Simplicius: On Aristotle On the Heavens 3.1-7 9781472552273, 9780715638439

The subject of Aristotle’s On the Heavens, Books 3-4, is the four elements of earth, air, fire and water, which exist be

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Simplicius: On Aristotle On the Heavens 3.1-7
 9781472552273, 9780715638439

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Acknowledgements The first draft of my translation of Simplicius’ commentary on Books 3 and 4 of Aristotle’s On the Heavens (De Caelo, Cael.) was completed in 2005-6 when I was a Visiting Scholar at Christ’s College, Cambridge. I would like to record my gratitude to the fellows of the College and particularly to the then Master, the late Malcolm Bowie, who provided me with an ideal working place and a most convivial intellectual and social atmosphere in which to live. I would also like to thank the Classics Faculty at Cambridge for both the use of its library and the continuing stimulation of its seminars and lectures, in which the interventions of Nicholas Denyer, Geoffrey Lloyd, Malcolm Schofield, David Sedley, Robert Wardy, and others reminded me again and again that no interpretive question can safely be considered settled. In making this translation I have constantly had to rely on others for help with linguistic and substantive issues. I am sure I cannot remember the names of all of those others, but I would like to mention Elizabeth Asmis, Benno Artmann, Myles Burnyeat, Alan Code, Stephen Menn, Jan Opsomer, David Sedley, and James Wilberding, Dirk Baltzly, and Daniel Graham. Baltzly and Graham are the only official vetters whose names are known to me, but the suggestions and corrections of the other three were also extremely helpful. I am especially grateful to the general editor of the ancient commentators series, Richard Sorabji, whose advice and encouragement were a sine qua non for my completion of this translation. The most important mainstay for all my endeavours continues to be my wife and intellectual partner of almost fifty years, Janel Mueller. How lucky I have been to be able to have dinner conversations with her on the translations of both Simplicius’ commentary and the texts of Queen Elizabeth I written in foreign languages. Ian Mueller Chicago

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Abbreviations Cael. = Aristotle’s On the Heavens. CAG = Commentaria in Aristotelem Graeca, Berlin: G. Reimer, 1882-1909. DK = Hermann Diels and Walther Kranz (eds and trans.) (1954), Die Fragmente der Vorsokratiker, 6th edn, Berlin: Weidmann. DPA = Goulet, Richard (ed.) (1989- ), Dictionnaire des philosophes antiques, Paris: Éditions du Centre national de la recherche scientifique. GC = Aristotle’s On Coming to Be and Perishing. Guthrie = W.K.C. Guthrie (ed. and trans.) (1939), Aristotle, On the Heavens, Cambridge, Mass: Harvard University Press, and London: William Heinemann. in Phys. = Simplicius’ commentary on Aristotle’s Physics (CAG, vols 9 and 10). Karsten = Simon Karsten (ed.) (1865), Simplicii Commentarius in IV Libros Aristotelis De Caelo, Utrecht: Kemink and Son. Metaph. = Aristotle’s Metaphysics. Moraux = Paul Moraux (ed. and trans.) (1965), Aristote: du Ciel, texte établi et traduit par Paul Moraux, Paris: Les Belles Lettres. OED = The Oxford English Dictionary, 2nd edn, Oxford: Clarendon Press, 1989. Phys. = Aristotle’s Physics. Rivaud = Albert Rivaud (ed. and trans.) (1925), Timée-Critias (Platon, Oeuvres Complètes, vol. 10), Paris: Les Belles Lettres. Sider = David Sider (ed. and trans.) (2005), The Fragments of Anaxagoras, 2nd edn, Sankt Augustin: Academia Verlag. Stocks = J.L. Stocks (trans.) (1922), De Caelo, Oxford: Clarendon Press, also in vol. 2 of W.D. Ross (ed.) (1928-52), The Works of Aristotle, 12 vols, Oxford: Clarendon Press. Theophrastus: Sources = William W. Fortenbaugh, Pamela M. Huby, Robert W. Sharples and Dimitri Gutas (eds and trans.) (1992), Theophrastus of Eresus: Sources for his Life, Writings, Thought, and Influence (Philosophia Antiqua 54), 2 vols, Leiden and New York: E.J. Brill. Tim. = Plato’s Timaeus. TL = Timaeus of Locri, On the Nature of the World and the Soul; cited after Marg (1972).

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Introduction This volume is a translation of Simplicius’ commentary on book 3 of On the Heavens from its beginning until 305b28 in chapter 7. The remainder of the commentary on book 3 and all of book 4 will be published in a separate volume (Mueller (2009)). Most of Simplicius’ commentary on book 1 has been translated in Hankinson (2002), (2004), and (2006). Missing from the translation of the commentary on chapters 1 to 4 are Simplicius’ exchanges with John Philoponus on Aristotle’s cosmology. Simplicius’ representations of Philoponus’ criticisms of Aristotle are translated in Wildberg (1987); Simplicius’ responses are for the most part still untranslated. The commentary on book 2 is translated in Mueller (2004) and (2005). Simplicius was born in Cilicia (in southeastern Turkey) in the late fifth century of the Common Era. He studied philosophy with Ammonius of Alexandria (DPA, vol. 1, pp. 168-9) and with Damascius (DPA, vol. 2, pp. 541-93) in Athens or Alexandria. At the time of the closing of the so-called Platonic school in Athens (529), Simplicius went with Damascius and five other philosophers to the court of Chosroes, King of Persia. They did not stay long but returned in or around 532 to the confines of the Byzantine Empire under a treaty provision protecting them from persecution. It is not known where Simplicius went; Athens, Alexandria, and, more recently, Harran in southeastern Turkey east of Cilicia have been suggested.1 But it is now generally agreed that the three great Aristotelian commentaries safely attributable to Simplicius, those on the Categories, Physics, and On the Heavens2 were written after Simplicius departure from Persia when, one assumes, he had the leisure to write these extensive works and to do the research and thinking they presuppose. 1. The contents of Cael. 3 and 43 Books 3 and 4 of On the Heavens are not about the heavens, the world between the fixed stars and the moon. Their subject is, as Simplicius says (551,13), ‘the sublunary simple bodies’, that is, the ultimate components of everything in the world beneath the moon, for Aristotle earth, air, fire, and water, frequently referred to as elements. Here I give a brief summary of books 3 and 4 to provide the reader with a general orientation. Toward the beginning of chapter 1 (298b8-12) Aristotle announces that he is going to raise the question whether anything comes to be. This leads him into a dichotomous doxography of the views of his predecessors. Three

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of the categories are filled by Presocratics, namely (i) those who said that nothing really comes to be or perishes, Parmenides and Melissus; (ii) those who said that all things come to be, but some of these last forever, others perish (Aristotle mentions Hesiod); (iii) those who say that there is one thing which endures, everything else being a transformation of this which comes to be and is in flux (Aristotle mentions Heraclitus). I shall discuss Simplicius’ treatment of these people in sections 2-4 of this introduction. Aristotle puts off treatment of these three people to another discussion4 and turns to those ‘who make every body come to be, composing them from planes and dissolving them into planes’ (298b34-299a1). The criticism of this view, which Aristotle finds in Plato’s Timaeus, occupies the rest of chapter 1. Books 3 and 4 of Cael. place a great deal of pressure on Simplicius’ self-proclaimed belief in the harmony of Plato and Aristotle because they contain extended, explicit criticism of the Timaeus. I shall discuss how Simplicius proceeds in section 7. Many of Aristotle’s arguments against Plato in chapter 1 involve assigning to Plato the view that bodies are composed of points and arguing that since points are weightless, bodies must be too, contradicting the fact that bodies have weight. For Simplicius what I have called a fact is a hypothesis which Aristotle makes for the purpose of his arguments and then ‘demonstrates’ in chapter 2. Cael. is our source for Aristotle’s doctrine of weight and its many difficulties, which emerge particularly in book 4, when Aristotle does as much as he ever does to establish the existence of four simple bodies. In fact, his theory of weight would work much better if there were only two simple bodies, earth and fire. For Aristotle, earth is heavy and fire is light, or more specifically, earth has heaviness and no lightness, fire lightness and no heaviness. The heaviness of earth is exhibited in (or defined by) its motion down to the centre of the spherical cosmos and its resting around that centre, the lightness of fire in its motion up to the periphery of the sublunar cosmos, the lunar sphere, and its resting at or near the periphery. For Aristotle this motion and rest of earth and fire is natural. In the light of these remarks we can say that the first purpose of chapter 3 is to show that bodies have weight or lightness. Aristotle begins the chapter by arguing that every simple body has a natural motion, taking as obvious that they move and arguing that they must move either naturally or unnaturally and that unnatural motion presupposes natural motion. He then argues that things rest naturally at the place to which they move naturally. There follows, starting at 300b8 arguments against people who, in Aristotle’s view give a priority to unnatural motion, the atomists and Plato in the Timaeus, and then some brief remarks about the cosmogonical priority of rest in Anaxagoras and Empedocles. At 301a22-b31 Aristotle uses abstract arguments to show that bodies must be light or heavy, and gives his problematic account of projectile motion. Toward the end of chapter 2 Aristotle says (in Simplicius’ understanding), ‘That not everything comes to be and that not absolutely

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nothing comes to be is clear from what has been said previously’ (301b313), and gives a difficult argument that not everything comes to be. To explain where Aristotle showed that not everything comes to be Simplicius refers to his argument that the heavens are eternal in Cael. 1.3 and to the discussion of Parmenides and Melissus in chapter 1, a discussion which includes no argument at all. In any case Aristotle’s remark provides the transition to chapter 3 which begins: It remains to say what things come to be and why they do. Since in all cases knowledge is based on primary things and the elements are the primary things which inhere , we should investigate which sort of bodies of this kind are elements and why, and thereafter investigate how many there are and what they are like. (302a10-14) For Simplicius (600,19-22) Aristotle does not really answer this question until his work On Coming to Be and Perishing, where we are told that the four elements or simple bodies are characterised using two pairs of opposites, earth being dry and cold, water wet and cold, air wet and hot, fire dry and hot, changes among them being explained in terms of changes of these qualities. At the beginning of chapter 3 Aristotle defines an element as ‘something into which other bodies are divided and which inheres in the bodies … and which itself cannot be divided into things different in kind from it’, and argues that there are and must be such things. He then says a little bit about the Presocratics, mentioning the doctrine that there is only one element and the views of Anaxagoras and Empedocles. His next goal is to determine the number of elements. He proceeds by eliminating the views of predecessors. In chapter 4 he dismisses the ones who believed that there are infinitely many elements, Anaxagoras (302b13-303a3) and the atomists (303a3-b3). In chapter 55 he rejects the doctrine that there is only one element, distinguishing between those who say it is fire (304a7304b11) and those who make it something intermediate between fire and earth (303b13-304a7). He concludes the chapter with two general arguments against monism based on his doctrine of natural motion. With the elimination of the alternatives that there are infinitely many elements and that there is only one, one would expect Aristotle to turn to showing that there are, in fact, four. But Aristotle starts chapter 6 by saying that if it is first shown whether the elements are eternal or come to be it will be evident how many there are and what they are like, and he does not get to the question of how many elements there are until chapter 4 of book 4. In 4.4, after the discussion of heaviness and lightness in 4.1-3, Aristotle argues that fire is absolutely (haplôs) light and moves to the periphery of the cosmos and then that earth is absolutely heavy and moves to its centre and at 312a8-12 says,

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Introduction There is also something between periphery and centre and it is named differently relative to each of them, since what is intermediate is a kind of extremity and centre for both. As a result there is also something else which is both heavy and light; such are water and air.

In chapter 5 Aristotle introduces the idea that each of the four elements has (in some sense) its own kind of matter. The next and final chapter of Cael. is a kind of addendum on the role of shape in certain kinds of motion. (Why does a ball of lead, which sinks in water, float if it is flattened out sufficiently?) I discuss all of this material and the transition to it at the end of 3.8 in the introduction to Mueller (2009). In 3.6 Aristotle gives abstract arguments that the elements are not eternal and come to be from one another, and in chapter 7 he turns to criticism of accounts of the way in which they come to be, first criticising the view, which he associates with Empedocles and Democritus, that a changing into b is a matter of bits of b contained in a being ‘separated out’ (ekkrinesthai) from a. This brings to an end the material discussed by Simplicius in this volume.6 In the next material Aristotle offers a lengthy series of criticisms directed mainly at Plato’s account of elemental change in the Timaeus. After it Aristotle ends book 3 with a remark which serves as the transition to the discussion of weight in book 4: But since the most important differentiae of bodies are those which relate to affections and acts and powers …, it would be right to speak first about these so that by studying them we can grasp the differences of each element with respect to each. (307b19-24) In the next seven sections of this introduction I discuss some of the important names mentioned by Simplicius. These discussions of what Simplicius says about various figures are not exhaustive, and one should consult the Index of Names for listings of all the passages relating to a particular person. 2. The Presocratic ‘monists’ (Thales, Anaximenes, Anaximander, Hippo, Heraclitus, Hippasus, Diogenes) Simplicius’ commentaries are a major source of information for the history of early Greek philosophy, principally because he quotes many texts which would otherwise be lost to us, but also because his interpretative discussions, although sometimes infected with anachronistic Neoplatonist ideas, contain important information. The only one of the so-called ‘monists’ whom Aristotle mentions in Cael. 3 and 4 is Heraclitus in his brief doxography at the beginning of 3.1: Other people say that all other things come to be and are in flux and none of them is fixed, but only one thing endures and all the other

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things are natural transformations of it. This seems to be what Heraclitus of Ephesus and many others mean to say. (298b29-33) In commenting on this passage Simplicius invokes ‘the people who are called students of nature in the strict sense, those who said that all things come to be but that only one thing, which does not come to be, endures and that the other things come to be from it and are resolved into it: Thales said that this one thing is water, Anaximenes air, Anaximander what is intermediate (to metaxu), Heraclitus fire’ (561,25). Simplicius repeats this kind of recitation, the sort of thing scholars associate with ‘handbooks’ whenever Aristotle mentions the view that there is one element. I quote the passage which stimulates Simplicius to give his fullest recitation: Some people hypothesise one only, some hypothesising water, some air, some fire, and some hypothesise that it is finer than water but denser than air, which they say contains all the heavens, being infinite. (3.5, 303b10-13) Simplicius explicates: There are several such people, and different people hypothesised this one element to be something different. Thales of Miletus and Hippo said it is water because they saw that the seeds of animals and the nourishment of both animals and plants are made of water. Anaximander, a fellow citizen and pupil of Thales, said it is something indefinite which is finer than water and denser than air because the substratum should be naturally adapted for the change to either; he was the first to hypothesise that this one is infinite, so that he could use it for comings to be without stinting; and, it is thought that he hypothesised infinite worlds and that each of the worlds came to be from an infinite element of this sort. Anaximenes, a pupil and fellow citizen of Anaximander, also hypothesised that the principle is infinite, but not also indeterminate; he said it is air, thinking that the volatility of air is sufficient to account for change. Diogenes of Apollonia hypothesised the same thing , and Hippasus of Metapontum and Heraclitus of Ephesus, taking into consideration the active power of fire, said that it is the principle. (615,10-23) Simplicius mentions all of these people at 602,19-20 when Aristotle considers a consequence of saying there is only one element, and he mentions Thales, Anaximenes, and Heraclitus as people who ‘make the cosmos come to be from one thing’ at 590,18-19 in connection with 3.2, 301a13-14, where the monists are not clearly relevant. Heraclitus and Hippasus are mentioned again in connection with 3.5, 304a7-18 where Aristotle criticises ‘those who hypothesise fire as the element’, but Simplicius is confused by

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Aristotle’s criticism of people who associate a figure such as the pyramid with fire. He writes, It should be asked who holds this view which says that fire is a pyramid because it is the first body. For Heraclitus, who does say that fire is the element of other things, does not say that fire is a pyramid, and the Pythagoreans, who say that fire is composed from pyramids, do not say that fire is the element of other things since they also say that fire comes to be from water and air just as air and water come to be from fire. (621,6-11) The ‘Pythagorean’ of whom Simplicius is thinking is the fictitious author of the post-Platonic pseudepigraph based on the Timaeus, which I discuss in section 7.7 3. Hesiod At 3.1, 298b26-9 Aristotle says, There are some people who say that there is nothing which does not come to be, but that everything comes to be, and some things that have come to be endure without perishing, and, again, others perish. This is especially true of Hesiod and his followers, and later, of others, the first people who studied nature. Simplicius (560,16-27) explains Aristotle’s account of Hesiod by invoking line 116 of the Theogony, ‘In truth at the very first Chaos came to be’, and he assumes that the other people to whom Aristotle refers are Orpheus and Musaeus. For Simplicius the writings of these people (many of which are now considered later productions) are to be interpreted as mythical representations of Neoplatonist truths. Their talk of coming to be is really about procession from causes, so the first cause does not come to be, and when Hesiod says that Chaos came to be, he is indicating (enedeixato) that there is something prior to Chaos and (by not saying what it is) that this something is beyond (huper) knowledge or even being named. 4. Parmenides and Melissus At 3.1, 298b14-24 Aristotle says, Some of the earlier philosophers did away with coming to be and perishing entirely. They say that nothing that is either comes to be or perishes, but is only thought by us to do so. Examples are Melissus and Parmenides and their followers, who, even if they say other correct things, should not be considered to speak in a way appropriate to the study of nature, since the existence of some things which

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do not come to be and are entirely without change is a matter for another prior enquiry rather than for enquiry into nature. Because these people assumed that there is nothing else apart from the substance of perceptible things, but were the first to understand that there must be certain entities of this kind if there is going to be any knowledge or thought, they transferred accounts of those entities to these. Simplicius is convinced that this account is incorrect and that Aristotle is following his customary procedure of objecting on the basis of a superficial reading of the text in order to prevent other people from adopting a superficial Eleaticism as the truth (557,19-20). He even resorts to sarcasm: ‘And it is clear that Parmenides was not unaware that he himself came to be, just as he was not unaware that he had two feet, even though he said that being is one’ (559,26-560,1), and he refers to a passage in the Metaphysics (1.5, 986b27-987a2) to show that Aristotle understood Parmenides better than what is suggested by the Cael. passage he is commenting on. Simplicius assumes that the claim that Parmenides and Melissus believed only in the substance of perceptible things and transferred accounts of intelligibles to perceptibles rests on a misunderstanding of their view that being is one. In fact Parmenides and Melissus make the standard Platonist distinction between what really is, the intelligible object of knowledge, and what comes to be, the perceptible objects of opinion. In support of this claim Simplicius cites fragment 1, lines 28-32, fragment 8, lines 50-2, and fragment 19 of Parmenides and the lengthy fragment 8 of Melissus, his citations here being our only source for the last two of these. He cites fragment 8, line 21 for Parmenides’ belief that what really is does not come to be, but can only assert that Melissus agrees with Parmenides. And for their belief that perceptibles come to be he refers again to fragment 8 of Melissus and gives us our only citation of fragment 11 for Parmenides. 5. Empedocles Aristotle first mentions Empedocles at 3.2, 300b2 where he says that Empedocles thought the earth is at rest because of the vortex. Simplicius paraphrases this statement without comment (582,29-583,1). In the course of arguing that natural or ordered motion is prior to disordered motion Aristotle says, Furthermore, one might further ask whether it would not be possible that, when things were moving in a disorderly way, some things would undergo mixtures of the kind from which bodies which are put together naturally are put together (I mean, for example, bones and flesh) in the way Empedocles says happens under Love (epi tês philotêtos). For he says, ‘Many heads without necks grew’. (3.2, 300b25-31)

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In commenting (586,5ff.) Simplicius says that Aristotle intended us to draw the absurd consequences of such a possibility, namely that if disorderly motion could produce neckless heads and things like bones and flesh, it could also produce a cosmos at some time, but no reason could be given why a cosmos should be produced at one time rather than another. Simplicius goes on to discuss the meaning of ‘under Love’. He tells us that Alexander of Aphrodisias thought the words referred to the time when Love dominates everything, but objects that isolated limbs wandering about (for which he also gives us our only citation of the continuation of the line quoted by Aristotle) indicate that Strife still has some power and Loves is just coming to dominate.8 After he finishes his argument that the cosmos could not arise from a condition of disorderly movement, Aristotle commends Anaxagoras for making the cosmos from things at rest. He then says, Empedocles also passes over coming to be under Love, since he was not able to put the heavens together by constructing them out of separated things, making Love the cause of their blending. (3.2, 301a15-16) According to Simplicius (590,19ff.), Empedocles said that ‘the elements, which were earlier blended by Love, make this cosmos when they are later separated by Strife’. Instead of supplying the certainly correct genesis when he essentially quotes Aristotle he writes, ‘Therefore, Empedocles also passes over the condition of the elements under Love’, so that here he is taking ‘under Love’ to mean at the time when Love is in total control.9 But, since for Simplicius the total domination of Love represents the (Neoplatonist) intelligible world in which all things are unified, he is quite comfortable saying that for Empedocles Love is not responsible for the coming to be of the cosmos, rather the separation which occurs under Strife is. Although Simplicius does accept that Love and Strife interact and rise and fall in power in our cosmos, what he says in connection with this passage does not help us understand his conception of what we call Empedocles’ cosmic cycle. At the beginning of 3.6 Aristotle argues against the eternity of the elements on the grounds that we see the simple bodies being dissolved; he argues that this dissolution must reach a stopping point and says: If the dissolution were to stop at some point, either the body with which it stopped would be indivisible or it would be divisible but would never in fact be divided – Empedocles seems to mean to say something like this. (305a1-4) Simplicius repeats this and then says of Empedocles: He says that the elements are divisible, and, unlike Democritus and his followers, he does not hypothesise that the principles are indivis-

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ible; but he does suppose that the four elements do not change into one another and do not perish because he does not allow for a common matter, but says that their coming to be from one another, which we see, occurs because of separation out, since everything, being an actuality, inheres in everything. (628,8-13) The idea that for Empedocles coming to be of anything is a matter of separation out of actually inherent bits (rather than the Aristotelian qualitative change of a substratum) is articulated further at 632,2-16 in conjunction with 3.7, 305b1-5, where Aristotle begins to criticise theories according to which change is a matter of separation out (he mentions Empedocles and Democritus). In the course of that argument at 305b16-20 Aristotle makes a dichotomy between those who say that there is no void and those who accept it. Simplicius (631,21-34) says that the former are Empedocles and Anaxagoras. Aristotle says the same thing about these two men at 4.2, 309a19-21, in connection with his assertion that they made no distinction between light and heavy. 6. Anaxagoras In 3.4 Aristotle argues against those who make there be infinitely many elements, starting with Anaxagoras, whom he treats at 302b13-303a3. At the end of his discussion of Aristotle’s arguments Simplicius queries the claim that Anaxagoras thought there was an infinite number of elements in the literal sense. Perhaps, he says, ‘infinite’ means ‘unknowable by us’.10 He continues: It seems that Anaxagoras is indicating a cosmic ordering in two senses. One ordering is intelligible and unified; in it all things were together and each thing was all the others because of intelligible unification. The other is perceptible and made separate from that unification by demiurgic Mind, which he says itself also proceeds from the intelligible and orders everything. (608,31-609,3) At the beginning of 3.3 Aristotle offers as a universally accepted definition of element that it is something into which other bodies are divided and which inheres in them and which cannot be divided into things different in kind. Aristotle leaves open the question whether elements are actually present in compounds in the way puzzle pieces are present in a completed puzzle or rather potentially present in the way that Aristotle thinks that water is present in blood, not as little bits but as blended throughout it. Simplicius explains, ‘That the elements inhere actually follows for those, such as Empedocles and Anaxagoras, who say that coming to be is the result of blending and separation out, but that they inhere potentially follows for those who say it is a result of qualitative change’ (601,7-9). Aristotle himself goes on to say,

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Introduction If an element is what we have said it is there must be some things of this sort among bodies. For fire and earth are contained potentially in flesh and wood and everything of this sort, since they are obviously separated out from them. But neither flesh nor wood inheres in fire either in potentiality or in actuality, since if they inhered they would be separated out. (302a19-25)

At 602,3, after pointing out that Aristotle is here not using ‘separated out’ in the technical sense in which only things which inhere actually can be separated out, Simplicius gives alleged examples of the kind of process Aristotle has in mind and concludes, ‘If fire and earth and the others are contained in flesh and wood, and there is no flesh or wood in fire or earth either potentially or actually (“since if they inhered they would be separated out” at some time), it is clear that fire and earth and the others are elements of flesh and wood, since they inhere in them, but the latter are not elements of the former’. Aristotle now invokes Empedocles and Anaxagoras: Anaxagoras speaks about the elements in a way contrary to Empedocles. Empedocles says that fire and earth and the things co-ordinate with them are the elements of bodies and that all things are composed of them, but Anaxagoras says the contrary; he says that the homoiomeries (I mean flesh and bone and everything of that sort) are elements and says that air and fire are mixtures of these and all the other seeds – for each of them is a collection of all the invisible homoiomeries – so that everything comes to be from these homoiomeries. (302a28-b4) In Aristotle the adjective ‘homoiomerous’ (homoiomerês; the neuter singular of which is also translated as the noun ‘homoiomery’11) is applied to something which in his theory are only divisible into things similar to themselves; homoiomeries includes Empedocles’ four elements, earth, water, air, fire, and such things as flesh and bone, by contrast with such things as a hand or face. Although Anaxagoras almost certainly did not use any word like ‘homoiomerous’, which appears to be an Aristotelian coinage, it would seem from what we know of his theory of nature that it might be said (perhaps with reservation) that he believed that the elements included all of Aristotle’s homoiomeries, simple or composite. In the passage just quoted Aristotle says that, in saying that the homoiomeries are elements, Anaxagoras took a position contrary to Empedocles. Simplicius sometimes appears to take this to mean that Empedocles’ four elements were not included among Anaxagoras’ homoimerous elements, most explicitly when he says: Anaxagoras himself says that these four are not elements, even though they are homoiomerous. (605,10-11; cf. 603,17-28)

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On the other hand at one point he does say: Anaxagoras calls not just the four elements but also all other things (the homoiomereities) elements, and says that everything is in everything but all things are characterised by the dominant thing in them; and so, when several bits of fire which have been separated out combine, it is thought that fire comes to be. (632,13-16) In 3.7 Aristotle begins to discuss the way in which the elements come to be from each other, beginning with Empedocles and Democritus, who, according to Aristotle, say that they do so by separation out. Aristotle never mentions Anaxagoras in the course of the discussion, but Simplicius is confident he is to be included (632,5.9.13), perhaps because, as Simplicius notes (635,6-7) at 3.7, 305b20-8 Aristotle uses an argument very like one he makes against Anaxagoras in the Physics. 7. The Pythagoreans, Timaeus of Locri, Plato’s Timaeus, and Democritus12 For the most part (the exceptions are 580,11 and 610,7) when Simplicius mentions ideas as Pythagorean he is speaking about things said in Plato’s Timaeus. Simplicius believed that Plato based his Timaeus on a work called On the Nature of the World and of the Soul,13 allegedly written by Timaeus of Locri, the title character of Plato’s dialogue. I refer to this work as TL. It is now generally believed that TL was written at least 300 years after Plato’s death. Simplicius treats Plato’s dialogue and TL as equally reliable sources for the ideas of the (for us non-existent) person whom he sometimes calls the Pythagorean Timaeus. When he mentions, e.g., what Timaeus thought, it is not always necessary or even possible to decide whether he means the author of TL or the speaker in Plato’s Timaeus. For the most part Simplicius relies on the Timaeus for the representation of views being criticised by Aristotle, but there are several points for which he cites or relies on TL. The most important of these is the TL invocation (215,13-17) of form and matter as prior to the construction of the elements (564,3-8; cf. 641,10-14 in the commentary on 3.7); for others see the entry ‘Timaeus’ in the Index of Names. I have already mentioned that Simplicius is completely committed to the idea that Aristotle understands and agrees with Plato and that his criticisms of Plato are directed against superficial readings of Plato’s text with the aim of dissuading others from adopting such readings and perhaps the doctrines they express. Unfortunately Simplicius does not always tell us how he would explain an Aristotelian criticism along these lines, but the absence of such an explanation should not be treated as the abandonment of the explanatory principle. As I have indicated in section 1 Aristotle begins his criticism of Plato in 3.1. In his first criticism (299a2-11) he insists that the construction of the fundamental solids out

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of planes yields serious contradictions with mathematics by implying that a line is divisible into points and that a line is not infinitely divisible. Commenting, Simplicius says, These are Aristotle’s words, but, as I always say, he is objecting to the apparent meaning of the theory. However, it should be said that if those who say that solids are composed of planes and resolve solids into planes said that the planes are mathematical and have only length and breadth, then Aristotle is correct to introduce against them these absurdities and the ones which he adduces next. But if they say that the planes are natural and have not only length and breadth but also depth (which is the first natural thing capable of entering into combinations), the absurdities adduced against the planes as being without depth do not follow from their position. And that they hypothesise that the planes are natural and not mathematical is clear from their saying that they involve matter, and so they set out matter first and say that it has been given shape by forms and numbers. (563,26-564,3; the last words are a paraphrase of Timaeus 53B3-5; similar ideas at 573,3-11, 577,17-19, and 579,3-4, 26-9) And in order to justify his claim that the planes of the Timaeus involve matter Simplicius cites TL. Simplicius is now led into a more general discussion of the interpretation of Plato’s geometrical chemistry.14 Some, including Iamblichus, thought Plato was speaking symbolically, that is, I assume, they did not think the chemistry was intended as a literal truth. Others left out the chemistry altogether (I assume that they too believed it was ‘symbolic’) and proposed to ascribe to Plato the apparently Aristotelian view that earth, water, air, and fire are composites of qualities and matter: More recent Platonic philosophers try to show that, according to what is written, the theory of nature of the Timaeus holds in the following way: since the four elements are composites of matter and form and therefore do not satisfy the definition of a principle, they say that the qualities which are called affective, heat and dryness and their opposites, coming to be first in matter (or qualityless body) also compose the four elements …. And if someone were to ask why fire heats and water cools, they would say ‘Because fire is hot, water cold’. For they posit these things as principles and do not seek further for a cause beyond the principles. (564,13-24) Simplicius does not respond to this position directly, although he clearly thinks it is in some sense incorrect, but instead he brings in Democritus’ atomistic explanations as an alternative and then the ‘Pythagoreans’:

Introduction

13

Democritus ascended to atoms on the grounds that those who offer explanations in terms of hot and cold and such things do so in an amateurish way (idiôtikôs).15 And in the same way the Pythagoreans ascend to planes, considering figures and magnitudes to be causes of heat and cold, since things that separate and divide produce an awareness of heat, those that blend and pull together an awareness of cold. (564,24-9) And after he has explained the Pythagorean/Platonic theory Simplicius says: I have set out these considerations in order to indicate that it was not unreasonable for the Pythagoreans and Democritus in seeking the principles of qualities to rise up to the figures. (565,26-8) Simplicius concludes his discussion by suggesting that Plato did not think of his geometrical chemistry as an absolute truth but as a hypothesis, which is like astronomical theories in being a way of accounting for what happens in the world. Later, in response to a suggestion that Plato’s and Democritus’ theories are the same, Simplicius offers the following account of the slight differences between Plato and Democritus in this regard: Plato’s view is presumably different from Democritus’ because it gives priority to something simpler than bodies, namely the plane, which is simpler than the atoms (which are bodies) and because it recognises that symmetries and proportions are demiurgic of the figures, and because it treats earth differently . (576,16-19) The reader is referred to the text and translation for further information about Aristotle’s objections to Plato in 3.1 and Simplicius’ interpretation of them. In 3.2, 300b8ff. Aristotle argues against the atomists for only talking about the constrained (unnatural) motion of the atoms resulting from collision and not their natural motion and against Plato for saying that prior to the cosmos there was a disorderly motion, a motion which he says must be unnatural because if it were natural it would produce a cosmos. Simplicius invokes the standard Neoplatonist view that the pre-cosmic motion of the Timaeus should not be understood literally: If Timaeus said that before the cosmos came to be there really was a disordered motion of the elements, Aristotle has made correct and real objections based on natural considerations against Timaeus’ doctrine. But if Timaeus wanted to make the point that all cosmic order comes to matter from the demiurgic goodness by treating in discourse matter in and of itself without its clothing with

14

Introduction only its suitability to receive form and indicated that it moves in a discordant and disorderly way, and what Timaeus says is productive of an intellectual doctrine, then Aristotle is doing adequate battle with the apparent meaning of what is said but not with its true meaning. (587,26-588,3)

In discussing what Aristotle has to say about atomism, Simplicius mainly describes and clarifies what Aristotle says against the atomists, but at the end of his discussion he brings up Alexander’s charge that the atomists would also be subject to the objection raised against the Timaeus by Aristotle, since the natural is prior to the unnatural, and the natural produces a cosmos. Simplicius’ response suggests that he may view constrained atomic motion in the same way he views the disorderly motion of the Timaeus: Perhaps saying this does not follow for Democritus and his followers since they said that there is always motion by constraint even when there is a cosmos and not just before the making of the cosmos, as Timaeus writes. (585,32-586,2; for an analogous understanding of Empedocles and Anaxagoras see 305,20-306,8 in Simplicius’ commentary on Cael. 1.10) Except for one passing mention of the disordered motion of the Timaeus at 591,15 Plato plays no role in the remainder of the commentary translated in this volume. Democritus does continue to play a role, but Simplicius provides us with very little information about Democritean atomism which we would not know from other sources, especially Aristotle himself. In 3.4 Aristotle argues against those who hold that there are infinitely many elements. He turns to the atomists at 303a3: However, the consequences of what some other people, such as Leucippus and Democritus of Abdera, say are not reasonable either. They say that the primary magnitudes are infinite in number and indivisible in magnitude and that several things don’t come to be from one thing or one thing from several, but that all things are generated by the weaving together and interlocking of the primary magnitudes. And in a way these people also make everything to be numbers and to be composed of numbers. For even if they don’t indicate this clearly, nevertheless this is what they mean. (303a3-10) Simplicius explains that Leucippus and Democritus: call atoms, which are indivisible because of their smallness and solidity and also infinite in number and in shapes, elements. And they said that only these things are continuous, since other things

Introduction

15

which are thought to be continuous draw together by contact. Accordingly they also did away with division by saying that apparent division is the parting of things in contact, and so they said that ‘several things don’t come to be from one thing’ since an atom cannot be divided and that one thing which is truly continuous doesn’t come from several, but each thing is thought to become one because of the weaving together of atoms. (609,18-24) As to the comparison of atoms with numbers, Simplicius says, Aristotle says that the atoms are ‘in a way’ numbers because the atoms resemble monads and because they are not divisible, just as monads are not, and because nothing continuous comes to be from the atoms, which are divided by the void, just as nothing continuous comes to be from monads; for the Pythagoreans say that monads are distinguished by the void. He adds ‘in a way’ because there is also some difference between the absurd consequences for those who generate things from atoms and the absurd consequences for those who generate them from numbers. For those who say there is generation from numbers the absurdity that they generate bodies from incorporeal parts follows, but those who generate things from atoms escape this. (610,1-11) Aristotle goes on (303a10-16) to claim that, although the atomists posited atoms of infinitely many different shapes, they only specified that fire atoms were spherical. ‘However, they did distinguish air and water and the rest by largeness and smallness, as if their nature was a sort of universal seedbed (panspermia) of all the elements’. Without mentioning the term ‘seedbed’ Simplicius explains that the atomists ‘said that the simple bodies are infinite because they differ in shape and shapes are infinite, but … they did not specify what sort of shape or what shape the elements which generate each body have, except only in the case of fire. They said that air and water and the rest come to be from elements which have the same shapes and differ only by largeness and smallness’ (611,611; cf. 617,22-6 and 624,29-625,3; at 690,24-6 in his commentary on 4.2 Simplicius says that fire is composed of small spheres, earth of larger atoms, and water and air of atoms of intermediate size). Just prior to this Simplicius cites Alexander’s account of the reason for assigning the sphere to fire: ‘the shape of fire and of the atoms from which it is generated is spherical, so that it is also reasonable that fire penetrates and moves and causes motion and divides and burns the things to which it comes near because it is circular and smooth and furthermore because the elements from which it is composed are small’ (610,18-22). Subsequently Simplicius, commenting on 303a24-9, explains the problem which is supposed to arise from distinguishing the atoms of things other than fire only by size:

16

Introduction If they say both that these things come to be from one another and that they differ from one another by the largeness and smallness of their atoms, it is necessary for them to contradict themselves, since these clash with one another. For if they say that earth comes to be from water when the largest in the water are separated out, then, since it is possible that at some time, all of the largest atoms having been separated out from the water, the separation out from the air of the largest atoms also gives out, the coming to be of earth from water and of water from air can also give out with the result that there is some water from which earth cannot come to be and some air from which water cannot come to be. So these people contradict themselves in saying both that these things come to be from one another and that they differ because of the largeness and smallness of their elements. And if when the smallest atoms are separated out they will give out, then water will not come to be from earth or air from water. However, we do see that every part of water changes into air and every part of air into water. And if fire is composed only of spherical atoms and the others out of all nothing else will come to be from fire and fire will never come to be from other things. (612,24-613,6) 8. Alexander of Aphrodisias16

Alexander of Aphrodisias lived around 200 CE.17 He is standardly regarded as the most Aristotelian of the commentators on Aristotle’s works. His commentary on Cael. does not survive, but Simplicius’ numerous references to his opinions on passages and related matters show clearly that Simplicius had it before him in writing his own commentary. However, although Simplicius sometimes relies on Alexander’s reading of a difficult passage, he more often cites Alexander to disagree with him on both major and minor points, and it is clear that he regards him as falling for the superficial reading of Plato and treating Aristotle’s criticisms as decisive.18 A textual question about 3.2, 300b21-2 provides a good illustration of Simplicius’ conception of Alexander’s unreasonable disdain for Plato. According to Simplicius (584,27-585,1) Alexander was unhappy with the standard text, which makes the first mover a self-mover and altered it because the notion of self-movement is Platonic, whereas for Alexander’s Aristotle the first mover is without motion. Several of the passages from in Cael. relating to Alexander have been discussed in Moraux ((19732001), vol. 3, pp. 181-241), and I shall content myself with a few remarks here.19 At 575,27 Simplicius reports Alexander’s rejection of an interpretation of the Timaeus according to which the geometrical chemistry is not to be taken literally, the only significant point being the ‘similarity’ of earth, water, air, and fire to the four solids assigned to them. Alexander thinks that the chemistry must be literal and not merely symbolic since Plato is

Introduction

17

willing to deny that earth interchanges with the other elements. Simplicius, who believes (and believes that Plato believes) that earth does interchange, is willing to invoke the symbolic interpretation as a basis for rejecting Alexander’s objection, but he still insists that explanation of elemental change in terms of shapes reveals something more fundamental than Aristotle’s reliance on qualities in On Coming to Be and Perishing. Later at 578,20 Simplicius reports Alexander’s response to another attempt to escape difficulties associated with the Timaeus by saying that Plato constructs the forms of the simple bodies from planes rather than the bodies themselves. Alexander responds that it is still the case that Plato generates solids from planes. Simplicius counters by insisting again that Plato’s planes are not mathematical. Alexander continues his response by saying (578,31-579,2), ‘In addition to this it is unreasonable for them to say that there is a generation of form; for just as there is no generation of matter, so there is no generation of form by itself, but generation is of the two together, and this is what comes to be by the presence of form and perishes by the absence of form’. Here Alexander sketches a standard view of change, a view which he also expresses at 598,26-599,2. Simplicius queries Alexander’s suggestion that form does not come to be, casting doubt on the idea that form couldn’t arrive through a temporal process rather than instantaneously. He adds that if there were any people who took the line being attacked by Alexander, they would have been talking about the emergence of form into existence, not the change of one thing into another (579,8-12). At the end of 3.2 Aristotle says, It is impossible for all body to come to be, unless it is also possible for there to be a separate void, since if it were to come to be, it would be necessary that in the place in which what is coming to be now will be there was previously void, with no body existing. It is possible for one body to come to be from another, for example, fire from air, but in general it is impossible for a body to come to be from no previously existing magnitude. Certainly a body could come to be actual from something which is potentially a body. But if the body which is potentially is not already another actual body, there will be a separate void. (301b33-302a9) For Simplicius there is a sense in which all body (or, as he puts it, body simpliciter) comes to be since the existence of body depends on higher metaphysical causes, but he does not want to concede that this fact implies the existence of void. He begins (at 598,26) by citing Alexander, according to whom Aristotle in this passage is setting out his doctrine of matter: Aristotle does not think that matter is actually incorporeal, but that both matter and form are separable in thought, although actually neither of them exists separately; rather, when something is said to

18

Introduction come to be from matter, it is said to come to be from something which is actually but with respect to what is potentially the thing which comes to be it is said to come to be from that thing as from matter. For Aristotle says that ‘in general it is impossible’ that something ‘come to be from no previously (actually) existing magnitude’, that is, from no body. For if this happened there would be a void. (598,27-599,4)

Simplicius responds to this view first with an unclear argument that Alexander’s position could be extended to the claim that no common qualities come to be, and continues: What then? Are there this many sublunary forms which do not come to be? And why do we say that all sublunary things come to be and perish? Or is it the case that just as there are common forms in this world, so too they come to be and perish? But these forms do not exist per se; rather they exist in individuals, since in this world no colour or shape which is not a particular thing exists per se, and similarly in the case of body. So, just as common things exist in particulars, so too they come to be and perish in those things, but they are always interchanging in particulars …. Common things appear in the continuous flux of particulars, and they seem to stand still as one thing because they are an appearance of the intellectual form which always is. It is as if one were looking at a face in an eternally flowing river: the appearance of the face in the water seems to be one and the same, although it is not the same but gives the impression of being one because of the enduring face. (599,14-26) Simplicius concludes by saying, However, even the Peripatetics, who place all common things in particulars, think that what is common and lies under particulars which are always in flux endures while changing. And perhaps one should say that body simpliciter does not come to be for this reason rather than because otherwise one would be forced to hypothesise a void. (599,27-31) I end this section with a remark on Simplicius’ quotations of Alexander. Heiberg marks the following passages as quotations: 578,2-7; 578,20579,2; 583,13-14; 585,1-5; 590,3-11; 594,18-22; 607,7-16; 618,10-619,8; 621,20-5; 624,10-13; 627,21-32; 631,13-15; 634,11-17. I have also treated as quotations: 617,11-21; 623,4-8; 623,8-16. I do not know why Heiberg does not mark the first of these as a quotation. The second and third are ‘that’-constructions (‘Alexander says that …’), but I see no reason to doubt that they essentially reproduce what Alexander said, and, indeed, they require minimal alteration to be turned into quotations.

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9. The text This translation is based on Heiberg’s edition of Simplicius’ commentary on Cael. printed as volume 7 of CAG, which I wish to discuss briefly here. My remarks are based on Heiberg’s preface to his edition (cited here by Roman numeral page) and his earlier, more detailed but slightly discrepant report to the Berlin Academy (Heiberg (1892)). What I say here applies to books 2-4, the situation for book 1 being significantly different. For Heiberg the most important manuscript is: A Mutinensis III E 8, thirteenth-fourteenth century, in the Este Library in Modena (Wartelle (1963), no. 1052). Heiberg ((1892), p. 71) singles out A for its correctness and purity. But he admits that it is badly deficient and hastily written, with frequent incorrect divisions of words, misunderstandings of abbreviations, arbitrary use of accents and breathing marks, extremely many omissions, and frequent insertions in a wrong place of words occurring in the vicinity. A glance at the apparatus on almost any page of Heiberg’s edition makes clear how often he feels forced to depart from A. On the whole these departures seem justified, but there are some cases where he follows A and produces a text which seems to me impossible or at least very difficult. Heiberg thought that A and another text, which he calls B, derived independently from a lost archetype. B stops in book 1, the remaining pages being torn out. Among the other manuscripts which Heiberg cites are:20 C Coislinianus 169, fifteenth century, in the National Library in Paris (Wartelle (1963), no. 1560). D Coislinianus 166, fourteenth century, in the National Library of Paris (Wartelle (1963), no. 1558). E Marcianus 491. thirteenth century, in the library of San Marco, Venice. (Mioni (1985), pp. 299-300; not in Wartelle (1963)). F Marcianus 228, fifteenth century, in the library of San Marco, Venice (Wartelle (1963), no. 2129). K Marcianus 221, fifteenth century, in the library of San Marco, Venice (Wartelle (1963), no. 2122). Heiberg took D and E to be significantly different from A and B, and C to be intermediate between D and E, on the one hand, and A and B, on the other. C and D are, in fact, not complete texts of Simplicius’ commentary, but texts of Cael. with extensive marginalia, the majority of which are derived from Simplicius’ commentary (not necessarily word-for-word quotations). According to Heiberg E, which is a complete (although lacunose) text, and D were copied from the same prototype, E being copied by an uneducated scribe. E was corrected by Bessarion (E2), using the Latin translation of William Moerbeke, a work to which I shall return shortly.

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Introduction

Heiberg decided on quite inadequate grounds, that F is a descendant of the archetype of A. He cites it only where it seems useful, so that, as he says, nothing can be concluded about its contents in places where it is not mentioned in the apparatus. Books 2-4 of K were copied from F and again corrected by Bessarion on the basis of the Moerbeke translation (K2). Not surprisingly Heiberg makes very little use of K, but he does sometimes adopt readings of C, D, E, and F. Heiberg also cites three printed versions of the commentary in his apparatus: (a) The editio princeps of the Greek text. Simplicii Commentarii in Quatuor Libros de Coelo, cum Textu Ejusdem, Venice: Aldus Romanus and Andrea Asulani, 1526. (b) The editio princeps of the Latin translation of William Moerbeke. Simplicii philosophi acutissimi, Commentaria in Quatuor Libros De coelo Aristotelis. Venice: Hieronymus Scotus, 1540. (c) Karsten, Simon (ed.) (1865), Simplicii Commentarius in IV Libros Aristotelis De Caelo, Utrecht: Kemink and Son. Citations of (a) are rare because Heiberg ((1892), 75) realised that it was a translation back into Greek of Moerbeke’s Latin translation.21 However, he did not realise that (b) was ‘corrected’ in the light of (a). The new edition of Moerbeke’s translation, begun in Bossier (2004), is an essential precondition of a satisfactory edition of Simplicius’ commentary, since Moerbeke relied on a Greek text which was more complete and less corrupted than any known today.22 In my reports on what is in Heiberg’s apparatus criticus I omit what he says about (b). Karsten’s edition was published one year after his death. It includes no critical apparatus, and has no preface by Karsten. Throughout it is based on single manuscripts, in the case of book 3 on a manuscript which Heiberg ((1892), 65) takes to descend from A: Paris Suppl. 16, sixteenth century, in the National Library in Paris (Wartelle (1963), no. 1575). In the absence of a critical apparatus or inspection of this manuscript, it is impossible to tell what alterations of his source Karsten made, but there is little doubt that he made ‘improvements’.23 I have sometimes thought it desirable to adopt them rather than what Heiberg prints. For Karsten’s readings I have relied on Heiberg’s apparatus, which includes an extensive, although not complete, record of Karsten’s text. My departures from Heiberg’s text are recorded in the footnotes and in the appendix ‘Departures from Heiberg’s text’. For the text of De Caelo itself I have relied on Moraux, and for the text of Plato’s Timaeus Rivaud.

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10. Brackets and parentheses In lemmas square brackets are used to enclose those portions of the text of Aristotle Simplicius is to discuss which are not included in the lemmas printed by Heiberg, which typically give the first and last few words of the passage separated by ‘up to’ (heôs). Frequently differences between Greek and English syntax make an exact correspondence impossible. In the text square brackets are placed around lower case Roman numerals which I have inserted for clarification. Angle brackets are used to set off major and possibly debatable insertions made for clarification. (Many minor insertions such as the substitution of a noun for a pronoun are made without remark when they are judged to be relatively certain; in particular I have frequently inserted a proper name where Simplicius has only a ‘he’ or a third person singular verb.) If an insertion represents an addition to the Greek text a footnote explaining this is attached. Parentheses are used as punctuation marks and to enclose Greek words inserted as information. Occasionally they are used to mark an insertion by Simplicius in a quotation. Notes 1. There is now a fairly extensive literature on the subject of Simplicius’ later life. For a useful brief summary with references see Brittain and Brennan (2002), pp. 2-4 (= Brennan and Brittain (2002), pp. 2-4). 2. On Simplicius’ works see Hadot (1990), pp. 289-303. The authorship of the commentary on Aristotle’s On the Soul, which comes down to us under Simplicius’ name, is disputed. For arguments see Huby and Steel (1997), pp. 105-40 (contra Simplicius’ authorship) and Hadot (2002) (pro), and Perkams (2005) (contra). Simplicius’ other extant work is a commentary on Epictetus’ Manual. 3. In this introduction I take for granted a number of points which are discussed in the notes on relevant passages in the footnotes to the translation. 4. For Simplicius’ explanation of Aristotle’s procedure here see 561,26-562,18. 5. I have outlined the argument of this chapter in an appendix on the argument of Cael. 3.5. 6. There is also a brief discussion of an obscure theory according to which elemental change is a matter of change of shape (305b28-306a1). 7. Simplicius’ only other reference to any of these monists in the commentary on books 3 and 4 comes in his discussion of 4.1, 308a17-29 at 679,2-6 where he associates Anaximander and Democritus as people who believe there is no up or down in the cosmos because the universe is infinite. 8. For the Simplicius’ other citations of Empedocles in the discussion of 300b2531 see the notes on 587,8-26. 9. cf. O’Brien (1969), p. 176. 10. At this point Simplicius provides us with our only citation of Anaxagoras’ fragment 7. 11. ‘Homomereity’ translates homoiomereia, a word not used by Aristotle. 12. Democritus’ forerunner Leucippus is mentioned only in phrases such as

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Introduction

‘Leucippus and Democritus’. For the six times he is mentioned see the entry on him in the Index of Names. 13. Marg (1972); text and English translation in Tobin (1985); extensive commentary in Baltes (1972). For Simplicius’ conception of Plato’s relation to Timaeus of Locri and TL see 561,10-11 and 646,5-6 in the commentary on 3.7. 14. For further discussion of this material see Mueller (forthcoming). 15. cf. 576,14-16 and 641,5-7 in the commentary on 3.7, where the same statement is repeated. 16. I regret very much that I have not been able to take into account the thorough and acute edition and translation with extensive discussion of the fragments of Alexander’s commentary on Cael. 2-4 now available in Andrea Rescigno (ed. and trans.), Alessandro di Afrodisia, Commentario al de Caelo di Aristotele, Frammenti del Secondo, Terzo, e Quarto Libro, Amsterdam: Hakkert, 2008. In the Addenda at the end of this volume I have provided an index of the passages in this translation presented and discussed by Rescigno. 17. On Alexander see Sharples (1987). 18. See Guldentops (2005). In the entry on Alexander in the Index of Names I have divided the relevant passages into those where Simplicius accepts what Alexander says and those where he does not and divided the latter into cases of significant and not so significant disagreement. 19. I have already mentioned Simplicius’ disagreement with Alexander on the interpretation of Empedocles (section 5) and Democritus (section 7). 20. I mention only the MSS cited in my notes. 21. A fact first noticed by Peyron (1810). 22. cf. Bossier (2004), p. CXXXII. The introduction to this work provides a comprehensive account of the complex situation relating to the manuscripts of the Moerbeke translation(s), (a), (b), and subsequent Renaissance publications of the Moerbeke translation. 23. cf. Bergk (1883), p. 143, n. 1 and p. 148.

SIMPLICIUS On Aristotle On the Heavens 3.1-7 Translation

on the third of Aristotle’s On the Heavens

551,1

There is presumably nothing to prevent us from now recalling the purpose of this whole treatise. Its subject is the simple bodies in the cosmos, the first ones which are composed from the principles. There are five of them, as he proved1 on the basis of the simple motions, that of the thing which moves in a circle and those of the four sublunary elements. And in the first two books he set out all sorts of theorems concerning the body which moves in a circle. And in those two books he also mentioned the things which he thought should be said about the cosmos since they belong to it because of the heavens: that it is one and finite, and does not come to be and is imperishable. And what he said about the earth2 was not said simply about the earth, but about it as having a relation to the heavens; and so he spoke about the position of the earth in the universe and its rest and shape and the comparison of its magnitude with that of the heavens. But now he begins to teach things about the sublunary simple bodies: that they are neither infinite nor one in number, but they are four in number; and that they come to be, but not from incorporeal things nor from another body but from one another, and not by separation out nor by composition and dissolution of planes or atoms. He will teach about these things in the present book, just as in the fourth book he will teach about the powers of the sublunary simple bodies. That he discusses these topics as concerning simple, primary bodies, just as he did in discussing the heavens is made clear by the fact that here he again uses the same proemium and shows that the subject of the study of nature is bodies. This will also be made clear by what will be said in proemium.3

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298a24-7 We have previously gone through the discussion of the first heaven [and its parts and further the stars which move in it – what they are composed of and what their nature is like, and also said that they do not come to be and are imperishable.] Here the proemium recalls briefly what was already explained in the first and the second book. He is calling the whole ethereal body the first heaven, since even if the whole cosmos is also called ‘heaven’

552,1

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Translation

because of the first heaven, this first heaven, the heaven in the strict sense, would be the unitary thing which is composed from eight spheres which he went through in the first book. He refers directly to the eight spheres as ‘parts’ of the first heaven since the stars are also parts of it, but they are parts of parts. He discussed the parts of the first heaven and the stars in the second book. One should understand what comes next as being spoken about everything together, that is, the first heaven and its parts and the stars; for ‘what they are composed of’ – the fifth substance – and ‘what their nature is like’ – that they are not soulless bodies, but bodies with soul, which share in mind and practical activity (praxis),4 and that they are spherical in shape, and, in addition, ‘that they do not come to be and are imperishable’ and that they do not undergo alteration or passion and are free from all the difficulties to which mortals are subject,5 were said and proved about everything together. But if, as Alexander thinks, Aristotle is pointing out with the words ‘what they are composed of and what their nature is like’ that are similar to the spheres in which they are located and are spherical and unmoving, then also the words ‘do not come to be and are imperishable’ cannot apply to everything, as Alexander says, but only to the stars, and one should understand them because in the first book it was proved that the whole heaven does not come to be and is imperishable.6 298a27-b5 Since7 some of the things which are called natural [are substances, others are acts and affections of substances (I call the simple bodies, that is fire and earth and the things co-ordinate with them, and what is composed of them, that is, the entire heaven and its parts, and, again, animals and plants and their parts, substances; and I call the motions of each of these things and the motions of all other things of which these are causes by dint of their own power and, further, their alterations and changes into one another acts and affections), it is evident that it results that the greatest part of enquiry about nature concerns bodies; for all natural substances are either bodies or come to be together with bodies and magnitudes. This is clear from the determination of what sorts of things are natural8] and from particular investigation. As I said,9 because he is going to again discuss other simple bodies, the sublunary ones, he again uses the same proemium which he used at the beginning of the treatise. The argument, which proceeds on the basis of the first hypothetical mode,10 is the following: If some of the things which are called natural are substances and some are acts and affections of such substances, ‘it results

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that the greatest part of enquiry about nature concerns bodies’ (since the discussion of the acts and affections of bodies makes reference to bodies); but the first; therefore the second as well. The words inserted in the middle make clear what natural substance is, namely that it is bodies, and what acts and affections are. In hypotheticals in which the antecedent is not only true but also clearly true and undisputed they use the causal (parasunaptikos) connective ‘since’ instead of the hypothetical (sunaptikos) connective ‘if’, and so more recent thinkers call this sort of proposition causal. And in the first book of his Prior Analytics Theophrastus makes clear the reason for this way of speaking.11 And it is for this reason that now Aristotle, too, does not say ‘if some of the things which are called natural’ but ‘since some of the things which are called natural’, it being evident that some of the things which are called natural are substances and some are acts and affections of substances. But since there are also hypernatural substances, he reasonably distinguishes by induction which substances are natural, namely the corporeal ones; for hypernatural substances are incorporeal. Consequently when he said ‘some of the things which are called natural are substances’ he was speaking about the corporeal substances; therefore, the consequent, that the greatest part of enquiry about nature concerns bodies, follows from this antecedent. Having said ‘fire and earth’ he adds ‘and things co-ordinate with them’, meaning the other three simple bodies, the fifth and air and water. The words ‘and what is composed of them’ indicate all the composites which he goes on to name, ‘the whole heaven’ (meaning everything ethereal) ‘and its parts,12 and, again (in the sublunary realm) animals and plants and their parts’; for all sublunary things are either animals or plants or their parts. Having said what the natural substances are, he indicates what the natural affections and acts of bodies are, mentioning the changes of place, which are rather acts of the substances he has mentioned and the other things of which these substances are causes by dint of natural power. For fire does not only change place; it also heats and dries things naturally. And each of the other natural bodies is active by dint of its own power. And what comes about is the act of what acts and the affection of what is acted on. Alterations are also of this kind, being acts of what alters something and affections of what is altered. And so are their changes into one another, that is, their coming to be and their perishing; these are acts of what makes or destroys and affections of what comes to be or is destroyed. So if both natural acts and natural affections belong to natural (that is, corporeal) substances, it is reasonable that the conclusion of the argument said that the greatest part of natural science concerns bodies.

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Either he says ‘the greatest part of’ instead of ‘all’ with the measuredness of a philosopher, or he means it in the strict sense since the discussion of soul and the first mover also falls to some extent to the student of nature. For the student of nature also uses arguments about the unmoving cause for circular motion is continuous and eternal. Or perhaps he says the greatest part concerns bodies because it also concerns the acts and affections of bodies and these are different from bodies, even if they also involve reference to bodies. Or perhaps he says it because natural substances are not bodies without qualification; rather they are either bodies or they are, as he adds, ‘together with bodies’; as a result the greatest part would concern bodies, if, indeed, some natural substances are souls, not bodies. He says that ‘it is clear from the determination of what sorts of things are natural’ that ‘natural substances are either bodies or (in the case of the communion of soul with body) come to be together with bodies’, since previously he mentioned fire and earth and spoke of ‘things co-ordinate with them, and what is composed of them’ and generally the things which have in themselves per se a starting point of motion; but all of these are either just bodies or they are together with bodies. He says that this is also clear ‘from particular investigation’. For each investigation of these which we call natural concerns bodies or things which are together with bodies. These statements are practically the same as what was said at the beginning of the treatise, namely ‘Most of the science of nature, in fact, concerns bodies and magnitudes and their affections and changes’.13 298b6-8 We have discussed the first of the elements [and what sort of nature it has and said that it does not perish or come to be.] It remains to speak about the two.

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He has shown earlier and also just now that the study of nature concerns bodies – and obviously it concerns the prior, simple bodies and as a result the composite ones, and he no longer needs to teach about the nature of body or how many simple bodies there are, having already given proofs about these subjects. However, having recalled that he has already discussed one of the simple bodies, the heavenly body, which he reasonably calls ‘first’, since it is prior to the sublunary bodies in position and in time and in the account of the cause, he turns to the remaining simple bodies, the sublunary ones. He calls the heavenly an element because it is simple since it is not an element of the cosmos, as Alexander says it is, but rather a part of it; for an element extends through the whole of what is composed of elements and mingles with the elements which are together with it. The words ‘what sort of nature it has’ that it has the nature of a certain fifth substance which is transcendent and moves in a circle and ‘that it does not perish or come to be’. So ‘it remains to speak about the two’, which come to be and perish. He calls the four sublunary bodies two because he is uniting them in terms of their motions up or down and in terms of their impulsions, that is, lightness and heaviness. Having shown previously14 on the basis of the simple motions that generically there are three simple bodies, that which moves in a circle, that which moves up, and that which moves down and having spoken about the one which moves in a circle, he reasonably adds, ‘It remains to speak about the two’.

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298b8-14 At the same time it will follow for those who speak about these things [that they also investigate coming to be and perishing. For either there is no coming to be whatsoever or it only occurs among these elements and things composed of them. Perhaps we should first investigate this very thing: is there coming to be or isn’t there? The earlier philosophers who were concerned with truth were in disagreement with what we are now saying] and with one another. Having spoken about the eternal body and being about to speak about ones which come to be, he first asks if there is or there isn’t any coming to be at all since some people said there is not. And, if there is, he asks in what way it does not occur and in what way it does, since some of those who say there is coming to be do not explain it in an appropriate way. He shows first that the discussion of coming to be is necessary for the person who is going to speak about sublunary things, since either there is no coming to be whatsoever or it is only in these sublunary elements and the things composed of them. He then asks whether there is coming to be or not. For when, as is the case with coming to be, it is not completely evident and undisputed whether the thing under consideration is, this is the first problem: whether the thing is or is not. For the first people who philosophised about the truth theoretically and did not concern themselves practically or politically with matters of choice and avoidance were in disagreement both with our statements and with one another; they were in disagreement with us because we say that there is coming to be and not in all things but only in sublunary ones, whereas some of them say that nothing comes to be and others that all things come to be (and so they also disagree with one another). Consequently, since discord on this subject is great, it is also necessary for the person who is investigating sublunary things to enquire about coming to be in general and to ask whether there is coming to be and what things come to be.

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Translation 298b14-24 Some of the earlier philosophers did away with coming to be [and perishing entirely. They say that nothing that is either comes to be or perishes, but is only thought by us to do so. Examples are Melissus and Parmenides and their followers, who, even if they say other correct things, should not be considered to speak in a way appropriate to the study of nature, since the existence of some things which do not come to be and are entirely without change is a matter for another prior enquiry rather than for enquiry into nature. Because these people assumed that there is nothing else apart from the substance of perceptible things, but were the first to understand that there must be certain entities of this kind if there is going to be any knowledge or thought,] they transferred accounts of those15 entities to these.

He divides beliefs about coming to be into four kinds.16 Some people completely do away with coming to be and say that no things that are come to be because there is no knowledge of things which come to be and perish since they are always in flux; Parmenides and Melissus have been thought to speak this way. But others, such as Hesiod, speak in the contrary way; he says that the very first of the things which he recognises has come to be: In truth at the very first Chaos came to be.17

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Other people, such as Heraclitus, say that, other things come to be, but there is only one thing, the common substratum from which the others come to be, which does not come to be. And others say that there is no body which does not come to be, but they all come to be by being compounded from planes. He first discusses Melissus and Parmenides and their followers. Of these Melissus says that there is no coming to be at all, whereas Parmenides says that there is none as far as truth is concerned, but that there is as far as opinion is concerned, and it is for this reason that Aristotle adds the words ‘but is only thought by us to do so’.18 He says that, even if these people say other correct things (they really understood correctly and in a divine way the one being and intelligible nature, and they disclosed to their followers that there cannot be knowledge of things that come to be and change because they are always in flux), they ‘should not be considered to speak in a way appropriate to the study of nature’ since they philosophise about hypernatural things. For it is a matter for another , first philosophy, to demonstrate what they demonstrate, namely ‘the existence of some things which do not come to be and are entirely without change’, and it is not a matter for enquiry into nature, which concerns changing things, since nature is a starting point of change

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and those who do away with change also do away with nature and natural things. Someone might say the following. ‘What prevents one from saying that these people are students of nature and are to be criticised as students of nature? In fact both Melissus and Parmenides entitled their treatises On Nature.’19 But this might not mean so much, since the word ‘nature’ might be general insofar as also dare to speak frequently of the nature of god and we speak of the nature of things. Moreover, they did not only discuss hypernatural things; they also discussed natural ones in these same treatises and perhaps for this reason they did not refrain from entitling these treatises On Nature.20 But what Aristotle’s censures them for in dismissing the reason for their mistake would be really harsh if it were correct. For he says that they assumed that there is nothing else in reality apart from the substance of perceptible things, although they were the first to understand that it is necessary for there to be entities which do not come to be or change if there is to be scientific knowledge; for there is no knowledge of what is always in flux, and Plato’s Parmenides says21 that a person ‘will have no place to turn his mind’ if the eternal forms are not hypothesised to exist. And so , understanding these things, these people transferred accounts which fit intelligible, unchanging things to perceptible things which come to be, at least if, proposing to speak about nature, they said things which are appropriate to intelligible things. And if Melissus entitled his work On Nature or On Being,22 it is clear that he considered nature to be being and natural things to be beings. But these things are perceptible. And it is perhaps for this reason that Aristotle says that they ‘assumed that there is nothing else apart from the substance of perceptible things’: because they say being is one; for, if perceptibles are thought to clearly exist, if being is one there cannot be anything apart from what is perceptible. And Melissus says:23

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If it were it would be one, since if it were two things, those two could not be infinite, but they would have limits relative to one another. And Parmenides says:24 It is a whole, of one kind, unshaking and without coming to be. But, as is his custom, Aristotle here too raises objections against the apparent meaning of what is said, taking care that more superficial people do not reason incorrectly.25 However, those men hypothesised a double reality (hupostasis), one consisting of what really is, the intelligible, the other of what comes to be, the perceptible, something

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which they did not think it right to call being without qualification, but only apparent being. And so Parmenides says that truth concerns being, and opinion what comes to be. For he says:26 25 558,1

You should learn all things, both the unshaken heart of wellrounded truth and the opinions of mortals in which there is no true belief. But nevertheless you must also learn these things: how the things which are believed should be acceptably, since they permeate all things everywhere. But also, having completed his account of what really is and being about to explain perceptibles, he says:27

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Here I end28 my trustworthy account and thinking about truth; hereafter learn the opinions of mortals, listening to the deceptive ordering of my words. And, in setting out the ordering of perceptibles, he again says:29

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Indeed, in this way, as belief has it, these things were born and now are and hereafter they will grow and reach an end; for them humans have laid down a name, a distinctive one for each. So in what sense did Parmenides, who philosophised in this way about the intelligible, assume that only perceptible things exist – this is now an extraordinary charge to make. And how did he transfer things which fit intelligibles to perceptibles when he clearly sets out the unity of the intelligible, which really exists, and the ordering of perceptibles, each separately, and does not think it right to apply the word ‘being’ to the perceptible? But Melissus, too, writing still more clearly in prose, discloses his own understanding of these things throughout his discussion and not least in the words which I shall present. Having said that being is one and without coming to be or change and not divided by any void, but is a whole which is filled by itself, he adds:30 This argument is the greatest sign that it is one alone, but these are also signs: if it were several things, these things would have to be like what I say the one is; for if there is earth and water and air and iron and gold and fire and if one thing is living, another dead, and one thing is white, another black, and if all the other things which humans assert are true – if these things are so and we see and hear correctly, each thing must be the way we first believed it to be, and it does not change or become different but each thing is always exactly as it is. We now claim to see and hear and understand correctly, but we believe that

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what is hot becomes cold, what is cold hot, what is hard soft, what is soft hard, and that what is alive dies and comes to be from what is not alive, and that all these things become different and what they were and what they are now are not at all similar, but that iron (and also gold and stone and everything else thought to be strong), which is hard, is rubbed away by the finger when they are in contact,31 and that earth and stone come to be from water. (The result is that we do not see the things that are nor know them.)32 But these things do not agree with one another, since we say that there are many eternal things which have forms and strength, but we think that they all become different and change from what is seen at any time. So it is clear that we did not see correctly and we are not correct to think that those things are many, since they would not change if they were real but each thing would be like what it was thought to be; for nothing is stronger than what is real; for if it changed, what is has been destroyed and what is not has come to be. And so, in this way, if there were many things, they would have to be like the one. So Melissus, too, clearly states the reason why these people say that perceptible things are not but are thought to be. How then could someone assume that they think that only what is perceptible is? But they also deny that what really is comes to be. On this topic Parmenides says:33

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In this way coming to be is extinguished and destruction is unheard of. And Melissus agrees with Parmenides. However, they do say clearly that perceptibles come to be, Melissus when he says34 ‘What is hot becomes cold’ and so on 35 ‘Earth and stone come to be from water’; and Parmenides, having begun36 to speak about perceptibles, says:37 … how earth and sun and moon and the common ether and heavenly Milky Way and outermost Olympus and the hot strength of the stars strove to come to be. And he sets out38 the coming to be of things that come to be and perish up to the parts of animals. And it is clear that Parmenides was not unaware that he himself came to be, just as he was not unaware that he had two feet, even though he said that being is one. However, one should think that Aristotle adds everywhere after his refutation of Parmenides’ apparent meaning what he correctly gives voice to in the Metaphysics when he says ‘But Parmenides seems somehow to perceive …’. 39

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Alexander says that these people make the following kind of syllogism: Only perceptibles exist; there is knowledge of what exists; the things of which there is knowledge do not change; therefore, perceptibles do not change.

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Alexander says that, following this argument, these people incorrectly transferred what is said truly about unchanging substances to perceptible things, and so it resulted that these people did away with nature by speaking about natural things in a way inappropriate to the study of nature. 298b24-299a1 Certain others, as if deliberately, [held the contrary opinion to these people. For there are some people who say that there is nothing which does not come to be, but that everything comes to be, and that some things that have come to be endure without perishing, and, again, others perish. This is especially true of Hesiod and his followers, and later, of others, the first people who studied nature. (298b29) Other people say that all other things come to be and are in flux and none of them is fixed, but only one thing endures and all the other things are natural transformations of it. This seems to be what Heraclitus of Ephesus and many others mean to say. (298b33) And there are some people who make every body come to be, composing] them from planes and dissolving them into planes.

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After those who are thought to do away with coming to be completely,40 he introduces the people who speak in a way contrary to them, and say that everything comes to be and nothing does not come to be, but that, although all things come to be, some remain without perishing while others perish. He says that Hesiod is one of these people. Hesiod makes the very first of the things which he says are, Chaos, come to be when he says: In truth at the very first Chaos came to be.41

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Aristotle says that Hesiod ‘especially’ made all things come to be because Hesiod says that what is for him the first thing came to be. Of the others it is plausible to say that Orpheus and Musaeus and their followers, who say that everything except what is first came to be, are the first who studied nature. But it is clear that these people were using myths to talk about divine things (theologein) and called

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the procession from causes coming to be. Accordingly they all preserve the first cause from coming to be. For even Hesiod, when he says that Chaos came to be first, indicates that there is something prior to Chaos from which Chaos came to be, since it is absolutely necessary that what comes to be comes to be by the agency of something. And Hesiod indicates this in addition: that the first cause is beyond both knowledge and being named.42 (298b29) Having distinguished in this way views which are contrary to one another, he adds third the view of the people who are called students of nature in the strict sense, those who said that all things come to be but that only one thing, which does not come to be, endures and that the other things come to be from it and are resolved into it: Thales water, Anaximenes air, Anaximander what is intermediate (to metaxu), Heraclitus fire. But it is clear that even if those people said that the one does not come to be, nevertheless it is not unchanging since they say that other things come to be when it is transformed. But these people did say that this primary thing, from which the other things come, is a body and does not come to be. (298b33) He adduces as fourth those who say that every body comes to be in the sense that it is composed from planes and again divided into planes. The doctrine of nature of the Pythagorean Timaeus is something of this kind, and it has been set out by Plato in the dialogue bearing Timaeus’ name.43 They hypothesise two kinds of triangles,44 one the scalene which is half of an equilateral triangle (for which reason it is called a half-triangle45), the other the isosceles right triangle. From the latter they construct the cube and earth, and from the former, the pyramid, the octahedron, and the icosahedron, from which they say fire, air, and water are composed, fire from pyramids, air from octahedra, water from icosahedra. They say that as a result these three change into one another because they are composed from the same half-triangle; but, since earth came into being from its own element, the isosceles right triangle, they say that it does not either come to be from one of those three or change into them. Aristotle says that these people ‘make every body come to be’ instead of ‘make body itself come to be’, and thereby he already reduces their argument to absurdity. For the people who speak in this way make body come to be, something which he rejects. For when they say that body comes to be from what is not body, they are not speaking about the coming to be of some body, but of body simpliciter.46 [299a1-2 The other views are to be discussed elsewhere.]47 Aristotle dismisses the other three views about coming to be, the one which says that nothing comes to be, the one which hypothesises that

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all things come to be, and the one which says that there is only one body which endures without coming to be and from which other things come to be and into which they are resolved, and he turns to deal with the last view mentioned, the one which constructs bodies from planes. Or as the most honoured of those dear to Plato says with elegant banter: But Achilles most of all desired to enter the crowd and meet with Hector ….48

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However, Alexander explains that because this view was more recent and consequently more persuasive, not yet having met with any counter-argument. But Alexander also says that this hypothesis is first in order because the generation of body is prior to generation from bodies, since the simple bodies which they generated from planes (and then the bodies composed from them come to be) ought to be prior. But perhaps Aristotle now passes over the other views because in the Physics49 he gave a lengthy argument against them. And perhaps what was said by Parmenides and Hesiod on the basis of other conceptions50 would not require much discussion. And of the students of nature one said water , another air, another fire, another what is intermediate. Accordingly, Aristotle, having shown51 on the basis of the simple motions that there are four simple bodies which move in a straight line and being about to explain that these bodies come to be and how they come to be by changing into one another, is reasonable in first examining this view which also says that the four elements come to be and does not hypothesise that one of them does not come to be (as the students of nature did) and which also sets out the manner in which they come to be in a new way and most effectively does away with their natural impulsions, that is, heaviness and lightness, the things which Aristotle wishes to use to give form to the four elements.52 299a2-11 As for those who speak in this way [and construct all bodies from planes, it is very easy to see in how many ways they turn out to speak in a way which is contrary to mathematics; but it is right either not to change mathematics or to change it using more believable theories than its hypotheses. (299a6) And then it is clear that by the same reasoning solids are composed from planes, planes from lines, and lines from points; and if this is the way things are, it is not necessary that a part of a line be a line. We have investigated these things previously in our discussion of change, and said] that there are no indivisible lengths.

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He adduces his first criticism against these people: that they do away with geometrical principles. And he says that recognising this is easy, and as a result he omits this recognition. He means that they do away with the geometers’ very definitions of point, line, and surface. For if the geometers say that a point is that of which a part is nothing, a line is breadthless length, and a surface that which has length and breadth only,53 a line would never come to be from points, so that neither would a surface come to be from lines nor would a body, which has depth, come to be from a surface, which has no depth; but if a body came to be from a plane, the plane would have depth; and if a plane came to be from lines, the line would not be breadthless; and if a line came to be from points, a point would not be partless. He says that one should either not change the principles of mathematics, which has so much worth in scientific precision that what is demonstrated in a way which admits no dispute is said to be demonstrated by geometrical necessities; or, if one is going to cast aside things of this kind, one should use theories which are themselves more believable than those which are done away with, but not ones which are novel as these are and absurd. He calls mathematical principles hypotheses because assume them hypothetically. They hypothesise that the point has no parts and such things, since it is not possible to demonstrate a principle in the discipline for which it is assumed as a principle because demonstration is always from prior things,54 but there is nothing prior to a principle. As a result the higher sciences demonstrate the principles of the lower ones: mechanics demonstrates the principles of architecture, geometry those of mechanics, and first philosophy those of geometry. (299a6) And next he adduces a second argument also capable of reducing the theory to the same absurdity,55 but he reduces it to a different absurdity which is itself also clear, namely that a part of a line is not a line and what is continuous is not divisible to infinity (which itself is also contrary to mathematics). What he says is the following. Whatever relation a plane has to a body, a line has the same relation to a plane and a point has the same relation to a line, since all of them are limits. So it belongs to the same theory to generate a body from planes, and a plane from lines, and a line from points. However, if a line is generated from points, those points will be part of the line, since a thing which is composed from other things has those things as parts. Consequently not every part of a line will be a line if points also are parts of a line. Consequently also the division of a line will come to an end, and a line will no longer be divisible to infinity, if a line is composed from points. However, it has been proved in the Physics56 in the discussion of change in which Aristotle argued against Xenocrates, who said there are indivisible

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lines, that there are no indivisible lengths, that is, that there is no indivisible part of a line but it is divisible to infinity. Consequently a line is not composed of points so that neither is a plane composed of lines, nor a solid of planes. These are Aristotle’s words, but, as I always say, he is objecting to the apparent meaning of the theory. However, it should be said that if those who say that solids are composed of planes and resolve solids into planes said that the planes are mathematical and have only length and breadth, then Aristotle is correct to adduce against them these absurdities and the ones which he adduces next. But if they say that the planes are natural on the grounds that the first natural thing capable of being constructed should have not only length and breadth but also depth, the absurdities adduced against the planes as being without depth do not follow from their position. And that they hypothesise that the planes are natural and not mathematical is clear from their saying that they involve matter, and so they set out matter first and say that it has been given shape by forms and numbers.57 And Timaeus himself in his own treatise has written this:58 The principles of things which are generated are matter as substratum and form as logos of shape. What is generated from these are the bodies earth and water, air and fire. The generation59 of these is as follows: every body is composed of planes, and a plane is composed of triangles, one of which is the isosceles right triangle, which is a half-square. And then next, having set out the difference among the triangles, he constructs from them the four figures, which he assigns to the four elements. Some interpreters of Plato think that this doctrine of nature based on the figures is spoken symbolically60 – these include the divine Iamblichus, who also interprets Plato’s Timaeus in this way –, but more recent Platonic philosophers61 try to show that, according to what is written, the theory of nature holds in the following way: since the four elements are composites of matter and form and therefore do not satisfy the definition of a principle, they, like Aristotle, say that the qualities which are called affective,62 heat and dryness and their opposites, coming to be first in matter (or qualityless body) also compose the four elements. (Aristotle also takes into account lightness and heaviness and maintains that these are causes of simple natural motion, nature being characterised most of all by motion.) And if someone were to ask why fire heats and water cools, they would say ‘Because fire is hot, water cold’. For they posit these things as principles and do not seek further for a cause beyond the principles. Theophrastus in his Physics reports that Democritus ascended to

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atoms on the grounds that those who offer explanations in terms of hot and cold and such things do so in an amateurish way.63 And in the same way the Pythagoreans ascend to planes, considering figures and magnitudes to be causes of heat and cold, since things that separate and divide produce an awareness of heat, those that blend and compress an awareness of cold. For every body is immediately determined quantitatively in substance, but shape, even if it is a quality,64 has nevertheless been taken from the genus of quantities, so that every body is a quantity which has been given a shape. For in itself matter is incorporeal, and the second substratum is a body which is in itself qualityless but which has been given form by a variety of figures; and the second substratum differs from mathematical body by involving matter and being tangible, touch apprehending it because of its bulk and not because of heat or coldness. And so they say that this second substratum, being painted with different figures, produce (huphistanein) the elements which are more fundamental than the four elements: the elements which are more fundamental than earth are painted with the cubical figure, not because the entirety of earth has a cubical shape but because each part of earth is composed from many cubical figures which are invisible because of their smallness. And the other elements are composed from the other figures in this way. They say that all the other powers and their changes into one another follow from the difference among figures of this kind. For these people easily explain how so great an amount of air comes to be from a small amount of water on the grounds that the elements of water are many, since the figures for water are icosahedra, and when they are divided they make many octahedra and much air, which is composed of octahedra. But how can those who make rarefaction and condensation responsible say that bodies expand and contract when an incorporeal power65 enters in? And in general how is an incorporeal power of fire so constituted as to divide?66 For the incorporeal passes through a body with no contact, but division occurs because of the shape of the divider. And they say the same things in the case of coldness. And how, they say, does the addition of a quality make a bulk heavier? For heaviness is a quantity and not a quality since it is divided in terms of equality and inequality. In general, if Aristotle, too, thinks that qualityless body, the substratum of qualities, comes to be first from matter and form, and he says that it is finite, how is it not necessary that it have shape and that shapes exist prior to qualities?67 I have set out these considerations in order to indicate that it was not unreasonable for the Pythagoreans and Democritus in seeking the principles of qualities to rise up to the figures. But perhaps the Pythagoreans and Plato did not hypothesise that the construction from such triangles was certainly like this in every respect, but

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rather they did so in the way that astronomers make certain hypotheses, different ones making different hypotheses and not insisting that the variegation in the heavens is certainly like this but that when principles of this kind are hypothesised the phenomena can be preserved with all the heavenly bodies moving in a circle in a uniform way.68 In this way too these people, who in discussion of a principle honour quantity and figure more highly than quality, hypothesise these more fundamental figures, which are under the rule of similarity and symmetry, as principles of bodies, principles which they considered to suffice for giving accounts of the causes of what comes to be. And that they did not assume these principles of bodies as absolute in every respect, listen to what Plato says:69 Of the two triangles the isosceles is of one kind only, but the scalene is of infinitely many kinds. Therefore, we should choose the most beautiful of these if we are going to begin in a proper way. And so if someone can pick out a more beautiful one for the construction of these things and say what it is, he will prevail since he is not an antagonist but a friend. But also before these words he has written the following:70

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Let us hypothesise71 the72 principle of fire and the other bodies, proceeding in accordance with the reasonable account which involves necessity. God and the man who is dear to him know the principles which are yet higher than these. We must specify the four most beautiful bodies which are dissimilar among themselves but some of which are capable of coming to be from one other when they are dissolved.73 If we hit upon this, we have the truth about the coming to be of earth and fire and the things intermediate between them which are in proportion. But I shall proceed to what comes next, desiring as much as possible to articulate the precision with which Aristotle examines the apparent meaning of texts of this kind and to indicate in the case of each argument that the true meanings are not at all hurt by the things he says. 299a11-17 [We will now investigate briefly the impossibilities] concerning natural bodies which [follow for those who make there be indivisible lines; for the impossible consequences will also follow for natural things, but not always vice versa, since mathematical things are spoken of by abstraction,] but natural things are spoken of by addition. He now sets aside what someone might think are objections arising

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from mathematics against those who generate bodies from planes because they are easy to see and because he has spoken about them in On Indivisible Lines74 (some people ascribe this work to Theophrastus), but, in reality, proceeding in accordance with the figure which is called paralipsis75 by rhetors, he has also brought in the more important of these objections, namely that the view would do away with the definitional principles of mathematics, that a part of a line will not be a line, that a line will be composed from points, and that magnitudes will not be divisible to infinity. He now adduces the impossibilities concerning natural bodies which follow for those who make there be indivisible lines, that is to say, for those who construct bodies from planes. For if the primary bodies are composed of planes, then the primary lines are also composed of points and therefore divisible not into lines but into points, and they are called indivisible lines for this reason: they are not divisible into lines. He shows that these things are more absurd than the mistakes made in mathematics on the grounds that there are more consequences for natural things because the absurdities from mathematics which follow from the theory also follow for natural things, but not all the things which follow from this theory for natural things follow for mathematical ones. Again the confirmation of this is that mathematical things are ‘by abstraction but natural things are spoken of by addition’. For if matter and affections such as heat, coldness, heaviness, and lightness, and all resistances and changes are separated in thought from natural body, what remains is mathematical body; but if these things are added to mathematical body, the result is natural body, so that mathematical body is in natural body. Consequently the absurdities which follow for mathematical body also follow for natural body, but the absurdities which follow from this theory concerning the change and affections of natural bodies, such as that there would be no change among bodies if they were composed from planes nor would there be heaviness or lightness or affections in general, do not follow for mathematical bodies.76 So Aristotle will show that those who hypothesise that the generation of bodies is of this sort are not able to preserve the affections of bodies apart from which it is impossible for there to be any natural body. 299a17-25 There are many things which cannot belong to indivisible things [but must belong to natural ones. …77 For it is impossible for something divisible to belong to an indivisible thing, but all affections are divisible in two ways, in species or accidentally: in species as light and dark belong to colour, accidentally if that to which an affection belongs is divisible

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Translation (and so all simple affections are divisible in this way).] Therefore we should investigate what is impossible in such things.78

If he is calling mathematical things indivisible because they have the point, which is indivisible, as principle, these things would be proved as consequences of what he has said previously, and he would be saying what the things are by which natural things exceed mathematical ones by addition. For he includes all mathematical things in a common formula and calls them indivisibles. For all natural bodies are divisible, but it is impossible for something divisible to be in an indivisible.79 He adds what the divisibles in natural bodies are, saying that they are the affections. He says that affections are divisible in two ways: in species as when colour is divided into light and dark, accidentally when that to which the affection belongs is divisible. This second sense is most of all specific to division of affections since there is also division in species in the case of mathematical things. And so, he says, whichever affections are simple, that is, whichever are individual (atomos) and do not contain other things in the way species do are accidentally divisible. So if it is impossible for something divisible to be in an indivisible thing, the affections in natural bodies are not in mathematical ones. This if by the initial occurrence of ‘indivisible things’ he means ‘mathematical things’. However, if by ‘indivisibles things’ he means ‘the planes from which they construct bodies’, then either because these planes, being without depth, also do not undergo the division of bodies or because, if bodies are composed from planes, planes from lines, and lines from points, bodies will, according to them, also be composed from points and so from indivisibles. But there are many things which belong to natural bodies, but do not belong to points, and so80 bodies would not be composed from indivisibles; for if indivisible things do not have anything divisible, neither would what is composed from them. Consequently, using this argument, he could have proved universally from the universal that divisibility belongs to all affections of bodies that body is not composed from planes. And he does prove this using heaviness and lightness, which are particular affections, immediately hereafter. And it is better that one understand what Aristotle says in this way. I base this judgment on his saying ‘Therefore we should investigate what is impossible in such things’ to introduce the demonstration based on heaviness and lightness. He says that what is impossible should be investigated in such things because it will be obvious from the investigation of affections that it is impossible for bodies to be composed from planes. (He says that all affections are divisible in two ways not because each affection is divisible in the two ways, since simple affections are

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not divisible in species, but because all affections are included in this division in such a way that some are divisible in one sense, others in the other.) 299a25-b7 If it is impossible [that each of two parts have no weight and both together have weight, but either all or some perceptible bodies have weight, e.g. earth and water have weight, as even they would say,81 then if a point has no weight it is clear that lines won’t have weight either; and if they don’t neither will planes, so that neither will any bodies. But it is evident that a point cannot have weight, since everything which is heavy can also be heavier than something and everything which is light can also be lighter than something. But it is perhaps not necessary that what is heavier or lighter be heavy or light. (In the same way what is large is larger, but not everything which is larger is large, since many things which are absolutely small are nevertheless larger than something else.) If, then, what is heavy is heavier, it must be greater in weight, and everything heavy is divisible.] But a point is assumed to be indivisible. He has shown universally on the basis of divisibility that it is impossible that bodies be composed from planes, and he now shows the same thing on the basis of one affection of bodies, weight. He assumes to start three axioms or hypotheses of the following kind:

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[i] If something is composed from certain things, it is impossible for the composite to have weight, if none of the components have weight; [ii] all or some ‘perceptible’ (that is, ‘natural’) bodies have weight. For Democritus and his followers and, later, Epicurus say that since all atoms have the same nature they have weight, but because some are heavier, the lighter are pushed out by the heavier ones, which sink down, and they move upward; and they say that it is for this reason that some things seem to be light, others heavy.82 And if not all natural bodies are heavy, nevertheless it is agreed by everyone that at least some, such as earth and water, are. And Aristotle tacitly assumes what he has already said:83 [iii] by the same reasoning solids are composed from planes, planes from lines, and lines from points. These things being assumed:

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Translation [iv] If bodies are composed of planes and a point has no weight, it is clear that lines won’t have weight either, because of the first assumption;84 but [v] if lines don’t have weight, neither will planes; and [vi] if planes do not have weight neither will any body because of the third ; but [vii] all or some bodies have weight because of the second thing which is assumed in advance as agreed upon; therefore [viii] bodies are not composed from planes.

These are the conditional, the additional assumption, and the conclusion.85 First in what follows he demonstrates in many ways what is hypothesised in the antecedent of the conditional, namely that a point does not have weight; he does so on the basis of the that everything heavy is divisible, but the point is indivisible and it is not possible for to be divided into what is indivisible. He proves that what is heavy is divisible first from the that everything which is heavy is also heavier, just as what is light is also lighter and what is large is also larger. But if everything heavy is also heavier, it is necessary that it exceed by some weight, so that everything heavy is divisible; for it is divided into the excess . But a point is indivisible. And the conclusion in the second figure86 is that a point is not heavy, that is, does not have weight. And this is what it was proposed to show. There is a difficulty which grows out of what he has said. Why does he say that everything heavy is heavier? For if what is heavier is heavier than something heavy, but the heavy thing than which the heavier is heavier is itself heavier than something else which is heavy, and this other thing is again heavier, it is necessary to proceed to infinity.87 This is the difficulty which Aristotle opens up when he says that everything which is absolutely heavy is also heavier, just as the light is lighter and the large larger, but that it is not necessary that what is heavier or lighter also be absolutely heavy or absolutely light. And, indeed, we do not say that everything which is larger than something is thereby large. For a millet seed is larger than a mustard seed, and nevertheless a millet seed is not absolutely large. Nor is what is more worthy of choice absolutely worthy of choice, since illness is more worthy of choice than wickedness, and being harmed is more worthy of choice than doing harm, but neither of these is absolutely worthy of choice. For Socrates says in the Gorgias88 that ‘I would not wish to do either, but if one or the other were necessary, I would choose to be harmed rather than to do harm’. Consequently even if everything heavy is heavier, it is not the case that everything heavier is heavy, so that these things do not convert. Nor is ‘heavy’ said of what is heavier although ‘heavier’ is said of what is lighter and ‘lighter’ of what is heavier.89

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What does the addition of the word ‘perhaps’ mean when he says, ‘But it is perhaps not necessary that what is heavier or lighter be heavy or light’? Is it added because, if someone is speaking precisely he would say that what is not worthy of choice is not to be called more worthy of choice in the strict sense nor is what is not large to be called larger, so that what does not share in weight is not to be called heavier; rather things of this kind which do not share in the name90 are not more worthy of choice or larger or heavier, but one should say instead that such things are less of the contrary, that what is not absolutely worthy of choice is less to be avoided, that what is larger but not large is less small, and that what is heavier but not heavy is less light. But since weight indicates a quantity, it is always divisible, and therefore it is always heavier. Alexander points out that it is possible to show, using the same argument, that no other affection attaches to a point, if, indeed, everything which has an affection absolutely also exceeds something else with respect to the affection. For even if it does not exceed something else , it would at least exceed what absolutely does not have the affection.91 Consequently nothing is accidentally divisible into something indivisible. 299b7-14 Furthermore, if what is heavy is something dense, [and what is light is something rare, and dense differs from rare in that more inheres in an equal bulk, then, if a point is heavy or light, it is also dense or rare. But what is dense is divisible, a point indivisible. (299b11) And if everything heavy must be either soft or hard, it is easy to infer something impossible, since soft is what withdraws into itself, hard what does not,] but what withdraws is divisible. Having shown, using the heavier, that weight is divisible, he inferred that since a point is indivisible, it does not have weight. Next he proves the same thing using the dense and the rare:

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[i] If a point is heavy or light (he is making a common argument for both), it will be dense or rare; [ii] but it is neither dense nor rare; [iii] therefore, it is neither heavy nor light. And he proves the conditional [i] by defining dense and rare. For if dense is what contains more bodies than what is rare in an equal bulk (obviously the bodies have been pressed together), rare what contains fewer in an equal bulk (naturally the bodies have been dispersed), then the dense is heavy, the heavy dense, and the rare is light, the light rare. For water which is evaporated and rarefied becomes

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lighter, and air which is liquefied becomes denser. (However, the Platonists do not say that the heavy is heavy because of denseness; for they say that fire is denser than earth; however, they do say that having larger parts produces heaviness.)92 He proves the additional assumption [ii] categorically in the second figure93 as follows: The rare and the dense are divisible (since, if94 the bulks are equal, the dense consists of more, the rare of fewer bodies); a point is indivisible; 95 a point is neither dense nor rare.

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So, if points are neither heavy nor light, bodies will not be light or heavy either, if lines are composed of points, planes of lines, and bodies of planes. (299b11) Having proved by means of dense and rare that a point is neither heavy nor light, he proves the same thing categorically96 using soft and hard.

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What is heavy is either hard or soft (since it is necessary that every body be occupied by one of these); hard and soft are divisible (if, indeed, the hard does not withdraw into itself, the soft does, and both of these things are said of what is extended, and what is extended is divisible); consequently, again, what is heavy is divisible whether it is hard or soft; but a point is not divisible; therefore a point is neither heavy nor light.

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Therefore neither are bodies heavy or light. And so if bodies are heavy or light, they are not composed of planes. 299b14-23 Nor will a weight be composed of weightless things. [For with how many weightless things and with what sort will this occur? How can they determine this, if they are unwilling to make things up? (299b17) And if every weight is greater than a weight by weight, it will also follow that each thing without weight has weight. For if four points have weight, and what is composed of more is heavier than this thing, which is heavy, and it is necessary that what is heavier than something heavy be heavy, just as what is whiter than something white must be white, what is greater by one point will be heavier, and if an equal amount is subtracted,] one point will also have weight.97

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heavy nor light; and he has proved with three arguments that a point is neither heavy nor light. Next he proves his first hypothesis,98 that if something is composed from certain things, then it is impossible for the composite to have weight, if none of the components have weight. And the first argument is itself99 the following. If what has weight comes to be from weightless things, then how many weightless things will produce a weight when they come together? For it is clear that a number of weightless things will produce some weight when they come together. But how will they define this number? For, unless they are just going to formulate an inexplicable fiction, they will not be able to say why the number which they state is more correct than a number which is less or more by one, since the things which come together are all equally weightless. (299b17) He adduces a second which shows that those who say a weight comes to be when weightless things come together run into contradiction, since it will be proved that each thing which they call weightless has weight. He proves this, assuming to start a clear lemma: every weight which is greater than a lesser weight is greater by weight. For what is heavier than something does not exceed it by sweetness but by weight. And he makes another assumption: ‘it is necessary that what is heavier than something heavy be heavy, just as what is whiter than something white must be white’. If, then, what is composed of four points has weight, and what is composed of more (e.g., from five) than the heavy thing which is composed of four is heavier, and what is heavier than a heavy thing is heavy and exceeds by weight, then it is necessary that what is composed of five points exceed what is composed of four by weight, and it exceeds by a point. If, then, an equal amount is subtracted, that is, if four points are subtracted from the five, there remains one point by which the five points exceed the four, and they exceed by weight; for they exceed by weight and they do not exceed by anything else than by a point. Consequently each point will have weight. And Alexander develops the argument as follows: If when a thing is subtracted a greater weight becomes less, that thing is heavy; but if a point is subtracted a greater weight becomes less; therefore a point is heavy.

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But since Aristotle does not say ‘if a point is subtracted’ but ‘if an equal amount is subtracted’, perhaps one should rather develop the argument in this way: What remains in a heavier thing when an equal weight is subtracted is heavy; but what remains is a point.

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These things which Aristotle says, insofar as they are said against men who actually do generate bodies from mathematical planes, are well said and said from the point of view of the study of nature. But what he says might not be suitable insofar as it is said against the Pythagoreans, who say that the planes are natural and involve matter and have some depth. For Timaeus himself says that bodies become heavier because of the number of planes, when he says, ‘Third the icosahedron, with twenty bases and twelve angles, the element of water, having the most parts and being heaviest’.100 And Plato’s Timaeus says that what is ‘composed of the fewest identical parts101 is lightest (elaphrotaton)’. Some people also disapprove of his saying that it is impossible that each of two things have no weight and both together have weight.102 They say that even according to him, although neither matter nor form has weight, the composite of them does. But Aristotle has anticipated this difficulty and dissolved it. For matter and form really are elements of the composite; they are potentially heavy and when they come together they make the composite of them actually heavy. But Aristotle has shown that, if one hypothesises that bodies are composed from planes, a point is not potentially but actually heavy. For also those who say that bodies are composed of planes or planes of lines or lines of points do not say that they are composed as if from matter and form, but as if from those things as parts. For matter and form and in general elements in the strict sense, being potentially proceed into actuality when they come together. And in this way flesh and bone and each of the other composites come to be from the four elements when they are altered together and in the composite no longer have their own nature purely. But a wall comes to be when stone and clay are put together, as opposed to being altered together, and so the nature of the parts, existing in actuality, is also in the whole. And it is in this way that a body would be composed from planes. 299b23-31 Furthermore, it is absurd if planes can only be compounded along (kata) a line. [For, just as a line is compounded with a line both in (kata) length and in breadth, so too a plane ought to be compounded with a plane in the same way. But a line can be compounded with a line along (kata) a line if it is laid next to it, but not if it is added to it. However, if a plane can also be compounded in breadth, there will be a body which is neither an element nor composed of elements, since it is composed] of planes which are compounded in this way. Those who generate bodies from planes do not compound the

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planes by making them coincide in breadth, but by making them coincide along their linear limits; for they generated the different bodies by making solid angles which differed from one another in terms of the number of planes . For when three equilateral triangles are drawn together at one vertex and are joined along the containing lines and have an equilateral triangle as base, the result is a pyramid having four solid angles, each of which is composed of three angles, each two thirds of a right (because the triangles are equilateral). And the octahedron is composed of eight equilateral triangles in all containing twenty-four plane angles, so that it has six solid angles, each composed of four plane angles. The icosahedron is composed of twenty equilateral triangles, the plane angles being sixty and each of the solid angles in it being composed of five similar planes, so that it has twelve solid angles. The cube is composed of four squares, each of which is composed of four isosceles right triangles having their vertices joined in the centre of the square, their sides being the segments of the diagonals of the square and their bases the sides of the square; the cube has eight solid angles, each composed of three plane right angles. The dodecahedron is composed of twelve equilateral and equiangular pentagons; it has twenty solid angles, each composed of three plane angles of a pentagon, each of which is one and a fifth of a right angle.103 This kind of compounding of planes being ‘along a line’, Aristotle says against these people that they speak in an absurd way if they say that planes are of such a nature as only to be compounded in this way, since < planes ought to be compounded> ‘just as a line is compounded with a line both in length and in breadth’. He says that a line is compounded with a line ‘in breadth’ (which he subsequently calls ‘along a line’) if it is laid next to it, but it is compounded ‘in length’ when it is not laid next to it but is added to it not along a line but at (kata) a point, and in this way it increases the length; but when something is compounded ‘along a line’ the breadth is increased, if, in fact, when lines are compounded a plane results, just as when planes are compounded a body results.104 So, just as a line is compounded in two ways, a plane should also be compounded not only along a line or in length, as these people say, but also in breadth, so that the planes fit on one another, just as lines which are laid next to each other fit on one another along the whole of their length, but lines which are added do not. But if planes can also be compounded in breadth just as lines can also be compounded in length, then there will be a body which comes to be from planes compounded in this way which is neither an element nor composed of elements, if, in fact,

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what is compounded from planes is a body; for it will not be one of the four bodies which is generated are compounded along a line, since it will not be a pyramid or any other of the co-ordinate with it; nor will it be a body composed of these; nor will it be fire or air or any other one of these. But it is not possible for there to be a body which is neither an element nor composed of elements. Concerning what Aristotle asserts here, one should say that if the people who made this sort of hypothesis said that every compounding of planes and not compounding along lines makes a body Aristotle would be speaking correctly, but what he says would have no relevance to those people, if, like Plato,105 they said that body is made only in accordance with that compounding by which plane nature contains what is solid. Moreover, it is not surprising if, when planes are compounded in breadth, something incomplete and unnatural is produced in last things. For also according to Aristotle,106 there will be some misfirings in the changing of the elements since there will be things which are neither elements nor composed of elements. Since Alexander also tries to give his own refutation of the doctrine, let us see what he has to say. For he says that since they say that the other bodies change into one another because in their case generation is from the scalene right triangles, which are similar to one another and from which the equilateral triangles are composed, but earth does not change into any of the others because only it came to be from isosceles right triangles it is clear that these people really did make things come to be from planes and did not the similarity of these figures107 to the simple bodies and that Aristotle is arguing against them in a reasonable way. But it should be prima facie clear that it is not necessary to reject the interpretation which invokes the similarity of the figures to the elements on the grounds that not all the elements are said to be composed from the same triangle. For if other things are expressed symbolically what is to prevent understanding this doctrine as symbolic? But it is clear that causes involving the figures are more fundamental than those involving the qualities , since even Aristotle himself thinks that shapes come to be in matter prior to the other qualities. That he does so is clear from the fact that what he108 calls the second substratum is called qualityless body. And, as he demonstrates, shape and most of all shape when it has been limited, is made substantial together with three-dimensional body insofar as it is body.109 But how, Alexander asks, will the view which says from planes differ from the view of Democritus if, indeed, it too says that natural bodies are given form because of figures? And it is easy to say in response to this that it does not differ at all in this

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respect. (As I have said previously,110 Theophrastus reports that Democritus ascended to atoms on the grounds that those who offer explanations in terms of hot and cold and such things do so in an amateurish way.) But Plato’s view is presumably different from Democritus’ because it gives priority to something simpler than bodies, namely the plane, which is simpler than the atoms (which are bodies) and because it recognises that symmetries and proportions are demiurgic of the figures, and because it treats earth differently . 299b31-300a7 Furthermore if bodies are heavier because of the number of their planes, [as is stated in the Timaeus, it is clear that line and point will have weight since they are related proportionally, as we have also said previously.111 (300a3) However, if they do not differ in this way but because earth is heavy, fire light, then some of the planes will be heavy and some will be light, and likewise in the case of lines and points.] For the plane of earth will be heavier than that of fire. He also adduces this argument against them again on the basis of heaviness. It goes as follows. If bodies are heavier because of the number of their planes112 and lighter because of their fewness, as is written in the Timaeus, line and point will also have weight, which has been proved to be impossible. (The Timaeus says,113 ‘And furthermore what is composed of the fewest identical parts is lightest’, implying that all planes have equal impulsion.) For if a body is heavier because of the number of its planes, it is clear that each of the planes makes a contribution to its heaviness. For the greater weight, that is, the heavier one, is heavier by weight. So if the planes of which a body is composed are heavy, the lines of which the planes are composed are also heavy, and so are the points of which the lines are composed. The argument is the same because all of these things are limits in the same way. However, it has been proved in several ways that it is impossible for a point to have weight, since a weight is divisible and a point is indivisible. (300a3) But if the difference in weight of bodies does not follow from the number of planes, but, on the contrary, it follows because earth is heavy and fire light, then the planes of earth are heavy and those of fire light. (He expresses this by saying ‘For the plane of earth will be heavier than that of fire’ instead of saying ‘For the plane of earth will be heavy, that of fire light’.) But if this is so, there will again be the same difference among lines and among points, so that in this way too the impossibility, that a point has weight or lightness, will follow. So, if it is necessary that if bodies are composed of planes they be heavier and lighter either because of the number of their planes or because some bodies are naturally

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heavy and some are naturally light and some of the planes of which they are composed are heavy and some light, and an impossibility, namely that a point has weight or lightness, follows from each of the hypotheses, then the initial that bodies are composed of planes is impossible. And in response to this one should say the same thing, namely that they do not suppose the planes to be mathematical planes in such a way that they are proportional and as planes are to a body so are lines to a plane and points to a line. 300a7-12 In general it follows that at some time there is no magnitude [or at least that magnitude can be done away with, if point is related to line in the same way as line to plane and this to body. For all things which are resolved into one another can be resolved into what is primary, so that it would be possible that there be only points] but no body. This argument, which is even more forced (biaioteron), is not based on compounding planes but on resolution . He says that it will follow from this argument either that at some time no existing thing is a magnitude or that it is possible that there be none. (‘Possibly is not’ and ‘is not’ differ only temporally.114) How will this follow? He says, ‘if point is related to line in the same way as line to plane’ and plane to body, then just as, according to them, body is dissolved into planes because it is composed from them, so too plane can be dissolved into lines and lines into points. So that it is possible that at some time there be only points and no magnitude. (He took the monad instead of the point because both have no parts.115) In this connection Alexander, perceiving a similar objection , says: It does not follow for those who say that bodies are composed of form and matter that it is possible that there be no magnitude. For according to them it is not body which comes to be but only particular body, and a body which comes to be also perishes. Furthermore, according to them, matter is not actual, but, according to these people, the planes are actual. But perhaps matter, too, would not be without magnitude in and of itself.116 One should say the following against this. If Aristotle says,117 ‘There is a matter for a body and the same matter for a great body and a small one’, how, according to its own definition, can matter have magnitude if matter is matter of a body and is obviously different from the body, and if there is the same matter for a great body and a

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small one? For if it has magnitude, it is certainly limited to a certain size. And against Aristotle’s argument the following should be said. If things which come to be were only resolved and they were not also compounded because of the everactive demiurgic logoi and the heavenly motion and because of acting on one another and being acted upon by one another,118 then also according to those who say that things come to be from matter and form, even if it is not possible that magnitude not exist because in the case of simple bodies the perishing of one is the coming to be of another, but it is possible for there not to be a human being or a horse if everything is dissolved into the elements and other things do not combine, this is no less absurd than the non-existence of magnitude. Again Alexander says: There are those who say that in the Timaeus Plato does not construct natural bodies from planes but rather constructs the form of each body which makes the body the very thing it is; but the form is incorporeal, and when this form which is generated from planes comes to be in matter, one form makes fire, another water, another earth, and another air; so what Aristotle says is not the case and Plato does not generate material body from planes.119 Against these people it should be said that even if one were to accept that Plato intended to say this, nevertheless it would be true that he generates depth from planes. For the pyramid which is generated from triangles is not without depth, since a pyramid is not a plane, nor are any of the other co-ordinate with the pyramid planes. But it follows for the person who generates depth from things with no depth that they also make breadth from things without breadth and length from things without extension. In addition to this it is unreasonable for them to say that there is a generation of form; for just as there is no generation of matter, so there is no generation of form by itself, but generation is of the two together, and this is what comes to be by the presence of form and perishes by the absence of form. This is what Alexander says. But it has been said many times that these people do not generate depth from things with no depth and their planes are not mathematical. However it should have been recognised that we also120 make a body with qualities from matter and form, which are not bodies and are qualityless, unless someone were to say what I have also said before,121 that planes are taken as parts, but form and matter as elements. But how can Alexander say that there is no generation of form? If it is on the grounds that form does not arrive via a process of coming to be but arrives atemporally,

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this also can be doubted. However, those who say that form comes to be from planes – if there were people who said this – say it because it is brought from non-being into being, whether this happens in time or atemporally. 300a12-14 Moreover, if time [is similar, it would or could be done away with at some time; for the indivisible instant] is like a point in a line.122

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On the basis of the same argument he reduces the theory to something else even more absurd. He says that since the instant (not the extended instant, but the indivisible one) ‘is like a point in a line’ (for these stand in proportion to one another: as point is to line so is instant to time), if someone were to say that time is similar to bodies so that it is composed of instants as bodies are composed of points (through the intermediary of lines and planes) or that time is similar to lines, which are composed of points, time would be done away with at some time when it was dissolved into instants, or it could be done away with. But it is most absurd that there be some time when there isn’t time, since, if some time is a time, to say there is some time when there isn’t time is the same as saying ‘there is a time when there will not be time’. But since each thing is thought to be dissolved into the things from which it is composed, the person who introduces the resolution of time into instants leaves room for those who say that time is composed of instants. But it is clear that those who say that bodies are composed of planes which involve matter and are natural will not be forced to say that the line is composed of points or that time is composed of instants. 300a14-19 The same thing results for those who construct the heavens out of numbers. [For some people construct nature from numbers, for example, certain Pythagoreans. For natural bodies obviously have weight and lightness, but monads cannot make bodies when they are compounded,] nor can they have weight. He says that the same thing results for those who make the cosmos and natural things out of numbers as results for those who construct bodies from planes or, in general, things having weight from weightless things. For when monads are compounded they do not make bodies. This is not because monads are absolutely indivisible, since when two or three is compounded it does not make a body either; rather it is because the monad is from a different species of quantity, the discrete, but body is from the continuous, and nothing continuous is composed of what is discrete. But there is no weight in numbers either. It is prima facie clear that it follows for those who say that things are composed of numbers that they say that things are com-

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posed of monads, since numbers are composed of monads. However, it is clear that these people said that things are composed from numbers on the grounds that numbers pre-contain in themselves all the forms in a fundamental way and that all the forms in the cosmos have been ordered by numbers, because they sang the praises of number as ‘father of the blessed ones and of men’123 and said that ‘all things resemble number’.124

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300a20-7 That it is necessary that some motion belong by nature to all the simple bodies [is clear from the following considerations. Since they obviously move, it is necessary that they be moved by constraint unless they have their own proper motion. But ‘by constraint’ and ‘unnatural’ are the same thing. However, if some motion is unnatural, it is necessary that there also be a natural motion which it diverges from. And if there are several unnatural motions it is necessary that there be a single natural motion, since each thing has a simple natural motion,] but many unnatural motions. He has proved the first axiom,125 which says that it is impossible for what has weight to be composed of things which do not have weight, and also proved that a point does not have weight because a weight is divisible but a point is indivisible; and he has added other arguments against the original theory.126 Now he demonstrates the second of the things which he assumed to start or hypothesised, namely that all or some perceptible bodies have weight. He proves this by showing that it is necessary for a motion to belong to the simple bodies naturally and that this motion comes about because of (kata) natural impulsions, that is, because of heaviness and lightness. But if this is so, bodies cannot come to be from planes since bodies are heavy or light but planes possess neither weight nor lightness, since neither lines nor points possess these things. He proves that a natural motion belongs to each of the simple bodies by assuming as clearly true that the simple bodies move; for they obviously do move. But if he assumed that they move naturally he would have assumed in an offhand way what he is seeking to prove. For if the things which move up or down were hypothesised to move naturally, they would be assumed to move because of lightness and heaviness, and this is what he proposed to prove. And so, assuming as clearly true that in general these things move, he hypothesises that they move unnaturally and by constraint. For if they do not move naturally (to hypothesise that they did would assume in advance what is sought), but it is necessary that what moves move either naturally or unnaturally, it is clear that they would move unnaturally. But it has been proved

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in the Physics127 that it is not possible for something which does not move naturally and by nature to move unnaturally. For what is not at all naturally constituted so as to move at all would never move at all, but it is clear that if something simple is naturally constituted so as to move with a simple motion it is also naturally constituted so as to move somewhere. Consequently what moves by constraint also has a natural motion, since unnatural motion is posterior to natural motion. So if the simple bodies move unnaturally it is necessary that they also have a natural motion. However, even if what moves unnaturally always also moves naturally, it is not thereby the case that it is necessary that there be as many natural motions as there are unnatural ones, since in all things there is just one way to go right, but many ways to deviate from what is right and err, and unnatural motion is a kind of error and deviation from the natural. In this case, too, Alexander does well to raise a difficulty:128 since Aristotle says in the first book of this treatise that the unnatural is contrary to the natural and one thing is contrary to one thing,129 how can he say here that ‘each thing has many unnatural motions’? And in this case Alexander resolves the difficulty in many ways, but more appropriately on the grounds that in the case of the simple bodies several motions can be said to be unnatural if one takes into account not only the motion which a simple body has but also the motion which it is not possible for it to have. For motion down from above, which a thing which moves up from below has by constraint, is unnatural for it; and motion in a circle, which it does not even have at all, might also be called unnatural for it.130 But if Aristotle has assumed motion as clearly true and hypothesised that motions are unnatural, I do not think he should take those motions which something is not naturally constituted so as to have as unnatural; rather he should take those which it is naturally constituted so as to have.131 A clod of earth does not only move up unnaturally, it also moves obliquely when it is thrown, and these oblique motions are not simple and not motions in a circle unless they are around the centre of the universe. Consequently there is one simple unnatural motion and it is contrary to natural motion, but it is possible for simple bodies, when subject to constraint, to also move with non-simple motions, as was said. Alexander also knows this way of resolving the difficulty. 300a27-b8 This is also clear from the consideration of rest. [For it is necessary that rest be either constrained or natural. But a thing remains fixed by constraint, where it also moves by constraint, and it remains fixed naturally where it also moves naturally. So, since something obviously remains fixed at the

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centre , it is clear that if it remains there naturally, its motion there is also natural for it. (300a32) But if it remains there by constraint, what prevents it from moving? If it is something at rest we will recirculate the same argument, since it is necessary that either there be a first thing which is naturally at rest or the argument proceeds ad infinitum – which is impossible. But if what prevents moving is itself in motion (as Empedocles says the earth is at rest because of the vortex), where would it move since moving ad infinitum is impossible? Nothing impossible occurs, but it is impossible to have passed through an infinite. Consequently it is necessary for the moving thing to stop somewhere and to remain there naturally, not by constraint. But if rest is natural , there is also a natural motion , namely the] motion to that place. Having proved on the basis of unnatural motion that it is necessary for there to be a natural motion for each of the simple bodies, he now proves the same thing on the basis of rest. He again hypothesises that it is clearly true that something is at rest – as the earth is at rest at the centre – and asks whether it rests there naturally or unnaturally. For if it rests there naturally, it is clear that motion there is natural for it, since if something rests somewhere naturally it also moves there naturally. But motion to the centre occurs because of heaviness, so that there is a natural motion which has its starting point in heaviness or lightness.132 (300a32) But if what is at rest at the centre rests by constraint, it would be easy to say that it moves from the centre naturally, since if something rests somewhere unnaturally, it moves from there naturally. Consequently, again, there is a natural motion which has its starting point in lightness. However, Aristotle adduces a longer and perhaps more precise demonstration, arguing on the basis of what is constrained. For what rests by constraint at the centre always rests because it is constrained and prevented by something, and what prevents it prevents it either by being at rest or by moving. But ‘if it is something at rest we will recirculate the same argument’. For either it rests naturally (and it also moves naturally to where it rests), or it rests unnaturally and by constraint. If the latter it is possible to again ask the same things about what constrains and prevents it. But if what prevents moving prevents not by being at rest but by moving (as Empedocles says that the earth is at rest because it is prevented from moving by the vortex), one should ask this question: if the earth were not prevented from moving by the vortex, where would it move? For it is necessary for it either to move ad infinitum or to move somewhere and stop. But it is impossible for it to move ad infinitum since it is impossible to have passed through

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an infinite .133 For nothing comes to be at all if it is impossible for it to have come to be.134 For since it is impossible for the diagonal to have become commensurable with the side, it is impossible for it to become commensurable at all. For in every case if something comes to be naturally, it is also possible for it to have come to be, but it is impossible to have passed through an infinite , so that nothing can move through this. So, if something would move if nothing prevented it, it is necessary that when it moves it moves through a finite and stop somewhere – not by constraint, but naturally. ‘But if rest is natural , there is also a natural motion , namely the motion to that place’, since a thing moves naturally to the place in which it rests naturally. Alexander understands the question ‘where would it move’ to apply to what prevents the earth from moving and not to the earth. He says, ‘It would seem that he has not proved what is proposed for proof’.135 300b8-25 Therefore, Leucippus and Democritus, [who say that the primary bodies are always in motion in the infinite void, ought to say what their motion is and what their natural motion is. For if one of the elements is moved by another by constraint, nevertheless it is necessary that each of these have some natural motion from which their constrained motion is a deviation. And it is necessary for the first cause of motion to cause motion naturally, not by constraint. For it will proceed ad infinitum if there is not something which first causes motion naturally, but the prior thing is always moved by a constrained motion. (300b16) It is necessary that the very same thing result if the elements were moving in a disorderly way before the cosmos came to be (as is written in the Timaeus). For it is necessary that this motion be either constrained or natural. But if they were to be moving naturally, it is necessary that there be a cosmos, if one wishes to investigate attentively. For the first cause of motion, moving naturally, must cause itself to move,136 and things which do not move by constraint must rest in their proper places and make the same order which they have now, things having weight to the centre and things having lightness away from it] – the cosmos has this separation.137 Having proved that there is a natural motion of bodies and that it is prior to unnatural motion, since there wouldn’t be unnatural motion unless there were natural, he now criticises those who say that disordered and unnatural motion is prior to natural motion. There are two forms of this view: Leucippus and Democritus and their followers said that the things they considered to be primary bodies, that is, the atoms, are always moving by constraint in the infinite

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void; and Timaeus says that the elements moved in a disorderly way before the cosmos came to be. Aristotle says the following against the first view. If one atom is always being moved by another by constraint and unnaturally, what is the natural motion of the atoms? For it is necessary that the natural motion of anything, from which its unnatural motion is derivative (this is also the reason it is called unnatural138), be prior. So if atoms are moved by one another by constraint, it is necessary either that the first cause of motion cause motion by moving naturally, not by constraint, or that it be moved by itself or that it be moved by an unmoving cause, in order for us not to proceed to infinity. For what is moved by constraint, since it is moved by some kind of pushing or levering, is moved by something moving. So if this went on to infinity, then nothing would move. Consequently it is necessary that natural motion be prior to unnatural – let them say what this prior natural motion is – and moreover it is necessary that unnatural motion not be forever, since natural motion must be prior to it. Aristotle also indicates the impossibility of atomic motion when he says that the primary bodies move in the infinite void. For if all motion is from one determinate point to another determinate point, but nothing is determinate in the infinite, nothing would move in the infinite. Moreover, every motion is either up or down, but in the infinite there is no up or down, as has been proved in the fourth book of the Physics.139 (300b16) Having said these things against Democritus and his followers, he turns next to the view of Timaeus and says of it that if the elements were moving in a disorderly way before the cosmos came to be, it is necessary that this motion be either constrained and unnatural or natural. And it is clear that if it were disordered, it would be unnatural. But he also takes natural motion in order to make the division complete and at the same time in order to make clear the consequences of being in a natural condition. And so he says that if the motion were unnatural and constrained, the same things would follow as before . For again it is necessary that natural motion, from which unnatural motion is derivative, be prior. And let them say what this natural motion is. For if things are moved by one another or by something else by constraint, it is necessary that the first cause of motion cause motion by moving naturally in order that we not proceed to infinity, positing one constrained thing as prior to another, thereby doing away with all motion, since it is necessary that, if there is motion, natural motion be prior to unnatural. But if someone were to say that the motion prior to the cosmos is natural, it would be necessary that there be a cosmos prior to the cosmos ‘if one wishes to investigate attentively’ what ordering relative to one another the natural motion produces in bodies. For the first cause of motion, moving naturally,

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must cause motion140 in such a way that in seeking the natural motion which is prior we do not proceed to infinity by hypothesising that one thing is always moved by another by constraint. The first thing which moves naturally is the heavens. It is moved by itself if Aristotle wrote ‘, moving naturally, must cause itself to move’. But if he wrote, as Alexander maintains, ‘, moving naturally, must cause motion’, it is obviously moved by the unmoving cause. Alexander renders the text this way, even though many books have ‘itself’ and not ‘it’, afraid, I think, that one should find Aristotle to be saying that the first cause of natural motions is what is self-moving.141 Alexander says: For, according to Plato, before the cosmos came to be, there was nothing self-moving, that is, no soul. Or perhaps a thing is self-moving if it is not moved by something else, although it is not always true that if something is self-moving it is soul, since even the things which move naturally are in a way self-moving since they have the starting point of motion in themselves. But one should notice that there are two kinds of starting point of motion, one related to causing motion, the other to being moved. Or rather there are three, since there is also one related to causing motion and at the same time being moved. The starting point related to causing motion only is in the unmoving cause which first causes motion; the one related to causing motion and at the same time being moved is in what is self-moving in the strict sense, that in which the cause of motion and what is moved are the same in substratum; and in natural things the starting point of motion related to being moved is nature; for this is the first thing moved by soul and it moves the body along with itself.142 Now, if the first cause of motion causes motion naturally, it is clear that things which are moved by it are also moved naturally, and, being moved naturally, they would move to their proper places and rest. And in this way they would make a cosmos with the present ordering of bodies, since things with weight would move to the centre and rest there, and light things would move upward away from the centre; for the cosmos also has this separation of bodies from one another now. Consequently there would be a cosmos before the cosmos came to be. So it is clear that there cannot be a motion prior to the cosmos, if such a motion cannot be either by constraint or natural. Alexander also adds the following. If the elements were moving in a disorderly way on their own for an infinite time and then, starting at some time, are moved ad infinitum in an orderly way by something, the motion which these bodies were moving on their own,

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would be natural for them, since things which move because of a starting point of motion in themselves move naturally. But natural motion fits better with order and cosmos. And Alexander also adds this. This absurdity, that there was a cosmos before a cosmos came to be, does not just follow from what is said in the Timaeus; it also follows for Leucippus and Democritus and their followers, who say that the atoms move in an infinite void by constraint. For if it is necessary that the natural be prior to the unnatural, and if, when the natural is, it is necessary that there be a cosmos, there would be a cosmos before the cosmos came to be. But perhaps saying this does not follow for Democritus and his followers since they said that there is always motion by constraint even when there is a cosmos and not just before the making of the cosmos, as Timaeus143 writes.

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300b25-31 Furthermore, one might further ask [whether it would not be possible that, when things were moving in a disorderly way, some things would undergo mixtures of the kind from which bodies which are put together naturally are put together (I mean, for example, bones and flesh) in the way Empedocles says happens under (epi) Love. For he says,] ‘Many heads without necks grew’.144 He adduces another absurd consequence for those who say there was a disordered motion prior to the cosmos. It seems rather unclear because of the brevity of its formulation. He asks whether it would not be possible that before the cosmos there was disorderly motion such that ‘some things would undergo mixtures of the kind from which bodies which are put together naturally are put together’ (for example, bones and flesh and in general the parts of animals and plants, and animals and plants themselves) ‘in the way Empedocles says happens under Love’ when he says, ‘Here many heads without necks grew’.145 Having asked this, he leaves it to us to infer the opposite of what is expressed in the question and the absurd consequences.146 The opposite is that these things would sometimes mix in such a way that natural bodies would also be put together from them. The absurd consequences are the following. If it were not possible for things moving in a disorderly way to also move in such a way that sometimes the mixtures mentioned would be mixed together, the motion would not be entirely without order. For the disordered is indeterminate, so that there would be mixing and not mixing. And so there would not be disorder in every respect. But if it were possible for these things ever to mix together to make fire, earth, water, and air and the animals and plants composed of them (because in their generation of the cosmos those who say the cosmos comes to be obviously do not make animals out of animals, but out of bodies

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blended together), when this happened there would be a cosmos. For why if bodies can also mix in this way was there not a cosmos earlier, but there is now? Such then is the purpose of the whole passage. Alexander understands the words ‘just as Empedocles says happens under Love …’ as an example of mixture from which natural bodies are put together. And he thinks he is supporting his view that ‘Many heads without necks grew’ is said under Love,147 Love being the cause of mixture as Strife is the cause of separation. But how could the phrase ‘head without a neck’ refer to mixture? The same can be asked about other things mentioned by Empedocles in these lines: Naked arms needing shoulders roamed, And eyes lacking foreheads wandered by themselves,148 and many other things which are not examples of the mixing from which natural things are put together. Perhaps then Aristotle, having said ‘whether it would not be possible that, when things were moving in a disorderly way, some things would undergo mixtures of the kind from which bodies which are put together naturally are put together’ adds ‘in the way Empedocles says happens’, that is, that things moving in a disorderly way mix (for the words ‘wander’ and ‘roam’ indicate disordered motion). And how, one might ask, can Aristotle say that these things happen under Love, when Empedocles says that all things become one because of Love: All these things came together in to be just one thing.149 So perhaps Empedocles did not say that these things happen when Love rules, as Alexander thinks, but at the time when Strife did not yet:

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Stand entirely at the last boundaries of the circle, But parts of It remained in the limbs and parts had departed. And as much as It (he means Strife) continued to run out from below So much did a gentle, immortal rush of blameless Love continue in pursuit.150 So in this condition of things limbs, which existed after the separation produced by Strife, were still ‘isolated’151 but they wandered, desiring to be mixed with one another.

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And in addition to them many other things continued to emerge.152 So Empedocles said that these things happen under Love not in the sense of the time when Love already rules, but in the sense of the time when it is going to rule and is still making visible unmixed single limbs. But if Timaeus said that before the cosmos came to be there really was a disordered motion of the elements, Aristotle has made correct and real objections based on natural considerations against Timaeus’ doctrine. But if Timaeus wanted to make the point that all cosmic order comes to matter from the demiurgic goodness by treating in discourse matter in and of itself, removing its clothing with only its suitability to receive form and indicated that it moves in a discordant and disorderly way, and what Timaeus says is productive of an intellectual doctrine, then Aristotle is doing adequate battle with the apparent meaning of what is said but not with its true meaning. And just as in the Timaeus Plato indicated that matter in and of itself moves in a discordant and disorderly way before the making of the cosmos, so too in the Politicus he separates demiurgic providence from the cosmos in discourse and represents it as being turned back by fate.153

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300b31-301a4 As for those who make there be infinitely many things moving in an infinite, [if there is one thing which causes them to move, it is necessary that they move with one motion so that their motion will not be disorderly, but if they are caused to move by infinitely many things, they must have infinitely many motions; for if they were finite, there would be some order since disorder does not result because motion is not into the same ; for even now all things do not move into the same ,] only things of the same kind do. He adduces these things against Democritus and his followers, since these are the people who make there be infinitely many things moving in an infinite void. And so he says against them that what causes the things to move is either one or finite or infinite. When he says that what causes them to move is one, he does not mean ‘one in number’ but ‘one in form’, for example, that it is heaviness or lightness. And ‘if there is one thing which causes them to move, it is necessary that they move with one motion’, so that their motion is not disordered since they are always moving with this motion. But if they are moved by things which are infinitely many in form, they must have motions which are infinitely many in form. Having said this he does not add some other absurdity on the grounds that he has reduced the view to this absurdity: that there would be

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infinitely many motions. For the forms of simple motion are finite, either in a circle or up or down. And other motions are mixtures of these. But Alexander says that furthermore, if there are infinitely many things causing motion and infinitely many moving things, it will follow that there are two infinites, which is absurd. Or if there were infinitely many causes of motion, nothing would move at all.154 But if there are finitely many causes of motion, the motions will also be finite. But motions which are finite in form are ordered, so that the motions will be orderly, not disorderly. For disorder does not follow from there being several motions and all things not moving into the same , since heavy and light things do not move into the same , ‘only things of the same kind do’, since heavy things move to the centre, light things to the periphery. Aristotle unobtrusively hypothesises that the causes of motion are finite by saying ‘for if they were finite, there would be some order’, but he unobtrusively takes the motions, not the causes of motion, to be finite.155 He did this because if the motions are finite in form, the causes of motion will also be finite in form, and most of all because he has an immediate need for finitely many motions in order that there be an order. However, Alexander says that Aristotle leaves out the hypothesis that the movers are finite because what follows from their being one also follows from their being finite. 301a4-11 Furthermore, the disorderly is nothing other than the unnatural, [since order is the proper nature of perceptible things. (301a5) However, that what is infinite should have a disordered motion is also absurd and impossible, since the nature of things is the nature most of them have and for most of the time. But the contrary of this follows for these people: disorder is natural, and cosmic order is unnatural.] But156 nothing natural comes about in a random way. He also adduces this consideration mainly against Democritus and his followers, since they say that there are infinitely many moving things. He assumes to start that the disorderly is the unnatural, since order is what is natural (he calls what is natural nature), and he assumes something else, namely that ‘the nature of things is the nature most of them have and for most of the time’. For what belongs to most human beings and for most of the time is natural for a human being. Having posited these things, that it is absurd and impossible that what is infinite should have a disordered motion for an infinite time. For what is infinite and moving for an infinite time moves naturally, and it is impossible that what moves naturally move with a disordered motion because the disordered is the same as

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the unnatural. Therefore, it is impossible that what is infinite and moving for an infinite time move with a disordered motion. Thus there follows for these people the contrary both of the truth and of their own intention, namely that disorder is natural (since what belongs for most of the time to most things and belongs primarily is natural) but that cosmic order is unnatural (since these things move in a disorderly way for an infinite time and only for a short time weave together with one another and are given a cosmic order). ‘But’, Aristotle says, ‘nothing natural comes about in a random way’, but those who said that natural motion is disordered said that the natural comes about in a random way, since what is disordered and has no reference to a determinate end comes about in a random way.

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301a11-22 Anaxagoras seems to have grasped this same point correctly, [since he begins by making a cosmos from unmoving things. And others try to blend things somehow and then move and separate them. But it is not reasonable to make the coming to be be from separated moving things. Therefore, Empedocles also passes over 157 under Love, since he was not able to put the heavens together by constructing them out of separated things, making Love the cause of their blending. The cosmos is composed of separated elements, so it is necessary for it to come to be from one blended thing. (301a20) So, that each body has a natural motion, which it does not move by constraint or unnaturally] is evident from these things.

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He has censured those who make the cosmos out of elements which previously moved in a disorderly way both because they hypothesised that the unnatural is prior to the natural and because they said that disordered motion, which is unnatural because it is disordered, is natural because it is primary, infinite and a motion of infinitely many things. He now accepts what Anaxagoras says at least with respect to his not making the cosmos out of moving separated things but out of unified things at rest. For Anaxagoras says that all things were together and Mind put them in order by separating them. Alexander says: But it is also possible to say the following in this case. If Anaxagoras makes the cosmos from things at rest by separating them and this motion and separation is natural for bodies, their rest would be unnatural for them, since the motion of bodies starting from a rest which is unnatural is natural. But if the rest were unnatural for them and lasted an infinite time, the unnatural rest would be natural for them. Furthermore, if that

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Translation rest is unnatural, there would be some other prior condition which was natural for them, since it is necessary that the natural be prior to the unnatural. But if this is the case there would be a cosmos prior to the coming to be .

So Alexander. But Aristotle only accepts this one thing in Anaxagoras, the making of the cosmos out of unmoving unified things. And he adduces the reason in what he says next. If the cosmos is now composed of separated elements, then if it had come to be,158 it would be necessary for it to have come to be from the contrary condition, so that it would be necessary for it to have come to be from something blended and therefore one. Aristotle calls to witness the other natural philosophers, of whom some, such as Thales, Anaximenes, and Heraclitus, make the cosmos come to be from one thing while others, such as Empedocles, make it come from things which had been blended; for Empedocles says that the elements, which were earlier blended by Love, make this cosmos when they are later separated by Strife. Aristotle says that ‘it is not reasonable to make the coming to be of the cosmos be from separated moving things’, since if the things in the cosmos are separated and moving, but coming to be is from contraries, then the coming to be of the cosmos must be from things which are blended and at rest. Aristotle says, ‘Therefore, Empedocles also passes over the condition of the elements under Love’, that is, he does not make this condition, but only the separation which occurs under Strife, responsible for the making of the cosmos. Aristotle says that he was not able to put a cosmos together by constructing it out of separated things (as the cosmos obviously is now constituted), ‘making Love the cause of their blending’. For the cosmos is not composed of blended elements but of separated ones. So if coming to be is from contraries, ‘it is necessary for it to come to be from one blended thing’. Therefore, it is reasonable that in making the cosmos Empedocles did not also make use of this159 so that he could give an indication of the cosmic separation which comes to be by a change from this. And so interpreters have understood the term ‘passes over’ correctly. For in his construction of the cosmos he passes over under Love, since under Love it was not this perceptible cosmos but the intelligible one and the things unified in it which came to be: A round sphere, rejoicing in joyous rest.160 But some people interpret ‘passes over’ to mean that Empedocles separates Love from Strife as a cause and leaves it by itself.161 (301a20) So, having proposed to prove that some motion must belong naturally to the simple bodies and assuming as clear that they move, Aristotle has proved that if they move naturally he has ob-

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tained what he sought and that if they move by constraint and unnaturally, then too it is necessary that natural motion be prior to the unnatural motion. And he was compelled to turn away from his argument and speak against the people who hypothesise that the unnatural is prior to the natural. These people were Democritus and his followers, who say that before the making of the cosmos infinitely many indivisible things move for an infinite time in an infinite void, and Timaeus, who says that the cosmos comes to be from a prior discordant motion. Completing his refutation, Aristotle concludes with what he initially proposed, that ‘each body has a natural motion’ and says that this is evident from what has been said previously. 301a22-b1 That it is necessary that some things have an impulsion of weight or lightness [is clear from these considerations. We say that it is necessary for there to be motion. For162 if what moves does not have an impulsion by nature, it is impossible for there to be motion toward or away from the centre. For let A be weightless and B have weight, and let the weightless have moved through CD and B have moved through CE in an equal time; for what has weight will move through a greater distance. If the body having weight is divided in the ratio of CE to CD (it is possible for it to be related to one of the parts in it in this way), then if the whole thing moves through the whole CE, it is necessary that the part of it move through CD in the same time, so that what is weightless and what has weight will move through an equal distance, which is impossible.] (301b1) The argument is the same in the case of lightness. Having proved that it is necessary that some motion belong naturally to the simple bodies, he next proves that it is necessary that an impulsion of weight or lightness belong to bodies which move naturally – not to all but to some, namely, all those which move in a straight line, since the body which moves in a circle transcends these things. And he shows that the natural motion of these simple bodies is because of (kata) these impulsions. Having previously assumed163 as agreed upon that all the sublunary bodies have weight and lightness and having refuted on this basis those who construct bodies from planes which have neither heaviness nor lightness, he now proves what he previously hypothesised, namely that it is necessary that all the simple bodies which naturally move in a straight line have weight or lightness. He is not proposing to prove just that there are heavy and light bodies, since in his demonstration he did not hypothesise that some

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things are heavy and some are light. Rather he is proposing to prove that there isn’t any body which moves in a straight line which is not heavy or light, and he refers to them as ‘some things’ because of the heavenly body. He makes clear that he is proposing to prove that none of these bodies fail to have an impulsion, by saying straightaway, ‘For if what moves does not have an impulsion by nature’, and a little later164 ‘Furthermore if there were some moving body which had neither lightness nor weight’. The proof proceeds on the basis of what was previously proved, namely that downward and upward motion belong naturally to bodies, and further on the basis of the fact that in an equal time what has weight moves naturally downward a greater distance than what does not have it – this is clearly true if what doesn’t have weight moves at all165 –, and third on the basis of the fact that in the case of things moving by constraint because of the same power what does not have weight would move a greater distance, what has weight a lesser one in the same time.166 These things being assumed to start, he proves that if something moving does not have an impulsion of weight or lightness, it is impossible for it to move either away from the centre or to it. And he proves first that it is impossible for something which is weightless to move down, the way in which things having weight are naturally constituted to move. The proof is by reductio ad impossibile. A |——|

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Let B be a body with weight, A a weightless body. And let the weightless A have moved through a certain distance CD, and let B, which has weight, have moved through a certain distance CE in the same time. Obviously CE is greater than CD, since, moving down, B, which has weight, moves through a greater distance in an equal time than A, which does not have weight. If some part of B, which has weight, is to the whole B as the distance CD is to CE, which is greater than CD, let us take away F, since it is possible to cut what is uncut into the same ratio as what has been cut. The result is that the weight B is to F as the distance EC, through which B (which has weight) has moved, is to the distance CD, through which the weightless A has moved. So, by alternation,168 as the whole B is to CE, so is F to the distance CD. But B moves through the distance CE. Therefore F will also move through the distance CD in the same time; but the weightless A moved through the distance CD in an equal time; therefore the weightless A and F, which has weight, will move

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through the distance CD in the same time, which is absurd, since in an equal time what has weight will move downward farther than what does not have it – if one were to hypothesise that even what does not have weight moves. (301b1) It will be proved by the same argument that also something cannot move up if it does not have lightness, since what has lightness will move up through a greater distance than what does not have it. And if we make the light thing itself be to one of its parts as the distance through which the light thing moves is to the distance through which the thing not having lightness moves, then the light thing will be to its own part as the greater distance is to the lesser. And, by alternation, the lesser distance will be to the part of the light thing as the greater distance is to the whole light thing. Therefore, what has lightness and what does not will move up through an equal distance in an equal time, which is impossible. 301b1-17 Furthermore, if there were a moving body [which had neither lightness nor weight, it would be necessary that this be moved by constraint, and being moved by constraint would make the motion infinite. For since what causes motion is a certain power and the lesser or lighter, if moved by the same power, will move farther, let the weightless A have been moved through CE and B, which has weight, have been moved through CD in an equal time. If the body having weight is divided in the ratio of CE to CD, it will follow that what is subtracted from the body having weight moves through CE in an equal time since the whole moved through CD. For the speed of the lesser body will be to that of the greater as the greater body is to the lesser. So the weightless body and the body having weight will move through an equal distance in the same time. But this is impossible. Consequently, since the weightless body will move a distance greater than any assigned, it will move through an infinite distance. So it is evident that] it is necessary that every determinate body have weight or lightness.169 Having proved that it is impossible that a body having neither heaviness nor lightness move either up or down naturally, he now proves that it cannot move unnaturally and by constraint either, since it follows that it is moved ad infinitum by the power which moves it. So, if this is impossible, it is also impossible that something move by constraint by being thrown or pushed or dragged by something if it does not have weight or lightness. In proving this he again assumes to start what is clearly true, namely that what is lesser or lighter will be moved farther by the same power. So let A be weightless and B be the thing having weight, and let A have been moved through the distance CE and B, which has weight, through the

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distance CD, which is less than CE, in an equal time by the same power causing motion by constraint. If the body B, which has weight, is divided in such a way that as CE is to CD so is B to some part F of it, it will follow that F, which is taken away from B, the body having weight, moves through the greater distance CE in the time in which the whole B moved through CD, since the speed of the lesser body will be to that of the greater as the greater body is to the less. However, the weightless A was also moved by the same power through the distance CE in the same time. Therefore, in the same time the weightless body A and F, which has weight, will be moved an equal distance by the same power, which is impossible. But since what is weightless will move a distance greater than any assigned finite distance (for, whatever thing having weight is taken to move an assigned greatest distance of whatever size, what is weightless is more easily moved by what constrains it than the thing is), but it is not possible to move an infinite distance, since every motion is from one place to another, and what cannot have come to be cannot be coming to be, as he said previously,170 therefore a body which does not have either weight or lightness cannot move. So it is evident that it is necessary that every determinate body have weight or lightness. As Alexander says, Aristotle uses the word ‘determinate’ either to indicate the division or separation between one thing having lightness and another heaviness or to indicate moving in a straight line171 and not in a circle. ‘But’, he says: it is better to understand ‘determinate’ to indicate actually being and being in a place (and not potentially), since what is potentially a body is not yet either a body or in a place. And Aristotle may have added ‘determinate’ because of mathematical body which is not determinate and actual just as it does not have weight or lightness. But I do not know how he can say this since a mathematical body as mathematical is both determinate and actual. But I think that it is a reasonable that ‘determinate’ means ‘moving in a straight line’, as being distinguished by lightness and heaviness from what moves in a circle, which is above this determination. And I think that it is even more plausible to say that ‘determinate’ indicates what is circumscribed in itself and in a place. For such a thing can also change place. For what is continuous with something else in the way that parts are contained in a whole is not in a place per se nor does it change place per se according to the decree of Aristotle.172 So, since the detached parts of the elements, that is, of earth and fire and what is intermediate between these (and not their entireties or the parts connected with their entirety173) are what moves in a

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straight line, with the words ‘every determinate body’ he is indicating the parts of the sublunary elements which move in a straight line; for there is nothing determinate among heavenly things apart from the entirety of heaven,174 and among sublunary things the entireties are not determinate but have their parts continuous with one another. And so he says ‘every determinate body’ instead of saying ‘every body which moves in a straight line’. Having assumed that every sublunary body moves either naturally or by constraint and proved that what has neither lightness nor weight does not move either naturally or by constraint, he has as the conclusion from these assumptions that what has neither heaviness nor lightness is not a sublunary body.

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301b17-31 Since the starting point of motion which inheres in a thing is nature [and a in something else or qua something else is power, and some motion is natural, some by constraint – all of it –,175 what has power will make natural motion (for example, the downward motion of a stone) faster, and power is the entire of unnatural motion. (301b22) In both cases the power uses air as an instrument. For air is naturally constituted so as to be both light and heavy. And so, qua light, it will produce motion up when it is pushed and takes its starting point from the power, and, qua heavy, air will produce motion down; for the power transmits to each of them as if it were attached to them. Therefore, what is moved by constraint moves without the thing moving it following along. For if no such body as air existed, there would not be any motion by constraint. (301b29) And air ‘produces a fair wind’ for the natural motion of anything in the same way. (301b30) That everything is either light or heavy] and how unnatural motions occur in these things is evident. Having proved that a body which does not have either weight or lightness cannot move either naturally or by constraint, he next shows what the nature which moves the things which are said to move naturally is and what the power which moves things which are said to move unnaturally is, and he shows that nature is in the moving thing, power in something else. The starting point of change which inheres in a thing is nature, as he has already shown in the second book of the Physics.176 And a starting point of motion which inheres in something else is power, since if something is moved by something else, it has the starting point of motion in that thing. He adds the words ‘qua something else’ since some things which move but not naturally do have the starting point of their motion in

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themselves, but this power is in them not per se but accidentally – they are moved by a power which is in something else per se. An example is if an ill person who is a physician is cured by himself, since he is not cured by himself qua being an ill person, nor does he have the starting point of motion as being an ill person; nevertheless, the art of medicine because of which he is cured is in the ill person himself, but as if in another person and not as lightness is in fire (and so all fire is accompanied by lightness, but not every ill person has the art of medicine). By ‘some motion is natural, some by constraint – all of it’ he means all motion is either natural or by constraint. And natural motion occurs because of an inhering cause, namely nature, constrained motion because of a power in something else. And when a naturally moving thing is also pushed along by this power it moves faster than the motion which results only because of the power; in the case of a stone a power which pushes it along will make its motion downward faster than the motion which comes about only because of the power, as in the case of the upward motion of the stone; for only the power causes this upward, unnatural motion of the stone, but both this power, by pushing along, and nature produce its downward motion. (301b22) Next he says how the power causes motion both when it acts on its own and when it acts along with nature. He says that the power uses air as an instrument in the case of both motions, the motion up which the power activates in the case of weights when it alone constrains and the motion down when it pushes nature along. Air is suitable for both things because it is both light and heavy. He has said previously177 that the elements intermediate between earth and fire are like both, since neither of the intermediates is either absolutely heavy (since neither sinks to the bottom of all of the elements) or absolutely light (since neither rises to the top of all). But everything which is not absolute has the character it does by a kind of mixture of its contrary. And air, because it has fine parts, is easily moved, and so it activates things to move toward what is above because of its own motion and also by taking on another starting point of motion from a power; and air activates downward motion, both because it has a heavy aspect and because, again, it takes a starting point of motion from a power. For the power which causes motion transmits to each of the airs, the one which is pushed up and the one which is pushed down (or perhaps he means by ‘each of them’ the air and the stone) a kinetic power as if joining together with them and binding with them. And he adduces a sufficient sign that some power which is joined together is bestowed by the thing causing the motion, namely that what is moved unnaturally moves without what has moved it following along. For what moves naturally has nature as the cause of motion, but it is clear that what moves unnaturally takes on the power of moving from the power which is causing it to

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move by constraint and that air acts together with it; for if there were not some body of this kind acting together with it, motion by constraint would not be the way it is, since if air did not have a light aspect, it would not carry what is heavy up, and if it did not possess a heavy aspect, it would not move fire downward. (301b29) ‘And air “produces a fair wind for” (that is “pushes”) the natural motion of anything’ by receiving a share of the power from the cause of motion. The term ‘produce a fair wind for’ is taken from the winds which blow from behind and push a ship; these winds are called tail winds because they blow from the tail of the ship. But perhaps the term ‘tail wind’ is also a metaphorical expression involving lions, which, they say, drive themselves into a race by striking themselves with their own tail in place of a whip. (301b30) And then, completing the discussion, he says: that every body which is sublunary and therefore also moves in a straight line (since this is what the present discussion is about) is either light or heavy, ‘how unnatural motions occur in these things’ in which they exist, namely that these unnatural motions are posterior to the natural ones and last less time and that they are moved by the external power of the air, which contributes to the motion – that these things are this way – is ‘evident’ (obviously on the basis of what has been proved). Alexander178 thinks that the phrase ‘in these things’ is elliptical in formulation, since it lacks either the words ‘and it has been said previously’, or it is as if he said ‘in these things’ in such a way that we do not understand ‘in these things which have weight and lightness’, but rather understand ‘in these discussions’. Alexander thought this and he joined the term ‘is evident’ with the subsequent words and wrote, ‘But it is also evident that not all things come to be’. However, I find the word ‘evident’ written as the last word of the prior sentence and without the connective , so that the next words read, ‘That not everything comes to be and that not absolutely nothing comes to be is clear from what has been said previously’. But it seems that Alexander found in some copies ‘That not everything comes to be and that not absolutely nothing comes to be, as is clear from what has been said’ and was compelled to join ‘It is evident’ with what follows it. I think it would be better to call this a mistake of the scribe than to accept the interpretation according to which the text is elliptical. For it would not be plausible to join ‘evident’ and ‘clear’ with one another so that the text says, ‘But it is evident that not everything comes to be and that not absolutely nothing comes to be, as is clear from what has been said’. But whatever the text says has no bearing on the truth of things. So let us move to what comes next. 301b31-302a9 That not everything comes to be [and that not

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Translation absolutely nothing comes to be179 is clear from what has been said previously. For it is impossible for all body to come to be, unless it is also possible for there to be a separate void, since if it were to come to be, it would be necessary that in the place in which what is coming to be now will be there was previously void, with no body existing. It is possible for one body to come to be from another, for example, fire from air, but in general it is impossible for a body to come to be from no previously existing magnitude. Certainly a body could come to be actual from something which is potentially a body. But if the body which is potentially is not already another actual body,] there will be a separate void.

Having demonstrated the hypotheses and the whole syllogism of his argument against those who say that bodies are composed from planes,180 he next runs off (apotrekhei) to his original division181 concerning coming to be in which he said that some people, such as Parmenides and Melissus and their followers, did away with coming to be entirely, and some, such as the theologians associated with Hesiod, said the contrary of these people, that all things come to be. He says that it is clear from what has been said that not everything comes to be, since it has been proved182 that the body which moves in a circle does not come to be or perish, and it is clear that something does come to be, since he has taken issue with those who understand the statements of Parmenides and Melissus as saying that all being does not come to be.183 And he now proves that not everything comes to be on the basis of the fact that body simpliciter does not come to be. For air comes to be from water and one thing from another when their qualities interchange, but the body itself which underlies the qualities does not come to be. For if it comes to be it comes to be from what is not a body, since a particular body such as air comes to be from what is not air, but it comes to be from a body because it does not come to be qua body but qua air; but if a body comes to be as a body, it is necessary that it come to be from what is not a body. But if this occurs, it is necessary that there be a separate void. (Those who said that there is a void hypothesised it in two ways: first, as mixed with bodies because of the pores contained in them – we say that these pores are filled with air –, and, second, as the place of bodies which comes to be separate from bodies.) So, if a body comes to be and was not a body already, that requires a certain space which is empty of body and which can contain it. And then, I think, he resolves the objection which says, ‘Why isn’t matter potentially body just as it is potentially all other thing and why doesn’t what is actually body come to be from what is potentially body, as in other cases?’ And so he says, ‘Certainly a body could come to be actual from something which is potentially a body. But if the body which is potentially is not

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already another actual body’ (so that a body comes to be from a body which it is not like), but rather a body comes to be from what is incorporeal, ‘there will be a separate void’. Alexander says that Aristotle is now setting out his doctrine of matter.184 For does not think that matter is actually incorporeal, but that both matter and form are separable in thought, although actually neither of them exists separately; rather, when something is said to come to be from matter, it is said to come to be from something which is actually,185 but with respect to what is potentially the thing which comes to be it is said to come to be from that thing as from matter. For says that ‘in general it is impossible’ that something ‘come to be from no previously (actually) existing magnitude’, that is, from no body. For if this happened there would be a void. Consequently, according to , qualityless body, which he calls186 the second substratum, does not come to be, since, if it came to be, it would have to have come to be from what is not a body. But this is impossible if there is no separate void. But perhaps there is no coming to be of any other common genus either, since there is no coming to be of either colour or shape.187 For if colour or shape came to be it would come to be from what has no colour or what has no shape, but it is not possible for there to be a finite body which is entirely without colour or shape. By the same reasoning the other common qualities, such as heat and coldness, sweetness and bitterness, would not come to be, if it is necessary that every body be dominated by some contrary or intermediate. Rather in every case it is a particular thing188 which comes to be from something which is naturally constituted . What then? Are there this many sublunary forms which do not come to be? And why do we say that all sublunary things come to be and perish? Or is it the case that just as there are common forms in this world, so too they come to be and perish? But these forms do not exist per se; rather they exist in individuals, since in this world no colour or shape which is not a particular thing exists per se, and similarly in the case of body. So, just as common things exist in particulars, so too they come to be and perish in those things, but they are always interchanging in189 particulars, just as time in this world and motion are always interchanging. For there is no time which is not this certain time190 and no motion ; rather common things appear in the continuous flux of particulars, and they seem to stand still as one thing because they are an appearance of the intellectual form which always is. It is as if one were looking at a face in an eternally flowing river: the appearance of the face in the water seems to be one and the same, although it is not the same but gives the impression of being one because of the enduring face. However, even the Peripatetics, who place all common things in particulars, think that what is common and lies under

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particulars which are always in flux remains fixed while changing.191 And perhaps one should say that body simpliciter does not come to be for this reason192 rather than because otherwise one would be forced to hypothesise a void. For if things rarefy and condense, and it is not necessary that there be a void or that the universe swell (as Xuthus said it does), and it is not necessary to make the apparently artificial hypothesis that when one thing is rarefied another is condensed to the same degree,193 what prevents it from being the case that when one body comes to be another perishes or is condensed at the same time?

302a10-19 It remains to say what things come to be [and why they do. Since in all cases knowledge is based on primary things and the elements are the primary things which inhere , we should investigate which sort of bodies of this kind are elements and why, and thereafter investigate how many there are and what they are like. (302a14) This will be evident if one hypothesises what the nature of an element is. Let an element of bodies into which other bodies are divided and which inheres (potentially or actually – it194 is still to be debated which) and which itself cannot be divided into things different in kind . In all cases everyone means to say that] an element is something of this sort.

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Having shown that neither those who say that all things come to be nor those who say that nothing does are correct, he next asks what things come to be. For initially195 he proposed that after the discussion of the body which moves in a circle he would speak about the other simple bodies, in which there is already coming to be and perishing. Therefore he said196 it is necessary to investigate coming to be and perishing and first whether there is coming to be at all and whether all things come to be or only some. So, having refuted those who do away completely with coming to be and those who say that everything comes to be, he turns to the question of ‘what things come to be and why they do’. By ‘what things’ he means ‘which of the things which have affective qualities and move in a straight line’ and by ‘why they do’ he means ‘when what things occur does something come to be’. In all things for which there are principles, understanding and knowledge result from knowing the principles; and the elements are principles of things which come to be (for everything which comes to be comes to be from something); and the elements are the primary things which inhere in things which come to be, and knowledge is

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based on primary things; therefore, it is reasonable that the discussion of coming to be should start from the elements. He says, ‘We should investigate which sort of bodies of this kind are elements’. But since different people hypothesised different things, after he has first recounted their views, he will state his own doctrine in the books on coming to be,197 where he will also make clear the cause of the four bodies’ coming to be. He says that the elements are the primary things which inhere in things which come to be because accidents also inhere in them but they are not primary. So he says that we should investigate which sort of bodies which come to be are elements, since some bodies which come to be are elements, some are composed of elements. When it has been determined which sort are elements, namely the ones which are composed from contrary affective qualities, one should ask why these are the elements of bodies which come to be and in addition how many bodies and what sort are such as to be elements (in fact there are four, fire, air, water, earth). (302a14) He says that these things will be evident if we hypothesise ‘what the nature of an element is’. For by comparing bodies with the definition of an element we will find how many such things there are and what they are. And he next defines ‘element’, saying that an element of bodies into which other bodies, the ones composed of elements, are divided. For we are enquiring about the element of body not as body198 but as composite body. So he does well to say ‘into which other bodies are divided and which inheres in bodies (potentially or actually – it is still to be debated which)’. For that the elements inhere actually follows for those, such as Empedocles and Anaxagoras, who say that coming to be is the result of blending and separation out, but that they inhere potentially follows for those who199 say it is a result of qualitative change. Aristotle says that an element itself, even if it can be divided as a body, cannot be divided as an element into things different in kind. And it differs in this respect from what is composed of elements because the latter can be divided into the elements, which are different in kind , even if it can also be divided into homoiomeries;200 for flesh can be divided into flesh, but it can also be divided into the four elements, which differ in kind from one another, but fire cannot be divided into things different in kind. And the word ‘inhere’ distinguishes element from species. For ‘simple body’ is divided into the fifth and the four, but they do not inhere, since it is divided as a genus into species, not as something composed of elements into elements. He says, ‘In all cases (of things composed of elements) everyone means to say that an element is something of this sort’. For an element of speech201 is that into which speech is divided and which inheres in it and which itself is not divisible into things different in kind.

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Translation 302a19-28 If an element is what we have said it is [there must be some things of this sort among bodies. For fire and earth are contained potentially in flesh and wood and everything of this sort, since they are obviously separated out from them. But neither flesh nor wood inheres in fire either in potentiality or in actuality, since they would be separated out. (302a25) Similarly if there were only one element, flesh or wood would not inhere in it. For if flesh or bone or anything else of this sort is going to exist one should not immediately say that they inhere potentially, but] one should also investigate202 the way they come to be.

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[i] Since there is coming to be it is necessary that there be elements from which what comes to be comes to be, so if an element is of a certain sort, it is necessary that some bodies be of this sort; [ii] but elements are the sort of thing which has been described; [iii] therefore, there are some bodies of this sort. The conditional [i] is clear from the fact that there is coming to be, since if there is coming to be it is necessary that there be bodies of a certain sort from which what comes to be comes to be and into which it is dissolved. And he confirms the additional assumption [ii] on the basis of the common preconception that an element is of this sort. He next gives evidence for the conclusion [iii] that there are some bodies of this sort on the basis of induction, saying, ‘Fire and earth are contained potentially in flesh and wood and everything of this sort’. That they are contained is clear from the fact that they are separated out from them. But they are contained potentially. For saying that the elements are potentially follows for those who posit that the four bodies are elements which change into one another qualitatively. He uses the term ‘separation out’203 in its ordinary sense since it does seem to be used in the case of things which inhere actually. As for fire separating out from flesh, Theophrastus reports that a flame separated out from the eyes of a human being.204 But the Alexandrian physician Megethios205 described to me how he saw fire come out of the hip of a man suffering from sciatica and set blankets on fire, after which the pain stopped. And that fire separates out from flesh is also made clear by the scabs of carbuncles which come to be from fire206 and by very high fevers. And they expel fire from pieces of wood by rotating one piece of wood as a fire drill207 in another. That there is earth contained in these things is made clear by the ashes which are left after burning. And moisture which is separated out and vaporised air also make clear . So if fire and earth and the others are contained in flesh and wood, and there is no flesh or wood in fire or earth either potentially or actually (‘since they would be separated out’ at some time), it is clear that fire and earth and the others are elements of flesh and wood, since they inhere in them, but the latter are not elements of the former. (302a25) Since it has not yet been proved that there are four elements and there were some who said that there is only one, Thales and Hippo saying it is water, Anaximenes and Diogenes air, Hippasus and Heraclitus fire, Anaximander what is intermediate, it is reasonable for Aristotle to add that, even if the primary bodies were not four but one, the things which come to be from that primary body would not inhere in it either in actuality or in potentiality, but one should also investigate the way they come to be. For if someone says that they come to be by separation out, it is necessary that they inhere, but if it is by change, this is no longer the case. But since it is thought that elements come to be from composites when they are dissolved and composites come to be from the elements (since those who make the hypothesis that there is one element generate other things from it), one does not have to say for this reason that the element inheres in the composite and the composite in the element in the same way, nor are inhering in something and coming to be from it the same thing; for the simple things which come to be from composites did inhere in them; however, although composites come to be from simples, they do not thereby inhere in them, since having come to be from something is not a sufficient condition for inhering in it. Consequently even if flesh and bone and every composite come to be from simple things, one should not therefore say, as those who explain coming to be in terms of separation out do, that these composites inhere in the simples, ‘but one should also investigate the way they come to be’. For if coming to be is due to alteration, it is not necessary that these composites inhere. 302a28-b5 Anaxagoras speaks about the elements in a way contrary to Empedocles. [Empedocles says that fire and earth and the things co-ordinate with them are the elements of bodies and that all things are composed of them, but Anaxagoras says the contrary; he says that the homoiomeries (I mean flesh and bone and everything of that sort) are elements208 and says that air and fire are mixtures of these and all the other seeds – for each of them is a collection of all the invisible homoiomeries – so that everything comes to be from these homoiomeries.] (Anaxagoras gives the same name to fire and to ether.209) Having mentioned as elements ‘air and fire and the things co-ordinate with them’, which Empedocles also called elements, Aristotle 210

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next mentions the view of Anaxagoras as being contrary to that of Empedocles. That is not to say contrary with respect to the conception of an element since everyone said that an element is something which inheres in bodies and into which they are divided and which itself cannot be divided into things different in kind .211 Rather disagreement arose insofar as some people said that this sort of nature attaches to certain bodies and others that it attaches to other bodies. Empedocles said it attaches to the four and called them elements, Anaxagoras said it attaches to the homoiomeries, Thales to water, someone else to something else, but each of them invoked the same evidence and said that he called what he called elements because they are separated out from other things but other things are not separated out from them. On this ground Empedocles said the four are elements and Anaxagoras said the homoiomeries, such as flesh and bone and things of this sort are; he called them ‘seeds’ and said that what Empedocles called elements, air and fire and all the others, are mixtures of these, and all are collections of homoiomeries, although they do not seem to be composed from them because the homoiomeries are invisible and imperceptible because of their smallness. (Anaxagoras frequently used the word ‘ether’ to mean ‘fire’.) Aristotle has stated the view of the elements of each of these people and at the same time set out the opposition between them, namely that Empedocles says the homoiomeries are all composed from the four and that these are the elements of all things, whereas Anaxagoras constructs these four and everything else from the homoiomeries and from the homoiomeries in such a way that they themselves are also homoiomerous. And Aristotle took his view of what an element is from the common preconception as something agreed upon, but he does not take his view of what the bodies of this sort are from Empedocles and Anaxagoras, since they disagree about this. But, in showing next which bodies are simple, Aristotle will have shown which bodies are the elements. 302b5-13 Since there is a proper natural motion for every212 body [and some motions are simple, some mixed, and mixed motions belong to mixed bodies, simple motions to simple bodies, it is evident that there are certain simple bodies, since there are simple motions. Consequently it is clear both that there are elements and why there are.

(302b10) The next thing to investigate would be whether the elements are finite or infinite and, if finite, what their number

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is. And first] we should observe that they are not infinite, as some people think … . For the demonstration that there are simple bodies and that these are the four, he uses what he has already proved: that natural bodies are those which have the starting point of motion in themselves per se – this has been proved in the Physics;213 that some motions are simple and some mixed, and that a simple motion belongs to a simple body and a mixed motion to a mixed body, and that the motion of a simple body is simple (the simple motions of composite bodies result from the dominance of the simple bodies in them) – these things have been proved in the first book of this treatise.214 These things being assumed, since there are simple motions which occur along the simple lines, that is, the straight and the circular, it is evident that there will also be certain simple bodies, if, indeed, simple motions naturally belong to simple bodies. But simple bodies are elements because composite bodies are divisible into them, but they themselves are not divisible into things which are different in kind . The words ‘why there are’ may be said because of the simple bodies. For there are elements because there are bodies which naturally have a simple motion. But the words may also refer to coming to be because it has been proved that there are elements because there is coming to be, since if there were no elements it would be impossible for there to be coming to be.215 (302b10) Having proved that there are certain simple bodies, which are also elements, he next asks whether these are finite or infinite and, if finite, how many there are. It would be possible to grasp on the basis of the motions both that they are finite and how many they are, but he establishes that they are finite by first raising objections against those who say they are infinite.216 He then deals with those who posit that there is only one element.217 For in this way what he is going to prove will be more trustworthy because no view will be troublesome by being persuasive. 302b13-20 [And first we should observe that they are not infinite, as some people think] and consider first those who make all the homoiomeries elements [as Anaxagoras does. No one who maintains this takes ‘element’ in the correct way. For we see that many mixed bodies are divided into homoiomeries (I mean things such as flesh, bone, wood, and stone).218 Consequently, since what is composite is not an element, not every homoiomery will be an element, but only those which are not divisible into things different in kind ,] as has been said previously.

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Of those who say that the elements are infinite, Leucippus and Democritus hypothesise the infinitely many atoms, Anaxagoras and Archelaus219 the homoiomeries, and Aristotle deals with this view first. He has already spoken against it in the first book of the Physics,220 and he now asserts and proves that those who hypothesise that all the homoiomeries are elements do not make a correct hypothesis. For many composite bodies, which are not elements, are homoiomerous, since things which are divided into parts which are similar to the whole are homoiomerous. Flesh and bone and wood and stone are this sort of thing. And it is clear that they are not simple since, as he has said,221 the simple bodies, fire and earth and what is intermediate between them, are separated out from them, and they come to be from several ; for they come to be from nourishment which is variegated, and wood has some earth, air, and water, and there is no stone without water since it is impossible for earth to become continuous without water. And Anaxagoras himself says that these four are not elements, even though they are homoiomerous. So if nothing composite is an element (because an element is simple), but some composite body is homoiomerous, just as fire and earth and what is intermediate between them are, it follows in the third figure222 that not every homoiomery is an element, but only one which is not composite and not divided into things different in kind . But not every homoiomery is of this sort, since flesh and bone and such things are homoiomerous, but they divide into things different in kind, from which they are also composed. Having proved223 that those who say the homoiomeries are elements do not speak correctly, he adds the universal by which one should judge an element: not by homoiomereity or anything else of this sort, but by indivisibility into things different in kind. 302b20-30 Furthermore, even if one does take an element to be this sort of thing [it is not necessary to make the elements infinite. For all the same things would be explained if one assumed that they are finite; for he would produce the same thing if there are only two or three such things, as Empedocles also tries to show. (302b24) For since they too turn out not to make everything from homoiomeries (since they do not make a face out of faces nor do they make anything else which is shaped naturally), it is evident that it is much better to make the principles finite and as few as possible, provided all the same things will be provable. This is what mathematicians also espouse, since they always assume principles which are finite] either in kind or in quantity. He has just argued on the basis of homoiomereity and proved that

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not all homoiomeries are elements since they aren’t all simple. Now he confronts their infinity and, having accepted homoiomereity as a hypothesis, he says that even if one assumes that the elements are homoiomerous, it is not necessary for this reason to make them infinite; for if they are hypothesised to be finite it is possible to explain the same things, even if one hypothesises them to be few in number, two or three or four, in the manner of Empedocles. For he hypothesised that there are four elements and said that each of them is homoiomerous and explained all coming to be as coming to be on the basis of them. However, Empedocles hypothesises that these things are simple whereas Anaxagoras hypothesises that they too are composites of homoiomeries, just as he also makes all other perceptible things composites of homoiomeries which are characterised by the dominance of one thing in them. (302b24) And then Aristotle adduces a third argument based on both homoiomereity and infinity and directed against both. He says that since, even if they hypothesise that the elements are infinite in number, they turn out not to make all composites from homoiomeries; for they do somehow succeed in making perceptible flesh and gold and such things out of homoiomeries with the number of bits of flesh or gold (imperceptible because of smallness) dominating in the mixture, but it is not possible for them to compose a face (or the other so-called organic parts) out of many faces imperceptible in magnitude. Alexander says that a face is not composed from homoiomeries because an eye and a nose are not similar. But perhaps Aristotle is saying with more precision that they do not make a face out of faces because even if homoiomeries have parts which are similar to one another, they are not said to be homoiomerous for this reason but because they have parts similar to the whole. And he adds with complete precision, ‘Nor do they make anything else which is shaped naturally’. For not only does what is composed from things which are dissimilar to each other not have its parts similar to the whole (as was said in the case of the face), but also even things the parts of which are similar to each other and to the whole and the whole of which has been given shape in accordance with a natural configuration (as in the case of the bone of the skull or of the arm or of the thigh or a sinew or vein or artery) are not composed of parts which are similar to the whole. For even if a part of a bone or sinew is bone or sinew, the part is not given shape by the whole, whereas the whole with its shape is exactly what it is said to be.224 But if, according to them, it is also necessary that some things not come to be from homoiomeries and if infinity contributes nothing toward everything being composed out of homoiomeries, nothing prevents making the homoiomeries finite if, indeed, they are elements. For even if they are finite, some things will be composed of similar parts and some of dissimilar ones, in the same way as if they

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were assumed to be infinite. So if it is possible to preserve225 the same things if the principles are hypothesised to be finite and if they are hypothesised to be infinite, it is better, Aristotle says, to take them to be finite (as also in mathematics) and as few as possible. For if it is necessary that, if the principles are unknown, what comes from them is unknown, let the person who wishes to know what comes from the principles hypothesise finite principles and these as few as possible because what is infinite is unknowable and what is finite knowable, and what is finite is as much more knowable as it is more easily grasped and approaches oneness (hê monas). Therefore, mathematicians, who wish to have scientific knowledge of their subjects, assume principles which are finite either in kind or in quantity. They assume principles finite in kind when they define point and line and plane, since each of these is not finite in number but in kind and account. Potamon226 says that mathematical principles are definite in quantity when they assume that the monad is the principle of number, but Aspasius227 says that the five postulates are definite in quantity, since they are not five in kind but five in number. But Alexander says, It is possible to say that these themselves, each of which they took to be definite in form, are finite in quantity, since the things of which they give definitions as elements are definite in number. Or perhaps the elements are definite in kind according to them because they define ‘point’ and ‘straight line’ or ‘circular line’ and whatever they take as primary (what they also call definitions228); for their kinds are not infinite, but they have a number. And they are definite in quantity because use no infinite straight line or plane when they prove something. For even if they make the hypothesis that a thing is infinite, they always make use of it by cutting off a finite . But perhaps finite in kind because hypothesise nothing infinite but triangles, squares, circles, points, lines, and planes; and finite in quantity because the principles they assume were numbered, that is, so and so many229 definitions and axioms and postulates, which suffice for the demonstrations of the things which come after. 302b30-303a3 Furthermore, if one body is said to be different from another [with respect to their proper differentiae and the differentiae of bodies are finite (since they differ by perceptible

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things and these are finite – but this should be proved)] it is evident that the elements must also be finite. This argument also shows that the elements are finite in kind. The development of the argument proceeds hypothetically as follows. If all bodies differ from one another by differentiae which are finite in kind and things that differ by differentiae which are finite in kind are finite in kind, it is necessary that bodies be finite in kind. So if elements are also simple bodies, it is even more necessary that these be finite in kind than that the things derived from them be. And it is prima facie clear that bodies differ from one another with respect to their proper differentiae, since everything which is different differs by its proper differentiae. And that the differentiae by which bodies differ are finite in kind is clear from the fact that the differentiae are perceptible. And Aristotle proved that bodies differ by differentiae which are perceptible in book 7 of the Physics,230 and he proved that perceptible differentiae are finite in kind in On Perception and Perceptibles231 in the following way: Everything perceptible involves a contrariety; what involves a contrariety involves extremes in kind; what involves extremes in kind is finite in kind; therefore, the kinds of perceptibles are finite.

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And it is possible to develop the argument about the elements categorically in the following way: Elements are bodies; bodies differ from one another by their proper differentiae, which are perceptible; things which differ by perceptible differentiae differ by differentiae which are finite in kind; things which differ by differentiae which are finite in kind are finite in kind.232 Aristotle brings in these things against the doctrine of Anaxagoras here, but in the first book of the Physics233 he also dealt with the doctrine that all things are mixed in all things. For Anaxagoras said that every perceptible body has infinite homoiomeries in it, and that is why all things are seen to come from all things. Now Aristotle showed that it follows from this that every perceptible thing is infinite in magnitude,234 since a magnitude which is composed of actual magnitudes which are infinite in number must be infinite in magnitude. So if this is impossible, the elements cannot be infinite. And it is clear that

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this argument does away with infinity in number, but doing away with that does not also do away with infinity in kind.235 However, Anaxagoras says at the beginning of his treatise, ‘All things were together, infinite in both number and in smallness, since the small was also infinite. And since all things were together nothing was clear because of the smallness’.236 And he says that, ‘One should think that all things are in everything’.237 But perhaps he means by ‘infinite’ what we cannot grasp or know,238 as he indicates with the words ‘so that to know the number of the things separated either in theory or in fact’.239 He makes clear that he thinks that things are finite in kind by saying that Mind knows all things. But if things were really infinite they would be completely unknowable, since knowledge defines and limits what it knows. But he says, ‘And Mind knew all the things which are mixed together and separated, both how they were going to be and how they were …’.240 It seems that Anaxagoras is indicating a cosmic ordering in two senses.241 One ordering is intelligible and unified; in it all things were together and each thing was all the others because of intelligible unification. The other is perceptible and made separate from that unification by demiurgic Mind, which he says itself also proceeds from the intelligible and orders everything. That he indicates a certain intelligible cosmic ordering which is prior to the perceptible ordering and which pre-contained it as cause and spermatically is, I think, clearly confirmed by his words:242 ‘Since this is the way things are, one should think that there are many things of every sort in everything which is blended, and seeds of all things, seeds which have forms of every sort and tastes and colours243 and that humans244 and all the other living things which have souls are put together and that humans have cities which they inhabit together245 and artefacts, just as in our world, and a sun246 and a moon and other things just as in our world’. And obviously these things are pre-contained in that intelligible ordering spermatically and as ‘forms’, as he says. 303a3-10 However, the consequences of what some other people, [such as Leucippus and Democritus of Abdera, say are not reasonable either. They say that the primary magnitudes are infinite in number and indivisible in magnitude and that several things don’t come to be from one thing or one thing from several, but that all things are generated by the weaving together and interlocking247 of the primary magnitudes. (303a8) And in a way these people also make everything to be numbers and to be composed of numbers. For even if they don’t indicate this clearly,] nevertheless this is what they mean.

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are infinite in number and having spoken against Anaxagoras and his followers, who say that the elements are infinitely many homoiomereities, he turns to Leucippus and Democritus and their followers, who call atoms, which are indivisible because of their smallness and solidity and also infinite in number and in shapes, elements. And they said that only these things are continuous, since other things which are thought to be continuous draw together by contact. Accordingly they also did away with division by saying that apparent division is the parting of things in contact, and so they said that ‘several things don’t come to be from one thing’ since an atom cannot be divided and that one thing which is truly continuous doesn’t come from several, but each thing is thought to become one because of the weaving together of atoms. Abderites, such as Democritus, called weaving together ‘interlocking’. (303a8) Having said that ‘the consequences of what some other people say are not reasonable either’ and set out their view, Aristotle next throws out one reason why the consequences are not reasonable. He says, ‘And in a way these people also make everything to be numbers and to be composed of numbers’. So if this is impossible, the consequences of their doctrine would not be reasonable. He says that the atoms are ‘in a way’ numbers because the atoms resemble monads and because they are not divisible, just as monads are not, and because nothing continuous comes to be from the atoms, which are divided by the void, just as nothing continuous comes to be from monads; for the Pythagoreans say that monads are distinguished by the void.248 Aristotle adds ‘in a way’ because there is also some difference between the absurd consequences for those who generate things from atoms and the absurd consequences for those who generate them from numbers. For those who say there is generation from numbers the absurdity that they generate bodies from incorporeal parts follows, but those who generate things from atoms avoid this.

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303a10-16 And in addition, [since the bodies differ in shape and shapes are infinite, they say that the simple bodies are infinite. But they did not specify further what sort of shape or what shape each element has, but only assigned the sphere to fire. However, they did distinguish air and water and the rest by largeness and smallness, as if their nature was a sort of universal seedbed] of all the elements.249 Alexander250 understands these words as making the inference that the people who say that atoms are the principles are involved in a kind of self-contradiction because they say that the elements differ from one another in shape and not in substratum. But if this is the case, it is clear that the things which come to be from the elements will differ from each other in shape.251 It would follow that they

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should say what the shapes of each of the elements and of the things which come to be from them are, but they say only that the shape of fire and of the atoms from which it is generated is spherical, so that it is also reasonable that fire penetrates and moves and causes motion and divides and burns the things to which it comes near because it is circular and smooth and furthermore because the elements from which it is composed are small. However, they do not go on to say what the shape of air or water or earth or their elements is. They only explain the difference in the size of the elements of which252 these things are composed; they say that air is composed out of smaller things which are the same in shape , water out of larger ones, earth out of even larger ones, but these elements do not differ because of shape, but each of them comes to be from the same things which are of all sorts of shapes. Alexander says that Aristotle does not add what follows from this, but it would be that if they do not posit that the difference of elements which differ in kind is due to shape but say that it is due to size, then, since air and water and earth differ only because of the size of their elements, they do not differ in kind from one another. And so Alexander puts forward these things as a refutation and adduces the absurd consequence. But perhaps Aristotle has added these further things because they clarify their view, while at the same time giving the reason why they say the atoms are infinite in number. He is saying that they said that the simple bodies are infinite because they differ in shape and shapes are infinite, but that they did not specify what sort of shape or what shape the elements which generate each body have, except only in the case of fire. They said that air and water and the rest come to be from elements which have the same shapes and differ only by largeness and smallness. And next he makes a start on the refutation of this view when he says, ‘First of all these people also make the same mistake’.253 And Aristotle does not fail to mention (as Alexander thinks he does) the absurd consequences of the parts of the view, parts which he has just set out, but he adds a fourth refutation which begins, ‘And at the same time it is necessary for them to contradict themselves’. 303a17-29 First of all these people also make the same mistake, [not taking the principles to be finite, although it would be possible for them to say all the same things. (303a19) Furthermore, if the differentiae of bodies254 are not infinite, it is clear that the elements will not be infinite. (303a20 In addition, by asserting that there are indivisible bodies, they must be in conflict with the mathematical sciences

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and do away with many common opinions and perceptible phenomena – we spoke about these things earlier in On Time and Motion. (303a24) At the same time it is necessary for them to contradict themselves since if the elements are indivisible it is impossible that air and water and earth differ by largeness and smallness; for they could not come to be from one another; because the largest bodies will always be insufficient when they are separated out – and they do say that water] and air and earth come to be from one another in this way. And, having set out the view of those who say that the atoms are elements, he uses two refutations against them which he also used against those who say the homoiomereities are elements.255 The first says that they err if they hypothesise infinitely many principles when they can explain such things from finitely many. (303a19) The second runs as follows:

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If the differentiae by which bodies differ from one another are not infinite, neither will the elements be infinite in kind; but the first; therefore, the second. And the conditional is clear since the differentiae in kind from the elements to the composites. And it is clear that the differentiae in kind of bodies are not infinite since they are perceptible (as has been proved in the seventh book of the Physics), and perceptible differentiae are finite (as is demonstrated in On Perception and Perceptibles).256 However, Alexander understands the words ‘if the differentiae of bodies are not infinite’ to be said of the elements.257 Therefore, he says, either this is said with the sense that difference in shapes is not sufficient to produce a difference in the elements but only differences concerning perceptibles can do this, or it is said because the shapes with respect to which they say the elements differ are not infinite, as Aristotle will show. But perhaps, as I said, one should rather understand what is said as ‘if the differentiae in kind of composite bodies are not infinite, the elements are not infinite in kind either’. For this argument does away with infinity in kind, but not infinity in number. (303a20) He next adduces a third , which applies specifically to these people, namely that, by asserting that there are indivisible bodies, they are in conflict with the mathematical sciences. For, according to the mathematicians nothing continuous is indivisible; rather every magnitude is divisible to infinity. So if these people do away with continuity and the division to infinity of bodies, they also do away with division in general and with perception and

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awareness. For how could one be aware of an affection feeling in his foot if bodies were not unified? And how could something divisible into parts come to be from things which are indivisible and partless? He took issue with this in the Physics,258 which he is now calling On Time and Motion. And people who are thought to do away with all other common opinions, some held because they are part of the most precise science, others because they are clear on the basis of perception, will be thought to be absurd. And according to these people blending will be done away with, since there is only juxtaposition of bodies. (303a24) He next adduces a fourth objection, directing it toward the statement that ‘they did distinguish air and water and the rest by largeness and smallness’.259 For if they say both that these things come to be from one another and that they differ from one another by the largeness and smallness of their atoms, ‘it is necessary for them to contradict themselves’, since these clash with one another. For if they say that earth comes to be from water when the largest in the water are separated out, then, since it is possible that at some time, all of the largest having been separated out from the water, the separation out from the air of the largest also gives out, the coming to be of earth from water and of water from air can also give out with the result that there is some water from which earth cannot come to be and some air from which water cannot come to be. So these people contradict themselves in saying both that these things come to be from one another and that they differ because of the largeness and smallness of their elements. And if when the smallest are separated out they will give out, then water will not come to be from earth or air from water. However, we do see that every part of water changes into air and every part of air into water. And if fire is composed only of spherical and the others out of all nothing else will come to be from fire and fire will never come to be from other things. 303a29-b3 Furthermore, even on their conception [one would not think that the elements turn out to be infinite, since the bodies differ in shape and all shapes are composed from pyramids, rectilinear shapes from rectilinear pyramids, the sphere from eight parts. For it is necessary that there be some principles of shapes, so that whether there is one principle or two or more,] the number of simple bodies will also be this great.

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people it is not necessary to say that the principles are infinite. For if they said that the atoms are infinite because they differ in shape and shapes are infinite, if there is an argument proving that the primary shapes of bodies are definite and finite, it is clear that the principles of bodies will also be definite. He proves that composite shapes are composed from definite simple shapes on the basis of the fact that all the composite shapes of bodies are composed from pyramids. For just as in the case of plane figures every rectilinear plane figure is divided into triangles and is composed from triangles because the triangle is the simplest and most fundamental of plane figures, so too every solid which is limited by rectilinear planes is resolved into pyramids, and the pyramid is the simplest among solids and most fundamental, and rectilinear solid figures are composed from the pyramid and divided into it. But it is clear that it is also necessary that there be principles of composite figures. But interpreters really have need of prophetic power how he can say that the sphere is composed of eight parts. I think that Alexander is correct in pointing out that Aristotle is saying that all bodies are composed of pyramids, rectilinear bodies of rectilinear pyramids and the sphere of eight pyramids with spherical bases. For if we bisect a sphere with the circle of the horizon and we draw through the pole of the sphere two great circles (analogous to the celestial equator and the meridian) cutting each other and the horizon at right angles, the sphere will be divided into eight equal segments each of which is a pyramid composed of isosceles triangles drawn toward the centre of the sphere and having an equilateral triangle as base. If these bases take on a spherical surface, the sphere will be composed of eight such pyramids.262 And with these words Aristotle is saying that rectilinear bodies are composed of rectilinear pyramids and that a sphere is composed of eight pyramidish parts which it is not possible to call either simply rectilinear or circular or even pyramids in the strict sense. And in this way he indicates that the construction of the sphere is also from pyramidish figures, but when he says ‘eight parts’, he does not add either ‘rectilinear’ or ‘spherical’. He adds to what he has said, ‘For it is necessary that there be some principles of shapes’ because some shapes are simple, some composite, and in things which are divided in this way the simple things are principles of the composite ones. Consequently whether the pyramid is a single principle of shapes or it is shown that there are two or more principles, it is necessary that the primary bodies be this many in number and not infinite. As Alexander says, Aristotle adds ‘or two or more’ because he does not think that the pyramid is a simpler figure than the sphere, since he doesn’t think that the triangle is simpler than the circle either. These demonstrations show that the primary bodies are finite in

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kind. But it is necessary that what is finite in kind also be finite in number. For if one of the kinds were infinite in number, things falling under the other kinds would be outside what is infinite, which is impossible, since nothing is greater than what is infinite.263 303b4-13 Furthermore, if each of the elements [has some proper motion and the motion of a simple body is simple, but the simple motions are not infinite (because there are no more than two simple motions and places are not infinite), in this way too the elements will not be infinite.

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(303b9) But since it is necessary that the elements be finite it remains to investigate whether there is more than one. For some people hypothesise one only, some hypothesising water, some air, some fire, and some hypothesise that it is finer than water but denser than air,] which they say contains all the heavens, being infinite. He has overturned with several arguments the doctrines which hypothesise that the principles of bodies are infinite in number, whether they are homoiomereities, as with Anaxagoras or atoms, as with Democritus and his followers. Next, making a different kind of argument, he demonstrates that the simple bodies cannot be infinite and that if they cannot be infinite, neither can the elements be; for the elements are simple since they are indivisible into things which are different in kind. He proves that the simple bodies are finite in number on the basis of motions, as he did at the beginning of the first book.265 For if the things which move with the simple motions are naturally simple bodies, it is necessary that there be as many simple bodies as there are kinds of simple motions. So if the sublunary simple motions are not infinite or even more than two (since the simple motions of bodies are seen to be two, one up and one down, and the places to which the simple motions are directed are not infinite but two, up and down), the elements will not be infinite in kind but only two, one heavy and one light. (303b9) Having proved that the principles of bodies cannot be infinite and that it is necessary for them to be finite since the simple motions are finite, he now turns to those who say that there is one element. There are several such people, and different people hypothesised this one element to be something different. Thales of Miletus and Hippo said it is water because they saw that the seeds of animals and the nourishment of both animals and plants are made of water. Anaximander, a fellow citizen and pupil of Thales, said it is something indeterminate which is finer than water and denser than air

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because the substratum should be naturally adapted for the change to either; he was the first to hypothesise that this one is infinite, so that he could use it for comings to be without stinting; and, it is thought that he hypothesised infinite worlds and that each of the worlds from an infinite element of this sort. Anaximenes, a pupil and fellow citizen of Anaximander, also hypothesised that the principle is infinite, but not also indeterminate; he said it is air, thinking that the volatility of air is sufficient for change. Diogenes of Apollonia hypothesised the same thing , and Hippasus of Metapontum and Heraclitus of Ephesus, taking into consideration the active power of fire, said that it is the principle. 303b13-22 All those who make this one thing [water or air or finer than water and denser than air and then generate other things from this by rareness and denseness do not notice that they make something else be prior to their element. For they say that coming to be from their elements is composition and that dissolution is into the elements, so that it is necessary for what has finer parts to be prior by nature. So since they say that fire is the finest of all bodies, fire would be primary by nature. But it makes no difference,] since it is necessary that one of the others be primary and not the intermediate one. He first deals with those who posit that the intermediates are elements, water or air or what is between them, so that they are able to generate other things from their element by rareness and denseness, finer ones by rareness, ones with thicker parts by denseness. He says against these people that they themselves do not notice that they say that there is a body which is prior to their element. But this is absurd, since it is not possible for anything to be prior to an element. It is clear that they are subject to this contradiction if, indeed, condensation is composition and rarefaction is dissolution, and they say that what comes to be from the elements comes to be by composition and that the elements come to be from composites by dissolution. For what comes to be by rarefaction comes to be by the dissolution of the thing they say is an element and dissolution into the elements is resolution, so that what comes to be from rarefaction has finer parts and is more fundamental than what is rarefied. For what has finer parts does not come to be by composition, but by resolution, and resolution is 266 an element. The argument is the following: What is rarefied is resolved, but what is resolved is resolved into an element; therefore, even according to them, finer bodies will be prior and more elemental, since what is finer comes to be

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Translation from dissolution, and what comes to be from dissolution is an element.

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So if they agree that fire is finer than the intermediates and they say that it comes to be from the intermediates by rarefaction,267 then fire will be more elemental according to them. Aristotle says that it makes no difference even if fire is not primary and finer according to them. For even so it follows that they say that something else is finer and more elemental, something into which the resolution of the thing they hypothesise to be an element takes place, that thing being intermediate and, according to them, resolved into something finer by rarefaction. So whatever it is that comes to be by rarefaction is more elemental. 303b22-304a7 Furthermore, generating other things by denseness and rareness [is no different than generating them by fineness and thickness, since they intend that the fine is rare and the thick is dense. And again to generate things by fineness and thickness is the same as to generate them by largeness and smallness, since what has small parts is fine, what has large parts thick; for what is greatly expanded is fine, but a thing of this sort is composed of small parts. Consequently it follows that they divide the substance of other things by largeness and smallness. It will follow for those who distinguish all things in this way that they speak relatively, and it will not be the case absolutely that one thing is fire, another water, another air, but the same thing will be fire relative to one thing, air relative to something else. (304a1) This also follows for those who say there are several elements, but also say they differ by largeness and smallness; for, since each thing is distinguished by quantity, the magnitudes will have some ratio to one another; consequently it is necessary that of the things which have this ratio to one another one be air, another fire, another earth, and another water] because the ratios of lesser things inhere in greater ones.268

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He also brings in this other argument against those who generate other things from the intermediates by denseness and rareness. He proves that for them the absurdity follows that they speak of everything that comes to be from their own element as relative and that fire, water, and air are not per se. He gives the following syllogism to show that this follows for them: To generate other things by denseness and rareness does not

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differ at all from generating them by fineness and thickness since the fine is rare and the dense thick; but to define the differentiae of what comes to be by thickness and fineness is the same as to define them by largeness and smallness (and he adds why, saying, ‘since what has small parts is fine, what has large parts thick; for what is greatly expanded is fine (so that there is not a great deal of substance in the same place), but a thing of this sort is composed of small parts’); it follows for the people who say this that they distinguish ‘the substance of other things’ – obviously the things which come to be from their element – by largeness and smallness; so if large and small are relative, as is also specified in the Categories269 (even if in the Metaphysics270 Aristotle views them in terms of quantity and places them under the category of quantity), it will follow that those who distinguish things in this way say that everything which comes to be is relative, ‘and it will not be the case absolutely that one thing is fire, another water, another air, but the same thing will be fire relative to one thing, air relative to’ another thing.

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Alexander says: If water is as much greater than air as, being water, it is less than earth, water will be water relative to earth and earth relative to air; and, again, if air exceeds fire by as much as it is less than water, air will be air relative to water and water relative to fire; and again if air is as much less than water as fire is less than it, it will be the case that, just as it is air relative to that fire (since it is related to the body, fire, which is finer than it), so too the same thing will be water and air at the same time. For these people did not specify that air comes to be from so and so much of their element and water from so and so much of it, but they placed the difference from each other of the things which come to be from their element in being greater or less by a certain amount. (304a1) Next Aristotle assimilates the view of these people to that of Democritus and his followers, who hypothesise infinite atoms as principles and ascribe the difference among the things which come to be from them to smallness and largeness of atoms, as was said a little earlier.271 For they said that earth and water and air differ from one another because one is composed from larger , another from the same but smaller ones. He says that the same thing follows for these people. For since they say that the elements272 differ from one another by largeness and smallness, their magnitudes will stand in some ratio to one another. So if one thing is earth, another

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water, another air because of the ratio of the magnitudes of their elements to one another and because of such and such an excess, then if a first body exceeds a second by as much as the elements of earth exceed the elements of water, the first will be earth and the second water; consequently if the elements of water exceed those of air by as much as the elements of water are exceeded by those of earth, then, relative to one another, water will be earth and air water. And similarly in the case of the others. But it is possible, says, that Aristotle is not saying these things about Democritus’ view, but against those who say that there are four elements and that they differ from one another by largeness and smallness.273 And perhaps this position is reasonable since Democritus and his followers say that fire does not differ from the others only in size but also in shape, but Aristotle is making a common argument which also applies to fire. Alexander says, The words ‘because the ratios of lesser things inhere in greater ones’274 are somewhat unclear, but what they mean would be something like ‘because things which are greater than some things have to certain other things the ratio of the lesser’275; for if things are this way, then with respect to what has the ratio of the greater to some things there will be some greater things related to them and again with respect to what has the ratio of the lesser there will be some lesser things related to them , and thus the same thing will be water relative to one thing and earth relative to another. But it is possible that Aristotle adds something of the following sort with these words. Since the lesser is also contained in the greater276 (since the greater is as much as the lesser and more, and what is lesser than a particular thing by so and so much can be in some other body), the same body could have both the ratio of the greater and of the lesser at the same time. But if it has both ratios, the bodies would be both things, so that the greater body, which consists of greater things, will be both this and also be the body which consists of lesser things. Therefore, earth will be earth and water at the same time, and again water will be water and air, air air and fire, so that earth will be all things because of the relation of its parts to one another; for it contains the ratios of the lesser things because it is composed of greater ones, and it is possible to take away parts from it in whatever ratio one wishes. Or perhaps Aristotle says ‘the ratios of lesser things inhere in greater ones’ not about everything which is greater but about the things other than earth, so that what is meant would be ‘because things greater than other things are less’.277

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And as a result of this has both the ratios of the greater things and the ratios of the less, since water has a lesser ratio to earth and a greater one to air, and air has to fire a greater ratio and a lesser one to water, but earth has a greater ratio to all and fire a lesser one. And so because these things have both greater and lesser ratios, they will be relatives. For water will be earth relative to air since it has a greater ratio; but it will be water relative to earth, since it has a lesser ratio to earth; and again air would be earth or water relative to fire, but it would be air or fire relative to water; and even if the earth which is taken is greater than water, nevertheless it will be lesser than some other earth and as much lesser as it was greater than the water; and, this being so, it will be at the same time water and earth.

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I have set out this interpretation of Alexander in his own words, because of those who, as is probable, are better able than I to understand on the basis of the interpretation what Aristotle says. For I think Alexander’s argument is forced. For even if large and small are relative, those things to which they belong are not relative. For even if beloved is relative, nevertheless human, to which it belongs to be beloved is not relative; and two is exceeded by three by as much as it exceeds one, and nevertheless two is not one relative to three. Consequently, even if water were as much greater than air as it is less than earth, and insofar as it is greater and less it would be relative, nevertheless it is not the case that it is earth relative to air; nor is air fire relative to water even if it is as much less than water as fire is than air. For even if water and air are relative insofar as they are greater and less, they are not relative insofar as they are water and air. For even if, as Alexander says, these people placed the difference in being greater and less by a certain amount, this does not make the things to which being greater and less by a certain amount belongs relative. For two is defined to be greater than one by one and less than three by one. And I think that one should say that in what Alexander says at the end, namely that ‘even if the earth which is taken is greater than water, nevertheless it will be lesser than some other earth and as much lesser as it was greater than the water; and, this being so, it will be at the same time water and earth’, he is taking earth itself to be greater than water and not the elements of earth to be greater than the elements of water. But how reasonable would it be that water and earth are the same thing at the same time because a part of earth which is taken is greater than some part of water and less than some part of earth?

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Translation 304a7-18278 Those who hypothesise fire as the element [avoid this , but unreasonable results must follow for them. For some of them assign a figure to fire, for example, those who make it a pyramid. Of these some speak more simply by saying that the pyramid is the sharpest of figures279 and fire is the sharpest of bodies. But others argue more elaborately that all bodies are composed from what has the finest parts, and solid figures are composed from pyramids; consequently, since fire is the finest of bodies and of figures the pyramid has the smallest parts and is first, but the first figure belongs to the first body,] fire would be a pyramid.

Having spoken against those who posited one of the intermediates as element and generated the rest from it by rareness and denseness, he turns to those, such as Hippasus of Metapontum and Heraclitus of Ephesus, who say that the finest of the four, fire, is the element. He says that these people avoid putting the elements in the relational or relative and avoid saying that there are elements of the element,280 but he adduces some absurdities which follow for them, first making a division between their views: some of them attach a figure to fire, which they posit as element, some saying that the figure is a sphere, some that it is a pyramid, although he does not mention those who say it is a sphere at the moment;281 others do not attach any figure but only make it have the finest parts.282 But he also divides those who posit that the figure is a pyramid into those who ‘speak more simply’, whom he first discusses, and those who argue more elaborately. He says about those whom he calls simpler (using the word in a positive sense) that they use an asyllogistic argument in the second figure with two affirmative premises: Fire is sharpest; the pyramid is sharpest; therefore, fire is a pyramid.

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(As Alexander says, people who say that fire stands in a multiple ratio because both fire and a multiple ratio increase quickly are like these simpler people.283) But perhaps it is possible to develop the syllogism in the first figure: The pyramid is the sharpest figure; the sharpest figure is appropriate for the sharpest body; and fire is the sharpest body; therefore, the pyramid is appropriate for fire. But if this syllogism is correct, Aristotle would be saying that these people speak more simply by comparison with those whom he speaks

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of next as arguing more elaborately because they prefer something which is more appropriate to the study of nature and thus make the syllogism more technical. For they assume to start that ‘all bodies are composed from what has the finest parts’ (since what has the finest parts is simplest, and composites are composed from what is simple); and secondly they assume that all solid figures are composed from pyramids, so that the pyramid would be the first figure and the one with finest parts; and third they assume, what he has set down later, that the first figure belongs to the first body. Having posited these things, they syllogise that fire is a pyramid in the following way: Fire is the finest and first body; the finest and first body was given shape by the finest and first figure, which is the pyramid; therefore, as regards figure, fire is a pyramid. It should be asked who holds this view which says that fire is a pyramid because it is the first body. For Heraclitus, who does say that fire is the element of other things, does not say that fire is a pyramid, and the Pythagoreans,284 who say that fire is composed from pyramids, do not say that fire is the element of other things since they also say that fire comes to be from water and air just as air and water come to be from fire.

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304a18-21 Others do not make any claim about figure, [but only make have the finest parts and then say that other things come to be from it when it is compounded,] as if from shavings285 which are fused together. He has recounted the view of those who say that fire is a pyramid and argue for it either in a more simple or a more complicated way. He next describes those who do not assign it any figure but only say that fire has the finest parts and that other things then come to be from it when it is compounded, as from shavings which are ‘fused together’ or melted down. For thicker things come to be from fire when it comes together and is condensed, but not when something is mixed with it. Alexander says, I think that with this example Aristotle is pointing out the absurdity of the view: just as when shavings are fused together some thicker body comes to be from them, indeed, they even become gold,286 so too if thicker bodies were to come to be from fire in this way, they too would be fire, differing only in thickness and size.

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304a21-b6 The same difficulties follow for people who hold either of these views. [For if they make the primary body indivisible, the arguments which we have given previously against this hypothesis will come up again. (304a24) Furthermore, it is not possible for anyone who intends to investigate in a way appropriate to the study of nature to assert this. For if all bodies are comparable in quantity, the sizes of homoiomeries are proportional to one another and so are the sizes of elements (for example, the sizes of all water are proportional to all air and the sizes of the element are proportional to the element and similarly in other cases), and if air is greater than water and in general what has finer parts is greater than what has thicker ones, then it is evident that the element of water will be less than that of air. So if the lesser magnitude inheres in the greater, the element of air will be divisible, and so likewise will the element of fire and in general so will the element of things with finer parts. (304b2) But if it is divisible, it will follow for those who assign a figure to fire that a part of fire is not fire because a pyramid is not composed from pyramids; and it will follow further that not every body is either an element or composed of elements, since a part of fire] will not be either fire or any other element. 622,1

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He says that the same difficulties follow for those who assign a figure to fire and for those who say it has no figure if they make it the first of all things. For we will assert against those who think it is indivisible (whether or not it has a figure) the things we also asserted against those who make all things from atoms: that their saying that there is an indivisible magnitude conflicts with the mathematical sciences;287 the fact that in a way they generate other things from numbers or monads ;288 and whatever other things he said against these people. (He calls what is partless indivisible.) (304a24) He proves universally that it is not possible to assert that the element is indivisible and to make natural bodies come to be from indivisible things while speaking in a way appropriate to the study of nature as follows: If the elements of bodies are themselves also bodies and every body is comparable in quantity with every body (because no body is infinite), then the homoiomeries, such as air as a whole, water as a whole, and earth and fire as wholes, would also be comparable with each other; and whatever ratio of size these have to one another, their elements will also have the same ratio to one another since they have the sort of nature;289 but these bodies are related to one another in the following way: the finer of them has a greater bulk than one with thicker parts

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and extends farther, water than earth, air than water, and fire than air (and it is also clear from their change into one another that this is the way things are; for air which comes to be from water, which is less in bulk, becomes greater, and likewise in the other cases); therefore, the elements of things with finer parts are also , since they are of this sort and generate things of this sort; therefore, the element of fire will be greater in bulk than the elements of air; but if it is greater it is also divisible, since what is greater than something contains both that than which it is greater and its excess over it, so that it is divisible into what is equal < to the lesser magnitude> and the excess over it; therefore the element of fire is divisible. One might raise the following difficulty. How, when he said previously290 that what has small parts is fine and what has large parts thick (and in interpreting these statements Alexander says that what is composed of what is double what air is composed of is water, what consists of what is triple is earth), can he now say that ‘the element of water will be less than that of air’? Perhaps he said previously that water has larger parts than air because in the same bulk what is thicker and denser has more substance than what is finer and rarer, but here he says that the of water is less than that of air because when the substance is the same what is thicker and denser is more contracted than what is finer and rarer, as the coming to be of a great amount of air out of a small amount of water makes clear.291 Alexander does well to raise the following question: What Aristotle has proved in this passage, namely that the element of fire is not indivisible, might be fitting against those who say that atoms or planes are the principles of natural bodies, but how is it fitting against the people who were being discussed, who say that the element is fire?

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And he resolves the objection by saying: would also follow for these people if they said that the elements of fire are certain small fires which do not perish. For the fire in our world is seen to perish, but it is necessary that an element be imperishable. Therefore there are certain elements of fire. But if this is so and there are also certain elements of what comes to be from fire and these come to be because of the alteration and change of fire,292 then the

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elements of fire and of the other things would have a ratio to one another, a ratio which the things composed from them also have, and in this way the element of fire would be of greater bulk than the elements of those things. But if this is so the element of fire is also divisible (as has been proved293). (304b2) The inference of what comes next against the things presented previously makes clear that Aristotle is proving this for every sort of hypothesising of fire. For having said, ‘For if they make the primary body indivisible’ and having led this hypothesis around into its contrary and shown that it is necessary for the primary body to be divisible, he adds that if the element of fire is divisible (as has been proved) it will follow for those who assign the pyramid to it that a part of fire is not fire, which is absurd, since we see that fire is homoiomerous. This follows if the figure for the element of fire is a pyramid, and it is divisible, as has been proved. And the parts of a pyramid are not both294 pyramids (even if one of the parts is sometimes a pyramid). The result is that the parts of fire are not fire, at least if its being fire were to lie in having the shape of a pyramid. Aristotle adduces as a second absurdity for those who assign a figure to fire that not every body is either an element or composed of elements, which is really absurd. This follows because a part of a pyramid is neither a pyramid (and so an element) nor composed of pyramids (and so composed of elements). So if fire is a pyramid, a part of fire is neither fire (because not a pyramid) nor any other element, that is, it is not air or water or earth (he is now calling these simple bodies elements) since each of these came to be from a compounding of fire, but a part of a pyramid is a portion of fire.295 And it would be absurd in another way to say that a portion of fire is air or water or earth, since if this were so what comes to be from an element would be parts of it. But if someone were to say that even if a part of a pyramid is not a pyramid, nevertheless it is at least composed of pyramids because every solid figure is divisible into pyramids and a part of a pyramid has some shape and consequently there is some other body which is composed of fire, then on their view a part of a simple element will be composite and, although not a pyramid, will be composed of pyramids. Alexander says, Furthermore, division will go to infinity if, when a pyramid is simple, a part of it is composite, and, again, a part of a composite is a pyramid, which is simple, and a part of the pyramid is again, according to them, composite. But if this were so nothing would be an element.

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304b6-11 For those who distinguish by size [ there is an element prior to the element, and this proceeds ad infinitum, if every body is divisible and the one with the smallest parts is an element. (304b9) Furthermore, it follows for these people that they should say that the same thing is fire relative to one thing, air relative to another,] and again for water and earth. After those who assign a figure to fire, using the pyramid or even the sphere (for the same arguments would fit them296), he turns to those who distinguish by size and say that fire is the element because it is finest and has the smallest parts compared to other things. He says that ‘for those who distinguish by size’ it follows that ‘there is an element prior to the element, and this proceeds ad infinitum’. He shows briefly how this follows by saying ‘if every body is divisible and the one with the smallest parts is an element’. For if something is an element because it has the smallest parts, and it is divisible into its parts, then a part, because it is smaller, will be prior to it, and similarly again for a part of a part if every body is divisible and divisible ad infinitum. And so anything which is hypothesised to be an element because of having small parts will be done away with if what is small is divisible into what is smaller. (One should understand that this absurdity follows because he transforms ‘fine’ into ‘small’ and ‘having fine parts’ into ‘having small parts’.297) (304b9) He says that the absurdity which he previously showed to follow for those who define the difference of bodies by the largeness and smallness of their elements (as Democritus and his followers said that three bodies, air, water, and earth differ by the smallness of their elements, which have the same shape298) also follows for these people, namely that the elements are not what they are because of their own nature but they rather have their being in their relation to one another. So he says that this absurdity also follows for those who say that fire is an element because it has fine parts. For the same body has smaller parts than this one and larger parts than that and will be air relative to this and water or earth relative to that. For since fire is an element of air because it is finer than it and the excess in fineness which it has stands in some ratio, when air exceeds something else by this excess in fineness, it will be the element of that thing and will be fire relative to it, at least if being fire lies in being so and so much finer.299 And the same argument applies to the others. 304b11-22 There is a mistake which is common to everyone [who hypothesises that there is one element: they make there be only one natural motion, which is the same for all things. For we see that every natural body has a starting point of motion,

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so if all bodies are some one thing, all will have one motion. And a body must have this in such a way that it moves more to the extent that it becomes greater, just as fire moves faster with its own motion up the greater it becomes. But it turns out that many things move down faster . (304b19) Consequently, for these reasons, and in addition since it was determined previously that there is more than one natural motion, it is clear that it is impossible that there be one element. But since there are neither infinitely many nor one,] it is necessary that there be more than one and finitely many. He has spoken previously against those who say that one of the intermediates, water or air or what is between them, is the element and then against those who say that fire is the element. Now he adduces an absurdity which is common to everyone who says there is one element: they make the natural motion of everything to be one and the same, since they will all move with the motion which is proper to the element from which they are constructed. So since we see that every natural body has a starting point of motion, if all bodies are some one thing, insofar as they are composed of one thing from which they also get their starting point of motion, all bodies will have a motion which is one in kind. And the difference between them is in terms of more and less, and it is a consequence of greater or smaller, just as fire moves faster with its own motion up the greater it becomes. And if fire were the only element everything would naturally move up, some things faster and some slower. But in fact some things also move down. And that these things are not unnatural is made clear by the fact that in their case (as in the case of fire) the greater moves down faster, but if they were moving by constraint the greater would move slower, not faster. (304b19) Then in conclusion he says that because of everything which has been said against those who say that there is one element, whether it is an intermediate or fire, and because of all that has been said as a common objection to those who say that there is one element, and (he says) ‘since it was determined previously that there is more than one natural motion, … it is impossible that there be one element’. This argument based on the simple motions would give a common proof that there are elements and that they are neither infinitely many nor one. For, because there are simple motions and they are neither one nor infinitely many, but are more than one but finitely many, since the simple motions belong to the simple bodies and there are as many simple bodies as there are simple motions and simple bodies are elements, it is clear that on the basis of the motions it is true to say that ‘it is impossible that there be one element’, just as it is impossible to say there are infinitely many (he also did away with this with the argument about motions and many

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others). So, he says, since it is absolutely necessary that the elements be neither infinitely many nor one, there must be more than one and finitely many.

304b23-305a1 We should investigate first whether are eternal [or whether they come to be and perish; for if this is proved, both how many they are and what they are like will be evident. (304b25) It is impossible that they are eternal; for we see fire and water and each of the simple bodies being dissolved. But it is necessary that dissolution either be infinite or come to a stop. If it is infinite the time of dissolution (and, again, the time of composition) will also be infinite, since each of the parts is dissolved or composed in a different time. The result will be that there is one infinite time outside of another when the time of composition is infinite and still prior to it the time of dissolution is also infinite. The result is that there is an infinite outside of an infinite,] which is impossible. After proving that it is not possible for the elements to be infinitely many or one and inferring from this that it is necessary that for them to be more than one and finitely many, the next thing would be to ask ‘how many’ and ‘what are they like’. However, he says that first one should enquire whether they are eternal or whether they come to be and perish; ‘for if this is proved both how many they are and what they are like will be evident’. (304b25) He next proves that they are not eternal in the following way. He takes it to be clear that all the sublunary bodies which we acknowledge, the composite and the simple ones (he found the simple ones on the basis of the simple motions300), are seen being dissolved and perishing, the composite bodies more than the simple ones; and he sets out the ways in which it would be possible for the simple bodies to be dissolved and also be eternal, so that by refuting these ways he will obtain the result that the simple bodies are not eternal. It is reasonable that he singles out the simpler of the acknowledged bodies and argues with respect to them since the elements ought to be found among them, unless by doing this he would seem to be begging the question since he has not yet proved how many elements (that is to say, simple bodies) there are and what they are.301 He says that if the simple bodies are seen being dissolved and there is going to be something among them which is eternal (as it is appropriate for an element to be), it is necessary either that the dissolution proceed to infinity so that dissolution is never complete or that dissolution come to a stop and cease when the whole is not yet dissolved; for in

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either of these ways it is possible that some part endure eternally even if the whole does not. So, if it is not possible either for these things to be dissolved to infinity or for the dissolution to come to an end with something indissolvable, it is clear that these things will not be eternal. And he proves that the dissolution of them does not go on to infinity by first assuming that they are dissolved in a time, that they are dissolved and composed in different times (for they are also seen being composed, and it is not possible for the same thing to undergo both in the same respect ), and that the time of composition is as great or even greater than the time of dissolution, since composition is always more difficult than dissolution. When these things are assumed, ‘the result will be that there is one infinite time outside of another’, which is impossible, since it is not possible for there to be something finite outside an infinite, and certainly not something infinite. (He says ‘each’ of the parts because these four elements are parts of the universe.302) Alexander raises the difficulty why the time of composition will be different, since it is possible that there be a dissolution of one thing and a composition of another at the same time, e.g. a dissolution of air and a coming to be of fire. For although it is impossible for the same thing to be dissolved and composed simultaneously in the same respect, nothing prevents it being dissolved in one respect and composed in another. And he resolves the difficulty as follows: Even if each of them is dissolved into some things and comes to be from some things, the dissolution of each of them to infinity would in turn be the composition of something else to infinity with the very same things into which there was dissolution being again united and composed. So if the dissolution of fire proceeds to infinity, and at the time when the fire is dissolved it doesn’t come to be and it isn’t composed, it would be composed and come to be at another time and not that in which it is dissolved. But this time is infinite. Therefore the time in which fire is composed is outside an infinite time. And since it does not come to be in a shorter time than it perishes, but the time of perishing is infinite, the time of its composition will also be infinite. And if someone were to say that in the same infinity of time some of the fire comes to be and some perishes and what has come to be in turn perishes and other things come to be (and this is the truth), such a hypothesis does not keep any fire eternal. 305a1-14 But if the dissolution were to stop at some point, [either the body with which it stopped would be indivisible or it

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would be divisible but would never in fact be divided – Empedocles seems to mean to say something like this. (305a4) It cannot be indivisible because of the things we said previously. (305a5) But neither can it be divisible but never dissolved. For a lesser body is destroyed more easily than a greater. So if what is great is destroyed in this destruction in such a way that it is dissolved into lesser things, it is reasonable that what is less be even more subject to this. But we see that fire perishes in two ways: when it is extinguished and destroyed by its contrary and when it wastes away by itself. What is less undergoes this by the action of the greater and does so faster to the degree that it is less. (305a13) Consequently it is necessary that] the elements of bodies perish and come to be. Having done away with one way in which the elements could be eternal depending on the idea of dissolution to infinity, he has turned to the other in which it is hypothesised that dissolution stops at some point. And he proves that it is impossible that it stop at something which is such as to be no further dissoluble. For if it stops, it either stops with something which is indivisible or with something which is divisible but will not be divided (that is, destroyed), as Empedocles says. For he says that the elements are divisible, and, unlike Democritus and his followers, he does not hypothesise that the principles are indivisible; but he does suppose that the four elements do not change into one another and do not perish because he does not allow for a common matter, but says that their coming to be from one another, which we see, occurs because of separation out, since everything, being an actuality, inheres in everything.303 (305a4) But it is impossible that the division of bodies stop with what is indivisible, as Democritus said. For it has been proved that bodies cannot be composed of indivisibles, since if they were nothing would be continuous, and there would be no division, no awareness, and no blending. And it has also been proved that there is no indivisible body.304 (305a5) But neither can that with which dissolution stops be divisible but never divided, since we see in the case of all bodies that the lesser is destroyed more easily than the greater, if it is of the same kind and nature. So, if the greater is destroyed by being dissolved, as fire and air and each of the others are seen to be, it is much more reasonable that the lesser will be destroyed, since it is more easily affected. Consequently dissolution will not stop with something divisible. He shows that what is less is destroyed more easily with the example of fire. There are two ways in which fire perishes: ‘when it is extinguished by its contrary and when it wastes away by itself’;

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and in both cases what is less is more easily affected and is destroyed more easily. And this would be what is made clear by the fact that there are two ways in which fire perishes: fire does perish, and a lesser amount is always destroyed more easily than a greater one. (305a13) One should understand what he says about fire as also applying to the other . So if their dissolution does not proceed to infinity and it does not come to an end at some point with things that will not be further dissolved, it remains that ‘the elements of bodies perish and come to be’. By choosing these four bodies, he is not begging the question, as a person might suspect; rather, having singled out the simple bodies which were found on the basis of the simple motions, he is enquiring whether these or some one among them is eternal. For where else than in things which are generally acknowledged would there be ? 305a14-22 Since come to be [they will come to be either from what is incorporeal or from a body, and if from a body either from a different body or from one another. (305a16) Now the doctrine which generates them from what is incorporeal produces a separate void, since everything which comes to be305 that in which it comes to be will be either incorporeal or it will have a body. And if it has a body there will be two bodies in the same at the same time, the body which comes to be and the previously existing body. But if it is incorporeal it is necessary that there be a marked off void,] but it has been proved previously that this is impossible.

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He has proved that the elements come to be and perish. He next uses a precise division to enquire whether they come to be from what is incorporeal or from a body, and, having proved that it is impossible for them to come to be from what is incorporeal he obtains the result that they come to be from a body; but ‘if from a body either from a different body or from one another’. For it is necessary that either they come to be from themselves or they do not come to be from themselves; however, what comes to be comes to be by the activity of something else, not by its own activity, so that it does not exist before its own coming to be.306 If, then, they do not come to be from themselves, either they come to be from each other or they come to be but not from each other, which is the same as saying they come to be from other things. So having proved in turn that it is impossible for them to come to be from another body,307 he has the remaining alternative, that the elements come to be from one another; for, since the division is into contradictories, when the other alternatives are eliminated the remaining one is necessarily left over. (305a16) He proves first that it is impossible for to come to be from what is incorporeal because the doctrine which

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generates them from what is incorporeal produces a separate void, which has been proved impossible. He proves that this is so on the basis of the fact that every body which comes to be comes to be in some place.308 For it is necessary that every body, especially one which comes to be and is sublunary,309 be in a place. Therefore, elements which come to be from what is incorporeal, since they are bodies, will also be in some place. In that place in which the things which come to be come to be and which, coming to be, they occupy, either some body existed previously and occupied it or there was no body in it. But if there was some body occupying the place previously, there would be two bodies in the same place, the previously existing one and the one which has come to be, both contained in the same circumscribed place; and in this way there will be a body in a body and one body containing another, which he also proved impossible in the Physics (for the absurdity that the largest thing is contained in the least, the sea in a cup, follows).310 This is the meaning of what is said. But the text which says ‘since everything which comes to be that in which it comes to be will be either incorporeal or it will have a body’ is really unclear and, as Alexander also thinks, seems to be mistaken, a part of it being having been left out and the full text being ‘since everything which comes to be comes to be in something, and that in which it comes to be will be either incorporeal or it will have a body’, which means that everything which comes to be will be in a place and this place in which there is coming to be, that is, in which there is something which comes to be, will either contain some other body or it won’t. (He calls a place with no body incorporeal.) If someone were to say that what existed previously departed from the body which comes to be, there will be an empty place into which goes. For it cannot go into the place of that from which comes to be, since is assumed to come to be from what is incorporeal.311 This is the result if the place in which what comes to be will be contained some body before the one which comes to be. But if it contained no body there will be some marked off void which receives the body which comes to be from what is incorporeal, but it has been proved in the fourth book of the Physics that it is impossible that there be a void.312 305a22-32 However, it is not possible for the elements to come to be from some body313 either, [since it would follow that there is another body prior to the elements. But if this body has weight or lightness, it will be one of the elements, and if it has no impulsion, it will not be able to move and will be a mathematical body, and, being this way, it will not be in a place; for a thing which rests in a place can also move in it. And

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if it is moved by constraint it moves unnaturally, and if it is not moved by constraint it moves naturally. So if this body is in a place and somewhere, it will be one of the elements; and if it is not in a place, nothing will come from it since what comes to be and what it comes to be from must be together. (305a31) Since it is not possible for the elements to come to be either from what is incorporeal or from another body,] it remains that they come to be from one another.

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Having proved that it is impossible for bodies to come to be from what is incorporeal, he turns to proving that they cannot come to be from some other body either – the words ‘some body’ mean ‘some other body’. Once this is proved, that the elements come to be from one another remains. Proposing to prove that they do not come to be from some other body, he produces a brief syllogism for this by saying, ‘since it would follow that there is another body prior to the elements’. This is clearly absurd because the elements should be prior to other things, and because it is necessary to proceed to infinity if elements also come to be , and because would be the elements rather than the things which we hypothesise. Having indicated these things which are evident and more general, he next also raises objections to the doctrine from the point of view of the study of nature. If this body from which someone says that the elements has weight or lightness, it would be one of the hypothesised elements: if it had weight, it would be one of those which move toward the centre, and if it had lightness, it would be one of those which move toward the periphery. And if it had no impulsion, it would not be able to move and would be a mathematical body. For how would it move if it had neither weight nor lightness? And if it didn’t move either as a whole or in its parts, it would be mathematical, since natural body is distinguished from mathematical body most of all by the fact that has a starting point of motion in itself. And therefore, being this way and having no impulsion or starting point of motion it is nothing but mathematical and not in place. This itself is absurd in itself – that there is a natural body which is not in a place –, but Aristotle also recognises another absurdity if it is not in place:314 nothing comes to be from it. For what comes to be must be in the place in which the substratum from which it comes to be is, since what comes to be takes on the place of the thing from which it comes to be, so that nothing can come to be from what is not in a place. He proves by impossibility that if did not have impulsion, it would not be in a place. For if it were in a place, not moving and being at rest, it could move ‘in’ (that is, ‘to’)315 this place, since a thing is naturally constituted so as to move to the place

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in which it rests. And if it rests in a place by constraint, it also moves to it by constraint and unnaturally, but everything which moves by constraint also has a natural motion, since in all things what is unnatural is posterior to the natural. And if it rests in a place naturally, it can also move to the place naturally. So, if it is completely unmoving, it will neither rest in a place nor be in a place at all; nor will anything come to be from it. But if it is in a place, it will also change place,316 and it will have weight or lightness and be one of the four elements. Alexander says, ‘If it is not in a place, it can be added that there is a void in which what comes to be will be, since there is the same consequence as for those who generate body from what is incorporeal’.317 (305a31) Having proved these things, Aristotle reasonably concludes that the elements come to be from each other, since, as has been demonstrated, they cannot come to be either from what is incorporeal or from another body.

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305a33-b10 Again we should investigate the way in which they come to be from each other, [whether in the way in which Empedocles and Democritus say they do or in the way those who dissolve into planes say they do, or whether there is some other way beside these. (305b1) Empedocles and Democritus and their followers are not aware that they do not make come to be from one another really, but only in appearance. For they say that each thing is inherent and separated out, as if coming to be were from a reservoir, but not from some matter; nor do they say that coming to be occurs when there is change. (305b5) And then, even if this were how things are, the consequences would be no less unreasonable since the same magnitude is not thought to become heavier when it is pressed together, but it is necessary for those who assert that water is separated out from air in which it inheres to say this,] since when water comes to be from air it is heavier. He has proved that the remaining is that the elements come to be from each other, since he has proved that they come to be and come to be neither from what is incorporeal nor from another body. He next enquires about the way in which they come to be from each other. And there are different views on this subject: Empedocles says that the elements are eternal and explains coming to be by their mixture and separation; Anaxagoras318 says that everything is in everything and posits that coming to be is separation out; and Democritus (and also those who speak about planes) make the com-

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ing to be of the elements from each other occur by the blending and separation of atoms (or of planes). He first deals with Empedocles and Democritus and Anaxagoras and their followers because he recognises that it is common to their views that each posits elements which are eternal and thinks that they come to be when they are separated from the other things. For Empedocles of Acragas seems to say that when water comes to be from air or air from water they previously inhere actually in a blend and then are separated out. And Anaxagoras calls not just the four but also all other things (the homoiomereities) elements, and says that everything is in everything but all things are characterised by the dominant thing in them; and so, when several fire which have been separated out combine, it is thought that fire comes to be. And Democritus says that his elements, that is, the atoms, come to be from one another in the sense of being separated from a mixture, since when water is dissolved the atoms are separated and combine into air, one kind of atom being woven together with another.319 (305b1) Aristotle says that these people do not make the elements come to be from one another really, ‘but only in appearance’ because they say that each of their elements inheres in actuality and is separated out ‘as if coming to be were from a reservoir, but not from some matter’, and did not occur because of change. The difference here is that what comes to be from a reservoir exists actually and is separated out, but what comes to be from matter changes from being potentially into being actually. (305b5) He says that even if it were granted to these people that separation out is coming to be (even though this is an intrinsic absurdity) – even if this were how things are –, nothing less absurd would follow for them. He assumes as clearly true that the same magnitude does not become heavier when it is pressed together; for a cloak, when folded, is not heavier than itself when unfolded, nor is wool, when compressed, heavier than itself when carded. But saying this follows for those who make things come to be by separation out; for if water comes to be by separation out from air, nothing else happens to it than a sort of compression and condensation, since there was equally water in the air but it was diffused. However, the water which is separated out would be heavier than it was when it was in the air. Therefore, according to these people the same body becomes heavier when it is compressed. However, taken by itself, no body which has weight is lighter with air than apart from air, if its weight is judged in air rather than in water; for the mixture of air contributes to the lightness of heavy things which are in water because air rises to the top of water, but it does not rise when it is in air, because air does not have lightness when it is in air. And Aristotle too says this when he says ‘since the same magnitude is not

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thought to become heavier when it is pressed together’; for the term ‘pressed together’ indicates being deprived of the air which lies in between. 305b10-20 Furthermore it is not necessary that if bodies which are mixed together [are separated one of them always occupies more space. But when air comes to be from water, it does take up more space since what has finer parts comes to be in a greater space. And this is certainly evident in change since, when what is moist is evaporated and vaporised, vessels containing the masses burst because they do not have enough room. (305b16) Consequently, if there is no void at all and bodies don’t expand (in the way those who say these things assert), the impossibility is evident. But if there is a void and bodies do expand] it is unreasonable that what is separated must always take up more space. He adduces a second absurdity for these people. To start he assumes, again as clearly true, that it is not necessary that if from bodies which are mixed together one of them is separated it occupies more space. But ‘when320 air comes to be from water it does take up more space’ (not just more space than it occupied when it was in the water but also more than it occupied together with the water, since when what has finer parts is rarefied it occupies more space than what has thicker parts). And, if when air comes to be air without previously being such, it is reasonable that when it comes to be air it occupies more space, but if the air was such and existed before, it is not reasonable that it would occupy more space after being separated out.321 Having given credence on the basis of argument that air which comes to be from water occupies more space because it has finer parts, he also adds clarity on the basis of perception: in a change in which sweet wine is resolved into vapour, that is, vaporised, the containing vessels often burst ‘because they do not have enough room’. (He says ‘it is not necessary that if bodies which are mixed are separated one of them always occupies more space’ because of what he will say next.322 For even if there were a void so that bodies could expand out somewhat, nevertheless this would not always or necessarily happen, as it does in the case of air.) (305b16) Having previously323 argued in this way on the basis of water that it will be heavier when it is separated out and then on the basis of air that it occupies more space , he now produces a third argument based on space, saying that if (as he has proved324) there is no void at all into which bodies can expand, the impossibility is prima facie clear in itself. For in what way or how can a body always remain the same and also take up more

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space if there is not any empty space which contains no body into which a body with finer parts can spread? But if (as Democritus and his followers say) there is a void into which bodies expand, insofar as the space is concerned bodies could spread out into it, but it is unreasonable that the other body (such as air) must always take up more space when it is separated from the mixture. Alexander initially interprets the passage in this way as directed at a separate void (since this would be a space into which bodies expand), but without notice he turns to the interspersed void325 and says: It is unreasonable to make the intervention of the void the explanation of spreading out. For by what necessity or power could this intervening void separate and divide bodies since it is incorporeal and suited to giving way, not to acting? Furthermore, why wouldn’t everything separated out spread and occupy more space if the intervening void is the explanation of this? But when water is separated out from air it does not spread, it contracts, whereas when air is separated out from water it always spreads. But perhaps Aristotle is speaking about the interspersed void in the whole argument, since, according to Democritus and his followers, this is the explanation of the expansion of bodies; for the separate void is not the explanation of expansion, but it supplies the room for expanding things. And this is the reason why Aristotle says ‘if there is no void at all’ (that is, no separate void and no interspersed void), bodies would not expand, as Democritus and his followers say they do because of the intervention of the void; rather they would keep their own nature even when they were mixed together , as Empedocles and Anaxagoras declared (these are the people who say these things).326 Aristotle says that the impossibility is evident because even when air was separated it would be necessary that air remain the same and occupy an equal space and not take up a greater one, as it is now seen to do. But, he says, if there is an interspersed void and expansion in the way Democritus wishes, it is unreasonable that the atoms not have been divided by the void when they were mixed together, but undergo this when they are separated, so that what is separated occupies more space. And if this is what he is saying, what he says first would be referring to Anaxagoras and Empedocles, who said there is no void, and what he says subsequently refers to Democritus and his followers, a person who accepts that there is a void interwoven .327 305b20-8 It is also necessary that coming to be from each other give out [since infinitely many finite things do not inhere in a

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finite magnitude. For when water comes to be from earth, some of the earth has been extracted, if coming to be is by separation out. And again the same thing happens when water comes to be from the remaining earth. So if this always happens, it will turn out that infinitely many things inhere in a finite magnitude. But since this is impossible, things will not always come to be from each other.] We have, then, said that change into one another is not by separation out. With this argument he does away with the that coming to be is because of separation out, with all things inhering in all things in actuality, as Anaxagoras said. Aristotle also used this argument against Anaxagoras in the first book of the Physics;328 there he was enquiring about the principles of bodies, but here he is enquiring about the way in which they come to be from each other. And so he says that if coming to be is due to separation out and this because all things exist in all things, it is necessary that coming to be from each other give out, which is not what those who make this hypothesis intend. And this is proved by first assuming that infinitely many finite things do not inhere in a finite magnitude. He is careful to say ‘infinitely many finite things’ since even if bodies are divisible to infinity, ‘to infinity’ is one thing and ‘actually infinite’ is another; and things which are divisible to infinity are continuous, but the things Anaxagoras is talking about are bounded, since they do not unite with one another because they are of different kinds. So if things which are finite in magnitude are infinite in number, when they are added together they produce something infinite in magnitude, but the whole, which is not infinite in magnitude but finite, would not consist of infinitely many bounded things, that is, things which are actually circumscribed.329 This being posited, if the330 coming to be of water were by separation out from earth, then when water came to be from earth and likewise again came to be from the remaining earth, if this happened always, it would turn out that infinitely many finite things inhere in a finite thing, since this division to infinity is not of something continuous but is a separation out of things which are actually distinct. So if it is impossible that infinitely many finite things inhere in something finite, it is impossible that water always come to be from that earth, if coming to be is by separation out; therefore, the coming to be of water from the earth will give out. So if these people want it to be the case that water always comes to be from earth (and the other elements are seen to come to be from each of the elements), the coming to be of the elements from each other would not be by separation.

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Appendix The argument of Cael. 3.5 In 3.5 Aristotle argues against the view that there is only one element. At the end of the chapter (304b11-21) he offers a clear argument for this conclusion: if there were only one element there would be only one natural motion, but there is more than one such motion. However, what precedes that argument is notoriously unclear. Here I want to try to provide an outline of the chapter, indicating some of Simplicius’ interpretive stances. Aristotle’s general strategy is clear. He considers only (I) those who make the element something intermediate between earth and fire and (II) those who make it fire. He does not consider earth presumably because, as he says in the Metaphysics (1.8, 989a5-6), no one thought earth was the only element because earth has large parts. Aristotle first (303b13-304a7) argues against (I) that such people ought to make fire the element and then (304a7-b11) against (II). I. 303b13-304a7. Against those who make the element something intermediate between earth and fire. A. 303b13-22. Aristotle assigns to these people the view that non-elements come from elements by condensation (puknôsis) or composition (sunthesis) and elements come to be from non-elements by rarefaction (manôsis) or dissolution (dialusis; Simplicius also introduces the term ‘resolution’ (analusis)). But what is produced by rarefaction or dissolution is fine (leptos), so the one element ought to be what is finest, for Aristotle fire. Aristotle will take up the view that fire is the element at 304a7 but he first adds another argument against those who use rarefaction and condensation: B. 303b22-304a7. This kind of view really makes the difference among things a matter of size since what is rare or fine has small parts and what is dense has large parts. Aristotle claims that this makes what something is relative. He goes on to extend this objection to ‘those who say there are several elements, but also say they differ by largeness and smallness’. Simplicius first (617,22-5) suggests on rather weak grounds that Aristotle is thinking of the atomists, but he then admits that Alexander might be right to deny that the atomists are Aristotle’s opponent; it seems clear that neither Alexander nor Simplicius is in a position to name an alternative. At the end of his lengthy discussion of this passage (619,9-31), Simplicius rejects Aristotle’s argument. As he puts it, ‘Even if water and air are relative insofar as they are greater and less, they are not relative insofar as they are water and air’.

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Appendix: The argument of Cael. 3.5

At 304a7 Aristotle says that those who make fire the only element escape ‘this’. Simplicius reasonably enough assumes that ‘this’ is making what something is relative, but Aristotle may simply mean that they escape the argument of 303b13-22, as they obviously do. For it is not clear why if someone were to say that other things come to be by condensation and rarefaction from fire and from each other he wouldn’t face the same difficulty, and indeed, at 304b6 Aristotle apparently refers to people who make fire the element and assign it no particular shape as distinguishing things by size, and he argues that they are committed to the relativity to which he has already objected. II. 304a7-b11. Against those who make the element fire. A. 304a7-21. Description of the position. 1. 304a7-18. Those who assign a figure, e.g. the pyramid, to fire. (Simplicius (621,6-11) is perplexed about what monist might have assigned the pyramid to fire.) a. Those who argue simply. b. Those who argue more elaborately. 2. 304a18-21. Those who assign no particular figure to fire, but make other things result from fire when it is compounded or condensed in the way in which shavings are fused together. (Simplicius makes no suggestion as to whom this might be.) B. 304a21-b6. The arguments. 1. 304a22-b1. If the element fire is indivisible. a. 304a21-4. Invocation of previous arguments against indivisibles. b. 304a24-b1. This is a very obscure argument which speaks about the ‘elements’ of water, air, and fire (apparently indivisible particles of them), and assumes that the sizes of the great masses of water, air, and fire are proportional to the sizes of their particles, so that the element of fire will be larger than that of air and hence (at least theoretically) divisible. (At 622,24-623,3 Simplicius raises an objection to the argument and offers a weak response. He goes on to describe Alexander’s curious suggestion that on the view being considered the elements of, e.g., fire are small fires.) 2. 304b2-11. If the element of fire is divisible, then: a. 304b2-6. If a figure is assigned to fire (A.1) a part of fire will not be fire, and a part of fire will be neither an element nor a composite of elements. b. 304b6-11. If a figure is not assigned to fire (A.2), it being assumed that these people distinguish elements by ‘size’, then: i. 304b6-9. there is a contradiction if all bodies are infinitely divisible and an element is taken to be something with smallest parts (because there is no such thing as smallest parts); ii. 304b9-11. for the reasons stated at 303b22-304a7 (I.B), what something is will be relative.

Textual Questions (a) Departures from Heiberg’s text

Listed here are places where I have translated a text different from the one printed by Heiberg. In many cases notes on the lines in the translation provide more information. 556,26 Replace the question mark with a full stop. 557,16 After gar insert apeiron with DK. 559,3 (Melissus) For homou rheôn read homoureôn, a suggestion of Bergk (1843). 559,16 (Parmenides) For to read tôs with DK. 559,19 After hexês insert kai, a suggestion of Heiberg. 559,21 For arxasthai read arxamenos, a suggestion of Stein (1864-7). 559,27 For paradedôkasi read paradidôsi with D, E, and Karsten. 563,5-6 For eis proteron read ek proterôn with D, E, and F. 568,13 After ara insert ouk, a suggestion of Heiberg. 571,14 For kai read kan with Karsten. 572,4 For autôi read auto with D and E. 573,10 For hautou read autôn, the accepted text of Plato. 576,26 For hautou read autôn, the accepted text of Plato. 579,5 Omit kai hêmeis with F and Karsten. 594,18 For diêirêmenon read euthuporoumenon with Karsten. 599,1 Bracket men ti with C. 599,14 For to read tode with Karsten. 599,20 For hôs read en with D, E, and Karsten. 605,17 Bracket ê. 605,20 Replace the question mark with a full stop. 607,19 Place the accent on the second syllable of posoi rather than the first. 610,24 For autôn read hôn, a suggestion of Heiberg. 613,10 For elegon read elegen, a suggestion of Heiberg. 616,15 Replace the raised dot with a comma. 618,18 Insert a raised dot after periekhetai, a typographer’s omission. 631,22 Bracket ton with D, E, and Karsten. 632,19 For toiôsde read toiaisde with D. 633,14 For ei oun, hotan read hotan d’ with Karsten. 635,20 For ontôs read hê with D and Bessarion.

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Textual Questions (b) Simplicius’ citations of Cael. 3.1-7, 305b28

Here I bring together places where Simplicius apparently read a text different from that printed by Moraux. In general Heiberg’s text reproduces A. I have paid no attention to the numerous differences regarding elision (e.g. de vs. d’) or minor variations in spelling (e.g. hauton vs. heauton or teleiotaton vs. teleôtaton). Moraux 298a27 epei de 298b5 ta poia 298b5 phusei 300b25 diataxin 301a24 de 302a17 gar 303a19 skhêmatôn

Heiberg 553,6 epeidê (citation) 554,12 poia (citation) 554,13 ta phusei (citation) 585,18 diastasin (paraphrase) 592,4 gar (citation) 601,6 de (citation) 611,23 sômatôn (paraphrase)

(c) Simplicius’ citations of other texts

Here I bring together places where the text of a citation by Simplicius of a passage from a text other than Cael. 3.1-7, 305b28 as printed by Heiberg differs from the text of a standard edition of the work. In general Heiberg’s text reproduces A. I have paid no attention to the numerous differences regarding elision (e.g. de vs. d’) or minor variations in spelling (e.g. hauton vs. heauton or teleiotaton vs. teleôtaton). Anaxagoras Sider B1.2 smikrotêta B4b.8 tôi sumpanti B12.16 kai diakrinomena B4a.4 khroias kai hêdonas B4a.4 ge B4a.6 sunêmmenas B4a.7 te autoisin

Heiberg 608,22 mikrotêta 608,24 sumpanti 608,30 omit 609,8 hêdonas kai khroias 609,8 omit 609,9 sunôikêmenas 609,10 omit

Aristotle, De Caelo Moraux 268a1 phainetai

Heiberg 554,20 tunkhanei Empedocles

DK31 B27.4 periêgei

Heiberg 591,5 perigêthei Melissus

DK30 B6.3 apeiron eiê

Heiberg 557,16 eiê

Textual Questions B8.20-1 homoireôn

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559,3 homou rheôn Parmenides

DK28 B8.4 esti gar oulomeles B8.4 ateleston B8.21 tôs B8.50 pauô

Heiberg 557,18 oulon mounogenes 557,18 agenêton 559,16 to (not as part of fragment) 558,5 pausô

Plato, Timaeus Rivaud 54D4 tautên 54D5 hupotithemetha 54E2-3 atta dialuomena 56B1 ex oligistôn 56B2 autôn

Heiberg 566,10 tên 566,11 hupotithômetha 566,14 auta dialuomena atta 573,10 ex oligôn 576,26 ex oligôn 573,10 hautou 576,26 hautou

[Timaeus of Locri], On the Nature of the World and the Soul Marg (1972) 215,15 ha gennasis

Heiberg 564,6 apogennasis (d) Lemmas

Here I bring together places where the text in a lemma printed by Heiberg differs from Moraux’s text of Aristotle. In general Heiberg’s text reproduces A. I have paid no attention to the numerous differences regarding elision (e.g. de vs. d’) or minor variations in spelling (e.g. hauton vs. heauton or teleiotaton vs. teleôtaton). I should perhaps note that the lemmas in Heiberg generally give only the first and last few words of a passage, and so represent less than 10 per cent of the text of De Caelo. Moraux 298b24 ekeithen 300b25 diataxin 301a11 kaitoi ouden 302a27 prostheôrêteon 302b5 pantos

Heiberg 556,2 ekei 583,16 diastasin 589,5 ouden gar 601,21 theôrêteon 604,1 omit

Notes 1. In 1.2. 2. In 2.13 and 14. 3. Simplicius compares the beginning of this chapter, 298a24-b8 with the beginning of the whole work, 268a1-6; see also his commentary on that passage at 6,30-8,8. 4. cf. 2.12, 292a20-1. 5. cf. 2.1, 284a14. 6. Alexander’s claim can be represented in English by saying that the ‘they’ and ‘their’ in ‘what they are composed of and what their nature is like’ refer to the stars and indicate that they are like the spheres, but that ‘they’ in ‘they do not come to be and are imperishable’ applies to everything (that is, either the first heaven or it and the spheres and the stars). His position is grammatically possible because of the ‘further’ and the ‘and also said’, but Simplicius’ claim that the two ‘they’ and the ‘their’ should have the same referent seem more likely. 7. The lemma agrees with our text of Aristotle in having epei de, but at 553,6 Simplicius cites this text with epeidê. 8. Moraux prints ta poia esti phusei; in a citation at 554,12 Heiberg prints poia esti ta phusei with D and E. A has ta poia esti ta phusei, Karsten ta poi’ esti phusei. 9. At 551,18-22. 10. i.e. modus ponens, the first Stoic unprovable; see, e.g., Kneale and Kneale (1962), pp. 162-3. 11. 552,31-552,4 are text 112C of Theophrastus: Sources and text 1015 of Hülser (1987-8). On the distinction see also, e.g., Diogenes Laertius (Marcovich (1999)), 7.71. 12. Simplicius substitutes merê for Aristotle’s moria. 13. Simplicius quotes the first sentence of Cael. with tunkhanei in place of phainetai. 14, In 1.2. 15. Heiberg prints ekei with A, although D, E, F, and Karsten have ekeithen, the reading of our texts of Aristotle. 16. This first paragraph relates to both this and the next lemma. 17. Theogony (West (1966)), line 116. 18. It is not clear why Simplicius reads this distinction into what Aristotle says here, but see Metaph. 1.5, 986b10-987a2, where Aristotle suggests that Parmenides was more commendable than Melissus because he made some attempt to deal with phenomena; see 560,1-4 with the note. The lengthy fragment 8 which he quotes below shows clearly that Melissus claimed that things are only thought to come to be. 19. Replacing Heiberg’s question mark with a full stop, as in DK28A14. If the question mark is retained, the question (Is it because both Melissus …?) would be sarcastic. 20. Most of this paragraph is DK28A14. For other indications that Parmenides’ poem was called ‘On Nature’ see Diogenes Laertius (Marcovich (1999)), 8.55) and Sextus Empiricus (Mutschmann (1914)), Adversus Mathematicos 7.111, and the two texts of Galen cited in DK30A4, which also mention Melissus, for whom see

124

Notes to pages 31-34

line 10 below with the note. The standard work on the title ‘On Nature’ is Schmalzriedt (1970). Schmalzriedt denies that Parmenides would have used such a title or any title at all, and he is doubtful that Melissus used it. 21. Plato, Parmenides 135B8. 22. Most of this sentence is part of DK30A4, which also includes in Phys. 70,16-17, which says the same thing about the title of Melissus’ treatise; see also 556,25-30 with the note. 23. DK30B6. The word ‘infinite’, not printed by Heiberg, is inserted in DK on the basis of Simplicius’ paraphrase at in Phys. 103,28-9; cf. [Aristotle], On Melissus, Xenophanes, and Gorgias 1, 974a11-12. 24. This is a version of DK28B8.4, although the version in DK is substantially different. For discussion see Tarán (1965), pp. 82, 88-95. 25. That is, Aristotle gives arguments against a text based on a superficial reading of it, but his purpose is to prevent people from reasoning the way the superficial reading suggests is proper. 26. DK28B1.28-32, on which see Tarán (1965), pp. 210-16. Simplicius is our only source for the second sentence. 27. DK28B8.50-2. 28. Here Simplicius has a future ‘will end’ (pausô) rather than the present pauô, which is printed in DK. Simplicius has pauô at 146,23 of in Phys.; the manuscripts are divided at 41,8 of the commentary, where Diels, the editor, prints pausô. 29. DK28B19, quoted only here. 30. DK30B8, quoted only here. 31. Translating the homoureôn, printed by DK, following Bergk (1843), p. 106. Heiberg prints homou rheôn with all the manuscripts and printed texts he cites, and conjectures homou rheein. 32. The words in parentheses are probably inserted by Simplicius; cf. Barnes (1982), p. 622, n. 3. 33. DK28B8.21. I have translated the tôs printed by DK, following what Diels prints at 145,22 of in Phys. Heiberg prints to, Karsten hôs (neither as part of the quotation). 34. In fragment 8, just quoted. 35. The insertion of kai is a suggestion of Heiberg; Karsten prints heôs tou (‘and so on up to’). 36. Reading arxamenos, a suggestion of Stein (1864-7), p. 797, for the arxasthai printed by Heiberg. 37. DK28B11, only quoted here. 38. Reading paradidôsi with D, E, and Karsten rather than the paradedôkasi (‘they have set out’) of A, printed by Heiberg. There is no evidence that Melissus set out any kind of cosmogony. 39. Simplicius refers in a rather obscure way to Metaph. 1.5, 986b27-987a2, where Aristotle says: ‘But Parmenides seems somehow to speak with more perception; for thinking it correct that beside what is what is not is nothing, he necessarily thought that being is one …, but, being constrained to follow appearance and accepting that what is one according to reason is more than one according to perception, he next posits that the causes are two and the principles are two, calling them hot and cold, that is fire and earth; and he ranges the hot with what is and the other with what is not’. 40. That is, Parmenides and Melissus, who, Simplicius has just argued do not do away with coming to be. 41. Theogony (West (1966)), line 116.

Notes to pages 35-38

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42. For Simplicius, Hesiod, Orpheus, and Musaeus all expressed in mythological terms Neoplatonist ideas of the unfolding of what is from an ineffable, timeless first principle. 43. See section 7 of the introduction. 44. The geometrical constructions which are summarised here correspond to Tim. 53C5-56E8. There are useful diagrams in Vlastos (1975), pp. 74-9. It should be borne in mind that Aristotle and Simplicius use the words ‘pyramid’, ‘octahedron’, ‘icosahedron’ (and ‘dodecahedron’) to refer to the regular, so-called Platonic, solids; they do not use the words generally to mean, e.g., ‘a solid figure bounded by plane surfaces, of which one (the base) is a polygon of any number of sides, and the other surfaces triangles having as bases the sides of the polygon, and meeting at a point (the vertex) outside the plane of the polygon’ or ‘a three-dimensional figure having eight plane faces’, to quote the relevant definitions of ‘pyramid’ and ‘octahedron’ in the OED. 45. hêmitrigônon, a term found in TL at 216,2. 46. Simplicius’ position might be expressed this way. For Aristotle body is eternal but the simple bodies come to be from each other by qualitative change, and he treats the Timaeus theory as an alternative physical theory of the change of the simple bodies into one another. But the Timaeus theory is a metaphysical account of the principles from which body is constructed. (It is to be borne in mind that for Simplicius this construction is not the description of a temporal process but a way of representing an eternal truth about the structure of things; see especially 305,14-306,25 in his commentary on 1.10.) 47. This sentence, which marks the transition to a discussion of the Timaeus view of the coming to be of body, is not included in the scope of any lemma. I have inserted it here. 48. Homer, Iliad (West (2000)) 20.75-6. 49. Aristotle discusses the first and third views in Phys. 1.2-4, but he does not, as far as I know, discuss the ‘Hesiodic’ view. 50. cf. 556,15-24 and 560,22-7. 51. Actually, for Simplicius, Aristotle has not yet shown this (see, e.g., 602,18), but will do so starting in 4.4. 52. Here Simplicius refers to the difference between Aristotle’s account of natural motion up and down and Plato’s account of heaviness and lightness. See, e.g., 679,18-682,3 in his commentary on 4.1. 53. Simplicius recalls the first, second, and fifth definitions of Euclid’s Elements (Heiberg (1883) 4,1-6). 54. Reading the ek proterôn of D, E, and F rather than the eis proteron of A, printed by Heiberg; Karsten has ek proterou. 55. Presumably the absurdity of contradicting mathematics. 56. 6.10. 57. Simplicius paraphrases Tim. 53B3-5. For Simplicius what we might call the geometrical chemistry of the Timaeus is not a case of something like mathematical physics. It is a purely physical theory which presupposes a doctrine of matter very similar to (and perhaps identical with) the doctrine of prime matter traditionally ascribed to Aristotle. The triangles of Plato’s Timaeus result when this matter is given a geometrical shape. 58. TL, 215,13-17. Simplicius quotes all but the description of one of the triangles at 641,11-14 of his commentary on chapter 7; see also in Phys. 7,23-7. 59. Marg (1972) prints ha gennasis, Heiberg apogennasis. The MSS of Simplicius show considerable variation.

126

Notes to pages 38-42

60. See also below 575,27-576,10 with the note on 576,10. 61. Among these was presumably Pericles of Lydia, the dedicatee of Proclus’ Platonic Theology (Saffrey and Westerink (1968), 5,6-7); see in Phys. 227,23ff., where the view that matter is qualityless body is ascribed to the Stoics among earlier people and to Pericles among recent ones. It seems to me very unlikely that the ‘recent Platonic philosophers’ is a reference to Proclus’ himself (so Steel (2005), p. 187, n. 72), since the view described here bypasses Plato’s geometrical chemistry and associates the qualities of the simple bodies directly with matter, whereas, as Steel himself indicates, Proclus is a defender of that chemistry; see Mueller (forthcoming). 62. The term ‘affective quality’ (pathêtikê poiotês) is taken from Aristotle’s Categories. See 8, 9a28-10a10, and see also Simplicius’ discussion of this passage at 252,23-261,16 of his commentary on the Categories (CAG 8) and the note on 9a28 in Ackrill (1963). 63. 564,24-6 are text 238 of Theophrastus: Sources; 24-9 constitute DK68A120 and are part of Luria (Krivushina and Fusaro (2007)), 171. Simplicius more or less repeats these words at 576,14-16 and 641,5-7; see also in Phys. 35,22-36,7. 64. As Aristotle says it is at Categories 8, 10a11-16. 65. That is, a quality. These defenders of Plato argue that the (Aristotelian) view that the change from, say, water to air is a qualitative change cannot explain why the resulting quantity of air is greater than the original quantity of water. 66. cf. Plato’s description of fire at Tim. 56A4-B2. 67. As Plato is held to have said. 68. Simplicius also makes this suggestion about the character of Plato’s geometrical chemistry at 641,23-8 in his commentary on chapter 7. 69. Plato, Tim. 54A1-6. 70. Plato, Tim. 53D4-E5. 71. Heiberg prints hupotithômetha, a reading of some MSS of Plato, Rivaud (and Karsten) hupotithemetha. 72. The Timaeus has tautên. Heiberg prints tên, noting that D, Bessarion, and Karsten have tautên. 73. Heiberg prints auta dialuomena atta ginesthai, Rivaud and Karsten atta dialuomena gignesthai. 74. Although this treatise comes down to us among the works of Aristotle, its ascription to him has been much doubted, as has its ascription to Theophrastus. It is listed as a work of Theophrastus by Diogenes Laertius (Marcovich (1999)) 5.42. Themistius (in Cael. (CAG 5.4), 148,39-149,2) and Philoponus (in GC (CAG 14.2), 34,2-3) also mention the possibility that the treatise is by Theophrastus. Simplicius treats it as Aristotelian at 423,3-4 of in Phys., and it is included in a list of Aristotle’s works in Arabic (see Düring (1957), p. 222). 75. Defined in the OED as ‘the rhetorical device of emphasising or drawing attention to something by professing to say little or nothing about it, or affecting to dismiss it …’. 76. It would perhaps be better to say that Simplicius’ examples are not absurdities for mathematical bodies, but rather truths about them. 77. Omitting the words ‘For example if there is something indivisible’ (hoion ei ti estin adiaireton), which are bracketed by Moraux and not mentioned by Simplicius. 78. The lemma is difficult, and Simplicius struggles with it. He considers two interpretations, the second of which he says he prefers. On the first (567,26-568,7) the word ‘indivisible’ here means ‘mathematical’, and Aristotle is simply pointing

Notes to pages 42-46

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out that the affections of natural bodies, such as colour and weight or lightness do not belong to mathematical entities. On the second (568,8-23) he is claiming that natural bodies cannot be composed of indivisibles because indivisibles cannot have affections (since affections are divisible (accidentally)) and what does not attach to the components of something does not attach to the thing. 79. Here ‘indivisible’ is used in the ordinary sense and not to mean ‘mathematical’, and Simplicius’ first reconstruction is infected by ambiguity. 80. Inserting ara, following a suggestion of Heiberg. Karsten’s hôste is equally plausible. 81. For Aristotle fire and air have lightness rather than weight (in the sense that they move from the centre), but for Plato they too are heavy (in the sense that they too are drawn to be with their like). 82. Aristotle discusses the atomist theory of weight in 4.2, 308b30-309,18. For an account with references see Taylor (1999), pp. 179-84. 83. cf. 299a6-8 (562,20). 84. Technically the third hypothesis is also needed here. 85. [vii] is the additional assumption, [viii] the conclusion; [iv],[v], and [vi] together give the conditional; if bodies are composed from planes and a point has no weight, bodies will not have weight. 86. In the mood Camestres. The syllogism is: What is heavy is divisible; a point is not divisible; therefore, a point is not heavy. 87. This is not a serious difficulty for someone who accepts, as Aristotle does, the idea of infinity as only potential, not actual. 88. Simplicius paraphrases 469C1-2 of Plato’s Gorgias. 89. That is, one thing can be heavier than a second and lighter than a third. 90. i.e. the positive form of the adjective. Simplicius’ point here is that Aristotle uses ‘perhaps’ because ‘What is heavier is heavy’ is true if we use ‘heavier’ in the strict sense, applying it only to things which do have weight rather than lightness. 91. This addition is apparently designed to avoid the (harmless) infinite regress signalled by Simplicius at 569,28-570,2. 92. The basis for this parenthetical remark is unclear, but it is presumably something said in Plato’s Timaeus. I suggest tentatively that when Simplicius says that fire is denser than earth, he is thinking of 58B1-6 where it is said that the particles of fire are more pressed together than those of the other elements; for the idea that larger parts produce heaviness see, e.g., 58D8-E2, where it is said that the kind of water which is composed of large and uniform things is heavy. 93. Camestres. 94. Reading Karsten’s kan rather than the kai printed by Heiberg; the sense is not in doubt. 95. The ara inserted after hê by Bessarion in K and Karsten or after stigmê by Bessarion in E is plausible. 96. Simplicius is careless about whether the major term is ‘heavy’ or ‘heavy or light’, but the syllogism he has in mind is again in Camestres and may be represented as: What is heavy or light is divisible; a point is not divisible; therefore, a point is not heavy or light. 97. I have tried to translate the vulgate text along the lines of Simplicius’ interpretation rather than the altered text of Moraux, who explains his decisions

128

Notes to pages 47-52

in Moraux (1961), 25-7. As Moraux himself says, there is no question that Simplicius read (and struggled with) the vulgate text. 98. cf. 569,2-4. 99. I have translated the auto of D and E rather than the autôi of A. With the latter the sense would be ‘And the first argument for him is the following’. 100. TL 216,18-19. 101. Simplicius cites 56B1-2, which in Rivaud’s text runs elaphrotaton ex oligistôn sunestos tôn autôn merôn. Heiberg prints elaphrotaton to ex oligôn sunestôs tôn hautou merôn, while noting that D and E have oligostôn (?) and A, D, E, and Karsten have autou. I have translated elaphrotaton to ex oligistôn sunestos tôn autôn merôn. See also 576,25-6 with the note. 102. At 299a25-6 (568,26). 103. Simplicius’ description in this paragraph is based on 54D3-55E6 of Plato’s Timaeus. For perspicuous pictures of the five regular solids see the article ‘Platonic solid’ on Wikipedia (http://en.wikipedia.org/wiki/Platonic_solid). 104. It would be possible to object that when one mathematical plane is laid on another the result is not a body or two juxtaposed planes, but a single plane. Aristotle knows this, but he thinks that believers in atomic magnitudes such as Plato cannot adopt this alternative. For Simplicius the alternative is not available as a defence of Plato because Simplicius believes that Plato’s planes have depth; see, e.g., 563,26-564,10. Simplicius gives his own response to Aristotle in the next paragraph. 105. Heiberg cites Tim. 53C6-8, where, in introducing the construction of the regular solids, Timaeus says, ‘Every kind of body has depth, and it is entirely necessary that the plane nature enclose depth’. 106. Simplicius apparently assumes that in Aristotle’s theory the qualitative change of one simple body into another might involve intermediate stages at which neither an element nor a compound of elements would be present. One can imagine arguments to this effect, but I do not know what exactly Simplicius has in mind. 107. Cube, pyramid, octahedron, icosahedron. 108. Aristotle does not use the term ‘second substratum’. Perhaps ‘he’ is Alexander; cf. 599,5 with the note. 109. Apparently the ‘symbolical’ interpretation of the chemistry of the Timaeus stressed similarities between the four elements and the solids associated with them. Alexander thinks that the chemistry must be literal and not merely symbolic since Plato is willing to deny that earth interchanges with the other elements. Simplicius is willing to invoke the symbolic interpretation as a basis for rejecting Alexander’s objection, but he still insists that explanation of elemental change in terms of shapes reveals something more fundamental than Aristotle’s reliance on qualities in GC. 110. At 564,24-6. 111. cf. 299a6-8 (562,19). 112. Simplicius changes Aristotle’s word order to make what he means clearer. 113. Simplicius invokes 56B1-2. Cf. 573,10-11 with the note. Here Heiberg prints eti te elaphrotaton to ex oligôn sunestôs tôn hautou merôn, noting that D, E, and Karsten have oligistôn and that A, D, E, and Karsten have autou. I have translated eti te elaphrotaton to ex oligistôn sunestos tôn autôn merôn, as in the previous passage. 114. An obscure remark, which has the appearance of a gloss and is omitted in D and inserted by Bessarion in E. Simplicius ought to be describing the difference between ‘is not at some time’ and ‘possibly is not’. Perhaps, then, one should insert

Notes to pages 52-57

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a pote, so that Simplicius is pointing out that ‘is not at some time’ has a temporal qualification which is lacking in ‘possibly is not’. Or one might keep the text as it stands and say that Simplicius is marking a (not really relevant) distinction between ‘is not now’ and ‘might not be at some time or other’. 115. This parenthetical remark is difficult to construe. I take it that either ‘he’ is Plato, and that Simplicius is referring either to Plato’s so-called unwritten doctrines in which the one or monad, and not points, is made primary or to Aristotle’s lost report of those doctrines. It is, however, possible that, as Moraux ad 300a9 suggests, Simplicius’ text said ‘monad’ rather than ‘point’. 116. I take Alexander to be suggesting that the matter of a composite might be of some size. Simplicius does not accept this doctrine and proceeds to argue that Aristotle is in no position to espouse it. 117. Phys. 4.9, 217a26-7. 118. Simplicius shares Aristotle’s view that the universe is sustained eternally because the perishing of one thing is the generation of another and that this process is kept going by the eternal motion of the heavens. As a Neoplatonist he also believes that the process of coming to be involves the action of incorporeal principles (demiurgic logoi). These factors make it impossible for things to be resolved into planes (or points), and without them Aristotle himself would have to admit the absurd view that everything could be resolved into the four elements. 119. At 579,12 Simplicius casts doubt on the existence of such people. Alexander discusses the same sort of interpretation of the Timaeus in Quaest. 2.13 (Bruns (1892), p. 58). 120. Reading with F and Karsten only the first of the two kai hêmeis printed by Heiberg. 121. cf. 573,15-28. 122. I have not found a good way to render this lemma and Simplicius’ comment on it into English. In the translation the words ‘at some time’ and ‘some time’ render the Greek pote, the word ‘time’ by itself renders khronos. 123. Simplicius quotes the line which he is here paraphrasing at in Phys. 453,12 and 1102,20. The line is also quoted by Asclepius in his commentary on books 1 to 7 of Aristotle’s Metaphysics (CAG 6.2) at 38,19 and paraphrased by Proclus in his commentary on Plato’s Timaeus (Diehl (1903-6)) at 1,16,32. Lydus (On the Months (2.11.24 (Wünsch (1898))) cites a very similar line as a saying of Orpheus about the number six, and in the Orphic Hymn to Kronos (Quandt (1955), 13.1) Kronos is addressed as ‘father of the blessed gods and of men’. 124. Simplicius also quotes these words at 1102,22 of in Phys.; for other citations see the note on this passage in Hagen (1994), p. 125. 125. cf. 569,2-4 126. i.e. Plato’s theory. 127. Simplicius refers to Phys. 4.8, 215a1-6. 128. The difficulty does not affect the main argument of the lemma. 129. cf. 1.2.269a9-10. 130. Here Alexander proposes to interpret ‘unnatural’ (para phusin) as ‘not natural’ rather than as ‘contrary to the natural’. Simplicius proposes that, in the case of the simple motions up and down, only the simple motion contrary to a thing’s natural motion should be considered unnatural for it. 131. The formulation here is too compressed. Simplicius should say ‘he should take only the contraries of those which it is naturally constituted so as to have’. 132. The words ‘or lightness’ are irrelevant here; a reader has suggested bracketing them.

130

Notes to pages 58-62

133. Here and at line 7 Simplicius writes tên apeiron adunaton dielthein where Aristotle has to apeiron dielthein. I have supplied grammên on the basis of 1.5, 272a28-9, where Aristotle says adunaton tên apeiron dielthein … and tên apeiron is clearly an infinite straight line. At 583,8 and 9 Simplicius writes kineitai and peperasmenên kinêthênai, and I have translated ‘move through an infinite (or finite) straight line’. These supplements are not certain and the translation of the present and aorist tenses in this passage is difficult, but Simplicius’ point is clear: something cannot be in the process of doing something (present tense) if it is not possible for it to ever have done it (aorist). 134. cf. Phys. 6.10, 241b6-7. 135. Although Alexander’s reading is grammatically possible, it does not seem that the question ‘Where would it move’ is appropriate to the vortex, which is only supposed to revolve around the earth. However, one cannot be sure that Simplicius is not reporting just one possibility considered by Alexander. On Simplicius’ own, more plausible reading Aristotle proves at most that the earth rests naturally somewhere, not necessarily at the centre. 136. On the text of this sentence see the note on 585,1. 137. diastasin, which Heiberg prints with A and F. Moraux prints diataxin (arrangement), which is in D and E and printed by Karsten. The manuscripts of Aristotle are divided between the two. In his paraphrase at 585,18 (where Karsten prints diataxin) Simplicius has diastasin. 138. para phusin, which Simplicius associates with ‘is derivative from’ (paruphestêken). 139. Simplicius refers to chapter 8, 215a8-11. 140. In this paraphrase of 300b21-2 Simplicius substitutes auto for heauto, adopting a reading of Alexander which he goes on to reject in the next paragraph; see the note on 585,1. Moraux (1973-2001), vol. 3, p. 234, n. 246 argues that all of 584,9-585,20 with the exception of 584,27-585,1 and 585,5-12 derives from Alexander. 141. And so say something that resembles what is said at 245C5-246A2 of Plato’s Phaedrus. The issue addressed in this paragraph is the text of 300b21-2, for which I have translated Moraux’s text, to te gar prôton kinoun anankê kinein heauto kinoumenon kata phusin. This is the reading of most manuscripts, and as Simplicius says, ‘many books’. Alexander substituted auto for heauto, giving a text which might be translated ‘For the first cause of motion, moving naturally, must cause motion’. A number of modern scholars, including Allan (1936), adopt this text. In this paragraph I have used my two translations to render what Simplicius describes in terms of the choice between the two pronouns. 142. Here Simplicius expresses his disagreement with Alexander’s suggestion that nature is an unmoved mover. He finishes up his exegesis of the lemma in the next paragraph. 143. Marg ((1972), pp. 107-8) quite reasonably takes Simplicius to be referring to TL 206,11-17. 144. See 586,12 with the note. 145. Line 1 of DK31B57, from which Aristotle omits the initial ‘here’ in the lemma. For other citations see Wright (1981), p. 115. 146. Simplicius’ formulation is not perspicuous, but he proceeds to explain his meaning. 147. The issue raised here is the meaning of Aristotle’s phrase ‘under Love’. Alexander thinks it means ‘when Love dominates everything’, Simplicius (almost certainly correctly; see O’Brien (1969), pp. 172-5) ‘when Love is gaining the ascendancy’. The discussion is not as clear as it might be.

Notes to pages 62-69

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148. The rest of DK31B57. These two lines are only preserved here. On Simplicius’ accuracy in citing Empedocles see O’Brien (1969), pp. 276-86. 149. Line 5 of DK31B35. Simplicius quotes the first fifteen lines of this fragment at 529,1-15 of the commentary on 2.13. 150. Lines 10-13 of DK31B35. 151. mounomelê, a hapax incorporated in DK31B58. 152. DK31B59. This passage is our only source for the full fragment, although Simplicius quotes the words ‘as all (hapanta for hekasta) of them chanced to meet’ at 327,20 and 331,2 of in Phys. 153. cf. Politicus 272E5-6 where the cosmos is spoken of as being turned back by its fated, innate desire. In this paragraph Simplicius gives the standard Neoplatonist interpretation of the Timaeus as a cosmogonical myth designed to reveal eternal truths about the universe. 154. Perhaps the idea is that with infinitely many different causes any one would be counteracted by another and the sum could produce no cumulative effect. 155. Simplicius thinks that Aristotle’s argument should be based on the trichotomy: one cause of motion, infinitely many causes of motion, finitely many causes of motion. And he wants the third case to be taken up with the words ‘for if they were finite’. But since ‘they’ is feminine it clearly refers to the motions (phorai), not the causes of motion (kinounta). 156. Heiberg prints ouden gar with A and F, although D and E have kaitoi outhen, and Karsten has the reading of our texts of Aristotle, kaitoi ouden, words which Simplicius cites at 589,21. 157. Aristotle’s text requires that genesin be understood here. At 590,25 Simplicius supplies diathesin (‘condition’). 158. As, of course, it has not. 159. The condition of total blending under Love. 160. This is line 4 of DK31B27 and line 2 of DK31B28, except that DK print periêgei (‘encircling’) instead of the perigêthei (‘joyous’) printed by Heiberg – the manuscripts are quite various here. For other citations and their problems see Wright (1981), pp. 104-5. In construing the sphere of Empedocles as an intelligible cosmos, Simplicius Platonises his ideas. 161. I take this to mean that Empedocles took Love as an independent cause operating in opposition to Strife in cosmic processes, an interpretation much more congenial to modern scholars than Simplicius’ Platonising one. 162. At 592,4 Simplicius cites these words with a gar. Aristotle and Karsten (at 592,4) have de. 163. cf. 569,2-10, although the assumption there only concerned weight. 164. At 301b1 at the beginning of the next lemma (593,19). 165. But, in fact, what doesn’t have weight would not naturally move down at all; cf. 593,8-9. 166. This third assumption is used in the argument of the next lemma (593,19). 167. This figure is based on the one printed by Heiberg, which, he says, is slightly different from the one presented by A, D, and Bessarion. It is perhaps not perspicuous to the modern reader because the whole line segment beneath ‘B’ and ‘F’ represents what is called ‘B’ in the text. The same figure can be used with the proof in the next lemma. 168. Note that the move here is technically illegitimate because it supposes that it makes sense to talk about the ratio between a weight and a distance. See also 593,14-16. 169. Taking the diorismenon of 301b17 with sôma and not with baros, as, e.g.,

132

Notes to pages 70-74

Guthrie and Stocks do. Simplicius and Alexander clearly take diorismenon with sôma – Simplicius even quotes the words as anankê pan sôma diôrismenon baros ekhein ê kouphotêta at 594,14 – although they have difficulty explaining what Aristotle means; see 594,16-595,8. 170. cf. 583,4-5 with the note. 171. Heiberg prints diôrismenon to diêirêmenon (‘“determinate” indicates divided’). It seems to me that something like Karsten’s euthuporoumenon, which I have translated, must be right; cf. 595,24-6. 172. cf. Phys. 4.4, 211a17-b5. 173. The great masses of earth, water, air, and fire remain where they are. 174. Because parts of the heaven never change their position and are never separated from it. 175. At 595,30 Simplicius explains that Aristotle means to say that all motion is either natural or constrained. 176. cf. 2.1.192b21-2. 177. Simplicius is apparently referring to 1.3, 269b23-9, as Heiberg indicates, but Aristotle is much more explicit on this subject later at 4.4, 311a15-29. 178. The discussion in this paragraph concerns the last sentence of the present lemma and the first sentence of the next. In Moraux’s text, which I have translated, these read: Hoti men oun hapan ê kouphon ê baru, kai pôs hai para phusin kinêseis ekhousi en toutois, phaneron. Hoti d’oute pantôn esti genesis outh’ haplôs outhenos, dêlon ek tôn proeirêmenôn. On the basis of what he found in some texts Alexander thought that the final phaneron of the first sentence should attach to the second, which should read: Phaneron de hoti oute pantôn esti genesis outh’ haplôs outhenos, hôs dêlon ek tôn eirêmenôn (But it is evident that not everything comes to be and that not absolutely nothing comes to be, as is clear from what has been said). This forced Alexander to say that something was left out of the first sentence, namely the words kai proeirêtai, so that the first sentence would be: Hoti men oun hapan ê kouphon ê baru, kai pôs hai para phusin kinêseis ekhousi en toutois kai proeirêtai. Alexander says (and Simplicius apparently concurs) that this text would have to be read as saying ‘And it was said before in these discussions that everything is either heavy or light and it was said how unnatural motions exist’. Simplicius concludes by espousing the kind of text we find in Moraux, while admitting that the dispute has no substantial interest. 179. outh’ haplôs outhenos . Guthrie’s translation ‘nothing is generated in a absolute sense’ represents the usual way these words are rendered. But it appears from 597,31-598,7 (cf. 600,5) that Simplicius understood the words in the way I have translated them. This difference goes hand-in-hand with a difference in understanding of Aristotle’s words ‘what has been said previously’. On the standard modern view (see, e.g., Stocks or Moraux ad loc.) Aristotle is referring to his rejection of a void in Phys. 4.6-9; contrast 598,3-7. 180. cf. 568,30-569,18.

Notes to pages 74-78

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181. cf. chapter 1, 298b12-299a1 (555,13; 556,1; 560,11). 182. cf. 1.3, 270a12-22. 183. Simplicius refers to 298b14-24 in the previous chapter (556,1). Aristotle’s main discussion of Parmenides and Melissus in Phys. 1.2-3 does not address the issue of coming to be. 184. I take it that in the remainder of this paragraph Simplicius sets out Alexander’s account of Aristotelian doctrine; he goes on to express his misgivings. It is, however, possible that where I have inserted the name ‘Aristotle’ one should insert ‘Alexander’. 185. Agreeing with C in eliminating men ti in 599,1. It would also be possible to read mentoi with E, F, and Karsten. I take the point of this opaque sentence to be that when, e.g., air is said to come to be from matter, the truth is that it comes to be from, e.g., water, but we say it comes to be from matter because water is potentially air; cf. Moraux (1973-2001), vol. 3, p. 230. 186. ‘He calls’ is the reading of A, ‘they call’ that of D, E, and F. Moraux ((1973-2001), vol. 3, p. 230) takes ‘he’ to be Alexander. But Simplicius appears to assign the term ‘second substratum’ to Aristotle at 576,7-8. 187. Simplicius thinks that Alexander’s argument against the coming to be of body could be generalised to various genera. What he says about colour and shape is clear enough, but I do not understand his argument in the case of things like heat and coldness. 188. Reading tode with Karsten rather than the to printed by Heiberg; cf. line 18 below. In this sentence Simplicius expresses the view of Alexander: only particulars come to be. Simplicius proceeds to express his own contrary view. 189. Reading the en of D, E and Karsten rather than the hôs of A and F printed by Heiberg. 190. Or ‘is not some time’, if we follow D and E. 191. Simplicius compares the Peripatetic view that there is a permanent substratum underlying all change with his (Platonist) view that there are common qualities in the perceptible world which (in another sense) underlie constant qualitative change. 192. i.e. because only particular bodies come to be, whereas body in general is eternal. 193. cf. Phys. 4.9, 216b22-30, where Aristotle refers to Xuthus as holding this same doctrine. In his comment on this passage at in Phys. 683,24 Simplicius says that Xuthus was a Pythagorean. In his note ad 216b25-6 Ross (1936) indicates how little is known about Xuthus. 194. Our texts of Aristotle have a gar here. At 601,6 Simplicius cites these words with a de. 195. cf. the beginning of this book at 298b6-8. (554,22ff.) 196. cf. 3.1, 298b8-12 (555,13ff.). 197. GC. It is important to bear in mind that for Simplicius Aristotle does not establish his account of the four simple bodies until this work. 198. That is, about form and matter. 199. Like Aristotle. 200. A homoiomery (such as flesh) is something which can be divided (in the ordinary sense) only into parts like itself. 201. i.e. a letter. 202. Heiberg prints theôrêteon with A. D and E have protheôrêteon, Karsten prostheôrêteon, which is what Moraux prints and what Simplicius uses at 602,23.

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Notes to pages 78-81

Heiberg also prints prostheôrêteon at 603,2 with F, although A and D have protheôrêteon. 203. ekkrisis, a noun, the verb related to which Aristotle uses in the lemma. Simplicius thinks that this word is applied in philosophical contexts to things which inhere actually in something, and not to things which inhere only potentially in the way Aristotle says here that fire and earth are contained in flesh and wood. 204. This sentence is text 281 of Theophrastus: Sources. In a note the editors point out that in his description of Alcmaeon’s account of vision Theophrastus says, ‘It is clear that the eye contains fire, since when it is struck fire flashes out’ (De Sensu (Stratton (1917)), 26). 205. I have been unable to identify this person further. 206. cf. [Galen], Medical Definitions 337 (Kuhn (1821-33) 19, 434,15-16): ‘A carbuncle is a scabrous ulceration which is accompanied by spreading and discharges and sometimes by swelling and fever’. 207. trupanon. The OED explains that the term ‘fire drill’ is used for ‘a primitive contrivance, consisting of an obtuse-pointed stick which is twirled between the hands with the point in a hole in a flat piece of soft wood till fire is produced’. 208. On this remark see section 6 of the Introduction. 209. cf. 1.3, 270b24-5 and Meteorology 1.3, 339b21-3 and 2.9, 369b11-15. 210. ‘Air’ is presumably Simplicius’ mistake. 211. cf. 302a16-18 at the beginning of this chapter (600,3). 212. Heiberg follows A in omitting pantos. It is printed by Moraux and occurs with some variation in the MSS Moraux cites and in D, E, F, and Karsten. 213. cf. 2.1, 192b8-23. 214. 1.2, 268b14-269a2. 215. cf. 600,5-30. 216. In the remainder of this chapter. 217. In chapter 5. 218. This sentence is obscurely expressed. Simplicius understands Aristotle to mean only that many composite bodies (non-elements) are homoiomerous. 219. cf. in Phys. 27,23-8. 220. see chapter 4, 187a26-188a18. 221. cf. 302a21-5 in the preceding chapter (601,21) with Simplicius’ commentary. 222. By Ferison. 223. Bracketing the ê and changing the question mark to a full stop. 224. Simplicius claims that a thigh bone, for example, is not homoiomerous because, even if pieces of it have the same material composition as the whole, they do not have the same form, the form which makes the thigh bone a thigh bone. 225. sôzein as in sôzein ta phainomena (preserve the phenomena). 226. I assume Potamon (also mentioned at 652,9 in the commentary on chapter 7, on which see the note in Mueller (2009)) is the eclectic philosopher, probably of early imperial times mentioned by Diogenes Laertius (Marcovich (1999), 1.21); cf. the Suda, s.v. Potamôn (2126) (Adler (1930), p. 181). 227. A Peripatetic of the earlier second century CE, on whom see Moraux (1973-2001), vol. 2, pp. 226-93. The five postulates are the postulates of Euclid’s Elements. 228. Or terms (horoi). This whole discussion of what Aristotle means by saying that mathematical principles are finite (peperasmenon) is infected by the introduction of the word ‘definite’ (hôrismenon) and the related words ‘define’ and ‘definition’. 229. Placing the accent on the second rather than the first syllable of posoi.

Notes to pages 85-87 b

d

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230. cf. chapter 2, 244b5 -5 with the note on 244b5-5d in Ross (1936). 231. cf. 6, 445b20-446a20. Simplicius gives a rather abstract representation of Aristotle’s argument, which is roughly that perceptible qualities occur as opposites or extremes (e.g. white/black, sweet/bitter) and intermediates between them, and that, although the intermediates constitute a continuum, there are only finitely many perceptibly different intermediates. 232. Simplicius omits the conclusion: elements are finite in kind. 233. Chapter 4, 187a26-188a18. 234. This is not a point stressed by Aristotle, but Simplicius finds it in 188a2-5, which he calls (in Phys. 171,31-2) the strongest refutation of the apparent meaning of Anaxagoras’ position. 235. It is hard to see how this statement can be true, since if there are not infinitely many things (e.g. elements), there can’t be infinitely many kinds of things; cf. 614,19-23 with the note. 236. This is the first part of fragment 1 of Anaxagoras (DK59); for the fragments of Anaxagoras I use the versions of Sider, which preserves the numbering of DK. In this case Simplicius’ text of Anaxagoras differs from Sider’s only in having mikrotêta where Sider has smikrotêta. Simplicius quotes the whole of the fragment at 155,26-30 of in Phys.; for the extent of the quotation see Sider, pp. 75-6. 237. These are the last words of fragment 4b. Simplicius’ text differs from Sider’s only in having en sumpanti where Sider has en tôi sumpanti. The whole fragment is pieced together from two citations in in Phys. at 34,21-6 and 156,4-9. 238. For this interpretation of Anaxagoras see also in Phys. 165,30-166,2 and 174,4-18. 239. Anaxagoras fragment 7, preserved only here. 240. A version of a small part of Anaxagoras fragment 12, almost the whole of which is quoted by Simplicius at in Phys. 156,13-157,4; for numerous other quotations of parts of the fragment in that commentary see Sider, p. 125. The citation here differs from the version printed by Sider only in having apokrinomena where Sider prints apokrinomena kai diakrinomena. And Simplicius’ partial quotation distorts the grammar of what Anaxagoras wrote. 241. Having defended Anaxagoras against Aristotle’s charge that he made the elements literally infinite, Simplicius now offers a Neoplatonist interpretation of Anaxagoras. 242. What follows is the beginning of Anaxagoras fragment 4a. Simplicius quotes the whole fragment at in Phys. 34,29-35,9. 243. Sider has ‘colours and tastes’. 244. Simplicius omits a ge printed by Sider. 245. Simplicius has sunôikêmenas, where Sider ‘after much hesitation’ prints sunêmmenas. 246. Simplicius omits a te autoisin printed by Sider. 247. Reading the epallaxei of several MSS of Aristotle rather than the peripallaxei printed by Moraux, although it is found in no MSS. For discussion see McDiarmid (1958). 248. This claim appears to be derived from Phys. 4.7, 213b22-7, where Aristotle says that according to the Pythagoreans the void distinguishes the nature of numbers. In his comment (in Phys. 652,4-6) Simplicius speaks of distinguishing the monad from the dyad and the dyad from the triad; cf. in Phys. 880,22-3. 249. Simplicius does not comment on this last clause or the word panspermia (‘universal seedbed’). Aristotle apparently means that earth, water and ‘the rest’ contain atoms of a variety of shapes.

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Notes to pages 87-95

250. Simplicius explains Alexander’s view that the present lemma is an (incompletely expressed) objection to atomism. Starting at 611,4 Simplicius presents his own view that Aristotle is here explicating, not attacking, atomism; rather his refutation begins in the next lemma, and, in particular, his refutation of the doctrine set out in the present lemma starts at 303a24. 251. It is not clear to me why this should be true. There is no obvious connection between the shape of, say, fire atoms and the shape of fire. 252. The text is problematic here. I have tried to translate Heiberg’s suggestion that the autôn of A and the autou of D and E might be hôn. 253. Simplicius quotes 303a17 in the next lemma and then 303a24-5 in the same lemma. 254. Moraux prints skhêmatôn here. It is clear that Simplicius (611,23-7) and Alexander (612,1) read sômatôn. 255. cf. 302b20-30 (605,21) and 302b30-303a3 (607,22). 256. For the references see 608,1-3 with the notes. 257. Simplicius reads the conditional of the second argument as ‘if the differentiae in kind of composite bodies are not infinite, neither are the elements (= atoms) infinite (in kind)’, that is, roughly, if differences in shapes of the atoms are supposed to explain qualitative differences in composites, the atoms don’t have to have infinitely many different shapes. Alexander apparently offered two interpretations of the conditional, both based on the claim that ‘bodies’ here means elements, that is, primary things, and on the idea that for the atomists the differentiae of elements are shapes. Alexander’s first interpretation is not clear to me since it only seems to say that differences of shapes won’t produce qualitative differences. On the second reading the conditional goes together with Aristotle’s subsequent argument at 303a29-303b3 (613,7) that there are finitely many primary shapes, which should mean that there are finitely many elements. The last sentence in this paragraph suggests that Alexander was talking about infinity or finiteness in number, but nothing in the representation of his position makes reference to number as opposed to kind. At 614,19-23 Simplicius gives an unfortunate argument that what is finite in kind is also finite in number. 258. It is difficult to give a precise reference here. Heiberg gives 6.3-4. I think 6.1 is more likely. 259. 303a14-15 (610,12); see Simplicius’ discussion at 610,13-611,16. 260. Translating Heiberg’s suggestion of elegen rather than the elegon which he prints. 261. cf. 302b30-303a3 (607,21) with Simplicius’ discussion. 262. The construction can be visualised by dividing an orange into two halves and the halves into four quarters each. The eight segments obtained are, of course, not pyramids, but, as Simplicius says, ‘pyramidish’ (puramoeidês). 263. This argument has nothing to do with finiteness in kind, and could be used to show directly that nothing can be infinite in number: let C be an infinite class which has a as member; then C without a is infinite and a falls outside it. 264. I have outlined the argument of this chapter in an appendix on the argument of Cael. 3.5. 265. cf. 1.2, 268b14-26. 266. Translating the eis inserted by Heiberg. 267. Heiberg’s raised dot should be replaced by a comma. 268. Simplicius’ discussion of this paragraph starts at 617,22; he takes up the obscure last phrase at 618,10-619,31. 269. cf. 6, 5b11-29.

Notes to pages 95-103

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270. cf. 5.13, 1020a17-25. 271. cf. 303a10-16 in the preceding chapter (610,12). 272. i.e. the atoms. 273. I do not know who these people might be. 274. The remainder of the discussion of this lemma is about this obscure phrase. At 619,9 Simplicius, having giving three (not entirely clear) suggestions of Alexander about it, dismisses Alexander’s exegesis but confesses his own inability to understand what Aristotle means. 275. Here and in what follows ‘ratio of the lesser (or greater)’ and also ‘lesser (or greater) ratio’ seem to mean what we would represent by a fraction less (or greater) than 1. Alexander’s point here might be expressed by saying that there is always something greater (or less) than something which is greater (or less) than something. 276. The typographer has omitted a raised dot after periekhetai. 277. Alexander’s suggestion is that the lesser things are water, air, and fire, amounts of which, being less than earth, are ‘contained in it’. 278. For the next material see the appendix on 3.5. 279. cf. Tim. 56A7. 280. cf. 303b13-22 (615,24) with Simplicius’ discussion. 281. These are the atomists (cf. 303a12-14 in the preceding chapter (610,12)), although they did not make fire the only element. 282. See the next lemma. 283. For this argument see Aristotle, Posterior Analytics, 1.12, 77b40-78a2. 284. i.e. Timaeus. For arguments that the person whom Aristotle has in mind is Xenocrates see Cherniss (1944), pp. 143-4. 285. psêgma. For the association of Heraclitus with minima called psêgmatia or psêgmata see ‘Aetius’ (Diels (1879)), 1.13.2. Cherniss ((1935), p. 14) assumes that Aristotle is here talking about Heraclitus, an assumption which Simplicius does not even consider. 286. Alexander is thinking specifically of gold shavings. 287. cf. 303a20-3 in the preceding chapter (611,17). 288. cf. 303a8-10 in the preceding chapter (609,13). 289. Apparently this means that, e.g. the magnitude of the total mass of air is to that of the total mass of water as the magnitude of the atomic ‘element of air’ is to that of the atomic ‘element of water’. It is never made clear what this means or why it should be true. 290. At 303b24-6 in the previous chapter (616,21). 291. An attempt to prop up Aristotle’s loose way of talking about quantities in this part of Cael. 292. Alexander imagines a theory in which the change of earth, water, air, and fire into one another is explained by the change of their ‘elements’ into one another. 293. In the present lemma. 294. Simplicius considers only division into two parts. 295. The point is perhaps that nothing other than fire could result from a compounding of portions of fire. 296. cf. 620,11. 297. cf. 303b25-7 (616,21). For Simplicius Aristotle is here criticising the view he set out at 304a18-21 (621,12), where he spoke of ‘finest parts’. 298. cf. 303a10-16 (610,12) and 303b22-304a7 (616,21) with Simplicius’ discussion. 299. An assumption Simplicius has rejected at 619,9-31.

138

Notes to pages 105-114

300. cf. chapter 3, 302b5-9 (604,1), where Aristotle infers the existence (but not the number) of simple bodies from the simple motions. 301. cf. 629,2-5. 302. It seems more likely that Aristotle simply means that a body will be dissolved or composed one part at a time. 303. With this discussion of Empedocles see Wright (1981), pp. 36-40. 304. With this paragraph see also 612,10-21. 305. I have translated the ‘really unclear’ text which Simplicius read. At 630,1-5 Simplicius, following Alexander, proposes to insert the words ‘comes to be in something, and’ here. Modern editors have followed this suggestion. 306. Simplicius supplies an argument to rule out a fourth alternative not considered by Aristotle: that something might come to be from itself. 307. As Aristotle does in the next lemma. 308. Here Simplicius presupposes the insertion which he describes in the next paragraph. 309. The whole heaven not being in place. 310. Simplicius refers to Phys. 4.6, 213b4-15. See his comment on that passage (in Phys. 649,4-650,14). See also his comment on Phys. 4.1, 209a4-7 (in Phys. 529,29-530,30). And for a general discussion of the issue raised here see Sorabji (1988), pp. 60-122. 311. I am not sure what Simplicius is thinking here. Perhaps it is that what is incorporeal could not occupy a place. 312. cf. Phys. 4.8. 313. i.e. some other body; see 305a31-2. 314. Simplicius skips over 305a26-9 (‘for a thing … elements’); he returns to these words in the next paragraph. 315. That is, when Aristotle says ‘move in it’ (en toutôi) he means ‘move to it’ (epi touton). 316. The kata topon of D, E, and Karsten seems preferable to the kata ton topon (presumably something like ‘move with respect to that place’) of A, which Heiberg prints. 317. cf. 305a16-21 (629,6). 318. Aristotle does not mention Anaxagoras in the discussion which follows, but Simplicius takes him to be arguing specifically against Anaxagoras at 305b20-8 (635,1); see his discussion of that passage. 319. Translating the toiaisde of D rather than the toiôsde printed by Heiberg. 320. Translating Karsten’s hotan d’ rather than the ei oun, hotan, printed by Heiberg. 321. That is, air which actually exists in a mixture should not occupy more space when it is extracted from the mixture, but something which is only potentially air might occupy more space when it becomes actually air. 322. In the last sentence of the lemma. 323. At 305b5-10 in the preceding lemma (631,29). 324. in Phys. 4.8. 325. The distinction between the separate void and the interspersed void (to paresparmenon kenon) is roughly the distinction between empty space outside of bodies and empty spaces inside them. Arguments that motion would be impossible without a void (cf., e.g., Phys. 4.6, 213b4-15) are taken to invoke a separate void, arguments that a void is required for condensation and rarefaction or nutrition and growth (cf., e.g., Phys. 4.6, 213b15-22) an interspersed void. See, for example

Notes to pages 114-115

139

in Phys. 683,1-4. The explicit distinction may go back to Strato of Lampsacus, on whom see Furley (1985). 326. cf. 4.3, 309a19-21 with the note on 686,14 in Mueller (2009). 327. Simplicius distinguishes between the targets of the first and second sentences of 305b16-20: without a void Empedocles and Anaxagoras cannot explain why when water changes to air the volume of air is greater than that of the water because they think that the air was actually in the water; and Democritus’ void cannot explain why air atoms move farther apart when they are separated from water. 328. cf. chapter 4, 187b22-188a2. 329. perigegrammenôn. Simplicius’ treatment of infinite division is surprisingly sophisticated in this passage. He is aware that the division of a finite magnitude into finite portions can go on forever (that is ‘to infinity’), but he accepts Aristotle’s view that such a division can never be completed (that is, the number of divisions can never be ‘actually infinite’). Following Aristotle, Simplicius thinks of such division as a matter of marking off previously unmarked portions of a continuous magnitude. But, according to Simplicius, this sort of division isn’t relevant to Anaxagoras’ separation since what is separated is already marked out in the original whole. 330. I have translated the hê which appears in D and as a Bessarion insertion. Heiberg prints ontôs with A; he reports that E and F have nothing.

Bibliography Ackrill, J.L. (trans.) (1963), Aristotle’s Categories and De Interpretatione, Oxford: Clarendon Press. Adler, Ada (ed.) (1930), Suidae Lexicon, pt. 4, Leipzig: Teubner. Allan, D.J. (1936), Aristotelis De Caelo Libri Quattuor, Oxford: Clarendon Press. Baltes, Matthias (1972), Timaios Lokros, Über die Natur des Kosmos und der Seele (Philosophia Antiqua, 21), Leiden: E.J. Brill. Barnes, Jonathan (1982), The Presocratic Philosophers, London: Routledge and Kegan Paul. Bergk, Theodor (1843), De Aristotelis Libello Xenophane, Zenone, et Gorgia, cited after Peppmüller (1886). Bergk, Theodor (1883), Fünf Abhandlungen zur Geschichte der Griechischen Philosophie und Astronomie, Leipzig: Fue’s Verlag. Bossier, F. (ed.) (2004), Simplicius, Commentaire sur le Traité du Ciel d’Aristote, Traduction de Guillaume de Moerbeke, vol. 1 (Corpus Latinum Commentariorum in Aristotelem Graeca, 8.1), Leuven: Leuven University Press. Brennan, Tad and Brittain, Charles (trans.) (2002), Simplicius: On Epictetus Handbook 27-53, London: Duckworth. Brittain, Charles and Brennan, Tad (trans.) (2002), Simplicius: On Epictetus Handbook 1-26, London: Duckworth. Bruns, Ivo (ed.) (1892), Alexandri Aphrodisiensis Scripta Minora, Quaestiones, De Fato, De Mixtione (Supplementum Aristotelicum 2), Berlin: Reimer. Cherniss, Harold (1935), Aristotle’s Criticism of Presocratic Philosophy, Baltimore: Johns Hopkins University Press. Cherniss, Harold (1944), Aristotle’s Criticism of Plato and the Academy, Baltimore: Johns Hopkins University Press. Diehl, Ernst (ed.) (1903-6), Procli Diadochi in Platonis Timaeum Commentaria, 3 vols, Leipzig: Teubner. Diels, Hermann (ed.) (1879), Doxographi Graeci, Berlin: Reimer. Düring, Ingemar (1957), Aristotle in the Ancient Biographical Tradition (Studia Graeca et Latina Gothoburgensia 5), Göteborg: Elander. Furley, David (1985), ‘Strato’s theory of the void’, in Jürgen Wiesner (ed.), Aristoteles Werk und Wirkung, vol. 1, Berlin and New York: Walter de Gruyter, 1985, 594-609, reprinted in Furley (1989), 149-60. Furley, David (1989), Cosmic Problems, Cambridge, England: Cambridge University Press. Guldentops, Guy (2005), ‘Plato’s Timaeus in Simplicius’ In De Caelo. A confrontation with Alexander’, in Leinkauf and Steel (eds) (2005), 195-212. Hadot, Ilsetraut (1990), ‘The life and work of Simplicius in Greek and Arabic sources’, in Sorabji (ed.) (1990), 275-303. Hadot, Ilsetraut (2002), ‘Simplicius or Priscianus ?’, Mnemosyne 4.55, 159-99. Hagen, Charles (trans.) (1994), Simplicius: On Aristotle Physics 7, London: Duckworth.

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English-Greek Glossary This glossary is derived from the Greek-English Index and gives standard Greek equivalents for many nouns, verbs, adjectives, adverbs, and a few prepositions in the translation. It does not include equivalents for most Greek words which are used only once by Simplicius or words which have no relatively simple equivalent in English. The reader will get a better sense of the range of a Greek word by looking at the Greek-English Index for the word and ones closely related to it. able: dunatos above: anô absolutely: haplôs absurd: apemphainôn atopos accept: apodekhesthai, dekhesthai, enkrinein, sunkhôrein accident: sumbebêkos accidentally: kata sumbebêkos acknowledge: sungignôskein act (v.): energein act together with: sunergein acted on, be: paskhein activate: energein actuality: energeia add: epagein, epipherein, prostithenai addition: prosthesis adduce: epagein, paragein adequate: hikanos affected easily: eupathês affection: pathos, pathêma affective: pathêtikos agree: homologein air: aêr alter: alloioun alter together: sunalloioun alteration: alloiôsis alternation: enallax always: aei amateurish: idiôtikôs angle: gônia animal: zôion antecedent: hêgoumenon appearance: emphasis approach: plêsiazein appropriate: oikeios appropriate, be: prosêkein argue: epikheirein, sullogizesthai argument: epikheirêma, epikheirêsis

ascend: anabainein ascribe: anapherein, anatithenai ask: erôtan, zêtein assign: apodidonai, protithenai assume: hupolambanein, lambanein assume in advance: prolambanein assume to start: prolambanein assumption, additional: proslêpsis atemporally: akhronôs atom: atomos attach: prosaptein avoid: diapheugein, pheugein aware, be: eidenai awareness: sunaisthêsis axiom: axiôma base: basis beautiful: kalos begin: arkhesthai beginning: arkhê belief: doxa, pistis believable: pistos belong: huparkhein beloved: philos between: metaxu black: melas blend (v.): sunkrinein blending (n.): krasis, sunkrisis body: sôma bone: ostoun book: biblion bounded: peperasmenos breadth: platos breadthless: aplatês briefly: suntomôs bring in: paragein bring in against: prosagein bulk: onkos

144

English-Greek Glossary

call (v.): kalein categorically: katêgorikôs causal: parasunaptikos cause: aitia, aition cease: pauein censure (v.): aitiasthai, enkalein centre: kentron, meson change (intrans.): exallattesthai, kineisthai, metaballein change (trans.): kinein change (n.): kinêsis, metabasis, metabolê characterise: kharaktêrizein choose: hairein, prokheirizesthai circle: kuklos circle, moving in a: kuklophorêtikos circular: peripherês circumscribe: perigraphein clarify: saphênizein clear: enargês, dêlos, saphês clearly true: enargês cold (adj.): psukhros cold (n.): psuxis coldness: psukhrotês colour: khrôma colourless: akhrômatos combine: sunistanai come to be: gignesthai come to be in: engignesthai coming to be (adj.): genêtos coming to be (n.): genesis coming to be, not: agenêtos commensurable: summetros common: koinos common thing: koinotês comparable: sumblêtos compare: paraballein compel: anankazein complete (adj.): teleios complete (v.): sumperainesthai, sumplêroun completely: pantelôs compose: sunistanai, suntithenai composite: sunthetos composition: sunthesis compounding: sunthesis compress: pilein conception: ennoia, prolêpsis conclude: sumperainesthai conclusion: epiphora condensation: puknôsis condense: puknoun condition: diathesis, katastasis confirm: paristanai, pistousthai

confirmation: pistis conflict, be in: makhesthai connect: sunaptein connective: sundesmos consequence: akolouthon consider: nomizein constrain: biazesthai constrained: biaios constraint: bia construct: kataskeuazein, sunistanai, suntithenai construction: sustasis contact (n.): aphê contain: khôrein contained in, be: eneinai continuous: sunekhês contract: sustellein contradiction: antiphasis, enantiologia contrariety: enantiôsis contrary: enantios, hupenantios contribute: suntelein coordinate (adj.): sustoikhos corporeal: sômatikos correct: orthos correct, be: katorthoun correctly: hugiôs, kalôs cosmos: kosmos cosmos, to make the: kosmopoiein credence, give: pistousthai criticise: euthunein cubical: kubikos cure (v.): hugiazein cut (v.): temnein dark: melas deal with: hupantan dear: philos define: horizein definition: horos demiurgic: dêmiourgikos demonstrate: apodeiknunai demonstration: apodeixis dense: puknos denseness: puknotês depth: bathos depthless: abathês derivative from, be: paruphestêkenai describe: diêgeisthai, historein destroy: phtheirein destroyed easily: euphthartos destruction: phthora determine: diorizein develop: sunagein diagonal: diametros

English-Greek Glossary differ: diapherein difference: diaphora different: allos, diaphoros, heteros differentia: diaphora difficult: duskherês difficulty: aporia, duskhereia difficulty, raise a: aporein directly: prosekhôs disagree: diapherein disagreement: diaphônia disclose: ekphainein discord: diaphônia discordant: plêmmelos discrete: diôrismenos discuss: dialegein, hupantan, prokheirizesthai disorder: ataxia disordered: ataktos dissimilar: anomoios dissolution: dialusis dissolve: dialuein distance: diastêma distinction: diorismos distinguish: antidiairein, diairein, diakrinein, diistanai, diorizein divide: diairein, dialambanein, diistanai divine: theios divisible: diairetos division: diairesis, tomê doctrine: areskon, theôria dominance: epikrateia dominate: epikratein, kratein down: katô earth: gê easy: hetoimos, prokheiros elaborate: kompsos element: stoikheion elements, composed of: stoikheiôtos empty: kenos end (n.): peras, telos end, come to an: katalêgein endure: diamenein, hupomenein, menein enquire: zêtein enquiry: historia entire: holos entirety: holotês entitle: epigraphein entity: phusis equal: isos equilateral: isopleuros establish: kataskeuazein

eternal: aidios ether: aithêr ethereal: aitherios evaporated: araioumenos, exaerizomenos evidence: tekmêrion evident: phaneros, prophanês example: paradeigma exceed: huperekhein excess: huperokhê exist: huparkhein exist previously: prohuparkhein expand: epekteinesthai expansion: epektasis expel: ekballein explain: aitiasthai, aitiologein, apodidonai, apologizesthai, didaskein, exêgeisthai explanation: aition extreme: eskhatos eye: ophthalmos face: prosôpon fair wind, produce a: sunepourizein fast: takhus fellow citizen: politês few: oligos fewer: elattôn fewest: elakhistos figure: skhêma figure, assign a: skhêmatizein figure, without: askhêmatistos find: heuriskein fine: leptos fine parts, having: leptomerês fineness: leptotês finite, be: peperanthai fire: pur first: prôtos fit (v.): epharmozein, harmozein flesh: sarx flow (v.): rhein follow: akolouthein, hepesthai, sumbainein foot: pous force: anankazein forced: biaios form: eidos, idea form, give: eidopoiein frequently: pollakis full: plêrês fundamental: arkhoeidês fused together: sumphusômenos general: koinos

145

146

English-Greek Glossary

generally: katholou generate: gennan generation: genesis generative: gennêtikos genus: genos geometrical: geômetrikos give out: epileipein, hupoleipein god: theos gold: khrusos good: kalos great: megas half-triangle: hêmitrigônon happen: prosgignesthai hard: sklêros harm (v.): adikein harsh: sklêros hear: akouein heat (n.): thermotês heat (v.): thermainein heaven: ouranos heavenly: ouranios heavens: ouranos heaviness: barutês heavy: barus higher: anôthen homoiomereity: homoiomereia homoiomerous: homoiomerês horizon: horizon hot: thermos human being: anthrôpos hypernatural: huper phusin hypothesis: hupothesis hypothesise: hupotithenai hypothetical: hupothetikos ill: nosôn immediately: euthus imperceptible: anaisthêtos imperishable: aphthartos impossible: adunatos impulsion: rhopê include: perilambanein incorporeal: asômatos increase (v.): auxein indeterminate: aoristos indicate: dêloun, emphainein, endeiknusthai, epideiknunai, hupodeiknunai indissolvable: adialutos indivisible: adiairetos, atomos induction: epagôgê infer: sullogizesthai, sunagein infinite: apeiros

infinity: apeiria inhere: enuparkhein, huparkhein en insofar as: kath’ ho, kath’ hoson instant: to nun insufficient, be: hupoleipein intellectual: noeros intelligible: noêtos interchange (v.): ameibesthai intermediate: mesos, metaxu interpret: exêgeisthai interpretation: exêgêsis interpreter: exêgêtês interspersed: paresparmenos intervention: paremptôsis introduce: epagein, paratithenai investigate: episkeptesthai, skeptesthai, skopein, theôrein investigate also: prostheôrein investigation: theôria invisible: aoratos isosceles: isoskelês join: sunaptein, suntattein join together: sunartan keep: phulattein kind: eidos know: eidenai, epistasthai, gignôskein, gnôrizein knowledge: epistêmê, gnôsis large: megas large parts, having: megalomerês largeness: megethos last: eskhatos later: husteros lay next to: epitithenai least: elakhistos leave out: paraleipein left over, be: hupoleipesthai length: mêkos lesser: elattôn light: kouphos, leukos lightness: kouphotês limit (n.): peras limit (v.): peratoun line: grammê living thing: zôion Love: Philia, Philotês magnitude: megethos maintain: axioun man: anêr mass: onkos

English-Greek Glossary material: enhulos mathematical: mathêmatikos mathematics: mathêmata matter: hulê meaning: ennoia meaning, apparent: phainomenon medicine, art of: iatrikê meet: tunkhanein mention: hupomimnêskein, mnêmoneuein mind: nous mistake: hamartêma mix: mignunai mixed: miktos mixture: migma, mixis mode: tropos monad: monas motion: kinêsis, phora move (intrans.): ienai, pheresthai, kineisthai move (trans.): kinein moved easily: eukinêtos multiple: pollaplasios name: onoma natural: eikos, phusikos, phusei, kata phusin natural philosopher: phusiologos nature: phusis nature, doctrine of: phusiologia nature, student of: phusikos nature, study: phusiologein necessary: anankaios necessity: anankê need (v.): deisthai new: kainoprepês next: ephexês, loipon nourishment: trophê novel: kainoprepês number: arithmos object (v.): hupantan objection: enstasis observe: theôrein obvious, be: phainesthai obviously: dêlonoti occupy: epekhein, katalambanein, katekhein often: pollakis one: monas only: monos opinion: doxa opposite, be: antikeisthai opposition: enantiôsis

147

order (n.): taxis order (v.): diakosmein, tattesthai ordering: diakosmêsis outermost: eskhatos own, one’s: idios part: meros, morion particular: kata meros, kath’ hekaston partless: amerês pass over: paraleipein, parienai pentagon: pentagônon per se: kath’ hauto, kath’ hautên perceptible: aisthêtos perception: aisthêsis perhaps: isôs periphery: perix perish: phtheiresthai perishable: phthartos perishing (adj.): phthartos perishing (n.): phthora persuasive: pithanos phenomena: phainomena philosopher: philosophos philosophise: philosophein philosophy: philosophia phrase: lexis physician: iatros place (n.): topos place (v.): tithenai plane: epipedon plant: phuton Platonic: Platônikos plausible: eikos, pithanos point: sêmeion, stigmê point out: ephistanein portion: morion posit: tithenai position: thesis possible: dunatos possible, be: endekhesthai, eneinai posterior: husteros postulate: aitêma potentiality: dunamis potentially: dunamei power: dunamis precise: akribês precision: akribeia pre-contain: prolambanein present, be: prokeisthai preserve: sôzein, phulattein pressed together, be: sumpileisthai presumably: isôs prevail: kratein prevent: kôluein

148

English-Greek Glossary

previous: proteros prima facie clear: prodêlos primary: prôtos principle: arkhê prior: proteros prior, be: prohuparkhein proceed: badizein, ienai, proienai, prokhôrein produce: huphistanai, parekhein proemium: prooimion proper: oikeios proportion: analogia proportional: analogos propose: protithenai proposition: axiôma prove: deiknunai pupil: hetairos purpose: skopos push: epôthein, ôthein push along: sunepôthein push out: exôthein pyramid: puramis pyramidish: puramoeidês qua: hêi quality: poion, poiotês qualityless: apoios quantity: poson question, raise the: ephistanein rare: manos rarefaction: manôsis rarefy: manoun, khein rareness: manotês reality: hupostasis reason: aitia, aition reasonable: eikos, eulogos recall: hupomimnêskein receive: dekhesthai, tunkhanein recent: neos recognise: enidein, ennoein recount: historein rectilinear: euthugrammos reduce: apagein reductio ad impossibile: apagôgê eis adunaton refer: anapherein, apoteinesthai refutation: antilogia, elenkhos refute: antilegein, dielenkhein, elenkhein region: topos reject: ekballein relation: skhesis

remain: hupoleipesthai, kataleipesthai, leipesthai, menein remaining: loipos report (v.): historein require: deisthai resemble: eoikenai reservoir: angeion resistance: antitupia resolution: analusis resolve: analuein, luein rest (n.): êremia, monê rest (v.): êremein result (v.): sumbainein right: orthogônios room: khôra rule (n.): epikrateia rule (v.): epikratein scalene: skalênos, promêkês science: epistêmê scientific: epistêmonikos see: horan, idein, theasthai seed: sperma seek: epizêtein, zêtein seem: eoikenai segment: tmêma self-moving: autokinêtos separate (v.): aphistanai, apokrinein, diakrinein, diistanai, khôrizein separate out: ekkrinein separation: diakrisis separation out: ekkrisis set down: tithenai set out: ektithesthai, paradidonai, paratithenai shape: skhêma shape, give: skhêmatizein shape, without: askhêmatistos share (v.): metekhein sharp: tmêtikos shavings: psêgma shorter: elattôn show (v.): deiknunai side: pleura sign: sêmeion, tekmêrion similar: homoios similarity: homoiotês simple: haplous simply: haplôs sinew: neuron single out: eklegesthai sink down: huphizanein sink to the bottom: huphistanai size: megethos

English-Greek Glossary small: mikros, oligos small parts, having: mikromerês smaller: elattôn smallness: mikrotês soft: malakos solid: stereos soul: psukhê space: khôra, topos speak against: anteipein species: eidos specific: idios specify: horizein spermatically: spermatikôs sphere: sphaira spherical: sphairikos, sphairoeidês spreading (n.): khusis square: tetragônon stand (v.): histanai star: astêr, astron stone: lithos stop (v.): histanai straight line: eutheia straight line, move in a: euthuporein straightaway: euthus strict sense, in the: kuriôs Strife: Neikos study (n.): pragmateia subject, be a: hupokeisthai subject to, be: paskhein sublunary: hupo selênên, huposelênos substance: ousia substratum, be a: hupokeisthai subtract: aphairein suffice: arkein sufficient: hikanos suitable: epitêdeios suitable, be: harmozein supply: parekhein surface: epiphaneia sweetness: glukutês syllogism: sullogismos syllogism, produce a: sullogizesthai symbolically: sumbolikôs symmetry: summetria tacitly: dunamei take: lambanein, metalambanein, paralambanein take up: epilambanein teach: didaskein text: lexis thick: pakhus thick parts, having: pakhumerês thickness: pakhutês

thing: pragma, khrêma think: nomizein, oiesthai thought: epinoia time: khronos together: homou touch (n.): aphê transcend: exêirêsthai transfer: metapherein transform: metalambanein transmit: paradidonai treatise: pragmateia, sungramma triangle: trigônon true: alêthês trustworthy: pistos truth: alêtheia try: peirasthai turn (v.): trepein, metabainein turn out: sumbainein turn to: metienai unaware, be: agnoein unchanging: akinêtos, ametablêtos unclear: asaphês undergo: hupomenein, paskhein underlie: hupokeisthai understand: akouein, eidenai, ekdekhesthai, gignôskein, gnôrizein, noein undisputed: anamphilektos unification: henôsis unify: henoun unite: henoun unity: henôsis universally: katholou universe: to pan unknowable: agnôstos unmoving: akinêtos unnatural: para phusin unreasonable: alogos up: anô use (v.): khrasthai, khrêsthai use also: proskhrêsthai variegated: poikilos vertex: koruphê vessel: angeion view (n.): doxa view (v.) theasthai void: kenos wander: planasthai, plazesthai water: hudôr way: tropos weave together: sumplekein

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English-Greek Glossary

weaving together (n.): sumplokê weight: baros weightless: abarês well: kalôs white: leukos whole: holos

withdraw: hupeikein wood: xulon word: onoma, rhêma words: lexis, rhêta write: graphein

Greek-English Index This index, which is based on Heiberg’s text with my emendations, gives the English translations of many nouns, verbs, adjectives, and some adverbs used by Simplicius; certain very common words (e.g. einai, ekhein, legein) and number words are omitted, as are words which only occur in quotations (or apparent quotations) of other authors. When a word occurs no more than ten times, its occurrences are listed; in other cases only the number of occurrences is given. Occurrences in lemmas and as part of a book title are ignored. Sometimes comparatives, superlatives, and adverbs are included under the positive form of an adjective, sometimes they are treated separately. There is a separate index of names. abarês, weightless, 18 occurrences in Simplicius, 7 in Aristotle abathês, without depth, 562,27; 563,33; 568,9; 578,28.30 (both Alexander); 579,3 adiairetos, indivisible, 33 occurrences in Simplicius, 8 in Aristotle; see also atomos adialutos, indissolvable, 627,5 adikein, to harm, 570,9-11(4) adunatos, impossible, 59 occurrences in Simplicius, 23 in Aristotle aei, always, 28 occurrences in Simplicius (1 Melissus), 8 in Aristotle aêr, air, 123 occurrences in Simplicius (18 Alexander, 1 Melissus, 1 TL, 1 Plato), 21 in Aristotle agathotês, goodness, 587,20 agenêtos, not coming to be, 24 occurrences in Simplicius (1 Parmenides), 4 in Aristotle agnoein, to be unaware, not know, 559,27; 606,29 agnôstos, unknowable, 606,31; 608,25.28 agônizesthai. to do battle, 588,3 aidios, eternal, 15 occurrences in Simplicius (1 Melissus, 1 Alexander), 2 in Aristotle aidiotês, eternity, 628,3 aisthanesthai, to perceive, 578,1

aisthêsis, perception, 612,14.19 (both with 303a23); 613,11; 633,22 aisthêtos, perceptible, 38 occurrences in Simplicius, 4 in Aristotle aitêma, postulate, 607,6.19 aithêr, ether, 559,23 (Parmenides); 603,22 (with 302b4) aitherios, ethereal, 552,2; 553,17 aitia, reason, cause, 17 occurrences in Simplicius, 0 in Aristotle; see also aition aitiasthai, to censure, make responsible, explain, 565,16; 589,27; 590,26; 634,11 (Alexander) aitiologein, to offer explanations, 564,26; 576,15 aition, cause, reason, explanation, 12 occurrences in Simplicius (1 Alexander), 1 in Aristotle; see also aitia akhrômatos, without colour, 599,9.10 akhronôs, atemporally, 579,9.11 akinêtos, unchanging, unmoving, 17 occurrences in Simplicius, 3 in Aristotle akolouthein, to follow, be a consequence, 36 occurrences in Simplicius (2 Alexander), 1 in Aristotle akolouthia, translated using the verb ‘follows’, 623,17 akolouthon, consequence (567,27); next (626,18)

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akolouthôs, next, 600,6 akouein, to hear, understand, 15 occurrences in Simplicius (2 Melissus, 1 Parmenides, 1 Alexander), 0 in Aristotle akribeia, precision, 562,31; 566,18 akribês, precise, 582,23; 606,11.14; 612,19; 629,9 akribologeisthai, to speak precisely, 570,16 alêtheia, truth, 555,25; 556,13; 557,23.26 (Parmenides); 558,6 (Parmenides) (all 5 with 298b13); 566,15 (Plato); 589,17; 597,27; 609,23 alêthês, true, 14 occurrences in Simplicius (3 Melissus, 1 Parmenides, 1 Alexander) alloiôsis, alteration, qualitative change, 553,27 (with 298b1); 601,9; 603,3; 623,13 (Alexander) alloioun, to alter (active), 553,27(2) alogos, unreasonable, 565,26; 634,6.12 (Alexander).29 (all 3 with 305b18); also 304a9 and 305b6 ameibesthai, to interchange, 598,9; 599,20 amereia, partlessness, 577,28 amerês, partless, 562,30; 563,4; 612,16; 622,6 ametablêtos, unchanging, 628,10 amiktos, unmixed, 587,25 amphidoxein, to doubt, 579,9 amphisbêtêsimos, to be debated, 601,6 (with 302a17) anabainein, to ascend, 563,7; 564,26; 576,16 anagein hupo, to place under, 617,8 anairein, to do away with, 27 occurrences in Simplicius, 5 in Aristotle anaisthêtos, imperceptible, 603,21; 606,7.9 anaitios, inexplicable, 572,9 analambanein, to return to, 596,19 analloios, not undergoing alteration, 552,12 analogein, to be analogous, 613,32 analogia, proportion, 576,18; 579,17; 620,19.20 (both Alexander) analogos, proportional, 566,16 (Plato); 577,18 (with 300a2); also 304a26 analuein, to resolve, 561,4.29;

563,29; 578,12 (with 300a11(2)); 613,22; 616,10(2).11.19 analusis, resolution, 577,23; 579,25; 616,6.9(2) anamignusthai, to be mixed with, 598,15 anamphilektos, undisputed, indisputable, 553,1; 555,24; 562,32 anankaios, necessary, 555,19.31; 576,1; 588,16 (with 301a1); 590,16 (with 301a19).31; 591,8; 606,30; 629,17; 10 other occurrences in Aristotle anankazein, to compel, force, 579,28; 591,12; 597,22; 599,30 anankê, necessity (usually translated using ‘necessary’), 80 occurrences in Simplicius (2 Alexander, 1 Plato), 34 in Aristotle anapherein, to refer, ascribe, 554,8; 566,26; 589,24; 604,18 anaphora, reference, 552,19 anaphôs, with no contact, 565,19 anaphuesthai, to grow out, 569,28 anastrephesthai, to be turned back, 588,6 anatithenai, to ascribe, 617,24 anatrepein, to overturn, 614,26 anemos, wind, 597,2 anepisêmantôs, without notice, 634,10 anêr, man, 557,21 (Parmenides); 566,12 (Plato); 573,3; 580,14 (Pythagorean saying); 602,7 anerkhesthai, to rise up, 565,28 angeion, reservoir, vessel, 632,22.24 (both with 305b4); 633,24 (with 305b15) anisotês, inequality, 565,22 anô, up, above, 24 occurrences in Simplicius, 2 in Aristotle anomoeidês, of different kinds, 635,16 anomoios, dissimilar, 566,13 (Plato); 606,15.26 anôthen, from above, higher, 566,12 (Plato); 581,31 anteipein, to speak against, 591,12; 609,16 antepikheirein, to make a different kind of argument, 614,29 anthrax, carbuncle, 602,9 anthrôpos, human being, 558,11 (Parmenides),25 (Melissus);

Greek-English Index 578,17; 589,10; 602,6; 609,8.9 (both Anaxagoras); 619,23 antidiairein, to distinguish, 594,25 antigraphê, copy of a text, 597,21 antikeisthai, to be opposite, 564,17; 586,13.14 antilambanesthai, to apprehend, 565,5 antilegein, to argue against, refute, 563,22; 575,27.31 antilogia, refutation, argument against, 562,2; 591,17; 611,12.15.20 antiphasis, contradiction, 572,11 antiphatikos, contradictory, 620,16 antistrephein, to convert, 570,12 antitupia, resistance, 567,15 aoratos, invisible, 565,9; 603,21 (with 302b3) aoristos, indeterminate, 586,18; 615,14.20 apagein, to reduce, 561,22; 563,10(2); 579,15; 588,15 apagôgê eis adunaton, reductio ad impossibile, 592,16 apathês, not undergoing passion, 552,12 apeiria, infinity, 605,25; 606,3.23; 608,19(2); 612,8; 627,29 (Alexander) apeiromegethês, infinite in magnitude, 608,16 apeiros, infinite, infinitely many, 172 occurrences in Simplicius (8 Alexander, 2 Anaxagoras,1 Melissus, 1 Plato), 32 in Aristotle; see also eis apeiron and ep’ apeiron apemphainôn, absurd, 563,2 aperilêptos, ungraspable, 608,25 aphairein, to subtract, take away, 11 occurrences in Simplicius (2 Alexander), 3 in Aristotle aphairesis, abstraction, 567,12 (with 299a16) aphê, touch, contact, 565,6; 609,20 aphistanai, to separate, 588,5 aphthartos, not perishing, imperishable, 10 occurrences in Simplicius (2 Alexander), 3 in Aristotle aphthonôs, without stinting, 615,16 aplatês, breadthless, 562,25.29; 578,30 (Alexander) apoblepein, to take into consideration, 615,23 apodeiknunai, to demonstrate, 13

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occurrences in Simplicius, 0 in Aristotle apodeixis, demonstration, 563,5; 568,21; 582,24; 592,1; 604,3; 607,20; 614,9 apodekhesthai, to accept, 589,30; 590,13; 597,24 apodidonai, to assign, explain, give, 13 occurrences in Simplicius (1 Alexander), 2 in Aristotle apoginôskein, to reject, 561,23 apogumnoun, to remove the clothing, 587,30 apoios, qualityless, 564,18; 565,3.23; 576,8; 579,5; 599,5 apokrinomenos, separated, 608,26.30 (both Anaxagoras); 632,18(2) apoleipein, to allow for, 628,11 apologismos, giving of an account, 566,4 apologizesthai, to explain, 562,1 apolusis, parting, 609,21 apopheugein, to escape, 610,11 apophthengesthai, to give voice to, 560,2 aporein, to raise a difficulty, 581,25; 622,24; 627,16 aporia, difficulty, 569,28; 570,2; 573,15; 581,28; 582,9; 627,20 aposkôptein, to say with banter, 561,31 apospômenos, detached, 595,1 apoteinesthai pros, to refer to, 634,32 apotrekhein, to run off, 597,32 apotunkhanomena, misfirings, 575,25 apsukhos, soulless, 552,10 araioumenos, evaporated, 571,8 (to) areskon, doctrine, 598,26; 600,20 arithmeisthai, to be numbered, 607,18 arithmos, number, 32 occurrences in Simplicius (2 Alexander), 5 in Aristotle arkein, to suffice, 566,3; 607,19; 615,20 arkhê, principle, starting point, beginning, 75 occurrences in Simplicius (3 Alexander, 2 Plato, 1 TL), 7 in Aristotle; other uses: ex arkhês, initial, 568,7; 577,16; 580,23; 591,17; 598,1; 600,6; tên

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arkhên, at all, initially, 581,15.16; 583,6; 634,8; en arkhêi lambanein, to beg the question, 626,28; 629,2 arkhesthai, to begin, 551,13; 559,21; 566,8 (Plato); 585,22; 608,21; also 301a13 arkhitektonikê, architecture, 563,7 arkhoeidês, fundamental, 565,8; 566,2; 576,5; 580,12; 613,20.22; 616,7 artêria, artery, 606,19 asaphês, unclear, 586,6; 630,3 askhêmatistos, without shape, without figure, 599,9.10; 621,28; 622,2 asômatos, incorporeal, 26 occurrences in Simplicius (3 Alexander), 3 in Aristotle asphalôs, carefully, 635,12 astêr, star, 552,6.7; see also astron astron, star, 552,9.17 (both with 298a25); 559,24 (Parmenides); see also astêr astronomos, astronomer, 565,30 asullogistos, asyllogistic, 620,16 ataktos, disordered, 28 occurrences in Simplicius, 5 in Aristotle ataxia, disorder, 586,19; 588,24.26 (both with 301a3); 589,17 (with 301a10) atelês, incomplete, 575,23 athroisma, collection, 603,20 atmêtos, uncut, 592,24 atmos, vapour, 633,2 atomos, indivisible, 53 occurrences in Simplicius (2 Alexander), 7 in Aristotle; the feminine hê atomos, used by Simplicius and Alexander (from the Epicurean hê atomos phusis) is usually translated ‘atom’. atopia, absurdity, 561,12 atopos, absurd, 45 occurrences in Simplicius (1 Alexander), 2 in Aristotle autarkês, sufficient, 602,32 autokinêtos, self-moving, 585,1.2-4 (4, all Alexander); 585,9 auxein, to increase (transitive), 575,3; see also auxesthai auxesthai, to expand, increase (intransitive), 565,17; 620,20 axiôma, axiom, proposition, worth, 553,3; 562,31; 569,2; 580,20; 607,19 axiopistos, trustworthy, 604,26

axioun, to maintain, think right, 557,22; 558,16; 564,19; 584,29; also 302b14.29 badizein, to proceed, 624,20 (with 304b8) baros, weight, 91 occurrences in Simplicius (1 Alexander), 32 in Aristotle barus, heavy, 115 occurrences in Simplicius, 24 in Aristotle barutês, heaviness, 17 occurrences in Simplicius, 0 in Aristotle basis, base, 573,8; 574,8.19; 613,30; 614,2.3 bathos, depth, 562,28; 563,31; 573,5; 578,28.30 (both Alexander); 579,3 bebathusmenos, having depth, 562,27 beltiôn, better, 606,27 (with 302b27) bia, constraint, 34 occurrences in Simplicius, 20 in Aristotle biaios, constrained, forced, 577,22; 584,11-19 (4 with 300b19); 619,11 biazesthai, to constrain, to be constrained, 582,8.24.25.29; 594,10; 596,11 biblion, book, 551,6.17; 552,1.4.7.19; 584,31; 600,21; 614,32 blaptesthai, to be hurt, 566,20 bôlos, clod of earth, 582,4 boulêsis, intention, 589,17 boulesthai, to mean, intend, wish, want, 12 occurrences in Simplicius (2 Alexander, 1 Plato), 8 in Aristotle brakhiôn, arm, 587,1 (Empedocles); 606,18 brakhulogia, brevity of formulation, 586,6 brakhus, brief, 630,22 deiknunai, to show, prove, 130 occurrences in Simplicius (4 Alexander), 4 in Aristotle deisas, afraid, 584,31 deisthai, to need, require, 554,26; 562,9; 598,18; 613,27 dekhesthai, to receive, accept, 578,26 (Alexander); 630,13 dêlonoti, obviously, 554,25; 571,5; 578,10; 584,30; 586,22; 592,19; 609,11; 617,6 dêlos, clear, 44 occurrences in

Greek-English Index Simplicius (1 Melissus), 12 in Aristotle dêlôtikos, indicative, 633,9 dêloun, to make clear, indicate, mean, 18 occurrences in Simplicius, 1 in Aristotle dêmiourgikos, demiurgic, 576,18; 578,13; 587,30; 588,6; 609,2 diabebaiousthai, to insist, 565,31 diaduesthai, to penetrate, 610,20 diairein, to divide, distinguish, 40 occurrences in Simplicius (1 Alexander), 7 in Aristotle diairesis, division, 10 occurrences in Simplicius, 0 in Aristotle diairetikos, dividing, 564,28 diairetos, divisible, 50 occurrences in Simplicius (1 Alexander), 12 in Aristotle diaitasthai, to treat, 576,19 diakaês, burning, 602,9 diakosmein, to put in order, 580,14; 590,3; 609,3 diakosmêsis, (cosmic) ordering, 558,8.16; 587,29; 608,31; 609,4 diakrinein, to separate, distinguish, 12 occurrences in Simplicius, 2 in Aristotle diakrisis, separation, 586,29; 587,19; 590,5 (2, both Alexander).27; 591,1; 632,4.7 diakritikos, separating, 564,28 dialambanesthai, to be divided, 558,20; 610,6; 634,29 dialegein, to take issue with, to discuss, 556,30; 598,6; 612,17 dialogos, dialogue, 561,11 dialuein, to dissolve, 28 occurrences in Simplicius (4 Alexander, 1 Plato), 6 in Aristotle dialusis, dissolution, 21 occurrences in Simplicius (2 Alexander), 5 in Aristotle diamenein, to endure, 634,3 (hê) diametros, diagonal, 574,19; 583,5 diapherein, to differ, disagree, 45 occurrences in Simplicius (1 Alexander), 10 in Aristotle diapheugein, to avoid, 620,7 (with 304a8) diaphônia, discord, disagreement, 555,32; 603,11 diaphora, difference, differentia, 33

155

occurrences in Simplicius (1 Alexander), 3 in Aristotle diaphoros, different, 565,7; 574,6; 632,3 diarthroun, to articulate, 566,18 diaskhêmatizesthai, to be given shape, 564,2 diaskopein, to investigate, 555,31 diastasis, separation, 585,18 (with 300b25) diastêma, distance, 28 occurrences in Simplicius, 0 in Aristotle diataxis, decree, 594,30 diathesis, condition, 584,14; 590,25 diatribein, to concern oneself, 555,26 diazôgraphein, to paint, 565,7 didaskein, to teach, explain, 551,13.17; 554,26; 558,4; 562,12 diêgeisthai, to describe, 602,7 dieinai, to pass through, 565,19 diêkein, to extend, 555,4 dielenkhein, to refute, 598,6; 612,17 dierkhesthai, to go through, 552,7; 583,4.7 (both with 300b5); also 298a27 diestôs, extended, 571,23 diexasmenos, dispersed, 571,6 diistanai, to separate, divide, distinguish, 561,1; 590,21 (with 301a14); 634,12 (Alexander); see also diestôs dikhôs, in two ways, 567,32; 568,24 (both with 299a20); 575,5 dinê, vortex, 583,1.2 (both with 300b3) diôrismenos, determinate, discrete, 14 occurrences in Simplicius (2 Alexander), 1 in Aristotle diorismos, distinction, 594,26 diorizein, to determine, distinguish, 11 occurrences in Simplicius, 7 in Aristotle; see also diôrismenos diplasios, double, 622,2 dôdekaedron, dodecahedron, 574,21; also 307a16 dokein, to seem, to be thought, 47 occurrences in Simplicius (2 Melissus, 2 Anaxagoras, 2 Alexander, 1 Parmenides, 1 Aristotle), 3 in Aristotle dokêsis, impression, 599,26 doxa, view, belief, opinion, 38 occurrences in Simplicius (1 Parmenides, 1 Alexander), 1 in Aristotle

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dran, to do, 578,14 drastêrion, active power, 615,23 dromos, race, 597,4 dunamei, potentially, tacitly, 19 occurrences in Simplicius (2 Alexander), 6 in Aristotle dunamis, power, potentiality, 59 occurrences in Simplicius (1 Plato, 1 Alexander), 7 in Aristotle; see also dunamei dunasthai, to be possible, able, 24 occurrences in Simplicius (3 Alexander, 1 Melissus), 2 in Aristotle dunatos, possible, able, 36 occurrences in Simplicius (1 Plato, 1 Alexander), 5 in Aristotle duskhereia, difficulty, 552,13 (Aristotle) duskherês, difficult, 622,1 (with 304a22) eidenai, to understand, know, be aware of, 566,12 (Plato); 582,8; 594,23; 600,14; 608,26 (Anaxagoras) eidopoieisthai, to be given form, 562,17; 576,12; 606,18 eidos, form, kind, species, 94 occurrences in Simplicius (9 Alexander, 1 Melissus, 1 TL), 5 in Aristotle eikos, plausible, reasonable, 560,21; 566,11 (Plato); 597,24; 619,20 eikotôs, reasonably, naturally, 11 occurrences in Simplicius, 0 in Aristotle eilikrinês, pure, 573,25 eis apeiron, ad infinitum, 583,3 (2 with 300b1 and 4); 585,23 (with 300b14); 593,23; 624,20.25 (both with 304b8) ekballein, to reject, expel, 576,2; 602,10 ekdekhesthai, to understand, 568,19; 610,14 ekkhôrein, to depart, 630,8 ekkrinesthai, to be separated out, 19 occurrences in Simplicius (3 Alexander), 5 in Aristotle ekkrisis, separation out, 19 occurrences in Simplicius, 2 in Aristotle eklegesthai, to pick out, single out, 566,8 (Plato); 626,27; 629,4

ekphainein, to disclose, 556,17; 558,18 ekteinesthai, to extend, 622,15 ektithesthai, to set out, 598,27; 609,27; 611,13.19; 626,25 ektrepein, to turn away from, 591,12 elakhistos, fewest, least, 606,29.31 (both with 302b28); 629,30 elattôn, fewer, lesser, smaller, shorter, 54 occurrences in Simplicius (21 Alexander), 11 in Aristotle elaunein, to drive, 597,5 elenkhein, to refute, 591,27; 600,10; 626,26 elenkhos, refutation, 560,3; 611,3 elleiptikôs, elliptically, 597,13 ellipês, elliptical, 597,23 emblepein, to look at, 599,25 emphainein, to indicate, 570,22; see also emphainesthai emphainesthai, to appear, 599,23 emphasis, appearance, 599,24.25 enallax, by alternation (mathematical term), 593,1.15 enantiologia, contradiction, 610,13 enantios, contrary, 26 occurrences in Simplicius, 2 in Aristotle; enantia legein translated ‘contradict’; see also hupenantios enantiôsis, contrariety, opposition, 603,24; 608,3.4 enapodein, to bind, 596,21 enargeia, clarity, 633,22; ek tês enargeias lambanein translated as ‘to assume as clearly true’ at 581,6.10; 582,2; 591,9; 633,27 enargês, clear, clearly true, 12 occurrences in Simplicius, 0 in Aristotle endeiknusthai, to indicate, 560,24; 584,3; 595,4; 608,25.31; 609,3; 614,8; 630,26 endeixis, indication, 565,26 endekhesthai, to be possible, 575,10 (with 299b24.29); 577,24-578,17 (6 (1 Alexander) with 300a11); 579,22 (with 300a13); 622,6 (with 304a24) endidonai, to bestow, 596,23 endoxon, common opinion, 612,18 (with 303a22) eneinai, to be possible, to be contained in, 590,3; 601,31-602,13

Greek-English Index (5 with 302a32); 608,24; 609,26 (both Anaxagoras) energeia, actuality, 573,22.27; 602,22 (with 302a24); 628,13; 632,22; 635,5; see also energeiai energeiai (dat.), actually, actual, 24 occurrences in Simplicius (3 Alexander), 3 in Aristotle energein, to act, be active, activate, 553,25; 578,13; 596,9.11.18.19 engignesthai, to come to be in, 564,17; 576,7 enhulos, involving matter, material, 564,1; 565,4; 573,5; 578,25 (Alexander); 579,27 enhuparkhein, to inhere, 30 occurrences in Simplicius (1 Alexander), 11 in Aristotle enidein, to recognise, 576,19; 631,8; 632,9 enistanai, to object, 604,25 enkalein, to censure, 557,1 enklêma, criticism, 562,21 enkrinein, to accept, 636,16 enkukliôs, in a circle, 565,32; 594,18 ennoein, to understand, recognise, 557,4.8; 579,4 ennoia, conception, meaning, 562,8; 566,19; 603,10; 630,1 enokhlein, to be troublesome, 604,27 enstasis, objection, 566,23; 578,2; 598,19; 612,22; 623,8 enthade, in this world, 599,16.21 eoikenai, to seem, resemble, 560,3 (Aristotle); 597,21; 608,31; 610,4; 630,3; also 298b32; 301a11; 305a3 epagein, to adduce, introduce, add, say, 37 occurrences in Simplicius (1 Alexander), 0 in Aristotle epagôgê, induction, 553,9; 601,30 epallaxis, interlocking, 609,25 (with 303a8, on which see the note at 609,14) epamphoterizein, to be like both, 596,14 ep’ apeiron, to infinity, 25 occurrences in Simplicius (5 Alexander), 0 in Aristotle epekhein, to occupy, 633,14.26; 634,31 (all 3 with 305b11); see also katekhein epektasis, expansion, 633,27-634,28 (7 with 305b18)

157

epekteinesthai, to expand, 634,1.20.23 epeoikenai, to resemble, 580,16 (Pythagorean saying) epharmogê, coincidence, 574,4 epharmozein, to fit, 557,9; 558,14; 575,7.8 ephêkein, to come to, 587,30 ephexês, next, 18 occurrences in Simplicius, 0 in Aristotle ephiesthai, to desire, 587,9 ephistanein, to point out, raise the question, notice, 570,24; 584,23 (with 300b21); 585,5; 613,27; 623,4; 624,27 epideiknunai, to indicate, 566,20 epigraphein, to entitle, 556,25.30; 557,11 epikheirein, to argue, 582,24; 605,23; 633,29 epikheirêma, argument, 17 occurrences in Simplicius, 0 in Aristotle epikheirêsis, argument, 579,15; 633,31; 635,4.6 epikrateia, rule, dominance, 587,12; 604,8; 606,1 epikratein, to rule, dominate, 587,21.24.25; 606,6; 632,15 epilambanein, to take up (space), 633,11; 634,3.8.28 (all 4 with 305b19) epileipein, to give out, 612,29(2); 613,2; 635,26 epinoia, thought, 567,13; 598,28 epipedon, plane (figure), 119 occurrences in Simplicius (8 Alexander, 1 TL, 1 Plato), 16 in Aristotle epiphaneia, surface, 562,24.25.27(2) epipherein, to add, 560,4; 588,17; 614,11 epiphora, conclusion, 553,31; 569,18; 601,29 epipolaios, superficial, 557,20 epipothein, to yearn, 641,8 episêmainein, to disapprove of, 573,12 episkeptesthai, to investigate, 568,22; 626,19; also 299a10; episkepteon occurs at 568,20 (with 299a25), 304b23, and 305a33 epistasthai, to know, 600,14 epistêmê, science, knowledge,

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554,1.19 (Aristotle); 556,17; 557,6; 560,6(2); 563,7; 612,11.19 (both with 303a21); 622,4 epistêmonikos, scientific, 557,5; 562,31; 607,1 epitêdeios, suitable, satisfying, 564,16; 596,12 epitêdeiotês, suitability, 587,31 epitithesthai, to be laid next to, 575,1-9 (3 with 299b28) epizêtein, to seek, 565,27 epôthein, to push, 596,22.32 epsukhômenos, having soul, 552,10 eptugmenos, folded, 632,29 êremein, to rest, be at rest, 26 occurrences in Simplicius (1 Alexander), 5 in Aristotle êremia, rest, 582,13 (with 300a27); 583,10 (with 300b7); 590,6.9 (both Alexander) ergôdês, difficult, 627,10 erion, wool, 632,30 erôtan, to ask, 564,21; 582,15.29; 583,1; 586,6.13(2) erôtêsis, question, 586,13 eskhara, scab, 602,9 eskhatos, extreme, last, outermost, 559,24 (Parmenides); 575,24; 587,14 (Empedocles); 608,4(2) ethos, custom, 557,19 eualloiôtos, volatile, 615,21 eukinêtos, easily moved, 594,10; 596,17 eulogos, reasonable, 10 occurrences in Simplicius (1 Alexander), 3 in Aristotle eupathês, easily affected, 628,21.26 euperilêptos, easily grasped, 605,33 euphthartos, easily destroyed, 628,19-28 (4 with 305a6) euphuês, naturally adapted, 615,15 eutheia, straight line, 11 occurrences in Simplicius (2 Alexander), 0 in Aristotle euthugrammos, rectlinear, 14 occurrences in Simplicius, 2 in Aristotle euthunein, to criticise, 556,25; 583,18 euthuporein, to move in a straight line, 594,25; 597,7 euthus, immediately, straightaway, 564,30; 592,4 exaerizomenos, evaporated, 571,8

exallattesthai, to change (intransitive), 599,27 exammenos, carded (wool), 632,30 exatmizomenos, vaporised, 602,12 exêgeisthai, to interpret, explain, 555,18; 564,12; 591,6; 622,25 exêgêsis, interpretation, 576,2; 619,9; 634,9 exêgêtês, interpreter, 564,11; 591,2; 613,27 exêirêsthai, to transcend, 555,5; 591,24 exelenkhein, to dismiss, 557,1 exerkhesthai, to come out, 602,8 exetastikos, examining, 566,18 exetazein, to examine, 562,13 exôthein, to push out, 569,7 exôthen, external, 597,10 exumnein, sing the praises of, 580,15 gê, earth, 90 occurrences in Simplicius (17 Alexander, 3 Melissus, 1 TL, 1 Plato), 13 in Aristotle genesis, coming to be, generation, 114 occurrences in Simplicius (4 Alexander, 1 Parmenides, 1 Plato), 16 in Aristotle genêtos, coming to be (adjective), 20 occurrences in Simplicius, 3 in Aristotle gennan, to generate, 21 occurrences in Simplicius (5 Alexander, 1 TL), 4 in Aristotle gennêma, offspring, 588,2 gennêtikos, generative, 610,19; 611,8; 622,19 genos, genus, 555,10; 565,1; 599,8; 601,17 geômetria, geometry, 563,8 geômetrikos, geometrical, 562,21.32 geômetros, geometer, 562,23 gignesthai, to come to be, 264 occurrences in Simplicius (21 Alexander, 7 Melissus, 2 Hesiod, 2 Plato, 1 Parmenides), 38 in Aristotle gignôskein, to know, understand, 559,5 (Melissus); 606,30; 608,27.29.30 (Anaxagoras) gleukos, sweet wine, 633,22 glukutês, sweetness, 572,13; 599,12 gnômê, understanding, 558,18

Greek-English Index gnôrizein, to know, understand, 600,15; 619,11 gnôsis, knowledge, 556,5; 557,5 (both with 298b23); 560,27; 600,17 (with 302a11); 607,1; 608,28 gnôstos, knowable, 606,32 gônia, angle, 15 occurrences in Simplicius, 0 in Aristotle grammê, line, 172 occurrences in Simplicius (1 Alexander), 16 in Aristotle grammikos, linear, 574,5 graphein, to write, 15 occurrences in Simplicius, 3 in Aristotle guion, limb, 587,18 gumnoun, to remove clothing, 587,30 hairetos, worthy of choice, 570,7-20(8); haireta translated ‘matters of choice’ at 555,26 hamartêma, mistake, 611,13.17 (both with 303a17); also 304b11 haplôs, absolutely, simply, without qualification, 15 occurrences in Simplicius, 4 in Aristotle haploun, to unfold, 632,29 haplous, simple, 121 occurrences in Simplicius (2 Alexander), 16 in Aristotle haptesthai, to be in contact, 609,21 haptos, tangible, 565,5 harmozein, to fit, be suitable, 573,6; 585,26; 623,7.8 (both Alexander); 624,17 hêgoumenon, antecedent (of a conditional), 553,1.11 hêkista, least (adverb), 558,9 helkein, to drag, 593,25 hêmartêsthai, to be mistaken, 630,3 hêmitrigônon, half-triangle (the word used by TL for the right triangle with angles of 30 and 60 degrees), 561,13.18 henôsis, unity, unification, 558,15; 609,1,2 henoun, to unite, unify, 590,2.13; 591,6; 608,32; 612,16; 627,23 (Alexander); 635,16 hepesthai, to follow, be a consequent or consequence, 17 occurrences in Simplicius (1 Alexander), 1 in Aristotle hetairos, pupil, 615,13.18 hetoimos, easy, 565,13; 581,8

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heuriskein, to find, 585,1; 597,18.21; 601,1; 626,23.28; 629,4 hikanos, sufficient, adequate, 588,3; 596,24; 612,3 himation, cloak, 632,28 hippos, horse, 578,17 histanai, to stand, stop, 12 occurrences in Simplicius, 3 in Aristotle historein, to report, recount, describe, 564,24; 576,14; 600,20; 602,6; 621,14.16 historia, enquiry, 552,27; 553,12 (both with 298b2) holos, whole, entire, 30 occurrences in Simplicius, 3 in Aristotle; see also holôs holôs, in general, entirely, at all, 22 occurrences in Simplicius, 8 in Aristotle holotês, entirety, 595,3(2).6(2) homalôs, in a uniform way, 565,33 homoeidês, of the same kind, 628,19 homoiomereia, homoiomereity, 11 occurrences in Simplicius, 0 in Aristotle; see also homoiomerês homoiomerês, homoiomerous (the neuter usually translated ‘homoiomery’), 32 occurrences in Simplicius,7 in Aristotle; see the note on 601,12 homoios, similar, 15 occurrences in Simplicius (1 Melissus), 0 in Aristotle; see also homoiôs homoiôs, similarly, in the same way, 11 occurrences in Simplicius, 4 in Aristotle homoioskhêmos, having the same shape, 625,3 homoiotês, similarity, 566,2; 575,30; 576,2 homologein, to agree, 559,6 (Melissus); 569,10.17; 591,26; 603,29; 616,14 homônumos, having the same name, 561,11 homou, together, 590,2; 608,21.23 (both Anaxagoras); 608,32 horan, to see, 17 occurrences in Simplicius (4 Melissus, 1 Alexander), 4 in Aristotle horistikos, definitional, 566,28 horizein, to define, specify, 571,4; 572,7; 601,2; 607,3.12; 608,29;

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616,31; 617,28 (Alexander); 625,1; see also horizon, hôrizesthai hôrizesthai, to be determinate or definite or defined, 13 occurrences in Simplicius (4 Alexander), 0 in Aristotle horizon, horizon, 613,20.32 hormasthai, to arise from, 566,23 horos, definition, 562,23; 607,13 (Alexander).19 hôs etukhe, in a random way, 589,21-4 (3 with 301a11) hudatoumenos, liquefied, 571,9 hudôr, water, 125 occurrences in Simplicius (26 Alexander, 1 Melissus, 1 TL), 19 in Aristotle hugiazesthai, to be cured, 595,26.27.28 hugiôs, correctly, 560,9; 605,17 hugrotês, moisture, 602,12 hulê, matter, 33 occurrences in Simplicius (5 Alexander, 1 TL, 1 Aristotle), 1 in Aristotle hupantan, to deal with, discuss, object to, 13 occurrences in Simplicius, 0 in Aristotle huparkhein, to belong, to exist, 22 occurrences in Simplicius, 6 in Aristotle hupeikein, to withdraw, 571,22 (2 with 299b13 and 14(2)) hupenantios, contrary, 563,12 (with 299a4); see also enantios huperekhein, to exceed, 15 occurrences in Simplicius (1 Alexander), 0 in Aristotle huperokhê, excess, 569,26; 617,30.32; 622,22(2); 625,10.11 hupertithesthai, to set aside, 566,24 huphestôs, fixed, 599,27 huphistanai, to produce (565,8; 575,24); to sink to the bottom (596,15); to suppose (628,11); see also huphestôs huphizanein, to sink down, 569,7 hupodeiknunai, to indicate, 588,1.5; 591,1 hupokeisthai, to underlie, be a substratum or subject, be assumed, 18 occurrences in Simplicius (1 TL), 1 in Aristotle hupolambanein, to assume, 557,3.14; 558,12; 559,14 (all 4 with 298b22); 566,5

hupoleipein, to give out, be insufficient, 635,21 (with 305b20); also 303a27; see also hupoleipesthai hupoleipesthai, to remain, be left over, 572,21; 602,12; 631,32; 635,21 (with 305b24) hupomenein, to endure, undergo, 561,3 (with 298b31).28; 568,9; 627,4.9 hupomimnêskein, to recall, mention, 551,2; 554,28; 620,11 hupomnêsis, recollection, 551,25 hupo selênên, sublunary, 20 occurrences in Simplicius, 0 in Aristotle; see also huposelênos huposelênos, sublunary, 595,5.12; 629,21; see also hupo selênên hupostasis, reality, 557,3.21 hupothesis, hypothesis, 13 occurrences in Simplicius (1 Alexander), 2 in Aristotle hupothetikos, hypothetical, 552,25.31; 607,24 hupotithenai, to hypothesise, 68 occurrences in Simplicius (1 Plato, 1 Alexander), 4 in Aristotle hupotopein, to surmise, 629,3 hupourgein, to contribute to, 597,11 husterizein, to fall more slowly, 693,16 (with 310a10) husteros, later, posterior, 569,5; 581,18; 590,20; 597,9; 621,1; 631,18; 634,33 iatrikê, art of medicine, 595,28.30 iatros, physician, 595,26; 602,7 idea, form, 609,7 (Anaxagoras).11 idein, to see, 566,25; 575,28 idios, one’s own, specific, 561,19; 568,1; 591,7; 593,14; 612,10 idiôtikôs, amateurish, 564,25; 576,14 ienai, to proceed, move, 570,2; 583,29.30; 584,20.26 (all 4 with 300b1.14); 597,28; 630,25 isêmerinos (kuklos), celestial equator, 613,32 iskhiadikos, suffering from sciatica, 602,7 iskhion, hip, 602,7 isogônios, equiangular, 574,22 isopleuros, equilateral, 561,12; 574,7.8.10.11.14.22; 575,33; 614,2

Greek-English Index isorrhopos, having equal impulsion, 576,26 isos, equal, 17 occurrences in Simplicius, 7 in Aristotle; see also isôs isôs, presumably, perhaps, 10 occurrences in Simplicius, 2 in Aristotle isoskelês, isosceles, 561,13.19; 564,8 (TL); 566,6 (Plato); 574,17; 575,34; 614,1 isotês, equality, 565,22 kaiein, to burn, 610,21 kainoprepês, new, novel, 562,16; 563,1 kainos, recent, 562,1 kalein, to call, 18 occurrences in Simplicius (1 Alexander), 0 in Aristotle kalos, beautiful, good, 566,7-13 (3, all Plato); 597,2; see also kalôs kalôs, correctly well, 13 occurrences in Simplicius, 2 in Aristotle katalambanein, to occupy, 633,14 (with 305b12) katalêgein, to come to an end, 563,19; 627,5; 628,30 kataleipesthai, to remain, 567,15; 573,1.2; 630,20 katalimpanein, to leave, 591,7 katalogadên, in prose, 558,17 katanoêsis, recognising, 562,22 kataphatikos, affirmative, 620,16 kataskeuazein, to construct, establish, 590,28 (with 301a17); 604,25; 609,10 (Anaxagoras) kataskeuê, construction, 591,3 katastasis, condition, 587,18; 590,9 (Alexander).16 kata sumbebêkos, accidentally, 567,33; 568,4 (both with 299a21 and 22) katêgoria, category, 617,8 katêgorikôs, categorically, 571,12.20; 608,6 katekhein, to occupy, 571,21; 629,24(2); 633,15-30(7); 634,15 (Alexander).27 kath’ hauto, kath’ hautên, per se, in itself, 19 occurrences in Simplicius, 0 in Aristotle kath’ hekaston, particular, 552,21; 554,16 (both with 298b5)

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kath’ ho, insofar as, 619,20; 625,22; see also kath’ hoson kath’ hoson, insofar as, 603,12; 619,16.19; see also kath’ ho katholikos, universal, 568,15 katholou, universally, generally, as a whole, 554,14; 568,16.30; 605,18; 622,8; 631,3 katô, down, 24 occurrences in Simplicius, 3 in Aristotle katorthoun, to go right, be correct, 581,22; 600,5 katôthen, from below, 581,31 kausis, burning, 602,11 kausoun, to set on fire, 602,8 keisthai, to be assumed, 604,10 kenkhros, millet seed, 570,7(1) kenos, void, empty, 37 occurrences in Simplicius (3 Alexander), 8 in Aristotle kentron, centre, 574,18; 614,2; see also mesos Khaos, Chaos, 556,8 (Hesiod). 560,17.18 (Hesiod).24.25(2) kharakterizesthai, to be characterised, 564,21; 606,1; 632,15 kharientôs, elegantly, 561,31 kheisthai, to be rarefied, spread out, 633,16; 634,14.16.17 (all 3 Alexander) khôra, room, space, 579,25; 598,18; 634,20; see also topos khôrein, to contain, 598,18; 629,27.28.30 khôristos, separate, 634,22 khôrizesthai, to be separated, 18 occurrences in Simplicius, 1 in Aristotle khrasthai, to use, 16 occurrences in Simplicius (2 Alexander), 1 in Aristotle khrêma, thing, 590,3; 608,21.24 (both Anaxagoras).32; 609,7 (Anaxagoras) khrêsis, way of speaking, 553,5 khrôma, colour, 567,32 (with 299a21); 599,8.9.19 khronos, time, 49 occurrences in Simplicius (5 Alexander), 10 in Aristotle khrusos, gold, 558,24; 559,3 (both Melissus); 606,5.7; 621,22 (Alexander) khusis, spreading, 634,4.11 (Alexander) kinein, to cause motion or change, to

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move or change (transitive), 38 occurrences in Simplicius, 11 in Aristotle; see also kineisthai kineisthai, to be moved or changed, to move or change (intransitive), 281 occurrences in Simplicius (2 Alexander), 29 in Aristotle; see also pheresthai kinêsis, motion, change, 236 occurrences in Simplicius (3 Alexander, 1 Aristotle), 29 in Aristotle; see also phora kinêtikos, kinetic, 596,21 kinêtos, moving, 581,15 koinônia, communion, 554,12 koinopoiein, to assimilate, 617,22 koinos, common, general, 22 occurrences in Simplicius, 1 in Aristotle koinotês, common thing, 599,11.23 kôluein, to prevent, 16 occurrences in Simplicius, 2 in Aristotle kompsos, elaborate, 620,14.25 (both with 304a13) koruphê, vertex, 574,7.18; to kata koruphên tês sphaires translated ‘pole of the sphere’ at 613,31 kosmeisthai, to be given a cosmic order, 589,21 kosmikos, cosmic, 591,1 kosmopoia, making of the cosmos, 586,2; 588,4; 590,26; 591,15 kosmopoiein, to make the cosmos, 589,28; 590,2.4(Alexander).13.32 (all 5 with 301a30) kosmos, cosmos (plural: worlds), 43 occurrences in Simplicius (2 Alexander, 1 Parmenides at 558,7, where translated ‘ordering’), 3 in Aristotle kouphos, light, 53 occurrences in Simplicius, 12 in Aristotle kouphotês, lightness, 42 occurrences in Simplicius (1 Alexander), 7 in Aristotle kranion, skull, 606,18 krasis, blending, 612,20; 628,16 kratein, to rule, dominate, prevail, 566,2.9 (Plato); 599,13 krinein, to judge, 633,4 kuathos, cup, 629,30 kubikos, cubical, 565,8.9(2) kuklikos, moving in a circle, 594,26 kuklophoria, circular motion, 554,4

kuklos, circle, 582,1.6; 587,14(Empedocles); 588,19; 591,24; 607,17; 613,30.31; 614,17 kukloun, to recirculate, 582,27 (with 300a33) kuklophorêtikos, moving in a circle, 551,5.6; 555,5.10.11; 598,5; 600,7 kumainein, to swell, 599,32 kurios, authoritative, 566,28; see also kuriôs kuriôs, in the strict sense, 552,3; 554,2; 561,2; 570,16; 573,22; 585,9; 614,7 lambanein, to take, assume, 38 occurrences in Simplicius (3 Alexander), 7 in Aristotle; to en arkhêi lambanein translated as ‘to beg the question’ at 626,28 and 629,3 lanthanein, to not notice, be unaware, to do unobtrusively, 588,28.29; 615,29 (with 303b16); also 305b2 leiotês, smoothness, 610,21 leipein, to lack, 597,14; see also leipesthai leipesthai, to remain, 629,1.15.17; also 305a32 lêmma, lemma, 572,12 leptomerês, having fine parts, 13 occurrences in Simplicius, 6 in Aristotle leptos, fine, 24 occurrences in Simplicius (1 Alexander), 7 in Aristotle leptotês, fineness, 616,29 (with 303b24).30 (with 303b25); 625,10.11 leukos, white, light, 558,25 (Melissus); 567,33 (with 299a22); 572,15 (3 with 299b21(3)) lexis, phrase, words, text, 597,13; 618,17 (Alexander); 630,1 lithos, stone, 10 occurrences in Simplicius (3 Melissus), 2 in Aristotle logos, argument, discussion, account, statement, speech, text, theory, view, doctrine, reasoning, definition, ratio, 118 occurrences in Simplicius (14 Alexander, 1 Parmenides, 1 Melissus, 1 Anaxagoras, 1 TL, 1 Plato), 15 in Aristotle

Greek-English Index loipos, remaining, next, final, 19 occurrences in Simplicius, 3 in Aristotle loxos, oblique, 582,5 luein, to resolve, 581,28; 598,19; 623,8; 627,20 lusis, resolution, 582,9 makar, blessed, 580,14 (Pythagorean saying) makhesthai, to be in conflict with, 612,10 (with 303a21); 622,3 makros, long, 582,23 malakos, soft, 571,19-24 (4 with 299b11 and 13) manos, rare, 14 occurrences in Simplicius, 4 in Aristotle manôsis, rarefaction, 565,16; 599,31; 616,3.5.8.14.19.20 manotês, rareness, 615,27.28 (both with 303b15); 616,21.24.28 (all 3 with 303b23); 620,3 manousthai, to be rarefied, 599,13; 616,7.10 manteia, prophetic power, 613,26 marainesthai, to waste away, 628,25 (with 305a11) mastix, whip, 597,4 mathêmata, mathematics, 562,31; 563,12 (both with 299a4); 566,23.28; 567,7.9; 606,28 (with 302b29) mathêmatikos, mathematical, 30 occurrences in Simplicius (1 Alexander), 3 in Aristotle; ho mathêmatikos translated ‘mathematician’ at 606,33 and 612,12 megalomerês, having large parts, 571,11; 617,2 (with 303b27); 622,25.29; 625,8 megas, large, great, 10 occurrences in Simplicius, 2 in Aristotle; see also meizôn and megistos megethos, size, magnitude, largeness, 45 occurrences in Simplicius (2 Alexander, 1 Aristotle), 16 in Aristotle megistos, largest, greatest, 558,21 (Melissus); 594,10; 612,27-9 (3 with 303a28); 613,31; 629,29 meiousthai, to contract, 565,17 meizôn, greater, larger, 70 occurrences in Simplicius (23

163

Alexander, 1 Empedocles), 13 in Aristotle mêkhanikê, mechanics, 563,7 mêkos, length, 12 occurrences in Simplicius (1 Alexander), 2 in Aristotle melas, dark, black, 558,24 (Melissus); 567,33 (with 299a22) menein, to remain, endure, 560,15; 599,28; 634,26; also 300a29 and 30 and 300b6 meristos, divisible into parts, 612,17 meros, part, 67 occurrences in Simplicius (3 Alexander, 2 Plato), 6 in Aristotle; ta kata meros translated ‘particulars’ mêros, thigh, 606,19 mêsembrinos (kuklos), meridian, 633,9 mesiteuein, to lie in between, 633,9 mesos, intermediate, 20 occurrences in Simplicius (1 Plato), 6 in Aristotle; to meson usually translated ‘centre’; dia mesou translated ‘by means of’ at 571,18 mestos, filled, 598,16 metabainein, to turn, go, 609,17; 624,17; 628,4; 630,10 metaballein, to change, 561,18.20; 575,34; 613,4; 632,25 (with 305b5) metabasis, change, 553,28 (with 298b1); 615,5; also 305b14 and 27 metabolê, change, 11 occurrences in Simplicius (1 Alexander), 0 in Aristotle metalambanein, to take, receive a share, transform, 596,32; 597,2; 624,27; 631,11 metapherein, to transfer, 557,8; 558,14; 560,8 (all 3 with 298b24) metaphora, metaphorical expression, 597,3 metaskhêmatizesthai, to be transformed, 561,6 (with 298b31) metaxu, (intermediate) between, 15 occurrences in Simplicius, 0 in Aristotle, to metaxu usually translated ‘intermediate’ metekhein, to share in, 570,18.19 methodos, discipline, 563,5 metienai, to turn to, 555,1; 584,9; 615,10; 630,19 metokhos, sharing in, 552,11 metriotês, measuredness, 554,2

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metron, measure, 600,1 migma, mixture, 606,7; 621,20; 632,18; also 302b1 mignusthai, to be mixed, 17 occurrences in Simplicius (1 Empedocles), 2 in Aristotle mikromerês, having small parts, 617,1 (with 303b27); 622,25 (with 304a16); 624,18-22 (3 with 304b9).26.28; 625,7 mikros/smikros, small, 14 occurrences in Simplicius (1 Anaxagoras, 1 Aristotle, 1 Alexander), 3 in Aristotle mikrotês/smikrotês, smallness, 19 occurrences in Simplicius (2 Anaxagoras), 5 in Aristotle miktos, mixed, 588,20; 604,6-7 (3 with 302b6.7(2)); also 302b16 mixis, mixture, 12 occurrences in Simplicius, 1 in Aristotle mnêmê, mention, 551,9 mnêmoneuein, to mention, 603,7.9 mokhleia, levering, 583,29 monakhôs, in one way, 581,22 monas, monad, one, unitary thing, 15 occurrences in Simplicius, 1 in Aristotle monê, rest, 551,12; 590,6.7 (both Alexander) monoguios, consisting of a single limb, 587,26 monos, only, 57 occurrences in Simplicius (1 Empedocles, 1 Alexander), 2 in Aristotle morion, part, portion, 14 occurrences in Simplicius (2 Alexander), 6 in Aristotle morphousthai, to be given shape, 565,4 muthos, myth, 560,22 nastotês, solidity, 609,18 naus, ship, 597,1.3 Neikos, Strife (Empedocles), 21 occurrences in Simplicius, 0 in Aristotle (hoi) neôteroi, more recent thinkers, 553,3; neôteroi applied to Platonic philosophers at 564,13 neuron, sinew, 606,19-20(3) noein, to understand, 556,16 (with 298b22); 591,2 noeros, intellectual, 588,1; 599,24

noêtos, intelligible, 11 occurrences in Simplicius, 0 in Aristotle nomizein, to think, consider, 15 occurrences in Simplicius, 1 in Aristotle (ho) nosôn, ill person, 595,26-30(4) nosos, illness, 570,8 nous, mind, 552,11; 590,3; 608,28.30 (both Anaxagoras); 609,2 (both references to Anaxagoras) oiesthai, to think, 552,14; 582,3; 584,32; 597,23; 598,19; 608,27; 609,5; 613,27; also 302b12 oikeios, proper, appropriate, one’s own, 564,3; 585,14 (with 300b23); 607,19.30; 608,7 (all 3 with 302b31); 620,22.23; 625,20; also 300a22; 301a5; 302b5; 303b4 oligokhronios, lasting a short time, 597,9 oligos, few, small in amount, 565,13; 573,10 (Plato); 576,26 (Plato); 605,28; 623,2; also used with a temporal sense in the phrases ep’ oligon (‘for a short time’), met’ oliga (‘a little later’), pro oligou (‘a little earlier’) oligotês, fewness, 576,25 onkos, bulk, mass, 10 occurrences in Simplicius (1 Alexander), 2 in Aristotle onoma, word, name, 556,27; 558,11 (Parmenides).16; 570,19; 602,3; 603,22 onomasia, being named, 560,27 onomazein, to name, 553,16 opheilein, to be obligated, 626,28 ophthalmos, eye, 602,5; 606,10 organikos, organic, 606,8 organon, instrument, 596,10 (with 301b22) orthogônios, right (said of a triangle), 561,13.19; 564,7 (TL); 574,17; 575,33; 576,1 orthos, right, said of an angle: 574,10.21.24; 613,31; in moral sense: 581,23; see also orthôs orthôs, correctly, 558,26-559,9 (4, all Melissus); 605,2 (with 302b15); 620,24 ôsis, pushing, 583,29 ostoun, bone, 573,23; 586,9 (with 300b29); 602,33 (with 302a26);

Greek-English Index 603,18 (with 302a32); 605,5.15 (both with 302b17); 606,18.20(2) ôthein, to push, 593,25; 597,1 (with 301b24) oura, tail (of an animal), 597,4 ouraion, tail (of a ship), 597,2 ouranios, heavenly, 554,28; 555,2; 559,23 (Parmenides); 565,33; 578,14; 592,3; 595,5 ouranos, heaven, heavens, 13 occurrences in Simplicius, 4 in Aristotle ourios, tail (wind), 597,2 ousia, substance, 25 occurrences in Simplicius, 5 in Aristotle pakhumerês, with thick parts, 615,29; 622,15 (with 304a31); 633,17 pakhus, thick, 616,30; 617,1 (both with 303b25 and 27); 621,19.22.24.25 (last 2 Alexander).30; 623,1 pakhutês, thickness, 616,29.30 (both with 303b24 and 26); 621,24 (Alexander) pantakhou, everywhere, in every case, always, 560,3; 583,6; 599,13; 627,11 pantêi, in every respect, entirely, 565,28; 566,4; 574,11; 586,18; 599,10 pantelôs, completely, 555,23; 608,28; 631,20 pantodapos, of all sorts, 551,6; 610,27 pantoios, of every sort, 609,6.7 (both Anaxagoras); 623,17 pantôs, always, absolutely, certainly, 11 occurrences in Simplicius (1 Alexander), 0 in Aristotle paraballein, to cast aside, compare, 562,33; 601,1; 620,25 parabolê, comparison, 551,12 paradeigma, example, 586,27; 587,3; 621,21 (Alexander); 628,23 paradeiknunai, to represent, point out, 588,7; 621,21 (Alexander) paradidonai, to set out, transmit, 551,7; 558,8.15; 559,27; 561,11; 562,16; 564,2.9; 596,22 (with 301b26); 603,24 paragein, to bring in, adduce, 566,28; 579,11; 596,24 paragignesthai, to arrive, 579,9

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paragraphein, to make a charge, 558,13 paraiteisthai, to refrain from, 556,30 parakolouthein, to follow along, 596,25 (with 301b27) paralambanein, to take, 577,27; 579,7; 584,14 paraleipein, to pass over, leave out, fail to mention, 589,2; 590,25; 591,2.3.6 (all 4 with 301a16); 611,14 paraleiptikon skhêma, paralipsis, 566,27 paralogizesthai, to reason incorrectly, 557,20 parapempesthai, to dismiss, 561,26 pararriptein, to throw out, 609,27 parasunaptikos, causal (connective), 553,2.3 parathesis, juxtaposition, 612,21 paratithenai, to set out, introduce, 560,14; 565,26; 619,9 parekbainein, to deviate, 581,23 parekbasis, deviation, 581,24 parekhein, to produce, supply, 564,29; 584,24; 634,21 paremballesthai, to be inserted, 552,30 paremplokê, interweaving, 634,34 paremptôsis, intervention, 634,11 (Alexander).23 paresparmenos, interspersed, 634,10.18.22.28 parienai, to pass over, 562,6.22 paristanai, to make a point, confirm, 587,29; 609,5 paruphestêkenai, to be derivative from, 583,26; 584,17 paskhein, to be subject to, be acted on, undergo, 553,26; 597,16; 616,2; 634,30; also 305a9 and 11 pathêma, affection, 568,3 (with 299a23) pathêtikos, affective, 564,16; 600,12.27 pathos, affection, 30 occurrences in Simplicius (1 Aristotle), 3 in Aristotle pauein, to cease, 558,5 (Parmenides); 602,8; 627,2 peirasthai, to try, 564,14; 575,27; also 306b3 peisis, being acted upon, 578,14 pêlos, clay, 573,26

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pemptos, fifth, 552,9; 553,15; 555,5; 601,16 (only references to the fifth element included here) pentagônon, pentagon, 574,22.23 peperanthai, to be finite, 608,5 (with 303a1); also 303b9; see also peperasmenos peperasmenos, finite, finitely many, bounded, 73 occurrences in Simplicius (2 Alexander), 13 in Aristotle pephukenai, to be (naturally) constituted, 565,18; 574,26; 581,15.16.17; 582,4(2); 592,15; 599,14; 631,16; also 298b32 and 301b23 peposôsthai, to be determined quantitatively, 564,30 peras, limit, end, 557,17 (Melissus); 563,14; 574,5; 577,2; 619,24 peratoun, to limit, 608,29; 613,21 periagein, to lead around, 582,6; 623,19 periekhein, to contain, 574,8; 575,21; 614,25 (with 303b12); 618,18.25 (both Alexander); 630,7.12(2); 633,24 (with 305b15) periektikos, containing, 568,4 perigraphê, circumscription, 629,27 perigraphein, to circumscribe, 594,28; 635,19 perilambanein, to include, 567,29; 568,26 perileipesthai, to remain, 629,17 (hoi apo tou) Peripatou, the Peripatetics, 599,28 periphereia, circularity, 610,21 peripherês, circular, 604,11; 607,12 (Alexander) peripherogrammos, circular, 614,7 peripiptein, to run into, 572,11 peristrephein, to rotate, 602,11 perittos, extraordinary, 558,13 (to) perix, periphery, 588,26; 631,1 phainesthai, to be obvious, 581,6 (with 300a22); 590,28; also 300a17 and 30; see also phainomena and phainomenon phainomena, phenomena, 565,32; also 303a22 phainomenon, apparent meaning, 557,19; 560,3; 563,26; 566,17; 588,2 phaneros, evident, 14 occurrences in Simplicius, 14 in Aristotle

pherein, to carry, 596,30; see also pheresthai pheresthai, to move (intransitive), 30 occurrences in Simplicius, 21 in Aristotle; see also kineisthai pheuktos, to be avoided, 555,26; 570,20 Philia, Love (referring to Empedocles), 587,12; 590,20; see also Philotês philos, dear, beloved, 561,31; 566,12 (Plato); 619,13(2) philosophein, to philosophise, 555,25 (with 298b12); 556,19; 558,13 philosophia, philosophy, 556,21; 563,8 philosophos, philosopher, 554,2; 564,13 Philotês, Love (referring to Empedocles), 586,11.26.28; 587,9.17.21.24.25 (all 8 with 300b30); 590,25.29; 591,3 (all 3 with 301a16 and 18); see also Philia phleps, vein, 606,19 phlox, flame, 602,6 phora, motion, 20 occurrences in Simplicius, 1 in Aristotle; see also kinêsis phthartos, perishing, perishable, 556,5; 599,15; 629,1 (with 305a13).8 phtheirein, to destroy, 553,29; see also phtheiresthai phtheiresthai, to perish, be destroyed, 18 occurrences in Simplicius (6 Alexander), 6 in Aristotle phthora, perishing, destruction, 553,28; 555,7; 578,5 (Alexander).16; 600,8.9; 627.28 (Alexander); 628,27 (with 305a8); also 298b9.15 phulattein, to keep, preserve, 560,23; 627,32 (Alexander); 634,24 phusei, natural, by nature, 552,20.25; 553,6(2).7.10; 554,13 (all 7 with 298a27 and b5); 577,13; 581,14 (with 300a21); 592,5 (with 301a24); also 303b19 and 21; see also (kata) phusin (hê) phusikê, study of nature, 551,20 (ho) phusikos, student of nature, 554,4; 556,24.25; 561,2; 562,9.15 phusikos, natural, 57 occurrences in Simplicius (2 Alexander), 12 in

Greek-English Index Aristotle; see also phusikôs, (hê) phusikê and (ho) phusikos phusikôs, naturally, in a way appropriate to the study of nature, based on natural considerations, 553,24; 556,18 (with 298b18); 560,9; 573,5; 587,28; 620,26; 622,8 (with 304a25); 630,27 (huper (tên)) phusin, hypernatural, 553,8.10; 556,19.29 (kata) phusin, natural, naturally, 117 occurrences in Simplicius (6 Alexander), 28 in Aristotle; see also phusei (para) phusin, unnatural, unnaturally, 58 occurrences in Simplicius (6 Alexander), 9 in Aristotle phusiologein, to study nature, 560,20 (with 298b29) phusiologia, doctrine of nature, 561,10; 564,10 phusiologos, natural philosopher, 590,18 phusis, nature, entity, 40 occurrences in Simplicius (1 Plato, 1 Aristotle), 10 in Aristotle; see also phusei, (huper (tên)) phusin, (kata) phusin, (para) phusin phuton, plant, 553,18.19 (both with 298a32); 586,9.10.21; 615,13 pileisthai, to be compressed, 632,29; 633,1 pilêsis, compression, 632,32 pilêtikos, compressing, 564,29 pistis, belief, confirmation, 557,27 (Parmenides); 567,12 pistos, believable, trustworthy, 558,5 (Parmenides); 563,1 (with 299a5) pistousthai, to confirm, give credence, 601,29; 633,20 pithanos, persuasive, plausible, 562,2; 594,27; 604,27 planasthai, to wander, 587,2 (Empedocles).8.19 plasma, fiction, 572,9 plasmatôdês, artificial, 599,32 (hoi) Platônikoi, Platonists, 571,9 Platônikos, Platonic, 564,12.13; see also (hoi) Platônikoi platos, breadth, 11 occurrences in Simplicius (1 Alexander), 2 in Aristotle

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platukos, extended, 579,16 plazesthai, wander, 587,8 plêmmelos, discordant, 587,31; 588,4; 591,16 pleonazein, to exceed, 567,28 plêrês, full, 558,21; 630,4 plêsiazein, to come near, 606,23; 610,21 plêthos, number, 17 occurrences in Simplicius (2 Anaxagoras), 3 in Aristotle plêttein, to strike, 597,4 pleura, side, 574,19.20; 583,6 pneein, to blow, 597,1.3 pneumatousthai, to be vaporised, 633,23 (with 305b14) poikilia, variegation, 565,31 poikilos, variegated, 565,4; 605,8 poion, quality, 565,22; 566,1 poiotês, quality, 14 occurrences in Simplicius, 0 in Aristotle politês, fellow citizen, 615,13.19 politikôs, politically, 555,26 pollakhôs, in many ways, 581,23.28 pollakhou, frequently, 603,22 pollakis, frequently, often, 556,27; 633,23 pollaplasios, multiple, 620,19.20 polueidôs, in many ways, 569,20 polutimêtos, most honoured, 561,30 poros, pore, 598,16 poson, quantity, 13 occurrences in Simplicius (2 Alexander), 3 in Aristotle potamos, river, 599,24 pous, foot, 560,1; 612,15 pragma, thing, 556,24; 580,5; 589,9 (with 301a8); 597,27; also 298b26 pragmateia, treatise, study, 551,2.21; 552,24; 554,19.24; 581,26; 604,9 pragmatoeidês, complicated, 621,15 praktikôs, practically, 555,25 praxis, practical activity, 552,11 proagesthai, to proceed, 607,24 proanastellein, to open up, 570,3 proaxioun, to prefer, 620,6 proballesthai, to be put forward, 611,3 problêma, problem, 555,23 prodedeikhthai, to have been proved previously, 592,7 prodêlos, prima facie clear, 576,3; 580,11; 607,30; 634,2

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prodidakhtheis, previously explained, 552,1 proeirêkenai, to have been said previously, 567,27; 591,18; 597,14.20; also 301b33 proerkhesthai, to proceed, 552,25; 609,3 prohodos, procession, 560,23 prohuparkhein, to be prior, exist previously, 16 occurrences in Simplicius (2 Alexander), 2 in Aristotle prohupotithenai, to hypothesise in the antecedent, give priority to, 569,19; 576,17 proienai, to proceed, 566,17; 573,22; 592,7 prokeisthai, to be proposed, to be present, 551,17; 569,27; 581,10; 583,14 (Alexander); 591,30; 592,3 prokheirizesthai, to discuss, to choose, 556,12; 629,2 prokheiros, easy, 562,22; 566,25; 582,20 prokhôrein, to be possible, to proceed, 606,6; 627,1 prolambanein, to assume in advance or to start, to pre-contain, 18 occurrences in Simplicius, 0 in Aristotle (koinê) prolêpsis, (common) conception, 601,28; 603,28 prologizesthai, to take into account also, 564,19 pronoein, to take care, 557,20 pronoia, providence, 588,6 prooimion, proemium, 551,20.21.25; 552,23 prophanês, evident, 555,24; 630,27 prosagein, to bring in against, 608,11; 616,24 prosaptein, to attach, 620,9.12 (both with perihaptein at 304a10) prosêkein, to be appropriate, 555,8; 557,10; 626,31 prosekhôs, directly, 552,5; 588,32; 611,13 prosengizein, to draw near, 609,20 prosgignesthai, to enter in, happen, 565,17; 632,32 proskeisthai, to be added, 610,8 proskhrêsthai, to use also, 554,5; 590,32

proslambanein, to take on also, 596,19 proslêpsis, additional assumption, 569,18; 571,12; 601,28 prosôpon, face, 599,24-6(3); 606,8-16(5, with 302b25(2)) prosthêkê, addition, 565,21 prostheôrein, to investigate also, 602,23; 603,2 (both with 302a27) prosthesis, addition, 567,13 (with 299a17).28 prostithenai, to add, 20 occurrences in Simplicius (2 Alexander), 1 in Aristotle; see also proskeisthai proteros, previous, prior, 41 occurrences in Simplicius, 19 in Aristotle prôteuein, to be prior, 555,1 prothumeisthai, to desire, 566,19 protithenai, to propose, assign, 555,23; 557,9; 591,8.17; 594,8.10 (both with 301b15); 600,6; 609,15; 630,22; see also prokeisthai prôtos, first, primary, 101 occurrences in Simplicius (2 Hesiod, 1 Alexander), 24 in Aristotle psêgma, shavings, 621,18.22 (Alexander) (both with 304a21) psukhê, soul, 554,3.10.11; 585,2.3 (both Alexander).12; 609,9 (Anaxagoras) psukhein, to cool, 564,22 psukhros, cold, 558,29.30; 559,19 (all 3 Melissus); 564,22.25; 576,15 psukhrotês, coldness, 565,6.20; 567,14; 599,12 psuxis, cold, 564,28.29 ptaisma, mistake, 597,23 puknos, dense, 16 occurrences in Simplicius, 7 in Aristotle puknôsis, condensation, 565,16; 599,31; 616,3; 632,32 puknotês, denseness, 571,9; 615,27.28 (both with 303b15); 616,25.28 (both with 303b23); 620,4 puknousthai, to be condensed, 599,33; 600,1; 621,19 pur, fire, 148 occurrences in Simplicius (28 Alexander, 2 Plato, 1 Melissus, 1 TL), 31 in Aristotle puramis, pyramid, 56 occurrences in Simplicius (5 Alexander), 8 in Aristotle puramoeidês, pyramidish, 614,6.8

Greek-English Index puretos, fever, 602,10 Puthagorikos, Pythagorean (applied to the author of TL), 561,10 rhadios, easy, 576,12; also 299b12; see also euperilêptos, eupathês, euphthartos rhêgnusthai, to burst, 633,23 (with 305b15) rhein, to be in flux, flow, 556,5.18; 557,5; 599,24.27; also 298b30 rhêma, word, 619,9 (ta) rhêta, words, 558,19; 609,5 rhêteon, one should say, 563,27; 570,20; 575,18; 577,17; 578,7.22.26; 602,28; 603,1 rhêtôr, rhetor, 566,27 rhoê, flux, 599,22 rhopê, impulsion, 13 occurrences in Simplicius, 3 in Aristotle saphênizein, clarify, 552,30; 611,4 saphês, clear, 558,17; 559,12.18; 609,5; also 303a10 sarx, flesh, 15 occurrences in Simplicius, 6 in Aristotle sbennumenos, extinguished, 628,25 (with 305a10) (to) sêmainomenon, sense, 568,1 sêmantikos, referring to, 586,30 sêmeion, point, sign, 15 occurrences in Simplicius (2 Melissus, 1 Alexander), 0 in Aristotle; see also stigmê sinêpi, mustard seed, 570,7 skalênos, scalene, 561,12; 575,33; Simplicius quotes Plato using promêkês at 566,6 skepsis, enquiry, 556,12 (with 298b20) skepteon, we should investigate, 600,18.24 (both with 302a12) skhêma, figure, shape, 82 occurrences in Simplicius, 12 in Aristotle skhêmatizein, to assign a figure or figures, 621,28; 623,21.28 (all 3 with 304b2); 624,16; see also skhêmatizesthai skhêmatizesthai, to be shaped, given a shape, 565,2; 606,15.21 (both with 302b26); 621,5 skhesis, relation, 551,10; 618,25 (Alexander); 620,6; 625,5 sklêros, hard, harsh, 557,2;

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558,30(2); 559,3 (all 3 Melissus); 571,19-24 (4 with 299b11 and 13) skopein, to investigate, 600,9 (with 302b11) skopos, purpose, 551,3; 586,25 sôma, body, 413 occurrences in Simplicius (21 Alexander, 2 TL, 2 Plato, 2 Aristotle), 74 in Aristotle sômatikos, corporeal, 553,9.11.31; 569,1 sôzein, to preserve, 565,32; 567,22; 606,26 sperma, seed, 603,18 (with 302b2); 609,7 (Anaxagoras); 615,12 spermatikôs, spermatically, 609,4.11 sphaira, sphere, 17 occurrences in Simplicius (1 Empedocles), 2 in Aristotle sphairikos, spherical, 552,11; 610,19; 613,29; 614,3.9 sphairoeidês, spherical, 552,16; 613,5 stasimos, stable, 660,12 stenokhôria, lack of room, 633,24 (with 305b16) stereos, solid, 16 occurrences in Simplicius, 2 in Aristotle sterêtheis, deprived, 633,9 stigmê, point, 676,6; see also sêmeion stoikheiôtos, composed of elements, 555,4; 601,3.11.17.19 stoikheiôdês, elemental, 616,17 stoikheion, element, 259 occurrences in Simplicius (15 Alexander), 56 in Aristotle strôma, blanket, 602,8 sullogismos, syllogism, 597,32; 621,21.24.26 sullogizesthai, to produce a syllogism, infer, argue, 560,5; 586,14; 616,28; 620,17; 621,3.15; 630,22 sumbainein, to follow, result, turn out, 26 occurrences in Simplicius (1 Melissus, 1 Alexander), 27 in Aristotle; see also sumbebêkenai sumbebêkenai, to attach, 570,25; see also sumbebêkos sumbebêkos, accident, 600,23; see also kata sumbebêkos sumblêtos, comparable, 622,9.11 (both with 304a26) sumbolikôs, symbolically, 564,11; 576,4(2) summetria, symmetry, 566,2; 576,18

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summetros, commensurable, 583,5 sumpepilêmenos, pressed together, 571,5 sumperainesthai, to complete, conclude, 591,17; 597,6; 625,31; 631,26 sumperasma, conclusion, 569,26 sumphusômenos, fused together, 621,18.22 (Alexander) (both with 304a21) sumpileisthai, to be pressed together, 571,5; 632,28; 633,8(2) (all with 305b7) sumplekesthai, to be woven together, 589,21; 632,19 sumplêroun, to complete, 558,3; 591,16 sumplokê, weaving together, 609,24.25 (both with 303a7) sunagein, to infer, develop (an argument), draw together, 570,32 (with 299b12); 572,24; 573,1; 574,7; 595,11; 605,13; 608,6; 610,14; 620,21.24; 626,17 sunagôgê tou logou, development of the argument, 607,24 sunairein, to unite, compose, 552,4; 558,8 sunairesthai, to support, 586,27 sunaisthanesthai, to be aware, 612,15 sunaisthêsis, awareness, 564,29; 612,14; 628,16 sunalloioun, to alter together, 573,24.26; 602,2 sunanairein, to do away with also, 608,20 sunaptesthai, to be joined, connected, 574,8.18; 595,3; sunêmmenon translated ‘conditional’ at 569,18.19; 571,3; 601,26; 611,25 sunaptikos, hypothetical, 553,3 sunartan, to join together, 596,21.24 sundesmos, connective, 553,2; 597,19 sunekheia, continuity, 612,13 sunekhês, continuous, 15 occurrences in Simplicius, 0 in Aristotle sunelthein, to come together, 572,5.6.10; 573,17 sunepôthein, to push along, 596,3.5.8.12 sunepourizein, to produce a fair

wind for, 596,31; 597,1 (both with 301b29) sunergein, to act together with, 596,27.28 sungenês, of the same kind, 588,27 (with 301a4) sungignôskein, to acknowledge, 626,22.26; 629,5 sungramma, treatise, 556,25.29; 564,3; 608,21 sunienai, to come together, 572,9; 573,23; 621,18 sunistanai, to construct, compose, put together, combine, 45 occurrences in Simplicius (3 Alexander, 2 Plato), 8 in Aristotle sunkeisthai, to be composed, 45 occurrences in Simplicius, 5 in Aristotle; see also suntithenai sunkerannusthai, to mingle with, 555,4 sunkhôneuomenos, melted down, 621,18 sunkhôrein, to accept, 605,25; 634,34 sunkrima, blend, 632,13 sunkrinein, to blend, 586,23; 590,16-31 (5 with 301a20); 590,19 (with 301a14); 609,7 (Anaxagoras) sunkrisis, blending, 590,29 (with 301a18); 601,7; 632,7 sunkritikos, blending, 564,29 sunolos, entire, 553,17 (with 298a31) sunousiousthai, to be made substantial together with, 576,9 suntattein, to join, 597,17.22.24 suntelein, to contribute, 576,29; 606,23; 633,4 sunthesis, composition, compounding, 15 occurrences in Simplicius (2 Alexander), 3 in Aristotle sunthetos, composite, 38 occurrences in Simplicius (2 Alexander), 1 in Aristotle suntithenai, to compose, compound, construct, add together, 30 occurrences in Simplicius (2 Alexander), 11 in Aristotle; see also sunkeisthai suntomôs, briefly, 551,25; 624,21 (ou) suntrekhei, to clash, 612,26 sustasis, construction, 565,28; 566,9 (Plato); 614,9; 625,20

Greek-English Index sustellesthai, to be contracted, 623,1; 634,16 (Alexander) sustoikhos, coordinate, 553,14; 554,13 (both with 298a30); 575,14; 578,29 (Alexander); 603,7 (with 302a29) takhos, speed, 594,3 (with 301b11) takhu, quickly, 620,20 tattesthai, to be given order, 585,23; 588,24; 589,21 taxis, order, 10 occurrences in Simplicius, 4 in Aristotle tekhnikos, technical, 620,27 tekmairesthai, to base a judgment, 568,19 tekmêrion, sign, evidence, 596,24; 603,15 teleios, complete, 556,3; 560,13; 584,13; 600,10 teleutaios, last, 561,29 telos, end, 589,23; 597,18 temnein, to cut, 592,23.24; 613,30.32 tephra, ashes, 602,12 tetragônon, square, 574,17.18.19.20; 607,17 thalassa, sea, 629,30 thattôn, faster, 596,3.5 (both with 301b20); 625,25-30 (4 with 304b17 and 19); also 305a12 thaumastos, surprising, 575,22 theasthai, to see, view, 602,7; 617,8 theios, divine, 556,16; 564,11 theologein, to talk about divine things, 560,22 theologos, theologian, 598,3 theôrein, to investigate, observe, 584,23 (with 300b20); 604,2 (with 302b12); also 298b11; 299a13; 304a25 theôrêma, theorem, 551,7 theôrêtikôs, theoretically, 555,25 theôria, investigation, doctrine, 554,16.17 (both with 298b5); 568,22; 588,2 theos, god, 566,12 (Plato).27 thermainein, to heat, 553,24; 564,22 thermos, hot, 558,29.30; 559,19 (all 3 Melissus).24 (Parmenides); 564,22.25; 576,15

171

thermotês, heat, 564,16.27.28; 565,6; 567,14; 599,11 thesis, position, 551,11; 554,29; 563,32 tithenai, to posit, place, set down, 18 occurrences in Simplicius (1 Alexander), 0 in Aristotle tmêma, segment, 574,19; 613,33 tmêtikôtatos, sharpest, 620,17-22 (5 with 304a12) toikhos, wall, 573,25 tolman, to dare, 556,28 tomê, division, 563,19; 609,21; 612,14(2); 624,10 (Alexander); 635,23 topos, place, space, region, 58 occurrences in Simplicius (4 Alexander), 11 in Aristotle; see also khôra trepein, to turn, 557,7 (Plato); 600,12 trigônon, triangle, 24 occurrences in Simplicius (1 TL, 1 Plato, 1 Alexander), 0 in Aristotle; see also hêmitrigônon trikhêi diastatos, three-dimensional, 576,9 triplasios, triple, 622,22 trophê, nourishment, 605,8; 615,12 tropos, way, mode, 21 occurrences in Simplicius (1 Plato, 1 Alexander), 10 in Aristotle trupanon, fire-drill, 602,10 tunkhanein, to receive, meet, hit upon, 551,9; 554,20 (Aristotle); 562,2; 566,15 (Plato); see also hôs etukhe xêrainein, to dry, 553,24 xêrotês, dryness, 564,17 xulon, wood, 601,31-602,16 (6 with 302a21 and 23); 605,5.8 (both with 302b17) zêtein, to ask, enquire, seek, 18 occurrences in Simplicius, 0 in Aristotle zôion, animal, living thing, 11 occurrences in Simplicius (1 Anaxagoras), 1 in Aristotle

Index of Passages (a) Testimonia and fragments I list here passages from Simplicius which are the only or a principal source for a testimonium about or fragment of various ancient authors. MELISSUS (DK30) A4: 557,10-11; B6: 557,14-17; B8: ANAXAGORAS (Sider) 558,19-559,12 B7: 608,26 ANAXIMANDER (DK12) PARMENIDES (DK28) A17: 615,13-18 A14: 556,25-30; B1.31-2: 557,25-558,2; B8.21: 559,17; B11: EMPEDOCLES (DK31) 559,20-7; B19: 558,8-11 B35.5, 10-13: 587,8-17; B57: 586,29-587,4; B58: 587,18-19; THEOPHRASTUS (Theophrastus: B59: 587,20-3 Sources) 112C: 552,31-552,4; 238: 564,24-6; DEMOCRITUS (DK68) 281: 602,5-6 A61: 569,5-9; A120: 564,24-9 LEUCIPPUS (DK67) A16: 583,20-2 (b) Passages quoted or paraphrased by Simplicius (Sider) B1.1-3: 608,21-3; B4a.1-8: 609,6-11; B4b.8-9: 608,24; B12.15-17: 608,29-31

ANAXAGORAS

ARISTOTLE

Cael. (not including 3.1-7) 2.1, 284a14: 552,12-13; 2.12, 292a20-1: 552,11 Metaph. A.5, 986b27-987a2: 560,1-4 Phys. 4.9, 217a26-7: 578,7-8 EMPEDOCLES (DK31) B27.4 (=B28.2): 591,5; B57.1: 586,12 EUCLID

Elements (Heiberg (1883)) 1, defs. 1,2,5: 562,24-6

HESIOD

Theogony (West (1966)) 116: 556,8; 560,18 PARMENIDES (DK28) B1.28-32: 557,25-558,2; B8.4: 557,18; B8.50-2: 558,5-7 PLATO

Gorg. 469C1-2: 570,9-11 Parm. 135B8: 557,6-7 Plt. 272E5-6: 588,5-7 Tim. 53B3-5: 564,2-3; 53C5-56E8: 561,11-21; 53D4-E5: 566,10-16; 54A1-6: 566,5-9; 54D3-55E6: 574,3-24; 56B1-2: 573,10-11; 576,25-6 [TIMAEUS OF LOCRI] (Marg (1972)) 215,13-17: 564,4-8; 216,18-19: 573,8-9

(c) Early texts cited in the notes Only passages not cited in (a) or (b) are mentioned here. References are to the line in the Greek text on which a footnote number occurs. ALEXANDER OF APHRODISIAS

Quaest. (Bruns (1892)) 2.13: 578,26

ARISTOTLE

Cael. (not including 3.1-7) 1-2: 551,5;

1.2, 268b14-26: 614,32; 1.2, 268b14-269a2: 604,10; 1.2, 269a9-10: 581,27; 1.3, 269b23-9: 596,13; 1.3, 270a12-22: 598,1;

Index of Passages 1.3, 270b24-5: 603,6; 1.5, 272a28-9: 583,4; 4.2, 308b30-309a8: 569,9; 4.3, 309a19-21: 634,25; 4.4 ff.: 562,11; 4.4, 311a15-29: 596,13 Cat. 6, 5b11-29: 617,7; 8, 9a28-10a10: 564,16; 8, 10a11-16: 565,1 Metaph. 1.5, 986b10-987a2: 556,14; 5.13, 1020a17-25: 617,7 Meteor. 1.3, 339b21-3: 603,6; 2.9, 369b11-15: 603,6 Phys. (Ross (1936)) 1.2-3: 598,7; 1.2-4: 562,7; 1.4, 187a26-188a18: 605,1; 608,12; 1.4, 187b22-188a2: 635,7; 1.4, 188a2-5: 608,16; 2.1, 192b8-23: 604,6; 2.1, 192b21-2: 595,20; 4.1, 209a4-7: 629,30; 4.4, 211a17-b5: 594,30; 4.6-9: 597,29; 4.6, 213b4-15: 629,30; 634,11; 4.6, 213b15-22: 634,11; 4.7, 213b22-7: 610,7; 4.8: 630,15; 634,1; 4.8, 215a1-6; 581,14; 4.8, 215a8-11: 584,8; 4.9, 216b22-30: 600,1; 6.1: 612,17; 6.3-4: 612,17; 6.10: 563,21; 6.10, 241b6-7: 583,5; 7.2, 244b5b-5d: 608,1; An.Po. 1.12, 77b40-78a2: 620,20 Sens. 6, 445b20-446a20: 608,3; 612,1 [ARISTOTLE]

MXG 1, 974a11-12: 557,16

ASCLEPIUS

in Metaph. 1-7 (CAG 6.2) 38,19: 580,14 DIOGENES LAERTIUS (Marcovich (1999)) 1.21: 607,5; 5.42: 566,15; 7.71: 551,5; 8.55: 556,30 GALEN (Kühn (1821-33)) On the Elements according to Hippocrates 1 1.487,11-14: 556,30 Commentary on Book 1 of Hippocrates’ On the Nature of Man 15.5,10-11: 556,30 [GALEN] (Kühn (1821-33)) Medical Definitions 337 (19, 434,15-16): 602,9 LYDUS

On the Months (Wünsch (1898)) 2.11.24: 580,14 ORPHIC HYMNS (Quandt (1955))

173

13.1: 580,14 PHILOPONUS

in GC (CAG 14.2) 34,2-3: 566,26

PLATO

Phdr. 245C5-246A2: 585,1 Tim. 53C6-8: 575,21; 56A4-B2: 565,18; 56A7: 620,1; 58B1-6: 571,11; 58D8-E2: 571,11

PROCLUS

in Tim. (Diehl (1903-6)) 1,16,32: 580,14 Platonic Theology 1 (Saffrey and Westerink (1968)) 5,6-7: 564,13

SEXTUS EMPIRICUS

Adversus Mathematicos (Mutschmann (1914)) 7. 111: 556,30

SIMPLICIUS

in Cael. (outside of 551-635) 529,1-15: 587,11; 641,5-7: 564,26; 641,11-14: 564,4; 641,23-8: 565,33; 679,18-682,3: 562,18 in Cat. (CAG 8) 252,23-261,16: 564,16 in Phys. (CAG 9 and 10) 7,23-7: 564,4; 27,23-8: 604,31; 34,21-6: 608,24; 34,29-35,9: 609,5; 35,22-36,7: 564,4; 41,8: 558,5; 70,16-17: 557,11; 103,28-9: 557,16; 145,22: 559,16; 146,23: 558,5; 155,26-30: 608,23; 156,13-157,4: 609,11; 165,30-166,2: 608,25; 171,31-2: 608,16; 174,4-18: 608,25; 227,23 ff.: 564,13; 327,20: 587,23; 331,2: 587,23; 423,3-4: 566,26; 453,12: 580,14; 529,29-530,30: 629,30; 649,4-650,14: 629,30; 652,4-6: 610,7; 683,1-4: 634,11; 683,24: 600,1; 880,22-3: 610,7; 1102,20: 580,14; 1102,22: 580,17 SUDA pt. 4 (Adler (1930)) 2126: 607,5 THEMISTIUS

in Cael. (CAG 5.4) 148,39-149,2: 566,26

THEOPHRASTUS

De Sensu (Stratton (1917)) 26: 602,6 (Marg (1972)) 206,11-17: 586,2

[TIMAEUS OF LOCRI]

Index of Names (a) Names mentioned by Simplicius In many cases information on a person or persons or a reference to where information can be found is provided in a note on a given passage. Page and line numbers indicate where a given name is found. Achilles: 561,32 (quotation of Homer’s Iliad 20.75-6) Alexander of Aphrodisias: 1. Cases in which Simplicius says nothing negative (15): 570,24 (extension of Aristotle’s argument at 299a25-b7 that points have no weight to the claim that points have no qualitative properties); 585,21 (claim that if things moved in a disorderly way on their own for an infinite time that motion would be natural); 613,27 (interpretation of Aristotle’s claim at 303b1 that a sphere is composed of eight pyramids); 614,16 (assertion that Aristotle ‘does not think that the pyramid is simpler than the sphere or that the triangle is simpler than the circle); 617,11 (explanation of Aristotle’s statement at 303b30-304a1 that certain people are committed to the idea that the same thing will be fire in relation to one thing and air in relation to another); 618,11; 619,9.20 (various interpretations of Aristotle’s statement at 304a6-7 that ‘the ratios of lesser things inhere in greater ones’); 620,18 (gives as an example of ‘people who speak more simply’ (304a11) ‘people who say that fire stands in a multiple ratio because both fire and a multiple ratio increase quickly’); 621,20 (explanation of Aristotle’s reference (304a21) to fused-together shavings); 622,25 (in connection with 303b24-6 said that ‘what is composed of what is double what air is composed of is water, what consists of what is triple is earth’); 623,4 (his explanation of why at 304a22-3 he associates indivisibility with the doctrine that fire is the element of all things); 624,10 (argument against the claim that even if certain parts of a pyramid are not pyramids, they are divisible into pyramids); 627,16 (answers the question why Aristotle assumes at 304b28-33 that in a certain hypothetical situation the times during which there is composition and dissolution are different); 630,3 (generally accepted emendation of the text at 305a17); 631,24 (adds another absurd consequence to the assumption (dismissed by Aristotle at 305a29-31) that the elements might come to be from a body without a location); 634,8 (uses both the ‘separate void’ and the ‘interspersed void’ in interpreting 305b18-20) 2. Cases of disagreement of some significance (9): 575,27 (criticism of the Timaeus answered by Simplicius); 578,1 (defends Aristotle against the charge that bodies might all dissolve into form and matter and suggests that matter might have a size; this suggestion rejected by Simplicius); 578,20; 579,2 (criticism of the Timaeus answered by Simplicius; assertion that form does not come to be rejected by Simplicius); 581,25; 582,29 (one of his explanations of why Aristotle seems to say both that a thing has only one natural motion and more than one rejected by Simplicius, who acknowledges that Alexander also was aware of his solution); 584,29.31 (his proposal to substitute auto for heauto in 300b21 explained by Simplicius in terms of

Index of Names

175

Alexander’s fear that Aristotle might be saying something Platonic); 585,1 [italics indicate that the name ‘Alexander’ does not occur] (his view that naturally moving things are in a way self-moving rejected by Simplicius on the ground that nature is moved by soul and moves the body along with itself); 585,27 (his claim that the atomists are committed to the view that there was a cosmos before the coming to be of the cosmos rejected by Simplicius on the ground that disordered motion continues after the cosmos has come to be); 586,26; 587,13 (his view that at 300b30 Empedocles’ phrase ‘under (epi) Love’ refers to the time when Love is under control rejected by Simplicius, who says it refers to the time when Love is gaining the ascendancy); 598,26 (his explanation of Aristotle’s theory of matter and why the assumption that all body comes to be would imply a void rejected by Simplicius) 3. Cases of disagreement of less significance (15): 552,14 (his grammatical construal of a 298a24-7 rejected by Simplicius); 555,3 (his explanation of why Aristotle uses the term ‘first of the elements’ at 298b6 rejected by Simplicius); 560,5 (his summary explanation of Aristotle’s description of Eleatics at 298b14-24; it is clear from what has preceded that Simplicius does not accept this explanation); 562,1.3 (his explanation of why at 299a1 Aristotle turns to Plato first countered by Simplicius); 572,24 (his construal of the argument at 299b17-23 rejected by Simplicius); 583,12 (his view that at 300b3 Aristotle’s question ‘where would it move’ concerns what prevents the earth from moving whereas Simplicius thinks it concerns the earth); 588,20 (his suggestion that to extend what is said at 301a1 with the further inference that if there are infinitely many causes of motion and infinitely many moving things there will be two infinities, which is absurd, countered by Simplicius with the claim that an infinity of movers is sufficiently absurd; Simplicius adds the suggestion that infinitely many causes of motion would mean that nothing moved); 589,1 (his claim that at 300b31-301a4 Aristotle leaves out the alternative that the number of movers might be finite rejected by Simplicius, who says that Aristotle makes the hypothesis unobtrusively); 590,4.12 (his arguments when commenting on 301a11-22, against the cosmogony of Anaxagoras countered by Simplicius’ assertion that Aristotle’s only point was to commend Anaxagoras for making the cosmos come to be from unmoving things); 594,16 (his remark in discussing the meaning of the word ‘determinate’ at 301b17 that mathematical body is neither determinate nor actual rejected by Simplicius); 597,13.21 (his rendering of the text of 301b30-3 rejected by Simplicius, who characterises the issue as insignificant); 606,9 (his explanation of ‘homoiomery’ at 302b25 refined by Simplicius); 607,7 (his explanation of why Aristotle says (302b29-30) that mathematicians always assume finite principles rejected by Simplicius); 610,13.28; 611,3.14 (his claim that at 303a10-16 Aristotle is making an at least implicit argument against the atomists rejected by Simplicius, who holds that Aristotle is merely setting out atomist views); 612,1 (his interpretation of ‘bodies’ at 303a19 as ‘elements’ rejected by Simplicius, who takes it to mean ‘composite bodies’) Anaxagoras: 589,30; 590,13 (both with 301a12; commendation for making the cosmos out of unmoving things); 601,8 (he and Empedocles say that coming to be is the result of blending and separating and so are committed to the view that elements exist actually rather than potentially in compounds); 603,8-26 (4 with 302a28; made the homoiomeries elements); 603,22 (with 302a31; often referred to fire as ether); 604,31 (he and Archelaus hypothesised the homoiomeries as the elements); 605,10 (with 302b14; was mistaken to make the homoiomeries elements); 605,31 (says perceptible

176

Index of Names

things are characterised by the dominance of one thing in them); 608,11 (in Physics 1 Aristotle showed that Anaxagoras was wrong to think that all things are mixed in all things); 608,21-609,12 (3; a Platonising interpretation of Anaxagoras); 632,5-13 (3; his basic ideas); 634,25.32 (he and Empedocles denied that there is a void); also 609,16; 613,9; 614,28; 635,5.15 Anaximander: 561,4 (held that all things are transformations of an intermediate which endures forever); 602,20 (what is intermediate is the only element); 615,13 (a pupil and fellow citizen of Thales, took the principle to be ‘finer than water and denser than air because the substratum should be naturally adapted for the change to either; he was the first to hypothesise that this one is infinite, so that he could use it for comings to be without stinting; and, it is thought that he hypothesised infinite worlds and that each of the worlds came to be from an infinite element of this sort’; 615,18 (a fellow citizen and teacher of Anaximenes) Anaximenes: 561,4 (held that all things are transformations of air, which endures forever); 590,18 (makes the cosmos come to be from one thing); 602,19 (air is the only element); 615,18 (a pupil and fellow citizen of Anaximander, took the principle to be infinite air because he believed that change could be accounted for by reference to air’s volatility) Archelaus: 604,31 (he and Anaxagoras called the homoiomeries elements) Aristotle (named 46 times) Aspasius: 607,5 (his explanation of why Euclid’s postulates are definite in quantity) Democritus of Abdera: 564,24.27 (the value of atomistic explanations of qualities; see also 576,14 and 641,7 in the commentary on 3.7 (Mueller (2009)); 569,5 (for him and later Epicurus all atoms have weight and the heavier ones push out the less heavy ones, making them seem light); 576,11.14 (the differences between his atomism and the geometrical chemistry of the Timaeus); 588,10 (holds that there are infinitely many things moving in an infinite void; cf. 589,6; 591,14); 609,17 (with 303a4; calls atoms, which are indivisible because of their smallness and solidity and also infinite in number and in shapes, elements; cf. 604,30); 609,25 (also with 303a4; called the weaving together (sumplokê) of atoms interlocking (epallaxis?)); 617,22 (ascribes the difference among things which come to be from atoms to the smallness and largeness of atoms); 618,7 (said that atoms of fire differs from other atoms in shape); 625,2 (atoms of air, water, and earth have the same shape but differ in smallness); 628,10 (believed in indivisibles; also 628,24); 632,6.9.17 (all with 305a4 and 305b2; makes the elements come to be because specific atoms separate out from collections); 634,5-29 (says there is a void into which bodies expand; also 634,23.33); 634,19 (explains the expansion of bodies in terms of the void interspersed (paresparmenos) between the atoms, the separate void providing room for expansion; also 642,29); also 614,28; 618,5 Diogenes of Apollonia: 602,19; 615,21 (hypothesised air as the only element) Empedocles: 583,1 (with 300b2; thought the earth is at rest because of the vortex); 586,10-587,24 (7, with 300b29; says that neckless heads were formed epi tês philotêtos; Simplicius argues against Alexander on the meaning of the Greek phrase); 590,19-591,7 (3 with 301a16; Aristotle says that he passes over the coming to be of the cosmos epi tês philotêtos, but Simplicius interprets him to be saying correctly that for Empedocles the cosmos came to be from an intelligible reign of Love because of the incursion of Strife); 601,8 (he and Anaxagoras say that coming to be is the result of blending and separating and so are committed to the view that elements exist actually rather than potentially in compounds); 603,8-24 (6 with 302a28; Empedocles

Index of Names

177

held that there are 4 elements); 628,8 (with 305a3; held that the elements are infinitely divisible but will never be divided ad infinitum; he did not believe in a common matter); 632,3.9.11 (all with 305a34 and 305b1; explained the change of something as a matter of bits in the thing separating out); 634,24.32 (he and Anaxagoras say there is no void) Epicurus: 569,6 (‘Democritus and his followers and, later, Epicurus say that since all atoms have the same nature they have weight, but because some are heavier, the lighter are pushed out by the heavier ones, which sink down, and they move upward; and they say that it is for this reason that some things are thought to be light, others heavy’.) Hector: 561,32 (quotation of Homer’s Iliad 20.75-6) Heraclitus of Ephesus: 556,10; 561,5 (both with 298b3; held that all things are transformations of fire, which endures forever); 590,19 (makes the cosmos come to be from one thing); 602,18 (fire is the only element); 615,22 (he and Hippasus made fire the only element in the belief that the volatility of fire is sufficient to account for change); 620,6 (he and Hippasus made fire, the finest of the four simple bodies, the element); 621,7 (did not say that fire is a pyramid) Hesiod: At 298b26-9 Aristotle says, ‘For there are some people who say that there is nothing which does not come to be, but that everything comes to be, and some things that have come to be endure without perishing, and, again, others perish. This is especially true of Hesiod and his followers, and later, of others, the first people who studied nature’. In discussing this Simplicius mentions Hesiod at 560,16.24. and 562,8, and disputes Aristotle’s claim. Simplicius refers ahead to this passage at 556,6 and back to it at 598,3. Hippasus of Metapontum: 602,19 (he and Heraclitus made fire the only element); 615,11 (he and Heraclitus made fire the only element in the belief that the volatility of fire is sufficient to account for change); 620,5 (he and Heraclitus made fire, the finest of the four simple bodies, the element) Hippo: 602,19 (he and Thales said that water is the only element); 615,11 (he and Thales held that water is the only element ‘because they saw that the seeds of animals and the nourishment of both animals and plants are made of water’) Iamblichus: 564,11 (treats Plato’s Timaeus as symbolic) Leucippus (always mentioned together with Democritus): 583,20.29 (with 300b8); 604,30; 609,17 (with 303a14) Megethios: 602,6 (Alexandrian Physician, otherwise unknown, described to Simplicius a case of fire coming out of the hip of a man) Melissus: 556,6-559,9 (8 with 298b17, which is referred back to at 597,32-598,7, where Melissus is mentioned twice; Simplicius offers a Platonising interpretation of Melissus’ thought in which he insists that Melissus recognised that there is coming to be) Musaeus: 560,21 (used myths to talk about divine subjects) Orpheus: 560,21 (used myths to talk about divine subjects) Parmenides: 556,5-562,8 (14 with 298b17, which is referred back to at 597,32-598,7, where Parmenides is mentioned twice; Simplicius offers a Platonising interpretation of Parmenides’ thought in which he insists that Parmenides recognised that there is coming to be) Plato: 557,1 (sets out the ideas of Timaeus of Locri in the Timaeus); 561,30 (Homer dear to Plato); 557,6 (reference to 135B8 of the Parmenides); 564,11 (some interpreters of him think the Timaeus was written symbolically); 565,29 (put forward his geometrical chemistry as a hypothesis); 566,5 (quotation of Tim. 54A1-6); 573,10 (citation of Tim. 56B1-2); 575,21 (how he thought planes were compounded); 578,21.26; 585,2 (all 3 Alexander)

178

Index of Names

Potamon: 670,5 (his explanation of what it means to say that mathematical principles are definite in quantity) Pythagoreans: 564,26; 565,26.29; 573,5; 621,9 (all 5 associating them with doctrines expressed in Plato’s Timaeus); 580,11 (with 300a17; said that all things are composed from numbers because numbers pre-contain in themselves all forms); 610,7 (say that monads are distinguished by the void) Socrates: 570,10 (says in the Gorgias that he would not wish to harm or be harmed, but, if required to choose, he would choose to be harmed) Thales of Miletus: 561,4 (held that all things are transformations of water, which endures forever); 590,18 (makes the cosmos come to be from one thing); 602,19 (he and Hippo said that water is the only element); 603,14 (water is the only element); 615,11 (he and Hippo held that water is the only element ‘because they saw that the seeds of animals and the nourishment of both animals and plants are made of water’); 615,13 (fellow citizen and teacher of Anaximander) Theophrastus: 553,4 (made a distinction in his Prior Analytics between the connectives ‘if’ and ‘since’); 564,24 (reports in his Physics that Democritus invoked atoms because he found qualitative explanations amateurish; also 576,14); 566,26 (some people ascribe On Indivisible Lines to Theophrastus rather than Aristotle); 602,5 (reports that a flame separated out from a person’s eyes) Timaeus: a (Plato’s dialogue Timaeus), 564,13; 576,25 (with 300a1); 578,21; 585,28 (both Alexander); 588,1.3; also 300b17 b (the ‘author’ of TL), 561,10; 564,3; 573,7; 586,2 c (the character in a), 573,10 d (either b or c), 583,22; 584,10; 587,26.28; 591,15 Xenocrates: 563,22 (his belief in indivisible lines argued against in Aristotle’s Physics) Xuthus: 599,32 (invoked the swelling of the universe to explain rarefaction) (b) Scholars cited in the notes This index does not include editors of texts unless they are mentioned for their position on an editorial or interpretive issue; reference to a page and line indicate the position of a note in which the scholar in question is mentioned. Ackrill, J.L., 564,16 Allan, D.J., 585,1, p. 22 Baltes, Matthias, p. 22 Barnes, Jonathan, 559,5 Bergk, Theodor, 559,3, p. 22 Bessarion, Basilius, 566,10; 571,14; 577,25; 635,20 Bossier, Fernand, p. 22 Brennan, Tad, p. 21 Brittain, Charles, p. 21 Cherniss, Harold, 621,9.13 Diels, Hermann, 558,5; 559,16 Furley, David, 634,11 Guldentops, Guy, p. 22 Guthrie, W.K.C., 593,20; 597,29 Hadot, Ilsetraut, p. 21 Hagen, Charles, 580,17 Heiberg, J.L., passim

Index of Names Huby, Pamela, p. 21 Karsten, Simon, passim Kneale, Martha, 552,25 Kneale, William, 552,25 Marg, Walter, 564,6; 586,2 McDiarmid, J.B., 609,13 Moraux, Paul, passim O’Brien, D., 586,28; 587,2, p. 21 Perkams, Matthias, p. 21 Peyron, Amedeo, p. 22 Rivaud, Albert, 566,11.14; 573,10 Ross, W.D., 599,32 Schmalzriedt, Egidius, 556,30 Sharples, R.W., p. 22 Sider, David, 608,23.24.31; 609,7.9.10 Sorabji, Richard, 629,30 Steel, Carlos, 564,13, p. 21 Stein, Heinrich, 559,21 Stocks, J.L., 593,20; 597,29 Tarán, Leonardo, 557,17 Taylor, C.C.W., 569,9 Vlastos, Gregory, 561,12 Wright, M.R., 586,12; 591,7; 628,13

179

Subject Index This index lists places where Simplicius’ discussion goes beyond straightforward exposition of Aristotle’s text. See also the other indices, and the table of contents. Aristotle discusses the surface meaning of texts, 557,19-20; 563,26-7; 566,17-20; 575,18-22; 587,26-588,7 atoms, shapes and sizes of, 610,13-611,11; 612,1-9 coming to be denial of by Parmenides and Melissus, 556,12-560,10 Simplicius’ doctrine of, 599,7-600,2 connectives, causal and hypothetical, 552,31-553,6 elements number of, 555,7-12; 604,3-27; 607,23-608,20 Plato’s theory of the elements, 564,10-24; 575,27-576,19; 578,20; 579,2 what are the elements, 603,7-31; 604,30-605,20; 615,8-23 what is an element, 600,30-601,20 elemental change Aristotle’s account is given in GC, 600,19-21 explanations of, 564,24-565,28; 578,7-11; 631,32-632,25; 635,19-29 Plato’s explanations are hypotheses, 565,28-566,16 formalisation of argument, 554,24-31 (first hypothetical mode); 568,30-569,27 (second figure);

570,32-571,17 (second figure and second hypothetical mode); 571,18-26 (a categorical argument) infinity, 635,11-19 inherence, what inheres in what, 600,30-602,17 mathematical principles, finitude of, 606,22-607,20 matter Aristotle’s doctrine of, 598,26-599,7 matter and form are not parts of a composite, 573,12-28; 579,4-12 ‘planes’ of the Tim. are material, 563,27-564,10; 573,3-11; 577,17-19; 579,24 Plato believed in prime matter, 563,33-564,10 Neoplatonist interpretations of earlier figures, 560,19-27 (Hesiod, Orpheus, Musaeus); 590,19-591,6 (Empedocles); 608,31-609,12 (Anaxagoras) numbers, construction of cosmos from, 580,3-17 simple bodies, the subject of Cael., 551,1-13; 554,24-555,1 Timaeus of Locri as source for Plato’s Timaeus, 561,8-11 void, 500,99-600,2; 598,7-25; 610,3-7; 629,18-630,15; 633,29-634,34

Addenda (added in proof)

1. I wish to add a further thank you to Jan Opsomer, who sent me some excellent corrections of my translation of 563,26-566,20, which I have incorporated. 2. Readers interested in an interpretive overview of Simplicius’ commentaries on Aristotle should now consult Han Baltussen, Philosophy and Exegesis in Simplicius: The Methodology of a Commentator, London: Duckworth, 2008. 3. As mentioned in the Introduction the ‘fragments’ of Alexander’s commentary on Cael. (mostly from Simplicius, but also including some material from Themistius and Averroes) have been presented, translated, and thoroughly discussed in Andrea Rescigno (ed. and trans.), Alessandro di Afrodisia, Commentario al de Caelo di Aristotele, Frammenti del Secondo, Terzo e Quarto Libro, Amsterdam: Hakkert, 2008. For the reader’s convenience I give here a list of the passages from Simplicius included as fragments by Rescigno; an asterisk indicates that the name ‘Alexander’ does not occur in the passage. Passage

Rescigno number

Pages in Rescigno

552,14-19

174

374-5

554,24-553,13*

175

374-7

555,1-6

176

377-8

560,5-10

177

380-1

561,25-562,6

179

381-3

566,23-567,4* 567,11-21*

180a 180c

384-8

569,28-570,28

181a

389-96

572,24-6 573,12-28

182a 182b

397-400

575,27-576,12

183

400-7

578,1-7 578,20-579,2

184a 184b

408-10

581,25-582,9

185

410-13

583,12-14

186

413-17

584,21-585,5 585,21-32

187a 187b

417-25

182

Addenda 586,5-29 587,8-23

188a 188c

425-32

588,14-22 588,28-589,3

189a 189b

432-8

590,3-11 590,24-591,7*

190a 190b

439-43

591,21-592,3*

191b

443-5

594,16-22

192a

445-8

596,31-597,3

193a*

448-50

597,13-26

194

451-3

598,26-599,7

195a

453-6

604,3-10

196*

457-8

606,9-10 606,33-607,16

197a 197b

458-60

607,24-608,20*

198a

460-4

610,13-611,4 611,13-16

199a 199b

465-468

612,1-6

200

468-9

613,25-614,10 614,15-18

201b

201a 469-73

617,6-21 618,10-619,8 619,20-4 622,24-7

202a 202b 202c 202d

474-80

620,15-20

203

480-2

621,20-5

204

482-3

623,4-16 624,4-13

205a 205b

483-6

627,16-32

206

486-9

628,6-13*

207a

489-90

629,18-630,15

208a

491-8

631,21-5

209

498-9

632,25-633,2*

210a

499-501

633,29-634,17

211a

502-507