denying the existence of the void. Nonetheless, philosophers of antiquity, late antiquity and the Middle Ages and,

if the arguments are true, it is actually pointless to refute the reality either because of an inability to explain the causes for its existence or because it is impossible to solve the apparent difficulties dealing with the account of it; it is as if someone were to refute the existence of an animal part because he was incapable of explaining its cause’, in Phys., 687.22-27. Earlier he claims the same in a similarly provocative manner: see in Phys., 578.28-32. 281 In contrast, as Sedley (2002: 367) argues, Epicurus’ conception of place faces the following difficulty: ‘[h]e [i.e., Epicurus] is failing to maintain a distinction between full and empty space.’ That would be another differentiation between the Epicurean and the Philoponan conceptions of place.

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later, physicists up to the twentieth century tried to restate arguments providing a theory of the existence of the void.282 Philoponus opts for a theory that allows for the subsistence of the void without committing himself to the complications that Aristotle and his adherents have pointed out. The digression on the void consists of six parts and is placed in the middle of the running commentary on the Physics IV.9, which extends over two lectures. The principal aim of the digression on the void is twofold: first, to correct the Aristotelian doctrine that excludes the possibility that the void exists in any sense; second, to establish the view that motion through the void is possible.283 Aristotle posits a distinction between natural and forced motion. In natural motion we can observe differentiae because the natural motion of the elements (and, by implication, of all bodies, since all bodies are composed of the four elements) requires that heavy elements and bodies move downwards and light elements and bodies move upwards, each one towards its natural place in different speads and in time depending on their natural impulses and the mediums through which they move. In a void condition, Aristotle believes, we are unable to distinguish between ‘up’ and ‘down’ and, as a result, a body will necessarily either be at rest or move in equal speeds, both being absurd. Any kind of natural motion in any direction seems impossible because the void is undifferentiated, thus jeopardizing the fact that the natural motions are differentiated.284 Philoponus starts by criticising the Aristotelian arguments which deny the possibility of motion through void, especially the arguments concerning the unequal speed of bodies, corresponding to Physics 215a24-216a21.285 Here I concentrate on the second part of the digression on the void (676.4-686.29), in which Philoponus builds up three arguments concerning the motion of the bodies through the void: a. it is not necessary that bodies moving through the void must move at equal speed, b. the mediums through which motion happens are not the causes of unequal motion, even when the motion happens in the void, and c. the void has no proportional relation to the full (τὸ πλῆρες).

282 Aristotle’s rejection of the idea that motion through void is possible, especially, survives for a long time. Discussions on the issue continue from Philoponus to Averroes, Avempace, St. Thomas Aquinas, Nicholas Bonetus, Jean Buridan, Hasdai Crescas, Albert of Saxony, Franciscus Toletus, Franciscus Suarez, Francesco Patrizi, René Descartes, Galileo and Isaac Newton. See Grant 1964 and 1965. On Philoponus’ conception of the void in relation to later theories see section 4.5. 283 The beginning of the digression informs us about Philoponus’ exact intentions (in Phys., 675.26-676.2): ‘My objection is to the arguments of Aristotle, who tried to show that if void existed, nothing would move through it, and that, even if there is no void in any way separated from bodies, instead there is the void that is filled, which is also the place of bodies, as we proved in the previous arguments. Now we will again show that the arguments refuting it are not cogent, although they persuade with their plausibleness.’ 284 ᾗ γὰρ κενὸν, οὐκ ἔχει διαφοράν, Phys., 214b33-215a1; 215a6-11. 285 τὰ ἐκ τῆς ἀνισοταχοῦς τῶν κινουμένων κινήσεως, in Phys., 675.16-20.

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The problem of the motion of bodies through the void can be regarded as a problem of the relationship between the void and the full (τὸ πλῆρες), namely a full body, something not empty. The extension theory proposed by Philoponus needs to re-establish this relationship. Aristotle objects to theories which establish the concept of void and counters them by showing that the void has no proportion ( λόγος) to the full. Motion through void suggests that bodies (even if they are of different shapes and weights) will still move with equal speed.286 Philoponus devotes a long section of the digression to the refutation of Aristotle’s arguments. As we shall see, he rejects Aristotle’s thesis, which presupposes the arguments on unequal speeds of bodies, that we should look for any proportion that exists between the void and the full. Philoponus introduces three arguments, which are jointly demonstrated.287 a. The first argument (in Phys., 677.9-680.23) goes against Aristotle’s thesis that different bodies will move at equal speed through void. Aristotle establishes two causes of unequally rapid motions: (i) differences between bodies (for example, their natural impulses) and (ii) differences in the mediums through which the bodies move—for instance, water and air (Physics, 215a25-29). Philoponus’ first argument deals with the first case. According to Philoponus, if two bodies of different weights are moving through the same medium, which happens to be void, nothing forces these bodies to move at equal speeds, as Aristotle claims. The heavy body will move faster than the light body, and the same will happen if we replace the void with air: the heavy body will still move through the air faster than the light body. But what is the cause of unequal speed? The medium through which bodies move cannot be the cause of the unequal speed of the bodies in this case. If the medium is not the cause, then the cause relates to the body. Philoponus claims that bodies move with unequal speeds (one body moves fast and the other slowly) because there are different moving causes in them (αἱ κινητικαὶ αἰτίαι). He stresses the evident contradiction in Aristotle’s argument, which recognises the importance of the different impulses of bodies but denies that their differentiations can still cause unequal speed when they move through the void. Indeed, Philoponus suggests that the cause of unequal motion, in the case of two bodies moving through the void, is the heaviness (ἡ βαρύτης) of the bodies, the efficient cause (τὸ ποιητικὸν αἴτιον) of their motion downwards. The natural impulses of bodies, which are responsible for their natural motions towards their natural places, do not cease to exist when the bodies move through a corporeal medium, for instance water or air. Heaviness is a quality of bodies. Qualities do not belong to 286 See

Phys., 213a15-213b2; 215a24-216a21 and Hussey 1991: 227-230.

287 ‘τὸ συναποδεδειγμένον’ is the term used by Philoponus, in Phys., 680.27; 684.10. The term is rare

and appears in the work of authors of late antiquity to describe arguments that are parts of a logical sequence, in the sense that these arguments presuppose one another and somehow prove one another. It is not clear whether this constitutes a demonstrative method or not. Here Philoponus offers three arguments that are jointly proved, the aim being to prove that motion through void is possible.

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bodies by virtue of something else, i.e., in that case of the medium through which bodies move, in the sense that the blackness of a swan belongs to it by virtue of itself: a black swan possesses its blackness. In Philoponus’ words, ‘its being colour does not belong to it by virtue of something else, but rather by virtue of itself’, in Phys., 679.26-27. Accordingly, heaviness as a quality of a particular body belongs to it by virtue of itself, even when the body moves through the void. As a result, when two bodies differ in respect of their heaviness and the medium through which they move is the void, nothing prevents unequal speeds from occurring, since each body bears its own natural impulse. Thus, one body can move faster than the other, and bodies moving through the void will not necessarily move at equally rapid speeds. The first argument points out how the Aristotelian doctrine, which claims that motion through void could produce the absurd consequence of equally rapid motion, might bear some internal contradictions.288 Philoponus shows that Aristotle, on the one hand, accepts that differentiated bodies might cause unequally rapid motion but, on the other hand, misses the point: for, even if the void itself is not the cause, still bodies in the void possess their own natural impulses and can move either fast or slowly depending on their heaviness. b. The second argument (in Phys., 680.24-684.10) suggests that the mediums through which motion happens are not the causes of unequal motion and that motion through void takes time. Aristotle maintains, in a perplexing argument (Phys., 215b22-216a11), that traversing the full and the void in equal times is impossible, since the hypothesis that bodies traverse the void in time is absurd. He assumes an analogy between the proportion ( λόγος) that a body has to another body and the proportion the time of motion has to another time (of motion). Motion has a proportion to motion and, because motion happens in time, the time has a proportion to time; but that the full should have a proportion to the void is out of the question. Having proved that the ‘fast’ and the ‘slow’ occur in the motion through the void because of the natural impulses of the bodies, Philoponus infers that this motion necessarily happens in time. The ‘fast’ and the ‘slow’ are distinguished with respect to time. Motion in the void takes time and this can be established because of there being motions with different speeds (and this latter fact is due to the difference of impulses of bodies).289 This is another way to show that bodies traverse the void in time and that they do not necessarily take an equal time to traverse the same distance through the full and through the void. The analogy of proportions between motions, times and mediums can also be shown to be false in a different way. If we accept the analogy of proportions in the case of two different bodies moving through one and the same medium, the result will be that the proportion of impulses will be analogous to the proportion of times of motion; and the proportion 288 Philoponus points out: ἐκείνῳ δὲ τέως ἐπιστῆσαι χρή, ὅτι δι’ ὧν τοῦτο κατασκευάζει , αὐτὸς τὰς ἑαυτοῦ θέσεις ἀναιρεῖ, in Phys., 677.12-13. 289

See Philoponus, in Phys., 680.28-681.1

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of the moving bodies will be analogous to the proportion of their motion times. Philoponus seems to be pointing out here a fallacy of a regress of proportions, which makes no sense.290 The whole argument includes one of Philoponus’ most fascinating examples, which he uses against Aristotle and the Peripatetics. If two weights differing from each other by a very wide margin are dropped from the same height, the proportion of the times of their motions will be analogous to the proportion of their weights; we will observe, however, that the difference between the times of their motion will be much less than the difference in their weights. Assume that one weighs half as much as the other. If we drop these weights from the same height, we will see that the times they take to fall the same distance will not differ; or, if they differ, it will be by an almost imperceptible amount of time, even though the ratio of their weights is considerable, one being double the weight of the other.291 To conclude, Philoponus states that in cases where different bodies move through the same medium, the ratio of the moving bodies will not be the same as the ratio which the times of their motion have; consequently, the ratio of the medium (if any) will also not be the same as the ratio the bodies have or the ratio the times of their motion have. Thus, to comprehend how motion of bodies through the void is possible, we should keep two things in mind: first, the natural impulses of the bodies make them take unequal times when moving either through the air or through the void; and, second, that the proportion (if any) of the mediums cannot be the same as the proportion that the bodies have, or of the times of their motions, because natural impulses differentiate bodies from each other. c. Philoponus’ third argument (in Phys., 684.10-686.29) establishing the motion through the void goes as follows. Aristotle suggests that those who accept the existence of the void—those would be the atomists—establish a proportion between the void and the full, which is absurd.292 He ascribes to this view the consequence of 290 Philoponus argues that there is no need to go through the analogy of proportions at all (in Phys., 683.7-17). However, his response appears without any demonstrative argument, maybe because he believes that he is just stating the obvious from observations of the natural cosmos (ἐκ τῆς ἐναργείας). 291 I quote Philoponus’ argument, which in modern physics is known as ‘the law of fall’: καὶ τοῦτο ἔστι πιστώσασθαι κρεῖττον πάσης διὰ λόγων ἀποδείξεως ἐξ αὐτῆς τῆς ἐναργείας. πολλῷ γὰρ πάνυ μέτρῳ

διαφέροντα ἀλλήλων δύο βάρη ἅμα ἀφεὶς ἐκ τοῦ αὐτοῦ ὕψους ὄψει ὅτι οὐχ ἕπεται τῇ ἀναλογίᾳ τῶν βαρῶν ἡ ἀναλογία τοῦ χρόνου τῶν κινήσεων, ἀλλὰ πάνυ ἐλαχίστη τις ἡ διαφορὰ κατὰ τοὺς χρόνους γίνεται, ὡς εἰ μὴ πολλῷ πάνυ μέτρῳ διαφέροιεν ἀλλήλων τὰ βάρη, ἀλλ’ οἷον τὸ μὲν διπλάσιον εἴη τὸ δὲ ἥμισυ, οὐδὲ διαφοράν τινα σχήσουσιν οἱ χρόνοι τῶν κινήσεων, ἤ, εἰ καὶ σχήσουσιν, οὐκ αἰσθητὴν ἕξουσι, καίτοι τῶν βαρῶν οὐ τοιαύτην ἐχόντων τὴν διαφοράν, ἀλλὰ διπλασίῳ λόγῳ ἔχοντος τοῦ ἑτέρου πρὸς τὸ ἕτερον, in Phys., 683.17-

25. Grant (1965: 80-81; 84-88) underlines the impact of Philoponus’ argument on Galileo’s views on motion and on ‘the law of fall’ in the De motu by pointing out the respects in which the two arguments differ. According to Grant, a major difference between Philoponus and Galileo is that the latter uses the concept of ‘specific weight’ to explain the velocities of falling bodies, whereas Philoponus uses a conception of ‘absolute or gross weight’. 292 See Phys., 215a24-216a21. Aristotle says, κενοῦ δὲ πρὸς πλῆρες οὐκ ἔστιν (e.g., λόγος), Phys., 216a8-11. Themistius elaborates this idea, providing the syllogism of the proponents of the void (in Phys. paraphr., 132.6-14). Philoponus refutes exactly this argument of Themistius’.

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assuming a proportion between the void and the full, deriving from the proportions between moving bodies, the proportions of the speed of their motions and their times and, ultimately, the proportion between the mediums (for instance, void and air). For Aristotle, the void never could have a quantitative proportion to the full; the proponents of the void, however, are forced to assume that it does because they think that the void exists. To that effect, Aristotle posits the essential question: how can something empty have any kind of quantitative proportion to the full?293 Let us see how Philoponus replies to this kind of objection. His argument has a bizarre form, which may confuse the reader because, initially, he partly accepts one of the theses Aristotle endorses, but for different reasons from Aristotle’s (in Phys., 684.17-685.23). Philoponus’ argument implies that Aristotle unreasonably assumes that the void, if it exists, must have a quantitative proportion to the full. We are provided with a set of conditions which show that it is impossible for the void to have a proportion to the full, on grounds of composition (κατὰ τὴν σύστασιν). Philoponus’ argument may be schematically presented as follows (in Phys., 684.19-32): 1. There are two causes of difference in motion (τῆς διαφόρου κινήσεως): the medium and the bodies. 2. The medium is the hindering cause (αἴτιον ἐμποδιστικὸν) of the time of motion; it hinders by virtue of its corporeal composition, which requires passing of time. 3. When the medium through which the motion occurs is the void, time is consumed because every motion occurs in time—otherwise, the moving body would be at both edges of the distance at the same time; but the time is of this or that length by virtue of the impulse each body itself has. 4. Moving bodies do not consume time at all by virtue of the void qua void as they do by virtue of a body when they move through a body, for, generally, the void has no corporeal composition; but the void lies under the moving body as a bodiless extension and space (χώρα) that does not hinder the whole. 5. If time is passing during the motion by virtue of the corporeal composition of the medium, and if time is not consumed by virtue of the void qua void, then, given the absence of compared times—i.e., the time through the void and the time through the body—we can neither compare the void with the full nor say that the void has any (quantitative) proportion to it. The core of the argument draws on the distinction between the two causes of unequally rapid motions, namely the different moving bodies and the different me293 Themistius complies with Aristotle by noting several absurdities in theories supporting the motion through void such as the elimination of the fast and the slow in motion, timeless motion, the proportion between the full and the void (in Phys. paraphr., 130.18-133.14).

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diums through which they move. If the void had any proportion to the full, then we would certainly have to commit ourselves to examining the case in which the medium is always the cause of unequally rapid motion. But Philoponus replies that the void cannot be the cause of unequal speeds, even if it is the medium through which the body is moving. For in this case, when two bodies move through the void, i.e., something that is not a corporeal composition, then only the proper impulses are the cause of unequal speeds of the moving bodies. As a consequence, the case of a body moving through the void suggests that it is the natural impulse that causes the unequally rapid motion, and not the medium. In other words, we need to understand motion through the void as a constant filling of the extension of place, which means a constant exchange of positions within the extension of place. The lack of natural impulses would suggest that the body is at both limits of the distance at the same time, which is absurd. Every part of the motion of a body occurs in a different time and this is how we can perceive the motion of the body. The natural impulse of the body ensures that the motion of the body takes time, otherwise without an impulse the body would seem to be standing nowhere in particular and therefore we could say that it could be either in the beginning or at the end of the distance at the same time. Motion through the void occurs in time because motion always occurs in time, as Aristotle notes for motion through bodily mediums, but, furthermore, because the bodies have their own natural impulses. For only two things cause time to be parted when a body moves, namely the corporeal composition of the medium and the natural impulse. To put it another way, Philoponus’ argument is based on the following idea: moving bodies move through a medium; whatever the medium, it consists of something material spread over space (space that, in abstraction of matter, is just void). In this quasi-composition of void plus matter, it is not void that is the cause of slowing down, but rather matter.294 Philoponus’ argument maintains that we are speaking of two different cases, in which the respective causes of unequally rapid motion are different. We are not comparing two cases in both of which the mediums (air and void) cause the different times a motion may have. Instead, if we hypothesise the void as the medium, the cause of unequally rapid motion will only be the natural impulse of the body. In the case where the medium is bodily, the unequal speeds of bodies are caused by both the medium (which is a hindering cause) and the natural impulses of the bodies. It is thus unreasonable to assume that the existent void produces a quantitative and qualitative (since Philoponus adds that there is difference between corporeal composition and the void) proportion of the void to the full; it is futile to compare times through the full and times through the void because the reason they are different is that they have different kinds of causes.

294

I am grateful to Jan Opsomer for this further elaboration of the argument.

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Aristotle concludes, according to Philoponus’ interpretation, that the proponents of void’s existence assert that the void has a proportion to the full on the basis that the times of motion have a proportion to one another. But Aristotle argues against them that, on the one hand, in the case of motion through body qua body (namely a medium) some time is added, but, on the other hand, in the case of motion through void qua void no time is added. So Aristotle thought that the times of motion through the void and through the full necessarily could not have any proportion to one another; hence, the void cannot have any proportion to the full. However, Philoponus insists that Aristotle missed a critical point: we can think of a proportion between the void and the full with respect to their extensionality alone. The void and the full, regarded simply as extensions, have a proportion to one another in the following sense. Since both are extensions, we can compare the ratio of their extension—for instance, one stade long or one cubit long. The ratio(s) that they have to one another relates to their extensionality, to their nature as incorporeal magnitudes, and to their quantity.295 The commentator maintains that we are not dealing with a proportion between the full and the void, but rather with the proportion between two incorporeal magnitudes or between two extended quantities. If the mediums are seen as simply extensions, the times of motion through the mediums have a proportion to one another too. But when we take a case in which we think of the bodily medium with respect to its corporeality (and not to its incorporeal extensionality), then it is pointless to compare a corporeal medium with the incorporeal void. The cause of Aristotle’s and Themistius’ fallacious reasoning can be firmly identified: the philosophers transpose the relationship of the times of motion to that of which the time is predicated, namely the mediums through which the motion takes place.296 Philoponus illustrates this with an example. We assume that when we think of a specific theorem some time has passed—for instance, one hour; and let us say that there is a stone that covers a distance through the water in, for instance, two hours. At first glance, the example appears to be unclear: Philoponus compares the thinking of the theorem with the motion of a stone. The thinking of the theorem represents a kind of motion through the void, whereas the motion of the stone occurs through water. Aristotle maintains that the times of these motions will have a proportion to one another, and the mediums of which time is predicated will necessarily have the same proportion to one another. Consequently, the water will have a two-to-one proportion to thought (διανόησις) with respect to composition (κατὰ τὴν σύστασιν); and the same for the motion to thought and the stone to

295 I quote Philoponus (in Phys., 685.10-12): ‘For the void and the full simply as extensions have a proportion to one another by virtue of their incorporeal magnitudes and their quantity, for instance cubits or stades long.’ 296 καὶ ἐπὶ ταῦτα ὧν ὁ χρόνος κατηγορεῖται , Philoponus, in Phys., 685.23-25.

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the theorem respectively.297 Obviously, this is absurd.298 The void and the full will never have a proportion to one another because they are of completely different kinds (non-homogeneous).299 But is that not what Aristotle also says? Let us explain Philoponus’ point more precisely. The whole treatment analysed so far in this section examines locomotion in terms of a void-full relationship. Philoponus agrees with Aristotle on the impossibility of the relationship between the void and the full, but for different reasons. Aristotle, on the one hand, points out that void cannot have any proportion to the full, since the void is a non-being; Philoponus, on the other hand, states that the properties of the subsisting void cannot be put side by side with those of a corporeal composition and thus cannot have any proportion to the full. We have already seen that place cannot be the cause of anything, for otherwise we have to admit that place consists of matter and form, so that it can act on bodies or be acted upon by them.300 Aristotle rightly avoids ascribing to void a causal role in cases of unequal speeds of bodies. But he reaches this conclusion on the basis of two false assumptions: first, that the void does not exist and, second, that every medium through which a body moves needs to be a cause of unequally rapid motion. For Aristotle bodies can have proportions to other bodies with respect to their composition. Philoponus’ theory does not presuppose the corporeality of every medium through which bodies move; certainly, bodies can move through water or air (i.e., mediums of corporeal composition), but the theory additionally suggests a concept of void, claiming that locomotion signifies the traversing of a bodiless extension. In the latter case we need to re-establish the relationship between a body and its empty—in its own definition—place. In fact, Philoponus’ theory allows the existence of an incorporeal medium through which bodies move. The void is an intrinsic reality of the universe. Locomotion, as we shall see, means filling up empty place. As stated in the digression on place, the concept of unaffected place prevents any causality from being attributed 297 See ibid., 685.29-686.2. In addition to the example of the theorem and the stone, Philoponus sets out a number of examples (in Phys., 686.5-23) dealing with changes of different kinds (warmth, change of colour and motions of planets). 298 Philoponus uses a less polite characterisation: τοῦτο δὲ καταγέλαστον, in Phys., 686.2. I need to make a general remark here: impolite characterisations are common in Philoponus’ digressions and running commentary; we have many other examples of insulting and disrespectful expressions on Philoponus’ part. When a claim appears to him to be completely absurd, he uses the expressions ‘γελοῖον’, ‘καταγέλαστον’ or ‘εὐήθης ἡ ἀπάντησις’ (in Phys., 572.25; 581.18-19; 686.2; 691.12; 692.32; 693.16; 576.22). Expressions of that sort appear in the running commentary too (in Phys., 534.22-23; 628.20; 669.13). Nonetheless, we should be aware of the fact that these expressions either are not directly addressed to Aristotle or are not directed to Aristotle at all. We could perhaps safely say that the target is Themistius’ argument in some cases. But, if we want to form the right picture of Philoponus’ reaction to his sources, we should certainly note that he approves some well-structured arguments without hesitating (in Phys., 559.24-29; 565.19-21; 566.31; 572.10; 582.26-28; 675.18-19). 299 ἀνομογενῆ γὰρ ταῦτα ἀλλήλοις, in Phys., 686.29. 300 We saw Philoponus’ views in Chapters 2 and 3.

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to the void.301 In the first part of the digression on the void, the ontological difference between void and body appears in terms of non-homogeneity (ἀνομογένεια). The way Philoponus treats the relationship between void and full aims to prove that the existence of the void does not necessarily mean that the void has to have a proportion to the full. We cannot be sure whether Philoponus intends to criticise other theories of the void in this way, especially that of the atomists who assert that the cosmos consists of body and void or, in other words, of the full and the empty. I would comment that since, for Democritus and Leucippus, body (full) and void (empty) were conceived of as a pair of opposites, then we cannot see how they would admit a proportion between body and void with respect to their composition. However, Aristotle thought that this absurdity derived from theories which claimed the existence of the void. Scholars express their doubts whether Aristotle correctly interprets the theory of the void he has in mind (that of the atomists) and question the fairness of Aristotle’s critique.302 It is safe to assume that Aristotle’s critique is considered by Philoponus as another argument against an incorporeal extension through which bodies move and, for that reason, he forms his own refutation, which protects his theory of place without aiming at jeopardizing the atomist theory. Bodies differ from void in many respects. It is false to treat the void as a body as Aristotle did by attacking those who posit the void for producing absurd proportions between the void and corporeal mediums. We can find some proportions among bodies, but it is unfair to apply this principle to the void-full (κενόν-πλῆρες) relationship. The only way to outline a proportion between the void and the full, from Philoponus’ point of view, would be to think of their extensionality per se. But the (three-dimensional) extensionality of the void is the only essential characteristic it possesses, whereas in the case of physical bodies extensionality is not their only characteristic; they consist of matter and form, and that is what makes them ontologically different in kind from the void, which does not partake of matter or form. Up to this point Philoponus’ analysis of the motion of bodies posits two cases: first, motion through the (void) extension of place, i.e., the case of locomotion, and, second, locomotion through a corporeal medium, like motion through air or water. However, an assessment of Philoponus’ theory, though not straightforwardly argued, shows that his analysis in a sense cancels the motion of a body through a corporeal medium. For a body, according to Philoponus, moves only through the void (the extension of place), i.e., it traverses it, while the body changes position within it and along with its surrounding bodies. In my view, a significant outcome of Philoponus’ theory regarding the motion of bodies is that air or water is not a medium through which a body, let us say a human, is moving. In Philoponus’ system, the human body passes through the extension and in the meantime the body 301 See

in Phys., 559.9-18. For instance, Sedley (1982: 179; 185; 186) expressed his doubts concerning the fairness of Aristotle’s objections. 302

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around it, for instance the air, changes position too within the extension. The air is a body (a corporeal extension) that exchanges position with the human body and in this sense not the medium through which the motion occurs. Philoponus limits the role of air and water in motion by accepting that they are just hindering causes of motion. But what does it mean exactly to move through void in Philoponus’ natural philosophy? This is the question under consideration in the following section.

4.4 Motion of bodies in Philoponus’ cosmological system We can now recapitulate our discussion about the concept of the void introduced by Philoponus up to this point. We emphasised the importance of the concept of plērōsis in Philoponus’ account of place and we saw in detail his definition of place as void. We further examined how Philoponus builds the relationship between the void and the full, which re-establishes interest in the locomotion of bodies. Here I shall put forward a different matter, viz. the void as a sine qua non for the existence of locomotion, and, moreover, Philoponus’ examination of every kind of motion through the void. To do so first we need to focus on the fifth part of the digression on the void (in Phys., 693.28-694.27), where he responds to the Aristotelian claim that there cannot be motion at all in the void.303 Philoponus expresses a clear opinion about the necessity of void for locomotion. His response, apart from showing that motion through the void is possible, also asserts that the void is a necessary condition for motion. Again, Philoponus’ method is to provide arguments based on natural phenomena and thought experiments. Let us think, Philoponus proposes, of the following case. A body moves through a body, for instance air; the parts of air (in which the body comes to be) must yield (ἀντιπαραχωρεῖν) their places to (all the parts of) the body. The volume of air that gives way to the body is as great as the body’s volume. How is it possible for the air to give way to the body? According to Philoponus, the ἀντιπαραχωρεῖν would not be necessary if there were not a void extension which was occupied by the displaced body (air)—i.e., when the moving body displaced the air. The air steps aside in order to give the body space to move.304 For Philoponus the displacement of the air indicates that there is a remaining extension that the moving body immediately fills. The syllogism goes as follows (in Phys., 694.4-12): 1. If the moving body always passes by (παραμείβει) a certain extension equal to itself, 2. and if this extension must be either void or body, 3. and if it is impossible for body to pass through body, 303 Themistius, as expected, follows Aristotle; the difference is that, as well as the opponents Aristotle had in mind (especially Democritus), there are clear objections to the Epicurean tradition and the Stoics. See in Phys. paraphr., 127.28-133.14. 304 εἰς τὸ κινηθῆναι , in Phys., 693.35.

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4. and if it is, therefore, necessary that the moving body occupies something void, 5. and if the moving body is three-dimensional, and changes position as a whole, 6. then it will need to occupy an equal space to it—i.e., three-dimensional space, 7. therefore, if this extension did not exist, it would be impossible for the moving body to displace a quantity of air equal to itself. The whole syllogism saves the phenomena of motion and bodies’ impenetrability and appears as a scientific formalism in modern terms. Philoponus’ argument offers a number of scientific observations regarding moving bodies, such as the filling up of something empty, the impenetrability of bodies, and the equality of a three-dimensional body to the space it occupies. Sentences 4 and 7 conclude that there is an empty extension that the moving bodies fill and that, without this voided extension, the mutual replacement of bodies (ἡ ἀντιμετάστασις τῶν σωμάτων) in a space equivalent in size to their three dimensions would be impossible. Philoponus’ conclusive sentence marks another important differentiation between his own view on the nature of space and Aristotle’s conception. King pointed out that, according to Aristotle, we acquire the notion of place because of the notion of locomotion.305 Philoponus comes to repudiate Aristotle’s view by supporting the inverse: it is the conception of the voided place that comes prior to the conception of the mutual replacement of bodies, namely locomotion. The empty extension of place is conceptually and physically prior to locomotion. At this point, once more we need to point out that most likely Philoponus’ syllogism owes much to older arguments expressed by proponents of the void, though he does not name his sources. To begin with, the conclusion of the syllogism is in agreement with Epicurus’ claim that place, which he also calls ‘void’, is necessary for the motion of bodies: without the void there would be nothing through which bodies could move.306 Moreover, Philoponus’ syllogism (sentences 1-7 above) echoes the Stoic view on the concept of void and how bodies come to be in it. To make this claim clearer, let us read the following text by the astronomer Cleomedes (Caelestia, I.1.25-30): [C2] ὅτι δὲ ἔν τινι τοιούτῳ τὰ σώματά ἐστι, μάλιστα ἐπὶ τῶν ὑδάτων καὶ πάσης τῆς ὑγρᾶς οὐσίας πάρεστιν ὁρᾶν. ὁπόταν γὰρ ἐκ σκεύους ὑγρὸν ἔχοντος καὶ στερεόν τι ἐν αὐτῷ σῶμα ἄρωμεν τὸ στερεόν, συμπίπτει τὸ ὕδωρ ἐπὶ τὸν τοῦ ἐξηρμένου 305

King 1950: 78. Aristotle, Physics, 211a12-13.

306 Epicurus, Epist. Herod., 39-40: τόπος δὲ εἰ μὴ ἦν, ὅν κενόν καὶ χώραν καὶ ἀναφῆ φύσιν ὀνομάζομεν,

οὐκ ἄν εἶχε τὰ σώματα ὅπου ἦν οὐδὲ δι’ οὗ ἐκινεῖτο, καθάπερ φαίνεται κινούμενα. Inwood (1981: 275) holds

the view that, for Epicurus, place ‘was not a sort of extension that could be filled or not filled.’ But, in objecting to Inwood’s view, if the atoms and bodies are moving through the void, already they must be in a void that surrounds them and that presupposes the extensionality of the void itself.

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τόπον, καὶ οὐκέτι ἡ αὐτὴ ἔξαρσις αὐτοῦ φαίνεται, ἀλλὰ τοσούτῳ ἐλάττων, ὅσον τὸ τοῦ ἐξαρθέντος μέγεθος ἦν.

That bodies are present in such a thing [e.g. void] can be seen primarily in the case of liquids (i.e. all liquid substance). When, for example, we extract the solid from a vessel that contains liquid and some solid body, the liquid converges on the place of the object that has been extracted, and is no longer seen at the same level, but is reduced by an amount equal to the size of the object that was extracted. (trans. Bowen-Todd 2004: 23)

Cleomedes describes a mutual replacement of bodies in a vessel that is possible only because there is a void that bodies occupy each time they move and is equal to their size. Locomotion, for Philoponus, means that bodies pass through an extended place, but not in the sense that they pass through different limits that constitute their place. Place should be considered a kind of void extension that has no limits in the sense that bodies do. It is impossible for a body to pass entirely, as a three-dimensional whole, through a body. So, if the body traverses a void extension, the bodies around it have to exchange positions; bodily exchanges are ruled by the principle of equality that place should have to body. In order for the mutual replacement of bodies to happen, bodies need to move through, and fill, a kind of place that can receive them in all their three dimensions. Otherwise, if the place could not receive the body as a whole, the body could never exchange place as a whole; and the mutual replacement of bodies—i.e., locomotion—would be impossible. Philoponus’ argument follows the same lines, though it is not identical to the argument in Cleomedes’ text [C2]. In addition to the previous argument pertaining to our experience, Philoponus gives an extra argument in favour of the necessary existence of the void with another thought experiment (in Phys., 694.12-17):307 [P11] ἄλλως τε τὸν ἀντιμεθιστάμενον αὐτῷ ἀέρα εἰ νοήσεις αὐτὸν μὲν τοῦ οἰκείου μεταστάντα τόπου, μήτε δὲ τὸ κινούμενον ἐγγενόμενον ἐν τῷ αὐτῷ τόπῳ, μήτε τὸν πέριξ ἀέρα συμπεσόντα, τί ἂν εἴη ἄλλο τὸ μεταξὺ τοῦ πέριξ ἀέρος, ἢ διάστημα

κενὸν εἰς ὃ χωρεῖ τὸ κινούμενον;



Again, if you think of the air displaced by its shifting from its own place without being replaced there by the moving body or by the entrance of the surrounding air, what else would the extension in between the surrounding air be except a void extension into which the moving body moves? (trans. Furley 1991: 72-73, modified)

307 Philoponus claimed the existence of the extension of place in the digression on place with a similar thought experiment (in Phys., 574.13-19; 575.17-20).

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If we think of a case in which air is removed from its proper place, and neither a moving body nor the surrounding air comes to be in that place, then there would remain an empty extension in which the moving body could come to be. The thought experiment aims to show that if this extension is not void, then a moving body can never pass through it; in other words, locomotion is impossible. Again, here we need to stress the similarity between Philoponus’ way of proving that motion through void is possible and the relevant Stoic attempt to prove it. The following thought experiment appears in Cleomedes’ Caelestia, I.1.39-43: [C3] καὶ μὴν καὶ τὸν κόσμον αὐτὸν δυνάμεθα ἐπινοῆσαι κινούμενον ἐκ τοῦ τόπου, ὃν νῦν τυγχάνει κατειληφώς. ταύτῃ δὲ αὐτοῦ τῇ μεταβάσει συνεπινοήσομεν τόν τε ἀπολειφθέντα τόπον κενὸν ὄντα, καὶ εἰς ὃν μετέστη, κατειλημμένον καὶ κατεχόμενον ὑπ’ αὐτοῦ· οὗτος δ’ ἂν εἴη κενὸν πεπληρωμένον.

We can also conceive of the cosmos itself moving from the place that it currently happens to occupy, and together with this displacement of it we shall also at the same time conceive of the place abandoned by the cosmos as void, and the place into which it is transferred as taken over and occupied by it. The latter [place] must be filled void. (trans. Bowen-Todd 2004: 24)

In Cleomedes’ thought experiment the displacement of the whole cosmos proves the extra-cosmic void, since it implies that the whole cosmos moves from its place and occupies another place which is now filled void. The connection to Philoponus’ thought experiment derives from the fact that Cleomedes presents the cosmos as being in motion and denotes three places: first, the place of the cosmos that it currently happens to occupy; second, the abandoned void place when the cosmos moves; and, third, the place that the cosmos now occupies, that is the filled void. Philoponus accepts that bodies come to fill the void when they move; the mutual replacement of bodies presupposes an empty space to be filled. But the discussion of the void in [C3] is not totally in agreement with Philoponus’ theory, since Cleomedes supports the Stoic view of an extra-cosmic void which Philoponus rejects, as we saw in section 3.2. The locomotion of bodies is redetermined by Philoponus in the sense that it is the lack of corporeal compounds of the void that allows bodies to move. The efficient cause of motion through void is not the extension (void) but the bodies themselves, whether we are speaking of natural motion or forced motion. Bodies change position within the extension because of their natural impulses or the intrinsic power that they keep (impetus) when they are forced to move. The relationship between the void and the full and, accordingly, the motion of bodies through the void are best described by Philoponus himself, when he says that the body is in the void ‘as the full is in what is filled’.308 308

ὡς πλήρωμα ἐν πληρουμένῳ, in Phys., 689.22.

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Let us now present how Philoponus applies his theory of the extension of place to any kind of motion. Philoponus, in the fourth part of the digression on the void (689.26-693.27), studies examples pertinent to motions, such as circular motion (ἡ κύκλῳ κίνησις), motion in a straight line (ἡ εὐθυφορία), motion of choice (ἡ προαιρετική κίνησις) and forced motion (ἡ παρὰ φύσιν κίνησις, ἡ βίᾳ κίνησις).309 His considerations are not brought up here as responses to Aristotle, Themistius or anyone else; they are not rejections of any sort. Philoponus chooses kinds of motion and examines whether his empty extension of place is concordant with them or not. In fact, Philoponus uses various aspects of his theory which have already been stated in the objections to Aristotle and Themistius. Both assumptions—(i) that motion through void requires time to be parted and, consequently, (ii) that bodies through void can still move fast or slowly—are again on the table. Celestial bodies in circular motion (for instance, the sphere of fixed stars) can move fast or slowly. This kind of motion, namely rotation, occurs in time and the same holds for bodies moving in a straight line. When celestial bodies rotate through the void the same principle applies, namely that the void, as the medium through which they move, plays no causal role in their movement, but their natural impulses guarantee that some bodies move faster or more slowly than other bodies. Furthermore, if a man decides (according to his προαίρεσις) to walk from Athens to Thebes, but this time not by traversing air, i.e., assuming that the air is removed, what do we observe? Philoponus hypothetically states that the space between heaven and earth is empty. Does the man walk from Athens to Thebes in no time? If one replies that the walk is timeless, it is implied that the motion of the man is instantaneous, which, in turn, is absurd, since a walk cannot be instantaneous, for otherwise the man could be at the same instance both in Athens and in Thebes, and grosso modo he could be everywhere at the same time. The answer to the hypothesis that one could walk faster than someone else from Athens to Italy in the void will be similar: whoever is more powerful can walk faster, without the void preventing or acting upon his body while walking. The motion of arrows shot by archers can take place in the void and, nonetheless, still take time; and some arrows may be faster than others. The cause of the arrows’ movement does not entirely relate to the medium through which they move. If the arrows move through the undifferentiated void, the power of each of the archers determines how fast or slowly the arrows move in time. The example of the archer and the arrow found in the digression on the void directly refers to the short excursus on projectiles that appears at the end of the second lecture on Physics IV.8. Philo309 Philoponus’ examples are intentionally exhaustive, covering all cases of locomotion.  In my view, the excursus on projectiles (impetus) ties in with this approach of locomotion as well (in Phys., 639.3-642.26). We should also include the very last part of the digression on the void, in which Philoponus briefly examines the causes of the differentiated motions that bodies of unlike form (τὰ ἀνομοιοσχήμονα) might have (in Phys., 694.28-695.8).

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ponus attacks the theory of the Aristotelian tradition, since he finds it unpersuasive and fictitious (πλασματώδης). He suggests a theory regarding the projectile motion that had a significant impact on physics. Philoponus’ explanation of the motion of projectiles is that the archer transmits to the arrow a bodiless moving power (κινητικήν τινα δύναμιν ἀσώματον ἐνδιδόσθαι) and that air either does not contribute at all to the motion or just a little. The bodiless power (impetus) transmitted to the projectile by the thrower guarantees that the projectile will move, even if it moves through the void. If the space through which the projectile moves is of that sort, namely void, the cause of this motion will only be the man that impresses the impetus to the projectile.310 Philoponus discusses motions of choice (αἱ προαιρετικαὶ κινήσεις) and forced motions in order to show that, if it is possible for those motions to occur in time through the void, then the same should hold for natural motions too. The last thought experiment found in the digression on the void illustrates that claim. The thought experiment assumes, once more, that the space between heaven and earth is completely empty.311 If we let go of a stone from the sphere of fixed stars, will it arrive on earth in no time? A timeless motion would lead to absurd consequences, for instance the stone will be up and down at the same instant or the stone remains at rest. The answer is similar to those given for the other kinds of motion we saw earlier: the stone’s motion should take time in regaining its natural place (in this case earth). In a sense, Philoponus worries more about proving that natural motions can occur in the void than forced or deliberately chosen motions; one reason may be that the natural motions of bodies are more essential to the constitution of nature than motion involving an agent who produces the motion of another body (for instance, a woman throwing a stone).312 Natural motions of bodies are the primary way for a body to move. To conclude, two conditions, so to speak, play a decisive role in Philoponus’ theory of place: the voidness and the mutual replacement of bodies. The universe is well-ordered when bodies fill their proper positions within the extension and gaps do not appear; actual void is prohibited by nature’s laws. The dependence of locomotion on the extension of place expresses a special conception of locomotion: bodies’ motion is considered as a mutual replacement within the extension of place that happens according to their natural impulses or the agent transmitting the power of moving (in case of forced motion); without the void extension the mutual replacement of bodies would be impossible. It is therefore the nature of the 310 See Philoponus, in Phys., 639.3-642.26. On the impetus theory of Philoponus see Wildberg 1999: 122-123. 311 Philoponus, in Phys., 693.12-27. 312 It may be the case that Philoponus tries to cover his back from the criticisms of Aristotle (Phys., 215a4-6) and Themistius (in Phys. paraphr., 129.1-3; 14-15) who try to show that natural motion through void is impossible and therefore kinds of forced motion will be impossible too.

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extension of place that allows the mutual replacement of bodies: the reality of place either seen as an absolute space conceived by mental operation or directly grasped as a filled place is the sine qua non of locomotion. Τhe voided extension cannot be the cause of locomotion. We have seen that the void plays no causal role for the motion of bodies, whether we speak of natural motion or different kinds of forced motion. Instead, the void assures the existence of locomotion, in the sense that locomotion is explained with respect to voided extension and not with respect to bodies. Since the void extension is bodiless, as Philoponus pointed out in the digression on place too, it cannot cause anything to a body, but it is a sine qua non for locomotion. For Philoponus causality pertains to corporeals; the void is the extension to be filled by corporeals. In connection with this, Philoponus comments on the ‘epistemological’ priority of place over locomotion and over simple and composed bodies: one needs to possess knowledge of the natural place of bodies in order to comprehend the natural motions of bodies, namely locomotion.313 Philoponus arrives at the denial of the void’s causality from a different path from Aristotle and Themistius. Aristotle denies that the void is the cause of (unequally rapid) motion because the void is a non-being.314 Themistius attacks those who maintain that the separate void is the cause of motion, claiming too the non-existence of the void.315 Philoponus rejects the view that the void, either separate or not, can be the cause of motion, for the ontology of place, he proposes, permits an extension which is capable of being filled with bodies, of being three-dimensional and equal to bodies, and is in any respect unaffected. His extension theory holds that the void is the only prerequisite for locomotion. Locomotion may well be nothing more than an incessant mutual replacement of bodies within the extension of place; this means that motion occurs since there is a voided place to be filled. Motion without void is unrealisable in Philoponus’ natural philosophy. In other words, if there were not void, then the universe would consist of a group of static bodies haphazardly gathered and the cosmic extension would be occupied by a mass of bodies at rest.

313 Philoponus’ argument in his first lecture on Physics, IV.1 (in Phys., 497.10-20) is plausibly taken from Aristotle (Phys., 200b20-21). 314 See Aristotle’s Physics, 214b28-29. Aristotle’s attack should refer to Democritus and his circle, who believed that void was necessary to the motion of bodies, though without specifying whether the void was the cause of locomotion. 315 Themistius, in Phys. paraphr., 128.24-130.2; 130.18-133.14 and 127.28-128.23. Perhaps Themistius’ discussion of this opinion at the beginning of his paraphrase of Physics IV.8 reflects Aristotle’s discussion of the void as the cause of motion in IV.9 (Phys., 216b33-217a10; 217b20-28). Alternatively, Themistius may be refering to a different context and attacking the early atomists and Epicurus. I should point out that Iamblichus interprets the concept of place in Plato’s Timaeus in terms of causality, in the fifth book of his commentary on the Timaeus (Simplicius, in Phys., 639.25-36); place, according to Sambursky (1977: 177), seems, then, to be the active cause of the coherence of the bodies.

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4.5 Philoponus on physical place In concluding this discussion of Philoponus’ concept of topos, I would like to draw attention to the following question that relates to the thesis of the whole book: does Philoponus’ account of place as extension exceed the task of the study of physics? To be specific, is the extension of place a physical object and is it necessary for explaining physical objects? The digression on place ends with a fascinating passage in which Philoponus recalls and cites a discussion with his master, Ammonius Hermeiou (in Phys., 583.13-585.4). In this section, we learn that Ammonius raised an objection to Philoponus’ view about the extension of place by accusing him of introducing a non-physical extension. The aim here is to examine whether Ammonius’ criticism is justifiable or misinterprets Philoponus’ account of place. Philoponus does not mention Ammonius by name; he just calls him ‘the philosopher’ three times.316 The passage is important for two reasons. First, it shows that Philoponus had the chance to discuss his thoughts while Ammonius was still alive.317 Second, it is the only testimony of Ammonius’ reaction to Philoponus’ account of place we possess. But I would like to make a few further points concerning the relationship between master, Ammonius, and disciple, Philoponus. The fact that Philoponus could discuss his criticism with Ammonius either in private or within a course of the school, i.e., in front of an audience, additionally shows two things: first, that in the school of Alexandria a student had the freedom of speech to raise critical questions, besides the clarification of Aristotle’s words; second, that it was possible for a student to make an ἀντιλογία against Aristotle and for the master, in turn, to make an ἀπολογία in favour of the philosopher. So this dispute shows us the spirit of the Platonic school of Alexandria under Ammonius.318 Probably the discussion took place before Philoponus wrote his digressions of the commentary on the Physics, since he presents his discussion with the master of the school in the past tense.319 It is, therefore, plausible that Philoponus expressed his doubts earlier during Ammonius’ lectures on the Physics and then wrote his own critique on Aristotle’s theory of place, in this way incorporating his theory of place in the edited version of Ammonius’ lectures that he prepared. Of course, given that Ammonius most probably was dead by the time Philoponus was writing the digression on place, we may reasonably suspect that Philoponus presents a distorted version of their 316

See Philoponus, in Phys., 583.14; 583.33-34; 584.3-4. It seems that the discussion took place before the year 517, when Philoponus attended and most probably started the edition of Ammonius’ lectures on Aristotle’s Physics. It is generally accepted by modern scholarship that Ammonius’ death must have happened between 517 and 526. See Golitsis 2008: 23-25; Perkams 2009; Verrycken 1990: 239-240; 243-254; Blank (2012). 318 Phrases referring to Ammonius such as ‘the philosopher’s defence (ἀπολογία) of Aristotle is shown to be fictitious (πλασματώδης)’ show Philoponus’ freedom to criticise even his master (in Phys., 584.3-4). 319 The participle ‘ἡμῶν ἀντιλεγόντων’ and the imperfect tense ‘ἔλεγεν’ (in Phys., 583.13-14) are evidence of this. 317

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disputation or even that Philoponus took into consideration Ammonius’ points adjusting his arguments so as to avoid this kind of critique. Be that as it may, let us turn to the dispute between Ammonius and Philoponus. Ammonius’ opposition is presented by Philoponus as a defence of Aristotle (ὑπὲρ Ἀριστοτέλους ἀπολογία). Ammonius’ syllogistic runs as follows. Aristotle works as a physicist in the Physics; he merely talks about the things governed by nature; nature is a principle of motion and rest; natural things are those in which there is a principle of motion and rest; and the things that do not have this principle are not natural things and, hence, the physicist will not take them into account. The sort of extension Philoponus introduces could not be a natural one, according to Ammonius, because it has not itself got a principle of motion and rest, nor does it increase or change or undergo locomotion, generation and corruption.320 Thus Philoponus’ extension of place does not fit the study of physics. Ammonius bases his objection on the Aristotelian intention to examine the natural place of natural things. He thinks that Aristotle does not consider this kind of extension to be the place of natural bodies, for it is not natural itself. Reasonably Aristotle, Ammonius said, holds the view that the only natural kind of place to be found is the limit of the surrounding body in respect of containing the contained: [P12] εἰκότως οὖν τὸ μὲν τοιοῦτον διάστημα οὔ φησι τόπον εἶναι τῶν φυσικῶν σωμάτων εἴτε ἔστιν εἴτε μή (οὐδὲ γάρ ἐστι φυσικόν), μόνον δὲ εὑρίσκει ἐν τοῖς φυσικοῖς

ὄντα τόπον τοῖς σώμασι φυσικὸν τὸ πέρας τοῦ περιέχοντος καθὸ περιέχει τὸ περιεχόμενον. (in Phys., 583.25-29)



It is understandable, then, that he (e.g. Aristotle) denies that an extension such as we describe is the place of natural bodies, whether it exists or not (for it is not natural), and that the only natural place for bodies that he finds among natural things is the boundary of the container with which it contains the contained. (trans. Furley 1991: 46)

Philoponus’ reply (in Phys., 583.30-584.4) starts with the point made by Ammonius in text [P12], namely that Aristotle did not discuss whether or not the extension of place exists. Ammonius’ view may be plausible under two conditions: (a) if Aristotle never tried to show that the extension either exists or not in the Physics; (b) if Aristotle’s only worry was to show that such extension cannot be the natural place of bodies; indeed, then, Aristotle was not denying the existence of a physical extension as such, but only the possibility that this extension is the place of natural bodies. Ammonius appears in [P12] saying that whether this extension exists or not, Aristotle does not consider it as the physical place of physical bodies. In other words, he suggests that the existence of such extension does not imply that the 320 Philoponus,

in Phys., 583.15-23.

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extension is physical. However, I think that Philoponus is right in replying that Aristotle’s view is stronger. For Aristotle explicitly attempts to demonstrate that no extension other than the corporeal exists in his discussion about place and void (Physics, IV.1-9). The philosophical inconsistency which Ammonius attributes to Philoponus’ extension of place is that its immobility and unchangeability exclude it from the discussion about physics. Natural philosophy deals with beings that undergo change (μεταβολή) of any kind such as locomotion, generation, growth and diminution or, as Aristotle claims, the physicist should acquire knowledge of natural bodies which are ruled by a principle of motion and rest. It is not clear, however, what Ammonius means when he claims that Philoponus’ kind of extension should be excluded from the discussion about physics. Does Ammonius imply, for instance, that this kind of extension is not a physical object in the sense in which a corporeal extension is? Philoponus’ claim is that holding the view that place is immobile and unchangeable does not require a non-physical concept of place. Aristotle too establishes a theory of immobile, unchangeable notion of place in the Physics.321 For this reason, Philoponus exploits several examples taken from Aristotle to show that the same conditions are used in his theory of place as in Aristotle’s.322 Both the immobility and unchangeability of place are defended by Aristotle (see Phys., 212a18-21 and 211b23-25). If place qua place changes, holds Philoponus, then it should change with respect to either substance or quantity or quality or place.323 Place could change neither with respect to substance, since it is not itself a substance, nor with respect to quality, since it is not a quality, nor with respect to quantity in the sense that it cannot increase or diminish, nor with respect to place for there will be some other place of the place, which is absurd.324 The extension of place, as we have discussed in the previous chapters, is not subject to any kind of change, just as the Aristotelian doctrine requires. Thus Philoponus replies to Ammonius, ‘If he [i.e., Aristotle] means place to be unchangeable, then he would not reject the extension as the place of natural bodies because of its unchangeability: he attempted to do away with it for this reason, that he believed that such an extension as we describe does not exist at all.’325 The ontological dif321

578.4).

Philoponus states that he follows the principles Aristotle set out in the Physics (in Phys., 577.10-

322 Philoponus,

in Phys., 584.4-25. Obviously referring here to Aristotle’s theory of κίνησις (μεταβολή): ἀνάγκη τρεῖς εἶναι κινήσεις, τὴν τε τοῦ ποιοῦ καὶ τὴν τοῦ ποσοῦ καὶ τὴν κατὰ τόπον, Phys., 225b7-8. Also read Physics, 224b35-225a10. 324 Griffin (2012: 163-164) points out an argument concerning Proclus’ conception of immobile place which, I think, is similar to Philoponus’ argument about place’s unchangeability with respect to place: ‘[b]ut place itself, which Proclus conceives in Aristotelian terms as the place embracing the cosmos, is immobile. If it were to move, it would require some place in which to move, and place would in turn require a place. Since this is impossible, as Theophrastus and Aristotle agree, place must not move (612.7).’ 325 Philoponus, in Phys., 584.25-28 (trans. by Furley 1991: 47-48). 323

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ference between the extension of place and bodies filling it is drawn within the framework of natural philosophy; being immobile and unchangeable does not imply that something is not physical even if it does not meet the definition of a physical being like a corporeal physical being. Natural philosophy deals with various natural things that are immobile, as for instance the centres of the spheres, the poles326 and souls, which, according to Aristotle, are not moving too; all these things belong to the task of the natural philosopher, even though they are bodiless and at rest, as after all Philoponus’ extension of place is.327 It is striking that Philoponus does not repeat any argument exposed in the digression on place as an afterthought defending his view against Ammonius. He rather remarks through the Aristotelian text that Ammonius missed the point of the suggested conception of the extension of place. At first glance Ammonius’ point seems to be futile, for it is obvious that many natural things are incorporeal but relate to natural bodies and the study of physics examines them, as for instance, the soul. But I am inclined to think that Ammonius’ critique could be expressed also by modern scholarship. In an attempt to guess what bothered Ammonius in Philoponus’ account of place, I will proceed to the following remarks. Such a critique does not arise from the ontological difference (ἑτερότης) between place and body. The ontological status of place has a clear aim to show that place is the physical extension filled with physical bodies, though Philoponus’ conception of place does not attach place to corporeality, in the sense that the Aristotelian tradition does. In addition, as we saw in Chapter 3, a cautious reading of the digression on place leads us to the conclusion that Philoponus’ extension theory does not establish the place of intelligible entities (such as the Intellect, the cosmic Soul, and the ideas) nor the place of mathematical objects and geometrical figures. The central goal—through examples pertaining to our direct experience with nature such as measurement, the mutual replacement of bodies and the ‘force’ of void—is to explain the nature of the cosmic extension of place filled with the cosmic body. So, I suppose what is troubling about Philoponus’ theory is the definition of place as void, i.e., the absolute place. To detach place from body is a mental operation. To grasp the void Philoponus exploits a number of thought experiments showing that place can be thought of as void. But we saw in Chapters 3 and 4 that Philoponus proposes this mental operation in order to comprehend how the void—namely a three-dimensional, bodiless, physical extension—is necessarily the place of bodies and the extension in which the mutual replacement of bodies, that is locomotion, occurs. An extension of place as such explains better, according to his view, some 326 Rashed argues (2007: 117-119) that this example is a sign that Philoponus was aware of a debate between Alexander of Aphrodisias and Galen also discussed in the Arabic tradition. 327 See in Phys., 584.28-585.4.

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physical phenomena.328 The mental operation defining place in its own right may have led Ammonius to suppose that Philoponus introduces a non-physical extension. It is true to say that Philoponus’ extension of place is not a physical object. But in my view Ammonius’ opposition is partly unjustifiable. Philoponus consciously avoids introducing a notion of place that exceeds the interests of natural philosophy. First, to state the obvious, he does not discuss the place of intelligible entities or mathematical objects anywhere in his commentary. Second, he denies the existence of a separate absolute place within or outside the cosmos by establishing the equality between place and what fills it; he carefully avoids implying that the empty extension of place is not filled with physical bodies. Third, to define place as an empty three-dimensional extension does not amount to a mathematical entity, if Ammonius also had this in mind. Three-dimensional extensionality is also conceived with respect to place, excluding in this way the mathematical aspect of three-dimensional extensionality. Nevertheless, one could argue that if we isolate the absolute space, that is the void, then Ammonius rightly claims that this void extension exceeds the task of natural philosophy. For instance, one could draw on arguments taken from Philoponus’ digression on the void to claim that he truly accepts the absolute void as existent and that this conception cannot define the physical place of physical bodies. One could also assume that the passages of the digressions in which Philoponus isolates the void, deprived of bodies, bring to mind the modern conception of the void, according to which we can actually create a space in which not even air exists. But that would be a terrible anachronism. Sambursky states that Philoponus is a strict adherent of Strato of Lampsacus’ notion of absolute space filled with bodies ‘conceived as an entity in itself’.329 I think that Sambursky’s claim is very strong, especially in the light of the absence of any substantial evidence concerning Strato’s argument. However, it is true to say that Philoponus clearly uses some thought experiments conceptually to grasp the condition of an absolute void and defines void as place: the place of bodies is itself empty. The only way to grasp the condition of absolute void is to think of the extension of place in its own right. But the reality of the absolute space in thought serves, in Philoponus’ account, as the logical step to state that bodies fill something empty and move within it. In this sense, i.e., as a void always filled, Philoponus comprehends the presence of the void in nature. In order to support the argument that Philoponus does not establish a concept of space that does not fit natural philosophy, I would like to draw attention to a 328 The truth and the real nature of the things play a central role for Philoponus (in Phys., 578.2832): ‘But as I said from the beginning and say now, let them either show that there is no such extension and destroy our demonstrations, or, so long as the latter still hold up, we shall not do away with the nature of the facts just because some people thought to argue in this way.’ (trans. Furley 1991: 41, modified) 329 Sambursky 1987: 6.

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passage in Philoponus’ theological commentary on the Book of Genesis, the De opificio mundi, where he discusses whether angels are in place or not. The passage goes as follows (De opificio mundi, 36.6-18): [P13] τοῦτο δέ ἐστιν οὐδὲν ἕτερον ἢ σώματα καὶ μεγέθη τοὺς ἀγγέλους ὑποτίθεσθαι· τὸ γὰρ ἐν τόπῳ εἶναι μόνων ἐστὶ σωμάτων, ἅπερ τριχῇ διέστηκε. καὶ γὰρ ὁ τόπος ἐστὶ διάστημα. δεδείχαμεν δὲ ὅτι μηδὲ σώματα εἰσὶν ἐκεῖναι μηδὲ ἀσωμάτοις οὔσαις ὀργανικὰ σώματα ἐξῆπται ὡς ταῖς ἡμετέραις ψυχαῖς, δι’ ὅπερ οὐ καθ’ αὑτὰς ἐν τόπῳ ἀλλὰ κατὰ συμβεβηκὸς εἰσὶν αἱ λογικαὶ ψυχαί, διὰ τὸ τὰ σώματα αὐτῶν, ἅπερ εἰδοποιοῦσιν, ἐν τόπῳ εἶναι, ὡς καὶ κινοῦνται κατὰ συμβεβηκὸς τοπικῶς

κινουμένων ἐκείνων· αἱ δὲ παντελῶς ἐξῃρημέναι σωμάτων οὐδὲ κατὰ συμβεβηκὸς εἰσὶν ἐν τόπῳ οὐδὲ κινεῖσθαι κατὰ τόπον αὐτὰς τῶν ἐνδεχομένων ἐστί.



But this does not differ from hypothesising that the angels have bodies and magnitudes; for being in place is only of bodies extending in three dimensions and place is extension. We have shown that [the bodiless orders of angels] are not bodies and that they, as incorporeals, are not fastened to organic bodies like the rational souls; for this reason, rational souls are not in place in their own right but accidentally because the bodies, that they endow with form, are in place and they move accidentally because their bodies move. And it is impossible that those [i.e., the angels] that are totally deprived of bodies either are in place accidentally or move in place.

Text [P13] makes a clear distinction, on the one hand, between natural (organic) bodies and bodiless angels and, on the other hand, between rational souls and angels. Apart from the obvious ontological difference between organic bodies and angels, Philoponus states that angels differ from rational souls too. The point that is significant for our purpose is that the discussion about angels does exceed the study of physics. It would be absurd to admit that a bodiless, non-organic entity is in place or moves in it. The only entity that can be (and move) in place is the natural body. The rational soul, exploited in [P13] as an example of a bodiless thing fastened to an organic body, is a subject of the study of physics for it is said to be in place accidentally since the body it endows with form is in place; consequently, rational souls are said to move accidentally in place because their bodies move in place. Angels are not fastened to natural, organic body, like rational souls, and therefore are not in place and they do not move in place. This argument, based on Philoponus’ account of place as presented in the Physics commentary, testifies that he proposes a natural extension of place in which only natural, organic and three-dimensional bodies are. Furthermore, text [P13] asserts that Philoponus consciously avoids involving intelligible entities in the study of physics to which the discussion of the extension of place pertains. To this I would like to add the following remarks as a short deviation from the dispute between Ammonius and Philoponus.

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The conception of space in the intelligible realm (τόπος νοητός) has a long history in late Platonism. Authors like Plotinus, Iamblichus, Syrianus, Proclus and Damascius claim that besides the physical place in the sensible realm there is an intelligible place.330 Philoponus does not seem to endorse such a conception of place, though one can observe similarities concerning the nature of place asserted by late Platonists and Philoponus (of which the most illustrative example is that most of them admit the extensionality of place). The definition of place as void never deprived of body, along with Philoponus’ statement that place is ontologically—i.e., essentially—different from the bodies that come to be in it, may have had a great impact on medieval and early modern thinkers, though the core of such a theory can be seen just as an instance in the evolution of ancient theories of space in the history of science. Edward Grant, for example, discusses in detail the distinction between internal and external space in philosophers such as Jean Buridan, Fransiscus Toletus and others.331 The concept of internal space implies that place is equated to the bodily extension, in the sense that place is the body’s dimensions—an idea that some thinkers, like Duns Scotus, link with the notion of mathematical magnitude. The concept of external space claims that place may well be external to the cosmic plenum, since it is different from bodily extension and it can extend beyond the universe as a separate, three-dimensional voided space. Toletus went as far as to ascribe to Philoponus the conception of an internal space because the latter assumed that space is always filled with bodies and that the three-dimensional extension of place is equal to the three-dimensionality of the body in it, so that the space of a body is nothing more than the internal extensionality of the body. In this sense, place is a proper accident of body and it can be conceived of only as a separate extension by mental operation.332 As Grant (1978: 555) signals, ‘The concept of internal space, whether medieval or early modern, is the physical counterpart of the purely geometric space of Euclid’s Elements.’ Grant’s point shows that apart from the mathematisation of the concept of internal space, it is clearly developed within the concerns of physics. The kind of absolute space adopted by Philoponus, namely the space that is always filled with bodies, does not invoke non-physical or mathematical connotations, and should be conceived of as a physical conception of space, a concomitant (παρακολούθημα) of physical bodies. Even if Philoponus’ extension of place does not meet the definition of a physical being, it is, nonetheless, studied in physics because it still is part of the physical world. In Chapters 2, 3 and 4 we examined Philoponus’ conception of topos. Philoponus’ extension theory suggests a physical extension that subsists. The extension is always filled with bodies, but this does not prevent Philoponus from establishing 330

A concise survey of these theories is offered by Sambursky 1977. Grant 1978: 554-562. 332 Grant 1978: 555, n. 18. 331

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the absolute conception of place, that is void, through mental operation. Isolating the absolute space of which we have no direct experience does not introduce a non-physical concept of topos, as Ammonius accuses his student. Philoponus keeps the discussion about place at the physical realm offering a physical, I would say cosmological, account of place as the extension in which physical bodies and the cosmos are located and move according to the order established by the demiurge. If asked to summarise, in conclusion, Philoponus’ definition of place, I would paraphrase his words throughout the digressions on place and void in the following manner: Τόπος is the three-dimensional (τριχῇ διαστατὸν) extension (διάστημα), which in its own definition extends over and above the bodies that come to be in it; it is space (χώρα) for body, and dimensions alone, void (κενὸν), immobile, and separate from all substance and matter. This extension neither ever is nor ever can be empty of all body, but rather it is something (ontologically) different (ἕτερον τι) from bodies, empty in its own definition; an extension concomitant to and equal to the natural bodies which always fill it (πλήρωσις). Having looked in detail at Philoponus’ theory of place in both the commentary’s digressions, the study now turns to Philoponus’ main opponent, namely Aristotle, and his attack on the Aristotelian definition of place and its reception by the Peri­ patetic tradition.

Chapter 5

Philoponus against Aristotle and the Peripatetic Tradition Philoponus, in the first part of the digression on place, mainly aims to challenge, or to redetermine, the following Aristotelian assumptions: (i) three-dimensionality is attached only to body, not to place;333 (ii) there is equality between place and what is in place;334 (iii) place cannot be an extension;335 and (iv) place is the first immobile limit of the surrounding body.336 The second part of the digression on place (in Phys., 563.26-567.28) deals with the last point, namely the Aristotelian definition of place as the limit of the surrounding body. Philoponus argues that Aristotle’s definition is insufficient for it fails to support even some of the main assumptions which Aristotle himself approves as true for place. Furthermore, as we shall see, Aristotle’s vagueness is the cause of misleading assumptions concerning the motion of bodies and the place of the heavens. Philoponus’ critique consists of five arguments in total. First, he repudiates the two-dimensionality of place implied by the definition; second, he attacks the Ari­ stotelian conception of equality between place and what is contained in it; third, he objects to the Aristotelian assumption of place’s immobility; fourth, he aims at making apparent how the Aristotelian definition is responsible for false opinions, as far as the place of the sphere of fixed stars is concerned. Finally, the fifth argument shows how the definition of place as the limit of the surrounding body fails to explain the motion of bodies. Philoponus’ criticism focuses on showing that the Aristotelian account of place can be turned against several aspects of place which Aristotle accepts as true. Having revealed his conception of place as a bodiless, unaffected and three-dimensional extension, the commentator applies his thoughts to the Aristotelian definition in order to see whether this definition is correct and the propositions derived from it are necessarily true. Eventually, the whole chapter points out the differences between the Aristotelian account that proposes a relativist conception of place and the Philoponan account supporting a substantialist conception of place.

333

Physics, 209a4-6. Ibid., 211a1-2; 211a27-29; 212a29-30. 335 Ibid., 211b19-25. 336 Ibid., 211b19-25; 212a5-6; 212a14-30. 334

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5.1 Aristotle’s definition of place In this section I will attempt to map the most important features of Aristotle’s definition of place. Aristotle initially defines place as the limit of the containing body (Phys. 212a5-6) and a few lines later as the first immobile limit of the containing body (Phys., 212a20-21). The first step towards clarifying how Aristotle conceives of place is to consider what it is for a thing to be contained, i.e., to be in a place. Then we will further ask what it means for something to be contained by a limit and determine this kind of limit. According to Aristotle’s definition of place, the proper place of a body is the immediate limit that contains it. For example, the place of earth is not only the whole universe in which it is contained or just the field in which the tree stands; instead the immediate air and earth that surround the tree should be conceived of as its proper place. In other words, the place of the tree is the limit of air (and earth) that is in direct contact with the (limit of the) tree, and which, so to speak, separates the position occupied by the tree from the position occupied by the plants next to it. But how does Aristotle arrive at this conception of being in place? To begin with, he spells out the distinction between common and proper place in terms of what is said to be τὸ καθ’ αὑτὸ and τὸ κατ ’ ἄλλο of a subject. In the same way, something can be in place in its own right (proper place) or by virtue of something else (common place): [A3] ἐπεὶ δὲ τὸ μὲν καθ’ αὑτὸ τὸ δὲ κατ ’ ἄλλο λέγεται, καὶ τόπος ὁ μὲν κοινός, ἐν ᾧ ἅπαντα τὰ σώματά ἐστιν, ὁ δ’ ἴδιος, ἐν ᾧ πρώτῳ ( λέγω δὲ οἷον σὺ νῦν ἐν τῷ οὐρανῷ ὅτι ἐν τῷ ἀέρι οὗτος δ’ ἐν τῷ οὐρανῷ, καὶ ἐν τῷ ἀέρι δὲ ὅτι ἐν τῇ γῇ, ὁμοίως δὲ καὶ ἐν ταύτῃ ὅτι ἐν τῷδε τῷ τόπῳ, ὃς περιέχει οὐδὲν πλέον ἢ σέ) […] (Physics, 209a31209b1)

Something can be said of a subject either in virtue of itself or in virtue of something else; and there is place which is common and in which all bodies are, and which is the proper and primary location of each body. I mean, for instance, that you are now in the world because you are in the air and it is in the world; and you are in the air because you are on the earth; and similarly on the earth because you are in this place which contains no more than you … (trans. Barnes 1991, vol. I: 52)

Text [A3] claims that the common place of all natural bodies is the universe. But when we come to specify the exact place of a body—i.e., its proper place—the universe cannot be the primary place of that body, though it is still its common place. The ‘τὸ κατ ’ ἄλλο’ case implies that I am in the universe by virtue of something else, but my proper and primary place is the part of air and the part of earth that now contain me. I am in the universe and on earth by virtue of something else (κατ ’

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ἄλλο)—i.e., by virtue of my other places.337 According to text [A3], something is the

place of something else, for it has a specific, such-and-such relationship with the contained body; in other words, it is place as far as it contains the body which is in contact with it. Place, which cannot contain two or more bodies, is the primary container of each body.338 However, because my proper place is thought to be a part of the place of the universe, I can also claim that in this respect I am in the universe in my own right and not just by virtue of something else.339 The Aristotelian definition of place necessitates that I am contained by the limits of the bodies that are immediately in contact with me. In this sense, Aristotle’s account suggests a sort of relativist theory according to which the proper and the common place of a body is always considered in relation to the body whose place it is and, secondarily one would say, in relation to the bodies that surround it. Scholars, however, hesitate to accept such a claim. King is the only one who attributes to Aristotle a relativist theory of place with not much justification.340 Morison and Bostock are reluctant to accept a relativist interpretation of Aristotle’s view of place. Morison denies that Aristotle’s account is strictly relativist, though he recognises that, for Aristotle, a body is located in relation to its surrounding bodies, and concludes that this question makes no sense at all when dealing with Aristotle’s account.341 But even if we admit that Aristotle’s account is relativist in a loose sense, this is enough to categorise this account among the theories suggesting a relative place. Bostock, on the other hand, seems not just to disregard the fact that Aristotle proposes a relative place, but rather implies that, according to Aristotle, places of bodies are absolute.342 I would agree that Aristotle may not have had the intention or the interest to characterise his view as relativist. Nevertheless, if we are to evaluate the Aristotelian theory of place in the course either of the history of ancient physics or, generally, of the history of science, one cannot ignore Aristotle’s view that bodies are somewhere in their own right and by virtue of something else, which suggests a kind of relativism. 337 Or, as Morison (2010: 75) argues about how Aristotle conceives of something as being in a place, ‘To be somewhere is to be either in a place, or appropriately related to something in a place, so “in a place” is the primary meaning of “somewhere”.’ 338 As Morison (2002: 59) puts it, ‘The idea behind a proper place is the following. My places differ in that some are more precise than others. The notion of a “more precise” place is easily defined: x is a more precise place than y iff anything in x is in y, but not vice versa.’ 339 However, it is crucial to underline that the universe, according to Aristotle, is not in place in the sense that nothing else exists outside the universe that contains it (De caelo, 278b21-279a12). In the Physics Aristotle explicitly says that the universe is not contained in anything else and, therefore, is not somewhere as a whole. Since all things are in the universe, nothing is external to it. The universe is in place accidentally (Physics, 212b7-22). The parts of the universe are in place, and in this sense the universe is said to be somewhere accidentally without the need of an external container. On Philoponus’ reaction to this puzzle of the Peripatetic tradition see section 5.5. 340 King (1950: 91) admits that Aristotle’s account is a relativist explanation of place. 341 Morison 2002: 170-171. 342 Bostock 2006: 133-134.

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The distinction between common and proper place also seems to be present in another text from Physics IV.4.343 The text rephrases how bodies are in place in their own right (καθ’ αὑτὸ) and by virtue of something else (κατ ’ ἄλλο). In the case of bodies in a vessel, the mutual replacement (ἡ ἀντιμετάστασις τῶν σωμάτων) between air and water (or their parts) happens in the thing in which they are (i.e., the vessel), that is to say in their proper place;344 it does not happen in the place in which they come to be (e.g., this room), which (place) is part of the broader place (e.g., the air), which is the place of the whole universe. In other words, in the case of the mutual replacement of bodies, the water and the air are primarily contained in their proper place, rather than in the other places in which they are contained (the whole earth, the whole air, the universe). Their proper place is the limit of the vessel; this is how they are meant by Aristotle to be in a place. So we need to explain what kind of limit Aristotle means. In the Metaphysics, limit (πέρας) is defined as follows: [A4] πέρας λέγεται τό τε ἔσχατον ἑκάστου καὶ οὗ ἔξω μηδὲν ἔστι λαβεῖν πρώτου καὶ οὗ ἔσω πάντα πρώτου, καὶ ὃ ἂν ᾖ εἶδος μεγέθους ἢ ἔχοντος μέγεθος, καὶ τὸ τέλος ἑκάστου […]. (Metaphysics, 1022a4-6)

We call limit the last point of each thing, i.e. the first point beyond which it is not possible to find any part, and the first point within which every part is; it is applied to the form, whatever it may be, of a spatial magnitude or of a thing that has magnitude, and to the end of each thing … (trans. Barnes 1991, vol. II: 77)

The definition of peras as ‘the last point of each thing’ in the Metaphysics seems to be used in the Physics where Aristotle defines place as ‘the extremities (if there is no extension over and above the bulk of the body which comes to be in it).’345 The term ‘extremities’ (τὰ ἔσχατα) refers to the limits of the bodies that define the boundaries of each body and therefore its place. In addition, based on the latter determination of place it seems that Alexander of Aphrodisias and Simplicius went on to interpret Aristotle’s definition of place as limit with the concept of surface (ἐπίπεδον, ἐπιφάνεια).346 To the extent that the limit of an object, and especially the limit of a physical body, is a surface, the place of a body should be identical to its surface.

343 ‘When the whole vessel changes place, the place in which the part moves is no other, but the same; for the air and water or the parts of the water exchange in the place they are, but not in the place they come to be, which is part of the place that is the place of the whole universe’, Phys., 211b27-29. 344 Also in Phys., 211a28-29: τοιοῦτος δ ’ ὁ πρῶτος ἐν ᾧ ἐστιν. 345 Aristotle, Physics, 211b8-9, trans. by Barnes 1991, vol. I: 56. 346 See Alexander of Aphrodisias, fr. 64 (=Rashed 2011: 213): ἐπίπεδον λέγει ἀντὶ τοῦ ἐπιφάνεια . ἀγγεῖον μὲν οὖν δοκεῖ ὁ τόπος ᾗ περιέχει, ἐπιφάνεια δὲ ᾗ πέρας τοῦ περιέχοντος; and Simplicius, in Phys., 587.16-22: διὰ τοῦτο καὶ ἐπίπεδον δοκεῖ ὁ τόπος, τουτέστιν ἐπιφάνεια, μῆκος καὶ πλάτος ἄνευ βάθους ἔχων. Philoponus too uses the term ‘surface’, ‘ἐπιφάνεια’ (in Phys., 546.2).

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A limit stands as the boundary of each body, separating one body from another. Being surrounded by a limit of something means that that limit is in contact with the surrounded body. Each time I am in contact with a specific part of the air, of the earth, and sometimes of other bodies around me, for instance, the chair on which I am sitting now or the table on which my hands now lie. All these bodies that are in contact with me are somehow limiting, determining my proper place. According to Aristotle, place primarily contains bodies, and it is a limit, in the sense that it cannot be infinite (ἄπειρον). Place limits bodies; the limits individualise the positions that bodies occupy. Moroever, since (proper) place is the extreme (or the first, as the definition says) limit of a body, it (place) should also be immobile. Having said what it is for a body to be in place and how the limit of a place is considered to be immobile by the Aristotelian definition, we can now move on to Philoponus’ first objection which depends on the very nature of what it is to be a limit of something else. For the problem with this kind of limit, as Philoponus will point out, is that a surface has two dimensions and lacks depth.

5.2 The equality between place and the bodies in it Philoponus’ critique of Aristotle’s definition of topos consists of five arguments in total (in Phys., 563.26-567.28): i) place cannot be the limit of the container, ii) place must be equal to what is in place, iii) place must be immovable, iv) the heavens must be in place, and v) place cannot be a two-dimensional surface. It seems, however, that Philoponus did not come up with this critique by himself. Already Theophrastus, Aristotle’s pupil, appears to have pointed out five difficulties concerning Aristotle’s account of place. Simplicius reports that Theophrastus posits the following five difficulties: i) that body will be in a surface, ii) that place will be moving, iii) that not every body will be in place, since the sphere of the fixed stars will not be in place, iv) that if the spheres are taken together, the whole of heaven will not be in place, and v) that the things being in place will no longer be in place if the bodies surrounding them are removed.347 Whether Theophrastus’ points, as presented by Simplicius, are in fact attacking Aristotle or not is a matter of debate in modern scholarship.348 The debate on Theophrastus’ attitude to the view of his master is not our concern here. For our purpose, we need to state that the simila­ rity between Philoponus’ arguments against Aristotle’s account and Theophrastus’ remarks shows that the former took the latter’s difficulties into consideration.349 347

See Simplicius, in Phys., 604.5-11; Fortenbaugh et al. 1992: 302, fr. 146. To mention some of the main instances of this debate: Jammer (1993: 23, 53) holds that Theophrastus objects to Aristotle’s account of place. Algra (1995: 231-248) seems to be in favour of the opinion that Theophrastus’ fragments show a ‘free handling of the Aristotelian material’. Sharples (1998: 48-53) thinks it is unclear whether Theophrastus repudiated Aristotle in order to propose a different theory of place. Finally, Morison (2010: 68-103) denies both that Theophrastus rejected Aristotle and that he proposed a new theory of place. 349 Golitsis (2008: 179) and Algra—Ophuijsen (2012: 1) accept that Philoponus uses Theophrastus. 348

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Indeed, in what follows we shall see that most of the points made by Theophrastus are also discussed by Philoponus whose arguments certainly aim at deconstructing the Aristotelian account. Philoponus argues that the concept of limit raises a crucial difficulty for Aristotle. If what is in place is a body, then it is in place exactly by virtue of being a body. When something is contained in the surface (ἐν τῇ ἐπιφανείᾳ) of the container, as Aristotle affirms, it must be in the container by virtue of being a body—i.e., by virtue of being a three-dimensional body. But is it legitimate to hold that three dimensions can be contained in a two-dimensional surface? Apparently, Philoponus points out, this is impossible; for if something is contained in the surface of the container, not by virtue of being a three-dimensional body, then this surface cannot be the place of that body. His attack is intended to underline the conceptual inconsistency with respect to natural facts. The whole discussion, as the following passage shows, relates to the question of what it means to be contained: [P14] εἰ γὰρ τὸ ἐν τόπῳ ὂν οὐδὲν ἄλλο ἐστὶν ἢ τὸ σῶμα, καὶ οὐ κατὰ ἄλλο τί ἐστιν ἐν τόπῳ ἢ καθὸ σῶμά ἐστι, τὸ δὲ ἐν τῇ ἐπιφανείᾳ τοῦ περιέχοντος ὂν οὐ καθὸ σῶμά ἐστιν ἐν αὐτῇ ἐστι (τὸ μὲν γὰρ σῶμα τριχῇ ἐστι διαστατόν, ἐν δὲ τῇ ἐπιφανείᾳ καθὸ τοιαύτη ἐστὶν οὐ δύναται εἶναι τὸ τριχῇ διαστατόν), οὐκ ἄρα ἐπιφάνειά ἐστιν ὁ τόπος. (in Phys., 563.27-31)

For if what is in place is nothing else but body, and it is not in place by virtue of something else, but rather by virtue of being body, but what is in the surface of the container is not in it by virtue of being body (for body is three-dimensional, but the three-dimensional cannot be in such a surface), then place is not a surface.

The two-dimensionality of a containing limit (surface) does not correspond to the three-dimensionality of any bodies which are contained in it. The philosophical problem, which Philoponus detects in [P14], is that a two-dimensional surface cannot entirely receive the three-dimensional body, for, contrary to Aristotle’s claims, the limit neither is entirely in contact with the body, nor does it contain the whole body.350 The lack of the third dimension (depth) in the limit makes place an envelope containing a body. At first glance Philoponus’ argument seems to be based on a serious confusion. The two-dimensional limits of a (three-dimensional) body seen together as one single limit make a three-dimensional limit. For example, the two-dimensional surfaces of a pyramid are made of four two-dimensional triangles, but all of them together are arranged in a three-dimensional space or constitute a

350 Aristotle’s physics claims that the cosmos is continuous because physical magnitudes are in contact with each other. The primary meaning of the continuous is that the limits of bodies are in contact. See Physics, 227a10-13; Ribera-Martin 2017: 225-228.

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three-dimensional space. In other words, the fact that a surface has no depth does not make it unfit to be three-dimensional. In text [P14] Philoponus argues that the Aristotelian definition of place links the place of a body to its two-dimensional surfaces. A similar attempt to restrict the shape of a body to its limit is attested to by Proclus: though Euclid calls ‘shape’ what is enclosed by a limit, Posidonius restricts the shape to the limit (for instance, the circumference of a circle).351 But what I think is Philoponus’ point in text [P14] is the following: since Aristotle attributes three-dimensionality only to body and nowhere affirms the three-dimensionality of the limits of a body (instead he admits that a limit can be one-dimensional or two-dimensional), he fails to show the equality between place and body. In this sense, place cannot be the limit of a body. Therefore, Philoponus suggests detaching the notion of surface (limit) from the definition of place, even if he is attempting to show it in a rather vague way. Philoponus defends the existence of a bodiless extension, which entirely fits on (ἐφαρμόζειν) the body that comes to be in it. As we have seen elsewhere, the three-dimensionality of the extension of place and that of a body fit on to each other, and in that sense they are considered equal.352 Connecting this thought to the current argument, we could say that the only way to conceive of something in place is to conceive the three-dimensionality of both the container and the contained or, in Philoponus’ terminology, to conceive that the three-dimensionality of the extension of place fits on the three-dimensionality of the body. All three dimensions of bodies should be in place. Thus those who accept a definition which implies that place is the limit of the surrounding body cannot answer the question how the depth of the body is in the surface, since a surface possesses only two dimensions (breadth and length). Philoponus puts forward another argument suggesting that the Aristotelian definition of place goes against the equality between place and what is in place (in Phys., 564.3-14). The principle of equality between place and what is in place is considered by Aristotle to be one of the true and commonly accepted characteristics of place.353 Yet, Aristotle’s theory undermines this principle, for it is impossible for a two-dimensional surface to be equal to a three-dimensional body. Aristotle suggests that the place of a body in a sense contains the three dimensions of the body, but this is not enough to determine the equality of place and body. The definition of place needs to be consistent with all the aspects of what it means for a body to be in place. Despite the obvious inconsistency of linking place with the limits of a body, Philoponus poses a possible objection to his own argument. For instance, one might claim that place is equal to what is in place when place fits on the limit of the contained body. The question is whether or not the place fitted on the limit indicates 351

See Proclus, in Eucl., 143.5-21. See Philoponus, in Phys., 558.19-559.9; 560.23-561.3. 353 See Physics, 211a2; 211a27-29. 352

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equality between place and what is contained in the limit. Philoponus takes it that the objection does not say that place is equal to what is in place, but rather that place is equal to the limit of what is in place, which (i.e., the limit) in its own right is not even in place.354 Aristotle fails to show, through his definition of place, that the limit can be equal to the whole of the body contained in it. So, how is it possible to say that the limit is equal to the contained body, and that place is equal to the limit? I think the key is the notion of ἐφαρμόζειν. The extension theory, as adopted by Philoponus, presupposes that bodies are in place if all their dimensions fill the place. In other words, something is not considered as being in place when at least one of its dimensions does not occupy an equal position to its entire bulk within the extension. This is how a body fits on (epharmozein) the bodiless three-dimensional extension of place in order to gain equality between place and a body filling it. The Aristotelian definition of place as the limit of the surrounding body implies that only the surface of the body is in place—i.e., its breadth and length, but not its depth. If we were to provide an analogy of how a body is in place, according to Aristotle, then we could say, perhaps exaggerating, that Aristotle’s concept of place resembles childish paintings. In a child’s painting bodies appear to be in place: the bodies can be distinguished in place by the mere fact that they have distinct limits from one another, but these limits do not signify that the bodies’ depth is actually in place; the limits just outline the figures. In that sense, place is only the outline of the body’s position. The principle of equality between place and what is in place collapses, since the limit of the surrounding body cannot be entirely equal to that body. Furthermore, Aristotle’s assumption could lead to various complications. For example, some parts of the body will be in place, but others will not, and thus place will be either greater or smaller than the whole body, which is impossible. The three-dimensionality of bodies cannot be ignored in the definition of place exactly because bodies occupy as much place as the extent of their three dimensions. Thus, a surface cannot be equal to a body, just as a line cannot be equal to a surface nor a point to a line (in Phys., 564.12-14). A different argument—yet related to the context of the digression on place— against Aristotle’s definition is made by Philoponus in his commentary on the Meteorology. He argues that Aristotle says that heavy bodies move to the centre and to what is around the centre because the centre, not being extended, is not a place. Aristotle says this in order to avoid people thinking that the centre towards which heavy bodies move is a place. When Aristotle wants to speak about the place of the 354 The objection is introduced as follows (in Phys., 564.6-9): ‘If one were to say, “I say that place is equal to what is in place when place applies to the limit of the contained,” let him be aware of the fact that he is not saying place is equal to what is in place, but rather equal to the limit of what is in place, which in its own right is not even in place.’ The ὅπερ (in Phys., 564.9) in the quoted passage refers to the limit that is not in place per se because it cannot exist per se (according to Aristotle). I owe this last observation to Frans de Haas.

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heavy bodies that is ‘down’, i.e., towards the centre, he admits that these bodies are around the centre and not on the centre which is the middle, not extended, point. This shows that the place of the heavy bodies is neither a body that contains the centre and with which the heavy bodies are in contact (and thus contained) nor a surface of a body, since the centre is not extended. Therefore place cannot be the limit of the surrounding body but rather an extension (in three dimensions).355 Aristotelian physics suggests that something is in place only because it is contained by the limit of its surrounding body with which it is in contact. Both the principle of equality between place and what is in it and the conception of limit indentified as place of a body, as Aristotle builds them, are repudiated by Philoponus. As Philoponus puts it elsewhere, the proponents of the Aristotelian view cannot save the idea of place’s equality to what is in it, for place within the Aristotelian framework is equal to the perimeter of the body and not to its entire three-dimensionality.356 This critique is based on the model that Philoponus proposes on how we should conceive of a natural body being in the physical extension of place. Philoponus’ thesis is that equality between place and what fills it (and not just with the limit of the contained body) is based on the principle of fitting a bodiless extension on to body and not being contained in a container. So, equality of place and what is in place means equality between the three-dimensional extension and the three-dimensionality of the body. Aristotle’s two-dimensional surface cannot be the place of natural three-dimensional bodies, because in that case place determines only their perimeter. Philoponus’ extension theory, on the other hand, permits place to be totally equal to what fills it, for the body comes to fill the extension with all its dimensions.

5.3 The immobility of place Aristotle, after defining place as the limit of the surrounding body, goes on to claim that the place of bodies must be immobile (Phys., 212a14-21). As was said in section 5.1, the universe seems to be the common place of all bodies. This can easily be understood, for all bodies are parts of the universe, and thus their places are parts of the place of the whole universe. Proper places are parts of the place of the whole universe, but it seems that they can also share other characteristics of the place of the universe, for instance, its immobility. This, I assume, is the reason Aristotle claims that the places of bodies are immobile. The idea seems to be that if the place of the universe (the common place of all bodies) is immobile, then the proper place of bodies should be immobile too. Aristotle holds that place is an immovable vessel, whereas the vessel is a transportable place. A body that moves in a moving body and changes is actually in a container in the sense of being in a vessel—as, for instance, 355 Philoponus,

356 Philoponus,

in Meteor., 35.9-21; Aristotle, Meteor., 340b19-23. in Phys., 587.26-30.

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in the case of a boat on a river. Place is immovable because the whole river is the place of the boat, and the whole river is immovable: [A5] ἔστι δ’ ὥσπερ τὸ ἀγγεῖον τόπος μεταφορητός, οὕτως καὶ ὁ τόπος ἀγγεῖον ἀμετακίνητον. διὸ ὅταν μὲν ἐν κινουμένῳ κινῆται καὶ μεταβάλλῃ τὸ ἐντός, οἷον ἐν ποταμῷ πλοῖον, ὡς ἀγγείῳ χρῆται μᾶλλον ἢ τόπῳ τῷ περιέχοντι. βούλεται δ’ ἀκίνητος εἶναι ὁ τόπος· διὸ ὁ πᾶς μᾶλλον ποταμὸς τόπος, ὅτι ἀκίνητος ὁ πᾶς. ὥστε τὸ τοῦ περιέχοντος πέρας ἀκίνητον πρῶτον, τοῦτ’ ἔστιν ὁ τόπος. (Phys., 212a14-21)

Just, in fact, as the vessel is a transportable place, so place is a non-portable vessel. So when what is within a thing which is moved, is moved and changes, as a boat on a river, what contains plays the part of a vessel rather than that of place. Place on the other hand is rather what is motionless: so it is rather the whole river that is place, because as a whole it is motionless. Hence the place of a thing is the innermost motionless boundary of what contains it. (trans. Barnes 1991, vol. I: 57)

The analogy of the boat on the river suggests that place should be considered as immovable inasmuch as it is seen as the common place in which a body is. Furthermore, the proper place of a body must be immovable because it is part of the immovable universal place. Aristotle redefines place as the first immovable limit of the containing body. But this, I take it, means the common place of all bodies, that is to say the universe. Additionally, I should point out that this also seems to refer, for Aristotle, to the proper place: the first immovable limit, in the example of the boat floating on the river, is the whole river. The immobility of place ensures that we can distinguish within the universe upper, middle and lower parts, and specify the position and the direction towards which heavy or light bodies move.357 In order to assimilate fully the development of Philoponus’ critique we need to go through three parts of Philoponus’ commentary on the Physics: first, his comments on the distinction between ‘proper’ and ‘common’ place (in Phys., 514.15-515.8); second, the digression on place, where he criticises Aristotle’s conception of immovable places (in Phys., 564.14-565.1); and, third, his exegetical comments and rejection of Aristotle’s analogy of a boat floating on a river (in Phys., 586.9-24; 587.9-588.27). To begin with, the exegetical comments on Aristotle’s distinction between common and proper place are of importance for our investigation. Philoponus explained this distinction, established by Aristotle, in the following manner. There is the place in which I am in my own right (καθ’ αὑτὸ) and primarily (πρώτως), and there is the place in which I am by virtue of something else (κατ ’ ἄλλο). The universe is not my primary place, since I am in it by virtue of something else. The same goes for air and earth: I am in these places by virtue of something else. The place in which I primarily am is the specific part of air and earth that contains me right now. Philoponus 357 Aristotle,

Physics, 212a21-28.

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phrases the Aristotelian concept of proper place by saying ‘this is primarily and in the proper sense the place of each body, the one that immediately contains only each one (i.e., of the bodies) and separates it from other bodies.’358 The notion of proper place is correctly conceived of by Philoponus within the Aristotelian framework: place proximately or immediately contains just one body at a time and marks off the boundaries of that body from other bodies. The argument against Aristotle’s immobility of place in the digression on place is based on that understanding of the concept of ‘proper place’, as we shall see later. Let us now turn to the third lecture on Physics IV.4, which appears right after the digression.359 In this lecture Philoponus explicates the analogy of the boat on the river according to his conception of the distinction between common and proper place. He argues that Aristotle’s claim is that when something moves in a movable thing we say that something is in something else as in a vessel, and not as in place. In the example of the boat which is moving on the river, the boat moves along with the stream of water and thus the water immediately containing the boat is considered more as a container-vessel than as a container-place (using Aristotle’s words). But the vessel is a case of transportable place (μεταφορητός), and what we are attempting is to establish the immobility of place: if place must be immovable, then the stream of the river is not this kind of place. Aristotle, as Philoponus underlines, considers the whole river to be the immovable place of the boat in order to avoid the absurdity of a movable place. The commentator argues that Aristotle meant that the common place of bodies is immovable, rather than the place in which things primarily are—i.e., their proper place. The outcome of Aristotle’s argument is that when something moves in the air and the air moves along with it, it could be said that that body is in a vessel, rather than in place. But when air is considered as a whole and stands still, then it could be said that the body is in place, for the place of the body should be immovable. This is how Philoponus explains the Aristotelian argument. Considering only the common place of all bodies as immovable does not seem to be an adequate solution for Philoponus. Right after the exegesis of the boat analogy, he attacks it with the following argument (in Phys., 587.30-588.27). If there is a body in the river under the water, for example a rock, and the water subsides, then the rock is no longer contained in the surfaces of the water, but now the surfaces of air contain it. The rock now has a different proper place without itself having moved at all. Hence, the place moves, and at the same time there also is a formal change of place (κατ ’ εἶδος): the place of the rock is no longer the water, but the air.360

358 Philoponus,

in Phys., 515.5-7. Ibid., 586.9-24; 587.9-588.27. 360 οὐδὲ γὰρ ἁπλῶς κατ ’ εἶδος ἀκίνητον δεῖ εἶναι τὸν τόπον, ἀλλὰ καὶ κατ ’ ἀριθμόν, in Phys., 588.1-3. The distinction that Philoponus draws is between different surrounding bodies and bodies different 359

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We should pause here to add a comment to the modern discussion about Aristotle’s immovable place, at least to the extent that it contributes to the understanding of Aristotle’s argument. Morison introduces Aristotle’s definition of place in a broader sense, according to which we deal with ‘an account of what it is for something to be located.’361 Based on that ground he interprets the analogy of the boat on the river as follows: So, for instance, the water which surrounds a boat on a river and which moves with it when the boat drifts downstream, carries the boat, whereas the whole river, which is immobile, locates the boat; the boat moves around within the whole river (considered as a ‘geographical entity’) rather as moving things move around within the universe. (Morison 2010: 77)

Morison argues that the river locates the boat, although the river is not the exact and proper place of the boat. It is not clear at all that Aristotle wants, using the example of the boat, to define the location of the boat in a broader sense and not to determine the proper place of the boat. Philoponus takes it that Aristotle is referring to the proper place and points out the complications of such an account. If we follow Morison’s interpretation, then there is, I believe, a serious objection to confront: the analogy Aristotle draws is between the vessel containing water and a boat floating on a river (212a16-18). The vessel is the proper place, according to Aristotle, of the water contained in it (only if the vessel is at rest), whereas the whole river cannot be the proper place of the boat on it, because there is always a specific part of water that contains the boat, which is its actual proper place. From this perspective, I cannot see how Aristotle can be speaking of the location of the boat in a broad sense, since his analogy involves in one of its counterparts the proper place of something (vessel). In my opinion Aristotle gives a weak example that further complicates his own theory. In other words, Aristotle would have to prove how his definition of the first immovable limit of the containing place is validated through the example of the boat. The whole river is obviously not the first immovable limit of the containing body, even if we see the whole river as a ‘geographical entity’. I agree with Morison that the whole river might be a way to locate the boat and that the water carries the boat. But I do not see in Aristotle’s text a clear argument that does not contradict his own definition of place. It seems that Aristotle cannot escape the absurdity of moving places, as Philoponus shows, because he cannot explain how the moving vessel cannot be the place of what is contained in it.362 in number, in the sense of several bodies specifying the place of one body (or, to put it differently, in the sense of the number of the surrounding surfaces each time). 361 Morison 2010: 75-76; see also Morison 2002: 150-152. 362 A reasonable criticism of Morison’s attempt to save the Aristotelian argument on the immovable place is introduced by Bostock 2006: 129-134.

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Furthermore, let us take into account the fact that the Aristotelian doctrine implies that the limit of the containing body has a specific relationship to the contained body, namely the container must be in contact with the contained.363 In this case, according to Philoponus, some further complications arise. Suppose that the air around Socrates is not moving, but Socrates moves. Now, whichever part of the air Socrates is in, it is necessary that he has the same particular relation to the air, according to which he is contained in it. In order to save the immobility of place, an Aristotelian proponent would have to commit himself to saying that the limits do not change; they always define the particular relationship between the container and the contained. But then, Philoponus replies, he would have to confront an absurd consequence; for if this is true, then Socrates is in one and the same place, whether he is in the agora or in the Lyceum. Hence, Socrates cannot move in place (κατὰ τόπον). For if Socrates is in place in terms of being always contained within the same limit of air, that is to say having a particular relationship to the air, then locomotion does not play any role in determining that Socrates has changed places.364 The objection found in the digression on place follows the same interpretative lines (in Phys., 564.14-565.1). Again, the difficulty derives from the Aristotelian definition of place, which implies that place and what is in place are determined by the specific relationship between the container and the contained that are in contact. Philoponus briefly discusses another possible objection in favour of the Aristotelian doctrine.365 The objection runs as follows. Place is immovable, as far as we consider the containing surface qua place, but if it is considered as surface it moves.366 Philoponus attacks this objection by providing, again, an example of an immobile body. For instance, if Hypatia does not move around, but stands still, the place containing her—i.e., the surface of the air which is in contact with her—is not the same, because the place changes as the air moves: there is always another part of air containing Hypatia.367 She is all the time contained in different plac363

See Aristotle, Phys., 211b19; 212a6. Additionally, Philoponus considers a possible objection in defence of Aristotle, which he in turn withdraws in Phys., 588.20-27: ‘And if someone says, ‘but it is not moving qua place, for it is a surface, and that is in its own right immobile, since it is also incorporeal’, I reply to this that the surface is not place without any further qualification, for then every surface would be a place, but only in so far as it contains; and as something that contains it changes. For if, while the object that is contained remains immobile, [the surface] at one moment contains and at another does not, or if it now contains this, now that, then it is clear that [the surface] itself is what is moving, moved along with the body of which it is a limit.’ (trans. Algra-Ophuijsen 2012: 74-75) 365 The objection resembles that expressed in the third lecture on IV.4, but the two are not identical. Philoponus additionally disproves the view that place is the limit of the containing body, which is always in contact with what is contained in it (καθ’ ὅ συνάπτει, Phys., 212a6), and the view that the limits are coincidental with the limited body (ἅμα τὰ πέρατα τῷ πεπερασμένῳ, Phys., 212a29-30; 212b27-29). Both points assert that place is coincidental with what is in it in a way that raises difficulties, just as in the defence of the immobility of place. See also in Phys., 587.30-33. 366 εἰ δέ τις εἴποι ὅτι ‘ἀλλ’ ᾗ τόπος ἐστὶν ἀκίνητός ἐστιν, εἰ καὶ ὡς ἐπιφάνεια κινεῖται’, in Phys., 564.16-17. 367 Hypatia does not occur in Philoponus’ text; this is my addition to Philoponus’ example. 364

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es, though she stands still, because the surfaces (the limits) move or they change. Hypatia’s proper place partially changes all the time, whereas another part of her place remains at rest (I say ‘partially’, for air is not the only limit that surrounds Hypatia; her feet, for example, are also in contact with earth). A different example of Philoponus’ may also illustrate the same consequences. In the case of the edge of the heaven nearest to us, it is not always the same part (μοῖρα) of the heaven’s inner surface that is in contact with the same part of the contained body, even when we assume that the contained bodies stay still, because all the other heavenly things keep their circular motion. Hence, again, when the body remains at rest, the place can move, if we define place as the limit of something. Τhe Aristotelian definition of place does not ensure that place is immovable, either when the body moves or when it is at rest. Aristotle posits the immobility of place as one of the main principles of place’s nature. If one refutes this principle, then one also damages the definition of place as the limit of the containing body. The Aristotelian definition of place is unsatisfactory, for it follows from the definition that the limit of the containing body can either move along with the body of which it is the limit or even move while the contained body stands still. Philoponus’ point is that the problem arises from attaching the concept of ‘being in place’ to the (limits of) bodies that are naturally capable of moving or being moved; in other words, what Philoponus attacks is the relationship between the container and what is contained that suggests a relative place. Philoponus’ extension theory is much closer to saving the principle of place’s immobility, since motion cannot be attributed to an extension. His extension theory defines place as an empty, physical extension which does not undergo any kind of change, thus showing that place is ontologically different from bodies. The bodies can move within the extension, but there is no way that the extension can move either along with the bodies that fill it or by itself when the bodies are at rest. The extension theory ensures that place qua place is immobile.

5.4 Motion through surfaces On a sunny day in the year 517 a young Athenian, a student of philosophy, decides to walk from his house, located in the neighborhood standing opposite the theatre of Dionysus on the southern slope of the Athenian Acropolis, to the public baths in the centre of the old city of Thebes. While leaving the walls of Athens behind him and passing through the low-planted land of Attica, he recalls the puzzling question of how his body traverses air while moving from here to there. Yesterday his teacher lectured on Aristotle’s theory of place. The young man thinks of the Aristotelian definition of place as the limit of the containing body. He decides to assume that this definition of place is right and tries to apply it to his own walk from Athens to Thebes. So, he ruminates on his body

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traversing the air. It happens that particles of air yield up their own place to his body (ἀντιπαραχωρεῖν). According to the definition, what is yielded should be the limits of particles of air with his body; in other words, what is yielded is the place of the particle of air and the place of his body. Now, he is wondering what the limit of a surrounding particle of air that contains and it is in contact with his body is. The limit should be the surface of the particle of air. The young Athenian yields his previous place to the surface of another particle of air in every step he takes.368 But, he ponders, how is this possible? Philoponus doubts that, according to the Aristotelian definition, the young Athenian can ever leave his house and attempts to show further that the definition entails a considerable difficulty for the motion of bodies. Philoponus holds that when the young Athenian moves he yields his place to the surfaces (limits) of air’s particles. But even if we add an infinite number of surfaces, each fitting on to one another, they do not produce a magnitude with depth. So, how does the body move forward?369 During the walk from Athens to Thebes the two-dimensional surface of the particle of air cannot give up its place; it cannot even move, for surfaces fitted on to one another make no magnitude in depth. What we need in order to explain the forward motion of a body is to have magnitudes with depth, so that the whole magnitude can cover a distance, exchanging places with another magnitude. As Philoponus puts it, it is not just surfaces that are yielded up to the moving young Athenian but the body of air that exchanged places with him. Place cannot be a surface (or a limit), for, if it were so, then the young Athenian could not move forward and reach the baths in the centre of Thebes.370 But if, leaving aside the surfaces, we think that a three-dimensional extension was yielded by the air to the moving body, the progression would result in a distance of some magnitude being covered because of the mutual replacement of bodies.371 Philoponus underlines the fact that two three-dimensional bodies can exchange position within the three-dimensional extension, but two three-dimensional bodies cannot exchange position within a two-dimensional place (surface). 368 Philoponus,

in Phys., 567.8-28. Philoponus says in in Phys., 567.22-25, ‘But if what is yielded is only a surface, and surfaces when put together make no magnitude with depth, how is it possible for the moving body to progress forwards?’ (trans. Furley 1991: 28). 370 τὸ δὲ ἀντιμεθιστάμενον τοῦ οἰκείου τόπου παραχωρεῖ τούτῳ ᾧ ἀντιμεθίσταται· οὐκ ἄρα ἐπιφάνεια ὁ τόπος, in Phys., 567.27-28. 371 Philoponus uses the same argument in two passages in the digression on the void. The first reference is part of the argument with which Philoponus shows that motion can occur through the void and in time (in Phys., 691.9-692.26); the second reference appears where Philoponus discusses motion through the void (in Phys., 693.28-694.19). The argument states that motion through the void is continuous and interruptible but does not occur in time. In that case the walker would be in Athens and in Thebes at the same instant, and one could actually be everywhere at the same moment—which is absurd (in Phys., 692.8-11). 369

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Philoponus states that motion is a change of places and a continuous exchange.372 But the motion of physical bodies implies that the whole body moves in its three dimensions. When bodies exchange places, they cannot exchange two-dimensional places, since they have to be entirely in place—they have to fill something which is equal to their magnitude. They cannot possibly fill something such as a two-dimensional surface (i.e., the limit) of something else. Thus, the three-dimensional extension plays the role of the place in which bodies exchange positions each time they move. Motion would be impossible if what was exchanged (namely the extension of place) was greater or lesser than its three-dimensional magnitude. As we saw, it is impossible for motion to occur without the existence of the void. Since place, namely the void, is a sine qua non for locomotion, obviously motion needs the concept of an empty three-dimensional space (χώρα), which the young Athenian traverses in order to walk from Athens to Thebes. Up to this point the chapter has discussed Philoponus’ direct criticism of Aristotle’s definition of place. Philoponus rejects the assumption that place can be the limit of the containing body, especially because the place of a body is relative to the surrounding bodies. His rejection of the Aristotelian definition of place uses various examples to show the weaknesses of Aristotle’s theory. Philoponus repudiates certain Aristotelian assumptions regarding the nature of place, such as the immobility of place and its equality to the bodies filling it. The whole refutation which he constructs to demonstrate these fallacies is based on the mere fact that place as the limit of the surrounding body is identical to the surface of the surrounding body. On the other hand, Philoponus’ criticism indirectly shows the advantages of his theory of place. The physical three-dimensional, incorporeal extension, which is ontologically different from the corporeal extension and empty in its own right, escapes several of the fallacies implied by Aristotle’s definition. But let us now look at another way of repudiating the Aristotelian doctrine, namely some further complications arising from the Aristotelian definition of place, as adopted by the Peripatetic tradition.

5.5 The place of the heavens The general tendency in the commentary’s digressions is to reveal absurdities which derive from Aristotle’s definition of place and his denial of the void’s existence. But apart from directly criticising Aristotle, Philoponus demonstrates how Aristotle’s account misleads other thinkers. Here I will discuss a section of the digression on place in which Philoponus points out a specific problem—arising from the belief that place is the limit of the surrounding body, in so far as it contains the contained—namely, that some commentators (οἱ ἐξηγηταί) cannot explain what the

372

ἡ κίνησις γὰρ τόπων ἐστί μεταβολὴ καὶ ἄμειψις κατὰ τὸ συνεχές, in Phys., 567.15-16.

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place of the sphere of fixed stars is (ἡ ἀπλανὴς σφαῖρα).373 These commentators are characterised as confused and unable to state anything clearly and convincingly; they are said to shift the account in different ways all the time like those playing dice, and even to end up refuting assumptions they had accepted at the beginning.374 Aristotle notoriously claims that ‘if a body has another body outside it and containing it, it is in place, if not, not.’375 Then the question is: if nothing exists outside the universe, then what is the place of the universe? It is useful to note from the beginning that a discussion of the problem can be traced back to Themistius’ para­ phrase of Aristotle’s Physics, on which Philoponus bases his criticism.376 So Philoponus’ obscure references to ‘the exegetes’ of Aristotle involved in the discussion of the place of the sphere of fixed stars are perfectly illuminated by Themistius’ text. Two such thinkers are Philoponus’ main targets: Eudemus, Aristotle’s pupil, and, of course, Themistius. Let us first present the problem and how Eudemus and Themistius strive for a solution. Since the outermost sphere (ἡ ἐξωτάτω σφαῖρα) moves in a circle, that is to say undergoes locomotion, it must be in place.377 But the sphere of fixed stars, according to Aristotle, is not itself in place, for nothing exists beyond the sphere, so there is nothing in which it is contained. Eudemus posits this question about the place of the heavens and replies that the stars and all the things inside the outermost body (i.e., the sphere of fixed stars, the heavens) are in its limit, in the sense that they are contained in it.378 These celestial bodies are said to be in place because they are 373 See in Phys., 565.1-567.7. Given that the argument connects to a problem found in some commentators and proponents of Aristotle, I think that in Vitelli’s edition there should be a paragraph separating this argument from the previous section, which deals directly with Aristotle. For, as Vitelli edits the text, the paragraph starting in in Phys., 565.10 seems to be completely parenthetical; it is not clear that it is connected to the previous nine lines, where a new argument obviously starts with ἔτι (in Phys., 565.1-9). 374 ‘When they try to give an account of how the sphere of fixed stars could move in place, while it is not in place, they confuse everything rather than saying something clear and convincing; … but they are just like those who play at draughts, altering their argument differently each time and refuting in every way their original views and agreements.’ Philop., in Phys., 565.12-14, 17-19. 375 Aristotle, Physics, 212a31-32, trans. by Barnes 1991: 57. The problem of heaven’s place, deriving from Aristotle’s account, as well as the proposed solutions in antiquity have been more recently examined by Morison 2002: 166-169, Bostock 2006: 132-134 and McGinnis 2006. 376 See Themistius, in Phys. paraphr., 119.17-121.20. This is also affirmed by two comments within Philoponus’ running commentary. Both of them are found in the one and only lecture on Physics IV.5, first, where Philoponus explicitly refers to the very same problem and to the way the exegetes conceive of it (in Phys., 594.14-28), and, second, where Philoponus names Themistius and cites his way of dealing with the problem (in Phys., 595.18-597.4). In addition to these, the same discussion is repeated in a comment, this time without naming Themistius (in Phys., 600.25-602.5). McGinnis (2006: 148-151) seems to disregard the role of Eudemus and Themistius in Philoponus’ attack against the Aristotelian tradition. 377 Philoponus follows (in Phys., 565.8-9) exactly the same aporia as expressed by Themistius. 378 Themistius paraphrases but also quotes Eudemus’ view from his third book of his Physics (see in Phys. paraphr., 119.17-25 and 119.26-120.3). Simplicius (in Phys., 595.3-14) also quotes from the third book of Eudemus’ Physics and gives a few more lines of the passage that Themistius quotes. See also Algra 1995: 255-258.

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in something; if we say that the parts of the whole are in a place, then the whole too is in that place. The universe is in place as regards its parts. Eudemus’ suggestion is based on the plurality of meanings that the expression ‘in place’ allows. Themistius also was puzzled by this issue. He asks whether the universe falls into the category of the things that are potentially in place or that of those that are actually in place. Themistius in his exegesis analyses the Aristotelian distinction between being potentially (κατὰ δύναμιν) in place and being actually in place (κατ ’ ἐνέργειαν). Aristotle distinguishes between the parts of a continuous whole that are in place potentially and separate bodies, which are in contact (like a heap), that are in place actually. And of those things that are in place actually, some are by themselves (καθ’ αὑτά) in place and others accidentally (κατὰ συμβεβηκός). The heavens, Aristotle states, is in place actually and accidentally.379 Themistius worries that Aristotle contradicts himself, because, on the one hand, Aristotle seems to argue that ‘accidentally’ is identical to ‘partially’ (that is to say, the universe is accidentally in place because its parts are in place), but, on the other hand, when Aristotle argues that nothing is in place in the same sense that something is in itself, he seems to accept that something is in itself in respect of its parts (if the parts of the whole are contained in it), without considering this a case of being accidentally in something.380 Themistius attempts to avoid this inconsistency by saying that Aristotle uses the term ‘accidentally’ (κατὰ συμβεβηκός) in a loose sense instead of using the expression ‘by virtue of something else’ (κατ ’ ἄλλο). So it is not problematic to assume that the universe is in place accidentally, since its parts are in place, because the parts of the universe are in contact, and they contain each other, and they undergo kinds of motion—the celestial spheres are an example of this. According to Themistius, Eudemus’ understanding of the problem seems to be right, for both explicitly hold the view that the heavens should be in place if their parts are in place. If Themistius were asked the place of the heavens, his answer would be that the outermost sphere in its inner surface is in place because it is in contact with the surface of Saturn, for in some way the heavens are contained by the surface of Saturn. Nevertheless, the problem remains: the outer surface of the outermost sphere does not entirely share a place, since there is nothing outside it that can contain it.381 379 Aristotle,

Physics, 212b3-13. See Themistius, in Phys. paraphr., 120.20-121.20. The whole argument takes up the discussion in Aristotle’s Physics, 210a25 ff. 381 It seems that Alexander of Aphrodisias’ exegesis is absent from Themistius’ examination. In brief, Alexander claimed that the parts, i.e., the spheres of stars (ἡ πλανωμένη σφαῖρα), are not continuous to the whole of the sphere of fixed stars; therefore the whole sphere does not undergo locomotion because its parts do (see fr. 67 in Rashed 2011: 214-216). Fragment 67 along with fr. 71 (Rashed 2011: 217-218) shows that Alexander claims that the parts undergoing locomotion are the spheres of the stars that are in contact with each other and that these are not continuous parts to the whole of the sphere of fixed stars. Also see Rashed 2011: 46-47 and McGinnis 2006: 147-148. 380

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Philoponus disagrees with the assumptions that the heavens are in place because their parts are and that the place of the heavens is the surface of Saturn’s sphere, which is immediately in contact with them. He structures his criticism in a twofold manner: first (A), against those who believe that the place of the sphere of fixed stars is the surface of Saturn’s sphere, and, second (B), against those who claim that the sphere of fixed stars is in place because its continuous parts are in place. Moreover, Philoponus shows that each of these two views refutes some Aristotelian points, and he adds his own objection to each of the two views.382 Let us begin with the first part, (A): if we accept that the place of the sphere of fixed stars is the convex (ἡ κυρτή) surface of Saturn’s sphere, then we refuse to accept the Aristotelian statements (i) that place is outside what is contained in it and (ii) that there is equality between place and what is in place.383 As far as the first point (i) is concerned, Aristotle does not explicitly make this statement, as Philoponus phrases it, nor do we find it in the list of the common characteristics of place presented in the Physics.384 Nevertheless, it derives from the Aristotelian doctrine of place. All things that are in place, according to Aristotle, are contained in it; all things are contained in the limit of the surrounding body. The surrounding body and its limit cannot be in the thing which is contained, but must be outside it. Now, if one asserts that the convex surface of Saturn’s sphere (which is part of the universe) is inside the universe, how can it possibly be the place of the sphere of fixed stars? Philoponus’ exact point here needs further investigation. To begin with, presumably, if place is an extreme part of the heavens385 which is in contact with the moving body, the heavens themselves cannot be contained in place; at least not in the same sense as Aristotle’s conception of ‘containing’ as regards the place that every natural body has. Furthermore, as Philoponus points out, the convex surface of Saturn’s sphere, with which the heavens are directly in contact, is not the limit of the surrounding body in that sense—i.e., something that contains the heavens—since it is not external to it. In this case, place is no longer the limit of the surrounding body insofar as it contains something; Eudemus and Themistius claim that the heavens must be in place because of something inside them—i.e., a part of the heavens, for example, the convex surface of Saturn’s sphere—but, according to Aristotle, this is not the primary way of ‘being in something’.386 The primary sense of ‘being in something’ is something ‘being in place’, as for instance water is in a vessel. The vessel is not in the water because each part of the water is in place (i.e., in the vessel). Being in something as the whole is in its parts constitutes a 382 Philoponus, in Phys., 565.1-567.7. One should also pay attention to Philoponus’ running commentary, in Phys., 594.14-28; 595.18-597.4, where he refers to the problem of the place of the ἀπλανής σφαῖρα. 383 Philoponus, in Phys., 565.21-566.7. 384 Aristotle, Physics, 210b32-211a6; 212b22-30. 385 This is taken from Aristotle: τοῦ οὐρανοῦ τι τὸ ἔσχατον, Phys., 212b18-19. 386 Ibid., 210a14-24.

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different category of ‘being in something’. In addition, the primary sense of ‘being in place’ means that something is directly contained by something outside which is in contact with it. Hence, the Aristotelian common characteristic of place—that place has to be outside what is contained in it—is refuted by the interpretations of his exegetes. In addition to this, I think that the way Aristotle builds on the notion of περιέχειν could also raise a further complication. Aristotle claimed in the Physics that the heavens are not place, but rather that place is something extreme to the heavens and something in contact with the moving body; for that reason, earth is in the water, water is in the air, air is in the aether, and aether is in the heavens.387 If this is true, then we cannot say the same thing if we put it the other way round—i.e., we cannot say that the heavens are in the aether, aether is in the air, air is in the water, and water is in earth. This is for three reasons. First, because the notion of περιέχειν τι should be defined differently—i.e., not in the way Aristotle’s definition of place implies; second, because we would have to commit ourselves to the claim that the heavens are place, a claim that Aristotle denies; and, third, because aether should be the place of heavens—i.e., aether should be outside the heavens—and, moreover, we could not determine the place of the earth, for there would be something beyond the centre of the universe, which is earth’s place. The second point (ii), regarding the equality between place and the contained body, is also confuted by Themistius’ and Eudemus’ interpretations, since the convex surface of Saturn’s sphere cannot be totally equal to the heavens. It might be suggested that it is the surface of the heavens that is equal to the surface of Saturn, but Philoponus would reply that surfaces cannot be equal to the three-dimensionality of the universe. The two dimensions of Saturn’s surface cannot be equal to the three dimensions of the heavens. According to Philoponus, if we endorse the exegesis of Themistius (or Eudemus), we cannot meet the necessary condition of Aristotle’s account of place that place should be equal to the contained body. Philoponus expressed a further worry concerning the view that the place of the sphere of fixed stars is the convex surface of Saturn’s sphere. Suppose that we accept this assumption. One consequence will be to commit ourselves to the idea that the very same thing, namely the sphere of Saturn, in respect of the same thing, namely its own convex surface, both is the place of the sphere of fixed stars and is in place because of the sphere of fixed stars. The objection is that it is impossible for the same thing to be the place of another thing and to have as its place that other thing. Philoponus draws an analogy to the relationship between father and son in order to illustrate his argument: it is impossible to say that a man is both the father and the son of the same man.388 The point is that the relationship between place 387

Ibid., 212b18-22. in Phys., 566.3-6.

388 Philoponus,

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and what is in place implies that Socrates cannot be the place of his surrounding body and have as his place that surrounding body whose place he is. However, a Peripatetic philosopher who accepts Aristotle’s definition of place cannot endorse the assumption (A) asserting that the place of the universe is Saturn’s sphere because it presupposes a different conception of the primary sense in which bodies are in place. Aristotle explicitly distinguishes between ‘being in place’ and ‘being in something’ as the whole is in its parts. The second assumption (B) of Themistius’ interpretation is that the sphere of fixed stars is in place because its continuous parts are in place (and each part is contained by its surrounding parts).389 According to Philoponus, the assumption goes against two Aristotelian theses: first (i), that the parts of a continuous body are in place accidentally and, second (ii), that place is not something of the thing. Point (i) states that Aristotle never claimed that the parts of the continuous are in place by virtue of themselves, but rather that they are accidentally in place because the whole is in place.390 Philoponus does not provide any demonstration of how this objection works against Themistius’ assumption. A possible way to present the first point may be the following. According to Philoponus, Aristotle states that the parts of the whole are in place accidentally because the whole is in place. The reference here is to Aristotle’s Physics 212b3-13. Aristotle says that when something is continuous, its parts are potentially (κατὰ δύναμιν) in place and that the parts of those that accidentally are in place—just as is the case for the soul and the heavens—are somehow in place (τὰ γὰρ μόρια ἐν τόπῳ πως πάντα, Physics, 212b12-13).391 In the case of the universe as a whole, the parts of the universe are in place accidentally because the whole universe is in place; but the inverse is not true, as Aristotle’s commentators imply with their argument. Aristotle does not say that the whole is in place because its continuous parts are in place accidentally. So Eudemus and Themistius should admit either that the universe has a proper place (implying a surrounding body that contains it and only it) or that the universe is in place accidentally because its parts are in place. Both options are unacceptable within the framework of the Aristotelian definition of place. The assumption (B) of Aristotle’s exegetes also is inconsistent with the Aristotelian claim (ii) that place is not something of the thing, as was stated in the Physics.392 389 See Themistius, in Phys. paraphr., 120.28-121.4. This assumption seems to be the same as that with which Alexander of Aphrodisias was also concerned, as Rashed (2007: 99-101) points out in his discussion of Alexander’s view on the problem of the heavens’ place. However, there is neither a direct nor an indirect reference to Alexander’s solution in Philoponus. 390 Philoponus, in Phys., 566.10-12. 391 Simplicius notes that the proponents of Aristotle’s view claim that the whole is in place by itself and the parts are in place accidentally: οἱ μὲν γὰρ τὸ πέρας τοῦ περιέχοντος τόπον εἶναι λέγοντες τὸ μὲν ὅλον καθ’ αὑτό φασιν ἐν τόπῳ, τὰ δὲ μόρια κατὰ συμβεβηκός, ἐπειδὴ οὐδὲ περιέχεται ταῦτα ὑπ’ αυτοῦ προσεχῶς, in Phys., 575.4-6. 392 μηδὲν τοῦ πράγματος, Physics, 211a1.

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Philoponus argues that in the case of a whole composed of parts, each of the parts contributes to the whole. This suggests that the parts are something of one another because the parts each contribute to the very being—i.e., to the whole—and if one of the parts is separated from the whole it runs the risk of ceasing to exist.393 The objection asserts that if the whole is in place because its continuous parts are in place, then place becomes something of the parts, and hence something of the whole. Thus the position contradicts the Aristotelian claim that place is the limit of the containing body, which is not something of the thing that is in place. The discussion of the place of the sphere of fixed stars ends up with a further objection from Philoponus. As we have seen, Philoponus withdraws the Aristotelian definition also because locomotion of natural bodies turns out to be problematic following the model it proposes (see section 5.4). He posits the same question for the circular motion of the heavens: what places do the parts of the sphere of fixed stars yield to one another during their motion? If the containing parts are the place of each part of the sphere of fixed stars, and if it is true to say that when the whole sphere moves the parts move, yielding, in turn, their proper places to one another, then it is necessary that the heavens are divided and that different parts then take up a different relationship, with respect to both the whole and themselves. But this is impossible, for the heavens are indivisible; it is also impossible either that the northern part of the heavens comes to be in the south part of it or that it appears to be somewhere else. Thus, this cannot happen to any of the beings that undergo generation and corruption.394 It is crucial, according to Philoponus, to distinguish between the cases where a thing is in something, as being in place, and the cases where a thing is in something, as being in a whole.395 Themistius’ explanation presupposes (based on Eudemus’ interpretation) that being in place and being in a whole are coextensive; consequently, when we claim that the parts of the whole are the places of one another and the place of the whole, we are actually claiming that the parts are so separated as to be the containers of other parts. But the parts of a whole should not be separate, for then these parts will not be the parts of a whole, but rather they will be distinct from the whole. When the heavens rotate, or when the parts of the heavens move, because the parts are places of one another, the parts should yield their proper places to one another and occupy different places, rather than their own; the parts should now take up different relationships with respect to both the whole and each other, and that is impossible, since the heavens are indivisible. Inasmuch as the exegetes believe that the place of the parts is the containing parts round about (πέριξ) and

393 Philoponus,

in Phys., 566.12-17. in Phys., 566.17-26. Philoponus observes some exceptions, for instance, water, air and meltable things composed of these, like gold, lead, wax and similar (in Phys., 566.27-29). 395 See Aristotle’s Physics, 211a29-31; 210a15-17. 394 See

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they consider the parts to be in the whole, as if they were in place, then the heavens cannot be in place in any respect. Philoponus thinks that the problem cannot be solved and that the explanations provided by Eudemus and Themistius are insufficient and do not solve the problem of the heavens’ place; on the contrary, they cause additional confusion. If the sphere of fixed stars is in place, then it must be contained by something external to it, as the Aristotelian definition of place requires. If not, then obviously the definition of place as the limit of the surrounding body in respect of containing the contained cannot be valid. A subsequent problem—which Philoponus just points out without going into the details of the long traditional discussion about it—is the kind of motion that the outermost sphere would undergo. For the outermost sphere cannot undergo locomotion (rotation) if it is not in place.396 Philoponus contributes nothing to the discussion of the place and the motion of the heavens, in the sense that he does not express any positive solution to the problem, with which the Peripatetic tradition dealt. The reason is that the origin of the problem is the troublesome Aristotelian definition of topos that needs to be rejected.397 After going through the criticism that repudiates the Aristotelian definition of place in various ways, I would like to conclude by drawing attention to Philoponus’ account of place and the way it avoids the problems which arise from the Aristotelian definition of place. The ontology of place, according to Philoponus, shows that the extension of place is a reality within the cosmos conceived of as separate (in its own right) from corporeal entitites. Philoponus’ extension theory substantiates place in the sense that it is an extension always filled with bodies. The filling (πλήρωσις) of place ensures that place is equal to what is in place, since both extensions (place and body) are three-dimensional. Bodies come to fill a place equal to their dimensions. The proper place of each body has nothing to do with the limits of its surrounding bodies as Aristotle’s relativist viewpoint asserts. Of course, we can locate a body by reference to the other bodies around it, since its position within the extension is determined by the surrounding bodies, but ‘locating’ and ‘filling place’ are not identical. Philoponus does not accept that a physical body, say a tree, is contained by the limits of the surrounding bodies, in the sense that the περιέχειν 396 See Philop., in Phys., 566.1-8. McGinnis (2006: 150-151) presents the problem of the kind of motion of the outermost sphere, but nothing can be said about Philoponus’ own view, since he is interested in posing the problem as a consequence of Aristotle’s doctrine. 397 Modern scholars attempted to make sense of the problem pointed out by Aristotle’s ancient commentators. Mendell (1987: 222-223, n. 40) notes that to avoid the problem Aristotle would have to commit himself to accepting the existence of an absolute independent place. Morison (2002: 163-168) believes that we can make sense of Aristotle’s view on the place of the heavens with respect to the definition of place and proposes a sophisticated solution that is partly based on the ancient answer, namely that since parts of the outer sphere are in place and undergo rotation then the outer sphere is in place too. Bostock (2006: 132-134) holds that the notion of the surrounding body defining that something is in place should be abandoned and therefore we will have to define a body’s place as relative to certain unmoving objects.

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does not define the place of the body—it rather defines its position in relation to other physical bodies. Bodies occupy this position in the extension now, and after a while they can occupy another position in the extension. Bodies change position when they move, and exchange positions with other bodies. The extension of place does not move in the case of the mutual replacement of bodies (ἡ ἀντιμετάστασις τῶν σωμάτων). Bodies move within the extension, which is immobile. Philoponus does not attach the extension of place to bodies; this view affirms the ontological difference between the extension and bodies and avoids the problem of moving places around the universe, as we argued in the previous chapters. In other words, according to Aristotle’s definition, in many cases the place of a body moves when bodies move, whereas, according to Philoponus’ definition, bodies change positions when they move, but place remains immobile. Locomotion of bodies is conceived of as the mutual replacement of bodies. In order to advance further in place, Socrates just needs to traverse the extension of place and exchange positions with another body that is three-dimensional; two-dimensional limits (surfaces) of bodies that yield one another do not determine Socrates’ motion. The extension theory states that Socrates can move only when he occupies a position as a three-dimensional whole; at the same time, Socrates is forcing other bodies immediately around him to move as wholes, not as two-dimensional surfaces. Philoponus in this way guarantees that the motion of bodies can actually happen within the extension of place, in contrast to the Aristotelian definition of place that could lead to absurd assumptions, for instance bodies that cannot move from one place to another, since it is surfaces that yield. Moreover, nothing forces Philoponus to accept that place is external to the bodies. If he did, he would have to endorse the view that the heavens need something external in which to be contained in order to be in place. This would definitely lead to an infinite regress of external places. Bodies are not contained in place in Aristotelian terms. Philoponus defines the relationship between place and what is in place in a different manner. The concept of plērōsis, as we saw, illustrates this relationship. Place contains bodies when it is defined as the limit of the containing body, but bodies, for Philoponus, are not contained by other bodies nor are they in place by virtue of being contained by other bodies; bodies occupy a place which is empty in its own right, but always filled with bodies. The universe does not need to be contained by something in order to be in place; it fills the physical cosmic extension in its own right, which is actually the entire space in which it exists and is placed (as well as all the bodies of the universe). For all these reasons Philoponus finds the Aristotelian definition of place unsatisfactory and rejects it, proposing, at the same time, a different theory to explain how physical bodies are in place and how they move through it.

Epilogue This study has focused on Philoponus’ conception of τόπος. Philoponus’ strategy in the digressions of his commentary, and also in parts of his exegeses, has three aspects: he repudiates the cogence of Aristotle’s and Themistius’ critiques of the concept of the extension of place and the void; he attacks the Aristotelian definition of place and the arguments against the void by showing their weaknesses and their inconsistencies with the nature of things; and he establishes his own theory of place as a void extension. The result is a valuable set of arguments regarding topos and a major contribution to the physics of late antiquity, which invigorated interest in place and void up to the seventeenth century. Philoponus conceives of place as one of the five concomitants common to all physical beings (the others being motion, time, form and matter), following the tradition established by Ammonius Hermeiou that comprehends place as an accompaniment of bodies. That place is a concomitant common to all physical beings indicates place’s significant role in nature. Philoponus, on the basis of this idea of the nature of place, attempts, throughout the digressions of the commentary, to provide a coherent ontology of place which is compatible with nature. The conception of place as a concomitant of a natural body already entails a distinction between two things, namely the accompaniment (place) and what is accompanied (natural body). This distinction, however, is expressed in radically different terms in Philoponus’ theory of place, which wishes to redefine the relationship between place and body. Philoponus underlines the ontological difference that an incorporeal extension must have from a corporeal extension. This kind of difference (ἑτερότης) transposes the centre of the relationship between place and body from the concept of something contained (body) in a container (place) to the concept of filling up what is capable of being filled (namely, the extension of place). Physical bodies fill an empty three-dimensional place which is their physical place; that is how place and bodies associate with each other. Philoponus’ theory manages to balance between the definition of topos in its own right, which is an absolute conception of space, and topos as we directly experience it, that is the place filled by bodies. The ontological determination of place as something different from bodies allows Philoponus to grasp the concept of absolute space with mental operation without being obliged to commit himself to the view of an intra-cosmic, absolute, void space like early atomists and Epicurus suggest or of an extra-cosmic separate space as the Stoics maintain. The Philoponan ontology of place, perhaps influenced by some Platonists and Strato of Lampsacus, accepts place as a reality coterminous with the cosmic body, a cosmic extension of place always

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filled with the body of the cosmos. The ontological difference of place from bodies implies that place is a three-dimensional, bodiless, immobile and unaffected extension. What we perceive in reality is a place always filled with bodies. It is because of place’s nature as a void extension that we can perceive this filling up and the motion of bodies. We cannot comprehend how bodies fill the extension without presupposing the notion of voided place. The void becomes inherent, so to speak, in nature because it explains the natural phenomenon of bodies being somewhere—i.e., filling a place. Bodies fill different positions within the extension of place with respect to other bodies. The concept of the void should be considered as an essential feature of Philoponus’ account of place and his cosmological point of view. Philoponus sets out an alternative model for explaining the motion of bodies (either natural or forced motion, introducing an impetus theory). For Philoponus, the mutual replacement of bodies (ἡ ἀντιμετάστασις τῶν σωμάτων) in nature amounts to a redetermination of locomotion and is linked to the conception of place. The extension of place must be bodiless, three-dimensional, and by nature capable of receiving physical bodies. The three-dimensionality of place, according to Philoponus’ account, guarantees the equality between place and the bodies filling it; hence it ensures the mutual replacement of bodies. The mutual replacement, however, requires a notion of place which is not an impediment to the bodies’ exchange of positions. Therefore Philoponus considers the voided place necessary for the locomotion of bodies: bodies are able to move because of their mutual replacement within the extension. With his extension theory Philoponus not only tries to establish a coherent view of place, but also displays his cosmological views on the order of the universe. Bodies prevent the emptiness of the extension of place, so far as possible, even behaving contrary to their nature in order to achieve this. Taking for granted that the intra-cosmic empty place cannot exist without bodies filling it, Philoponus asserts that the demiurge ordered the universe in such a way as to make possible a place always filled with bodies. This implies, for Philoponus, that the position of each body in the extension also reflects the body’s perfection (τελειότης). The cosmos achieves its perfection because it is positioned within the cosmic extension of place according to the order given by the demiurge. I have argued that Philoponus suggests a physical extension of place. But in antiquity a three-dimensional bodiless extension also signified a mathematical entity. For instance, geometrical figures are solids (στερεόν) and have three dimensions, but differ from physical bodies composed of form and matter. Indeed, Philoponus insists on the distinction between the three-dimensionality of place and that of a physical body. Nevertheless, how far does he go with this distinction? In contrast to those who would smoothly assert that Philoponus endorses a mathematical notion of place, I do not wish to suggest that Philoponus does so. Although Philoponus’ interest in mathematics is attested to by his commentary on Nicomachus of Gerasa’s

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Introduction to Arithmetic, no trace of a purely mathematical conception of place can be found in any of his surviving works. Philoponus establishes the ontological difference between a physical, three-dimensional, incorporeal extension and that of a physical, three-dimensional, corporeal extension. This ontological difference is based on the very nature of topos as a concomitant of physical bodies that in its own right is void, naturally capable of receiving physical bodies. The purpose of this distinction is to explain the way physical bodies are in their physical place. Philoponus constantly points out that to define place in its own right does not mean that place, namely the void extension, can ever appear as a gap in nature. Its subsistence becomes apparent by the direct experience of an extension already filled with bodies and other natural phenomena such as the mutual replacement of bodies (i.e., locomotion), the equality between physical body and the place it fills, the impossibility of having two bodies in the same place, and the immobility of place. The narration of the discussion between Ammonius Hermeiou and Philoponus at the end of the digression on place reinforces this claim. Philoponus clearly shows that he is not interested in proposing a theory of place that exceeds physics when he argues for an extension of place filled with the physical bodies. The difference (ἑτερότης) between place and the physical body reflects the necessary ontological differentiation of place from bodies within the natural cosmos. The digression on place and, partly, the digression on void deal with Philoponus’ attack on the views held by the Peripatetic tradition. Philoponus scrutinised, first, Aristotle’s definition of place as the first immobile limit of the containing body, with regard to containing the contained and, second, the argument against the definition of place as extension. Philoponus insists that Aristotle contradicts himself and refutes his own principles regarding place; moreover, Aristotle’s definition of place is counter-intuitive and to a great extent fails to express a consistent account of the nature of place and the locomotion of bodies. The study shows that Philoponus expounds an effective critique of Aristotle, but that at the same time he endorses all the fundamental principles set out by Aristotle: the kind of extension that is defined as the place of natural bodies is immobile, bodiless and unaffected; it does not belong to the body; it is equal to the body filling it; and it does not perish, whereas bodies do. This kind of extension substitutes for the conception of place as the limit which contains the contained, as implied by Aristotle’s theory and its proponents. This book turns one’s attention to Philoponus’ definition of place and the related theory he subsequent develops. As well as offering a philosophical commentary on the topic, I hope that the book opens the ground for further discussion of several issues related to Philoponus’ theory and its position in the history of science. For instance, it is important to note that Philoponus’ arguments were either literally used by later thinkers struggling with the difficulties implied by the existence of void or indirectly affected them. There are many aspects of the transmission of Philoponus’ arguments that still need to be clarified. I would like to conclude by addressing

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the question of the origins of Philoponus’ theory. Throughout the chapters of this book, I have consciously refused to touch upon Philoponus’ Platonic or Aristotelian identity, mainly because he himself gives no evidence on the question. Nevertheless, it seems that the Christian philosopher is presenting a re(de)fined theory of place of Platonic origin. Sources such as Syrianus and Simplicius seem to attest to a theory of place, attributed to some Platonists, that has several common characteristics with the theory of Philoponus but differs in that it asserts the intelligible place of intelligible beings that is not endorsed by Philoponus. If this proves to be true, then Philoponus stands in the Platonic tradition with a steady Aristotelian outlook. His account of place may reflect a long Platonic tradition concerning τόπος, while examining the physical place of physical beings by remaining loyal to the Aristotelian conception of the study of nature.

Bibliography Texts Note: Unless stated otherwise all the cited or quoted texts of Alexander of Aphrodisias, Themistius, Syrianus, Ammonius Hermeiou, Iōannēs Philoponus, Asclepius, Simplicius, Olympiodorus, David, Elias and Stephanus refer to their editions in the series Commentaria in Aristotelem Graeca, Academia Litterarum Regia Borussica, G. Reimer: Berlin (CAG). Arnim, I. von (1964), Stoicorum Veterum Fragmenta, vol. 1-4, Teubner: Stuttgart (SVF). Burnet, I. (1978), Platonis Opera, Oxford University Press: Oxford. Diels, H. (1879, repr. 2010), Doxographi Graeci, Cambridge University Press: Cambridge. —, Kranz, W. (1903/1922), Die Fragmente der Vorsokratiker, vol. 1-3, Weidmannsche Buchandlung: Berlin (DK). Ideler, J. L. (1841-1842), Physici et medici graeci minores, vol. 1-2, G. Reimer: Berlin (repr. Amsterdam 1963). Kühn, C. G. (1821), Claudii Galeni Opera Omnia, Medicorum Graecorum opera quae exstant, vol. 1-20, C. Cnobloch: Leipzig. Mutschmann, H., Mau, J. (1955/1961), Sexti Empirici Opera, vol. 2-3, Teubner: Leipzig. Rabe, H. (1899), Ioannes Philoponus. De aeternitate mundi contra Proclum, Teubner: Leipzig. Raeder, J. (1928/1929), Oribasius. Collectionum Medicarum Reliquiae, Corpus Medicorum Graecorum, Teubner: Leipzig/Berlin. Reichardt, G. (1897), Ioannes Philoponus. De opificio mundi, Teubner: Leipzig. Ross, W. D. (1936), Aristotle’s Physics, A revised text with introduction and commentary, Clarendon Press: Oxford. — (1950), Aristotelis Physica, Oxford University Press: Oxford. Schmidt, W. (1899), Heronis Alexandrini opera quae supersunt omnia. Pneumatica et Automata, vol. 1, Teubner: Leipzig. Trincavelli, V. (1535), Ioannis Grammatici in primos quatuor Aristotelis de naturalia auscultatione libros commentaria, Venetiis. Usener, H. (1887), Epicurea, Teubner: Lipsiae. Wachsmuth, C., Hense, O. (1884), Ioannis Stobaei Anthologium libri duo priores qui inscribi solent Eclogae physicae et ethicae, vol. 1-2, Weidmann: Berlin. Wehrli, F. (1950), Die Schule des Aristoteles. Texte und Kommentar. Heft V: Straton von Lampsakos, Benno Schwabe & Co Verlag: Basel.

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Translations Algra, K., Ophuijsen, J. van (2012), Philoponus. On Aristotle Physics 4.1-5, Ancient Commentators on Aristotle, Bristol Classical Press: London. Barbarus, H. (1542), Themistii Peripatetici lucidissimi Paraphrasis in Aristotelis Posteriora, Physica, In Libros item de Anima, Memoria et Reminiscentia, Somno et Vigilia, Insomniis et Divinatione per Somnum, Venetiis apud Hieronymum Scotum. Barnes, J. (ed.) (1991), The Complete Works of Aristotle: The Revised Oxford Translation, vol. I-II, Princeton University Press: Princeton, NJ. Bowen, A. C., Todd, R. B. (2004), Cleomedes’ Lectures on Astronomy. A Translation of The Heavens with an Introduction and Commentary, University of California Press: Berkeley/Los Angeles, CA/London. Broadie, S. (2011), Philoponus. On Aristotle Physics 4.10-14, Ancient Commentators on Aristotle, Bristol Classical Press: London. Charlton, W. (1992), Physics. Books I and II, Clarendon Aristotle Series: Oxford. Dillon, J. (1993), Alcinous, The Handbook of Platonism, Clarendon Press: Oxford. Dorotheo, G. (1542), Ioannis Grammatici cognomento Philoponi eruditis, sima commentaria in primos quatuor Aristotelis de naturali auscultatione libros. Nunc primum e Greco in Latinum fideliter translata, Impressum Venetiis per Brandinum et Octavianum Scotum. Edwards, M. J. (1994), Philoponus. On Aristotle Physics 3, Ancient Commentators on Aristotle, Duckworth: London. Furley, D., Wildberg, C. (1991), Philoponus: Corollaries on place and void. Simplicius: Against Philoponus on the eternity of the world, Ancient Commentators on Aristotle, Duckworth: London. Guthrie, W. K. C. (1960), Aristotle On the Haevens, Loeb Classical Library, Heinemann: London. Hadot, I. (1990), Simplicius commentaire sur les Catégories, Traduction commentée sous la direction de I. Hadot, Brill: Leiden. Huby, P. (2014), Philoponus. On Aristotle Physics 4.6-9, Ancient Commentators on Aristotle, Bristol Classical Press: London. Hussey, E. (1983), Physics. Books III and IV, Clarendon Aristotle Studies: Oxford. Lacey, A. R. (1993), Philoponus. On Aristotle Physics 2, Ancient Commentators on Aristotle, Duckworth: London. Lettinck, P., Urmson, J. O. (1994), Philoponus. On Aristotle Physics 5-8. Simplicius, On Aristotle on the Void, Ancient Commentators on Aristotle, Duckworth: London. Osborne, C. (2006), Philoponus. On Aristotle Physics 1.1-3, Ancient Commentators on Aristotle, Duckworth: London. Pacius, J. (1584), Aristotelis Stagiritae Peripateticorum principis Organum, Morgiis excudebat Guillelmus Laimarius.

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Secondary literature Algra, K. (1993), ‘Posidonius’ Conception of the Extra-Cosmic Void. The Evidence and the Arguments’, Mnemosyne 46/4: 473-505. — (1995), Concepts of space in Greek thought, Philosophia Antiqua 65, Brill: Leiden. Algra, K., Barnes, J., Mansfeld, J., Schofield, M. (eds.) (2002), The Cambridge History of Hellenistic Philosophy, Cambridge University Press: Cambridge. Bailey, C. (1964), The Greek Atomists and Epicurus, Russel & Russel: New York. Baltussen, H. (2007), ‘From Polemic to Exegesis: The Ancient Philosophical Commentary’, Poetics Today 28/2: 247-281. — (2008), Philosophy and Exegesis in Simplicius: The Methodology of a Commentator, Duckworth: London. Barnes, J. (1992), ‘Metacommentary’, Oxford Studies in Ancient Philosophy 10: 267281. Berryman, S. (1997), ‘Horror vacui in the third century BC: When is a theory not a theory?’, Bulletin of the Institute of Classical Studies, Supplement 68: Aristotle and After 41: 147-157. Blank, D. (2010), ‘Ammonius Hermeiou and his School’, in L. Gerson (ed.), The Cambridge History of Philosophy in Late Antiquity, vol. II, Cambridge University Press: Cambridge: 654-666. — (2012), ‘Ammonius’, The Stanford Encyclopedia of Philosophy, Edward N. Zalta (ed.), URL = . Böhm, W. (1967), Johannes Philoponos, ausgewählte Schriften, Paderborn & Ferdinand Schöningh: Munich/Vienna. Bostock, D. (2006), Space, Time, Matter and Form: Essays on Aristotle’s Physics, Oxford Aristotle Studies, Oxford University Press: Oxford. Canter, H. V. (1931), ‘Digressio in the Orations of Cicero’, The American Journal of Philology 52/4: 351-361. Clagett, M. (1959), Science of Mechanics in the Middle Ages, University of Wisconsin Press: Madison, WI. Duhem, P. (1914), ‘Roger Bacon et l’horreur du vide’, in A. G. Little (ed.), Roger Bacon. Essays, Oxford University Press: Oxford: 241-284.

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Index Locorum Aёtius (Diels) I.20,1: 94 n. 271 Alcinous Didaskalikos § 8.163.3-6: 66 n. 196 Alexander of Aphrodisias De mixtione 213.6-13: 93 n. 262 216.14-218.10: 93 n. 263 218.10-221.25: 93 n. 263 219.9-18: 39 n. 126 233.14: 93 n. 264 In Phys. (Rashed) fr. 7: 57 n. 171 fr. 8: 93 n. 262 fr. 64: 47 n. 152, 126 n. 346 Ammonius Hermeiou In Categ. 92.6-12: 85 n. 243 Aristotle Categoriae 1b25-27: 84 n. 240 5a8-14: 72 n. 215 11b10: 84 n. 242 De caelo 278b21-279a12: 125 n. 339 294b20-21: 71 n. 212, 73 n. 217 De generatione et corruptione 321a5-9: 92 n. 256 321a29-32: 92 n. 256

321b10-16: 92 n. 256 326b6-28: 92 n. 260 De respiratione 473a15-b10: 71 n. 212 Metaphysica 1020a11-14: 47 n. 152 1022a4-6: 126 Meteorologica 340b19-23: 355 Physica 185a32-37: 60 n. 180 187b13-21: 87 n. 251 200b20-21: 114 n. 314 202b30-208a23: 43 203b15-30: 44 n. 137 205a8-205b1: 43 n. 136 206a25: 12 206b3-20: 44 n. 138 207b10-12: 44 n. 138 207b19: 44 n. 138 208a27-29: 33 208a27-209a2: 18 209a2-30: 18 209a31-210a13: 18 208b8-11: 74 209a3-4: 63 209a4-6: 57 n. 169, 123 n. 333 209a16-18: 58 n. 174 209a23-25: 49 n. 158, 52 209a31-209b1: 124 209b6-17: 66 210a14-24: 141 n. 386 210a14-b8: 18

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210a15-17: 144 n. 395 210b8-31: 18 210b22-27: 49 n. 158 210b32-211b5: 18, 23 210b34-211a3: 38 211a1-2: 46 n. 151, 123 n. 334 211a12-13: 109 n. 305 211a27-29: 123 n. 334, 129 n. 353 211a29-b1: 51 211b5-212a7: 18, 23, 33 n. 112 211b8-9: 126 n. 345 211b14-19: 34 211b17: 34 n. 114 211b19-29: 35, 38, 39, 40, 41 n. 132, 43, 50 n. 160 211b20: 35 n. 118, 36 211b21-23: 36, 40, 41 n. 132 211b24-25: 49 n. 155 211b25-29: 35 n. 117 212a5-6: 123 n. 336 212a7-30: 18, 23 212a14-21: 131, 132 212a14-30: 123 n. 336 212a20-21: 34 n. 113, 124 212a21-28: 132 n. 357 212a29-30: 46 n. 151, 123 n. 334, 135 n. 365 212a31-32: 139 n. 375 212a31-213a11: 18 212b3-13: 140 n. 379 212b7-22: 125 n. 339 212b12-13: 143 212b18-19: 141 n. 385 212b18-22: 142 n. 387 212b27-29: 135 n. 365 213a12: 29 213a12-b29: 18 213a15-16: 37 213a15-b2: 100 213a24-27: 73 n. 217 213a27: 71 n. 212 213b6-12: 92 n. 257

213b18-20: 92 n. 257 213b30-34: 94 n. 266 213b30-214a26: 18 214a13-16: 97 n. 279 214a16-19: 96 n. 275 214a26-32: 78 n. 229 214a26-b11: 18 214b5-9: 92 n. 257 214b12-28: 18 214b13-23: 76 n. 227 214b23-24: 96 n. 274 214b28-215a6: 78 n. 229 214b28-215a24: 18 214b33-215a1: 99 n. 284 215a4-6: 113 n. 312 215a6-11: 99 n. 284 215a22-24: 70 215a24-216a11: 18 215a25-29: 100 215a24-216a21: 99, 100 n. 286, 102 n. 292 215b22-216a11: 101 216a8-11: 102 n. 292 216a11-b21: 18 216a26-b21: 96 n. 275 216b22-217a21: 18, 24 216b33-217a10: 114 n. 315 217a21: 19 217a21-b28: 18, 24 217b20-28: 114 n. 315 224b35-225a10: 117 n. 323 225b7-8: 117 n. 323 227a10-13: 128 n. 350 Problemata 16.8-9: 70 n. 207 Topica 101a28-30: 22 n. 90 Arius Didymus (Diels) fr. 25: 68 n. 199

Index Locorum

Asclepius In Metaph. 63.25-65.28: 4 n. 40 65.29-35: 4 n. 40 Cleomedes Caelestia I.1.20-26: 88 I.1.25-30: 109 I.1.39-43: 111 I.1.62: 46 n. 146 Damascius De primis principiis II.219.21-220.2: 56 n. 165 David In Categ. 108.14: 3 n. 39 117.13-14: 3 n. 39 123.11: 3 n. 39 124.24: 3 n. 39 178.12: 4 n. 39 190.23: 3 n. 39 In Isag. 83.6: 3 n. 39 99.28: 4 n. 39 107.19: 3 n. 39 113.8-9: 4 n. 39 Proleg. 2.24: 3 n. 39 6.21: 3 n. 39 8.19-20: 4 n. 39 Democritus and Leucippus (Diels-Kranz) fr. 54.1: 48 n. 153 fr. 55.40: 48 n. 153

Elias In Isag. 38.25-26: 3 n. 39 42.10: 3 n. 39 79.6-7: 3 n. 39 90.28: 3 n. 39 94.30: 3 n. 39 Proleg. 2.31-32: 2.31-32 29.2: 2.31-32 Empedocles (Diels-Kranz) fr. 100: 71 n. 212 Epicurus Epistula ad Herodotum 39: 94 n. 271, 109 n. 306 40: 94 n. 271, 109 n. 306 41-42: 68 n. 199 67: 46 n. 146 Euclid Elementa XI.1: 62 n. 187 Galen De instrumento odoratus 5.12.1-13.1: 71 n. 210 De naturalibus facultatibus 64.4-10: 71 n. 210 In Timaeum fr. 17.35-39: 70 n. 209 Quod qualitates incorporeae sint 19.469.10-13: 40 n. 129 19.471.16: 85 n. 244 19.474.2-10: 40 n. 129

163

164

John Philoponus on Physical Place

Hero of Alexandria Pneumatics I.16,20: 70 n. 208 I.80-91: 71 n. 210 Lucretius De rerum natura I.426: 56 n. 166 Olympiodorus In Categ. 70.11: 3 n. 39 In Gorgiam 48.10.1-3: 3 n. 39 In Meteor. 16.25-17.1: 3 n. 39 31.3-4: 3 n. 39 69.26: 3 n. 39 89.12-13: 3 n. 39 94.17-18: 3 n. 39 Oribasius Collectiones medicae 60.4.1-7.1: 71 n. 210 Philoponus De aeterninate mundi contra Proclum ΧΙ.1, 407.18-21: 8 n. 51 XI.4: 53 De opificio mundi 36.6-18: 120 In Anal. Post. 215.3-5: xii n. 10 322.14-19: 10 n. 55 In Categ. 1.12-13: 19 n. 74

6.22-28: 21 n. 88 163.4-164.5: 85 n. 243 In Meteor. 35.9-21: 131 n. 355 35.18-19: xii n. 14 41.25-29: 62 n. 186 106.9-10: xi n. 8 In Phys. 2.13-16: 60 n. 181 54.8-55.26: 10 55.24-26: 22 n. 92 65.3-6: 22 n. 92 81.25: 31 n. 110 102.13: 2 n. 34 119.26-27: 22 n. 92 125.27-28: 2 n. 30 191.9-192.2: 10 225.4-226.11: 10 349.5: 31 n. 110 356.8: 31 n. 110 384.3-385.11: 10 393.15-16: 8 n. 51 408.7-9: 16 n. 71 456.17-458.31: 10 458.15-16: 8 n. 51 492.3: 31 n. 110 496.5-9: 20 n. 76 496.5-501.20: 18 497.10-20: 114 n. 313 498.30-499.30: 74 n. 222 500.6: 20 n. 78 500.19-20: 20 n. 80 501.13-20: 5 n. 43 502.15: 22 n. 92 504.8-510.26: 18, 19 504.14-17: 22 n. 91 504.24-28: 57 n. 170 504.29-505.11: 56 n. 168 505.11-13: 58 n. 173

Index Locorum

507.17: 22 n. 92 508.9-20: 58 n. 174 509.15-510.2: 14 n. 66 and 68, 15 n. 69, 74 n. 222 509.22: 14 n. 66 513.11-13: 13 n. 64 514.7-519.8: 18 514.10-18: 20 n. 76 514.15-515.8: 132 515.14-24: 66 515.19: 60 n. 182 518.26-519.8: 5 n. 44 520.19-25: 60 n. 182 524.1-22: 10 526.10-528.22: 18 526.20-23: 57 n. 168 526.29-30: 20 n. 79 528.2: 20 n. 79 528.12: 31 n. 110 530.2: 14 n. 65 531.19-20: 20 n. 81 532.12: 14 n. 65 533.20-536.20: 18 534.22-23: 106 n. 298 535.15-20: 21 n. 82 539.17-543.4: 18 540.22-30: 21 n. 86 541.7: 20 n. 79 543.13-25: 20 n. 81 546.2: 47 n. 152, 126 n. 346 546.25-552.13: 18, 23 547.9-16: 58 547.15-16: 57 n. 168 547.20-22: 21 n. 83 548.16: 35 n. 117 548.16-18: 22 n. 93 548.30-549.4: 40 549.16: 57 n. 168 549.25: 57 n. 168 549.33: 57 n. 168 549.28-29: 22 n. 92

549.28-550.8: 42 n. 134 551.23-24: 57 n. 168 551.20-28: 40 n. 130 552.10-13: 2 n. 30 552.14-557.7: 23 557.8: 25 n. 98 557.8-10: 24 n. 95 557.8-559.27: 92 n. 255 557.8-585.4: 10, 7 n. 46 557.8-585.7: 18 557.9: 11 n. 56 557.10-14: 43 557.10-560.17: 43 557.10-563.25: 26, 54 557.18-19: 46 n. 147 557.21: 92 n. 259 557.23-24: 45 n. 144 557.24-28: 46 n. 148 557.31: 46 n. 147 558.3-10: 49 n. 157 558.10-19: 46 558.21-26: 49 n. 157 558.27-31: 47, 85 558.29-30: 51 559.9-12: 47 559.14-18: 75 559.19-27: 45 n. 145 559.24-29: 106 n. 298 560.3-11: 92 n. 259 560.17-19: 49 n. 156 560.17-562.1: 43, 49 561.5-25: 59 n. 178 561.25-27: 86 n. 248 562.1-563.25: 43, 49 562.17: 80 n. 234 562.25: 50 n. 159 562.28: 96 n. 274 563.5-15: 96 n. 274 563.6-12: 52 563.20-21: 95 563.23-24: 61

165

166

John Philoponus on Physical Place

563.26-567.28: 26, 27, 123, 127 563.27-31: 128 564.6-9: 130 n. 354 564.12-14: 130 564.14-565.1: 132, 135 565.1-9: 139 n. 373 565.1-567.7: 139 n. 373 565.10: 139 n. 373 565.12-14: 139 n. 374 565.19-21: 106 n. 298 566.1-8: 145 n. 396 566.3-6: 142 n. 388 566.10-12: 143 n. 390 566.12-17: 144 n. 393 566.17-26: 144 n. 394 566.27-29: 144 n. 394 566.31: 106 n. 298 567.8-28: 137 n. 368 567.15-16: 138 n. 372 567.22-25: 137 n. 369 567.27-28: 137 n. 370 567.29-569.17: 61, 64 n. 193 567.29-579.18: 26, 27, 55, 80 567.30-33: 95 567.32: 67 n. 197 568.13: 62 n. 185 568.14-569.7: 62, 64 n. 193 568.26-29: 63 n. 192 569.6-9: 96 n. 274 569.7-17: 64 569.13-17: 96 n. 273 569.10-11: 66 n. 195 569.17-20: 69 n. 203 569.18-573.21: 69 569.20-28: 71 n. 214 570.9-571.9: 72 570.17: 70 n. 205 570.28-29: 72 n. 215 571.8-9: 72 n. 215 571.18-27: 73 572.3-4: 74 n. 219 572.10: 106 n. 298

572.25: 106 n. 298 573.11-13: 96 n. 274 573.17-19: 74 n. 219 574.13-19: 110 n. 307 574.14: 80 n. 234 574.15: 80 n. 234 574.20: 80 n. 234 574.21-24: 82 574.28-575.2: 66 n. 195 575.2-3: 50 n. 160 575.4-6: 143 n. 391 575.17-20: 110 n. 307 575.18: 80 n. 234 575.21-30: 81 575.23: 80 n. 234 575.27-578.4: 80 n. 236 575.32-33: 79 n. 232 575.33-576.3: 81 576.1: 80 n. 234 576.22: 106 n. 298 577.4-9: 96 n. 274 577.7-9: 79 n. 232 577.10-578.4: 117 n. 321 577.14-16: 96 n. 274 577.25-578.4: 92 n. 259 577.30-578.4: 51 n. 161 577.32-37: 51 n. 161 578.2-5: 51 n. 161 578.5-579.18: 86 n. 248 578.10: 86 n. 249 578.11-15: 87 n. 252 578.18-23: 87 n. 251 578.27-32: 87 579.3-6: 66 n. 195 579.3-7: 87 n. 253 579.3-13: 60 n. 182 579.6-10: 96 n. 274 579.7-9: 94 n. 266 579.8: 80 n. 234 579.10-583.12 579.14-15: 79 n. 232 579.15-17: 86 n. 250

Index Locorum

579.19-583.12: 26, 28 580.24-30: 80 n. 234 581.8: 27 n. 101 581.18-19: 106 n. 298 581.18-21: 75 581.23-26: 75 581.28-29: 76 n. 226 582.19-583.12: 68 n. 198 582.25: 68 582.26-28: 106 n. 298 582.31: 80 n. 234 583.1: 80 n. 234 583.6-8: 96 n. 274 583.9: 80 n. 234 583.13-585.4: 26, 28, 115 583.13-14: 115 n. 319 583.14: 115 n. 316 583.15-23: 116 n. 320 583.25-29: 116 583.30-584.4: 116 583.33-34: 115 n. 316 584.3-4: 115 n. 316 and 318 584.4-25: 117 n. 322 584.25-28: 117 n. 325 584.28-585.4: 118 n. 327 585.5-589.26: 18 586.9-24: 132, 133 n. 359 587.9-588.27: 132, 133 n. 359 587.26-30: 131 n. 356 587.30-33: 135 n. 365 587.30-588.27: 133 588.1-3: 133 n. 360 588.20-27: 14 n. 67, 135 589.19-26: 5 n. 44 589.29: 22 n. 92 591.23-24: 2 n. 30, 3 n. 37 592.29-32: 16 n. 71, 92 n. 259 593.11-600.24: 18 594.14-28: 139 n. 376, 141 n. 382 595.18-597.4: 139 n. 376, 141 n. 382 598.3-30: 16 n. 71 598.17: 20 n. 78

598.20-21: 52 n. 162 598.24-30: 92 n. 259 599.11-12: 15 n. 70 600.25-602.5: 139 n. 376 601.25: 14 n. 65 606.25-610.23: 18 607.12-608.10: 73 n. 217 608.1-10: 71 n. 213 609.16: 20 n. 78 612.15-19: 71 n. 213 612.15-613.6: 73 n. 217 616.9-619.22: 18 616.11: 20 n. 78 620.4-5: 15 n. 70 623.19-628.24: 18 624.26-625.9: 92 n. 259 630.6-634.2: 2 n. 31, 18 631.21-632.3: 76 n. 227 632.4-8: 16 n. 71 632.4-634.2: 10, 74 n. 220, 76 632.4-8: 16 n. 71 632.7: 11 n. 56 632.7-8: 85 n. 245 632.13-633.5: 76 n. 228 633.5-14: 77 633.22-28: 77 635.24-25: 21 n. 87 636.23-642.26: 18 636.25-28: 19 n. 75 639.3-642.26: 7 n. 46, 10, 91, 112 n. 309, 113 n. 310 639.4-5: 11 n. 56 644.15-22: 10 645.19-26: 21 n. 84 645.27-651.4: 18 650.27-651.4: 24 650.30-651.1: 27 n. 101 651.1-4: 11 n. 57 651.19: 14 n. 65 653.17-22: 21 n. 86 660.7-662.27: 18 667.6-675.12: 18

167

168

John Philoponus on Physical Place

667.28-31: 22 n. 92 671.7-672.17: 10 672.7-12: 21 n. 83 and 87 675.12-14: 9 n. 54, 25 n. 96 675.12-676.3: 28 675.12-695.8: 7 n. 46, 10, 24, 28 675.13-695.8: 10, 18 675.15-16: 91 n. 254 675.18-19: 106 n. 298 675.21: 8 n. 52 675.23-29: 92 n. 259 675.26-676.2: 25 n. 96, 99 n. 283 675.29-676.1: 91 n. 254 676.1-2: 11 n. 56 676.4-677.8: 28 n. 103 676.4-686.29: 28, 29, 99 677.9-680.23: 28, 100 677.12-13: 101 n. 288 679.26-27: 101 680.24-26: 11 n. 56 680.24-684.10: 28, 101 680.28-681.1: 101 n. 289 681.15-17: 92 n. 259 681.24: 80 n. 234 681.33: 80 n. 234 682.17: 80 n. 234 682.18-19: 92 n. 259 683.7-17: 102 n. 290 683.17-25: 102 n. 291 684.10-686.29: 28, 102 684.13-685.23: 92 n. 259 684.17-685.23: 103 684.19-32: 103 685.10-12: 105 n. 295 685.23: 11 n. 58 685.23-25: 105 n. 296 685.29-686.2: 106 n. 297 686.2: 106 n. 298 686.5-23: 106 n. 297 686.29: 106 n. 299 686.30-687.35: 92 n. 259

686.30-689.25: 28, 29, 97 687.14-19: 91 n. 254 687.15-16: 8 n. 52 687.19-29: 27 n. 101 687.22-27: 98 687.23-24: 11 n. 57 687.29: 80 n. 234, 97 n. 278 687.30-35: 60 n. 182 688.2-5: 97 n. 279 688.14: 80 n. 234 688.21: 80 n. 234 688.24: 80 n. 234 688.31-34: 91 n. 254 688.33: 8 n. 52 689.6-7: 91 n. 254 689.14-16: 91 n. 254 689.14-20: 92 n. 259 689.22: 111 n. 308 689.26: 80 n. 234 689.26-693.27: 28, 29, 112 690.3-691.8: 28 691.9-692.26: 28, 137 n. 371 691.12: 106 n. 298 691.18: 80 n. 234 692.8-11: 137 n. 371 692.27-693.27: 28 692.32: 106 n. 298 693.12-27: 113 n. 311 693.15: 80 n. 234 693.16: 106 n. 298 693.28-694.19: 137 n. 371 693.28-694.27: 28, 30, 108 693.35: 108 n. 304 694.4-12: 108 694.12-17: 110 694.16-27: 91 n. 254 694.17: 8 n. 52 694.19-23: 66 n. 195 694.19-27: 92 n. 259 694.28-695.8: 28, 30, 112 n. 309 695.9-699.26: 18, 19

Index Locorum

696.17: 21 n. 87 697.25-699.20: 10 699.21-26: 5 n. 44 701.1-5: 20 n. 79, 21 n. 86 701.16-17: xii n. 13 738.24: 31 n. 110 741.21-742.28: 69 n. 202 745.20: 31 n. 110 748.7-33: 10 756.9: 31 n. 110 774.6-775.5: 10 854.14: 31 n. 110 891.1: 31 n. 110 Plato Timaeus 35A2-36B5: 92 n. 260 48E-52D: 56 n. 164 49A1-6: 94 n. 270 50B5-D3: 94 n. 270 52A8-B5: 94 n. 270 Plutarch De comm. not. cp.50, 1085e: 46 n. 149 De facie 927B-C: 75 n. 225 Proclus In Eucl. 143.5-21: 129 n. 351 Ps.-Alexander of Aphrodisias (Ideler) Problemata II.59: 71 n. 210 Sextus Empiricus Adversos Mathematicos VIII.263: 46 n. 146 X.2: 94 n. 271

X.3-4: 94 n. 271 X.7: 82 n. 237 X.142: 40 n. 129, 45 n. 142 Simplicius In Categ. 134.5-11: 84 n. 242 342.21-22: 84 n. 242 342.22-25: 84 n. 242 363.29-364.6: 56 n. 165 In De Caelo 26.17-19: xi n. 9 119.7: xi n. 5 284.28: 68 n. 199 295.1-5: 37 n. 121 524.17-525.4: 71 n. 213 594.33-595.3: 68 n. 199 In Phys. 529.34-530.3: 57 n. 171 530.9-14: 93 n. 262 574.19-21: 35 n. 117 574.23-26: 40 n. 130 574.19-578.13: 36 n. 119 575.1-2: 34 n. 115 575.1-12: 53 575.12-19: 53 575.21-26: 36 576.28-29: 35 n. 117 576.30-577.1: 40 n. 130 587.16-22: 126 n. 346 595.3-14: 139 n. 378 601.1-645.19: xii n. 15 604.5-11: 127 n. 347 618.20-25: 65 622.16-17: 39 n. 125 634.11-15: 63 n. 191 639.25-36: 114 n. 315 644.10-654.19: 63 n. 191 647.26-30: 71 n. 213 773.8-800.25: xii n. 15

169

170

John Philoponus on Physical Place

Stephanus In De Interpr. 2.9-10: 3 n. 39 6.32: 3 n. 39 8.28: 3 n. 39 37.29: 3 n. 39 65.26: 3 n. 39 Stobaeus Eclogae I.14.1e2-7: 40 n. 129 I.161.8: 68 n. 199 Stoics (I. von Arnim) I.95: 48 n. 153 II.331: 48 n. 153 II.363: 46 n. 146 II.380: 46 n. 149 II.381: 46 n. 146 II.482: 40 n. 129 II.501: 46 n. 146, 82 n. 237 II.503: 56 n. 167, 68 n. 199 II.505: 56 n. 167 II.619: 68 n. 199 Syrianus In Metaph. 84.31-85.15: 56 n. 165, 65 n. 194 Themistius In Phys. Paraphr. 103.6-8: 74 n. 221 104.9-22: 39 n. 126 104.20: 32 n. 111 106.6: 32 n. 111 107.13: 32 n. 111 108.4: 32 n. 111 112.18: 32 n. 111 113.7-13: 38 n. 122 113.7-116.9: 93 n. 264

113.7-119.2: 37 114.7-115.12: 38 n. 122 114.19-20: 83 n. 239 115.13-116.9: 38 115.21-22: 38 n. 123 115.31-35: 49 n. 155 115.33-116.1: 46 n. 150 115.34: 39 n. 125 115.36: 46 n. 148 116.11-12: 35 n. 117, 39 n. 127 116.27: 44 n. 140 116.27-32: 44 116.29-30: 39 n. 128 117.3-4: 32 n. 111 118.11: 32 n. 111 119.17-25: 139 n. 378 119.22: 32 n. 111 119.26-120.3: 139 n. 378 120.20-121.20: 140 n. 380 123.15-22: 94 n. 268 125.28-126.3: 94 n. 266 127.28-128.8: 76 n. 227 127.28-128.23: 114 n. 315 127.28-133.14: 108 n. 303 128.9-17: 76 n. 227 128.24-130.2: 114 n. 315 129.1-3: 113 n. 312 129.14-15: 113 n. 312 130.9: 32 n. 111 130.18-133.14: 114 n. 315 132.6-14: 102 n. 292 133.10: 32 n. 111 133.22-134.2: 73 n. 218 134.33-135.1: 96 n. 276 135.25: 32 n. 111 137.16-23: 96 n. 276 140.1: 32 n. 111 Theophrastus (Fortenbaugh et al.) fr. 146: 127 n. 347

Index Nominum A Aёtius: 94 n. 271 Albert of Saxony: 82 n. 237, 99 n. 282 Alcinous: 66 n. 196 Alexander of Aphrodisias: xvi, 2 n. 28, 3, 19 n. 75, 31, 32, 33, 36 n. 119, 39 n. 126, 40 n. 130, 41, 46 n. 150, 47 n. 152, 57 n. 171, 76 n. 227, 93, 98, 118 n. 326, 126, 140 n. 381, 143 n. 389 Algra, K.: ix, xii n. 12, xv, 3 n. 37-38, 15 n. 69-70, 20 n. 77 and 80, 21 n. 82, 22 n. 91, 23, 37 n. 121, 56 n. 167, 58, 68, 70 n. 208, 75 n. 223, 85 n. 243, 94, 127 n. 348-349, 135 n. 364, 139 n. 378 Ammonius Hermeiou: xi, xii, xviii, 2, 4, 15, 26, 28, 30, 31, 84, 85 n. 243, 86, 115, 116, 117, 118, 119, 120, 122, 147, 149 Anaxagoras: 73 n. 217 Andronicus: 84 Aquinas, Th.: 99 n. 282 Archytas: 84 Arius Didymus: 68 n. 199 Asclepius: 4 Atomists: 15, 16, 29, 31, 32, 33, 37, 42, 48, 55, 56, 65, 68 n. 199, 70, 92, 94, 102, 107, 114 n. 315, 147 Avempace: 99 n. 282 Αverroes: 99 n. 282

Blank, D.: xi n. 7, 115 n. 317 Böhm, W.: xiii n. 18 Bonetus, N.: 99 n. 282 Bostock, D.: 36 n. 119, 44 n. 138, 125, 134 n. 362, 139 n. 375, 145 n. 397 Bowen, A. C.: 46 n. 146, 88, 110, 111 Broadie, S.: xv n. 25 Buridan, J.: 99 n. 282

B Bailey, C.: 56 n. 166 Baltussen, H.: 2 n. 28 Barbarus, H.: 44 n. 140 Barnes, J.: 21 n. 89, 34, 124, 126, 132, 139 n. 375 Berryman, S.: 70

E Edwards, M. J.: xv n. 25 Elias: 3 n. 39 Empedocles: 71 n. 212, 92 Epicurus: 31, 33, 37, 45, 46, 48, 56, 68 n. 199, 88, 94, 98 n. 281, 109, 114, 147 Erasistratus: 70

C Canter, H. v.: 8 n. 49 Chrysippus: 37, 40, 41, 45, 48, 93 Cicero: 8 n. 49 Clagett, M.: xiii n. 19 Cleomedes: 46 n. 146, 88, 109, 110, 111 Crescas, H.: 99 n. 282 D Damascius: xiv, 56, 63 n. 191, 121 David: 3 n. 39 Democritus: 37, 48, 54, 107, 108 n. 303, 114 n. 314 Descartes, R.: 99 n. 282 Diels, H.: 8, 9, 68 n. 199, 94 n. 271 Dillon, J.: 66 n. 196 Diocletian: xii Dorotheo, G.: 8, 9 Duhem, P. L.: xiii n. 19, 69 n. 204

172

John Philoponus on Physical Place

Euclid: 62 n. 187, 129 Eudemus: 139, 140, 141, 142, 143, 144, 145 Évrard, E.: xiii n. 18, xiv n. 20, 3 n. 36 F Falcon, A.: 2 n. 28, 46 n. 146, 62 n. 187 Furley, D.: xiv, xv, 26, 29, 30 n. 106, 43, 49 n. 156, 51 n. 161, 63 n. 192, 65 n. 194, 70 n. 208, 71 n. 212, 75 n. 224, 83, 86 n. 250, 95, 96, 110, 116, 117 n. 325, 119 n. 328, 137 n. 369 G Galen: 37, 40 n. 129, 70, 71, 80 n. 236, 85 n. 244, 118 n. 326 Galilei, G.: 99 n. 282, 102 n. 291 Gerson, Ll. P.: xiii n. 17-18 Golitsis, P.: xi n. 3, XII n. 12, xiii n. 17, xiv, xv n. 24, 1 n. 28, 3 n. 36, 5 n. 4243, 8, 10 n. 55, 11, 12, 13, 16 n. 72, 17 n. 73, 26, 29, 31 n. 108, 63 n. 191, 115 n. 317, 127 n. 349 Grant, E.: xiii n. 19, 66 n. 196, 69 n. 204, 82 n. 237, 99 n. 282, 102 n. 291, 121 Griffin, M.: 117 n. 324 Guthrie, W. K. C.: 71 n. 212 H Haas, F. A. J. de: ix, xiii n. 18, xiv n. 20, 48 n. 154, 56, 60 n. 183, 130 n. 354 Hassing, R. F.: xiv n. 20 Hense, O.: 40 n. 129 Hero of Alexandria: 70, 71 Hesiod: 20 n. 77 Hintikka, J.: 44 n. 138 Hoffmann, Ph.: 5 n. 42, 63 n. 191 Homer: 2 n. 33 Huby, P.: xv, 19 n. 75, 24 Hussey, E.: 35 n. 117, 100 n. 286

I Iamblichus: 56, 114 n. 315, 121 Ideler, J. L.: 71 n. 210 Ierodiakonou, K.: ix, 80 n. 235 J Jammer, M.: 127 n. 348 K King, H. R.: 35, 36 n. 119, 109, 125 Kühn, C. G.: 40 n. 129, 85 n. 244 Kupreeva, I.: 30 n. 107 L Lacey, A. R.: xv n. 25 Lang, H. S.: xiv n. 20, 30 n. 106, 36 n. 119, 58, 59 Lang, U. M.: xi n. 2, xiii n. 18 Lautner, P.: 80 n. 235 Lear, J.: 44 n. 138 Lehoux, D.: 70 n. 208 Lettinck, P.: xv n. 25 Leucippus: 37, 54, 107 Lucretius: 56 n. 166 M Macierowski, E. M.: xiv n. 20 Martin, C. J.: xiv n. 20, 80 n. 235, 84 n. 240 McGinnis, J.: 139 n. 375-376, 140 n. 381, 145 n. 396 McGuire, J. E.: xiv n. 20 Melissus: 59, 60 Mendell, H.: 36, 37 n. 121, 84 n. 241, 145, n. 397 Morison, B.: 35, 36, 52, 53, 54, 125, 127, 134, 139 n. 375, 145 n. 397 N Newton, I.: 99 n. 282 Nicomachus of Gerasa: 148

Index Nominum

O Olympiodorus: 3 n. 39 Ophuijsen, J. Van: xii n. 12, xv, 3 n. 3738, 15 n. 69-70, 20 n. 77 and 80, 21 n. 82, 22 n. 91, 23, 58, 75 n. 223, 127 n. 349, 135 n. 364 Opsomer, J.: ix, 75 n. 225, 104 n. 294 Oribasius: 71 Osborne, C.: xv n. 25, 5 n. 43 P Papachristou, I.: xii n. 11 Patrizi, F.: 99 n. 282 Perkams, M.: 115 n. 317 Plato: xii, xiv, 10, 12 n. 73, 20, 37, 56, 62 n. 187, 66, 70 n. 207, 75 n. 224, 92 n. 260, 94, 114 n. 315 Platonists: 65, 89, 121, 147, 150 Plotinus: 66 n. 196, 121 Plutarch: 46 n. 149, 75 n. 225 Posidonius: 68 n. 199, 129 Proclus: 2 n. 28, 117 n. 324, 121, 129 Ps.-Alexander: 71 n. 210 Q Quintilian: 8 n. 49 R Rashed, M.: 31 n. 110, 36 n. 119, 40 n. 129, 41 n. 132, 45 n. 143, 47 n. 152, 49 n. 158, 57 n. 171, 76 n. 227, 93 n. 262, 118 n. 326, 126 n. 346, 140 n. 381, 143 n. 389 Ribera-Martin, I. de: 128 n. 350 Roey, A. van: xii n. 11 Ross, W. D.: 35 n. 118 Roux, S.: 79 n. 233 S Saffrey, H.: xi n. 6 and 9 Sambursky, S.: 56 n. 165, 114 n. 315, 119, 121 n. 330

173

Šanda, A.: xii n. 11 Scholten, C.: 26 n. 99, 27 n. 102, 60 n. 183, 62 n. 187 Scotus, D.: 121 Sedley, D.: xiv, 30 n. 106, 56 n. 166, 78, 94 n. 267, 96, 97 n. 277, 98 n. 281, 107 n. 302 Sellars, J.: xiii n. 17 Sextus Empiricus: 40 n. 129, 45, 82 n. 237, 94 n. 271 Sharples, R. W.: xiv n. 20, 127 n. 348 Shorey, P.: 57 n. 171 Simplicius: xi, xii n. 15, xiv, 1 n. 27, 5 n. 42, 8, 16, 32 n. 111, 34 n. 115, 35 n. 117, 36, 37 n. 121, 39 n. 125, 40 n. 130, 45 n. 141, 50, 51 n. 161, 53, 56 n. 165, 57 n. 171, 63 n. 191, 65, 68 n. 199, 71, 84, 85 n. 243, 93 n. 262, 114 n. 315, 126, 127, 139 n. 378, 143 n. 391, 150 Solmsen, F.: 56 n. 166 Sorabji, R.: xiii n. 17-18, xv n. 25 Stephanus: 3 n. 39 Stobaeus, I.: 40, 41, 45, 68 n. 199 Stoics: xvi, xvii, 31, 32, 33, 39 n. 126, 40 n. 129, 41 n. 132, 42, 45 n. 146, 46, 48, 54, 55, 56, 68, 85 n. 244, 93, 94, 108 n. 303, 147 Strato of Lampsacus: 31, 65, 70, 89, 119, 147 Suarez, F.: 99 n. 282 Syrianus: 56, 65 n. 194, 121, 150 T Tempelis, E.: xiii n. 18 Themistius: xvi, xvii, xviii, 10, 26, 27, 30, 31, 32, 33, 35, 36, 37, 42, 43, 44, 45, 48, 50, 53, 54, 57 n. 169, 73 n. 218, 74, 76 n. 227, 80 n. 236, 81, 83, 85, 93 n. 264, 94 n. 268, 96, 97, 98, 102 n. 292, 103 n. 293, 105, 106 n. 298, 108 n. 303, 112, 113 n. 312, 114, 139, 140, 141, 142, 143, 144, 147

174

John Philoponus on Physical Place

Theophrastus: 70, 117 n. 324, 127, 128 Todd, R. B.: 46 n. 146, 88, 110, 111 Toletus, F.: 99 n. 282 Trincavelli, V.: 6, 8, 9, 59 n. 179 Trombley, F. R.: xi n. 6

W Wachsmuth, C.: 40 n. 129 Wildberg, C.: ix, xi n. 3, xii n. 12, xiii n. 18, xiv n. 20, 17 n. 73, 113 n. 310 Wittwer, R.: 2 n. 35

U Urmson, J. O.: 65

Z Zabarella, G.: 66 n. 196 Zeno of Elea: 49 n. 158, 52

V Verrycken, K.: xi n. 3, xii n. 12, xiii n. 18, 75 n. 224, 115 n. 317 Vitelli, G.: 1, 5, 6, 7, 8, 9, 31 n. 109-110, 59 n. 179, 139 n. 373