Simplicius: On Aristotle On the Heavens 3.7-4.6 9781472552280, 9780715638446

Commenting on the end of Aristotle On the Heavens Book 3, Simplicius examines Aristotle’s criticisms of Plato’s theory o

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Simplicius: On Aristotle On the Heavens 3.7-4.6
 9781472552280, 9780715638446

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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 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, Myles Burnyeat, Alan Code, Stephen Menn, Jan Opsomer, David Sedley, 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 = Richard Goulet (ed.), Dictionnaire des philosophes antiques, Paris: Editions du Centre national de la recherche scientifique, 1989- . 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. LSJ = George Henry Liddell and Robert Scott, A Greek-English Lexicon, Oxford: Clarendon Press and New York: Oxford University Press, 1996. Metaph. = Aristotle’s Metaphysics. Moraux = Paul Moraux (1965) (ed. and trans.), Aristote: du Ciel, texte établi et traduit par Paul Moraux, Paris: Les Belles Lettres. Phys. = Aristotle’s Physics. Rivaud = Albert Rivaud (ed. and trans.), Timée-Critias (Platon, Oeuvres Complètes, vol. 10, Paris: Les Belles Lettres, 1925). 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 the end of Simplicius’ commentary on On the Heavens (De Caelo or Cael.) starting at 305b28 in book 3, chapter 7.1 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 2 to 4 are Simplicius’ exchanges with John Philoponus on Aristotle’s cosmology. Simplicius’ representations of Philoponus’ criticisms 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), the commentary on the first part of book 3 in Mueller (2009). 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, 168-9) and with Damascius (DPA, vol. 2, 541-93) in Athens or Alexandria. Sometime after 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.2 But it is now generally agreed that the three great Aristotelian commentaries safely attributable to Simplicius, those on the Categories, Physics, and On the Heavens3 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 the last part of Cael.4 In book 3 of Cael. Aristotle turns from the world above the moon to the sublunary world. For Aristotle, it is axiomatic that this world is composed of or from one or more elements, and an important task of book 4 is to prove that there are four such elements (or simple bodies), earth, water, air, and fire. However, Aristotle’s arguments are notoriously opaque, and Simplicius is ultimately driven to the conclusion that Aristotle is simply assuming this doctrine in Cael. and will demonstrate it in GC.5 By the beginning of 3.6 Aristotle has established that there is more than one element, but not infinitely many. Rather than proceeding directly to the

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question ‘how many’, he announces that the number and nature of the elements will be made clear by determining whether they are eternal or come to be. He argues that they are not eternal but come to be from one another. Aristotle’s own view, expressed most fully in GC, is that the earth, water, air, and fire come to be from one another through qualitative change, earth being cold and dry, water cold and wet, air hot and wet, fire hot and dry (cf. 636,14-17). In chapter 7 he eliminates competing accounts of elemental change, dealing particularly with Empedocles and Democritus. At the beginning of the material covered in this volume Aristotle says there are two remaining alternatives: (i) the elements come to be from one another by ‘reshaping as a sphere or a cube might come to be from the same wax’; (ii) they do so by dissolution into planes. Aristotle makes short shrift of the first alternative, saying that such a view would require a belief in indivisible bodies ‘since if they were divisible, a part of fire would not be fire nor would a part of earth be earth, since a part of a pyramid is not always a pyramid and a part of a cube is not always a cube’ (305b33-306a1). The associations of pyramid with fire and cube with air are, of course, Platonic, and, as Simplicius points out, Plato invokes the reshaping of material (gold) at Timaeus 50A5, to indicate the nature of the receptacle. Simplicius insists that this reshaping is not to be connected with elemental change but is rather ‘an illustration of the fact that the underlying matter endures while its forms change’ (636,27-637,1), and concludes that the doctrine of reshaping is not Platonic even if Aristotle introduced it on the basis of Plato’s words. Alternative (ii) is the theory of Plato’s Timaeus, and in connection with its introduction Simplicius offers a summary account of the theory. He accepts Alexander’s6 claim that in using the illustration of gold Plato was maintaining that all four elements change into one another but subsequently denied that earth interchanges with the other three because its particles are constructed from isosceles right triangles and those of the other three from ‘half-equilateral’ triangles (right triangles in which the hypotenuse is double the length of one of the legs). Alexander asks: If matter, according to Plato, is given form by the triangles and bodies are generated from them, why would it not be possible that the matter which underlies earth be subsequently given shape by the triangles which give form to water and air and fire? (640,9-12) Simplicius does not try to disarm this objection, but concedes that there is a sense in which earth does and a sense in which it does not interchange with the other elements. (640,12-21)7 Aristotle raises what by Simplicius’ count are 15 objections to Plato’s theory; Simplicius spends 30 pages discussing them. I shall treat this

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material in the next section. Here I remark only that in the prologue to his discussion Simplicius repeats his standard claim that Aristotle’s disagreement with Plato is only apparent because he knows Plato’s true meaning but argues on the basis of a superficial reading to combat people who adopt such a reading as the truth. Simplicius says that, like Democritus’ resort to atoms, the theory of the Timaeus is an attempt to rise to higher quantitative principles than the qualitative ones used by Aristotle in GC to explain elemental change. However, he insists, the Timaeus theory is not put forward as an absolute truth but is like the hypotheses of the astronomers, which are designed to preserve the phenomena. After completing his objections to Plato Aristotle ends book 3 by saying: But since the most important differentiae of bodies are those which relate to affections and acts and powers (since we say that everything natural has acts and affections and powers), it would be right to speak first about these so that by studying them we can grasp the differences of each with respect to each. (307b19-24) For Simplicius this statement is first and foremost looking forward to GC since every quality can be studied as an act or activity (e.g. heating) or as a power (e.g. the power to heat) or as an affection (e.g. being heated). But the statement is also related to weight and lightness, which Aristotle will discuss in book 4 ‘because it is more proper to natural motion’, (672,21) which Aristotle also discussed in book 1. For both Aristotle and Plato the sublunary world is a sphere with a centre and a periphery. For Aristotle the centre is below and the periphery is above, and what moves naturally to the centre (earth) is absolutely (haplôs) heavy and what moves naturally to the periphery (fire) is absolutely light; it is also possible to speak of one thing being heavier or lighter than another. According to Aristotle, his predecessors did not recognise lightness but thought that all things were heavy (had weight), and they discussed only relative heaviness. Aristotle says more or less all of these things at 308a7-33. But in that passage he also criticises Plato for denying that there is an above or below in the universe. Simplicius explains Plato’s position: From all parts of the earth it is possible for someone to come to be at his own antipodes; for at whatever place someone is it would be possible for him to come to be in turn at its antipodes. Why then is everything which stretches from under our feet to the heavens more below and what is above our head more above than the same at the antipodes? If the same thing is above and below because of similarity, there would not be anything in the cosmos which is determinately above or below by its own nature. (679,8-14)

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Simplicius explains the difference between Plato and Aristotle here as due to Aristotle’s attachment to the way people speak, something for which Plato has no regard. Plato does acknowledge the difference between centre and periphery,8 but he doesn’t think that that difference is relevant to weight and lightness. For Plato all the elements have weight because they have an impulsion to be in their proper places with things of their kind (those places being the same as Aristotle says they are). And so: Plato says that fire is heavy just like earth, and each of them rests in its proper place because of its own heaviness and is pulled away from its proper place to the degree that it is light. Accordingly heaviness alone belongs to the entireties , since they do not abandon their proper places and are not pulled away from them. But lightness also belongs to portions , and because of it they are also constituted so as to be transferred to unnatural places. (681,1-7) Later Simplicius asserts that the difference between Plato and Aristotle is purely verbal: Nothing prevents fire and everything else from having weight and the reason why each element moves to its proper place from being what Plato says it is. For Plato calls this kind of impulsion weight, differing with Aristotle verbally because Aristotle calls the impulsion to the centre weight and calls the centre below, and he calls the impulsion to the periphery lightness, in accordance with ordinary usage. But Plato says that what is common to them, the impulsion, is the same as weight …. (712,31-713,6) Simplicius adds that Aristotle himself says the same thing as Plato ‘spontaneously’ (autophuôs) at 4.5, 312b23-5, but his attempt to use that passage (726,18-20) is not convincing. In the material we have just discussed Aristotle himself does not mention what Plato says about weight at 63A5-E7 in the Timaeus, but is only concerned with Plato’s dismissal of a real above and below in the material preceding that. For Aristotle Plato states his theory of weight at 56B1-2 when he says that ‘what is composed of the fewest identical parts is lightest’,9 and assigns to Plato the view that, at least in the case of fire, air, and water, what is composed of more fundamental triangles of the same size is heavier. He argues that this position is incompatible with two things which he thinks are facts: (i) more fire moves up (i.e., for Aristotle, toward the periphery of the cosmos) faster than less; (ii) no amount of air is heavier than any amount of water. Simplicius would appear to think that Aristotle is representing Plato correctly;10 he even says (682,16) that Aristotle sets out Plato’s view clearly. And although Simplicius does not explicitly cite 56B1-2 in his comment on Aristotle’s criticism, he does cite it in his commentary on 3.1 at 573,9-11 and at 576,25-7 in ways which

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would seem to affirm Aristotle’s interpretation. However, he does not think that Aristotle is describing Plato’s entire account of weight and lightness when he invokes number of parts. Simplicius says: One should understand that Aristotle is following his own hypotheses when he infers that fire and air are … light and water is heavy, since, having made a distinction between natural above and below in the universe, he distinguishes light and heavy by motion up and down. But Plato does not distinguish them by the multitude or paucity of their planes. … (683,32-684,2) The sentence which follows is unfortunately lacunose, but Simplicius goes on to quote Timaeus 63E4-7 where Plato says that something is heavy because it moves toward its like, light because it moves toward what is different from it. Simplicius suggests that this passage indicates Plato’s notion of absolute weight and lightness: Consequently if someone wished to find also in Plato a distinction between absolutely light and absolutely heavy, he would find that in the words which have been set down just now they are not distinguished simply by motion up and down but by motion toward what is proper and motion toward what is alien. (684,9-12) Later he summarises his account of Plato’s views of weight and lightness: In the case of above and below we have said that Plato does not think these are natural in a cosmos which is spherical; in the case of the absolutely heavy and light we have said that he recognises them, but does not distinguish them in terms of motion downward and upward but distinguishes heavy in terms of motion toward what is proper to a thing and light in terms of motion toward what is alien to it …; and Plato does not say in a determinate way that one of the four elements is absolutely heavy, another absolutely light, but he says that everything is both heavy and light because everything is so constituted as to move both toward what is of the same kind and toward its contrary. (686,21-687,2) And, citing Timaeus 59C1-3, Simplicius purports to give Plato’s explanation of why a greater amount of one heavy thing can weigh less than a smaller amount of another: the greater amount contains more ‘gaps’. I discuss the remainder of chapter 2 (309a17-310a7), which is devoted to criticism of other views of weight, in section 3 of this introduction. At the beginning of chapter 3 Aristotle offers his explanation of ‘why some bodies always move up naturally and some always move down naturally and some move up and down’ (310a17-18) in terms of the change of something into its own form:

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Introduction If … what causes motion into what is above or below is what gives weight or lightness (to baruntikon kai to kouphistikon), and what is subject to movement is what is potentially heavy or light, then the motion of each thing into its own place is its motion into its own form. (310a31-b1)

Simplicius explains what this means: Why do bodies move down naturally? Because what it is to be heavy is naturally being below. Things which are at first potentially heavy are changed to being actually heavy by what is naturally constituted so as to cause motion with respect to heaviness, that is, by what produces earth or water; and they change into their proper form. … If these things are true and, as Aristotle says, ‘the motion of each thing into its own place is its motion into its own form’, what has taken on the form of heavy or light no longer moves. So if what moves toward the centre is heavy and what moves toward what is above is light, it is also necessary … that things in their proper places have heaviness or lightness (or rather only have them in actuality there) …. (697,27-698,7) Simplicius also describes the natural motion of fire, air, water, and earth in these terms: If the upper region gives form to light things which come to be when they come to be there and similarly for the lower region and heavy things, then for fire the upper extremity is the form because fire has its completeness in it, and for air fire is the upper extremity because air moves up as far as fire, and again for earth the centre is form and for water earth is, because when water has come to be in earth and taken on its form with respect to weight it rests. (699,26-31; for controversy over this specification of form see 700,3-30) At 310b31-311a1 Aristotle says that the four elements appear to have motive power in themselves ‘because their matter is closest to substance’. Simplicius offers the following explanation: By ‘matter’ he means their suitability and their potentiality, by ‘substance’ their complete form. For everything which is potentially is matter for that which it is potentially, and the substance of each thing is distinguished in terms of its complete form. Now since things which change place do not change with respect to something in themselves, but only with respect to place, things which are already complete with respect to their substance, even if they do have a certain incompleteness and consequently change place, are, in any case, close to completeness with respect to place. … Changing quali-

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tatively and growing and, still prior to these, coming to be are more matters of being affected, but changing place is more of an activity, so that things which are changing place, insofar as they are changing at all, have, indeed, not yet taken on their completeness in this respect, at least if they are changing toward actuality and their own form in this respect, but when they have arrived at their proper place through change of place they take on their proper completeness in this respect and become actually what they were only potentially until then. (703,13-29) When Aristotle says, And so when air comes to be from water and comes to be light from being heavy, it advances into what is above. At the same time it is light and is no longer coming to be light, but it is there. … And it is for the same reason that fire and earth which already exist and are fire or earth move into their own places if nothing impedes them. (311a1-8) Simplicius assumes that Aristotle is distinguishing between things which are changing into something and things which already are that thing: He says that when air comes to be from water and in general being light from being something heavy it advances into what is above, and, at the same time as it has taken on form and become completely light, it is no longer coming to be light – it is light. So if what rises to the top is light, it is already above; and so it is evident that, being potentially light and going into actuality, what rises to the top moves upward, and when it comes to be actually it is there. … Having spoken about things which are coming to be, he now adds a remark about things which are already actual, what is already fire or already earth, namely that in their case too, if nothing impedes them, they move into their own place for the same reason that those which are still coming to be fire or earth do. For also things that are actually and are held in an alien place by constraint or suddenly come to be in an alien place (as in the case of a fire which is ignited in our region or the stone which is produced in clouds ) move, if nothing impedes them, toward the place which is naturally appropriate for them and, having come to be there, they take on completeness of form. For a thing is in an alien place either because it came to be there and in a way still shares in the contrary nature from which it changed and which it discards when it moves to its own place, or because it is held there by constraint and thus in a way is disposed unnaturally; for if what is naturally constituted so as to rise to the top is constrained to lie below other things or if what is naturally constituted so as to lie below other things is forced to be detached and

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Introduction rise, it is then disposed unnaturally so that also when things which are thought to be already actual are in alien places they are in a way incomplete and have some degree of potentiality and move rapidly toward what is actual and complete. (704,31-705,24)

Aristotle begins chapter 4 by asserting things which seem to have been all along bubbling close to, if not at, the surface: Let us first make explicit what is obvious to everyone: what sinks to the bottom of everything is absolutely (haplôs) heavy, what rises to the top of everything light. In saying ‘absolutely’ I am looking at the genus and I mean those things to which both do not belong; for example, it is obvious that a chance quantity of fire moves up and one of earth down unless something else happens to prevent it, and a greater quantity moves faster in the same way. But things to which both belong are heavy or light in a different way, since they rise above some things and sink below others, as air and water do. For neither of these is absolutely light or heavy, since both are lighter than earth (since a chance portion of them rises above earth) and both are heavier than fire (since a portion of them, whatever its size, sinks below fire); but relative to themselves, one is absolutely heavy, the other absolutely light, since air of any quantity rises above water and water of any quantity sinks below air. (311a15-29) According to Simplicius Aristotle here assumes that there are absolutely heavy and light things and that they are earth and fire ‘on the basis of a common conception’ (707,10) or ‘on the basis of the phenomena’ (712,20), assumptions which he ‘demonstrates’ starting at 311b13. How Simplicius understands this ‘demonstration’ is not entirely clear to me. He seems to allow Aristotle the assumption that earth moves toward the centre and sinks to the bottom of everything, that is, satisfies the definition of absolute weight. 311b18-29 gives what might be called the core of Aristotle’s ‘demonstration’: And similarly there is something light. For we see, as was said previously , that things made of earth sink to the bottom of everything and move toward the centre. But the centre is determinate. So if there is something which rises to the top of everything, as fire, even in air itself, obviously moves up while the air is at rest, it is clear that this thing moves toward the extremity. … Therefore, fire has no weight and earth has no lightness, since it sinks to the bottom of everything and what sinks to the bottom moves to the centre.

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Simplicius gives a quasi-formal representation of the reasoning he finds here: Fire moves higher than air; what moves higher than air moves toward the extremity; what moves toward the extremity rises to the top of everything; but what moves toward the extremity and rises to the top of everything is lightest and absolutely light, just as what moves toward the centre and sinks to the bottom of everything is heaviest and absolutely heavy; therefore, fire is absolutely light, just as earth is absolutely heavy. (714,2-7) For Simplicius when Aristotle says that the centre is determinate he is making an assumption, which he goes on to demonstrate. He explains: He assumes it now because it is useful for showing that the extremity is also determinate, since what is equally distant from the extremity in every direction is the centre; so if the centre is determinate, the extremity must also be determinate. That the extremity is determinate is useful to him for showing that there is something absolutely light, since what moves to the extremity and rises to the top of everything is also absolutely light. (713,32-714,1) The demonstrations which Simplicius has in mind come at 311b29-312a3, but Aristotle makes no mention of determinateness and seems to be only concerned with showing that there is a centre toward which heavy things move (and perhaps away from which light things move). After these arguments Aristotle says, But since what sinks to the bottom of everything moves toward the centre, it is necessary that what rises to the top of everything moves toward the extremity of the region in which it makes its motion; for the centre is contrary to the extremity and what always sinks to the bottom is contrary to what rises to the top. Therefore it is also reasonable that heavy and light are two things, since the places, centre and extremity, are also two. (312a3-8) Simplicius comments: He has proved that the centre to which things having weight move is determinate; and since because of this it has also been proved that the extremity is determinate …, he proves that what rises to the top of everything moves to this extremity. For since sinking to the bottom is contrary to rising to the top, and the centre is contrary to the extremity, and what sinks to the bottom and is heavy obviously

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Introduction moves toward the centre, it is necessary that what rises to the top move toward the extremity. … Having proved that the centre and the extremity are two determinate places which are opposite to one another, he plausibly adds, ‘Therefore it is also reasonable that heavy and light are two things, since the places, centre and extremity, are also two’. For if the places to which the motions are directed are two and opposite, the impulsions related to these motions which are to these places would be two. (716,7-28)

I am not able to find any real demonstration in either Aristotle’s words or Simplicius’ account of them. Simplicius summarises what he thinks has happened and gives his account of what comes next by saying: He has proved that, since there are two opposite places, the centre and the extremity, it is necessary that there be two things which move to them, the absolutely heavy and the absolutely light. And he next proves on the basis of the opposition of these places to one another that there is also a place intermediate between them which has to each of them the relation of the other; for this is the specific feature of all things which are intermediate between other things, and so the intermediate place is above and an extremity relative to what is, in the strict sense, centre and below, and it is below and centre relative to what is, in the strict sense, above and an extremity. And, just as, since there are two extreme places, there are two extreme bodies, one absolutely light, the other absolutely heavy, so too, since there is an intermediate place having the specific feature of both , there is also an intermediate body, which is not absolutely heavy or light, but heavy and light relative to one or the other of the extremes: this is water and air. (717,23-718,2) In moving from one intermediate place to two bodies Simplicius is simply following Aristotle’s lead. Aristotle puts the maneouvre this way: There is also something between centre and extremity 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. (312a8-12) Simplicius is aware that there is something dubious about this reasoning. Aristotle, he says, could have divided places into above and below and proved that there are bodies which move naturally to them. ‘But, because the division is not exhaustive and the upper place is not all alike, nor is the lower one, but the last of the upper place and the top of the lower one are near to one another both in place and accordingly also by nature, and they are not absolutely above or absolutely below, the bodies in them,

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which are like parts, one of what is above, the other of what is below, are two and like one another’. (718,4-9). However, Simplicius concludes by referring the reader to On Coming to Be and Perishing for the more precise explanation of why there are two extreme elements and four all together. Simplicius says the same thing when Aristotle more or less repeats this assertion in 4.5, but now speaks of four ‘matters’: But since there is only one thing which rises to the top of everything and one which sinks to the bottom of everything, it is necessary that there be two other things which both sink below something and rise above something. Consequently it is also necessary that there be as many matters as there are of these things, namely four, but four in such a way that there is one common matter for all of them – in particular if they come to be from one another –, but a matter which is different in being. (312a28-33) Simplicius is bothered by Aristotle’s assertion that the existence of two intermediates is necessary. In saying this, he tells us, Aristotle is thinking of the particular contraries, the absolutely light and heavy. And he now indicates the necessity in an obscure way by indicating that what is intermediate between each of the absolute bodies is double because it is a limit; for just as the limit of what is absolutely light is light (even if it is not absolutely light, it is lighter than the things which come after it) and just as the limit of what is absolutely heavy is heavier than other things (even if it is not absolutely heavy), so too air is found to rise above other things (except for fire) and water is found to sink below other things (except for earth); and being confident about these things, he says that it is necessary that there be two things between the absolutely light and the absolutely heavy. But in On Coming to Be and Perishing he demonstrates in many ways that it is necessary that there are two intermediates and that there are four elements in all. (721,25-722,1) The doctrine that earth, water, fire, and matter have a common matter, but one which is different in being or account in each case is crucial for Aristotle’s substantive physics.11 The commonness of matter is needed to explain why the elements can change into one another, and the difference in being explains the different natural motions of the elements. It is perhaps difficult for some of us to think that the difference in being of what is really the same matter accounts for physical differences among the elements, but Simplicius seems to feel no difficulty whatsoever, thinking it sufficient to cite Aristotle’s assertion (Phys. 1.7, 190b23-4) in his discussion of coming to be that the subject of coming to be is one in number but two in form. Aristotle concludes 4.5 by arguing against those who make there be only

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one or two matters. In the final chapter of De Caelo, he considers Democritus’ attempt to explain why whether something sinks or floats in water sometimes depends on its shape or size. I discuss this material in section 3. 2. Aristotle’s criticism of Plato’s geometrical chemistry (Cael. 3.7, 306a1-3.8, 307b18; in Cael. 638,13-671,20) Simplicius’ discussion of Aristotle’s criticisms of Plato is a major document of late ancient philosophy.12 For, first of all, the criticisms put a severe strain on Simplicius’ view that Aristotle does not really disagree with Plato, but is only attacking superficial interpretations of him. But secondly and perhaps more importantly Simplicius brings in material from Alexander of Aphrodisias and from Proclus’13 responses to Aristotle’s criticism, situating himself between what might be called the hyper-Aristotelianism of the former and the hyper-Platonism of the latter. Here I shall be interested mainly in this aspect of Simplicius’ discussion. I mentioned in the previous section that Simplicius accepts Alexander’s claim that Plato commits himself to an analysis of his triangles as form/matter compounds and so should allow earth to interchange with the other elements, but that he departs from Alexander by saying that Plato does allow for this interchange. Proclus adopts the position that there is no such interchange and so dismisses Aristotle’s first objection (306a1-17; 642,1-644,18) that Plato’s view conflicts with the phenomena. The situation is similar in the case of Aristotle’s second objection (306a17-20; 644,19-646,25) that for Plato earth is more of an element than the others. After retailing Alexander’s formulation of the objection, Simplicius takes Alexander to task for not explaining what in Plato leads Aristotle to make it. After providing the explanation Simplicius gives Proclus’ response, according to which earth does have a special place among the elements, although it does interact (but not interchange) with them. Simplicius reasserts his view that interchange does take place, but concedes that in the case of earth it proceeds more slowly. It was pointed out in section 7 of the introduction to Mueller (2009) that a central feature of Simplicius’ interpretation of the Timaeus is his view that Plato’s triangles are natural rather than mathematical entities. Proclus adopts this position as well, and uses it (apparently with Simplicius’ approval) in responding Aristotle’s objection 4 (306a23-6; 648,11-23), and they both use it in response to objection 11 (307a19-24; 664,24-665,24) that Plato makes mathematical objects heat and burn). I suspect it underlies their response to objection 3 (306a20-3; 647,1-648,10) as well, although it is not mentioned. In 3 Aristotle objects that on Plato’s theory elemental change yields triangles hanging in suspension. Simplicius explains what Aristotle has in mind without indicating any misgivings, and presents an objection to Alexander’s suggestion that when water comes from air, the suspended triangles might combine to form fire. Simplicius responds (quite correctly) that Plato never made such a sugges-

Introduction

13

tion, and accepted that triangles would sometimes be suspended. Proclus puts the same point this way: ‘We should agree that in the change of what we call elements some parts often remain “half-breeds”’ (648,8-10). In two of Aristotle’s objections, it is claimed that Plato’s theory commits him to the existence of empty spaces because the fundamental solids cannot fill space (objection 6; 306b3-9; 650,16-657,9) and because objects could not completely fill their containers (objection 7; 306b9-22; 657,12659,10). Alexander also invokes the void against Plato at 646,14 in connection with objection 2 when he says that the dissolution of earth into triangles would create a void; in this case Simplicius responds by pointing out that the same thing could be applied to the other elements, but he maintains that it is irrelevant because the triangles are not mathematical objects. Neither Proclus nor Simplicius believes a void is possible. To deal with objection 6 Proclus, invoking a passage in the Timaeus, says that pyramids fill up the spaces among the octagons of water, and octagons fill up the spaces among icosahedrons of water and all three of these figures fill up the empty spaces in earth. Simplicius is aware that this answer is geometrically unsatisfactory, but he can only add to Proclus’ solution the inadequate suggestion that smaller particles will be sufficient for filling up empty spaces. In responding to objection 7 Proclus treats the relationship of the cosmic masses of the elements to what contains them differently from the relationships of the ordinary contents of a jar to the inner surface of the jar. For the latter case he postulates that ordinary containers have uneven rectilinear surfaces and can be completely filled by Platonic solids; however, the lunar sphere and the spheres beneath it contain no void because the surfaces of the masses they contain are bent to conform to their container. Simplicius, presumably relying on the notion that the surfaces of the solids are form/matter compounds, prefers to extend this solution to ordinary containers as well. These responses show how far both men are from the notion that in the Timaeus Plato is doing something like what we would call mathematical physics. In objection 8 (306b22-9; 659,11-661,14) Aristotle says that ‘they’ cannot accommodate the existence of continuous materials such as flesh. Simplicius says that Aristotle is arguing against both Plato and the atomists. He subsequently quotes Alexander: The elements, whether they are atoms or all the figures, do not fill out the space by being in contact with one another, but it is necessary for there to be a void between them, as was said previously. (659,23-6) Simplicius points out that the atomists embrace the existence of void, but agrees that their theories and Plato’s cannot account for continuity. Proclus’ response to Aristotle (and perhaps Alexander) is to say that in compounds ‘what has smaller parts moves between what has larger parts and fills the space, leaving no void’ (660,5-7). Simplicius commends this as an answer to Alexander, but is unwilling to allow a disharmony between

14

Introduction

Plato and Aristotle to stand uncontested. He suggests that Aristotle too did not believe in continuity: Perhaps, even according to those who say that the four elements … are primary, the bodies composed from them are not continuous in the strict sense or unified, but they are interwoven with one another in terms of small chopped up pieces, and when the single form of flesh or bone supervenes, it imposes apparent continuity and unity; this also happens with colours which are juxtaposed in small patches with the result that a single mixed form appears in them. I have also seen cloaks of this kind with their warp and woof of different colours. And even if, when the four elements are juxtaposed they pass on qualities and in a way alter one another in the direction of themselves, nevertheless the bodies themselves do not pass through one another nor are they unified with one another nor do they change completely into one another. (660,19-29) Simplicius takes a similar tack in connection with objection 14, where Aristotle says that, although Plato refers heat to the pyramid, he cannot give an analogous explanation for cold because cold is contrary to hot, but figures are not contrary to one another. Proclus responds that on Plato’s theory heat is not a pyramid, but a power of the pyramid; so too cold is a power of an unspecified figure. Simplicius is not satisfied with this answer and concludes, ‘But if someone were to insist that the contrarieties are due to the figures, one should recall what Aristotle says in this treatise, namely that there is also in a way contrariety of figures’ (669,17-18). Simplicius and Proclus agree that Plato’s fundamental particles are divisible and they accept Aristotle’s charge in objection 5 (306a26-b2; 648,24-650,15) that a part of fire is fire, but a part of a pyramid is not a pyramid. To avoid this objection Proclus insists that a single pyramid is a ‘seed’ of fire and is not fire. He suggests that a segment of a pyramid could be reshaped into a pyramid. Simplicius accepts that a single pyramid is fire, but proposes that division of an individual pyramid is a division into matter and that such matter can change its form. 3. Democritus14 (and others) Although the objections we have discussed in the previous section are primarily directed against Plato, Aristotle makes passing mention of atomistic ideas in the objections, usually by lumping together pyramids and spheres, the figures assigned to fire by Plato and the atomists (objections 5, 11, and 12; for objection 8 see the preceding section). Aristotle only mentions Democritus by name in objection 10 when he says, ‘For Democritus the sphere, being a sort of angle, cuts because it moves easily’; Simplicius says nothing about this assertion. However, he does mention Democritus in connection with objection 10 when Aristotle says that the

Introduction

15

sphere was correlated with fire because the whole of it is an angle; Simplicius remarks only that ‘the sphere moves easily because it touches a plane underlying it at a point’. When Aristotle has finished his criticisms of Plato on weight he turns at 4.2, 308b30 to the atomists’ treatment of the subject. What he says in the remainder of chapter 2 and again in chapter 4 at 312b19-313a6 about them and perhaps others and what the atomists themselves may have said have been the subject of much controversy which cannot be gone into here.15 A major topic of discussion has been the question whether the atoms themselves have weight. Here I shall only say that it looks to me as if Aristotle associates some kind of weight with the atoms and some kind of lightness with the void and concerns himself with the question whether the atomists can use the combination of atoms and void to explain what he thinks is the relevant behavior of the simple bodies. Aristotle begins by commending the atomists for dealing with a phenomenon with which Plato could not deal because he made weight depend only on the number of elements in a thing: the fact that a larger quantity of, say, wood, weighs less than a smaller quantity of, say, lead. Aristotle says that the atomists explain this phenomenon by saying that the wood contains more void. He adds, by way of criticism that they ought also to have said the wood contains less solid, that is, they ought to explain relative weight in terms of the proportionality of solid to void, because otherwise they would have to say that an amount of gold containing a sufficient amount of void would be lighter than a given amount of fire, whereas, in fact, any amount of fire is lighter than any amount of gold. At 309a27-b8, after indicating that Anaxagoras, Empedocles, and (apparently) Plato denied the existence of void, saying that the first two said nothing about the distinction between light and heavy, and briefly repeating the criticisms he had made of Plato (309a19-27), Aristotle repeats the same criticisms of the atomists and then adds that explaining relative weight in terms of the proportion of void to solid is also unsatisfactory because it would entail that more fire weighs the same as less. He then adds further objections based on the idea that the void is the cause of motion up, the solid of moving down. In the remainder of De Caelo Aristotle takes for granted that the atomists did not invoke proportionality of solid and void in their treatment of relative weight, but that they used more or less solid (or more or less void) as the only criterion. Simplicius himself reinvokes the proportionality criterion at 729,4-15, where he again gives Aristotle’s argument for rejecting it. Aristotle concludes his survey of his predecessors’ treatment of weight by (as Simplicius indicates) introducing general considerations applicable to all who discuss the subject while at the same time thinking of the people he has just discussed, Plato and Democritus. (309b29-310a13) In Simplicius’ representation Aristotle divides these people using two dichotomies:

16

Introduction (a) there is one matter; (b) there are two contrary matters; (i) weight is determined by size; (ii) weight is determined in some other way.

Simplicius indicates at 692,12-14 that Aristotle states his arguments against these alternatives more clearly at 4.5, 312b19-313a6, and he relies on that passage in interpreting what Aristotle says here. Against (a) Aristotle says: If there is only one kind of matter, there will be no such thing as absolutely heavy and light, as there isn’t for those who compose things from triangles. (309b33-4) Simplicius explains that the argument is that there will be no absolute lightness if the single matter is heavy and no absolute heaviness if it is light (cf. 4.5, 312b19-28). Against (b) Aristotle says: But if there are contrary matters, as there are for those who invoke void and full, there will be no reason why the things intermediate between the things which are absolutely heavy and light are heavier and lighter either than one another or than things which are absolute. (309b34-310a3) Here the characterisation of the full and void as two matters implies nothing else about the atomist conception of them than that they made ordinary things composites of full and void. To explain what Aristotle says Simplicius uses the example of void and full, and takes the intermediates as composites of them.16 He says that such people will identify the void with the absolutely light, the full with the absolutely heavy, but, he says, they will not be able to explain why the intermediates are heavier or lighter than anything since they cannot explain why the void is light and the solid heavy (cf. 309b18-23). Simplicius mentions that these people could say that composites are heavier than the void because they contain solid and lighter than the full because they contain void. But he asks, ‘Or is it the case that those who are not able to give an explanation why one composite is heavy and another light also cannot give the explanation why composites are heavier or lighter than anything at all?’ (691,30-2). He then considers the possibility of their saying that, given equal volumes, one composite is heavier than another if it has more solid and less bulk than the other. However, he says, this explanation could not be extended to cover the comparison of different amounts of fire and earth. Aristotle takes up alternative (b) again at 312b32-313a6, where he actually identifies void with fire and full with earth, and repeats the argument that there will be some amount of air which is heavier than a given amount of water. Aristotle may have this same argument in mind at 309b34-310a3.

Introduction

17

Aristotle takes up case (i) at 310a3, saying it is artificial, but at least provides – as he himself does – a way of distinguishing the four elements. Simplicius blurs or eradicates the distinction between (i) and (ii) by saying that Aristotle is now talking about ‘people who distinguish heavy and light in terms of having thick or fine parts, which is to say in terms of condensation and rarefaction and who also hypothesise a single matter for these differentiae’ (692,26-8). Simplicius contrasts Plato and the atomists, who cannot satisfactorily explain weight and lightness, with these people, for whom ‘each of the four bodies will have the impulsion of weight or lightness because of its participation in fineness and thickness and the proportion involved in it’ (692,31-693,2), but he does not tell us who these people are. However, Simplicius repeats Aristotle’s criticisms, that these people will not be able to explain absolute heaviness and lightness (repeating 309b33-4) and will be committed to saying that a lot of fire or air, consisting of more of the one matter, will be heavier than a small amount of earth or water. Aristotle makes this same objection against saying that there is only one matter at 4.5, 312b28-32. Aristotle devotes the last chapter of De Caelo to Democritus’ attempt to explain ‘why flat pieces of iron and lead float on water, but smaller and less heavy ones sink down if they are spherical or elongated like a needle; and why some things float because of their smallness – for example, shavings and other things made of earth or dust float in air’ (313a16-21). According to Democritus ‘hot things’17 which move up from the water support flat things which have weight, but narrow ones fall through because only a few hot things strike against them. Aristotle tells us that Democritus raised a difficulty for this solution by saying that the same thing ought to happen more frequently in air, but does not. Simplicius provides the reason it should happen more in air: ‘there are more hot things in air than in water’ (730,17). Aristotle gives a very hazy indication of what he calls Democritus’ feeble response, which Simplicius fills out: in air the hot things are dispersed and move in all directions whereas in water they are condensed and move up in one direction. Aristotle gives his own answer in terms of the varying capacities of things to divide and be divided. 4. 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:

18

Introduction 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 his 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 I, the remaining pages being torn out. Among the other manuscripts which Heiberg cites are:18 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), 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. 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:

Introduction

19

(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) Simon Karsten (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.19 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.20 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. For most of the material translated here Karsten followed 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). For Heiberg’s pages 722,1-726,3 and 727,17-731,29 Karsten used a manuscript which Heiberg takes to be copied from K: Paris 1910, dated 1471, in the National Library in Paris (Wartelle (1963), no. 1396). In the absence of a critical apparatus or inspection of these two manuscripts, it is impossible to tell what alterations of his source Karsten made, but there is little doubt that he made ‘improvements’.21 I have thought it desirable to adopt them even more often than Heiberg. 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. 5. Simplicius’ quotations This part of Simplicius’ commentary is marked by extensive quotation of other authors, notably Plato (the Timaeus), Proclus, and Alexander. Sim-

20

Introduction

plicius quotes TL twice, at 641,11-14 as evidence that the Timaeus involves a commitment to an Aristotelian conception of form and matter and at 646,6-9 to supply the reason for Plato’s saying in the Timaeus that earth is the oldest thing inside the heavens. The following list indicates the extent of Simplicius’ quotation of the Timaeus: 49B7-C2

642,11-14

49C6-7

642,15

49E6-50A4 637,6-11 50A4-B5

636,22-7

50B10-C6

643,31-644,4

50B10-C3

637,15-17

50B10-C1 53C2-4

658,5-7 641,25-7

53C6-8

656,21-3

54B6-D3

639,12-22

56B7-C3

641,18-21

56C8-E1

639,23-640,3

56E8-57A7 666,24-30 57C8-D5 656,28-657,2 57D1-2

671,9-10

59C1-3

687,4-6

61D6-62A5 664,14-23 62A5-B7 669,21-8 62C8-63A5 680,12-25 63A5-D4 63B1-C5

681,11-29 717,3-11

(as evidence that Plato thought earth does appear to interchange with the other elements) (as evidence that Plato thought earth does appear to interchange with the other elements) (as evidence that Plato believed in enduring matter) (as evidence that Plato believed in enduring matter) (as evidence that Plato believed in enduring matter) (as evidence that Plato believed in enduring matter) (Plato’s characterisation of matter) (as evidence that Plato thought figures are more fundamental than qualities) (three-dimensional objects are contained by planes) (the two kinds of triangles and the non-interchangeability of earth with the other elements) (as evidence that Plato thought his geometrical chemistry was a hypothesis) (the non-interchangeability of earth with the other elements) (on physical processes) (as evidence that Plato thought the primary triangles come in different sizes) (as evidence that Plato thought the primary triangles come in different sizes) (for Plato gaps explain why a larger thing may be lighter than a smaller one) (Plato’s account of heat) (Plato’s account of cold) (Plato’s denial that there is an above and a below in the universe) (Plato’s account of heavy and light) (Plato’s account of heavy and light)

Introduction 63D4-6

717,19-20

63E4-7 63E4-7

681,29-682,3 684,4-6

21

(as evidence that Plato knows the difference between motion toward and away from the centre) (Plato’s account of heavy and light) (Plato’s account of heavy and light)

Turning to Alexander, I first look at 652,11-655,27, which are clearly derived from him. Most of that passage presents geometric arguments of Potamon concerning space-filling figures. I have treated 652,11-653,6 and 653,10-654,11 as quotations of Potamon, although in the case of the latter Simplicius says he has added letters to clarify the argument. Heiberg presents 654,14-655,27 as a continuous quotation of two paragraphs, although it is preceded by the statement that Simplicius is going to give an alternative proof, using letters, concerning the hexagon due to Alexander. That proof takes up the first of Heiberg’s paragraphs, and then there are letterless arguments about solids, which, it seems, Simplicius again ascribes to Potamon. I, accordingly, treat the first paragraph (654,14-655,8) as a quotation of Alexander, the second (655,9-27) as a quotation of Potamon. Heiberg also marks the following as quotations of Alexander: 647,14-19; 655,29-31; 672,14-16; 686,4-6; 700,12-16; 720,9-11. I also treat 646,15-19, 659,23-6, 693,25-32, and 694,10-695,2 as quotations of Alexander.22 The case of Proclus’ responses to Aristotle’s objections to Plato is more difficult. Heiberg marks only five passages as quotations. Three of these (656,6-14; 658,27-659,7; 660,4-12) are safely treated as all Proclus had to say as a reply to an objection. The other two (650,7-10 and 670,20-671,5) are partial. The second of these is instructive. Simplicius begins with a sentence in indirect discourse, ‘Proclus says that we do not distinguish …’, and continues ‘For, he says, the number of planes …’. Heiberg treats the whole continuation as direct quotation. I have no doubt that the first sentence is just a grammatical reformulation of what Proclus said, and have opted to treat it as a quotation in my translation. I have done the same with the other cases, which are quite parallel except that the continuation does not include the words ‘he says’. Accordingly, I treat all of the following passages as quotations of Proclus (asterisks indicate those marked as quotations by Heiberg): 643,13-27; 645,17-28; 648,2-10; 648,1923; 649,30-650,3 + 650,7-10*; 656,6-14*; 658,27-659,7*; 660,4-12*; 663,4-15; 663,27-664,12; 666,9-15; 667,22-30; 668,20-669,3; 670,16-20 + 670,20-671,5*. The one representation of a response of Proclus which I do not take as a direct quotation is 665,16-22. 6. 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

22

Introduction

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 Aristotle’s 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. For simplicity I shall refer to the material covered in this volume as the last part of Cael. 2. 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), 2-4 (= Brennan and Brittain (2002), 2-4). 3. On Simplicius’ works see Hadot (1990), 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), 105-40 (contra Simplicius’ authorship) and Hadot (2002) (pro), and Perkams (2005) (contra). Simplicius’ other extant work is a commentary on Epictetus’ Manual. 4. In this introduction I take for granted a number of points which are discussed on relevant passages in the footnotes to the translation. 5. See p. 11. 6. On Alexander see section 8 of Mueller (2009). 7. This answer is stated more fully at 644,7-18. 8. See also 717,15-20. 9. In a note on this passage Cornford (1937) mentions two others in the Timaeus with a similar implication, 58D8-E1 and 59C1-2. 10. In criticising Aristotle, Cherniss ((1944), p. 165) dismisses 56B1-2 as a ‘single passing remark’. 11. I mention a difference between Alexander and Simplicius on the question of the characterisation of these matters: for Alexander these matters are three-dimensional bodies possessing only weight or lightness, but for Simplicius the matters are characterised by the fundamental qualities such as heat and cold, which are prior to lightness and heaviness. See 720,9-13. 12. I have treated this discussion in Mueller (forthcoming); here I deal only with some of its most significant aspects. 13. On Proclus see Siorvanes (1996). 14. On Democritus see also section 7 of the introduction to Mueller (2009). 15. For a concise statement of the standard view of what the atomist theory of weight was see Taylor (1999), 179-84, and for a thorough study of the evidence which reaches different conclusions O’Brien (1981). 16. Simplicius mentions an alternative account of these intermediates at 692,7-11.

Introduction

23

17. Nothing Aristotle says indicates that these things are atoms; Simplicius uses the word ‘seeds’. 18. I mention only the MSS referred to in my footnotes. 19. A fact first noticed by Peyron (1810). 20. 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. 21. cf. Bergk (1883), p. 143 n. 1 and p. 148. 22. 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.

SIMPLICIUS On Aristotle On the Heavens 3.7-4.6 Translation

on the third of Aristotle’s On the Heavens (contd.) 305b28-306a1 remains that come to be by changing into one another, [and this in two ways: either by reshaping as a sphere or a cube might come to be from the same wax or, as some people say, by dissolution into planes. (305b31) Now if they come to be by reshaping, it follows necessarily that they must say that bodies are indivisible, since if they were divisible, a part of fire would not be fire nor would a part of earth be earth, since a part of a pyramid is not always a pyramid] and a part of a cube is not always a cube. With separation out having been eliminated remains that the elements come to be from one another because of changing into one another. For if they come to be from one another it is necessary either that one be separated out from the other, each being actual (and this is not even coming to be in the strict sense but only apparent coming to be), or that that from which there is coming to be changed into the result. He says that this also might happen in two ways: ‘either by reshaping as a sphere and a cube might come1 to be from the same wax’ which is shaped differently at different times; or the coming to be follows from the dissolution into planes of that from which there is coming to be and by the composition from those planes of what comes to be because of change, as if a house were broken up and another house were composed from the same matter. And this too is also reshaping, albeit not the shaping of one continuous substratum but of several things which are combined together. It is clear that there is also a third way in which elements come to be from one another because of changing, the one which Aristotle accepts. This is not because of change of shapes but because of change of other qualities called active, namely heat, coldness, dryness, and moistness, from which the other qualities are derived. He first argues against the reshaping as the reconfiguration of a single substratum, and it seems that this way of coming to be is put forward for consideration on the basis of what is said in the Timaeus. For, in speaking there about the change of the elements, says:2 We should exert ourselves to speak again still more clearly about this. Suppose someone were moulding all kinds of figures from gold and3 he never stopped reshaping each figure into all the others; then if a person pointed to one of them and asked

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Translation ‘What is that’, it would be much the safest as far as truth is concerned to say ‘It is gold’, and never to speak of the triangle and whatever other figures were coming to be in the gold, figures which are changing while they are being posited, as beings.

That he offers these words not because the change from one another comes about because of reconfiguration but as an illustration of the fact that the underlying matter endures while its forms change is made clear by several things which precede this passage. Since the whole passage (which is long) makes the meaning clearer, it is necessary to quote a few things from it. Having said about the change of the elements into one another that it is not proper to use a determinate term to name what is always coming to be, such as ‘this fire’ or ‘this water’, because it is always changing but that one should call it ‘the ever such and such’,4 he adds:5 what is always such and such fire and the same with everything which comes to be. The only thing which we should refer to using the word ‘that’ or ‘this’ is that in which each of them is always coming to be and appearing and from which it in turn passes away. But as to what is of some sort, hot or white or any one6 of the contraries and everything which is composed from them, we should not call them7 any of these things . Then immediately after these words he brings in the passage I have just set out about the reshaping of gold as an example capable of showing more clearly what he has said; he uses the word ‘figure’ in place of ‘shape’ (morphê) or ‘form’ (eidos) in any sense, which is why he elsewhere uses both ‘shape’ and ‘figure’8 when he says about matter:9 It is always receiving all10 things, but it does not ever in any way take on11 any shape which is similar to the things entering it; by nature it lies as a matrix which is changed and given figure by the things entering it.

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It is clear, then, that the notion of reshaping is not Plato’s even if it is taken from the words of Plato. (305b31) Aristotle says against those who generate the elements from one another in this way that it follows for them that they must say that the elements are not divisible in such a way that a part of fire is not fire. For if elemental fire is fire because it has a pyramidal figure, if it were divided in such a way that the parts of the pyramid were no longer pyramids, a part of fire would not be fire, because it

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does not have the figure of fire, which is absurd. And it is the same with the other elements, since it is unreasonable that a part of water not be water or a part of air not be air. (He says that a part of a pyramid is ‘not always’ a pyramid because when it is divided in one way it is divided into pyramids; but when it is divided in another, one part will be a pyramid, but the rest will not be pyramids; and when it is divided in a third way, not even one part will be a pyramid.) So it will turn out that the elements are not divisible into things similar to them, but this has been proved impossible.12 This absurdity also follows for these people when a pyramid is divided: that there is a body which is neither an element nor composed of elements.13 But if someone were to say that, just as fire is seen to be divisible into fire, a fire-pyramid is divisible into pyramids because being fire lies in being a pyramid, he will be refuted on the basis of the other bodies. For if a part is subtracted from an earthcube, it does not change into a cubical figure, but it continues to have the shape it had when subtracted.14 But perhaps someone might say that fire is not a pyramid and earth is not a cube, but pyramid and cube are the elements of fire and earth;15 and all fire, even the smallest, is divisible into fire, and all earth is divisible into earth, but if a pyramid or cube were divided, there would be a destruction of the elements of fire and earth. And there also follows from this the absurdity that there is a body which is neither an element nor composed of elements.

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306a1 If by dissolution into planes16 He spoke against this hypothesis at the beginning of this book,17 and now he raises objections to it through fifteen arguments. However, there he was enquiring whether or not there is any coming to be at all and whether there is coming to be of everything or only of some things, and he attacked this hypothesis which makes every body come to be and perish;18 but here he is enquiring about the way in which the elements come to be, and, having proved that they come to be from each other and that it is not by reshaping, he is carried back again to this hypothesis, which says that solid figures are proximate elements of these four bodies, fire, air, water, and earth, bodies which we call elements but which, as Plato says,19 are not even to be ranked as syllables but are even more composite since they are composed of the solid figures, pyramid, cube, and the others, these figures are composed of planes, and the planes are composed of matter and form. We should again recall this hypothesis so that what Aristotle is going to say will be understood more precisely.20 They hypothesise two fundamental right triangles, one the isosceles, the other the

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scalene which has the greater side double in length of the lesser (they also call this a half-triangle21 because it is the half of an equilateral triangle which is bisected by a perpendicular from the vertex to the base). And a square is brought to completion from the isosceles triangle (which Timaeus also calls a half-square) when four of them have their right angles brought together into one centre; when six such squares are joined together they produce the cube, which has eight angles,22 and is the element of earth. The half-triangle produces the pyramid, the octahedron, and the icosahedron, which are assigned to fire, air, and water. And the pyramid is composed from four equilateral triangles each of which is composed from six half-triangles, the octahedron from eight equilateral triangles and23 forty-eight half-triangles, the icosahedron from twenty equilateral triangles and one hundred and twenty half-triangles. Because of this the three which are put together from one element, the half-triangle, are, according to them, so constituted as to change into one another, but earth, because it is composed from a triangle different in kind, can neither be resolved into the other three bodies nor composed from them. Plato says about these things:24 We should now be more specific about what was previously said in an unclear way. All four kinds appeared to come to be through one another and into one another, but this appearance is not correct. For four kinds come to be from the triangles which we have chosen, three from the one which has unequal sides, and only the fourth is put together from the isosceles triangle. Therefore, they cannot all be dissolved into one another in such a way that a few large things come to be from many small ones and vice-versa, although three of them can; for these three are by nature composed from one triangle, and when larger things are dissolved many small things will arise from them and take on the figures which are appropriate for them, and, again, when many small things are dispersed into the triangles they will bring to completion another single large kind of one mass. And a little later he adds the following about earth:25

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On the basis of everything we have previously said about the kinds, it is most likely that the following will happen. When earth encounters fire and is dissolved by its sharpness, whether it happens to be dissolved in fire itself or in a mass of air or water, it will keep moving until its parts again encounter one another somewhere and are put together and earth comes to be; for they will not ever enter into any other kind. But when water

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is broken up by fire or even by air, it is possible that combine into one body of fire and two of air. And he goes on to say the same sort of thing about air and fire. As Alexander also correctly recognised, what is said at the beginning of the passage, namely that ‘We should now be more specific about what was previously said in an unclear way’ is said because earlier Plato had hypothesised that all these things are composed of the same matter and said they change into one another, but later instead of matter he directly hypothesises different triangles for them and no longer accepts that they come to be from one another. Alexander objects to this doctrine in the following way: If, according to what they say, matter, according to Plato, is given form by the triangles and bodies are generated from them, why would it not be possible that the matter which underlies earth be subsequently given shape by the triangles which give form to water and air and fire?26 I think it should be said in response to this objection that the matter which underlies in common receives a different triangular form at different times and because of this all the bodies change into all the bodies when the triangles change directly with the common matter as substratum; but the figures assigned to the four so-called elements, the cube, pyramid, icosahedron, and octahedron, because they do not all have a common triangle directly underlying, do not all change into one another, but only the three composed from the half-triangle do. If this answer has been accepted it is possible to dissolve the objection stated by Alexander and the one which will be stated first by Aristotle.27 Different Platonists have responded to these objections brought against what is called the coming to be of bodies from planes, and Proclus of Lycia, one of the successors of Plato, who lived shortly before me, wrote a book28 which dissolves the objections made by Aristotle here. Accordingly, I thought it would be good to append Proclus’ resolutions of the objections as briefly as possible. It is now an appropriate time for me to say what it has been my custom to say frequently. The disagreement between the philosophers is not substantive, but Aristotle pays attention to those who understand Plato superficially and frequently raises objections against the apparent meaning of what Plato says and what can be understood in a worse way, and he seems to be refuting Plato.29 And I think it is clear to see that he also does this in connection with this material in which Plato has written the opinions of the Pythagorean Timaeus. For because he explains the differences between the qualities heat, cold, dryness, and moistness on the basis

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of difference of figures it is prima facie clear that he is seeking other principles of the coming to be of these four bodies, fire, air, water, and earth, principles which are prior to the qualities relating to heat, cold, dryness, and moistness and are found in differences in quantity because these differences are more akin to bodies. For as Theophrastus reports,30 Democritus said earlier that explanations in terms of heat and cold and such things are amateurish, since the soul yearns to hear another principle which is more appropriate to body than this sort of activity of what is hot. Timaeus himself makes clear in a succinct way that they say that these four elements come to be from form and matter when he says:31 The principles of things which come to be32 are matter as substratum and form as the logos of shape. What is generated from these are the bodies earth and water, air and fire. The generation33 of these is a follows. Every body is composed of planes, and a plane is composed of triangles ….

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Timaeus takes the plane to be more fundamental than body and among planes he takes the triangle to be more fundamental, since it is the first of plane figures; and among triangles Timaeus takes the ones that are more fundamental and then the bodies which are first constructed from them and are most beautiful, the pyramid and those co-ordinated with it. Plato says:34 One35 should think of all these things as so small that we see no one of any kind individually because of its smallness, but we do see the masses of them when many are collected together. And, as I said, it is prima facie clear that they thought the figures are more fundamental than the other qualities and that they hypothesise figures of this kind using a plausible account. And Plato makes clear that these things are like the hypotheses used by the astronomers with which, when they are hypothesised, it is possible to preserve the phenomena36 when he says in the words of Timaeus to those with Socrates:37 But since you take part in the paths followed in education (he means mathematical paths) through which it is necessary to exhibit what I say, you will follow.

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If what is said is can be exhibited,38 it does not hold absolutely, but either it holds or something like it does. Next, let us return to the text and look at Aristotle’s first objection.39

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306a1-17 If by dissolution into planes, [it is first of all absurd that they do not generate all of them from one another, but it is necessary for them to take this position and they do. For it is not reasonable that only one does not participate in the change, nor is this what appears to perception; rather all appear equally to change into the others. The result is that people who are speaking about phenomena say what does not agree with the phenomena. The reason for this is that they do not take their first principles correctly, but they want to lead everything back to certain definite opinions. But perhaps the principles of perceptible things should be perceptible, those of eternal things eternal, and those of perishable things perishable, or, to put it generally, principles should be homogenous with their subjects. But because of their love for these things, these people seem to act in the same way as those who protect their theses in discussion; holding on to their principles, they submit to all their consequences as true, as if one shouldn’t judge some principles on the basis of their results and most of all on the basis of their end. But the end of productive science is the product and that of natural science] is what always appears to perception in the strict sense. He first censures this hypothesis for not generating all from one another since, according to these people, earth does not come to be from something else nor does it change into something else. Having said that it is necessary for them to say this because it is a consequence of their hypothesising triangles, he adds that they do say this; for they do say it explicitly, and they give the reason why there is no transformation of earth. So he censures this doctrine in two ways: on the basis of reason because it is not reasonable, when the four are co-ordinate, ‘that only one of them does not participate in this sort of change’; and on the basis of perception because all are equally seen to change into one another. Plato himself says this:40

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First of all, we see (or think we see) what we now call water become stone and earth when it is solidified, and this same thing again become wind and air when it is dissipated and separated, and air become fire when it is enflamed. And then, having talked about the converse direction of the same things, he adds:41 And so, as it appears, they pass on coming to be to one another in a circle.

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And so it is thought to be naïve to do violence to what is clear among perceptibles because of hypothesising undemonstrated principles, which is what Aristotle says turns out to be the case with these people, since, although speaking about the phenomena, they say things which do not agree with the phenomena. And he says that the reason for this is that they do not take the first principles of perceptibles correctly, since they ought to have been homogeneous with what results from them, so that ‘the principles of perceptible things should be perceptible, those of eternal things eternal, and those of perishable things perishable’. Aristotle adds the word ‘perhaps’ because it is not necessary that the principles of perceptibles always be perceptible; for matter is a principle of perceptible things, but it escapes perception. Aristotle says that these people want to lead everything back to definite opinions, namely, as Alexander says, to the eternal principles; they do not take appropriate principles because they reduce numbers to the monad and bodies to planes. (But perhaps he means by ‘definite opinions’ the deeper understandings of mathematical principles, which they have determined.) He shows in what he says next that ‘because of their love of these things’ – meaning their love of mathematics – these people are like those who protect their theses in discussion. (A thesis is a paradoxical and undemonstrated assumption,42 for example, that anyone who says anything speaks truly.) He says that these people submit to and accept all consequences which are absurd to reason (such as that those who say they are speaking falsely are speaking truly) because they are completely confident that their own principles are true and think that not maintaining their principles is more absurd than any absurdity. However, he says, one should judge some principles which one hypothesises – obviously the ones which are not clearly true – on the basis of their results and most of all on the basis of the end which the principles have in view. ‘But the end of productive science is the product’, that is, the finished thing, e.g. a cloak in the case of weaving; for if someone were to say that bronze is the subject or matter or material principle of weaving he would be refuted when it was shown that the cloak was made from wool rather than bronze. But just as the end of a productive science is the product, so the end of theoretical science in general is truth in general and that of natural science is truth in that which appears to perception in the strict sense, successful perception.43 Proclus says the following against this objection: We should say the very contrary of this: those who make earth transform and change things that are unchanging are not following the phenomena. For it is not possible to see earth changing into other things anywhere. Rather things made of

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earth change insofar as they are filled out with air or water, but all earth is unchangeable when it is only earth, e.g., when it is ash or dust. For in metalworking, what is moist is entirely consumed, but what is made of ash remains unaffected. This is not because earth is in no way affected by other things, since it is divided by other things which strike it, but its parts remain until they again encounter one another and make of themselves a single thing. But if someone were to say that earth, which is cold and dry, changes into other things by means of qualities, then it would change into fire faster than water does. However, water is observed to catch fire as a whole, but earth just by itself does not catch fire.44 And the heavens are not divisible and do not change; but earth, which is the oldest of the things inside the heavens, is divisible and does not change; and what is intermediate is divisible and does change.45 The philosopher Proclus says these things. And we wish46 to preserve both what is suitable to the co-ordination of earth with other things and the necessity that things made from the same matter change into one another with the matter enduring through the change, something which Plato also bears witness to when he says:47 It is always receiving all48 things, but it does not ever in any way take on any form which is similar to the things entering it; by nature it lies as a matrix which is changed and given figure by the things entering it, and because of them it appears different at different times. And the things which enter into it and depart are copies of the things which always are and are modeled after them in a way which is difficult to describe …. and because one should also not ignore the passages which were set out a little while ago49 in which Plato says that in a way earth does come to be from the other simple bodies and in a way it is unchangeable, and also in order that Plato not be thought to disagree with himself nor Aristotle to disagree with Plato, what was said just a little while ago50 should be said : according to Plato, earth changes into the other simple bodies and changes from them insofar as it is composed from the same matter, first matter, but insofar as it is composed directly (prosekhous) from the isosceles triangle, it is unchangeable. For so long as the triangles keep their own specificity, earth cannot come to be from the half-triangle nor the other simple bodies from the isosceles triangle. But when the triangles themselves are broken up51 and re-combined and given shapes, then what was previously an isosceles – either the whole or a part of

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it – becomes a half-triangle and then the coming to be of earth from the others (and of the others from it) is made manifest since there is a resolution of the triangles down to their matter. And if this didn’t happen the doctrine of matter which is entirely without form and receives the forms of everything would be empty.

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306a17-20 It follows for them that earth is most of all an element [and only it does not perish, if, indeed, what is indissolvable is imperishable and an element; for only earth] cannot be dissolved into another body. This is the second argument, and it reduces to the absurdity that earth is most of all an element or even is the only element, even though earth is thought to be inferior to the other elements.52 He proves that this absurdity follows in this way: if [i] earth cannot be dissolved into another body, but remains the same, and [ii] what cannot be dissolved into something else is imperishable, and [iii] what is imperishable is primary, and [iv] what is primary is more an element than the others, then earth will be the element for them. (He says that earth cannot be dissolved into another body because they said that it is dissolvable but into the triangles of which it is composed; but even then no body other than earth comes to be again from those triangles.) Alexander offers this succinct interpretation, but he pases over any explanation of the argument. For why is only earth indissolvable into another body even though the other figures are also dissolved into planes just as the cube is? And why, if earth cannot be dissolved into another body, is it imperishable even though when it is dissolved into planes it perishes? However, Aristotle seems to be criticising what Alexander indicates briefly with the words ‘no body other than earth comes to be from those triangles’. For each of the three is dissolved into triangles from which the other two are also composed, and consequently it is said to be dissolved into another body, namely the one which is composed from the triangles belonging to the dissolved body; therefore, the body would be in a way composite and composed from that body of which the planes in it are elements. But even if earth is dissolvable into planes, it is not into the planes of another body. Consequently Aristotle calls earth imperishable because the planes of earth remain and do not become some other body; rather in a way they are earth and change from earth into earth, but what perishes changes into something else. So if it is proper to an element to be imperishable and neither composed from nor dissolved into a different body from which it is also composed, earth would be most of all an element. However, if an element is that from which other things come to be and into which they are resolved, earth would be less an element.

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The philosopher Proclus answers this objection, while conceding53 that earth does not change in any way into the other three bodies. He says: Plato has also called earth the first and oldest of the things inside the heavens54 because it does not change into others things and the other things fill out the earth, being seated in its hollows, that is, water, air, and the fire in sublunary things. But the very fact that earth is in a way divided by the others55 makes it one of the elements, since division is also a way of being affected which destroys continuity. And if earth is both affected by being divided by the others and also acts on them by compressing and contracting them and consequently breaking them up, it is reasonable that earth is to be co-ordinated with and distinguished from these things by which it is affected and on which it acts with respect to what is in a way the same affection. For each is a dividing even if finer things divide in different ways with their sharpness56 (as is the case in the arts with saws, drills, and knives), and thicker things compress and contract in different ways (as is the case with a rope used to hoist a sail57 and a pestle). This is what the philosopher says. But perhaps, as I have also said previously,58 even if earth does not change directly into the others, nevertheless the resolution of earth into the matter which is common also makes both earth come to be from the others and the others come to be from earth. And notice how this agrees with what happens. For even if earth both acts on the others and is acted on by them, nevertheless it takes time and is difficult. For earth is not acted on by fire in the way that air and water are, nor is it acted upon by water or air in the way the others are; and neither is it like things which easily cause things to change place in the way the others do; for since it was really given substance around the centre of the universe it needed to be not easily changed either in substance or in activity. Plato does not give the reason why earth is the oldest of the things inside the heavens,59 but Timaeus himself writes the following about earth in the treatise which Plato follows:60

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Earth is the oldest body inside the heavens. Water was never generated without earth; and air was never generated apart from moisture; and fire would not endure if it were isolated from moisture and matter, which it ignites. So earth is the root of all things and the support of everything else. Air and fire are seated in the hollows of the earth, but they are stagnant, not pure. And in the Phaedo Plato hymns the highest

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points of earth as extending right up to the ether, although I think that there he is using much that is mythical and hints at more obscure matters; for he does call his account of this a myth.61 Alexander adduces his own objection against those who say that earth is dissolved into planes but does not change into another body: If earth, which is a body and occupies space, is dissolved into plane triangles and does not change into any other body, the space which the dissolved earth occupied will be empty, so that if they do not think there is a void, earth could not be dissolved into the elements at all.

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But it is possible to generalise this difficulty. For these people say that when the other elements are dissolved the triangles are not immediately joined together into another body, but rather they remain dissolved for some time. And if they said that the triangles are mathematical Alexander’s objection would be reasonable, but if they say they are natural and have depth, it is clear that they also occupy space when they are dissolved and that at that time all occupy a space equal to that which they occupied when they were conjoined. Aristotle adduces this as the fourth objection.62

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306a20-3 In addition the suspension of the triangles in the dissolved [is not reasonable. But this comes about in the change into one another] because they are composed from unequal numbers of triangles. Having objected to what those who assert that bodies are composed of planes say about earth, he now objects to what they say about the other three elements. In the case of earth he censured them for not having it change into or from the others; in the case of the three which are said to change into each other he adduces the following absurdity: because they are composed of an unequal number of triangles, both the equilateral triangles and the things from which the equilateral triangles are composed, it follows that certain triangles are suspended when air comes to be from water or water from air. For if water is composed of twenty equilateral triangles and air of eight, then, if air comes to be from water dissolving and one water body is dissolved into twenty triangles, two bodies of air are produced and four triangles are suspended in an empty way, as someone might say. And if water comes to be from air and three bodies of air are dissolved into the construction of one body of water, there are again four triangles too many. Alexander says:

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Water and fire will not come from air at the same time in such a way that the four triangles produce fire (as is said in the Timaeus63); for air changes into water when it is made colder and denser, but this same cause cannot also generate fire. And how can it not be absurd to say that by necessity it must always be the case that fire also comes to be when water comes to be from air?

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So Alexander. But if I understand anything, Plato does not say that fire and water come to be from air at the same time,64 but that two bodies of fire come to be from one part of air when it is dissolved, and one body of fire and two of air come to be from water when fire both evaporates the water and changes it into fire.65 But Plato clearly does admit that some triangles do remain suspended for some time when he says of earth that when it is dissolved it moves ‘until its parts somewhere encounter … one another and become earth ’.66 And what is absurd about that when, if a composite is dissolved, the things which we call elements67 often remain by themselves until they are again put together? In discussing the resolution of water into air the philosopher Proclus says:

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Since fire is the resolving agent the result is two parts of air and one of fire, but when water comes to be in the contrary direction from air and three parts of air are resolved, the four triangles which are left over for the same reason compression, also make one part of water when they are blended with two parts of air.68 And it is not surprising that even some things with no form move, since one ought to accept that in all changes there is something which up to a certain point has no form but, when it is mastered by some form advances into the nature of what masters it. For we should agree that in the change of what we call elements some parts often remain ‘half-breeds’.69

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306a23-6 Furthermore, it is necessary for those who say these things [not to make things come to be from body. For when something comes to be from planes,] it will not have come to be from body. He adduces as a fourth absurdity that they make the coming to be of body the coming to be of body without qualification and not of a particular body. But he has shown previously70 that if a body comes to be from what is not a body,71 then there is a marked off void, which these people don’t want either. For if body were to come to be it would come to be from what is incorporeal, so that it is necessary that there

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be empty space receiving the body which comes to be. So if they say that body comes to be from planes, what has come to be will not be from body, since a plane has only length and breadth. Against this Proclus says: 20

Natural planes are not without depth, since if a body divides up the whiteness which occurs in it, the planes which contain it do so much more.72 But if they have depth, body does not come to be from what is incorporeal, but a more composite body comes to be from a simpler one.

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306a26-b2 In addition it is necessary for them to say that not every body [is divisible and to be in conflict with the most precise sciences. For some of these sciences, the mathematical ones, assume that even intelligible body is divisible, but these people do not even accept that all perceptible body is divisible because they want to preserve their hypothesis. For it is necessary that whoever makes there be a figure for each of the elements and distinguishes their substances in terms of it make them indivisible. For if a pyramid or sphere is divided somehow, what remains will not be a sphere or a pyramid. Consequently either [i] a part of fire will not be fire, but there will be something prior to this element because everything is either an element or composed of elements, or] [ii] not every body will be divisible. This is the fifth argument, and in a way it has been stated previously.73 The argument is directed generally at those who assign figures to the primary bodies, whether they compose them from planes or in the way Democritus does. And it does a reduction to one or the other of two absurdities. Those who distinguish the substances of the elements by a figure (for example, fire by a pyramid, air by an octahedron, and the others in the way which has been described), as well as those who say they are indivisible are forced to say that not all bodies are divisible and to be in conflict with the mathematical sciences, since they say what is absolutely contrary to them. For those sciences assume that even intelligible body, which is their subject (and it is intelligible because it is abstracted from perceptible ) is divisible, but these people don’t even assume that perceptible body is divisible. And this is the absurdity which follows for them: if they say that their figures are indivisible, they are in conflict with the most precise sciences; but if to escape this they say that the figures are divisible, then, if a pyramid or sphere (Democritus and his followers said that fire is a sphere74), is divided somehow, that is, is divided in a certain way, the pyramid by a plane

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parallel to its base, a sphere in such a way that an equal amount is taken off everywhere on its outside,75 then what is toward the centre remains a sphere and what is toward the apex remains a pyramid, but the other part of the sphere is not a sphere and the other part of the pyramid is not a pyramid. But, if this is the case, two absurdities will follow:

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A part of fire will not be fire, since one part is not a pyramid or sphere. But this is absurd since it deviates from the phenomena; for we see that a part of fire is fire. But furthermore, if every body is either an element or composed of elements but a part of a pyramid, which is a body, is not composed of elements, then there is an element which is even simpler than the pyramid (since it is a part of a pyramid) with the consequence that this element is more elemental than a primary element and prior to it. So it is necessary that the theory which assigns figures to the primary bodies either submit to these absurdities or that (as was just discussed) it not make every body divisible. (He is being careful when he says ‘if a pyramid is divided somehow’, since it can also be divided into pyramids if it is cut by a plane through the apex; but clearly divisions of this kind do not keep the triangles of the pyramid equilateral.) In objecting to this argument Proclus censures anyone who makes fire a pyramid and does not remain with Platonic hypotheses: Plato says that the pyramid is the seed of fire, not that it is fire.76 Fire is a collection of pyramids which are individually invisible because of their smallness, and as long as fire is divided into fire it is not yet divided into pyramids; but a single pyramid is no longer fire, but an element of fire which is invisible because of its smallness. So if this pyramid were divided, a part of it would be neither an element nor composed of elements, if, indeed, it could not be divided into pyramids or into planes.77 And what is so surprising about there being something disordered in bodies in this world?78 For, Proclus might say that even in the change of the things we call elements there occur certain differences which produce pestilential conditions for a whole genus by diverting the elements into what is unnatural. He says: And why is it impossible for this part which is cut off to be compressed and given form by what surrounds it and to be reshaped into a pyramid or some other element and assimilated to the things which surround it and compress it?

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But if this could happen what is the point of the dissolution into planes instead of a body which is surrounded being changed by what surrounds it?79 So perhaps when force is applied to a single pyramid it is dissolved into planes faster if, being composite, it is cut; but if it or a plane is also divided (since these things, being divisible, can perish), they become the matter of something else, either together with one another or with other things, when the parts which have been divided fuse together. 80

306b3-9 In general trying to assign figures to the simple bodies [is unreasonable, first of all because it will follow that the universe is not filled up; for it is agreed that there are three plane figures which fill a space, the triangle, the square, and the hexagon and that there are only two solid figures , the pyramid and the cube.81 But it is necessary for them to assume more than these] because they make there be more elements.

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He produces the sixth argument against the figures of the elements which have been described; it shows82 that, since the elements are given shape by the figures which have been mentioned, it is necessary that there be a void, something which those who assert planes do not want either. He shows this on the basis of the fact that there are a certain few figures, both among plane figures and among solids, which can fill the space around a point in such a way as to leave nothing vacant. Among plane figures there are equilateral and equiangular triangles, squares, and hexagons, six triangles , four squares, and three hexagons; and among solids there are only two which fill the space around one point, the pyramid and the cube, the former the element of fire, the latter the element of earth; and twelve pyramids fill the space, and so do eight cubes. So if the other elements, the octahedron and the icosahedron, do not fill the space, it is necessary that there be intermediate void both in air and in water, and that only fire and earth not have void between their pyramids and cubes, which are imperceptible because of smallness and capable of filling the space; from them, when they are combined, perceptible fire and earth come to be. However, these figures, that is, cube, icosahedron, octahedron, and pyramid, also cannot fill a space when they are set alongside each other.83 But the cosmos is composed from the combination of these things, so that a void will be left over in the cosmos.84 That among plane and solid figures only the equilateral and equiangular ones mentioned fill the space around one point in such

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a way that neither is any void left capable of receiving another figure in addition to what already exists in the space nor do the figures exceed the space, but the remaining interval is always pressed together and filled up by similar figures is proved by assuming two things to start. One is that if any number of straight lines are drawn from the same point on each side of the point, all the angles at the point are equal to four right angles. This is proved on the basis of the thirteenth theorem of the first book of the Elements, of which this is the enunciation: ‘In whatever way85 a straight line which is set up on a straight line makes angles, it will make either two right angles or angles equal to two right angles’. For it is clear that if the erected straight line is extended, the opposite angles will also be either two right angles or equal to two right angles; and, however many other straight lines are drawn through the same point they do not add anything to the four right angles. So one should assume this to start and also that any polygon has its angles equal to as many right angles as the number which is double the number which is two less than the number of angles;86 the triangle has angles equal to two right angles because one is two less than the number of its angles and two is double of one, the square has its angles equal to four right angles for the same reasons, the pentagon has its angles equal to six right angles, the hexagon to eight, and so on. These things being assumed to start, since however many angles the whole space around one point contains, it has angles equal to four right angles, if in the case of a rectilinear figure, such as a triangle or square, it is possible for several of the same to be constructed at one point and to make the angles at the point equal to four right angles, then these fill the space, which contains four right angles and neither more nor less, as was just said. But in the case of figures which do not make the angles at one point equal to four right angles, if they make them less than four, they leave an empty space, and if they make them more, they exceed the space. So since the three angles of any triangle are equal to two right angles and each of the angles of an equiangular triangle is two thirds of a right angle, if one constructs six equilateral and equiangular triangles at one point, the six angles at the point, each being two thirds of a right angle, occupy a space equal to four right angles. And similarly, if one constructs four squares at one point, they make angles equal to four right angles, because the angles of a square are right angles. And since the angle of the hexagon is one and a third right angles (because the six angles are in fact equal to eight right angles), if one constructs three hexagons at one point, their three angles will be equal to four right angles and they will fill the space. And, as Alexander reports, Potamon87 has set out in a succinct form the filling out of the figures mentioned, using diagrams.88 He says:

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Translation Let there be an equilateral triangle, and let two of its sides which make the same angle be extended in a straight line in the direction in which they converge toward one another; and at the point of division at which the two extended straight lines cut one another let there be drawn a straight line which does not cut either the angle of the triangle or the angle opposite to it but does bisect the remaining two angles. Around the point of division of the extended sides there will be six angles equal to each other. But the angle of the triangle is two thirds . Therefore, since they are equal to each other, the six angles will be equal to four right angles, and so the space is filled out by the triangles. For if we take away from each of the extended straight lines a straight line equal89 to the original ones, and join them together in a circle, there will be six triangles combined together and no empty space. Again, let there be a square, and let two of its sides which contain the same angle be extended in the same way in the direction in which they converge toward one another. The angles around the common intersection of the extended straight lines will be equal to each other and they will be four in number. But the angle of a square is right. Therefore the four angles will be four right angles, so that no empty space will be left. And if we take away from each of the extended straight lines a straight line equal to the side of the square and complete the drawing of the gnomon, there will be four squares filling out the space, just as the six triangles did.

Having drawn the hexagon using the same method, Potamon provides what is sought. I add letters in order to make clear what he says to my readers. 10

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Again let there be an angle A of a hexagon, and let two sides of it about the same angle A be extended in the direction in which they converge toward each other as BAC and DAE. And let the angle A of the hexagon and the angle which has come to be opposite it because of the extended lines be bisected by the straight line FH. There will be six angles around the point of division; they will be equal to each other, and each will be half of the angle of the hexagon. For EAB and CAD are each two thirds of a right angle, since they are the remainders in the two right angles with the angle of the hexagon,90 and the angle of the hexagon is one and a third right angles (since the six angles of the hexagon are equal to eight right angles). So if each of the six91 angles around A is two thirds of a right angle, the six angles are equal to four right angles. Therefore they fill up the space around A and do not fall short or exceed by any amount.

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So if from the three angles around A, FAB, BAD, DAF, of which each is the angle of a hexagon (and the three are equal to four right angles) we draw the hexagons AFGKLB, ABMNOD, ADPQRF, there will be three hexagons which fill up the space around A, and they will leave no void, and they will not exceed .

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This is the methodical way in which Potamon describes the hexagons. Alexander sets them out using another kind of diagram in the following way: If we describe a hexagon ABCDEF and on the side CD we describe a hexagon CDGHIK similar to it, the angle contained by BCK is also itself four thirds , as are the angles about the point C of the two hexagons which have been described. For since the three angles are equal to four right angles, that is, to twelve thirds , and each of the two is four thirds, therefore the remaining angle will be four thirds. If we complete the drawing of another equilateral and equiangular hexagon on CB, CK, we will fill the space and there will be no intermediate vacancy left around the point C capable of admitting another kind of figure. This does not happen in the case of any other plane figure. In the case of the pentagon, one angle is one and a fifth right angles, and no matter how many of these angles you take they will not fill out four right angles. For if you take less than four they will fall short, and if you take more than three they will exceed, so that the pentagon does not fill out the space. And it can be proved similarly that no plane other than the three which have been mentioned fills out the space. 92 In the case of the solid figures what need is there even to say that the cube fills out the space? For if one lays four cubes together along their sides he will fill out the space. To argue in another way:

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the role which the square has among plane figures, the cube has among solid figures; but among plane figures the square fills out the space; therefore, among solid figures the cube will fill the space. You will see clearly if on the four squares which have been constructed together at one point you erect cubes having the squares as bases. For, in the place of that point there will be

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Translation the straight line which is drawn at the point perpendicular ; the four cubes will touch one another at that line and together fill the solid space.

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And it is clear that the pyramid also , since a pyramid is nothing other than the angle of a cube.93 Consequently, since the angles of a cube filled up the space, the pyramid will also fill it up. To prove this another way, the cube itself has been completed from two pyramids. So if eight pyramids having their apexes at the centre of a sphere are combined they will fill out the space. Furthermore, the role which the triangle has among plane figures, the pyramid has among solid figures; but among plane figures the triangle fills out the space; therefore, among solid figures the pyramid . And it is evident through perception alone. For if someone were to combine eight pyramids, making their apexes incline toward one another like wedges, he would not leave an empty space. This is what Potamon says about the solids, as reported . I think it raises certain objections. Alexander says:

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nothing else than that what happens in the case of plane figures also happens in the case of solid ones and happens in three dimensions in the case of solid figures in the same way as it happens in one94 dimension in the case of plane figures. And this statement seems to me rather like an enigma. If planes are joined with respect to lines (it seems that ‘line’ is ‘one dimension’), why will solids be joined with respect to three dimensions, since they are put together with respect to planes? However, it is elegant to make the fitting together systematic that the manner of the putting together of solid figures is just like that of plane ones.95 And Proclus objects to argument by saying: The elements lie parallel . Those with finer parts are tightly bound in from above by the heavens and they are pressed into the spaces of thicker things; the thicker things create spaces because they do not fill the space about one point, and those with finer parts are compressed and enter those regions, and they fill up what is lacking. For Plato96 has presented us this as the reason why no void is left over when

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smaller things are placed alongside larger ones. For because of this the hollows in air contain pyramids in their midst filling the space, the hollows in water contain octahedra which are interspersed among them, and the hollows in earth contain all ,97 and there is no empty space. But perhaps should have proved this beforehand:98 that the spaces remaining in the combining of octahedra are filled up by pyramids and those remaining in the combining of icosahedra by octahedra and pyramids. Aristotle objects to the fact that space is not filled up by more of the solids, but perhaps it is also possible to raise for each of the solid figures the difficulty of how a pyramid is composed of four triangles, a cube of four99 squares, and so on, as has been described. For these things only fill out the surface of the solid figures, but, as Plato says,100 ‘Every form of a body also has depth, and it is in addition absolutely necessary that depth be contained by the plane nature’. So what is it that fills out the depth? Perhaps one should answer that the triangles themselves have depth and when they are pressed together, they fill up . Also in the case of each of the figures there are larger and smaller ones, for example, larger and smaller pyramids, because also the original triangles were larger and smaller. Plato himself also makes this clear when he says:101 One should explain the102 existence of different kinds in the forms by reference to the fact that the construction of each of the two elements did not originally beget a triangle having one size only, but larger and smaller ones, as many in number as there are kinds in the forms. Accordingly there is an infinite variety when they are mixed together with themselves and with one another …. Therefore, it is likely that the smaller things of the same kind advance into the vacancies and are pressed together, so that they do not preserve their figure pure. And why is this absurd when those who call air, water, and the others primary elements agree that there is some irregularity among them either because of their being mixed or because of differences in their change? Consequently if someone asks whether the things that are pressed together and do not preserve the figure pure are elements or composed of elements, it is easy to say that they are elements, but they are somehow arranged in an unnatural way and perhaps only for a short time.

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306b9-22 Next, all the simple bodies are seen [to be shaped by the space containing them, especially water and air. Therefore

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Translation it is impossible for the figure of the element to endure, since, if it endured, the whole of it would not touch what contains it at all points. But if the element were to be reshaped it would no longer be water, since it would differ in figure. Consequently it is evident that the figures of the elements are not determinate. (306b15) However, nature itself seems to indicate to us something which is also in accord with reason. For just as in other things the substratum must be without form or shape (since in this way the omnirecipient will be most capable of being shaped, as has been written in the Timaeus), so one should also think of the elements as matter for composites, which is why they can also change into one another] when they lose their qualitative103 differentiae.

This is the seventh objection and it refutes that the substance of the elements is distinguished in terms of these figures on the basis of the fact that one should not at all give these things form in terms of some figure which is specific to them. The argument proceeds from a division in the following way: 15

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If being one of the elements is distinguished by these figures, then either [i] their figures endure so that they remain what they are or [ii] their figures do not endure but are re-formed; but if [i] the figure of an element endures, the whole element would not touch what contains it at all points; however, ‘all the simple bodies are seen to be shaped by the space containing them, especially water and air’ (and also pure earth itself is shaped by what receives it – stone is not a simple body or just earth; and if someone could keep fire contained in some space or vessel so that it did not disperse, it would be shaped by what contains it; but clearly water and air are seen to be shaped by their container); therefore, it is impossible that these figures of the elements endure; but if [ii] they are reshaped and lose their figures by being shaped by what contains them, it follows that they are no longer water or fire, if, indeed, it was by their figures that they were given substance; consequently, if it is not possible [i] for the figures to endure in the elements or [ii] for them to be lost, but it is necessary that one or the other of these holds, the elements will not have determinate figures of their own.

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And if air and water are also seen to flow together, it is clear that they do not preserve their own figure. But if they do not preserve it, one of them would not be air and the other water, if their being these things lay in their having a certain figure. So there will be other bodies which are neither elements nor composed of elements, which is absurd. Consequently, the primary bodies would not have figures of their own. (306b15) However, he says, it seems that their nature indicates to us through their being without shape something which is also in accord with reasoning about causes, namely that these elements have the role of matter with respect to what comes to be from them. For matter ‘is always receiving all things, and it does not ever in any way take on any form which is similar to any of the things entering it’,104 so that it does not reproduce the forms bestowed on it badly by also displaying its own appearance. (These things have been written about matter in the Timaeus.) And so in this way it is appropriate that in the coming to be of composite bodies, which are clearly distinguished by their own shape, the elements do not bring in any shape of their own as well. Having said that ‘one should also think of the elements as matter for composites’, he adduces as evidence for this that they can ‘change into one another when they lose their qualitative differentiae’. For because they are in a sense matter it is possible for these to change into one another and not be preserved in every respect (for if they were preserved in every respect they would be precisely prime matter), but they lose their qualitative differentiae and change from one thing into another with respect to the matter in them. This is how he here briefly indicates the way in which the elements come to be from one another: the elements come to be from one another when their matter endures and their qualitative differentiae are exchanged. He will demonstrate this in On Coming to Be and Perishing.105 But those who assign figures to the first bodies would say that the elements come to be from one another when matter endures and their primary differentiae concerning figure are interchanged. Proclus also makes an objection to this seventh argument, an objection which does not accept that the elements have a specific figure if it is not possible for their shape to endure nor to be lost.106 He says: It is not the entireties of these four bodies which are shaped by the figures, it is their elements, which are small and invisible and from the coming together of which these perceptible things come to be: fire, water, and the others. But their entireties are accommodated to the heavens everywhere and formed into a sphere. For each of them receives something stronger than its

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Translation own specificity from things more divine, just as the things near the heavens receive the circular motion. Clearly then the limits of the pyramids and even of planes or107 triangles are made convex when they are tightly bound so that they fit with the concavity of the heavens. But when their parts are in other things such as vessels and are shaped by them, they do not lose the figures of the elements, since the containers are also composed of rectilinear elements, and nothing prevents container and contained from fitting together. However, we think that we see spherical or cylindrical surfaces of containers and we are perplexed because we forget that they too are composed of rectilinear elements. So, all containers as well as what they contain would be composed of rectilinear108 , and they all fit together along their planes.

But perhaps one should say that if the containers have been constrained by art or nature to be spherical, it is not at all surprising that what is contained is also made convex by them since it is easily moulded.

306b22-9 In addition how is it possible [for flesh and bone or any continuous body to come to be? For it is not possible for them to come to be either from the elements themselves because what is continuous does not come to be from combining things or from the planes when they are combined, since it is the elements and not what is composed from the elements which are generated by composition. Consequently if one wishes to be precise and not accept theories of the element casually,] he will see that they109 eliminate coming to be from existing things.

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This is the eighth , and it is directed generally against those who make the coming to be of bodies from one another occur because of the combining of magnitudes, whether the magnitudes are atoms, as Democritus110 and his followers say, or planes, as Timaeus says. And it proves that they eliminate coming to be entirely. Aristotle asks how it is possible for flesh or bone or any other continuous body to come to be, since it is not possible for them to come to be from the elements or from the planes. (By ‘elements’ he means the atoms in the case of Democritus and the four primary bodies, pyramid, cube, and the others, in the case of Timaeus.) For if from the combining of the elements by contact, it is not continuous; but the bodies are continuous; the bodies will not come to be by the combining of the elements. The inference is in the second figure.111 Alexander says,

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Furthermore, the elements, whether they are atoms or all the figures, do not fill out space by being in contact with one another, but it is necessary for there to be a void between them, as was said previously.112 However, Democritus and his followers do not think that this existence of a void is absurd. But both this and that what is compounded is not continuous follows both for them and for the others.113 (But someone114 might perhaps say that the planes can more easily be made continuous because they have no depth.) But, Aristotle says, it is the elements, that is, the pyramid and the others, which are generated by the combining of planes and not the bodies which are composed from the elements. So if a continuous body does not come to be either from the elements or from the planes, there would not, according to them, be a continuous body. So if, he says, someone will not accept theories about the element casually, but recognises that if there is coming to be, then what comes to be are bodies, and that bodies are continuous, and that continuous things cannot come to be in the way in which these people say they do, ‘he will see that they eliminate coming to be from existing things’. And against these things Proclus says: A compound does not come to be from air by itself or from water by itself. In these things what has smaller parts moves between what has larger parts and fills the space, leaving no void. And you shouldn’t be surprised if this is a matter of juxtaposition and not of unification, since it was necessary that these things also be dissolvable from one another. And, even if they are juxtaposed, they are hard to tear apart from one another. And this is not surprising either. For there are such things for us when we try to squeeze out from soft external things which are not constituted by nature to yield the things which are them, as what is composed from greater planes is not of a nature to yield to what is composed of smaller ones and what is composed of more stable ones is not of a nature to yield to what is composed of more mobile ones.115 And let these things have been said reasonably, most of all in relation to Alexander, who says that space is not filled out by the combining of either atoms or figures. But how does what says resolve Aristotle’s objection, which asserts that flesh and bone and such things are continuous, and that something continuous does not come to be from things in contact, but that the elements which are assigned figures are combined by contact? Or is the philosopher obviously not accepting that bodies which are again dissolved into the things from which they were composed are continuous

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in the strict sense or unified? For perhaps, even according to those who say that the four elements, fire, earth and those intermediate between them, are primary, the bodies composed from them are not continuous in the strict sense or unified, but they are interwoven with one another in terms of small chopped up pieces, and when the single form of flesh or bone supervenes, it imposes apparent continuity and unity;116 this also happens with colours which are juxtaposed in small patches with the result that a single mixed form appears in them. I have also seen cloaks of this kind with their warp and woof of different colours. And even if, when the four elements are juxtaposed they pass on qualities and in a way alter one another in the direction of themselves, nevertheless the bodies themselves do not pass through one another nor are they unified with one another nor do they change completely into one another. The fact that the elements are again separated in the perishing and each goes to its own entirety makes clear that they inhere actually . For if each of them loses its own form in a compound, how does it take it on again when the composite perishes? For even if some things in a composite change into one another and the water in us is turned into air and the air into fire, nevertheless their bodies are in contact and there is always something which is analogous to the glue used in the crafts: glue does not make things continuous; nor does it do away with the edges of the things which are glued; but, just as when several torches come together the flame of all of them mixes and seems to be one but when the torches are separated, the proper flame of each and the light from the flame are separated along with them, so too the coming together of the four elements, lying alongside one another and changing one another in their qualities, produces the appearance of one thing (just as the music which is composed from different sounds by juxtaposing them in small pieces seems to be blended and one). For what is called the blending of bodies which are juxtaposed is also something of this sort; and as long as they are juxtaposed there is mutual qualitative change.

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sharpest117 angles and burns and heats with its angles, as they assert. (307a3) Now first of all both groups were mistaken as regards motion. For even if these are the figures which move most easily, nevertheless they do not move easily with the motion of fire. For the motion of fire is up and in a straight line, but these figures move easily in a circle with a so-called rolling motion. (307a8) Secondly, if earth is a cube because it is stable and remains fixed, but it does not remain fixed in a chance place but in its own place, and it moves out of an alien place if it is not prevented and likewise with fire and the others, it is clear that both fire and each of the elements will be a sphere or a pyramid in an alien place] and a cube in its proper place. This is the ninth argument and it refutes the figure hypothesis on the grounds that the hypothesis does not achieve the purpose for which it was hypothesised. For with respect to the affections and powers and changes, at which they looked most in assigning figures as they did, the figures are out of harmony with the bodies. By affections he means the so-called affective qualities such as heat and cold and the like, by powers the things because of which there is natural motion, heaviness and lightness, and by changes, changes of place. Or perhaps by powers he means conditions which make active things ready to act, for example, that because of which a thing which heats heats, and by affection he perhaps means that because of which what is heated is heated, and by change what is between the two, being heated. But subsequently118 he divides things more in this second way, but now he does so in terms of the first point of view. (306b32) And so Aristotle first sets out how, in looking at these things, they distributed the figures to the bodies and he shows in this way that they do not achieve their purpose. For since, he says, fire moves easily and can heat and burn, Democritus and his followers made it a sphere and those who use planes made it a pyramid. The sphere moves easily because it touches a plane underlying it at a point and, as Plato says,119 it stands on the smallest foot. And a pyramid moves easily because it is contained by triangles, and these are the smallest of rectilinear figures, so that the pyramid also has the smallest base and is least stable; moreover, since the triangle is not similar to itself because it, unlike the square, does not have angles balancing with angles and sides balancing with sides, but rather it has sides balancing with angles, it inclines easily (like a balance) because of the dissimilarity of the opposite angles and sides. And they think these figures are most able to heat and burn because, as they say, bodies, which separate and divide into fine parts, burn and heat with their angles, but the pyramid has the sharpest angles and the whole of what is spherical is an angle; for, if

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what is bent is an angle and a sphere is bent in its entirety, the whole sphere is reasonably said to be an angle.120 (307a3) So, having said how these people fit affections and motions with bodies, he shows that, as regards motion, both those who made fire a sphere and those who made it a pyramid because it moves easily missed their mark. For even if these are the figures which move most easily because they touch what lies under them most slightly and are least stable, nevertheless, as regards the motion of fire, these figures not only do not move easily, they do not even have the motion of fire at all. For the motion of fire is up and in a straight line, but the easy motion of these figures is rolling, since they turn and roll easily. So what contribution do these bodies make to fire’s moving easily? (307a8) Secondly, he says, if earth is a cube because it is stable and remains fixed (since this figure is steady), but each of the elements remains fixed naturally in its proper place and moves from an alien place to its proper place if it is not prevented, it is clear that each of the elements is ‘a sphere or a pyramid in an alien place and a cube in its proper place’. And you can develop the argument in this way: Fire and earth and each of the other remain fixed when in their proper place; what remains fixed is a cube; therefore, each of the four is a cube when in its proper place. And again: Each moves when in an alien place; what moves is a sphere or pyramid; therefore, each is a sphere or pyramid when in an alien place.

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Consequently fire, too, will be a cube and earth a sphere. It is worth pointing out that Aristotle does know that Plato thinks the earth is steady, since it was Plato who said that it is a cube because it is stable and remains fixed. Consequently when in the preceding book he asserted that the earth is said by Timaeus to be wound and move ,121 he was confronting those who understand Timaeus’ words in this way. Let us see how Proclus has responded to this argument. He says: Even if elements are in their proper places, at least those which are composed of the figures which move easily are not without motion. For the pyramids are always moving about because their apex is dissimilar to their base. In this way, too, the elements of air seem to be always in flux when the air is in its proper place. And those of water are consistently always rolling.

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For the apexes encounter the bases of similar things122 and are struck, causing each whole to shake in the place in which it is. By moving in this way they imitate a circular motion and move neither from the centre nor to it, but turn around each other in their place. But the elements of earth remain fixed because their apexes are the same as their bases and similar things do not act on each other whether their similarity is in shape or power or size.

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307a13-19 Furthermore, if fire heats and burns [because of its angles, all of the elements will be able to heat, although perhaps one will do so more than another, since all, including the octahedron and the dodecahedron, have angles (and also for Democritus the sphere, being a sort of angle,123 cuts because it is moves easily). So the difference will be a matter of degree.] But it is evident that this is124 false. Having shown that the figures do not harmonise with their motions, he next shows that they do not harmonise with their affective qualities either. For if fire heats because of the angles and an angle can heat because it can cut (for in this way Plato also agrees that the hot is like something that cuts – the ‘r’ being inserted because of the motion125), then if all the elements have angles, all would be able to cut and heat, and therefore one thing’s differing from another in heating would only be a matter of degree. However, this is false, as is clear from the fact that some elements not only do not heat, they even cool. Therefore, the antecedent, which says that fire heats because of the angles, is also false. Proclus says against this tenth that Aristotle has wrongly assumed that an angle has the power to heat, and the falsehood follows from this assumption: For Timaeus takes it from perception that the affection of heat is something sharp and divides things, but what cuts does not cut just because of an angle, but because of the sharpness of the angle and the fineness of the sides. For it is in this way that the crafts make cutting tools and, in the case of teeth, nature sharpens the angles of the incisors and makes their sides fine and also broadens the molars. And fast motion is also needed. Therefore, one should not just ascribe this kind of power to the angle, but also to the stabbing sharpness of the angle, the slicing fineness of the side, and the speed of the motion. One should also take into account size, as in the case of pyramids, so that they can penetrate forcefully. So if it is only in fire that there is sharpness of angle, fineness of side and speed of motion, it is

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Translation reasonable that only fire is hot, and not all fire but only that which is composed of larger pyramids. Accordingly, as Timaeus says,126 there is some fire which gives light but does not burn because it is composed of the smallest elements, and because of this it is visible.

Perhaps it would not be a bad thing to set out the text of Plato itself, which runs as follows:127 15

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First, let us see why we call fire hot and make our investigation128 by considering the way it separates and cuts in the case of our body. We all perceive that the feeling is something sharp.129 But those who recall the coming to be of its figure should take into account the fineness of the sides, the sharpness of the angles, the smallness of the parts (obviously smallness relative to other things) and the130 speed of the motion, all of which make fire vigorous and make it always give a sharp cut to everything it encounters: it and no other thing most of all separates our bodies into small bits, minces them up, and it reasonably gives rise to what we now call hot, both the affection and the name.131

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307a19-24 At the same time it will follow that mathematical bodies also [burn and heat, since they also have angles and among them are indivisible spheres and pyramids, especially if there are indivisible magnitudes, as these people say. For if some bodies burn and others do not, they should state the difference and] not just speak in the unqualified way in which they do speak. This is the eleventh argument, and it reduces the theory to great absurdity and comedy. For if fire burns and heats because of angles, ‘it will follow that mathematical bodies also burn and heat’. So perhaps in their case as well making the sharpness of angles responsible does not help the theory either. For among mathematical things there are sharp angles and pyramids and spheres, and the pyramids and spheres are indivisible, like the ones hypothesised by these people, that is to say, they are not divisible into things which are similar to the whole; for a sphere is not divisible into spheres, nor is a pyramid always divisible into pyramids. So in this respect, too, there would be a similarity, and still more if mathematical things are certain separate substances, in the way that in the Metaphysics132 it was said in reference to Plato that he spoke this way. But also if there are indivisible, impassive, and qualityless magnitudes in the way Democritus and his followers and also Xenocrates, who hypothesised indivisible lines, said, those magnitudes would seem to be straightforwardly like mathematical things. But if the things which these

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people hypothesise heat and burn because of their angles, but mathematical things, which are given shape by angles in a way similar to those things, do not, they should state the difference and not speak in the unqualified way – that is in a rough and ready way without explanation – in which they do speak. For, in seeking to explain the difference which makes natural but not mathematical things burn, they would find that the angles, which are no less in mathematical things, are not the cause, but the affections none of which is found among mathematical things, are. This is what Aristotle says, and Proclus, in answering what he says in an excellent way, does exactly what Aristotle demands: following the hypotheses, he gives the difference because of which these things burn and mathematical things do not. For Plato says that these figures involve matter and are in motion. And this is why the letter ‘r’, which is an instrument motion,133 is added to the word. For not everything which has angles can heat, unless it has sharp angles and its sides have been made fine and further the thing involves matter and moves easily. (Aristotle left out the first two of these in fabricating the tenth objection and the last two in fabricating the eleventh.134)

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307a24-31 Furthermore, if what is burned is enflamed, [and fire is a sphere or pyramid, it is necessary that what is burned become spheres or pyramids. And let it be the case that cutting and dividing is a reasonable result of a figure. Nevertheless, that a pyramid should necessarily produce pyramids or a sphere spheres is completely unreasonable; it is as though someone maintained that a knife divides things into knives] or that a saw divides things into saws. This twelfth is also a jest (skôptikon). He says that if fire is a pyramid or sphere, and it heats and enflames by dividing, and what is enflamed and burned becomes fire, and fire is a sphere or pyramid, then it is necessary that what is burned become a sphere or pyramid. But let it be reasonable that cutting and dividing is a result of a figure which has sharp angles. ‘Nevertheless, that a pyramid should necessarily produce pyramids or a sphere spheres is completely unreasonable’. Juxtaposing something similar will show the unreasonableness most of all. It is as though someone maintained either that a knife divides what it divides into knives or that a saw divides it into saws. For it is not at all absurd that what is enflamed should become fire when what enflames turns what is enflamed into itself with a qualitative change, but it is absurd that what divides or cuts divides what it divides into things similar to itself

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Translation Proclus says the following against this:

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Fire which enflames a thing which is burned dissolves the elements of the thing and changes them into its own elements, but a knife does not act on the substance of what it cuts, since it does not resolve the substance of the thing, but by dividing it makes its size less from being bigger, since the knife has this shape accidentally, not substantially. So if it does not act at all on the elements of what is cut or change its form, how could it make a division into things similar to itself? But, one might say, let what is enflamed, for example water or air and their elements, icosahedra and octahedra, be dissolved into triangles. What is it that combines the triangles of these things into the figure of fire, the pyramid, so that, when many such pyramids are brought together, fire comes to be? Now Plato says that triangles which are dissolved by fire, do not cease to be dissolved, so long as, being combined into another form which is more divisible (as triangles dissolved from icosahedra combine into octahedra), they fight with the divisive form of fire, but they do cease to be dissolved if they combine into the nature of fire; for similar things do not act on and are not acted on by one another. But it would be good to hear Plato’s own words, which are extremely beautiful:135 Let us consider these things again in this way. When one of the other kinds is held within fire and is cut along its sides by the sharpness of angles, if it is combined into the nature of fire, it ceases to be cut; for no kind which is similar to and the same as something can either impose some change on or be acted on136 by what is similar to it and the same. But so long as it is coming to be of another kind137 and is a weaker thing fighting with a stronger, it does not cease being dissolved. It is clear that it is not a chance or random matter that the planes are combined into one figure at one time and into another at another. Rather the thing which dissolves them does away with the suitability for that figure (the icosahedron, for example) which they had (the suitability being something thicker and more turbid) and changes the figure to one which is close and is purer, that of air; and first they are joined together into octahedra and then, when these figures are also dissolved by the fire, they are made more pure and fine and become suitable for the construction of a pyramid. And it is clear that a thing easily takes on the form of the figure for which it is suitable, so that air first comes to be from water and then fire from air.

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307a31-b5 Furthermore it is ridiculous to138 assign a figure to fire only on the basis of its dividing; [for fire is thought of as something which blends and brings together more than as something which separates. For it separates things which are not of the same kind and blends things which are. And the blending is per se since bringing together and uniting belongs to fire, but the separation is accidental; for fire drives out what is alien by blending things of the same kind.139 So they should have assigned either on the basis of both] or, preferably, with regard to combining. His thirteenth complaint is against those who characterise fire only by its dividing and not rather by its blending or by both. ‘For’, he says, ‘fire is thought of as something which blends and brings together more than as something which separates’ since it separates things which are not of the same kind when it separates gold out from silver or extracts the slag out from iron by smelting, but it blends things of the same kind. So if blending is more worthy , fire should have this activity as its pre-eminent one, and separation accidental. ‘For fire drives out what is alien by blending things of the same kind’. So, he says, they should have assigned a figure to fire either on the basis of both if, indeed, it acts both by blending and by separating, or, preferably, with regard to combining, if fire blends per se, but separates accidentally. Proclus objects to this argument and says: The contrary is true: fire separates per se and blends accidentally. For by driving out things which are alien it facilitates the coming together with one another of similar things and their impulsion toward the same . For everything fiery has a power to separate with respect to all the senses since the hot divides touch, the bright vision, the acrid taste, and all medicines which are fiery have a dispersive power. Furthermore everything which blends wants to surround what it blends and compress it, but fire does not want to surround, but wishes to enter into bodies. And adds that fire has been thought to have fine parts even by those who do not assign figures to the elements, but things with fine parts are separating rather than blending since they enter into other things. That being able to divide belongs per se to fire is made clear by the fact that it not only separates things of different kinds from one another, but it also separates each individual thing; for it liquefies gold and silver and the other metals by separating them.

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307b5-10 In addition,140 since hot and cold [are contrary in their power, it is impossible to assign any figure to cold, since the assigned figure should be a contrary, but no figure is contrary to a figure.141 And so they have all left out of account,] but they ought to have distinguished either everything or nothing by their figures.

This is the fourteenth argument, and it is clear. It shows that it is impossible to distinguish hot and cold by figures. The argument goes as follows: 10

Hot and cold and in general things related to the affective qualities are contrary in their powers; things distinguished by figures are not contraries because no figure is contrary to a figure; therefore, it is impossible that hot and cold be distinguished by their figures. This inference is in the second figure,142 but it is also possible to carry it out hypothetically in the following way:

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If hot and cold, which are contraries, are distinguished by figures, their figures would be contrary; but a figure is not contrary to a figure; therefore, hot and cold are not distinguished by their figures. He says that it is clear143 that all those who distinguish hot by a figure leave out the figure which is appropriate to cold, but they should have distinguished all qualitative contraries or none by their figures. In dissolving this objection Proclus says the following: It is good to demand that the theory assign the appropriate figure to what cools, but one should also remember that in the case of heat we did not say that a pyramid is heat, but that a power to cut because of the sharpness of its angles and the fineness of its sides,144 and that coldness itself, like heat, is not a figure either, but a power of a certain figure; and just as heat cuts, so coldness blends by pushing; and as heat because of the sharpness of its angles and the fineness of its sides, so coldness in a contrary way because of the bluntness of its angles and the thickness of its sides. Therefore, the power of coldness is contrary to the power of heat not because their figures are contrary but because the powers in their figures are. argument demanded a contrary

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figure, but that is not necessary; rather a contrary power is. And so figures which have blunt and thick sides have powers contrary to the pyramid and blend bodies. The elements of the three bodies are of this sort, so that they all blend and blend through pushing, but, as has been said, only fire separates. Proclus says these things, but someone might raise the following difficulty. If, as he says, the powers in the figures are contraries, how can the figures not be contraries, since powers are proper to what have them? Perhaps means by figures the four figures, the pyramid and the others; their powers are contraries, but they themselves are not because their powers are not due to (kata) their figures. For thick and fine, having large parts and having small parts, being difficult to move and being mobile are not differentiae of figure, and perhaps sharpness and bluntness of angles are also not differentiae of figure without qualification, since an angle is not a figure without qualification. So if the conditions of hot and cold, which are contraries, are brought to completion because of (kata) these contrarieties, nothing absurd follows. However, the proposition which says that things distinguished by figures are not contraries needs some qualification: for they are not contraries because of figures, but it is not ruled out that they have contraries. But if someone were to insist that the contrarieties are due to the figures, one should recall what Aristotle says in this treatise, namely that there is also in a way contrariety of figures.145 Since I set out what Plato says about hot it would be good to add here what he says immediately after that about cold:146 The contrary of this147 is manifest, but let it not be left unexplained. When of the moist things around body the ones with larger parts enter, they push out the things with smaller parts.148 And, not149 being able to enter into their places, they compress what is moist in us together and solidify it, producing from something which was moving and not uniform something which does not move because of its uniformity and the compression. But what is brought together in an unnatural way naturally resists and pushes itself away into what is contrary. The names ‘trembling’ and ‘shivering’ are given to this resistance and shaking, and this whole experience and what produces it has the name ‘cold’.

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307b10-18 Some of those who try to speak about the power of cold [contradict themselves, since they say that what has large parts is cold because it presses together and does not pass

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Translation through the pores. So it is clear that the hot would be what does pass through, and what has fine parts is always of this sort. As a result it follows that hot and cold differ because of smallness and largeness, but not because of their figures. Furthermore, if the pyramids were unequal, the large ones would not be fire, nor would the figure cause burning,] but the contrary would be the case.

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He adds this fifteenth argument to everything which he has said, raising an objection based on size and showing that people who offer an explanation of the power of cold and make what has large parts responsible ‘because it presses together and does not pass through the pores’ (as in the passage from Plato which I have just set out), should also say that the hot does pass through. What has fine parts would be of this sort, and it was said previously150 that what has thick parts and what has fine parts differ in size. But if they distinguish cold and hot by having large or fine parts, it follows that ‘hot and cold differ because of smallness and largeness, but not because of their figures’. In general, if what is larger is cold, then, since some pyramids are also said to be large and some to be small, the large ones would not be fire but something which cools and in the case of the large ones the figure would not cause burning, but would cause cooling because of size, with the consequence that they contradict themselves, as he said initially. Also in this case Proclus says: We do not distinguish the elements of the simple bodies by size alone, but also by fineness and thickness, and sharpness and bluntness, and ease and difficulty of motion, things which change the forms and do not make it to be the case that things having the same form only differ in size. The number of planes makes bodies have large or small parts, since the elements are said to be parts of them, for example, pyramids are parts of fire from which fire is composed, and similarly in the case of octahedra and air. For if a pyramid and an octahedron are both composed from an equal triangle, the octahedron is larger. Together with a certain number, the composition produces sharpness or bluntness; for an angle is sharp or blunt depending on whether more or fewer triangles converge ; it is sharp when there are fewer, blunt when there are more. And a specific feature of the planes produces ease or difficulty of motion; the planes are stable because of similarity and prepared to move because of dissimilarity.151 Therefore, it is not the case that large pyramids are not fire; rather they are fire which has larger parts, just as large octahedra are air which has larger parts, and large icosahedra

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are water which has larger parts. From what sort of cause is some water fine and some thick, and why is some air fine, some thick? It is clear that these things are distinguished by quantity.152 In connection with these things I first raise the question why he says that ‘the number of planes makes have large or small parts’ and that the figures are composed from equal triangles when Plato clearly says,153 ‘ did not originally beget a triangle having one size only, but larger and smaller ones’. How could larger and smaller pyramids come to be if they are all composed from four triangles? himself seems to say that water has larger parts than air and air than fire even if they are composed from triangles equal in size because an icosahedron is composed from more triangles than an octahedron and an octahedron from more than a pyramid, but a pyramid is not greater than a pyramid because of a difference in the number of triangles but because of a difference in their size. And how is it true that ‘a specific feature of the planes produces ease or difficulty of motion’? A square is moved with more difficulty than a triangle, so that earth is moved with more difficulty than the other elements; but the three which are composed from the same triangle, the scalene, are more easily moved because of the fewness and smallness of their triangles.

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[307b18-19 So it is evident from what has been said that the elements do not differ because of their figures.]154 307b19-24 But since the most important differentiae of bodies [are those which relate to affections and acts and powers (since we say that everything natural has acts and affections and powers), it would be right to speak first about these so that by studying them we can grasp the differences of each with respect to each.]155 Having concluded what he previously proposed, namely that ‘the elements do not differ because of their figures’, he next makes clear what does differentiate the elements, namely their ‘affections and acts and powers’. Alexander distinguishes these things in several ways. Sometimes he calls lightness and heaviness, hardness and softness, rareness and denseness affections, and heat and coldness powers. But sometimes he calls the affective qualities affections, the things related to impulsions156 powers, and activities acts. And again sometimes he calls the qualities – heat, dryness, lightness – which are productive of them157 powers (for these powers are productive), and the opposites of these – coldness, moistness, and heaviness – affections because these are passive and more material. For also in On Coming to Be158 Aristotle says that the former are more produc-

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tive and the latter more passive, and he also calls159 the latter ‘privations’ of the former. Alexander says, ‘From another point of view power and affection are the same, an affection from the imposition of an affection or from coming to be when matter is affected,160 a power from the ability ’.161 And perhaps it is better to understand in this way. Aristotle wants the differences of the elements to be determined not in terms of figures because there is no contrariety in the strict sense between figures, but in terms of what are called affective qualities, heat, dryness, softness, lightness, and their opposites and everything of this sort, since in these things there is contrariety because of which the change of the elements into one another takes place, and this change is what is now being problematised. Each of these qualities is studied in three ways: [i] as power, which is the condition which makes a substance ready for activity162; it is on the basis of this that we say fire has the power to heat; [ii] as the activity related to this power, for example, heating; [iii] or as affection, which comes to be in what is affected from the power because of the activity, for example, being heated. Substances are understood and the change of the elements into one another is grasped on the basis of these things, power, activity, and affection. Having discussed one of these163 in the next book because it is more proper to natural motion, he will explain the others in On Coming to Be and Perishing, and he will demonstrate that the elements are given substance and make their change into one another because of these qualities and not because of the figures.

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This, then, is the end of the third book of the treatise On the Heavens. Let its development in brief be as follows. Having proposed to discuss the simple bodies in the universe and treated the eternal body which moves in a circle in the first two books of the treatise, in this book he teaches us about the things which move in a straight line and come to be, enquiring first164 whether or not there is coming to be, since some people, such as Parmenides and Melissus, completely did away with coming to be and said that what is does not come to be, but others, such as Hesiod, said absolutely everything comes to be, and others, such as those who compose bodies from planes, say that all bodies165 come to be. Having spoken against these people, he next166 says which things come to be, namely those which have contrary affective qualities and move in a straight line. But if someone is going to understand the substance of bodies which come to be, it is necessary for him to first understand their elements. Since different people say there are different elements, having first defined ‘ele-

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ment’, he then enquires whether the elements are infinite or finite in number. And having taken issue with those who say that they are infinite, Anaxagoras and Democritus and their followers,167 he turns to those who hypothesise one element, and, having also spoken against them, he concluded168 that it is necessary that there be more than one, but finitely many. And then, having proved that they are not eternal but come to be and perish,169 he enquires on the basis of a division whether they come to be from what is incorporeal or from a body, and if from a body, whether from some other body or from each other. And having refuted the other parts of the division and left that they come to be from one another,170 he next enquires about the way they come to be from one another. And having proved that it is not a matter of separation out, all things being separated out, or of blending and separation, as Empedocles and Democritus say,171 nor a matter of reshaping or of dissolution into planes, as Timaeus says, he infers at the conclusion that the change of the elements into one another is given form because of the contrary differences which give form to the elements, the most important differences being in the qualities; and these qualities are studied in three ways, as powers, as affections, and as activities.

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on the fourth of Aristotle’s On the Heavens

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Aristotle established the whole purpose of the treatise On the Heavens to be to teach about the simple bodies in the cosmos. He made the whole first book treat the heavenly body which moves in a circle in a general way. He made the second book treat the parts of the heavens, both those which are more whole, I mean the spheres, and those which are more particular, that is the stars in them. Next in the third book he proposed to speak about the sublunary simple bodies which move in a straight line and which are also, certainly, elements.172 And he showed that these things are neither infinite in number nor one, but finite and more than one; and that they are not eternal but come to be and perish; and that they do not come to be from what is incorporeal or from another body, but from one another and not by separation out or reshaping or resolution into planes, but with respect to their qualities. These qualities are studied in three ways: in terms of their power to act; in terms of their activity related to their power; in terms of the affection which is related to the power and comes to be in what is affected by the activity. And so it was reasonable for him to say173 that one should enquire about power, activity, and affection as they are related to qualities, since on the basis of these things we will understand the way in which the elements come to be from each other and on the basis of this understanding we will discover how many elements there are and what they are. And just as he discovered the first simple body on the basis of motion in a circle, so too he seeks after the other simple bodies on the basis of motion in a straight line. For it is appropriate for the student of nature to discover natural things on the basis of motions because nature is a starting point of motion. Accordingly, since natural motion in a straight line belongs to natural things because of the power of heavy and light, he proposes174 to enquire about heavy and light first; for the sublunary simple bodies, which move in a straight line and come to be and come to be from each other, are given form most of all by heavy and light, even if they have many other powers and affections and activities (for they are also given form by heat, dryness, and rarefaction and their contraries and other such things). Some people who have not paid attention to the sequence of discussions as I have described it have dared to declare this book spurious on the grounds that it is not appropriate to enquiries

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concerning the heavens, but if to anything to enquiries concerning coming to be and perishing. It has been said that heavy and light are most proper to the sublunary simple bodies, but we will now learn in a more precise way that they do not belong to heavenly things. That is why Aristotle himself says at the beginning of the first book,175 ‘We should lay down what we mean by heavy and light, at the moment in a way which is sufficient for present use, but in a more precise way later when we investigate the substance of the two’, making a postponement to the present discussions. And so, having distinguished at the beginning things which are absolutely heavy and light and those which are said to be so relative to other things and having set out the difference between them,176 he next recounts views of heavy and light held by his predecessors and shows that none of them discussed what is absolutely heavy or light but only what is heavy and light relative to something else.177 And the third section for him is the one in which he specifies why some bodies always move up naturally, some down, and some both up and down.178 Then, having given the general explanation , in the fourth section he sets out the difference of the extreme elements, fire and earth, relative to air and water.179 Fifth, he shows that earth is absolutely heavy, fire absolutely light on the hypothesis that the centre is determinate. Sixth, he shows that the centre is determinate, and from this that the extremity is also determinate, and from these things that the extremes of the elements, the absolutely light extreme and the absolutely heavy extreme (that is to say, fire and earth) are determinate. Seventh, he shows that the intermediate are air and water, each of which is light in a way and heavy in a way. Eighth, he shows that fire has no heaviness at all and earth no lightness at all, but that the intermediates have heaviness and not lightness when they are in their proper places and the places of the things which lie above180 them. And ninth he shows that the four elements differ because they have appropriate differences in their matter and that the intermediates are not composed from the extremes.181

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307b28-308a7 In the case of heavy and light, [we should investigate what each is and what their nature is and for what reason they have these powers. For the study of these things is appropriate to discussions of motion, since we call something heavy or light because of a power to move naturally in some way. (307b32) There do not exist names for the activities of these things, unless someone were to think that ‘impulsion’ is such a name. (308a1) Because the study of nature deals with motion and

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Translation these things contain in themselves certain ‘sparks’ of motion, as it were, everyone makes use of their powers, but they have not determined them except in a few cases. (308a4) Now, after we have first seen what has been said by others and raised the difficulties which have to be distinguished for this investigation,] we will then say what we think about these things.

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Heaviness and lightness are more proper to natural bodies than the other qualities because the natural motions are due to (kata) these, and natural bodies are given form on the basis of (kata) these motions. The discussion of these things is also necessary in another way, namely because earlier, using , he proved182 that it is impossible for natural bodies to come to be from points, lines, and planes since every natural body must be heavy or light, but nothing can come to be from these things. And he also proved183 that no body can move in a straight line unless it has heaviness or lightness. But also in the first book he used heaviness and lightness in proving184 that the heavens transcend them, and he used them to prove185 that there is no infinite body. So he has used these things frequently, and it is therefore reasonable that he now give the precise account of them, since he postponed the account to this appropriate time. And there is another reason why the discussion of these things is necessary: the students of nature are in doubt about them, and they give accounts of them which do not harmonise with one another. And Aristotle himself gives an even more relevant reason for the need for this discussion: the study of these things is appropriate to discussions of motion, or, as Alexander says, ‘of nature’ since nature is a starting point of motion, and this treatise concerns nature. But perhaps it is more relevant to say that the study is appropriate for those who are to discover the sublunary simple bodies on the basis of their motions, just as was also done in the case of the heavenly body. He asks ‘what each is and what their nature is’, that is, he is calling for the enquiry into what their nature is. He calls bodies heavy or light if they have heaviness or lightness, and he calls heaviness and lightness powers, and so he also says ‘and for what reason heavy and light things have these powers’. He will explain this in On Coming to Be and Perishing,186 just as he will also explain the facts about the other affections and the way in which the four elements come to be from one another; for On Coming to Be and Perishing is at the same time continuous with and separated from this treatise. And he showed187 that heavy and light are properly related to motion on the basis of the fact that things are not said to be heavy or light for any other reason than that heavy things move toward the centre, light things away from it.

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(307b32) Aristotle points out correctly that things which share are called heavy or light and their powers are heaviness and lightness, but that there does not exist a name for the activities – as in the case of heat the activity is heating, and in the case of house building it is building a house – unless, he says, someone were to think that ‘impulsion’ is one word indicating the activity of both heaviness and lightness. (308a1) He says the following. The study of nature deals with motion, since nature is a starting point of motion and the kind of starting point that is seen in motion. And a heavy or light body, insofar as it is such, has certain ‘embers’ of life, heaviness and lightness (and these are starting points of motion), since in the case of things constituted by nature the starting point of motion is a kind of life, as he himself said elsewhere.188 As a result all students of nature make use of the powers of heavy and light things, that is they make use of heaviness and lightness. However, except in a few cases they have not determined with respect to them either what the powers are or why natural bodies have these powers. If he means by ‘these things’189 the powers lightness and heaviness, and not the bodies, he is saying ‘contain’ with the meaning ‘are’; for these certain sparks of motion are in what contains them . Consequently, whether he uses ‘these things’ for the bodies or for the powers, the sparks are the powers. And what is said also makes clear that everyone makes use of their powers, so that the argument goes as follows: The study of nature deals with the starting point of motion, since it deals with nature, which is a starting point of motion; but a starting point of motion (or sparks) is heaviness and lightness; therefore, the study of nature deals with heaviness and lightness, and students of nature will speak about these things. So if the study of these things is also necessary for students of nature, and they have not made complete determinations about them, the discussion of them will be useful. (308a4) Aristotle says that now after we have first seen what has been said by others about these things, as is our custom, and set out in a division the difficulties confronting the theory, ‘we will then say what we think about these things’. 308a7-33 Some things are said to be absolutely heavy or light, [others relative to something else; for we say of things which have weight that one is lighter and another heavier, for example, we say that bronze is heavier than wood.

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Translation (308a9) Now our predecessors have said nothing about things which are said to be absolutely heavy or light, but they have spoken about things which are said to be this relative to something else. For they do not say what heavy and light are, but only what heavier and lighter are in the case of things having weight. (308a13) The following will make what we are saying clearer. Some things are naturally constituted so as to always move from the centre, others so as to always move toward the centre. Of these things I say that what moves from the centre moves up and what moves toward the centre moves down. (308a17) It is absurd to think that there is no above and below in the heavens, in the way that some people maintain there is not. They say that there is no above and below since the heavens are everywhere alike and anyone who moves forward from anywhere will come to his antipodes.190 But we call the extremity of the universe above, and it is above in position and first by nature. But since there is an extremity and a centre in the heavens, it is clear that there will be both above and below, just as ordinary people say, although without sufficient understanding. The reason for this insufficiency is that they think that the heavens are not everywhere alike but that there is only one hemisphere, the one above us; for if they accepted in addition that the heavens are this way all around and that its centre is related in the same way to everything, they would say that is above and the centre is below. (308a29) So we say that what moves up and toward the extremity is absolutely light, and that what moves down and toward the centre is absolutely heavy. But we speak about being lighter or light relative to something else when of two things having weight and an equal bulk] one moves down more quickly by nature.

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He first divides the heavy and light into things said to be such absolutely and things said to be such relative to something else. The latter are spoken of in a comparative way, as when we say of two things which have weight, bronze and wood, for example, that one, bronze, is heavier, the other, wood, lighter. In this case we say that the wood is lighter than what is heavier by comparison although in itself the wood has weight. (308a9) Having made this division, he says that his predecessors have said nothing about things which are absolutely light or heavy but have spoken only about things which are heavy or light relative to something else. For they do not say what heavy and light are (if they did they would have explained what absolutely heavy and light are); rather they say what heavier and lighter are, and they look at

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both in the case of things which have weight. And in this they were self-consistent, since they believed that every body has weight, but that one is heavier than another because it sinks down more, and they called what is less heavy lighter since it is more loose-textured and rises, and they called what is most loose-textured light. (308a13) Wanting to show that absolutely heavy and light things are one thing, things heavy and light by comparison another, and what each is, and that his predecessors said nothing about the absolutely heavy and light but spoke only about the heavy and light relative to something else, he assumes as clearly true that some bodies ‘are naturally constituted so as to always move from the centre, others to always move toward the centre’. And this is clearly true and a matter of common agreement, but what he says next he now asserts as his opinion, but later191 he will try to demonstrate it. Of these things which have been mentioned, he says, we say that those which move from the centre move up and that those which move toward the centre move down; and192 ‘we say that what moves up and toward the extremity is absolutely light, and that what (absolutely) moves down and toward the centre is absolutely heavy’. And he says being light relative to something else (which is also called being lighter) occurs when193 of two things which have weight, or rather lightness, and are equal bulks, the one moves up naturally more quickly than the other; and one thing is heavier when both things have weight and an equal bulk and one moves 194 naturally more quickly. (He has explained the lighter in relation to the heavier as the greater in relation to the lesser.195) And it is reasonable for him to add ‘and an equal bulk’; for if two things have unequal bulks it is possible that what is heavier than something not move down more quickly by its own nature but slower because it is smaller and in this way what is lighter by its own nature will not still be lighter.)196 (308a17) The next part of the discussion goes as follows. Having said what he thinks above and below are, in the interim Aristotle argues against those who think there is no above and below in the cosmos. Anaximander and Democritus held this view because they hypothesised that the universe is infinite; for there is no natural above or below in something infinite, since above and below are boundaries or limits of a spatial interval. Others, including Plato’s Timaeus (and Aristotle is mainly referring to him) do not think there is an above or below in the cosmos because of its similarity. They gave as an indication of this similarity the fact that from all parts of the earth it is possible for someone to come to be at his own antipodes; for at whatever place someone is it would be possible for him to come to be in turn at its antipodes. Why then is everything which stretches from under our feet to the heavens more below and what is above our head more above than the same at the antipodes? If the

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same thing is above and below because of similarity, there would not be anything in the cosmos which is determinately above or below by its own nature. So these people did away with above and below in this way. However, Aristotle says, since there is an extremity of the cosmos and a centre, we call the extremity above because it is above in position (since it is higher) and first by nature (since by nature above is prior to below just as right is prior to left). He says that we call the centre below, ‘just as ordinary people say’, but these people fall short of the truth because they do not think that the heavens are a sphere but that it is only the hemisphere above us, which they also see. And so if they thought further ‘that the heavens are the same all around and that its centre is related to everything in the same way’, they would say that the whole of the extremity is above and the centre is below. For at the present time they do not have a complete understanding of the extremity nor do they think that the earth is the centre, even though they do say it is below. And so if they did not think that there is an above and a below in the universe because of its similarity, but it has been shown that there is a difference between the extremity and the centre, what is there to prevent one thing being above and another below? It is prima facie clear from what has been said that what Aristotle has said has been taken from ordinary usage, which Aristotle does not want to dismiss (xenizein). Plato disdains ordinary usage and, although the cosmos is spherical, he does not think it right to call something in it above and something below, but instead thinks it right to call one thing the periphery, another the centre. For the periphery converges toward the centre as if to a starting point and it processes around it; but above, being contrary to below, would not converge to its contrary, nor would it process around it; rather it would move away from its contrary, since it flees it because it is separated from it by nature. Furthermore, if above and below are furthest separated in length, but in a sphere the limits of a diameter have the greatest separation, the perimeter would not be above and the centre below. In general above and below are limits of a rectilinear and not a spherical interval, so that in relation to us they are thought of as being configured in a straight line (orthion); and name the heavy and light by giving them in relation to us, calling heavy what strives toward what is beneath us and light what goes toward what is above us. And Aristotle himself says that the extremity is ‘above in position’, and from where else did he get this nomenclature than from comparison to us, just as in the case of ordinary people? And being first by nature does not compel reality, unless someone were to prove that the centre is below; for being prior by nature suffices for the periphery just as in another respect suffices for the centre.197

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It might be good to set out the passage of Plato in which he denies that there is an above and below in the universe:198 Since the whole heaven is spherical, things which, being equally distant from the centre, are extremities must be equally of such a nature as to be extremities. And one should think that the centre, which is equally distant from the extremities, lies in what is opposite to all the extremities. And, since the cosmos is of this nature, which of the things we have referred to could one posit as above or below without being justly thought to use an entirely inappropriate word? For it is not right to say that its central region is by nature either above or below, but only that it is central, and the periphery is certainly not central, and there is no difference in it by which one part of it or one of the opposite parts is closer to the centre than another part. And what sort of contrary names could someone apply to what is by nature similar everywhere and in what way could he be thought to speak correctly? For if there were a solid in equilibrium at the centre of the universe, it would not ever move toward any of the extremities because of their similarity everywhere; but if someone were to move in a circle about the solid, he would stand many times at antipodes and call the same part of it above and also below. So this is what Plato believes about above and below. And says that all the elements have weight, but not in the sense that all of them move toward the centre with the heavier ones sinking down and the less heavy being pushed out and rising above the heavier ones and as a result being called light, but rather in the sense that all have a motion toward their proper place because of their heaviness. For desire leads each thing toward what is of the same kind, but this leading is because of heaviness. And it is because of this power that each thing rests in its proper place, so that he says that fire is heavy just like earth, and each of them rests in its proper place because of its own heaviness and is pulled away from its proper place to the degree that it is light. Accordingly heaviness alone belongs to the entireties , since they do not abandon their proper places and are not pulled away from them. But lightness also belongs to portions , and because of it they are also constituted so as be transferred to unnatural places. But, just as Aristotle distinguished above and below on the basis of heavy and light and heavy and light on the basis of above and below,199 so too Plato says that people falsely suppose an above and below in the case of the universe because of their false belief about heavy and light. Immediately after the words just set out writes the following:200

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Translation Since, as we have just now said, the universe is spherical, it is not sensible to call one region below and another above. We should reach an understanding of the source of these names and their referents because of which we have become accustomed to speak of the whole heaven in terms of this kind of division; we can do so by hypothesising the following things. If a person were to stand in that region of the universe which is especially allotted to the nature of fire, where most of it would be collected and toward which it moves and, having the power to do so, he were to take out portions of fire and weigh them, placing them on the pans of a balance and lifting the balance up, dragging the fire by force into air, which is unlike fire, it is clear that a lesser amount of fire will be forced into the air more easily than a greater; for if two things are raised up together by one force, it is necessary that the lesser yield to the force more when pulled and the greater do so less and that the large amount be said to be heavy and move down, and the small one be said to be light and to move up. We should notice that we do the same thing in our region. We stand on earth and separate earthen things and sometimes earth itself and drag them into the dissimilar air by force and against nature (since both cling to things of their own kind). The smaller one yields more easily than the larger to what forces them into what is dissimilar, and so we call the smaller one light and the region into which we force it up, and we call the contrary of these heavy and down.

And then a little later, completing what he has to say, he adds:201 682,1

One ought to notice one thing about all of them: it is the movement of each thing to what is of the same kind which makes what moves heavy and makes the region to which it moves down, and the things which are different from these are the others .

308a34-b29 Practically all of those who have previously advanced to the investigation of these matters [have only spoken about things which are heavy and light in the sense that two things have weight and one is lighter. Having gone through things in this way, they think that a distinction has been made between absolutely light and heavy. But their account does not fit with these things. This will be clear to those who proceed further. (308b3) Some of these people speak about lighter and heavier in the way one finds written in the Timaeus, where it is said

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that what consists of more of the same thing is heavier and what consists of fewer is lighter just as a greater amount of lead or bronze is heavier . And similarly in the case of each of the other bodies of the same kind, since for each of them one’s being heavier lies in an excess of equal parts. And they say that lead is heavier than wood in the same way since all bodies are composed of certain things which are the same and of one matter. But this does not seem to be true. (308b12) If they make the distinction in this way, they are not speaking about absolutely light and heavy. For, in fact, fire is always light and moves up, but earth and everything which is made of earth moves down and toward the centre. Consequently fire is not naturally constituted so as to move up because of the fewness of the triangles from which they say each of these things is composed. For if it were, what is composed of more would move less and, being composed of more triangles, would be heavier. But in fact the contrary is obviously the case, since insofar as it is greater it is lighter and moves up faster; and a small amount of fire will be moved faster from above to below, and a great amount will be moved more slowly. (308b21) In addition, since they say that what has fewer of the same kind is lighter, what has more heavier, but air and water and fire are composed out of the same triangles but differ only in the triangles being few or many (which makes one of them lighter and another heavier), there will be some amount of air which is heavier than water. But what happens is completely the contrary, since more air always moves up more , and in general any portion of air moves up from water.] (308b28) So some people distinguish between light and heavy202 in this way. He has said what things are absolutely heavy or light and what things are said to be heavy or light relative to something else. And he now adduces what he has said previously as something clear,203 namely that his predecessors said nothing about things which are absolutely heavy or light but spoke only about those which are heavy and light relative to something else, which they investigated in the case of things having weight. The result was that they called what is less heavy light, that is, lighter. He says that, having distinguished the relatively heavy and relatively light from one another in this way, they think that they have also made a distinction between things which are absolutely heavy and light. However, the account which they have given of what is heavy or light relative to something else does not fit things which are said to be absolutely heavy or light, as will be clear to those who choose to take over their views.

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(308b3) And Aristotle first discusses the view of these things expressed in the Timaeus. And he objects to it after having set it out clearly in the following way. There are three elements, water, air, fire, and three figures assigned to them, icosahedron, octahedron, pyramid, which are composed of the same scalene triangle; and they say that the one composed of more of the same triangles is heavier, the icosahedron or water than the octahedron or air, and these two than the pyramid and fire. Consequently, according to these people ‘for each of them one’s being heavier lies in an excess of equal parts’, just as a greater amount of lead or bronze is heavier than a smaller one and, in general, bodies of the same kind are heavier than one another . If, then, a greater amount of lead is heavier than a smaller one not because of the nature but because of size, this account cannot fit what is absolutely heavy or absolutely light, since these differ in nature. And they said that in the case of things of different kinds a heavier thing is related to a lighter one in the same way as in the case of things of the same kind; for they also say that bronze is heavier than wood because it has more triangles in it since all bodies are composed of the same things and of one matter, that of the triangles, even if this does not seem to be true in the case of things which are of different kinds. (308b12) Those who make the distinction in this way are not discussing absolutely light and heavy but light and heavy relative to something else. Fire is seen to move up whether there is more or less of it, and earth, however much of it there is, is seen to move down and toward the centre. Consequently there is something which is absolutely light and something which is absolutely heavy, and not everything is heavy or light relative to something else, since ‘fire is not naturally constituted as to move up because of the fewness of triangles’. For if it were, more fire would move up less ‘and, being composed of more triangles, would be heavier’. But ‘in fact the contrary is obviously the case, since insofar as it is greater’ it moves up faster and is lighter. And, indeed, if what is greater were heavier it would also be necessary that if more fire were dragged down from above it would move down faster, if it were heavier, but in fact this is not what happens, but a small amount will be moved down faster, because a small amount is forced more easily, a great one with more difficulty. (308b21) Having proved in this way in the case of fire on the basis of both the apparent natural motion and the apparent unnatural motion of the simple bodies that one should not define heavy and light in terms of the multitude and fewness of components and consequently posit only heavy and light relative to something else while disregarding absolute heavy and light, he now proves the same thing on the basis of air. For if what is composed of more triangles is heavier, there will be some amount of air which is heavier than a

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small amount of water, since ten octahedra have twice as many triangles as two icosahedra. But in fact what happens is completely the contrary, as in the case of fire, since more air is not only not heavier than a small amount of water, but also more light than a smaller one. This is clear from the fact that more air moves up more , but what moves up is light. Having said that more air moves up more , he adds, ‘And in general any portion of air moves up from water’. For if any portion of air, whether greater or smaller, moves up above water, it is clear that air is light by nature and is not lighter than water because of fewness of triangles. One should understand that Aristotle is following his own hypotheses when he infers that fire and air are absolutely204 light and water is heavy, since, having made a distinction between natural above and below in the universe, he distinguishes light and heavy by motion up and down. But Plato does not distinguish them by the multitude or fewness of their planes; if he did, water would be heavier than earth, since an icosahedron is composed of twenty equilateral triangles, each of which is composed of four half-triangles … 205 However, says:206 It is the movement of each thing to what is of the same kind which makes what moves heavy and makes the region to which it moves down, and the things which are different from these are the others . That is, things which are not moving toward what is of the same kind as they are, that is, toward what they desire and have an impulsion for, but toward the contrary are light and the region toward which they move is above. Consequently if someone wished to find also in Plato a distinction between absolutely light and absolutely heavy, he would find that in the words which have been set out just now they are not distinguished simply by motion up and down but by motion toward what is proper and motion toward what is alien.207 As for the text of Aristotle, when he says, ‘what has fewer of the same kind is lighter’, since not all are composed of triangles of the same kind, but only three, fire, air, water, are, therefore he is also making the comparison in terms of these three most of all.208 308b30-309a18 But others did not think it adequate to distinguish in this way. [However, although their lives were earlier, they thought about the things we are now discussing in a more innovative way. For it is obvious that some bodies which are smaller in bulk are heavier. So it is clear that it is inadequate to say that equally heavy things are composed

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Translation of equal primary things, since then equally heavy things would be equal in bulk. Asserting this is absurd in the case of those who say that there are primary and indivisible planes of which bodies having weight are composed, but in the case of those who say they are composed of solids it is more possible to assert that a larger thing is heavier. As for composites, since it seems that each of them is not this way but we see many heavier things which are smaller in bulk, as, for example, is the case with bronze and wool, some people think there is another cause and they assert it. For they say that it is the void contained by bodies which makes them lighter and sometimes makes larger things lighter since they contain more void. For this reason bodies which are larger in bulk are often composed of equally many solids or even fewer. And in general the reason why anything is lighter is that more void inheres . (309a11) So this is the way they speak, but it is necessary for the people who make the distinction in this way to add that if something is lighter it not only contains more void, it also contains less solid. For if it exceeds such a proportion, it will not be lighter. They say that fire is lightest because it contains most void. And so it would follow that a great amount of gold is lighter than a small amount of fire because it contains more void unless it also has several times as much solid.] Consequently one should say this.209

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After those who distinguish heavy and light in terms of the multitude and fewness of planes, he turns to Leucippus and Democritus and their followers, who make the solidity of the atoms responsible for weight, and the interweaving of void responsible for lightness. And he says that, although the lives of these people were earlier, they thought about the subject before us in a more innovative way than the people who explain the difference between heavy and light in terms of the multitude and fewness of planes. (He says ‘more innovative’ instead of ‘more carefully thought out’ or ‘more insightful’.) And he gives the reason for his preference for these people when he says that it is obvious that some bodies are smaller in bulk but heavier, as in the case of bronze and wool. This contradicts those who explain the difference in terms of the multitude or fewness of components. For, according to them, things which are composed of things equal in number and in size, being equal in bulk, must always be equally heavy, since if what is composed of more such things is heavier and what is composed of fewer lighter, it is clear that things which are composed of equally many will have equal impulsion. But they are also equal in bulk. For what would produce a difference in size? So if, according to them, things which are equal in bulk must be equally heavy, how

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will they be in agreement with the phenomena, in which some bodies which are smaller in bulk are heavier? In general asserting that what is larger is always heavier is absurd in the case of those who say that there are primary and indivisible planes (that is, elements, things which are not divisible into things different in kind210) from which bodies having weight are composed; for things having weight could not come to be from planes which are weightless, as he said in the third book.211 But in the case of those, such as Democritus and his followers, who say that the primary things are solids, it is possible to say that a larger thing is heavier. For since the things from which are composed are also bodies but not planes, they too have some impulsion. And so these people can give the reason why larger things are heavier in a way which is self-consistent, but those people cannot. But since it seems that every composite is not this way (so that the greater is always heavier), ‘but we see many heavier things which are smaller in bulk, as, for example, is the case with bronze and wool’, it is no longer possible for them to make the atoms responsible, since because of them it is necessary that what is larger be heavier. However, they assert a different cause. ‘For they say that it is the void contained by bodies which makes them lighter and sometimes makes larger things lighter’ because things containing more void are larger in bulk even though they ‘are often composed of equally many solids or even fewer’. And they also think universally that the reason why anything is lighter is that more void inheres in it. (309a11) So these people resolve the difficulty better than those who say that things are composed of planes and give the reasons why larger things are heavier than smaller ones and why smaller ones are often heavier than larger. And he insists that the people who make the distinction in this way ought to add that ‘if something is lighter it not only contains more void, it also contains less solid’ and say that what is light or lighter is not simply what contains more void in itself but in addition contains less solid. For if it were to exceed such a proportion, that is, if it did not have less solid but more (just as it has more void), such a thing would no longer be lighter. But because these people leave out the proportion with respect to solidity and take into account only the excess of void, they make a mistake. For if ‘they say that fire is lightest because it contains most void’ ‘it would follow that a great amount of gold is lighter than a small amount of fire because it contains more void’ (to the extent that this is due to the void) unless it were to have several times as much solid. Consequently it should be added that, in addition to having more void, what is lighter must also have less solid. Most copies of the text say ‘unless it also has several times as much solid’ and give this meaning. But Alexander interprets a text which says ‘even if212 it has several times as much solid’. He says:

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Translation So, according to this, much gold would be lighter than a small amount of fire, but this is, in fact, not the case even if it has several times as much solid as is in the fire.

At this point Aristotle is censuring for not also taking into account this proportion, but a little later,213 having hypothesised that they do take it into account, he also criticises them for this.

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309a19-27 Some of those who denied that there is a void [did not make any distinction between light and heavy, for example, Anaxagoras and Empedocles. But others who did deny there is a void did make some distinction, but did not say anything about why some bodies are absolutely light or heavy and why some things always move up and some down; nor did they even mention that some bodies which are larger in bulk are lighter than smaller ones. Nor is it clear on the basis of what they say how] they can end up saying things which agree with the phenomena. These words pick up from what was said previously with some contraction and also further articulation of criticisms. He says that of those who say there is no void, some, such as Anaxagoras and Empedocles,214 ‘did not make any distinction between light and heavy’, but others, such as Plato, did; however, these latter did not give the reason why some bodies are absolutely light and some are absolutely heavy and why some things always move up and some always down; but they also did not ‘even mention that some bodies which are larger in bulk are lighter than smaller ones’. Nor is it clear on the basis of what they say how it can end up that they say things which agree with the phenomena. We have spoken previously about two of these three criticisms .215 In the case of above and below we have said that Plato does not think these are natural in a cosmos which is spherical; in the case of the absolutely heavy and light we have said that he recognises them, but does not distinguish them in terms of motion downward and upward but distinguishes heavy in terms of motion toward what is proper to a thing and light in terms of motion toward what is alien to it, as the passage set out216 made clear; and Plato does not say in a determinate way that one of the four elements is absolutely heavy, another absolutely light, but he says that everything is both heavy and light because everything is naturally constituted so as to move both toward what is of the same kind and toward its contrary. And Plato makes the great gaps inside them responsible for some things which are larger in bulk being lighter than smaller things, as he has made clear in the case of copper when he says:217

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But it is lighter because it has great gaps (dialeimmata) inside it, and this compound is copper, one kind of the bright and solid waters.

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309a27-b17 It is necessary that those who explain the lightness of fire [by reference to its containing a great amount of void also fall prey to practically the same difficulties. For fire may contain less solid and more void than other bodies, but even so there will be some amount of fire in which the solid and full exceeds the solids contained in some small amount of earth. (309a32) If they are going to say that the void also how will they distinguish the absolutely heavy? Either by containing more solid or by containing less void. (309a34) If they are going to say the former, there will be some small amount of earth in which the solid is less than in a great amount of fire. (309b2) Similarly, if they distinguish it as containing less void, there will be something which is lighter than what is absolutely light and always moves up and that something will always move down; but this is impossible since what is absolutely light is always lighter than things which have weight and move down, although what is lighter is not always light because even in the case of things having weight one is said to be lighter than another, as water is said to be lighter than earth. (309b8) But neither is it sufficient to resolve the difficulty stated just now in terms of the proportion of void, since impossibility will likewise result for those who speak in this way. For the solid will have the same ratio to the void in more fire and in less, but more fire moves up faster than less, and likewise too more gold or lead moves down . And similarly in the case of all other things which have weight. But this should not happen] if heavy and light were distinguished in this way. He has spoken against those who generate bodies from planes, saying that they have neither spoken about things which are absolutely heavy or light nor given the explanation why a body which is larger in bulk is lighter than smaller bodies. He now says that it is necessary that those who make the void responsible for lightness also fall prey to practically the same difficulties. For it followed for those who make fewness of elements responsible that they say that a small amount of water is lighter than a great amount of fire, and the same absurdity will follow for these people, at least if according to them what has less solid and more void is lighter. But it is possible that a great amount fire be taken and it have both more solid and more void than a small amount of air (or water or earth), so that the

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fire would not be lighter than the air; for what is lighter should have not only more void but also less solid. (309a32) Next he adduces an objection as if it came from them when he says, ‘But if they are going to say that the void …’, that is, if they were to say that a small amount of earth is not lighter than a greater amount of fire because it not only has less solid, it also has less void (for what is lighter was to have not only less solid but also more void). If they were to make this suggestion, he says, ‘Let them say clearly how they will distinguish the absolutely heavy’ (and obviously also the absolutely light). For it is necessary to distinguish the absolutely heavy ‘either by containing more solid or by containing less void’ (and conversely to distinguish the absolutely light either by containing more void or by containing less solid). So either they would make the distinction in this way or rather they would not make it by reference to only one of these but by reference to the proportion of both to one another thus: as in the case of the absolutely heavy the full, being more than the void, is to the void, so in the case of the absolutely light the void, being more than the full, is to the full. He has added ‘absolutely’ in the phrase ‘absolutely heavy’, perhaps to make the contrast with ‘heavy relative to something else’, since it is possible for them to say that what is in an equal bulk 218 is lighter but has more solid and less void. But this is not absolutely light. And similarly what is specified in this sort of a way is not heavy. For what is absolutely heavy or light must be such not because of size but because of its own nature. (309a34) He argues against these three ways219 of making the distinction and first against the first. If they distinguish the absolutely heavy in terms of having more solid then there will be a ‘small amount of earth in which the solid is less than in a great amount of fire’. So that fire will be heavier than that earth, and that earth will be lighter than that fire. Here one should also understand that if the absolutely light by having less solid, there will be some small amount of earth which has less solid than a great amount of fire, and therefore that earth will be lighter than that fire and that fire will be heavier than that earth. (309b2) Similarly, if they distinguish heavy and light in terms of void and so say what has less void is absolutely heavy and what has more void is absolutely light, there will be some amount of earth which has more void than a small amount of fire, and so what is absolutely heavy and always moves down, earth, will be lighter than what is absolutely light and always moves up, fire. But this is impossible because what is absolutely light is lighter than what has weight, however little it has. However, this statement does not convert to yield the result that what is lighter than something is

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thereby also absolutely light, since even in the case of things having weight one is said to be lighter than another, as a mina is lighter than a talent. (309b8) And next he says that the third way of making the distinction, which he himself suggested to them,220 by adding to having more void in the case of what is light the necessity of having less solid, is not ‘sufficient to resolve the difficulty stated just now’ either. According to this third way the distinction is made when the void in something is proportional to the full in such a way that as, in the case of the absolutely heavy, the full, which is more, is to the void, so, in the case of what is absolutely light, the void is to the full. He says that in this way too an impossibility will likewise result for them, even though they say they have a plausible theory. ‘For the solid will have the same ratio to the void in more fire and in less’, so that as far as it depends upon this ratio ought221 to move equally quickly and be equally light. But this is not so, as is made clear by the fact that more fire moves up faster than less. And similarly the ratio of solid to void will be the same in more gold and in less, and nevertheless more gold (or lead) moves down faster than less. ‘But this should not happen’, if the absolutely heavy and the absolutely light were distinguished by this proportion, since in that case things having the same ratios would move equally quickly. 309b17-28 [It is also absurd that, if things move up because of the void, the void itself does not move up.]222 (309b18) However, if the void [is naturally constituted so as to move up and the full so as to move down and, as a result, they are the causes of each of these motions for other things, it would not have been necessary to investigate in the case of composites why some bodies are light and some heavy, but concerning these very things it would have been necessary to say why one is light and the other has weight. (309b23) Furthermore the reason why the full and the void are not separate. (309b24) It is also unreasonable to make there be a space for the void, as if it was not itself a kind of space. But, if the void moves, it is necessary that there be some place for it, from which and into which it changes. (309b27) In addition, what is the cause of motion? It certainly isn’t the void,] since it is not the only thing which moves; so does the solid. And he next adduces other objections against those who make the void responsible for lightness and the full responsible for heaviness. The first is that it is absurd that bodies move up because of the

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interweaving of void, but that the void itself does not move up. For if the void is the cause of motion up for other things which do not move up for any other reason, why doesn’t it also move in the same direction by its own nature? (309b18) Having indicated in this way that it follows for those who say that the void is the cause of motion up, the full that of motion down, that they say that the void moves up and the full down naturally, he next infers the absurd consequences of this. The first is that ‘if the void is naturally constituted so as to move up and the full so as to move down and, as a result, they are the causes’, one of motion up, the other of motion down, for other things, it would not have been necessary to further investigate in the case of composites why some bodies are light and some heavy, since this would already have been clear for those who make this hypothesis. But concerning these very things (the void and the full) it would have been necessary to ask why one is light and the other has weight, which is the same as to say, why the void moves up and the full down. For Aristotle thinks that it is straightforwardly absurd to assign lightness or impulsion or, in general, any power to the void, since doing so does not preserve our conception of the void. However, if they asked this question they would be investigating the absolutely heavy and light and not be investigating only what is comparatively heavy or light, as they now do. (309b23) Secondly, he says, if the void moves up by nature and the full down, what is the reason why they do not stand apart from one another, but rather are mixed with one another and remain together? Perhaps it would be easy to respond to this by saying that it is for the same reason that fire and earth are mixed although the one moves up and the other down except that fire and earth are also separate223 but these people say that the void and the full are not separate. (309b24) Third he says that it is unreasonable to make there be a space for the void by saying that it moves up naturally. For, according to these people, the void is a space or place deprived of body, but to make there be a place for a place is absolutely absurd. Furthermore, it is not possible for those who hypothesise that space is infinite to speak of above or below or of where a motion comes from or where it goes to. But everything which changes place moves from one place to another. (309b27) Fourth, he asks, ‘In addition, what is the cause which is common to motion upward and motion downward’? For we make nature, which is a starting point of impulsion and motion in bodies, the cause, but these people cannot say that the void is the cause of motion because ‘it is not the only thing which moves; so does the solid’. 309b29-310a3 The same thing results if someone distinguishes these things in a different way [by making some things heavier or lighter than others because of largeness or smallness, or if he

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offers any other kind of explanation, whether he assigns only one kind of matter to all things or several matters but only contrary .224 (309b33) For if there is only one , there will be no such thing as absolutely heavy and light, as there isn’t for those who compose things from triangles. (309b34) But if there are contrary matters, as those who void and full, there will be no reason why the things intermediate between the things which are absolutely heavy and light are heavier and] lighter either than one another or than things which are absolute.225 Next he adduces these considerations relating generally to all those who discuss heavy and light. In the things he says now he also takes into account the views which he has just spoken against, both the view which distinguishes heavy and light by multitude and fewness of planes and that which distinguishes them by void and full. And he says that the same things result, namely that either they say nothing about the absolutely heavy and light or they say nothing about things intermediate between the things which are absolutely heavy and light. And so he speaks of someone who distinguishes heavier and lighter things in a different way by largeness and smallness and not in the way Plato did but as Democritus and his followers did or in the way that those who hypothesise that there is one element and generate other things using the denseness or rareness of the one element did. Democritus and his followers said that fire is composed of small spheres (so that it has the finest parts), earth of larger atoms, and the intermediates226 of intermediate atoms. And those who hypothesise one element also made the void responsible for rareness. The words ‘or if he offers any other kind of explanation’ (that is if he names denseness and rareness rather than largeness and smallness) ‘whether he assigns only one kind of matter to all things’, for example water or air or what is intermediate between them,227 fits these people228 and fits them most of all. (By ‘matter’ Aristotle means a substratum, since he also assigns the same matter to all things, the difference being that these people say that there is something which is already actual which is the substratum, for example, water or air or what is intermediate between them.) The words ‘or several matters but one contrary ’ may include those who speak of the void and full, and those who speak of earth and fire, as Parmenides did,229 and those who speak of dense and rare, and those who explain coming to be in terms of multitude and fewness of planes.230 (309b33) Having thus divided everyone into those who hypothesise one matter and those who hypothesise several but only one contraries, he adduces the absurdities which follow for each of them. The first is that if there is one matter (as there is for those who

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compose things from triangles, since for them the three elements, fire, air, and water, came to be from one thing, the scalene half-triangle231), then for these people who generate things from one and the same substratum there will be nothing which is absolutely heavy or absolutely light; for there is the same nature in all of them, and if it is heavy the absolutely light vanishes, and if it is light the absolutely heavy will not exist, but there will only be the relatively heavy, whether they say that things come to be heavier or lighter because of the multitude and fewness of the substratum or because of its largeness and smallness, with the element itself having no impulsion. (309b34) But if the matter or substratum is a contrary, as it is for those who speak of void and full, these people will think it right to say about the absolutely heavy and the absolutely light that the void is absolutely light, the full absolutely heavy, and that the intermediate bodies, fire, air, and the others (these are called intermediate because they are composed of both the extremes, full and void232) can no longer be . For they will not be able to determine why are heavier and lighter than one another or the elements, that is, the void, which is light, and the solid, which is heavy. For since they do not know why the void is light and the solid is heavy,233 they are not able to offer an account of the things sharing in them. 234 But they could give an explanation of why composites are heavier or lighter than the absolutely heavy or light things, since they could say that they are heavier than the void because they also contain solid, and lighter than the solid because they contain void. Or is it the case that those who are not able to give an explanation why one composite is heavy and another light also cannot give the explanation why composites are heavier or lighter than anything at all? But perhaps they can say that the intermediates are heavier and lighter than one another, lighter because they have more void and less solid in an equal bulk, and conversely for heavier. But they will not be able to say how they compare things which are not equal in bulk. For if a small portion of earth and a great amount of fire are compared, on what grounds will the fire be judged to be lighter when it is several times the size of the earth. For it is not possible to say in these cases that the one which is lighter when an equal portion is taken is always (haplôs) lighter, since, if an equal were lighter than an equal because it contained fewer solids and more void, then, if this equality were not preserved, the cause of one thing’s being heavier or lighter than another would not remain either. Alexander interprets the text in this way, understanding ‘things intermediate between the things which are absolutely heavy and light’ as composites of void and full. But perhaps Aristotle is calling earth and fire absolutely heavy and light, and air and water intermediate, and saying that these will not be because

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are not able to give an explanation of why air and water are heavier or lighter than one another or than the things which are absolutely light or heavy. At this point Aristotle has said only this much, but toward the end of the book235 he sets down the same argument more clearly and states the absurd consequences, both for those who say that the substratum is one and for those who say it is contraries. And there he says236 clearly that the intermediates are air and water. And one should know that Alexander writes the text with ‘either than one another or than the things which are absolute’, but he found some copies of the text in which ‘than things which are absolutely ’ is written.237

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310a3-13 To distinguish in terms of largeness and smallness [is more like a fabrication than the previous , but because it is possible to produce differentiae for each of the four elements, it is more resistant to the previous difficulties. (310a7) But if one makes the things which differ in size have one nature, it is necessary that there be the same consequence as for those who make there be one matter: there is nothing which is absolutely light and moves up, but it either falls more slowly or is squeezed out; and many small things are heavier than a few large ones, but if this is so, it will result that a great amount of air or fire is heavier than a small amount of water or earth.] But this is impossible. He has said what absurdities concerning heaviness and lightness follow for those who say matter or the substratum is one and for those who say that it is contraries, namely, that the former say nothing about the absolutely light and heavy and the latter do not determine the reason why some intermediates (these are either the natural bodies or the two intermediate elements238) are heavier, others lighter. And he now turns to those who explain the difference of the elements in terms of largeness and smallness. These would be the people who distinguish in terms of having thick or fine parts, which is to say in terms of condensation and rarefaction and who also hypothesise a single matter for these differentiae.239 He says about them that their theory is more of a fabrication than the one which hypothesises the void and the full, but that this theory which is now being put forward is more resistant to the difficulties which were brought against that theory. For each of the four bodies will have the impulsion of weight or lightness because of its participation in fineness and thickness and the proportion involved in it. This could not be said by those who compose things from planes, since things which do not have impulsion in themselves will not have it when more or less of them are combined; nor can those

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who make the void and the full responsible for the difference of the elements with respect to lightness and heaviness offer an account of the cause, since people who cannot say why the void is light and the solid heavy240 also cannot state the reason for the difference between things composed of the void and the solid. (310a7) He also censures those who distinguish in terms of largeness and smallness because by making there be one substratum and one nature of things which differ in size they are subject to the same as those to which the people who made there be one matter were subject, namely that, according to them, there is not something which is absolutely light and moves up and something which is absolutely heavy and moves down; for, according to them, everything will have the same natural impulsion, perhaps more, perhaps less, but not different in kind, because there is one substratum. But if there is nothing which moves up by nature, it is clear that things which are now thought to move up are either thought to be going241 up because they are falling more slowly and are overtaken by heavier things in their downward motion or they are moving upward by constraint and not naturally because they are being squeezed out by heavier things. Aristotle says that it follows for these people that many small things, that is, many things with fine parts, are heavier than a few things with large parts; for, since things with small parts are composed of the same substratum as things with large parts and they have the same natural impulsion, if more things with small parts are collected, they will be heavier than a few things with large parts. But if this is so, ‘it will result that a great amount air or fire is heavier than a small amount of water or earth. But this is impossible’. Alexander says: This can also be said against Democritus and his followers, who said that fire is composed of small spherical atoms. For, if all atoms, which are of the same nature, have weight and larger ones are heavier because they are larger (so that bodies which are composed of larger atoms will also be heavier), then242 many small atoms will be heavier than a few large ones. But if this is so, a great amount of fire will be heavier than a small amount of earth. Or perhaps243 this could be said against them if they did not make the void responsible. 244

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move down naturally and some move up and down, and then speak about heavy and light and the affections resulting from them and why they occur. One should think about the fact that each thing moves to its own place in the same way as one thinks about other cases of coming to be and changing. There are three kinds of change, change of size, change of form, and change of place, and in the case of each of them we see that the change comes to be from contraries and into contraries and intermediates and that change is not of just anything into just anything, and similarly that not just anything causes just anything to change, but that just as the subject of alteration differs from the subject of growth, so too what causes alteration differs from what causes growth. One should think in the same way that not just anything causes just anything to change place. (310a31) If, then, what causes motion into what is above or below245 is what gives weight or lightness, and what is subject to movement is what is potentially heavy or light, then246 the motion of each thing into its own place] is its motion into its own form. Having concluded his discussion and set out his predecessors’ views of heavy and light together with appropriate refutations of them, he would have the opportunity to turn next to his own views. However, he says that he should first make a determination on a difficulty which some people raise most of all, namely why some bodies, in moving naturally with their own motion, always move down, some always up, and some down and up, and then to give for heavy and light and the affections resulting from them the reason why heavy and light and what results from them occur. Alexander says:247 The difficulties raised about the motion of bodies into their proper places are the following. To start with248 people say that if the place of a thing is the limit of what contains it, it is clear that what does not yet contain something isn’t its place either. So how could bodies move to their proper places when places do not exist at all, since the bodies do not yet exist? For the bodies had not ever come to be in those places previously; if they had then the bodies could be said to move into their proper places, which had come to be at that time; for bodies move directly when they have come to be and are barely still coming to be. Now249 if moving bodies move toward similar things, fire toward fire, air toward air, and similarly with water and earth, and when they have come to be in them, they become parts of the wholes and continuous with them, and continuous parts are not per se in a place, then things which move naturally would not move to their proper places or even to

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Translation places at all, but, toward the things which had left250 the place which it had, and so no longer have a place or are in place. But251 if someone were to say that moving toward a proper place is moving toward a proper and similar body, he would not be speaking correctly either, since if (hypothetically speaking) earth were transported into the place of fire, it would be overpowered there. But if the fire were to be transferred below and then some earth were set free, where would the earth move if it moved naturally? Up, toward the entirety of earth because it is similar to it, or down toward the fire? If toward the entirety of earth, the lower region will not be proper for things having weight nor will they move to it. But if they move down because this place is proper to them, then, for bodies, moving naturally toward what is proper would no longer be equivalent to moving into their own place, nor would the place of an entirety and of a part of it be the same.

These, then, are the difficulties which are raised. But someone might say that if god and nature were to transfer the earth to where the moon is now because this is where it ought to be, then a clod of earth would move there, since the parts would also receive this same power as the entirety does from creation. 252 Aristotle will resolve these difficulties by showing that for bodies moving to their own place is equivalent to moving to their proper form and proper completeness. And he will show this using the fact that the completeness of everything which is potentially something is having come to be in that something; for the completeness and form of what is potentially literate is having come to be literate, and similarly in the cases of what is potentially cultured or hot. But if having come to be in that in which they can naturally be is the completion of potentialities, then the change to that in which they can be would be for them a path to completeness. Things being this way, since things which move to something in which they are potentially change to having come to be actually in that, everything which moves to the completeness and form with respect to which it is potentially is changed by things which are naturally constituted so as to cause them to move and change. Consequently things which change place would change to their proper form and the completeness with respect to which they are subject to change. But if this is so, changing into one’s own place would be changing into one’s own form and completeness. Alexander sets out the demonstration concisely in this way. Aristotle, having proposed to give the reason why some bodies move up, some down, and some, moving because of their own nature, go in both directions (something which he also demanded of those who say that the void is light, the solid heavy253), gives a general

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explanation applying to all the forms of change. There are three sorts of change. One is change with respect to growth, which he calls change of size. A second is change of quality, which he calls change of form, perhaps indicating coming to be and alteration simultaneously; for coming to be and perishing is change of form in the strict sense; even if coming to be is not in the strict sense change (as he specifies in the fifth book of the Physics254), nevertheless, what he is now saying about change also fits coming to be. The third sort of change is change of place. In the case of each of the three we see that the change comes to be from contraries and into contraries or intermediates and that change does not come to be from just anything or into just anything. For if what is white changes, it does not change into what is literate or into anything else but into the contrary of white or something intermediate . And similarly in the other cases. For the per se change of anything is determinate, the per se change of what is white is the change with respect to white, and the per se change of what is a certain size is the change of it qua of a certain size, and the change of something into this particular place is the change of it with respect to its being naturally constituted so as to go into that place. Consequently what changes place also does not change into just any place or from just any place, but from a contrary into a contrary or an intermediate; but the contraries related to place are above and below. Alexander says that the reason why a change must be into the contrary of what changes is that what changes must always abandon that from which it changes, since it cannot simultaneously remain in that from which it changes and change from it. And so when a substratum (which is also said to change) leaves its previous form it always comes to be in another form, since a substratum deprived of every form cannot exist. Thus it will have changed into something which is such that when it is in it, it can no longer be in that from which it has changed, and so it will have changed into something which cannot coexist with that from which it has changed. Contraries and intermediates are this sort of thing, since it is not possible for the same thing to be in contraries at the same time and in the same respect. And so something is not said to change from white to literate because it can be white and literate simultaneously, but it is said to change from white into black or the intermediates because it is impossible for it to be both white and either black or one of the intermediates simultaneously. Aristotle also uses the fact that changing things do not change into just anything but into contraries, in order to show that a thing is not changed by just anything but by what causes the contrary change; for with this he gives the reason why bodies move to their proper places. And so he says that not just anything causes just anything to change. For just as things which change in different ways are different from

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each other (since what changes in quantity, that is, the subject of growth, is one thing, and what changes in quality, that is, the subject of alteration, is another), so too the things causing change are different. For what grows is not caused to grow by something which causes alteration but by something which causes growth; nor is what is altered caused to alter by what causes growth, but by what causes alteration. But, just as in the case of changes of quality and quantity not just anything changes into just anything nor is it caused to change by just anything, but it changes into its contrary or into an intermediate and is changed by what has the power to cause change of this kind, so too in the case of change of place one should think in the same way; for not just anything that is moved moves to just any place nor is it moved by just anything, but what is moved is something definite, it moves to some definite place, and it is moved by something definite. (310a31) Having articulated this to start and made it credible on the basis of other kinds of change that what changes place is not just anything, does not change into just anything, and isn’t caused to change by just anything, but rather what is potentially changes into what is actually by the action of what is naturally constituted so as to bring something , he next gives the following syllogism: If what causes motion upward or downward is what gives weight or lightness and not just anything, and what is subject to movement is what is potentially heavy or potentially light, then for a thing to move to its own place, whether it moves up or down, is for it to move into its own form from being potentially to being actually; but, because of what was just proved,255 the antecedent is true: what causes motion is what gives weight and what is potentially heavy changes to what is actually heavy;

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therefore, the consequent is also true, namely that what moves up or down naturally moves from the potentiality of its own form to its actuality; for, also, if what gives heat causes change in the case of heat, and what is potentially hot is changed into what is actually hot, it is clear that a thing’s changing into what it is naturally is nothing other than its changing into its own form and becoming hot in actuality. And as long as it is moving up or down, it has not yet completely taken on its own form but is still coming to be; but when it has taken on its proper place, then it also takes on its proper form, since it then takes on the actuality of what it was potentially at one time.

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So why do bodies move down naturally? Because what it is to be heavy is naturally being below. Things which are at first potentially heavy are changed to being actually heavy by what is naturally constituted so as to cause motion with respect to heaviness, that is, by what produces earth or water; and they change into their proper form. For even if pieces of entireties are not in a proximate place when they have become continuous with their entireties,256 nevertheless they are at least together with the entireties in the place in which, when they have come to be in it, they have taken on actuality and completeness with respect to their own form. If these things are true and, as Aristotle says, ‘the motion of each thing into its own place is its motion into its own form’, what has taken on the form of heavy or light no longer moves. So if what moves toward the centre is heavy and what moves toward what is above is light, it is also necessary, first, that things in their proper places have heaviness or lightness (or rather only have them in actuality there) and, secondly, that if toward the centre is heavy and toward what is above is light, one should not characterise†257 but in terms of convergence. So much about the meaning of what has been said. As far as the text is concerned, if what was written is ‘If258 what causes motion into what is above or below is what gives weight or lightness’ as in some copies of the text, what is said is clear. But if it is, as Alexander writes it, ‘If what causes motion up or down is what gives weight or lightness’ ‘up or down’ is interpreted in an old-fashioned way and is said instead of ‘upward or downward’. 310b1-15 And one should rather understand in this way [what earlier thinkers said, namely that like moves to like. For this does not happen always; for it is not the case that if someone were to transfer earth to where the moon now is, every piece of earth would move toward the earth; rather it would move to where the earth is now. So, in general, it is necessary that this happen in the case of things which are similar and without difference and moved by the same motion, so that the whole is naturally constituted to move to wherever any single piece is constituted to move. But since place is the limit of what contains, and all things which move up or down are contained by the extremity and the centre, and they are in a way the form of what is contained, moving to one’s own place is moving toward what is similar. For adjacent things are similar to one another, for example, water to air and air to fire. It is possible to speak in the reverse way about the intermediates, but not about the extremes. For example, one can say that air is similar to water and water to earth, since the higher is always related to what is under it as form to matter.]

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Having said that for a thing to move into its own place is for it to move into its own form from being potentially to being actually, he now says that one should rather understand what earlier thinkers say when they say that like moves to like in terms of this fact. For what is potentially is similar to what is actually, and what is coming to be so and so is similar to what already is so and so. For it does not always happen that earth moves toward earth in the way that some people understand this statement; for it is not the case that if someone were to transfer the earth to where the moon is now that pieces of earth would still move toward it. For, in fact, pieces of earth do not move down because the earth is below, but because when things which are similar and without difference are moved by the same cause of motion, the result is they move with the same motion, and therefore each of the pieces is naturally constituted to move to where the whole is, but not because that is moving toward the earth. So like things (and not ones which are just like but ones which are of the same nature) would not be said to move to what is like in the strict sense; rather these things move to the same . In general, if someone wishes to discover motion to what is like in the more strict sense, he will find it to be motion to its own place. For since ‘place is the limit of what contains’, what moves to its proper place moves to the limit of what contains; but what contains is like what it contains because ‘adjacent things are similar to one another, for example, water to air and air to fire’. And it is true to say in the reverse way in the case of the intermediates that they are similar, not only that air is similar to fire but also that it is similar to water, so that it is similar to both what lies over it and what lies under it, and in the same way that water is similar to air and earth. However, this sort of reverse relation no longer holds for the extremes, that is, for fire and earth. For there is nothing which lies over fire and nothing which lies under earth.259 And that adjacent things are similar is clear from the fact that they change easily into one another since they are of the same kind because of the common quality which inheres in them. And perhaps in this respect fire and earth also have the reverse relation, since they possess dryness in common. And the whole development of the argument is the following: what moves to its proper place moves to what contains it, and what moves to what contains it moves to what is similar to it. Having said that ‘place is the limit of what contains’, he adds ‘all things which move up or down (and not absolutely all things which move) are contained by the extremity and the centre’; for the body which moves in a circle is itself the extremity, and is not contained by the extremity and the centre, only the things which move up or down are. I do not think he has added this qualification for no reason, but in order to indicate that of the things which move upward, the

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one which lies above contains the one which lies below, as fire contains air, and that of the things which move downward the one which lies below . For these things are nearer to what contains, that is, to the extremity and the centre. He says that what contains is in a way the form of what is contained – he says it is contained because it lies adjacent. For if the upper region gives form to light things which come to be when they come to be there and similarly for the lower region and heavy things, then for fire the upper extremity is the form because fire has its completeness in it, and for air fire is the upper extremity because air moves up as far as fire, and again for earth the centre is form and for water earth is, because when water has come to be in earth and taken on its form with respect to weight it rests. And the analogues of form are the extremes because they give form to what lies adjacent to them, and the analogues of matter are the intermediates because they are given form by the extremes. For fire endows air with lightness, and earth endows water with heaviness. This is one way of dividing the four elements into formal and material; another is that in which heavy and cold things have the role of matter, light and hot things that of form, as Aristotle says elsewhere and Theophrastus says in On the coming to be of the elements; Posidonius the Stoic borrows this idea from them and uses it all the time.260 The exegete Alexander points out that the division concerning the material and formal elements which is now being set out is different. He says that water is form for earth and not vice versa in the way I think. He writes this: Therefore, earth and water are material, fire and air formal, if they are spoken of in absolute terms, but, relative to one another and as proximate forms and as proximate matters, the which are close to each other vary slightly with respect to being material, since, although water is in a way form for earth, water is itself also material because it is related in this way to earth. However, if, as Aristotle says both the extreme place and the central one give form, and the natural impulsion for water toward form and completeness is toward the centre, but earth is more proximate to the centre than water, earth would have the relation of form to water more than water has it to earth; for earth first takes on the form of heaviness from the centre and gives a share of it to water. And as fire is related to air, so is earth to water. However, Alexander apparently is looking at Aristotle’s saying that ‘the higher is always related to what is under it as form to matter’. But perhaps Aristotle, having said that ‘all things which move up or down are contained by the extremity and the centre’, is saying that the centre is also higher than

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what it contains because it does contain them. And he says that the extremity and the centre are ‘in a way’ the form of the things they contain because not they but the things which they bestow are the form of the things they contain: the extremity bestows being above and lightness, which gives form to light things, and the centre heaviness and being below. 310b16-311a1 But to ask why fire moves up [or earth down is the same as to ask why if what is able to be cured changes qua able to be cured it advances toward health rather than toward whiteness; and similarly with all other things which are alterable. And when what is able to grow changes qua able to grow it does not advance toward health but toward an increment in size. And similarly with each of these, one thing changes in quality, another in quantity, and in place light things move up, heavy things down. (310b24) However, some of these things seem to have a starting point of change in themselves (I mean what is heavy or light), and others such as what is able to be cured or what is able to grow are not thought to have it in themselves but from outside. But sometimes these things also change on their own and, when there is a small change in the environment, advance toward health or growth. (310b29) And since the same thing is able to be cured and receptive of illness, if it is changed qua able to be cured it moves toward health, but if it is changed qua susceptible to illness it moves toward illness. (310b31) However, what is heavy and what is light appear to have the starting point of these things more in themselves because their matter is closest to substance. An indication of this is that motion belongs to things which have been cut off,261 and of the kinds of change it is last in generation], so that this kind of change would262 be first in substance. He has shown that things which move up or down naturally move toward their proper form and proper completeness and move from being potentially into the actuality of that for which they had the potential. Now he also confirms this on the basis of the other kinds of change by showing that just as in their case natural change is from what is potentially toward its proper actuality and not toward anything else, so too in the case of change of place. And so, he says, asking why fire moves up and earth down is not at all different from asking why if what is able to be cured changes insofar as it is able to be cured it ‘advances toward health rather than toward whiteness; and similarly with all other things which are alterable’. And when what is able to grow changes insofar as it is able to grow ‘it does not

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advance toward health (or toward any other quality) but toward an increment in size’ because the change is quantitative, not qualitative. It is also this way in the case of things which change place, light ones move up, heavy ones down, and they are not naturally constituted so as to move in any other direction. For when fire is below it is and is said to be light because it is able to rise and is still potentially on the top, and similarly when earth is above because it is able to sink and is still potentially lying on the bottom, as is also the case with what is able to be cured. But when these things move, insofar as they are light or heavy, fire moves upward and toward being at the top as toward its proper form and its own actuality and completeness; and earth moves downward and toward lying on the bottom. And neither moves naturally toward anything else. And as we also will learn shortly herafter,263 he says this about things which are still in the process of coming to be and changing and have not yet completely taken on their own completeness and their own actuality but are moving toward it, as is also true with fire which is below and of earth which is above. This is seen more clearly in the case of rising vapours when their change into air is not yet complete and in the case of things which are condensing into liquid, as is the case with dew and frost; for these things, which are not yet actually air or water, are in motion. Alexander raises objections to the text. He says that it would have been better if ‘Indeed, to ask’ had been written264 instead of ‘But to ask’ because this is adduced as something previously proved. But it is also possible that ‘but’265 has been written correctly to indicate the similarity of changes of place to the other kinds of change and to confirm this similarity on the basis of the other kinds of change. Alexander also says, ‘And the words “And similarly with each of these”266 should have been written as “And similarly with each of the others” or “similarly as with each of these”, since, he says, the inference is that just as these are, so too are those in place’. But perhaps the text does not need to be changed at all if it is read in its context. For Aristotle says ‘And similarly with each of these, one changes in quality, another in quantity, and in place light things move up, heavy things down’. Why would he say ‘each’ in the case of two things (things which change in quality or quantity) unless he were co-ordinating a third, what changes in place, with them? One should notice that Aristotle can also say the same thing in the case of things which change substantially, that is, things which come to be, as he says in the case of things which change qualitatively because things which come to be also change from being potentially to being actually. However, he passes over things which come to be because he does not wish to say that things which do not yet exist (as people say) change, and he leaves change out from the

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three , things that change in quantity, in quality, and in place. And accordingly, he confirms things which change place on the basis of similar things, things which grow and things which change qualitatively. (310b24) Having said that the question concerning things which change place ‘Why does earth move down and fire up’ and the questions in the case of things which change in quantity and quality are similar, he next sets out the difference between change of place and the other kinds of change, namely that things which change place seem to have the starting point of change, that is heaviness or lightness, in themselves, but things which change in quality or quantity are not thought to; rather they are changed by the changing of other external things, things which cause qualitative change or things which cause growth. And then he indicates the sort of similarity there is between these differing things by saying that there are times when these things which change qualitatively or grow also change on their own, since some people get healthy without needing any medical help or grow when the power to take in nourishment and grow acts. He properly adds the words ‘when there is a small change in the environment’ to show that these things are not similar to things which change place and have the whole cause of their change in themselves, since what grows also requires the ingestion of nourishment and what gets healthy also requires moderate climate. But what directly makes healthy or causes to grow is nature, which uses these things. (310b29) Having said that changes toward health on its own, needing only a little external assistance, he adds that the same thing is able to be cured and receptive of illness, so that if it is changed insofar as it is able to be cured it moves toward health, but if it is changed insofar as it is susceptible to illness, it moves toward illness, since everything changes toward that for which it has the capacity. (310b31) And so, having drawn the conclusion that things which change place (for these are ‘what is heavy and what is light’) have the starting point of their change in themselves more than things which change in other ways, he adds the explanation for this, namely that things which change place are more complete, and things which are more complete and are already in actuality have the starting point of change in themselves to a greater degree. It is for this reason also that animals and living things in general, which are more complete than other things, surpass these other things most in this: changing on their own. For what is incomplete and not yet is changed by the thing because of which it comes to be. When he adduces the reason why things which change place are more complete by saying that their ‘matter’ is ‘closest to substance’, he hints at the reason in an unclear way. By ‘matter’ he means their

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suitability and their potentiality, by ‘substance’ their complete form. For everything which is potentially is matter for that which it is potentially, and the substance of each thing is distinguished in terms of its complete form. Now since things which change place do not change with respect to something in themselves, but only with respect to place, things which are already complete with respect to their substance, even if they do have a certain incompleteness and consequently change, are, in any case,267 close to completeness with respect to place.268 For suitability for change of place does not strive toward substance but toward actuality. Accordingly, Aristotle does not deny that divine bodies change in this way269 since they are very active; for changing qualitatively and growing and, still prior to these, coming to be are more matters of being affected, but changing place is more of an activity, so that things which are changing place, insofar as they are changing at all, have, indeed, not yet taken on their completeness in this respect, at least if they are changing toward actuality and their own form in this respect, but when they have arrived at their proper place through change of place they take on their proper completeness in this respect and become actually what they were only potentially until then. And so it is reasonable that he say that the suitability for these things is closest to completeness with respect to that suitability, at least if, being complete with respect to their substance, they only need to act, and if they reach this completeness just through changing on their own without needing anything else. He brings in two indications that things which change place are close to completeness and more complete than things which change in the other ways. One is that this kind of change belongs to things which have been ‘cut off’, that is, to things which are complete substances and are not changing with respect to something in them. For things which come to be or grow or change qualitatively have not yet been cut off into being an independent reality. The second indication is based on the fact that things which change place are posterior in generation and things which are posterior in generation are more complete. For also in the case of animals incomplete ones precede complete ones in generation, for example, seed and katamenia and the formation little by little of the embryo and giving birth precede the completion in time of what has been born when it generates something like itself;270 and in the case of plants each of them proceeds from incompleteness to completeness in the same way. But what is more complete is prior in substance since the other things are taken in advance for the sake of it. However, change of place also accrues to other things, both animate and inanimate, later; for animals change place after they have already come to completion271 and natural bodies which have come to completion take on their own natural motion: when fire has come to be it takes on motion toward

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the extremity, and when earth has come to be, it takes on motion toward the centre. But qualitative change and, in addition, growth precede change of place, and thus change of place supervenes later and especially in the case of more complete things, such as animals, since when these things have come to completion and been cut off they move with the locomotion which is appropriate to animals. Consequently change of place would be prior in substance to the other changes and accrue to things later in time and order. 311a1-9 And so when air comes to be from water [and comes to be light from being heavy, it advances into what is above. At the same time it is light and is no longer coming to be light, but it is there. Indeed, it is evident that, being potentially and going into actuality, it advances into the place, size, and quality to which the actuality attaches.272 (311a6) And it is for the same reason that fire and earth which already exist and are move into their own places if nothing impedes them. For also nourishment] moves immediately [when what prevents is not present and so does what is able to be cured when what restrains is not present]. Having said that things which move into their own place move into their own form and their own completeness (since what is already earth moves downward and what is already fire upward), he sets out for us a distinction between things which are coming to be and changing from being potentially to being actually and are moving with their own motion and things which already are. And he says that when air comes to be from water and in general being light from being something heavy it advances into what is above, and, at the same time as it has taken on form and become completely light, it is no longer coming to be light – it is light. So if what rises to the top is light, it is already above; and so it is evident that, being potentially light and going into actuality, what rises to the top moves upward, and when it comes to be actually it is there. Having said about things place that, going into actuality, they advance ‘into the place’ (the word ekei is spatial), he adds a brief remark about the other changes, saying that things which go into actuality with respect to quantity advance into the size to which the actuality attaches and that things which go into actuality with respect to quality advance into the quality to which the actuality attaches; an example of place is above, of quantity, perhaps, two feet long, and of quality, perhaps, white. (311a6) Having spoken about things which are coming to be, he now adds a remark about things which are already actual, what is already fire or already earth, namely that in their case too, if nothing impedes them, they move into their own place for the same reason

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that those which are still coming to be do. For also things that are actually and are held in an alien place by constraint or suddenly come to be in an alien place (as in the case of a fire which is ignited in our region or the stone which is produced in clouds273) move, if nothing impedes them, toward the place which is naturally appropriate for them and, having come to be there, they take on completeness of form. For a thing is in an alien place either because it came to be there and in a way still shares in the contrary nature from which it changed and which it discards when it moves to its own place, or because it is held there by constraint and thus in a way is disposed unnaturally; for if what is naturally constituted so as to rise to the top is constrained to lie below other things or if what is naturally constituted so as to lie below other things is forced to be detached and rise, it is then disposed unnaturally, so that also when things which are thought to be already actual are in alien places they are in a way incomplete and have some potentiality and move rapidly toward actuality and completeness. And he makes clear that he means to say that things which are thought to be already actual but are impeded have some potentiality when he says that also nourishment and what is able to be cured move toward their own actuality when what prevents is removed, being potentially until then; for when nourishment has come to be actually what it was potentially, flesh for example, it is added and nourishes that of which it is said to be nourishment and causes it to grow. What is potentially is very different in the case of what has already come to be and in the case of what has not yet taken on the form. The latter is like the ability to read of a child , the former like the ability to read of the person who has acquired it but is not exercising it; what has the potentiality to change place is also of this kind. And with what he says Aristotle seems to resolve a certain objection274 which goes as follows: if what moves to its proper place naturally moves to its proper form, why does what has already taken on its proper form move toward its proper place? And Aristotle says that what changes place takes on its proper form completely when it has come to be in its proper place.

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311a9-14 The first agent causes a thing to change [and so does what removes or that off of which the thing bounces, as was said in our first discussions, in which we determined that none of these things moves itself. (311a12) So we have said for what reason each moving thing moves] and what motion into the place of the thing is. He has said that things which change place have the starting point of change in themselves more than things which change in other ways; and, because this was said as a comparison with other things

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which change either in quality or in quantity (these things being less complete than those which change place), he points out to his listener that things which change place do not have the starting point of their change in themselves in the strict sense either but that what was said in book 7 of the Physics275 is true of them, namely that nothing which changes naturally causes itself to change, but everything which changes is changed by something else. He calls those discussions first because they deal with the first principles of natural things. And so he is saying that [i] things which change place are also changed by something else; [ii] that everything is changed by the first agent (for what changes something into fire is itself a per se cause of the thing’s276 moving upward); [iii] but also that if something is preventing either fire from moving up or earth from moving down, what removes the obstacle is a cause of its motion, but an accidental cause; [iv] and he says that that off of which the thing bounces is also in a way a cause of the motion, in the sense that a wall causes the motion of a rebounding stone or sphere. One should understand if this kind of motion is simple and natural, since it is neither up nor down but to the side. (311a12) After this he concludes with what was directly proposed and has been demonstrated,277 the difficulty which he said some people raise, why some bodies move up naturally and some always down naturally and some both up and down.278 For he has shown that what moves to its own place moves into its own form and its own completeness, and he has shown that it is the same thing to ask why fire moves up and earth down and to ask why if what is able to be cured is changed insofar as it able to be cured, it advances into health but not into whiteness.

311a15-b1 We should now speak about their differences and their consequences. [Let us first make explicit what is obvious to everyone: what sinks to the bottom of everything is absolutely heavy, what rises to the top of everything light. In saying ‘absolutely’ I am looking at the genus and I mean those things to which both do not belong; for example, it is obvious that a chance quantity of fire moves up and one of earth down unless something else happens to prevent it, and a greater quantity moves faster in the same way. But things to which both belong are heavy or light in a different way, since they rise above some things and sink below others, as air and water do. For neither of these is absolutely light or heavy, since both are lighter than earth (since a chance portion of them rises above earth) and both are heavier than fire (since a portion of them, whatever its size, sinks below fire); but

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relative to themselves, one is absolutely heavy, the other absolutely light, since air of any quantity rises above water and water of any quantity sinks below air. (311a29) Since in the case of other things as well some have weight, others lightness, it is clear that the difference in things which are not composite is the cause of all these things. For some bodies will be heavy, some light in accordance with there being more or less of those . Consequently, since other things follow from first things, we should discuss these things, in the way we said that those who explain heavy in terms of the full] and lightness in terms of the void ought to do. Having responded to those who ask why some bodies move up, some down, and some both up and down by giving a common explanation, he now turns to the differences because of which some things are heavy, some light, and some are both, and to their consequences,279 namely that the same things do not seem to be heavy or light everywhere. He assumes first on the basis of a common conception that there is something which is absolutely heavy and something which is absolutely light and what these things are; later280 he will also demonstrate these things. And so he says that everyone thinks that what sinks to the bottom of everything is absolutely heavy, what rises to the top of everything which moves in a straight line281 is absolutely light. And then he explains how ‘absolutely’ is to be understood. He says, ‘For282 in saying “absolutely” I am looking at the genus and I mean those things to which both do not belong’, and so characterises ‘absolutely’ in terms of these two things. Those things to which both lightness and heaviness belong, such as the two intermediate elements, air and water, would not be absolutely light or heavy because each of them sinks below what lies over it and rises above what lies under it; rather they would be light relative to what sinks below them and heavy relative to what rises above them. Only that which is only light but not also heavy is absolutely light and only that which is only heavy is absolutely heavy. He says ‘I am looking at the genus’ instead of ‘I am looking at the very nature because of which they are light or heavy, but not at their comparison with something else’. He says that the following two things characterise what is by nature heavy or light. are not heavy or light because of being small or large, but rather are things of which even a chance portion has the same power as the whole, as, for example, a chance quantity of fire moves up ‘unless something else happens to prevent it’; consequently what is naturally constituted in this way is absolutely light even if at some time it does not rise because it is impeded – and similarly for what is absolutely heavy. A second mark of what is naturally constituted so

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as to be heavy or light is that more moves faster with the same motion; for if things are of the same nature, as the greater is to the lesser, so the motion is to the motion. The phrase ‘those things to which both do not belong’ seems to distinguish absolutely heavy and light things from the two intermediate elements, water and air, to each of which both heavy and light belong, and being heavy or light in genus seems to distinguish them from things which are determined by number or size. Having spoken about what is absolutely heavy and what is absolutely light, to each of which only one of heavy and light belongs, he adds that the intermediates are heavy and light in the sense that both heavy and light belong to each of them and consequently they have both properties. And even if the intermediates are not universally absolute so that one of them is absolutely heavy, the other absolutely light, nevertheless they too are absolute in another way, since relative to each other one is absolutely heavy the other light because air, either the whole of it or a part, and however much there is, rises above water, and in this respect even it would be said to be absolutely light relative to water; for it is not the case that some of it rises above water and some does not, but absolutely all of it, whole and part, does; and water, of any quantity, sinks below air and therefore it too is said to be absolutely heavy relative to air, although it is not universally absolutely heavy because it does not have the same relation to the extreme elements. But it is clear that air is heavy relative to fire in the same proportion as water is light relative to earth. (311a29) Having spoken about the simple bodies, both the one which is universally absolutely light and the one which is universally absolutely heavy and about the ones which are not universally one or the other but are absolute relative to one another, he next adds something about the other bodies, that is composites, since these are the other things besides the simple bodies. And he says that since also of these composites ‘some have weight, others lightness’, one should not make any great fuss about them, since it is clear that the difference in the simple bodies from which these are composed, insofar as one of them shares in more, another in less of them, is the reason why some composites are light and others heavy. Consequently the person who is enquiring about heavy and light should speak about them in the case of the simple bodies, since the composites follow them. And we demanded283 that those who say that bodies are heavy because of the full and light because of the void also do this and first say why the full itself is heavy and the void is light, since if this were understood it would then be clear why some of the things composed from them are light and some are heavy.

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311b1-13 It284 follows that the same things do not seem to be heavy or light everywhere285 [because of the difference of first things. I mean, for example, that in air a talent of wood will be heavier than a mina of lead, but in water it will be lighter. The reason is that everything except fire has weight and everything except earth has lightness. And so it is necessary that earth and whatever contains most earth have weight everywhere, that water have weight everywhere except in earth, and air everywhere except in water and earth; for everything except fire has weight in its own region, and that includes air. An indication is that an inflated bag weighs more than an empty one. Consequently if something has more air than earth or water it can be lighter than something in water and heavier than it in air, since it does not rise above air,] but it does rise above water. Having said that some composites are heavy and some light because of the difference of the simple bodies from which they are composed, sharing in more of one and less of another, he recognises a certain objection which says the following. If the same things are everywhere composed of the same simple bodies (as a talent of wood is composed of the same elements both in air and in water and similarly for a mina of lead), and the lightness and heaviness in composites is derived from the elements (as Aristotle has just said286), why aren’t the same things heavy and light everywhere, but rather the talent of wood is heavier than the mina of lead in air, but the reverse is true in water, where the wood rises and the lead goes down? This difficulty is not, as some287 have thought, placed here at an inappropriate time, but has been adduced in consequence of the statement that heaviness and lightness in composites are derived from the difference of the simple bodies of which the composites are composed. And Aristotle resolves it by saying that the reason why this results is that in their own region all simple bodies except fire have weight and all except earth have lightness. For, if each of the things after fire sinks, one sinking below more things, another below fewer, but what sinks is heavy, it is clear that everything has weight except fire; and if all things except earth rise and what rises is light, it is clear that everything except earth is light; for only earth rises above nothing, just as only fire sinks below nothing. This being the way things are, ‘it is necessary that earth and whatever contains most earth have weight everywhere’ since earth sinks below all things. But water will have weight in other bodies below which it is naturally constituted to sink, and in all of them it will preserve its impulsion toward what is below because it is heavy relative to them (since it sinks below them), but it will not also have weight in earth since it rises above earth. Therefore, if water which is heavier than some earth288 when they are

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in air is placed on earth together with the earth, it will rise above the portion of earth than which it was heavier when they were in air. But air itself is heavy relative to fire (which is absolutely light), since air sinks below fire which rises above it, but relative to water and earth air is light, since it rises above them. Consequently since lead, however much there might be, has the most earth, it also sinks through the water, but a talent of wood, having a great deal of air, rises above the water because air also rises above water. However, in air a talent of wood, which has much air, is heavier than a mina of lead because air also has weight in its proper place and what has much air has the impulsion of weight when it is in the place of air. And that air has weight in its proper place is confirmed on the basis of bags, which weigh more in air when they are inflated than uninflated ones do. This is what Aristotle says. However, the mathematician Ptolemy, who has a view contrary to Aristotle’s, also tries in his On Impulsions289 to establish that in their own region neither water nor air has weight. He shows that water does not have it on the basis of the fact that divers do not perceive the weight of the water lying on them although some of them dive to a great depth. Against this it is possible to say that the continuity between the water lying on a diver and that lying under him and that on each side, which provides support, makes him not perceive the weight (just as animals in holes in walls, even if they touch the wall in every direction, are not weighed down by it because the wall supports itself in every direction) so that, if the water were divided and lay on top of him he would probably perceive the weight of it. Ptolemy also shows that air in its own entirety does not have weight on the basis of the same evidence, that of the bag, not only arguing against the view, which Aristotle held, that an inflated bag is heavier than an uninflated one but also claiming that the bag becomes lighter when it is inflated. I experimented with the precision which is possible and found the same weight when the bag is uninflated and when it is inflated. One of my predecessors290 also made an experiment himself and wrote that he had found the same weight or rather that the bag was heavier by some very small amount before it was inflated (which agrees with Ptolemy). And if the truth lies with my experiment it is clear that the elements would be without impulsion in their own places and none of them have either weight or lightness, as Ptolemy agrees in the case of water. And this would not be unreasonable. For if natural impulsion is a desire for a thing’s proper place, if anything were to reach its own place it would no longer desire it or have an impulsion toward it, just as what has been satiated does not desire nourishment. But if, as Ptolemy says, the inflated bag is lighter than the uninflated one, then air has lightness in its own place, and water, in

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accordance with the same theory, has weight in its own place. For when we climb up out of water we think we have lost some weight – unless, of course, we perceive our relief at ceasing to hold our breath as a loss of weight. In general, if air is related to water in the way that the absolutely light is related to the absolutely heavy, it is reasonable that air, being more like what is absolutely light, also have lightness in its own place just as fire does, and water have heaviness because of its likeness to earth; for there is some difference between and accordingly, since they are this way, it is necessary that, if someone were to compare them only with one another, air be said to be absolutely light, water absolutely heavy, as Aristotle himself explained.291 Consequently it is necessary that air have heaviness only in fire, than which it is heavier, and water have lightness only in earth, than which it is lighter, and again that air have lightness both in itself and in things which come after it, and that water have heaviness both in itself and in the things which come before it. But let these opinions of the most philosophical Syrianus have been stated.292 But perhaps, even if these things have been said with truth, air is said to be light in one sense when it is in the elements which come after it – namely in the sense that it moves upward and away from them –, and in another when it is in its own region – namely that it lies above the others but not in the sense that it moves upward and away from the region (as it is necessary for those who think that the inflated bag is lighter than the uninflated one to say). For how is it at all possible to say that air in its proper place is light in the sense that it naturally moves toward what is above? For it cannot wish to abandon its proper place. However, even if the inflated bag weighs less than the uninflated one, I do not think that even this compels the elements to have some impulsion when they are in their own place, but rather it shows that they have no impulsion. For the air in the bag occupies the bag in its own place, but what is together with it, having an earthen composition and lacking air, has rather an impulsion toward what is below. And in this way, too, some part of the wood which floats on the water, having come to be in the place of air, causes what is earthen in the wood to rest in the region of air because of the air in the wood. But it would be more problematic if the air had weight in its own region and for this reason the inflated bag weighed more , since then the air would naturally sink downward from its proper region, which I believe Aristotle also thinks is absurd. Since, it is not easy, when Aristotle says that the inflated bag weighs more than the empty one, to ignore the judgement of a man who is so precise, perhaps sometimes the air which is introduced into the bag does add a certain slight weight, since it is usually blown in from human mouths and is more moist and is filled out by the continuity

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of what is blown in – unless one, because of precision, might also disregard such a quantity. 311b13-29 That there is something which is absolutely light and something which is absolutely heavy293 [is evident from the following considerations. I call absolutely light what is naturally constituted to always move up if nothing prevents it, and absolutely heavy what is naturally constituted to always move down if nothing prevents it. For there are some things of this sort and it is not the way some people think that everything has weight. Certain other294 people also think that there is something heavy and it always moves toward the centre. (311b18) And similarly there is something light. For we see, as was said previously,295 that things made of earth sink to the bottom of everything and move toward the centre. But the centre is determinate. So if there is something which rises to the top of everything, as fire, even in air itself, obviously moves up while the air is at rest, it is clear that this thing moves toward the extremity. Consequently this thing cannot have any weight, since if it did it would sink below something else. But if this were so, there would be something else which moves to the extremity and which rises to the top of everything which moves. In fact there is obviously nothing . Therefore, fire has no weight and earth has no lightness, since it sinks to the bottom of everything] and what sinks to the bottom moves to the centre. 20

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Previously296 he assumed on the basis of the phenomena that there is something which rises to the top of everything and something which sinks to the bottom of everything and said that one of these is absolutely light, the other absolutely heavy, and that neither shares in the nature of the other; and now he demonstrates that this is correct. Being about to speak about these things, he again recalls what exactly the absolutely light and the absolutely heavy are: what is naturally constituted to always move up if nothing prevents it is absolutely light, and what is naturally constituted to always move down if nothing prevents it is absolutely heavy. Having said this he adds, ‘For there are things of this sort’, meaning ‘there are bodies of this sort’, and it is not the way Democritus and his followers think that everything has weight, but fire, because it has less weight, is squeezed out by†297 things and moves up and consequently seems to be light. These people think that only what is heavy exists and this ‘always moves toward the centre’. But nothing prevents fire and everything else from having weight and the reason why each element moves to its proper place from being what Plato says it is.298 For Plato calls this kind of impulsion weight, differing with Aristotle verbally

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because Aristotle calls the impulsion to the centre weight and calls the centre below, and he calls the impulsion to the periphery lightness, in accordance with ordinary usage. But Plato says that what is common to them, the impulsion, is the same as weight, and it seems to me that shortly hereafter299 Aristotle has said this spontaneously. (311b18) Having said that some people think that there is only what is heavy, he adds, ‘And similarly there is something light’. For if what sinks to the bottom of everything is absolutely heavy, it is also necessary that what rises to the top of everything be absolutely light; but fire is this sort of thing. For if things which are made of earth and which sink to the bottom of everything move down and to the centre, and the centre is determinate, then it is necessary that the extremity be determinate and that there be something which moves to this and rises to the top of everything. But fire is obviously this sort of thing, since even in air itself which is at rest it moves toward what is above; for it is clear that it moves toward the extremity since it also rises above air. He says that the air is at rest so that no one can say that fire moves up because it is squeezed out by the air which sinks below it. But if fire rises even above air, it has no weight, since what has weight ‘would sink below something else’ (this is the specific feature of weight); but if fire had weight and sank below something, there would be something different which moves to the extremity and rises to the top of everything which moves. In fact, there is obviously nothing of this sort. Therefore, fire has no weight since it moves toward the extremity and rises to the top of everything, just as earth does not have any lightness since it sinks to the bottom of everything and what sinks to the bottom of everything moves toward the centre. For these are two things characterising the absolutely heavy, and the absolutely light: moving toward the centre and rising to the top of everything. For what does not rise to the top of everything sinks below something and is heavy relative to that and not absolutely light. So, if fire rises to the top of everything, it is not just light but lightest, but, if this is so, it is also absolutely light, since what is superlatively such and such is also always absolutely such and such; for what is sweetest is also absolutely sweet, and what is whitest is also absolutely white, and likewise in the other cases. Aristotle is now taking it to be evident that the centre is determinate, but he demonstrates it shortly herafter.300 He assumes it now because it is useful for showing that the extremity is also determinate, since what is equally distant from the extremity in every direction is the centre; so if the centre is determinate, the extremity must also be determinate. That the extremity is determinate is useful to him for showing that there is something absolutely light, since what moves to the extremity and rises to the top of everything is also absolutely light. With these things being assumed to start, the development of the argument is the following:

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Fire moves higher than air; what moves higher than air moves toward the extremity; what moves toward the extremity rises to the top of everything; but what moves toward the extremity and rises to the top of everything is lightest and absolutely light, just as what moves toward the centre and sinks to the bottom of everything is heaviest and absolutely heavy; therefore, fire is absolutely light, just as earth is absolutely heavy. 311b29-33 However, that there is301 a centre [toward which things having weight and away from which light things move is clear from many considerations. First because it is not possible for anything to move ad infinitum. For just as nothing impossible exists, so too nothing impossible comes to be.] But motion is a coming to be from somewhere to somewhere.

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Having previously hypothesised that the centre is determinate and obtaining on the basis of this that the extremity is also determinate,302 he now demonstrates the hypothesis that the centre is determinate and thus also demonstrates that the extremity is so as well. He proves what he proposes with two arguments.303 In one of them he gives the following syllogism using the second hypothetical mode:304 [i] If the centre, ‘toward which things having weight and away from which light things move’ is not determinate, it is necessary that what moves move to infinity; [ii] but this is impossible; [iii] consequently it is also impossible that the centre is not determinate; [iv] therefore, it is determinate. And the conditional [i] is clear because what moves to a limit (peras) moves to a termination (horos). He proves the additional assumption [ii] as follows. Taking it to be clearly true that something moves toward the centre and what is below and that ‘motion is a coming to be from somewhere to somewhere’ and that what cannot have come to be cannot be coming to be at all (he also said this previously305), he next makes the following tacit syllogism: What is moving is coming to be by moving; what is coming to be by moving might reach the end of the motion; therefore, what is moving might reach the end of its motion; but what is moving to infinity cannot reach the end of its motion; therefore, what is moving cannot be moving to infinity.

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He recalls that what cannot have come to be cannot be coming to be with the words ‘for just as nothing impossible exists, so too nothing impossible comes to be’. For, just as there isn’t a human being with wings, so one couldn’t be coming to be, since everything which is coming to be is coming to be because it is possible to reach the end of its coming to be. But that nothing impossible is coming to be does not mean that everything which is coming to be always reaches its end, but that it is not impossible that it have reached its end.

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311b33-312a8 Next, when fire moves up and earth and everything having weight moves down they move306 at similar angles, [so that it is necessary that they move toward the centre – whether they move toward the centre of the earth or the centre of the universe is another discussion since both are the same. (312a3) But since what sinks to the bottom of everything moves toward the centre, it is necessary that what rises to the top of everything moves toward the extremity of the region in which it makes its motion; for the centre is contrary to the extremity and what always sinks to the bottom is contrary to what rises to the top. (312a7) Therefore it is also reasonable that heavy and light are two things,] since the places, centre and extremity, are also two. This second argument proves that the centre ‘toward which things having weight and away from which light things move’307 is determinate on the basis of the fact that when fire moves up and earth and all heavy things down they move at similar (that is to say, equal) angles. (And it was also said previously308 that earlier people placed the angle under quality, not quantity and divided them by similar and dissimilar and not by equal and unequal, as more recent thinkers do.) It is clear from the fact that both walls and pillars only stand firmly when they are set at right angles that weights naturally move down at equal angles so that they make equal angles with the earth. But things which move up away from the centre in the opposite direction, as fire does, also themselves309 make the angles with that part of the earth from which they begin their motion equal on either side; for things which move from the centre always move to what is perpendicularly above with respect to themselves, so that they make the angles on either side of that from where they began to move equal. For things which move down from above do not move in parallel and neither do those that move up from below; but both things which move down from above and those which move up from below converge toward the centre,310 so that they always make their separation from each other greater as they are closer to what is above. So311 if they converge, they move at equal angles, and if they move at equal angles, they converge, and,

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converging, they meet together at some common limit to which they all move. For they could not move so that they crisscross, since if they did they would also move in the opposite direction upward in this way. Therefore, there is something determinate to which heavy things, moving from everywhere, will meet together, but this is the centre since things moving from everywhere converge at it. Having proved that what moves from above moves to the centre, which is determinate, Aristotle points out that it is312 necessary for the student to enquire whether it moves to the centre of the universe or of the earth, since the centre of both is the same. And he says that this enquiry belongs to another discussion and not to the discussion of heavy and light, since it suffices for the difference between heavy and light to posit that, whichever of the two the centre is, what moves toward it is heavy, what moves from it light. But when he asks this in the second book of this treatise in the discussion of the earth, he says313 ‘It314 is necessary that toward the centre of the universe, since light things and fire, which move in the contrary direction as heavy things, move toward the extremity of the place which surrounds the centre …, but315 they also move to the centre of the earth, but in an indirect sense insofar as it has its centre at the centre of the universe’. For, in general, if every portion of earth moves to the centre, it would not move to the centre of the earth.316 (312a3) He has proved that the centre to which things having weight move is determinate; and since because of this it has also been proved that the extremity is determinate (for if the extremity isn’t determinate no centre can be determinate either, at least if what is equally distant from everywhere on the extremity is the centre), he proves that what rises to the top of everything moves to this extremity. For since sinking to the bottom is contrary to rising to the top, and the centre is contrary to the extremity, and what sinks to the bottom and is heavy obviously moves toward the centre, it is necessary that what rises to the top move toward the extremity. For if a contrary moves toward a contrary, then a contrary also moves toward a contrary;317 for cannot move toward what is below, since then rising to the top would no longer be contrary to or different from sinking to the bottom; for it is necessary that things which are contrary in impulsion move to contrary places. He is being careful in saying ‘toward the extremity of the region in which it makes its motion’. For what is light does not move toward the extremity of the universe (since the sphere of the fixed stars occupies this region) but toward the extremity of the sublunary realm, in which heavy and light bodies, and in general bodies which move in a straight line, move. He adds ‘always’ to ‘sinks to the bottom’ to indicate what is absolutely heavy, since this is what always sinks to the bottom of everything. (312a7) Having proved that the centre and the extremity are two

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determinate places which are opposite to one another, he plausibly adds, ‘Therefore it is also reasonable that heavy and light are two things, since the places, centre and extremity, are also two’. For if the places to which the motions are directed are two and opposite, the impulsions related to these motions which are to these places would be two and not one, as Plato is thought to say in the Timaeus where he claims that the motion of each of the elements to its proper place is weight. For just as, because there are two simple distances (diastêmata), the circle and the straight line, there are two simple motions, that in a straight line and that in a circle, so too, because there are two places, the centre and the extremity, the impulsions and the bodies which move in accordance with them, the heavy and the light, are two. But it has been318 said that Plato, reckoning that ‘weight’ means the same thing as ‘impulsion’, says that, just as all things have an impulsion toward their proper places, so too they have weight, and he has made this clear through that image about which he has written the following (for it would be better to hear again319 the very words of Plato which outshine those of Aristotle as gold outshines silver): If a person were to stand in that region of the universe which is especially allotted to the nature of fire, where most of it would be collected and toward which it moves and, having the power to do so, he were to take out portions of fire and weigh them, placing them on the pans of a balance and lifting the balance up, dragging the fire by force into air, which is unlike fire, it is clear that a lesser amount of fire will be forced into the air more easily than a greater; for if two things are raised up together by one force, it is necessary that the lesser yield to the force more when pulled and the greater do so less and that the large amount be said to be heavy and move down, and the small one be said to be light and to move up. And in this way it would appear that fire is heavy. But if, standing on earth, we placed two unequal earthen bodies on the pans of a balance and we dragged the balance by force into air, which is unlike earth, the smaller would come along with the scale more easily than the greater. And so we call the smaller light and the place into which we force it up, and, on this account earth would be light. However, I think that even if Plato does not accept that there is above and below in a universe which is spherical and does not accept the distinction of light and heavy (since light things and heavy ones are found to be the same), he nevertheless has shown clearly that he does know the difference between motion to the centre and to the periphery by saying,320 ‘And so it is necessary that these things relate to one another in different ways because the great quantities of the kinds occupy places which are contrary to one another’.321

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312a8-28 There322 is also something between these323 [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. (312a12) And we say that what contains is formal, what is contained material. This contrast is found in all the genera, since in quality and quantity one thing is more formal, the other more material. And likewise in things concerning place, above is determinate, and below is material. Consequently, too, in the case of the matter itself of heavy and light, qua so and so potentially it is matter for heavy, but qua such and such it is matter for light. And it is the same, but its being is not the same in the same way as what is susceptible to illness and what is able to be cured; for their being is not the same, and that is why being for the ill is not being for the healthy.

(312a22) So one thing having a certain kind of matter is light and always above, the other having a contrary matter is heavy and always below. What has different matters from those, but ones which are related to one another in the way that those are absolutely and move both up and down.324 Therefore air and water have both lightness and weight, and water sinks below everything except earth,] and air rises above everything except fire.

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He has proved that, since there are two opposite places, the centre and the extremity, it is necessary that there be two things which move to them, the absolutely heavy and the absolutely light. And he next proves on the basis of the opposition of these places to one another that there is also a place intermediate between them which has to each of them the relation of the other; for this is the specific feature of all things which are intermediate between other things, and so the intermediate place is above and an extremity relative to what is, in the strict sense, centre and below, and it is below and centre relative to what is, in the strict sense, above and an extremity. And, just as, since there are two extreme places, there are two extreme bodies, one absolutely light, the other absolutely heavy, so too, since there is an intermediate place having the specific feature of both , there is also an intermediate body, which is not absolutely heavy or light, but heavy and light relative to one or the other of the extremes: this is water and air. He might have proved on the basis of the division of the places into two that there are also two bodies which move naturally to them. But, because the division is not exhaustive and the upper place is not all alike, nor is the lower

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one, but the last of the upper place and the top of the lower one are near to one another both in place and accordingly also by nature, and they are not absolutely above or absolutely below, the bodies in them, which are like parts, one of what is above, the other of what is below, are two and like one another. But Aristotle will say more precisely why there are two extreme and four altogether in On Coming to Be and Perishing.325 (312a12) Having established the four elements with an argument,326 he next sets out what relation they have to one another. Taking it as clearly true that matter is contained by form and form contains matter, he says that, also in the case of bodies which have already been given form and change place, one thing, what is contained, has the role of matter (what is heavy and at the centre is of this sort) and another, what contains, has the role of form (what is light and above is of this sort). These327 are absolutely , but each of the intermediates both contains and is contained and has the role of form and of matter to different things. But he applies this relation to the elements not only here but in other places;328 and so, in order that someone not say that this is true of substances but not also of things which differ spatially, he generalises the statement to other things. For, he says, this difference and the relation of form to matter does not only apply to substances, it is also found in all the genera; for in quality white and hot are analogous to form, black and cold to matter, and in quantity large and many are analogous to form, small and few to matter (and also getting bigger is analogous to form, getting smaller to matter); and in general the stronger (kreittôn) members of antitheses are taken as analogous to form, the more deficient as analogous to matter and privation. And so also in the antithesis concerning place, above is determinate, that is, formal (for this is determinate because form makes matter, which is indeterminate in itself, determinate), and below is material. Having said these things about places, he next would be saying329 about bodies in the places that since what is above, such as fire, contains, it has the role of form, being actually light and rising to the top of everything; and, since what is below is contained and sinks to the bottom of everything, being heavy in actuality, it has the role of matter. The person who passes over this stage is discussing the matter which is common to heavy and light and is only matter and not form.330 But this is different insofar as, being matter of light, it is matter of matter, not matter of itself but matter of heaviness; and although actual heaviness is form, it has the role of matter. Aristotle says that the matter of light and heavy is the same (that is why they change into one another), but being for this matter of light and heavy is not the same as well. And he clarifies this through the example of the body, which is the subject of illness and health and has the role of matter relative to them. For a body is both susceptible

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to illness and able to be cured since it is naturally constituted to be ill and to be healthy, and it is the same body and the same subject, but the being and account of what is susceptible to illness and what is able to be cured is different. The one is ‘being naturally constituted to be ill’, the other ‘being naturally constituted to be healthy’, and these are different because the actualities with respect to which these are potentialities are different. (312a22) So since being matter of light is not the same as being matter of heavy, and most of all being such matter proximately, but one thing becomes the matter of light, another that of heavy because of some differentia (either of heat or cold or dryness or moistness or something else of this sort) which comes to be in the matter, it is clear that one thing which has a matter suitable for lightness is light and always is or is coming to be above (is, when it already has matter of this kind, coming to be when coming to be), and another which has the contrary (that is, the matter which is suitable for heaviness) is heavy and is always below. (Here the word ‘always’ means ‘as long as it has this sort of matter’, since it is clear that these things themselves also change.) Moreover, he distinguishes the absolutely light and always above and the absolutely heavy and always below from things which come to be sometimes above and sometimes below, as the intermediate elements do. He says that the body which has different matters from those so that the matters are neither absolutely light potentially nor absolutely heavy, but have heavy and light relative to one another (since absolutely light and absolutely heavy are absolute and universal) also has matters which are both heavy and light and move up and down absolutely, not absolutely in the sense of universally, but in the sense of absolutely with respect to one another because they have the relation of absolutes to one another. Alexander also knows of another text which instead of saying ‘What has different matters from those, but ones which are related to one another in the way that …’ says ‘The limit331 of these things … having …’. He thinks this text is elliptical and is filled out as ‘The limit of these things is some body, but it has matters which are related to one another as those matters are absolutely and consequently move both up and down because they are light in one way and heavy in another’. For what is light in one way and heavy relative to something is the limit of what is absolutely light; and what is in a way heavy is the limit of what is absolutely heavy. For the first cessation of what is absolute is what is in a way; and so if being heavy in a way is predicated of what is light in a way and vice versa, they are predicated as limits. And so in the case of bodies in which the matters contain the limits of both of the things which are absolute, the bodies themselves are also both heavy and light. Alexander says, ‘He would be calling “matters” in the bodies the

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substrata with their impulsion but taken without the other qualities (dryness and the rest)’. But perhaps the supervening form is the impulsion, to which332 lightness or heaviness belongs, whereas the matters, some of which take on lightness, others heaviness, are accompanied by heat and coldness and moistness and dryness. By showing that the matters and substrata for all of the elements are different, he demonstrates that each of the intermediates too is the way it is because of its own nature and not because of being a mixture of the extremes. And so it will not follow for someone who says these things333 that a great amount of air is heavier than a small amount water, because air and water have both lightness and weight since they are intermediate between those things which are absolutely heavy or light and are in a way their extremities or limits; as a result water rises above earth and sinks below the others, and air sinks below fire and rises above all the others.

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312a28-b2 But since there is only one thing which rises to the top of everything [and one which sinks to the bottom of everything, it is necessary that there be two other things which both sink below something and rise above something. Consequently it is also necessary that there be as many matters as there are of these things, namely four, but four in such a way that there is one common matter for all of them – in particular if they come to be from one another –, but a matter which is different in being. For nothing prevents there being] both one and several things intermediate between contraries, as there are in the case of colours, since intermediate and centre are said in many ways.334 He has said that there is some body intermediate between the body which is absolutely light and the body which is absolutely heavy and that it is light in a way and heavy in a way and is a limit of each335 of the absolutely and consequently that there are two such bodies intermediate between fire and earth, namely air and water. He recalls these things briefly by saying ‘But since there is only one thing which rises to the top of everything’ etc. and then adds, ‘Consequently it is also necessary that there be as many matters’, namely four, but in such a way that there is one same matter for all of them. And in other words what was said in the first book of the Physics,336 he says further that if the four come to be from each other (as has been proved previously337), nevertheless the matters have338 a different being, since there is one account for the proximate matter of339 fire and in general of what is absolutely light, and a different account for each of the others. I think that he is giving an extended discussion of the matter which underlies the elements, showing that there is one matter for them and it is fourfold, and that having shown previously, when he

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said ‘What has different matters from those, but ones which are related to one another in the way …’,340 that there are two intermediates on the basis of their matters, the extremes being prior to them, he is now inferring341 that there are four matters on the basis of the fact that there are two extremes and two intermediates; for it was initially proposed342 to find out the way in which the elements come to be from one another, since in this way how many elements there are and what they are can be found. As he will teach in On Coming to Be,343 the way in which the elements come to be from one another can be explained in terms of the difference of the matter which underlies them proximately and its common character. But why, when he has said, ‘But since there is only one thing which rises to the top of everything and one which sinks to the bottom of everything, it is necessary that there be two other things344 which both rise above something and sink below something’345 does he go on to say, ‘For nothing prevents there being both one and several things intermediate between contraries, as there is in the case of colours’? For if the first statement is true, that it is necessary that there be two intermediates, in what way is it true that nothing prevents that there being one and several intermediates? It seems that the second statement has been made universally and says that nothing prevents there being one or several things intermediate between opposites. For it is true universally that some contraries do not have anything between them and others do have something, and, of those which do, some have one thing between them, others several. But when he said first, that ‘it is necessary that there be two other things’ he was speaking about these particular contraries, the absolutely light and the absolutely heavy, and so he speaks as follows: ‘But since there is one346 thing which rises to the top of everything and one which sinks to the bottom of everything, it is necessary that there be two other things …’. And he now indicates the necessity in an obscure way by indicating that what is intermediate between each of the absolute 347 is double because it is a limit;348 for just as the limit of what is absolutely light is light (even if it is not absolutely light, it is lighter than the things which come after it) and just as the limit of what is absolutely heavy is heavier than other things (even if it is not absolutely heavy), so too air is found to rise above other things (except for fire) and water is found to sink below other things (except for earth); and being confident about these things, he says that it is necessary that there be two things intermediate between the absolutely light and the absolutely heavy. But in On Coming to Be and Perishing he demonstrates in many ways that it is necessary that there are two intermediates and that there are four elements in all: [i] from the fact that there are two contrarieties which give form, heat/cold and dryness/moistness, and when they are

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paired, it is necessary that there be four elements in all which are composed from them;349 [ii] from the relation of the qualities from which the being of each of the elements is derived;350 [iii] and by means of the communion which the elements have with one another in a certain respect because of which their change into one another is easy, since it occurs with respect to a certain common ‘token’;351 [iv] and, furthermore, from the fact that what is intermediate has a similarity to each of the extremes, so that, since there are two extremes, it is necessary that what is intermediate also be double.352 However, these things at which he is also looking most of all when he says that ‘it is necessary that there be two other things’,353 come later, but, not having proved this completely, he reasonably makes use of the universal doctrine which says that nothing prevents there being one and several intermediates, and on that basis he takes as a hypothesis that there are several, since he is going to demonstrate this with many arguments . The divine Plato,354 who also posits that fire and earth are extremes and asserts that the cosmos must be composed from fire because it is visible and from earth because it is tangible, also demonstrates that there are two means; for, since the universe is solid and so are the extremes and it was required that the extremes be joined in a proportion, it was necessary for the generation of the universe that there be two means in proportion filling out the solid proportionality. But in the case of colours there are several intermediates, since not only is grey intermediate between light and dark, so are yellow and purple. 312b2-19 In its own region [each of the things which have both weight and lightness has weight – but earth in all regions –, but it does not have lightness except in the things which it rises above. And so when those things are removed, it moves down into what is next, air into the region of water, water into that of earth. But if fire is taken away air will not move up into the region of fire except by constraint, just as water also is drawn up when its surface becomes one355 and someone draws it up faster than the downward motion of the water. Nor does water go into the region of air except in the way we have just now mentioned, but earth does not undergo this because its surface is not one. For this reason water is drawn into a vessel which is heated, but earth is not. But just as earth does not move up,

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neither does fire move down when air is taken away, since it does not have weight even in its own region, just as earth does not have lightness either. But the two move down if is removed because, although what is absolutely heavy is what sinks to the bottom of everything, what is relatively heavy sinks into its own region] or into what it rises above, because of similarity of matter.

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He has introduced the two intermediate elements into the discussion and said that each of them has weight and lightness, weight relative to the ones which are before it (since it sinks below them), lightness relative to the ones which are after it (since it rises above them); and he has said previously356 that fire is light everywhere and has heaviness nowhere and that earth is heavy everywhere and has lightness nowhere. He now proves what he has also said previously357 about the intermediate elements, namely that both air and water have heaviness and neither has lightness in their own place, and he now goes through the argument with more precision. Previously he proved that air has heaviness from the fact that it sinks below fire and that inflated bags weigh more than uninflated ones. Now, having said that ‘it does not have lightness’, he adds ‘except in the things which it rises above’, air having lightness in water and earth, and water in earth (since they rise above these things). The next part of the argument is that each of the things which have weight and lightness (as do the intermediates) has weight in its own region, but it does not have lightness except in those things which it rises above. He inserts in between and standing on their own the words ‘earth in all regions’, taking the words ‘has weight’ as applying to earth in common .358 An indication that the intermediates have heaviness and not lightness in their proper places is provided by the fact that when the things under them are removed they themselves move down from their proper region, but when the things above them are taken away they do not move up into their places. And so when water is removed air moves into its place, and when earth is removed both water and air flow together into its place from their proper places; they move down because they have weight in their proper places. But when fire is taken away air does not move naturally into its place, nor does water move into the place of air if air is taken away. But because fire does not have heaviness even in its own place it does not move down when what is under it is removed, which is a clear indication that fire does not have an impulsion toward the centre. Having said that air does not move up into the place of fire which is taken away he adds ‘except by constraint, just as water also is drawn up when its surface becomes one’. For nothing prevents air moving up into the place of fire by constraint in the way that water

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is drawn by air into its place by constraint when (he says) the surface of the air which draws and of the water which is drawn become one. For in the case of siphons and medical cupping glasses, through which water and blood are drawn, both the air which draws and the water which is drawn move near to one another but, being bodies, they are divided from one another by their own surfaces as long as their surfaces are divided and only touch one another, and each remains in its own space; but when the two surfaces come together as one, pneuma359 or heat making them continuous and producing a certain sort of blending, then one of them, having become like a part of the other, is already being drawn by it when the motion of the air which is drawing upward is faster than the water’s proper impulsion toward what is below; for until the unity of the surfaces is dissolved and separated they are drawn up as one thing which is fastened together. Next he resolves an objection which asks why, then, earth is not also drawn up the way water is. And he says that the surface of the earth is not one, since it does not have one surface because the body of earth is not unified in the way water and air are. As a result the surface of the earth is not fused with other things in such a way as to be drawn up with them. For it is broken into pieces, and because of earth’s dryness the surfaces of earth are not united with one another nor are they united with those of water or air. And as a result, he says, earth is not drawn up, but water is drawn up into siphons and most of all into a vessel which is heated. For if we lower the mouth of a jar with a narrow mouth into water, water does not flow into it, but if the jar is heated with hot water, either by first washing it out or by pouring the water over the base of the jar and we lower its mouth into the water in the same way, it will draw the water and be filled because the surface of the water and that of the air in the vessel become one and are united by the fire, which is naturally constituted to dissolve their differences and fuse them. When the air in the vessel is heated it is made fine and rarefied, and, being less, it occupies more space; so when it is united with the water at their surface, then, when it comes nearer and is contracted by the cold, it draws the water and pulls it to itself, and the vessel receives as much water as the air which has been made denser can be contracted, having been previously separated by the heat. And for this reason vessels which are heated more draw in more water. And in the same way cupping glasses draw blood when the air in them has been previously diffused by the heat and is then contracted and drawn in, because of the unification of the surface of the air and that of the blood with the blood itself. In this connection one should notice that the surface will not be truly one since the bodies are actually divided from one another and different in nature; rather they are touching but not continuous. But

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because both bodies are moist and similar to one another Aristotle says that the surface becomes one when their limits are assimilated. Secondly one should understand that, just as air and water move up by constraint, so too they move down by constraint when what lies under them is removed, because there is no void; for it is not reasonable that when the elements are in their proper places they would have a natural impulsion either up or down, since what has a natural impulsion somewhere has an impulsion to its proper place. And so, if air and water naturally move toward what is below when what lies under them is removed, they move to places alien to them as if to their proper places, which is absurd. But if they move by constraint they do not have weight in their own places naturally, just as they don’t have lightness either, but, if, indeed, they do have weight in their own places, they do not have it in the sense that they have an impulsion to go lower but in the sense that they sink below the things which lie above them, since this is also a specific feature of heavy things. And they also have lightness in the same way, not in the sense of having an impulsion toward what is higher (for, behaving naturally, they would not rise upward), but rather as rising above what lies under them, just as fire in its own region has lightness, not because it moves somewhere higher naturally, but because it rises above what lies under it. Having said that earth is not drawn up in the way water is, he adds ‘neither does fire move down when air is taken away’. However, he said previously that earth is not drawn up because its surface is not one, but now he is also saying that it does not have any lightness in its own region, and fire, too, does not move down because it does not have any weight in its own region. But the two intermediate do move down when what lies under them is pulled away, but not in the same way as earth, which is absolutely heavy; for, although what is absolutely heavy sinks to the bottom of everything, what is heavy relative to something in the way the intermediate elements are moves down into its own region when it happens to be higher; and, since what is heavy relative to something also has weight in its own region, it also moves away from it to the things which it rises above, if they do not exist, since it rises to the top of the things which it would not rise to the top of if they existed.360 He gives as the reason why they move into the places of these things the similarity of their matter to what is absolutely heavy; for the matter which underlies the two intermediate elements is also potentially heavy, and in this respect the three have a similarity to one another. And like moves toward like. But someone might say that the intermediate are also potentially light, so that in their case there would also be a similarity of matter with respect to fire and they would also move toward it in the same way.

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312b19-28 That it is necessary to make the differences equal [to them is clear. For if there were one matter for all of them, for example, either the void or the full or magnitude or the triangles, then either everything would move up or everything would move down, and the other motion would no longer exist. Consequently, nothing would be absolutely light if everything had a greater impulsion because it was composed of greater bodies or more bodies or it was full; but we both see and it has been proved that there is always and everywhere equally motion down and up. (312b27) And if were the void or something of that sort which always moves up,] there would not be anything which always moves down. He has said that there is something absolutely heavy and something absolutely light and two things intermediate between these which are in a way light and in a way heavy and that each has a proper impulsion because of its own distinctive nature since the matters directly underlying them are different and equal in number to them; and he now proves that this is true and that each of the four has its own proper differentiae and is not constituted by a mixture of extremes, as is asserted by those who say that the void is what is light and the full what is heavy. For that he proposes this with the words ‘make the differences equal to them’ is clear from his introduction of the opposite; he says, ‘For if there were one matter for all of them, for example, the void or the full or magnitude or the triangles’, these absurdities which he adduces would follow. And so one should not hypothesise one proximate matter for the elements but a specific matter , the matters and the elements being made equal to one another because each of them has its own proper differentiae. So the point of what he puts forward is this. He361 says that if there is one proximate matter for all bodies, either the void or the full (he says ‘either the void or the full’ not because there is someone who hypothesised that the void in itself is matter but he is taking the void hypothetically as an example of lightness because those such as Democritus and his followers who hypothesised the void and full also said that the void is the cause of lightness in bodies), and so he says that if one of these is the proximate matter for all bodies ‘or magnitude’ – as is asserted by those who say that there is one element and make the difference of weights be due to the largeness and smallness or thickness and fineness of the underlying matter, which has weight in itself – ‘or the triangles’ (that is the planes), it is either light or heavy. But if this is so, it is necessary that either everything move up or everything move down and that the other no longer exist. For if the matter were heavy nothing would be absolutely light since everything would have an impulsion, that is, be heavy, even if one thing were heavier

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than another ‘because it was composed of greater bodies or more bodies or it was full’, that is denser. One should notice in the case of the words ‘if everything had a greater impulsion’ that they are spoken as if impulsion is weight. This is also how Plato uses the term when he says that everything which moves toward what is proper to it is heavy because it has an impulsion to that.362 (312b27) But if the void or something of this sort, which always moves up, is matter (for he put forward the void as an example of this sort of thing), what will always move down will not exist. But we see and it has been proved on the basis of the difference of places and of the simple motions that there are everywhere equally some things which move up naturally and others which move down naturally. 312b28-32 And of the intermediates there would be some363 which moved down faster than earth [since there will be more triangles or solids or small things in a great amount of air. But no364 portion of air is seen moving down. (312b31) And similarly in the case of lightness] if someone were to make365 that exceed because of matter.

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This is the second argument against those who hypothesise that the matter is of one nature, which is either heavy or light and is proximate to the bodies; and it is first against those who say that the one is heavy. He says that it follows for these people that certain intermediate bodies, which are not absolutely heavy, are heavier than earth, which is absolutely heavy. (However, those who hypothesise that matter is of this sort, say that earth is absolutely heavy and that the other three are both heavy and light because of the different mixing of the elements in largeness and smallness either in size or number.366) So if one took so great an amount of one of the intermediates that the solids or atoms or triangles in it were greater in number than those in some earth which is smaller in size, that intermediate would move down faster than the small portion of earth because that small amount of earth would have fewer of the causes of heaviness and motion downward. ‘But no portion of air is seen moving down’ either in general or, even more,367 moving down faster than earth in such a way as to sink below it. (312b31) So, having proved that the theory is out of harmony with the phenomena and has as a consequence that what is not absolutely heavy is heavier than what is absolutely heavy, he says that a similar thing follows in the case of lightness. For according to those for whom the void is matter and the cause of lightness, if someone were to take air or water which exceeds a small amount of fire in such a way that the void in the air (which they say is the cause of motion up) is greater than the void in the small amount of fire, it would be lighter than the fire, which is absurd. (He has set down these arguments both here

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and in the preceding book.368) So if it is absurd that there be one matter for all, it is necessary that their matters differ and that one make the differentiae equal in number to the elements so that they have a similar antithesis to one another.

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312b32-313a6 But if they are two, how could the intermediates behave as369 [air and water do? (For example, if someone were to say the two are the void and full; then fire would be void and so up, earth full and so down; and air would contain more fire, and water more earth.) For there will be some water which contains more fire than a small amount of air and a great amount of air which contains more earth than a small amount of water, so that some amount of air should move down faster than a small amount of water.] But this is never seen anywhere. He has shown the absurd consequences which follow for those who hypothesise that the proximate element is one and either heavy or light and not differentiated. One of these consequences was that everything composed of this element would be either only heavy or only light, whichever one the element370 was required to be. The 371 also be used to argue against those who said that the proximate elements are two, the void and the full, of which they said that one is the cause of lightness, the other of heaviness; for it is not still possible to say against these people that either everything will be light or everything will be heavy. And he carries out this argument, making this hypothesis which says that the void and the full are elements, and showing that its consequences are also absurd in this case. These people say that one thing, the full, is absolutely heavy, another, the void, absolutely light, and that the void is fire and therefore up and earth is full and therefore down, and that air contains more fire, water more earth. Now, if someone were to say that there are two elements, the void and the full, how could the intermediates, air and water, behave as they do? Air’s behavior is to rise above water, and water’s to sink below air. How, then, could they do these things? For there would be some amount of water which contains more fire than a small amount of air, and there would be a great amount of air which contains more earth than a small amount of water, so that some amount of air, since it has more earth than a small amount of water would have to move down faster than the water and sink below it. ‘But this is never seen anywhere’. But also there will be some amount of water which contains more fire or void than a small amount of air and consequently will be lighter than the air so that it will rise above it. But this isn’t seen to happen either. Aristotle contents himself with the inference to the first of the hypothesis that the air contains more

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because the same absurdity would be inferred whether the air sank below the water or the water rose above the air; for if the air sinks, the water rises, and if the water rises, the air sinks. 313a6-13 So it is necessary that, just as fire372 up because it contains something [such as void, but nothing else, and earth down because it contains the full, so too air into its own and above water because it contains some particular thing and water down because it is of a certain sort. But if both were some one thing, or two things and both belonged to each of them, there would be some quantity of each because of which water will exceed a small amount of air in up and air will exceed water in down,] as has been said many times.

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Having proved that there cannot be one substratum or two (such as the void and the full), he next adduces what was initially proposed,373 that it is necessary to make the differences equal to the simple bodies, since each of them is constituted in terms of its own proper differentiae. For, just as these people say that fire moves up because it contains wholly void, but nothing else, and that earth moves down because of the full, so too it would be necessary for them to say that the air moves into its own region and rises above water because of its own proper differentia, and similarly water sinks below air because it also has a certain sort of differentia. But if they were to say that both water and air are one in substratum, whether light or heavy, as was hypothesised previously,374 or that there are two substrata, such as the full and the void ‘and both (that is the two substrata …375) ‘belong to each of them’ – both to air and to water –, but one of them does not belong to the other, the absurdities mentioned previously, which he now briefly adduces, will result for them: there will be some quantity of each by which it will exceed the other, a greater amount of water exceeding a small amount of air in lightness and up and a great amount of air exceeding a small amount of water in weight and down, which disagrees with the phenomena and with reason. For if there were one substratum and their difference with respect to weight resulted from largeness and smallness in number or in size, a great amount of air would be heavier than a small amount of water because it had more of the things from which they are composed, and a small amount of water would be lighter because it was composed of fewer. But if the substrata were void and full and both air and water shared in both, but air shared in more void and water in less, the same absurdity would also result in this case, since a great amount of water would have more void than a small amount of air and so be lighter. But if they were to define being lighter in terms of fewness

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of what is solid, again a great amount of air would have more solid than a small amount of water and so be heavier. But if they say that neither of the elements is by itself the cause of being lighter or heavier but make their proportionality to one another responsible (about which Aristotle previously376 censured them for not doing what they ought to do) because a great amount of air, even if it has more solid than a small amount of water nevertheless has several times as much void and therefore is also lighter than the small amount of water and because more water, even if it has more void than a small amount of air, nevertheless has several times as much solid and is therefore heavier than the small amount of air, Aristotle also took issue with this sort of theory previously377 on the basis of the comparison of things of the same kind; for there is the same proportion of solid to void in more fire and in less, so that if the proportion is the cause, more fire and less ought to move equally quickly; however, more moves up faster and less moves down faster.

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313a14-b6 Shapes are not the cause of moving [absolutely378 either up or down but of moving faster or slower. The reasons for this are not difficult to see. (313a16) For the difficulty being raised now is why flat pieces of iron and lead float on water, but smaller and less heavy ones sink down if they are spherical or elongated like a needle; and why some things float because of their smallness – for example, shavings and other things made of earth or dust float in air. (313a21) On all these it is incorrect to think that the cause is what Democritus thinks it is. For he says that hot things which move up from the water support flat things which have weight, but narrow ones fall through because only a few hot things strike against them. But, as Democritus himself objects, these heavy things ought to do this even more in air. But, having made the objection, he gives a feeble resolution, since he says that the ‘surge’379 does not strive in only one direction, meaning by ‘surge’] the motion of the bodies moving up. He has said that the matter of each of the four elements is the reason why some bodies move down, some up, and why each of the two intermediates moves into its own region and into the region of those things lying under it when they are removed, this matter also being the cause of the substantial difference and of its motion to its proper place as to its proper form. Since there were some people who made the figures responsible for natural motion, such as those who assigned the pyramid or the sphere to fire because of its mobility, he says that ‘absolutely’ shape is not the cause of

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motion and nothing moves up or down because of such and such a shape; rather he makes such and such a shape the cause of things which are naturally constituted to move moving to their proper place faster. He says that it is not difficult to see the reasons why shapes contribute to the motions. (313a16) He first sets out the difficulties and questions concerning the difference of motions due to the figures, things which are thought to support those who make the figures responsible for the motions, and, then, resolving them, he will show380 that shape does contribute to the proper motions but it is not the cause. The difficulty is raised why of things made of the same matter, for example, iron or lead, those that are flat in shape, even if they are heavier, float on water, but those that are spherical or elongated, even if they are smaller and less heavy, for example, a needle, sink down. A second difficulty is why the portions of some bodies, even those having heaviness, float on water just as gold shavings or specks of dust float in air. For here again it would seem that gold has weight because of its size but not because of its own nature, at least if it is divisible into things which don’t have weight.381 (313a21) Having set out the difficulties, he first adduces the resolution of Democritus, and says that Democritus did well to object to it, but that he resolved the objection feebly. Democritus first attempted to resolve the difficulty by invoking hot things which move up from the water – for there are seeds of all things in all things so that all things also come to be from all things. He says that since these things which strike against the flat things are numerous because they come from the water under the flat things, which is greater, and ‘support’ them (that is, hold them up382), but narrow things slip through the resistance of the few hot things which strike them. Having resolved the initial difficulty in this way, Democritus raised a good objection against himself by saying that if this were the reason why flat things float on waters,383 they ought to do this even more in air since there are more hot things in air than in water.384 Having made this good objection, Democritus added a weak and insipid resolution. He says that in air flat things are not held up by the hot things which rise up because these hot things are not condensed in air, which is fine and diffused, in the way they are condensed in water, and, since they are dispersed, their motion does not strive in one direction and so hold up what lies over them, even if it is flat; but in water, which is thicker and more solid, the hot things which are moving up are driven together and condensed more. would perhaps also say that the mobility of the air is the cause of the dispersion. Aristotle calls this resolution, even though it was given in a persuasive way, ‘feeble’ because it is not able to support the obvious causes, which he himself will do.

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313b6-23 But since some continuous things are easily divided [and some are less so, and in the same way some things are better dividers and some are worse, one should suppose that these are the causes. The easily divided is what is given boundaries easily, the more easily divided what is given boundaries more easily. But air is more of this sort than water, and water is more of this sort than earth. And in each genus a smaller amount is more easily divided and more easily broken apart. And so things which are flat endure because they contain much, and a larger amount is not easily broken apart. Things which have contrary shapes sink down because they contain little and divide things easily. And this is much more the case in air insofar as it is more easily divided than water. Since a weight has a certain strength because of which it sinks down and continuous things have a certain strength for not being broken apart, these must come into conflict with each other. For if the strength of the weight exceeds the strength in what is continuous against being broken apart or divided, it will force its way down faster, but if the weight is weaker, it will float. (313b22) Let us have made this determination about heavy and light and their properties in this way.]385 He gives the reasons why different shapes make the motions of bodies different. And he says that there are two reasons, one being that some continuous bodies are easily divided and some are less easily divided, the second being that some bodies are better dividers and some are worse. And he says which are always easily divided, namely the moist ones, (since these are the ones which are given boundaries more easily because they are given shape and determined by the shape of what contains them; air and water are of this sort), and he says which are the more easily divided, namely the ones which are given boundaries more easily. ‘But air is more of this sort than water’ because it is more moist and given boundaries more easily, and water is more of this sort than earth. But also in the same genus a smaller amount is more easily divided than a larger one, and it is more easily broken apart. For a small amount of air is more easily affected than a great amount, and a small amount of water is more easily affected than a greater amount. This being the way things are, since things having weight which divide what lies under them have a certain strength because of which they sink down and since the continuous things lying under them which are divisible have a certain power for not being broken apart, these powers ‘must come into conflict with each other’. For if the strength of the dividing weight exceeds the strength for not being broken apart but remaining continuous in the continuous thing lying under it, the dividing thing, not with respect to anything

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else than breaking apart and dividing, will force its way, moving down more quickly and breaking apart what lies under it. But if the power of what divides is weaker than the power of what lies under it, what lies under it will not be divided by what divides, but what divides will rise. Therefore, since flat bodies cover over more water but more water is not equally easily divided they do not sink down; for they would need to divide what lies under them (and so they are borne up), but also this much water is not easily divided by what is this heavy. But things which are spherical or elongated and lying on a small amount water divide it easily, and, in dividing it, they sink down. But in air even flat things sink down because air is more easily divided than water is. 386

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I offer these things as a hymn to You, Lord, Creator of the whole cosmos and of the simple bodies in it, and to those who have been made by You, desiring to behold the greatness of Your works and proclaim it to the worthy so that, thinking nothing mean or merely human about You, we might kneel down to You because of the superiority which You have over all the things created by You.

Appendix 1

On the geometric arguments of 652,9-655,27 652,11-21 Potamon’s argument that equilateral triangles fill a space (Fig. 1)

Let ABC be an equilateral triangle. Extend BA past A to E and CA past A to F. Bisect the angles FAB and EAC with the straight line DAG. The six angles around A are equal and therefore equal to four right angles and therefore fill the space around A. Make AG, AF, AE, AD each equal to a side of ABC and join CD, DE, EF, FG, GB. The result is six equilateral triangles filling the space around A. 652,22-653,6 Potamon’s argument that squares fill a space (Fig. 2)

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Let ABCD be a square. Extend BC past C to F and DC past C to H. The four angles around C are equal and therefore equal to four right angles and therefore fill the space around C. Make CF, CH equal to a side of ABCD and draw the figure (‘gnomon’) BIHGFEDC, producing four squares filling the space around B. 653,10-654,11 Potamon’s argument that regular hexagons fill a space (Fig. 3)

Let BAD be an angle of a regular hexagon . Extend BA past A to C and DA past A to E. Let FAN bisect the angles EAC, BAD. The angles EAB, CAD are each equal to two thirds of a right angle, since EAB (CAD) is the difference between two right angles and BAD, the angle of the hexagon (which is equal to four thirds of a right angle). Since the six angles around A are equal to each other, they are each two thirds of a right angle and together equal to four right angles, and so fill the space around A. one can construct the regular hexagons AFGKLB, ABMNOD, ADPQRF, which will fill the space around A. 654,14-655,2 Alexander’s argument that regular hexagons fill a space. (I have re-lettered the proof to correspond to Fig. 3.) Let AFGKLB, AFRQPD be two regular hexagons sharing the side AF. The angle BAD is equal to four right angles minus the two angles DAF, BAF, which are each equal to four thirds of a right angle. Therefore angle BAD is equal to four thirds of a right angle and we can draw the regular hexagon BADONM, filling the space around A.

On the geometric arguments of 652,9-655,27

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655,9-18 Potamon’s argument that cubes fill a space (Figs 4 & 5)

‘Above’ the plane of the AEGI erect cubes on each of the four squares in Fig. 2. They will fill the space around the straight line CC ’ perpendicular to the plane of AEGI and above it. Potamon’s argument here would have been more satisfactory if he had also constructed four cubes beneath the plane of AEGI as in Fig. 5, so that the resulting eight cubes fill the space around point C.

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Appendix 1 655,18-27. Potamon’s arguments that pyramids fill a space (Figs 6 & 7)

Potamon first says: … A pyramid is nothing other than the angle of a cube. Consequently, since the angles of a cube filled up the space, the pyramid will also fill it up. The ‘angle of a cube’ should be a solid angle made by right three angles such as ABC, ABB’, CBB’ in Fig. 6. But there is no clear relation between such an angle and the angle of a regular pyramid which is contained by three 60o angles. From what follows it would seem that Potamon is referring to a triangular prism such as B’C’D’DCB in Figure 6 as a

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pyramid. For a cube is composed of two such prisms, and Potamon says, ‘To prove this another way, the cube itself has been completed from two pyramids’. Potamon adds: So if eight pyramids having their apexes at the centre of a sphere are combined they will fill out the space. The eight ‘pyramids’ here are the eight triangular prisms with CC’ or CC’’ as common edge in Fig. 7; they fill the space around C which would be the center of the sphere circumscribing the cube with opposite faces A’E’G’I’ and A’’E’’G’’I’’. After giving an argument by analogy which has no weight but plays a role in some later discussions (see Appendix 2), Potamon concludes by conjuring up a picture of the eight prisms with CC’ or CC’’ as common edge: If someone were to combine eight pyramids, making their apexes incline toward one another like wedges (sphênes), he would not leave an empty space.

Appendix 2

On some later discussions of 306b5-8 Here I wish to give a preliminary account of some of the most important treatments of Aristotle’s claim at 306b5-8 that ‘there are three plane figures which fill a space, the triangle, the square, and the hexagon and that there are only two solid figures , the pyramid and the cube’.1 For purposes of these arguments (and all early discussions of this claim) a figure is said to fill a space if some number of such figures can be joined with their vertices at a point without overlapping or leaving any empty space around the point. In more recent discussions plane figures are said to fill space if, to speak intuitively, they can be used to fill an infinite flat floor; and similarly solid figures are said to fill space if they can be combined in such a way as to fill an arbitrarily large volume while leaving no gaps.2 Simplicius preserves for us at least parts of the earliest extant treatment of Aristotle’s claim: the reasoning of Potamon intended to verify it. I have summarised those arguments in Appendix 1. The arguments for the equilateral triangle, cube, and regular hexagon are basically versions of the more abstract arguments given by Simplicius at 651,2-652,8, which become standard in subsequent literature, as does the argument at 652,28 that only these three plane figures fill a space. There are no problems with these arguments and there is no important issue concerning the cube, although, as I pointed out in Appendix 1, Potamon should have constructed four cubes below the plane of AEGI, so that eight cubes fill the space around point C. Later authors try to take the eight cubes as providing a solid analogue of the intersection of two perpendicular straight lines, by reference to which the criterion for plane figures filling the space around a point becomes having their angles at the point add up to four plane right angles (360o). The obvious move for solids is to say that those having their vertices at a point fill the space around the point if their angles are or are equal to eight solid right angles. The problem is to provide a criterion for adding, subtracting, etc. solid angles and comparing them in size, a problem which is not satisfactorily solved until the development of spherical trigonometry. Earlier authors, of whom the first known is Themistius (c. 360),3 correlate or identify the size of a rectilinear solid angle with the sum of the plane angles containing it. Since the angle of a cube is contained by three right angles and that of a regular pyramid is contained by three 60o angles, it is an easy matter to argue (incorrectly) that twelve pyramidal angles are equal to eight cubic angles so that twelve regular pyramids joined at a point fill the space around the point.

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In Simplicius’ report Potamon uses as a justification for the claim that pyramids fill a space the assertion that the pyramid has the same ‘role’ (logos) among solids as the triangle has among planes (655,23-4). Variations of this principle occur in subsequent authors. In Themistius it runs, quam … proportionem triangulus ad extremitatem habet, eandem sane pyramis habet ad solidum (199,29-31). In the next extant text discussing the issue of space-filling solids, Ibn al-Salah (d. c. 1150)4 says that Themistius made this correlation the principle of his demonstration. This interpretation does not seem to be correct. In our text of Themistius the basic argument for the pyramid is the one involving angle size which I have indicated. And there are other discrepancies, of which I mention Ibn al-Salah’s ascriptions to Themistius of the view that 24 regular pyramids fill a space, a claim not made in our text of Themistius, and of an argument involving the fact that (by proposition 12 of book 7 of Euclid’s Elements) the eight triangular prisms of Potamon’s argument can each be divided into three equal pyramids, to which Ibn al-Salah correctly objects that the pyramids in question are not regular. Ibn al-Salah gives a correct argument that regular pyramids cannot fill a space, based on the major results of book 13 of Euclid’s Elements, first that there are only five regular solids, i.e. pyramid, cube, octahedron, dodecahedron and icosahedron (cf. the remark after proposition 18) and second that if a regular solid is inscribed in a sphere its edge is not equal to the radius of the sphere (cf. propositions 13-17, which describe the relationship between edge and diameter more precisely). Now suppose that n regular pyramids with common vertex A and edges of length e filled a space; then they would form a regular solid with triangular faces, edges of length e, and inscribable in a sphere with centre A and radius of length e; by the remark after proposition 18 such a solid could only be a tetrahedron, octahedron, or icosahedron, but in none of these cases is the edge equal to the radius. Ibn al-Salah also gives analogous and only slightly more complicated proofs that regular octahedra, icosahedra, and dodecahedra cannot fill a space. Finally, I mention that he indicates that earlier people had raised the question why, given the principle of Themistius’ reasoning and the fact that regular hexagons fill a space, there is no space-filling regular solid with hexagonal faces. After rejecting the explanations of his predecessors, Ibn al-Salah simply cites the remark after proposition 18, which rules out the possibility of any such regular solid. There is no indication that any subsequent commentator on Aristotle’s claim about space-filling solids was aware of Ibn al-Salah’s decisive treatment. His argument against the claim for pyramids does not show up again in an explicit form until 1615, when Giuseppe Biancani publishes it as his own discovery (see below). In his long commentary on the De Caelo5 Averroes (Ibn Rushd; 1126-98) repeats in a clearer form the argument I have ascribed to Themistius that twelve pyramids fill a space:

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For six pyramidal angles are equal to four angles of cubes because the solid angle of a pyramid is composed of two right angles and the angle of a cube of three. Therefore three angles of a pyramid will be equal to two angles of a cube, since they are equal to six right angles. For the ratio of the angle of the pyramid to four cubical angles is as the ratio of the angle of the triangle to four right angles (proportio enim anguli piramidis ad quatuor cubicos est sicut proportio anguli trianguli ad quatuor rectos), since the angle of the triangle is two thirds of a right angle. Averroes goes on to claim that regular octahedra, dodecahedra, and icosahedra do not fill a space. He does only the last case, pointing out (as we might express it) that the solid angles of a regular icosahedron are contained by five 60o angles, and for no n does n(5 x 60) = 8(3 x 90).6 In his commentary on the De Caelo,7 Albert the Great (d. 1280) clearly depends heavily on Averroes, but he gives no argument against regular solids other than cube and pyramid filling a space. In chapter 40 of his Opus Tertium8 Roger Bacon (d. c. 1292), after giving Averroes’ account of why pyramids fill a space, remarks that he spent almost twenty years with experts on this material without finding anyone who even understood the terminology and that, even when he taught the truth to students and explained the terminology, they were unable to discuss it. He also relates that a prominent Parisian philosopher proclaimed that twenty pyramids would fill a space, a view which he rejects on the Averroean ground that 20(3 x 60) =/ 2160. However, Roger goes beyond Averroes by pointing out that by Averroes’ criteria nine octahedra also fill a space since 9(4 x 60) = 2160 = 8(3 x 90). He concludes that one cannot obtain certainty on this subject unless one has bodies, that is, I assume, physical models, which satisfy the descriptions in Elements 13, but he is satisfied that at least dodecahedra and icosahedra do not fill a space. Neither Ibn al-Salah nor Averroes nor Albert nor Roger had access to Simplicius’ commentary, but it became available in the Latin West in a translation made at the request of Thomas Aquinas by William of Moerbeke. Thomas’ commentary on the De Caelo was broken off at the end of 3.5 by his death in 1273. Peter of Auvergne (d. 1304), writing after Thomas’ death, wrote a commentary on books 3 and 4, the part picking up where Thomas leaves off being printed in editions of Thomas’ complete works.9 When he turns to the pyramid, Peter first brings in the triangular prism of Potamon’s argument as a kind of (quaedam) pyramid, and shows that such a figure fills the space around a point. He then gives his version of the principle enunciated by Potamon: this kind of pyramid has the same ratio as the right-angled triangle has in planes. And like Potamon he says that it is evident to perception that eight of these figures fill the space around a point. For the regular pyramid Peter cites Averroes for the view that twelve fill a space, and explains it in the way we have already indicated. But, he

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says, this view seems to contradict both perception and reason. He himself has done experiments (hoc ad sensum expertus sum), and seen that regular pyramids do not fill space. As for reason he appears to cite a configuration which Themistius had already cited, the construction of six regular pyramids on the equilateral triangles into which a regular hexagon divides both above and below the plane of the hexagon. These twelve pyramids do meet at a point, and they do fill the two-dimensional space around it. But they do not fill a three dimensional space about that point. Moreover, Averroes’ claim that a solid pyramidal angle is equal to two plane right angles is unintelligible: For it is necessary that equal magnitudes be of the same ratio; and so a line is not equal to a surface, nor is any of those bodies. And, in fact, the angle of a pyramid and a plane angle are not of the same ratio, because the one is solid, the other plane. And so they are not equal to one another; nor is a solid angle composed of plane angles, just as a body is not composed of planes. Moreover, if a pyramidal angle were two plane right angles it would be composed from them, since the ratio is the same. But this is false and against the thinking of Aristotle, who does not want bodies to be composed from planes, and, therefore and first, contrary to the commentator himself. But what Averroes says – that as the angle of an equilateral triangle is to a right angle among planes so is the angle of a pyramid to the angle of a cube – should be said not to be true in the case of filling space and perhaps not true at all. (180a) Peter adds that if Averroes were right there should also be a space-filling solid with hexagonal faces, something which neither Aristotle nor Averroes thinks is true, and concludes his discussion by referring to the other regular solids and saying that Averroes seems to explain why they do not fill a three-dimensional space, but that he will leave the evaluation of his explanation to industrious investigators (diligenti inquisitori). In his Theoretical Geometry10 Thomas Bradwardine (d. 1349) first proves (section 4.2) the remark after proposition 18 of book 13 of Euclid’s Elements, according to which there are only five regular solids. In the next section he explains what filling a space means and suggests that Averroes thought that only cubes and pyramids fill a space because of their correspondence (correspondet) with square and triangle respectively, there being no regular solid with hexagonal faces. This, he says, is only a case of conviction (persuasio). In truth the cube fills a space, but cube and pyramid fill a space only according to Averroes’ opinion. To validate the claim about the cube he cites sense experience, and as a secondary ‘cogent enough’ (satis cogens) confirmation from reason a pointless arithmetic argument that, since the product of two cubic numbers is a cube and 8 is the first cubic number, eight cubes will fill a space.11 Turning to the pyramid he first explains Averroes’ view and then notes that others, citing experience,

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say that twenty do so, a view which Bradwardine (or an elaborator) commends on the basis of a ‘subtle imagining of straight lines being drawn from the vertices of an icosahedron to the centre of the body’. Bradwardine objects to Averroes’ view on the grounds that greater plane angles might contain an angle of less ‘corpulence’ (corpulentia) than that contained by smaller angles, just as greater lines can contain lesser areas than shorter ones.12 He also makes Roger Bacon’s point that the view entails that nine octahedra will fill a space, something which is not asserted by either Averroes or Aristotle. In an elaboration it is argued that if twelve pyramids filled a space they would produce a regular dodecahedron with triangular faces, which he has already shown to be impossible. But he remains uncertain about whether the icosahedron might be composed of twenty pyramids meeting at a point: Concerning whether twenty pyramids fill a space, although this seems plausible (probabile), it is in no way certain, because anyone who would say that eight pyramids fill a space would say similarly that from them a body of eight faces results … and again he would similarly resolve that octahedron into eight pyramids by the subtlety of imagination. (p. 139) Now, of course, Elements 13 shows that neither the twenty nor the eight pyramids are regular, but Thomas is apparently unaware of this, since he says, ‘If … it were established that the pyramids into which the icosahedron13 was resolved … were regular, the matter would no longer appear to be in doubt’. In all MSS Thomas concludes by saying that the matter must be left in doubt. I have already mentioned that Giuseppe Biancani (1566-1624) was the first European to publish a proof that Aristotle’s assertion about the pyramid is wrong. In Mathematical Passages in Aristotle14 Biancani indicates that no one, Greek, Arab, or Latin, has questioned Aristotle’s assertion. After giving essentially the same proof for the pyramid as Ibn al-Salah,15 Biancani expresses his sense of uncertainty in the light of the fact that none of his predecessors had questioned Aristotle’s authority. He communicated his ideas and uncertainty to his teacher, Christopher Clavius (d. 1612), who, beginning a tradition of trying to defend Aristotle’s remark by reinterpreting it, took the option of saying that Aristotle only intended to say that six pyramids lying on a hexagon fill a two-dimensional space around a point, just as four cubes lying on top of a square do. Biancani, professing his desire to follow truth more than Aristotle, rejects this strained reading of the text. He also rejects the claim that twelve pyramids fill a three-dimensional space and constitute a regular solid of twelve faces, pointing out that such pyramids are not regular and referring his reader to Elements 13. Biancani completes his discussion by referring to two authors Francesco Maurolico (1494-1575) and Giovanni Battista Benedetti (1530-90), whose work he came across after writing up

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his analysis of Aristotle’s claim and who recognise its falsehood. One of the six sections of Benedetti’s Book of Diverse Mathematical and Physical Speculations16 is a set of 39 ‘disputations’ on the opinions of Aristotle, in the next-to-last of which Benedetti refers to the question of space-filling pyramids. His doing so comes in oddly since his real concern is to reject the idea that the pyramid is more mobile than the cube. (cf. Cael. 306b29307a13 (661,15)) However, he takes the trouble to point out Aristotle’s error and says that he made it because he thought that six pyramids constructed on either side of a hexagon fill a space, although, in fact these pyramids leave more empty than filled space on either side of the hexagon. His opinion here might well be based only on experiments, like those of Peter of Auvergne. Biancani rejects Benedetti’s explanation as childish and unworthy of Aristotle’s genius.17 With Maurolico I believe, but cannot now establish, we leave the domain of Elements 13 and enter the domain of trigonometry. Biancani cites Maurolico’s Cosmographia,18 at the beginning of which Maurolico gives a descriptive catalogue of his ‘works’, which includes the following: Our little book on regular plane and solid figures which fill a space. Although it is certain that John Regiomontanus has written very precisely about this matter, as far as I know, the book has not yet been published. However, in book we demonstrate that of the regular solids cubes fill a space by themselves but pyramids do so only when conjoined with octahedral19, from which it will be manifest that Averroes has made a childish mistake on this subject. The text to which Maurolico refers does not appear to have been published, and I have not seen it. But the manuscript of the text (some 20 folios) is preserved in Rome20 with the title ‘On the five solids, which are commonly called regular, which of them clearly do fill a space, and which do not, contra Averroes, the commentator of Aristotle’. Luigi De Marchi,21 who characterises the text as complete and ready for publication, has given a brief summary of the contents with no indication of the proofs, but it seems clear that Maurolico gave proofs based on a proper notion of a solid angle. Maurolico’s reference to Regiomontanus (1436-76) is almost certainly derived from a list,22 printed in 1473 or 1474, of works (by himself and others) which he intended to publish in Nürnberg, to which he had moved in 1471, some five years before his death. Most of the works were never published, including the one to which Maurolico refers, which in Regiomontanus’ list bears the title ‘On the five equilateral bodies which are commonly designated regular, which of them clearly do fill a natural space and which do not, contra Averroes, the commentator on Aristotle’. There is no way to know whether or not Regiomontanus completed the work which he announced for publication, but it seems extremely likely that Regiomontanus’ approach to the question of space-filling polyhedra was like Maurolico’s rather than Biancani’s.

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The first published application of trigonometry to the problem of spacefilling regular solids was made by Jan Brozek (1585-1652) in his defence of Aristotle and Euclid against Petrus Ramus and others.23 Ramus (151572) in his Two Books of Arithmetic and Twenty Seven of Geometry24 had defended on Averroean grounds the position that twelve pyramids and also nine octahedra fill a space. After stating the rule for calculating the size of a solid angle, Brozek gives trigonometrical arguments based on the assertion that the angle of the pyramid is 34 degrees (gradua), 42 minutes (scrupulae),25 so that twelve such angles fall well short of the 720 degrees of the full sphere; moreover, the angle of the octahedron is 73 degrees, 44 minutes so that eight pyramids + six octahedra fill a space (6(73o 44’) + 8(34o 42’) = 444o 24’ + 277o 36’ = 720o). But four pyramidal angles are less than nine octahedral ones, so how can twelve pyramids fill a space? (And one can also argue that nine octahedral angles don’t do so either.) Brozek is only interested in refutation and so does not give arguments about icosahedron and dodecahedron. He also tries to defend Aristotle by saying that he was not talking about regular pyramids, and defending Aristotle is his only concern in his discussions of Biancani, Benedetti, and Maurolico. He does not show any sense of the legitimacy of Biancani’s demonstration that pyramids do not fill a space. Finally I want to mention an earlier figure known to me only through Struik’s essay, Paul of Middelburg (1445-1534), best known as a proponent of the calendrical reform which ultimately produced the Gregorian calendar, adopted in 1582. Struik calls attention to passages in two texts of prognostication (for 1480 and 1481) in which Paul touches on the question of space-filling polyhedra. The texts are available only as manuscripts.26 In the first, which is generally contemptuous of contemporary scientists, Paul proposes 100 problems for them to solve, the 49th of which (unfortunately I haven’t seen the text) concerns space-filling solids. After stating it he says that the solution will make clear both that (i) Aristotle and Averroes have gone astray in asserting that twelve angles of a regular pyramid could fill a space, (ii) that twenty are not sufficient either, and furthermore (iii) that Bradwardine also fell short in his considerations of the subject. After giving his solution, which again I have not seen, Paul says that the mistake of Aristotle and Averroes is clear from Elements 13.15 (he presumably means 13.16) because the pyramids from which an icosahedron is constructed are not regular. Paul concludes that, therefore, regular pyramids cannot fill a space even if there are twenty of them; indeed, no other number of them will produce a regular body – that is impossible. I am inclined to think that Paul understood a version of the Ibn al-Salah proof rather than of a trigonometric one, although Struik seems to have thought otherwise. He sees Paul as well as Maurolico as continuators of the program announced by Regiomontanus.

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Notes 1. My account is very dependent upon, but supplements and sometimes diverges from, that in D.J. Struik, ‘Het Probleem “de impletione loci”’, Nieuw Archief voor Wiskunde, 2. ser. 15 (1925), pp. 121-37. I would like to thank Marjorie Senechal for providing me with a copy of her unpublished translation of Struik’s article, and Stephen Menn for some useful advice. A more detailed version of this appendix will appear in La Démonstration de l’Antiquité à l’Age Classique, edited by Ahmed Hasnoui, Annick Jaulin, Pierre Pellegrin, and Roshdi Rashed. 2. The standard modern treatment of space-filling figures in this sense is H.S.M. Coxeter, Regular Polytopes, 2nd edn, New York: Macmillan, 1963, where it is shown (pp. 68-9) that of the five regular solids only cubes fill space. 3. In his paraphrase of De Caelo, printed in CAG 5.4, which includes editions by Samuel Landauer of the two extant early versions of the paraphrase: a Hebrew translation, made in 1284, based on the Arabic translation of the original Greek, and a 1574 translation of the Hebrew into Latin, on which I have relied. On these editions and their problems see Mauro Zonta, ‘Hebraica veritas: Temistio, Parafrasi del De coelo. Tradizione e critica del testo’, Athenaeum 92 (1994), pp. 403-28. The text is very difficult and heavily edited, but it seems clear to me that Themistius is the originator of the argument given in the text above, an argument taken over by Averroes (see below), which came to be thought of as the correct account of what Aristotle had in mind. 4. For a list of his extant works see Max Krause, ‘Stambuler Handschriften islamischer Mathematiker’, Quellen und Studien zur Geschichte der Mathematik, Astronomie, und Physik B.3.4 (1936), pp. 437-532, 484-7. An edition of the Arabic text with Turkish translation is to be found in Muhabat Türker, ‘Ibnu’s-Salah’ in De Coelo ve onun serhleri hakkindaki tenkitleri’ (‘Ibn al-Salah’s criticisms of the De Caelo and the commentaries on it’), Arastirma 2 (1964), 1-79, 31-52 (translation) and 53-79 (text). These are preceded by an essay in Turkish and a shorter version of it in French, on which I have relied for the description of the content of Ibn al-Salah’s work. The French essay is also available in La Filosofia della natura nel medioevo (Atti del 3o congesso internazionale di filosofia mediovale, Passo della Mendola (Trento, 31 agosto-5 septembre 1964), Milan: Società Editrice Vita e Pensiero, 1966), pp. 242-52. 5. The whole is preserved only in Latin and is available in Francis James Carmody (ed.), Averrois Cordubensis commentum magnum super libro De celo et mundo Aristotelis (Recherches de théologie et philosophie médiévales. Bibliotheca 4), 2 vols, Leuven, 2003. A facsimile of the only known Arabic MS of parts of the commentary on books 1 and 2 is found in Gerhard Endress (ed.), Ibn Rushd, Commentary on Aristotle’s Book on the Heaven and the Universe, Publications of the Institute for the History of Arabic-Islamic Sciences, ser. C, vol., 57, Frankfurt, 1994. Averroes gives the same sort of argument in his paraphrase of De Caelo, the Latin version of which is available in the Junctas version of 1562 (reproduced in volume 5 of Aristotelis Opera cum Averrois Commentariis, Frankfurt am Main: Minerva, 1962). The relevant passage is found on 325v-326v. 6. The text actually says ‘for no n does n(5 x 60) = 4(3x 90)’. In the paraphrase, the argument is 4(5 x 60) > 4(3 x 90) > 3(5 x 60). Themistius also asserts that no other solid fills space, but in our text he only cites the fact that there are just five regular solids. 7. Paul Hossfield (ed.), Alberti Magni De Caelo et Mundo (Alberti Magni Opera Omnia v.5, pt. 1), Münster: Aschendorff: 1971.

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8. J.S. Brewer (ed.), Fr. Rogeri Bacon Opera Quaedam Hactenus Inedita, vol. 1, London: Longman, Green, Longman, and Roberts, 1859. 9. For the part of Peter’s commentary which picks up where Thomas leaves off see pp. 164-207 of vol. 19 of the Parma edition of his collected works (reprinted New York: Musurgia Publishers, 1948-50). The words (but not the pagination) of this edition are available on the web at http://www.corpusthomisticum.org/xcm.html. 10. George Molland (ed. and trans.), Thomas Bradwardine, Geometria Speculativa, Stuttgart: Franz Steiner, 1989. Molland places certain passages in brackets because they occur only in some MSS and look like elaborations. But they are certainly early elaboration since one of the two manuscripts with the elaborations on which Molland relies is dated to the fourteenth century, the other to the fourteenth or fifteenth. 11. Thomas goes on to ‘explain’ why, e.g. 27 cubes do not fill a space. 12. Compare, e.g., the solid angle contained by three right angles with that contained by two angles of 170o and one angle of 1o. 13. Why is there no mention of octahedra here? The prominence of the view about the icosahedron or the fact that in the case of the edge of an icosahedron is only 5% longer than the radius of a sphere circumscribing it whereas the edge of an octahedron is 40% longer? 14. Aristotelis loca mathematica ex universis ipsius operibus collecta et explicata …, Bologna, apud Bartholomaeum Cochium, 1615 (a page-by-page transcription of the text is available on the web at the Archimedes Project (http://archimedes2.mpiwg-berlin.mpg.de/archimedes_templates/biography.html?-table= archimedes_authors&author=Biancani,%20Giuseppe&-find). The relevant pages are 84-7. 15. Biancani raises no questions about octahedra, dodecahedra, or icosahedra filling a space. 16. Diversarum Speculationum Mathematicarum, & Physicarum Liber, Turin, apud Haeredem Nicolai Bevilaquae, 1585, printed again with the same pagination in 1599 as Speculationum Liber, Venice, apud Baretium Baretium, & Socios. 17. Earlier (pp. 85-6) Biancani has said that Aristotle might have been misled by the fact that an icosahedron is divisible into 20 triangular pyramids, not realising that these pyramids are not regular. 18. Venice, apud Haeredes Lucae Antonii Iuntae, 1543; another edition: Paris, apud Gulielmum Cavellat, 1558. 19. For a trigonometrical argument that this is so see the discussion of Jan Brozek below. 20. At the Biblioteca Nazionale Centrale Vittorio Emanuele II as San Pantaleo 117/33 dated 1529. 21. ‘Di tre manoscritti del Maurolico che si trovano nella Bibliotheca Vittorio Emmanuele di Roma’ (Continuazione e fine), Bibliotheca Mathematica 1885, pp. 193-5. 22. A smaller scale reproduction of the list is on p. 533 of Felix Schmeidler (ed.), Joannis Regiomontanio Opera Collecteana, Osnabrück: Otto Zeller, 1949. An even smaller one is plate 26 in Ernst Zinner, Leben und Wirken des Joh. Müller von Königsberg gennant Regiomontanus, 2nd. ed. Osnabrück: Otto Zeller, 1968. The English translation of this book (Amsterdam: North-Holland, 1990) does not include the plates. 23. Apologia pro Aristotele & Euclide, contra Petrum Ramum, & alios …. Autore Ioanne Broscio, Dantzig: Sumptibus Georgii Försteri, 1652 (available at http://imgbase-scd-ulp.u-strasbg.fr/displayimage.php?album=585&pos=0). Brozek’s discussion is very rhetorical and very long, covering pages 69-109.

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24. P. Rami Arithmeticae libri duo, Geometriae septem et viginti, Basel per Eusebium Episcopum & Nicolai Fratris haeredes, 1569; other printings in 1580, 1599, 1604, 1612, and 1627; I have used the 1599 edition, revised and enlarged by Lazarus Schonerus, Frankfurt apud Andreae Wecheli Heredes. 25. Brozek’s numbers are incorrect. The angle of a pyramid is slightly more than 31o, that of an octahedron almost 78o. 26. Struik lists the texts as Incun. 277 and 220 of the Biblioteca Alessandrina in Rome.

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. 639,7 Insert a comma after trigônôn. 643,30 Repunctuate hupomenousês, hoper as hupomenousês (hoper. 644,4 Insert a right parenthesis after the period. 644,6 Replace the period with a comma. 650,19 For deiknuôn read deiknuon with D and Karsten 652,19 For isa read isên. 658,25 Insert before ekhein. 658,34 For êi read ê with A, D, and E. 659,6 For hôn read euthugrammôn. 660,11 Insert after ta with Karsten. 664,16 For oxutêti read oxu ti with D, F, Karsten, and the text of Plato 668,17 For dêloi read dêlon. 675,29 For hupokeimenôn read huperkeimenôn. 682,8 For epi dêlois read epidêlon with Karsten. 689,2 For opheilein read opheilei with C. 693,17 For einai read ienai, a correction of Bessarion. 693,29 Bracket the ean and drop the comma after mikrai. 694,22 For to read ta; and for kataleiponta read kataliponta with F and Karsten. 701,32 For ei with an overbar read e with Karsten. 703,18 For oun read goun, a suggestion of Heiberg. 706,20 For hautôi read autôi with A and D. 706,27 For apotethen read apodeikhthen with D, E, and Karsten. 715,15 For auto read auta. 720,11 For ên read hêi. 720,17 Insert tôi before tauta with Bessarion and Karsten. 720,25 For hekateron read hekaterou with Karsten. 721,1 For ekhousas read ekhousin with Karsten. 721,1 For hôs read tês with Karsten. 721,7 For eisagein read sunagein with F.

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725,14 Bracket the mê before ontôn. 727,21 Fot auton read auto. 727,21 Insert de heteron dunatai after to. 730,13 For anokhein read anekhein with Karsten. (b) Simplicius’ citations of On the Heaven 3.7-4.6 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 311a18 de 312b34 phainetai 312a29-30 huphistatai tini kai epipolazei tini 312b30 oude hen

Heiberg 707,14 gar 715,7 (paraphrase) pheretai 721,14-15 epipolazei tini kai huphistatai tini 727,6 ouden

(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). Aristotle, De Caelo Moraux 296a12 dê 296a16 gar

Heiberg 716,1 omit 716,4 de

Euclid, Elements Heiberg (1883) 26,24 ean

Heiberg 651,11 hôs an

Plato, Timaeus Rivaud 50A4 mêden 50A3 hotioun 50A4 ekeino

Heiberg 636,23 mêden de 637,10 ti hotioun 637,10 ekeina

Textual Questions 50B10 ta panta 50C1 eilêphen 54D3 eidos hen 56B7 oun dê 57C8 to 50B10 te gar aei ta 61D7 hôde 61E1 oxu ti 61E4 to takhos 57A5 ti 57A6 allo ti 62A5 toutôn 62A8 smikrotera 62A8 ou 63D6 alla allois

149

637,15 panta 643,31 panta 637,16 aneilêphen 639,22 eidos 641,18 de 656,28 tou 658,5 aei 664,15 houtôs 664,16 oxutêti 664,18 takhos 666,29 tina 666,29 allo 669,21 toutôi 669,23 smikromerestera 669,23 mê 717,20 allêlois

[Timaeus of Locri], On the Nature of the World and the Soul Marg (1972) 215,13 gennômenôn 215,15 ha gennasis

Heiberg 641,11 ginomenôn 641,13 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 and Karsten 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 306b21 ta pathê 306b281 anairountas 307a18 pseudos 307a31 pros 307b5 de toutois 308b29 kouphou kai bareos 311a1 kata 311b1 dê 311b1 pantakhou 1

Heiberg 657,11 pathê 659,11-12 anairountas autous 663,17 esti pseudos 667,10 to pros 668,6 toutois de 682,5-6 bareos kai kouphou 701,2 kai kata 709,6 de 709,6 pantakhê

For Simplicius’ text here see the note on 659,12.

150

Textual Questions

311b13-14 haplôs kouphon kai haplôs baru 311b29 g’esti 312a8 de 312b28 dê enia estai 312b32 poiêi 312b33 ho 313a7 pur

712,18 haplôs baru kai haplôs kouphon 714,8 esti 717,21 dê 726,26 de estai enia 726,27 poiêsêi 712.17 ha 728,11 to pur

Notes 1. Simplicius changes Aristotle’s present optative to an aorist optative. 2. Tim. 50A4-B5. This quotation and the next are part of a passage (49C7-50B5), the traditional interpretation of which was called into question by Cherniss (1954). Defences of the traditional reading, which I have followed in my translation, are provided in Gulley (1960) and Zeyl (1975); see also the note on 637,10. 3. Simplicius has a de which is not in our text of the Timaeus here. 4. to aei toiouton, a paraphrase of the words ‘what is always such and such’ (to dia pantos toiouton) of the next quotation 5. Tim. 49E6-50A4. Simplicius has just briefly paraphrased 49D4-E4. 6. Simplicius has a ti which is not in our text of the Timaeus here. 7. I have translated Heiberg’s plural ekeina rather than the singular ekeino of our text of the Timaeus. (Heiberg reports that D and E have ekeinôi, E being corrected by Bessarion to ekeina, and that Karsten prints ekein’.) I am not interested in emending the text of Plato here, but only in calling attention to the fact that Simplicius’ reading would eliminate Cherniss’s account of 50A4, for which see Cherniss (1954), 114 and 124, and Gulley (1960), 60-2. 8. skhêma. In the passage which Simplicius proceeds to quote Plato uses the word diaskhêmatizomenon (translated ‘given figure’). 9. 50B10-C3. Simplicius quotes a little more of this passage at 643,31-644,4. 10. Heiberg prints panta, where our texts of the Timaeus (and Karsten) have ta panta. 11. Heiberg prints aneilêphen, where our texts of the Timaeus (and Karsten) have eilêphen. 12. I take the reference to be to chapter 3, 302a15-19, where Aristotle specifies that an element is not divisible into things different in kind. 13. cf. 3.5, 304b4-6. 14. Simplicius offers an unconvincing objection to an unconvincing proposal that when, e.g., a fire-pyramid is divided, its parts reform into pyramids. 15. Simplicius quotes Proclus as holding such a position; see below 649,32650,1. 16. This lemma consists of the first few words of the next lemma (642,1-2). In his discussion Simplicius explains his understanding of the geometrical chemistry put forward at Tim. 53C5-56E8, from which he quotes extensively. 17. In chapter 1 starting at 299a2. 18. cf. 298b8-299a1. 19. cf. Tim. 48B3-C2. Stoikheion (‘element’) is also the word for ‘letter’. 20. The diagrams in Vlastos (1975), pp. 74-9 are useful for following what Simplicius says here. 21. The terms ‘half-triangle’ and ‘half-square’ are taken from the work called On the Nature of the World and of the Soul (TL) and ascribed to Timaeus of Locri, the speaker of Plato’s Timaeus. For the terms see, e.g. 215,17 and 216,2, and on the work see section 7 of the Introduction to Mueller (2009). 22. The eight solid angles at the eight vertices of the cube.

152

Notes to pages 30-35

23. There should be a comma after trigônôn as there is in the next line. 24. Tim. 54B6-D3; a final hen, which is in our Plato, is not printed by Heiberg, although it is found in E and inserted by Bessarion, and also printed by Karsten. 25. Tim. 56C8-E1. 26. The same question is raised by Alexander in Quaest. 2.13 (Bruns (1892), 58,19-27). 27. In the next lemma. 28. For an attempt to reconstruct Proclus’ book see Steel (2005). Rashed ((2007), pp. 255-62) has published scholia which concern Aristotle’s first nine objections and, frequently, Proclus’ responses. I refer the reader to Rashed for discussion of the relationship between these scholia and Simplicius’ commentary. 29. For a rejection of Simplicius’ approach to apparent disagreement between Plato and Aristotle see Philoponus, Contra Proclum (Rabe (1899)), 29,2-8. 30. cf. 564,24-6 of the commentary on 3.1 with the note. 31. TL, 215,13-16. Simplicius quotes a few more words of this passage at 564,4-8 on chapter 1; see also in Phys. 7,23-7. 32. Marg (1972) prints gennômenôn, which Heiberg also prints at 564,4. Here Heiberg has ginomenôn. The MSS of Simplicius show considerable variation. 33. Marg (1972) prints ha gennasis, Heiberg apogennasis. 34. Tim. 56B7-C3. 35. Heiberg prints de, where our texts of Plato have oun dê. 36. Simplicius makes this claim in a more developed way at 565,28-566,1 of the commentary on chapter 1. 37. Tim. 53C2-4. 38. The verb used by Plato is endeiknusthai, which is often used by Neoplatonists to mean something like ‘to indicate in an obscure way’. See, for example its use at 608,25 and 31 in the discussion of Anaxagoras in the commentary on 3.4, where it is translated ‘indicate’. 39. I have discussed the material which follows (up to 671,20) in Mueller (forthcoming). 40. Tim. 49B7-C2. 41. Tim. 49C6-7. 42. cf. Aristotle, Topics, 1.11, 104b19-20. 43. hê en tois phainomenois kata tên aisthêsin tên kuriôs kai katôrthômenên alêtheia. 44. Proclus here criticises Aristotle for whom earth is cold and dry, water cold and wet, fire hot and dry, claiming that on Aristotle’s theory earth should burn up more quickly than water, because it shares a quality with fire, whereas water does not; in fact, he says, water is seen to be completely consumed by fire whereas earth ‘just by itself’ (kath’ hautên) does not burn. Proclus has a more extended criticism of the Aristotelian theory of elemental change at 2,37,3341,14 of his commentary on the Timaeus (Diehl (1903-6). I owe this reference to Dirk Baltzly.) 45. The provision of intermediaries between extremes is typical of Proclus’ philosophising; see, e.g., Siorvanes (1996), p. 66. In the scholia published by Rashed ((2007), pp. 256-7) this consideration is part of Proclus’ response to the second objection. 46. hina. I read this passage with the conviction that Simplicius is here disagreeing with Proclus and allowing that in a significant sense earth does interchange with the other elements. I therefore, take hina kai not as stating Proclus’ purpose in saying that earth does not change into the other elements, but

Notes to pages 35-39

153

to begin a series of considerations on the basis of which Simplicius affirms that earth does in some sense so change. Thus: in order to preserve (643,28) what is suitable to the co-ordination … and the necessity … (which Plato bears witness to) and because one should also not reject (644,5) … and also in order that (644,7) … what was said should be said again (644,8) …. In keeping with this understanding I would punctuate as follows: replace the comma before hoper (643,30) with a left parenthesis; insert a right parenthesis followed by a comma after the period in 644,4; and replace the period in 644,6 with a comma. 47. 50B10-C6. Simplicius quotes the first words of this passage again at 658,5-7. 48. Here, as at 637,15, Heiberg prints panta, where our texts of the Timaeus (and Karsten) have ta panta. 49. See the passages quoted at 642,11-15. To the contemporary reader it is striking that Simplicius does not stress Plato’s words ‘or think we see’ (hôs dokoumen) and ‘as it appears’ (hôs phainetai). But for Simplicius the phenomena are what appear to us and the distinction between appearance and reality is a distinction between the natural and the metaphysical world, not a distinction within the natural world. 50. cf. 640,12-19. 51. katathrauesthai, a verb used by Plato at Tim. 56E5 in connection with the dissolution of fire. 52. I do not know why or on what basis Simplicius adds this remark in his representation of Aristotle’s argument. 53. As Simplicius does not concede. 54. Tim. 40C2-3. 55. As it is in the chemistry of Plato’s Timaeus. 56. I am indebted to Jan Opsomer for the construal of this sentence. 57. And so ‘compress’ the air. 58. cf. 643,29-644,18 with the note on 644,8 59. Although Proclus just asserted (falsely for Simplicius) that the reason is that earth does not change into the other elements. 60. TL 215,9-12. 61. What Simplicius says in these two sentences is based on Phaedo 109B4-C3. Socrates first uses the word ‘myth’ slightly later at 110B4. 62. At 306a23 (648,11). 63. That is, Plato associates fire with the four-sided pyramid. In this quotation Alexander raises two objections to making the transformation of air into water come out even with no suspension by saying that three particles of air change into one particle of water and one of fire (3x8 = 20+4). 64. Simplicius is correct. Plato only says that 20 triangles from particles of air make one particle of water (Tim. 56E6-8) 65. cf. Tim. 56D6-E2. 66. Tim. 56D4-5 67. i.e.,earth, water, fire, and air, which are not elements on Plato’s account (Tim. 48B3-C2). 68. In other words, five particles of air make two particles of water (5x8 = 2x20). 69. hêmigenês, a word used by Plato at Tim. 66D2 in his discussion of smell. 70. Chapter 6, 305a16-22.

154

Notes to pages 39-44

71. Reading Karsten’s ex ou sômatos instead of the epi sôma of D and E printed by Heiberg; A has eiê sôma. 72. The reasoning here is not clear to me. Why does the fact that colour is located in different parts of a plane make the plane a body? 73. Aristotle has already invoked the incompatibility of atomism with mathematics in chapter 1 at 299a2-6 and in chapter 4 at 303a20-4. 74. cf. chapter 3, 303a12-14. 75. i.e. so that a smaller sphere with the same centre remains. 76. cf. Tim. 56B3-5. 77. That is, presumably, into squares or equilateral triangles. 78. e.g. the parts of pyramids. 79. Simplicius apparently feels that Proclus’ idea that small bits of planes or solids might change their shapes under pressure is unplatonic. He seems to think that when sufficiently small planes or solids are divided they combine with other bits to form proper planes or solids. 80. Unlike all editors of Cael. Heiberg treats the remainder of book 3 as part of chapter 7. 81. Aristotle’s assertion that pyramids can be made to fill a space is false; of the Platonic solids only the cube has this property; see Coxeter (1963), pp. 68-9 and also Türker (1966) and Heath (1949), pp. 177-8. I do not know what to make of Simplicius’ statement at 650,27 that twelve pyramids fill a space; see also 655,1827 for Potamon’s arguments that eight pyramids fill a space. 82. Reading the deiknuon of D and Karsten rather than the deiknuôn of A and E printed by Heiberg. 83. Below at 657,2-9 Simplicius suggests that solids of a variety of shapes and sizes can fill a space. 84. At this point Simplicius begins a long discussion of the geometric claims made by Aristotle. He takes up Proclus’ response to Aristotle’s argument at 656,6. 85. hôs an. In his edition of Euclid’s Elements (Heiberg (1883)), Heiberg prints ean (‘if’) both in the enunciation (26,24) and in the conclusion (36,24) of the theorem, although the manuscript evidence is almost unanimous in its support of Simplicius’ reading. At 291,20 of his commentary on book one of the Elements (Friedlein (1873)) Proclus also has hôs an, a reading which Heiberg ((1883) ad 26,24) calls a scribal error. 86. Proclus proves an equivalent result in his comment on Elements 1.32 (Friedlein (1873), 381,23-382,21). 87. I assume Potamon (also mentioned at 607,5 in the commentary on chapter 4) 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). For a thorough discussion of the evidence concerning Potamon, which argues that Simplicius’ Potamon is to be identified with the person described by the Suda rather than the one mentioned by Diogenes (the two have usually been assumed to be the same person) see Rescigno (2001). 88. On the next material see the appendix on Potamon’s arguments. Heiberg’s text includes diagrams after 652,12, 653,2 and 13, and 654,15, which are not in the MSS. 89. Reading isên instead of the isa printed by Heiberg; cf. 653,4. Or perhaps one might read isas, as a reader pointed out. 90. That is, e.g., the angle EAB is equal to EAB + BAD (= two rights) – BAD (the angle of the hexagon). But the formulation using eis with meta is unusual.

Notes to pages 44-51

155

91. Here and in the next line Heiberg prints ‘eight’ but notes that ‘six’ is correct. 92. I insert these words in the translation to make clear that Simplicius is again reproducing Potamon; see 655,28. I am not certain whether the preceding paragraph is Potamon, Alexander, or Simplicius. 93. Since Aristotle’s claim is false (see the note on the lemma) Potamon cannot possibly prove it. I have made as much sense of what he says as I can in the appendix on Potamon’s arguments. 94. Simplicius proceeds to question this odd use of ‘one’. 95. Simplicius contents himself with praising Potamon’s vague analogy rather than telling us whether Alexander developed his criticism of its use further, as he certainly could have. 96. cf. Tim. 58A5-B7. 97. That is, icosahedra, octahedra, and pyramids. Theoretically there wouldn’t need to be any ‘hollows’ in earth since a space can be filled by cubes. 98. Simplicius wants a geometric proof from Proclus. 99. Simplicius must mean ‘six’. 100. Tim. 53C6-8. 101. Tim. 57C8-D5. 102. Heiberg prints tou, which is the reading of three Timaeus manuscripts reported by Rivaud, who prints to. 103. Moraux prints kata ta pathê, which also occurs in Simplicius’ citation at 658,13. Heiberg prints kata pathê here although D and E have the ta. 104. Tim. 50B10-C1. Heiberg’s text begins dekhetai aei panta, where Rivaud prints dekhetai te gar aei ta panta. Simplicius quotes more from this passage at 643,31-644,4; his next words here are a paraphrase of 50E3-4. 105. 2.1-4. 106. It is difficult to construe this remark, and I propose to insert the negative mê as indicated. On the basis of the quotation which follows it would seem that Proclus proposed to escape Aristotle’s dilemma by saying that particles of the simple bodies do have a determinate shape which is changed in some conditions but not in others. 107. Reading the ê of A, D, and E rather than the êi of F printed by Heiberg. 108. Following the suggestion of a reader I have treated the hôn printed by Heiberg as a corruption of euthugrammôn, a word which occurs just above. 109. Reading tous tou stoikheiou, anairountas autous. The second part of Heiberg’s lemma starts with these last two words, and it appears from 659,33-4 and 660,2-3 that this is the text read by Simplicius. This text makes the reference of ‘they’ somewhat mysterious. Simplicius’ paraphrase at 660,2-3 (cf. 659,15-16) makes the ‘they’ refer to the holders of the theories Aristotle is attacking. Moraux and other editors print tous toioutous, anairountas (‘theories of this sort casually, he will see that they (i.e. these theories) eliminate’ …). 110. Simplicius attempts to include the atomists in the scope of this objection. From the quotation of Alexander which follows it appears he might have influenced Simplicius. 111. i.e. the second unprovable of the Stoics, modus tollens; see, e.g., Kneale and Kneale (1962), pp. 162-3. 112. cf. 306b3-9 (650,16), although the topic there would seem to be only the Platonic solids. 113. i.e. the Platonists. 114. But not Simplicius, for whom Plato’s planes do have depth; see, e.g., 646,21-4 and section 7 of the introduction to Mueller (2009).

156

Notes to pages 51-59

115. This sentence is quite perplexing, as Heiberg’s apparatus indicates. I have adopted Karsten’s suggestion of inserting ‘inside’ (entos) in line 11. But the sentence remains too abstract to provide a clear illustration of a case in which composites by juxtaposition are hard to pull apart. 116. For an analogous interpretation of Aristotle’s theory of homoiomerous compounds see Cooper (2004). 117. Here and for the next ten or so pages it is worthwhile to remember that the word oxus (translated ‘sharp’) is also the geometric term rendered ‘acute’; similarly the word amblus (translated ‘blunt’) is also the geometric term rendered ‘obtuse’. 118. cf. 307b19-24 (671,21) with Simplicius’ discussion. In that passage Aristotle uses the word ‘acts’ (erga) rather than ‘changes’. 119. Politicus 270A9. 120. This statement, which together with 307a17 (in the next lemma) constitutes DK68B155a, is frequently connected with the view that Democritus developed some form of a mathematics of infinitesimals; see, for example, Luria (1933), p. 145 or Krivushina and Fusaro (2007), pp. 1036-7. 121. 2.13, 293b30-32, on which see Simplicius’ commentary at 517,3-519,11. 122. In the last sentence of this paragraph Proclus refers to opposite faces of a cube as base and vertex (koruphê). Here he is talking about octagons and he would seem to be calling their faces bases and their vertices apexes. 123. See 662,10-12 with the note. 124. Heiberg’s lemma includes an esti, which is not printed by Moraux, although its absence in Moraux may be inadvertent, since it is included in the other main editions of De Caelo, and Moraux has nothing in his apparatus; Allan (1936) indicates that esti is missing in some manuscripts. 125. See the note on 664,23 and also 665,20-1 with the note. 126. cf. Tim. 58C4-D4, where kinds of fire, including flame and something which proceeds from flame, are said to differ because of the ‘inequality of the triangle’. TL (217,15-16) refers to what proceeds from flame as light. 127. Tim. 61D6-62A5. 128. Heiberg prints houtôs and reports that Karsten has hôide; Rivaud prints hôde. 129. I have translated Rivaud’s oxu ti rather than the oxutêti which Heiberg prints with A and E; D, F, and Karsten agree with Rivaud. 130. Heiberg’s text lacks a to printed by Rivaud, although several manuscripts of the Timaeus do not have the to. 131. Modern commentators accept the suggestion of Martin ((1841), vol. 2, p. 270) that Plato is playfully suggesting a connection between thermon (‘hot’) and kermatizein (‘mince up’). If Simplicius is referring to this passage at 663,20-2, he is imagining a connection between thermon and temon (‘cutting’). 132. There is, I think, no place in Metaph. where exactly this is said, but see, for example, 1.6, 987b14-33; 7.2, 1028b19-21; and 13.9, 1086a11-3. 133. As it is called at 426C1-2 of Plato’s Cratylus; see also 663,20-3 above and the note on 664,23. 134. I am indebted to Jan Opsomer for the correct interpretation of this sentence. 135. Tim. 56E8-57A7. 136. Heiberg prints a tina (sc. metabolên) where our texts of Plato have a ti. 137. Heiberg prints allo where our texts of Plato have allo ti. 138. Heiberg, following A, E, and F, prints a to before pros which is not printed by Moraux or Karsten; D also omits the to.

Notes to pages 59-64

157

139. cf. GC 2.2, 329b26-9 for a similar characterisation of hot. 140. Moraux prints de toutois, Heiberg toutois de with A, although D, E, and F (and also Karsten) have de toutois. 141. Aristotle makes this same objection against the atomists at De sensu 4, 442b17-21. 142. Camestres. 143. Reading dêlon for Heiberg’s dêloi. 144. cf. 663,27-664,12. 145. I am not sure what Simplicius is referring to. Heiberg suggests 1.4, but there Aristotle is concerned with the question whether circular motion is contrary to rectilinear motion, and he denies that it is. However, at 4.6, 313b11-2 Aristotle mentions ‘things which have contrary shapes’; perhaps this is the passage Simplicius has in mind. At 672,8 Simplicius says that in the strict sense there is no contrariety among figures. 146. Tim. 62A5-B7. 147. Heiberg prints toutôi, Rivaud toutôn; some MSS of Tim. have toutôi. 148. Heiberg prints smikromerestera, Rivaud smikrotera (‘smaller things’). 149. Heiberg prints mê with A; D, E, Karsten, and Rivaud have ou. 150. I take Simplicius to be referring to 3.5, 303b22-30. 151. cf. 662,1-7; 663,3-15 (where the topic is solids), and Tim. 57E7-58A1. 152. i.e. by the size of the component polyhedrons. 153. Tim. 57D1-2; fuller citation at 656,28-657,2. The objections raised by Simplicius in this paragraph seem superficial. I doubt that Proclus would disagree with anything he says. 154. I have inserted this sentence from Cael.; it is not included in the scope of any lemma, but Simplicius clearly refers to it at the beginning of his next discussion. 155. Here the lemma indicates only that the text goes to the end of book 3. 156. i.e. heaviness and lightness. 157. The obvious referent of ‘them’ is ‘activities’. 158. Heiberg refers to GC 1.6, but there is no explicit claim of this kind in that chapter, and at 2.2, 329b19-31 Aristotle says that heavy and light are neither productive nor passive, both hot and cold are productive, and both wet and dry are passive. For discussion of these last two claims see Joachim (1922) ad 329b24-6. 159. At Cael. 2.3, 286a25-8 Aristotle says that hot is an affirmation cold a privation and also that rest and heavy are privations of motion and light; cf. GC 1.3, 318b14-8 with Joachim (1922) ad loc. and Metaph. 12.4, 1070b9-16. At Parts of Animals 2.3, 648b34-649a20 Aristotle characterises cases in which cold is not a privation but a phusis. 160. That is to say, heat, for example, can be either the quality in a thing which imposes itself on us or the feeling which is imposed on us; cf. Categories 8, 9a35-b9. 161. For the double sense of ‘power’ see, e.g., Metaph. 9.1, 1046a4-28. 162. From this point on Simplicius substitutes ‘activity’ (energeia) for Aristotle’s ‘act’ (ergon); cf. 4.1, 307b32 (676,1). 163. That is, heaviness and lightness, the qualities related to motion up and down. 164. In chapter 1. 165. Although not all things. 166. Simplicius jumps from chapter 1 to chapter 3; for Simplicius’ characterisation of what Aristotle says at the beginning of chapter 3 see 600,11-13 in the commentary on chapter 3.

158

Notes to pages 65-72

167. In chapter 4. 168. At the end of chapter 5. 169. Chapter 6, 304b25-305a14. 170. Chapter 6, 305a14-32. 171. Chapter 7, 305b1-28. The remainder of what Simplicius describes is found in material discussed in the previous pages of this volume. 172. For this description of book 3 see the preceding paragraph with the notes. 173. See the last words of the preceding book at 307b19-24 (671,21). 174. Simplicius refers ahead to the next lemma. 175. 1.3, 269b20-3. 176. In chapter 1. 177. In chapter 2. 178. In chapter 3. 179. This and the next four sentences all refer to chapter 4. 180. Reading huperkeimenôn for the hupokeimenôn printed by Heiberg, which is certainly not what Simplicius meant to say. 181. In chapter 5. 182. In 3.1, 299a25-b23. 183. In 3.2, 301a22-b17. 184. 1.3, 269b18-270a12. 185. 1.6, 273a22-274a18. 186. It is not clear what in GC Simplicius has in mind here. 187. Presumably Simplicius is thinking of Cael. 1.3, 269b18-26. 188. At Phys. 8.1, 250b14-15 Aristotle characterises motion itself as a kind of life for all naturally constituted things. 189. Simplicius has the feminine tautas here, which presumably would refer to powers (dunameis), but our texts of Aristotle have tauta, which presumably refers to bodies; three lines later Simplicius has tauta. The alternative that ‘these things’ are heaviness and lightness leads Simplicius to the dubious proposal that ‘these things contain in themselves’ means ‘these things are in themselves’. But Simplicius has no doubt about what Aristotle’s doctrine is. 190. Aristotle paraphrases 62D11-63A7 of Tim. Simplicius quotes the passage and much of its immediate context starting at 680,12. 191. In chapter 3. Simplicius’ position is motivated by the fact that in Tim. Plato expresses an alternative view of above and below; see 679,27 ff. 192. Simplicius moves on to paraphrase 308a29-33. He returns to 308a17 at 679,1. 193. I have translated Moraux’s conjecture hote; cf. 678,28 where Simplicius has hotan; Heiberg prints ho, the reading of the MSS of Aristotle. 194. Heiberg’s insertion. 195. I take Simplicius’ point to be that Aristotle has said that a (which has weight) is lighter than b (which has weight) when b moves downward faster than a. 196. That is, for example, although bronze is heavier than wood, on Aristotelian principles a large piece of wood could move down more quickly than a small piece of bronze. 197. Simplicius’ point is perhaps this. The periphery of the cosmos is, as Aristotle says, first by nature, but that does not mean that it constitutes a genuine ‘above’ in the cosmos; it would mean that if one could prove that the centre, to which Simplicius assigns an unspecified kind of priority (but see Tim. 40B8-C3), constitutes a genuine ‘below’.

Notes to pages 73-83

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198. Tim. 62C8-63A5. 199. In the lemma and at 1.3, 269b18-26 Aristotle defines heavy and light in terms of motion up and down, but I do not know what Simplicius has in mind when he says that Aristotle also distinguished above and below on the basis of heavy and light. 200. Tim. 63A5-D4, a part of which is quoted again at 717,3-11. 201. Tim. 63E4-7, quoted again at 684,4-7. 202. Moraux prints kouphou kai bareos with all the Aristotle manuscripts. Heiberg prints bareos kai kouphou with F; A has kai bareos kai kouphou; D, E, and Karsten have the text printed by Moraux. 203. I have translated Karsten’s epidêlon rather than the epi dêlois printed by Heiberg. Simplicius here refers to 308a9-13 in the previous chapter (678,1). 204. The word ‘absolutely’ (haplôs) must be non-technical here, since only fire is absolutely light in the technical sense of always moving up if it is not as high as it can get, and is not impeded. 205. Heiberg indicates that ‘something about the triangles for a cube has dropped out’, but it is difficult to see how the text could be filled out since the triangles for the cube are different from those for the icosahedron, preventing any obvious comparison. Cf. the note on 684,16. 206. 63E4-7, already quoted at 682,1-3. 207. This does not provide a genuine distinction between absolute heavy and light but only a distinction relative to a location. 208. Heiberg calls the text of this paragraph ‘corrupt or lacunose’, but the sense seems clear enough: in 308b21-8 Aristotle is only discussing the relative weight and lightness of the three elements which are composed from the same triangles, that is fire, air, and water. 209. For the interpretation of these last words see 685,32-686,1. 210. For Simplicius Plato’s planes are only divisible into planes and not into anything different in kind, i.e. in this case, lines or points. 211. cf. ch.1, 299b14-17. 212. Alexander’s text apparently lacked a mê, which is found in all our texts of Aristotle and gives a better sense. 213. cf. 309b8-17 (687,7). 214. For Empedocles’ denial of the void see DK31B13 and Wright (1981), pp. 98 and 173-4. Aristotle also associates Anaxagoras with its denial at Phys. 4.6, 213a22-7. 215. cf. 679,1-682,3. 216. Starting at 680,12. 217. Tim. 59C1-3. The immediately preceding words might be translated: ‘Another has parts very like gold and comes in more than one kind. It is in one respect more dense than gold, and, because it has a small, fine portion of earth, it is harder. But …’. Simplicius gives no indication of how he understands these ‘gaps’; he clearly does not think they are void spaces. 218. The words in corner brackets in this sentence constitute an insertion by Heiberg. 219. i.e. defining heavy and light in terms of more or less solid (addressed at 309a34), or of less or more light (309b2) or of the proportion of solid to light (309b8). 220. cf. 309a11-18 (684,17). 221. Reading the opheilei of C rather than the opheilein printed by Heiberg. Bessarion corrected to edei, giving more or less the same sense. 222. This sentence is not included in the scope of Heiberg’s lemma, but Simplicius begins his discussion (689,11-16) by commenting on it.

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223. As large cosmic masses. 224. Aristotle seems to be proceeding with two dichotomies, one between (a) weight being a function of size and (b) weight being a function of something else, the other between (i) there being a single matter and (ii) there being a pair of contrary matters. He argues against (i) at 309b33 and (ii) at 309b34. In the next lemma he indicates that (a) is easier to defend and then attacks the composite of it with (i). 225. On the words translated ‘things which are absolute’ see 692,16-17 with the note. 226. Water and air. 227. The view Simplicius assigns to Anaximander; see, for example, 615,13-15 in his commentary on 3.5. 228. The ‘monists’ whom Simplicius has just characterised. 229. For this claim about Parmenides see Phys. 1.5, 188a20-2 and Metaph. 1.5, 986b27-34; see also Cherniss (1935), p. 48, n. 192. 230. These last words should apply to Plato, but nothing else Simplicius says explains why he should be treated as someone who took a pair of contraries as the substratum. And in the next paragraph Simplicius treats (again in a problematic way) Plato as someone who believed in a single substratum. 231. Simplicius apparently thinks that Aristotle’s reference to ‘those who compose things from triangles’ is intended to include Plato as someone who believed in a single matter, and he offers a far-fetched explanation of why this is so. But Aristotle need only mean that Plato couldn’t explain absolute heaviness and lightness. Simplicius’ understanding leads him to add the words ‘with the element itself having no impulsion’ at the end of the paragraph, Plato’s triangles having no weight on Aristotle’s understanding. 232. At 692,7-11 Simplicius ascribes this interpretation of ‘the things intermediate between the things which are absolutely heavy and light’ as compounds of atoms and void to Alexander and says that ‘perhaps’ they are water and air, Aristotle’s usual intermediates between fire and earth. However, this alternative does not affect the understanding of Aristotle’s argument. 233. cf. 309b18-23 (689,9) with Simplicius’ comment at 689,16-30 234. At this point Simplicius considers some possible explanations open to these ‘atomists’. 235. Simplicius refers to chapter 5; see especially 312b19-313a13 (725,22729,15). 236. Heiberg cites 312b28 in chapter 5 (726,26), but 312b32 (727,17) seems more likely. 237. The issue is whether Aristotle wrote haplôn (‘things which are absolute’) or haplôs (‘things which are absolutely ’). There is no indication that any interpretive issue was made to turn on this difference, nor does it seem likely that any should; see the note on 310a3 in Stocks. 238. cf. 691,23 with the note. 239. Simplicius adds this qualification because of 310a7-9. 240. cf. 691,23 with the note. 241. Reading Bessarion’s correction ienai for the einai printed by Heiberg. 242. Accepting the suggestion of an anonymous reader to bracket the ean printed by Heiberg; this change requires dropping Heiberg’s comma after mikrai. Bessarion’s and Karsten’s hai (for ean) seems to me unlikely because of the close parallel with 310a10-11 in the lemma. 243. An anonymous reader thinks that this ê is not disjunctive and proposes to

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translate it as ‘in fact’. In any case the point is that the atomists could escape the objection by invoking the void in their explanations of weight. 244. In modern editions the first sentence of the next lemma marks the end of chapter 2. 245. For textual issues concerning this clause see 698,10-14 with the note. 246. With the punctuation of modern editions this ‘then’ should be an ‘and’ or ‘but’, and the lemma would end with the antecedent of a conditional, the consequent of which begins at 310b16 at the beginning of the lemma after next (701,1), the next lemma being a parenthetical interruption. 697,9-26 makes clear that Simplicius chose to read 310a31-b1 as a complete conditional. It would appear from 701,30-2 that Alexander punctuated in the same way. 247. Alexander mentions difficulties about natural motion which do not seem to be in Aristotle’s mind, nor does Simplicius give any indication of how they might be addressed. For a discussion of what Alexander says here see Moraux (19732001), vol. 3, pp. 236-8. 248. Alexander first considers the behaviour of a piece of a simple body when it comes into existence and starts to move. The argument he presents is that since the body has never been in its proper place that place cannot yet exist, given the Aristotelian definition of the place of a thing as the inner limit of the body containing it. 249. The second difficulty is that when a portion of a simple body joins the mass of that body, it is no longer in place because it is blended in the mass and cannot be demarcated. 250. Reading ta for Heiberg’s to and the kataliponta of F and Karsten rather than the kataleiponta printed by Heiberg. But the sense remains opaque to me. 251. The third argument invokes a hypothetical situation in which the places of earth and fire are interchanged in order to show that moving to one’s proper place is not the same as moving toward one’s like. 252. It appears from 695,21 that the material in this paragraph is also derived from Alexander. 253. Simplicius makes a general reference to Aristotle’s discussion of atomist and related doctrines in the preceding chapter, 309a19-310a13 (686,9-693,32). 254. cf. chapter 1, 225a26-7; prior to this passage at 225a12-16 Aristotle makes the distinction between coming to be in the strict sense (coming to exist) and coming to be something (e.g. white). 255. That is, because of the general description of change. Simplicius leaves out the corresponding facts for lightness. 256. cf. 694,17-23. 257. Heiberg indicates that the text is corrupt here. His own suggestion is to read ‘one should not characterise above and below in terms of our perception but in terms of convergence’. 258. In the two versions of 310a31 mentioned by Simplicius in this paragraph there is a men here where Moraux prints an oun. Independently of that, the issue in this paragraph is whether the text should read ‘into what is above or below’ (eis to anô kai to katô) or, as Alexander thinks, ‘up or down’ (anô kai katô). Simplicius says that the latter is old-fashioned and means ‘upward or downward’ (epi to anô kai to katô). I have not been able to detect any difference in meaning between these terms, all of which Simplicius uses. 259. Simplicius understands Aristotle to be saying that although each of water and air is similar to something above it and below it, earth is only similar to something above it and fire only to something below it. In the sentence after this

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one Simplicius points out that fire and earth might be said to be similar to each other. An alternative interpretation would have Aristotle saying (mysteriously) that although air is like fire and water like earth, fire is not like air and earth is not like water; so Stocks, ad loc. 260. 699,14-700,8 is printed as fragment 93a of Posidonius by Edelstein and Kidd (1989), 700,3-8 as text 171 in Theophrastus: Sources. It is not at all clear what in Aristotle Simplicius has in mind. Heiberg cites GC 2.8, where, at 335a18-20, Aristotle says that only fire or mainly fire is form because it is so constituted as to move toward the boundary. There is a comparable remark about fire by contrast with the other three elements at Meteorology 4.1, 379a14-16, and at 718,13-19 Simplicius ascribes to Aristotle the view that fire is formal, earth material, air and water both formal and material. For some discussion see Sharples (1998), pp. 120-1. 261. apolelumena. Simplicius offers his explanation of this word at 704,4-8. 262. Heiberg prints an ‘also’ (kai) here with A and F. It is not in our text of Aristotle and not printed by Karsten. 263. In the next lemma. 264. At the start of the lemma. Alexander proposes writing dê instead of de. The previous ‘proof’ he has in mind is presumably at 310a21-31at the beginning of this chapter (694,1); see Simplicius’ commentary on that passage. 265. Heiberg’s text has ei with an overbar. He reports that Bessarion changes this to e with an overbar and Karsten prints plain e. I assume that e is right and is Simplicius’ way of referring to de as opposed to dê. 266. First a word about the text of the phrase under discussion. Moraux prints homoiôs de kai toutôn hekaston and notes that kai is omitted in one MS. Here the words are homoiôs kai toutôn hekaston and Alexander proposes two alternatives, first homoiôs de kai tôn allôn hekaston and second homoiôs de hôs toutôn hekaston. When Simplicius then quotes the phrase he writes the words printed by Moraux. I assume we should take for granted a de kai in all of these readings. Alexander thinks that Aristotle wants to infer from what is true of change in quality and quantity that the same thing is true of motion up and motion down. Both of his two suggestions are that Aristotle means ‘As it is with each of qualitative and quantitative change, so it is with motion up and down’. Simplicius’ response is that Aristotle would use hekateron, not hekaston, if he were talking about each of two things. He takes Aristotle to be saying ‘And it is similar with each of the three kinds of change mentioned’. Judging from their translations, Moraux and Guthrie accept this interpretation, but Stocks appears to side with Alexander. At the end of the next paragraph Simplicius seems to move closer to Alexander. 267. Adopting Heiberg’s suggestion of goun for the oun which he prints. 268. i.e. to being in their proper place. Closeness here is not necessarily spatial, but may refer to suitability. 269. i.e. change place. 270. i.e. fathers an offspring. 271. Here completeness apparently does not require capacity to reproduce as it did just above. 272. erkhetai ekei kai eis to tosouton kai to toiouton, hou hê entelekheia kai hosou kai hoiou. Aristotle’s formulation is opaque. At 705,5 Simplicius tells his audience that ekei, which I have translated ‘into that place’ is spatial. 273. Hail. 274. An objection raised by Xenarchus; see 21,33-23,10 of Simplicius’ commentary on book 1 of in Cael.

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275. At the beginning of chapter 1, 241b24-242a49; see also Phys. 8.4, 254b33256a3 and Simplicius’ remarks at in Phys. 1036,17-1037,8. 276. Reading the autôi of A and D (changed to auto in E and omitted in C) rather than Karsten’s hautôi, printed by Heiberg. 277. Reading the apodeikhthen of D, E, and Karsten rather than the apotethen of A, printed by Heiberg. 278. cf. 310a13-20 (694,1). 279. The consequences are taken up in the next lemma (709,6). 280. In the lemma after next (712,18). 281. Simplicius makes explicit that the fifth element is not to be included. 282. Simplicius has gar here where our texts of Aristotle have de. 283. cf. 309b18-24 (689,9) in the preceding chapter. 284. Heiberg prints a de with A. D, F, Karsten, and our texts of Aristotle have a dê. 285. Heiberg prints pantakhê, Moraux pantakhou, which is the reading of D, F, and Karsten, and is used by Simplicius in his reformulation at 709,10 and 14. 286. In the preceding lemma. 287. Rashed ((2007), pp. 232-5) argues that Simplicius is here referring to a lost commentary of which traces are preserved in certain scholia. The relevant scholium appears to propose that the next lemma, in which Aristotle argues for the existence of absolutely heavy and light things, should immediately succeed the previous lemma, in which Aristotle asserts that this is obvious to everyone. It also proposes that the present passage be placed together with ‘the other difficulties toward the end of the book’ apparently a reference to the last chapter. 288. I am unable to explain this sentence. Water is never heavier than earth. 289. Peri rhopôn, a work for which the present passage is our main source. Heiberg ((1907), pp. 263-4) gives two other ancient references. 290. Perhaps Syrianus; see 711,26. 291. cf. 311a27-9 in the preceding lemma (707,4) 292. It is unclear how much of what precedes is derived from Syrianus; I have paragraphed to suggest that the material derived from Syrianus picks up at 711,10. 293. haplôs kouphon kai haplôs baru is printed by Moraux and Karsten. Heiberg prints haplôs baru kai haplôs kouphon with A. 294. The force of ‘other’ is not clear here. Guthrie translates ‘others besides ourselves’. Moraux says that Aristotle is referring to others who believe that everything has weight. Simplicius (712,27-31) apparently ignores the word and treats this sentence and its predecessor as referring to the atomists. 295. cf. 311a15-21 (707,4). 296. cf. 311a15-29 with Simplicius’ comment at 707,10-14. 297. The obelus is Heiberg’s; he prints ‘assumed things’ (lambanontôn), the only manuscript alternative being prolambanontôn. 713,16 suggests that we might read huphistamenôn (‘things which sink below fire’). 298. Namely desire to be with its like; cf. 679,6-682,3. 299. cf. Simplicius’ comment on 312b24 in the next chapter at 726,18-20. 300. cf. 714,10-12 and 715,5-7. 301. The MSS of Aristotle have g’esti as does Karsten. Heiberg prints esti with A. F has a correction of gê esti into ge esti. 302. cf. 713,31-4. 303. For the second argument see the next lemma. 304. i.e. modus tollens, the second Stoic unprovable; see, e.g., Kneale and Kneale (1962), pp. 162-3.

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305. cf. 583,4-5 and 594,12-13 in the commentary on 3.2 with the notes. 306. Reading homoias pheretai gônias rather than the homoias phainetai gônias printed by Moraux. Heiberg’s lemma (in agreement with A) has only the four words Epeita pros homoias gônias; he notes that F has pheretai gônias, K and Karsten phainetai gônias. Phainetai appears in two of the MSS of Cael. cited by Moraux, pheretai in one and as a correction in another. Simplicius’ paraphrase at 715,6-8 indicates that he read pheretai. 307. Simplicius quotes 311b29-30 from the preceding lemma. 308. cf. 538,21-2 in Simplicius’ commentary on chapter 14 of book 2. 309. Reading auta for the auto printed by Heiberg. 310. That is, they travel on straight lines which converge toward the centre. 311. For the rest of this paragraph Simplicius focuses on downward moving things. 312. It is tempting to insert a ‘not’ here, but perhaps Simplicius takes Aristotle to be saying that the student should investigate this question on his own. 313. Cael. 2.14, 296b12-15, 16-18. 314. Simplicius omits a dê which is found in our text of Aristotle. 315. Simplicius substitutes a de for the gar which is in our texts of Aristotle. 316. I am not sure what point Simplicius is making here. Perhaps he is thinking about Aristotle’s claim in chapter 3 (310b3-6 (698,15)) that if the earth were moved into the position of the moon, pieces of earth would not move to it, but to the place where the earth is now. 317. The point of this apparent tautology is that since heavy and light are contraries and so are centre and extremity, if what is heavy moves to the centre, what is light moves to the extremity. 318. cf. 679,6-681,11; 684,1-12; 712,31-713,7. 319. cf. 681,15-23. Simplicius goes on to quote Tim. 63B1-C5. 320. Tim. 63D4-6. 321. Heiberg prints allêlois where the Timaeus has alla allois. 322. Heiberg prints dê with A, Moraux de, which is also the reading of F and Karsten. 323. That is, a place between centre and extremity; see the end of the preceding lemma. 324. The well-attested sentence in the manuscripts of Aristotle is anacoluthic, and various emendations have been proposed. Simplicius’ discussion of the sentence starts at 719,21; see the note on 719,29. 325. See 2.2-3 and especially 330b33-331a1. 326. As opposed to empirical observation. 327. i.e. what is heavy and at the centre and what is light and above. 328. See 310b7-15 in the previous chapter (698,15) with Simplicius discussion at 699,16-700,30 and the note on 700,8. 329. Simplicius recognises that his paraphrase of 312a17-18 is tenuous. 330. That is, prime matter as traditionally interpreted, Simplicius understanding of Aristotle’s ‘the matter itself of heavy and light’. In the obscure next sentence Simplicius says that prime matter is not its own matter but it is the matter of light and of heavy, these being in an unexplained way the matter of the four elements. As an actuality, he says, heaviness is formal, but it also plays the role of matter for the heavy elements. 331. At 312a23-5 all the MSS of Cael. read: to d’heteras men toutôn ekhousas d’houtô pros allêlas hôs hautai haplôs kai anô kai katô pheromenas. As remarked in the last note on the lemma the ‘sentence’ is anacolouthic. At 719,21-5 Simplicius

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paraphrases it as if something like ekhei tas hulas were inserted between kai and anô. But he tells us that Alexander found a text in which the ‘sentence’ read: to de peras men toutôn ekhousas …,and – in Simplicius’ representation – proposed that the text should be filled out as: to de ti sôma peras men toutôn estin ekhei de hulas houtôs ekhousas d’houtô pros allêlas hôs hautai haplôs kai dia touto kai anô kai katô pheromenas dioti pê men kouphai pê de bareiai eisi. (insertions in bold) According to Moraux (p. 165), who proposes his own emendation, the reading of peras is based on a misunderstanding. 332. Reading hêi for the ên printed by Heiberg. Simplicius is suggesting that the fundamental qualities of the simple bodies are prior to their weight and lightness, whereas Alexander took the opposite position. 333. Reading the tôi tauta legonti of Bessarion and Karsten. Heiberg does not print the tôi. 334. The words in italics are not in the scope of any lemma and are not discussed by Simplicius. They are missing in one manuscript of Aristotle (E) reported by Moraux. Longo ((1961), p. 353) thinks they are probably a marginal note. 335. Reading Karsten’s hekaterou for the hekateron of A, C, and F printed by Heiberg. 336. The reference is, as Heiberg says, to chapter 7, where Aristotle asserts that the substratum of change is one in number but more than one in form; however, there Aristotle does not appear to have in mind what Simplicius is now discussing; he never mentions the four simple bodies. 337. cf. 3.6, especially 305a31-2. 338. Reading the ekhousin of Karsten rather than the ekhousas of Heiberg. 339. Reading the tou of Karsten rather than the hôs of Heiberg. 340. 312a23-4 in the previous lemma. 341. Reading the sunagein of F rather than the eisagein of A, printed by Heiberg; Bessarion and Karsten have sunagôn. 342. In 3.3, 302a10-14. 343. Simplicius is thinking of GC 2.1-4; see, especially 2.1, 329a24-b3. However, in GC Aristotle distinguishes the elements in terms of their qualities rather than their ‘matters’, but Simplicius treats these qualitative differences as differences in matter. 344. Here and at 722,9 Simplicius writes einai alla where our texts of Aristotle have alla einai, but he has Aristotle’s order below at lines 22-3 and 25. 345. Simplicius interchanges Aristotle’s huphistatai and epipolazei. 346. Simplicius omits a monon (‘only’) which is in our text of Aristotle, but he has it above at 720,27 and 721,13. 347. i.e. earth and fire. 348. Simplicius’ introduction of the term ‘limit’ here is probably related to what Alexander is reported to have said at 719,28-720,8. 349. cf. GC 2.3, 330a30-b1. 350. Simplicius is perhaps thinking of GC 2.3, 330b1-6. 351. cf. GC 2.4, 331a23-b2. 352. cf. GC 2.3, 330b30-331a6. 353. See the note on 721,14. 354. With this paragraph see Tim. 31B5-32C4. 355. At 723,21-32 Simplicius explains this as the uniting of the surface of the water with the surface of the air. 356. Simplicius is presumably thinking of things said by Aristotle in the previous chapter, for example at 311a15-21 (707,4).

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357. cf. 311b1-13 in the previous chapter (709,6). This passage also contains the ‘proofs’ to which Simplicius refers next. 358. Simplicius makes the obvious point that the words ‘has weight’ which attach to ‘each of the things which have both weight and lightness’ should also be read with ‘but earth in all regions’. 359. On this multifaceted term, translated ‘wind’, ‘breath’, ‘spirit’ in different contexts see Verbeke (1945). Here ‘pneuma’ refers to something like the Stoic substance which penetrates all things and holds them together as coherent wholes. 360. I have bracketed the second mê in this obscure sentence, which I tentatively suggest says that, e.g., air, which normally lies above the region of water will move into a part of that region if and only if that part is void of water (‘does not exist’). 361. The eleven-line sentence which follows is cumbersome and anacolouthic, but the sense, which I hope my translation conveys, is clear. 362. cf. 679,6-682,3. The noun ‘impulsion’ (rhopê) does not occur in Tim., but it occurs twice in TL at 215,13 and 219,10, although he appears to adopt the Aristotelian account of above and below, heavy and light, and natural place. Plato does use the verb translated ‘have an impulsion’ (rhepein) at 79E5, but there he is not talking about weight. 363. Heiberg’s lemma has de estai enia where Moraux prints dê enia estai. Karsten has dê eni’ estai. 364. Moraux prints oude hen, noting in his apparatus that two MSS of Cael. have outhen. At 727,6 Simplicius appears to cite the sentence with ouden. 365. The lemma has poiêsêi where Moraux and Karsten print poiêi. 366. This sentence, which implicitly criticises Aristotle’s representation of the views he is opposing, comes in somewhat oddly here. But see 692,25-693,2, where Simplicius explains why Aristotle says at 4.2, 310a3-7 (692,18) that characterising weight in terms of size is less subject to difficulty than other views. 367. A correction of Aristotle, since, according to him, air will move down if what is beneath it is removed, but it will not move down faster than earth. 368. Heiberg cites 3.5, but the arguments there are not the same as the arguments here. Simplicius appears to be thinking of 309b29-34 (690,15), although they are in chapter 2 of the present book; see Simplicius’ remark at 692,12-14. 369. Heiberg prints ho with A; F and Karsten have ha, which is the reading of our texts of Aristotle and which Simplicius uses in a citation at 727,31. 370. Reading auto for the auton printed by Heiberg. 371. It appears that some words have dropped out after to in line 21. I have translated as if they were de heteron dunatai. In any case the sense is clear; the argument of 312b19-28 (725,22) applies only to ‘monists’, that of 312b28-32 (726,26) applies to them and ‘dualists’ (and so Aristotle repeats the argument again in the present lemma). 372. Heiberg prints kai pur with A, where Moraux and Karsten print kai to pur; F has to pur. 373. At 312b19-20 (725,22). 374. At 312b20-1 (725,22). 375. In the untranslated four words Simplicius explains that Aristotle is speaking ek parallêlou, a phrase which corresponds to our ‘hendiadys’, using two words for a single thing. Simplicius is saying that the second ‘both’ (amphô) in Aristotle’s ‘if both were some one thing or two things, and both belonged to each of them’ refers to the same thing as ‘two things’ (duo), and perhaps that Aristotle could simply have said ‘and these belong to each of them’.

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376. cf. 4.2, 309a11-18 (684,16) with Simplicius’ comment at 685,30-2. 377. cf. 4.2, 309b8-16 (687,7). 378. ta de skhêmata ouk aitia tou pheresthai haplôs, words which Simplicius paraphrases as haplôs … to skhêma kinêseôs ouk estin aition (729,24-5). 379. sous. On this word, about which Simplicius says nothing, see Plato, Cratylus 412B3-7. 380. In the next lemma. 381. i.e. if it is divisible into shavings which are light and float. 382. Reading anekhein with Karsten rather the anokhein printed by Heiberg; cf. lines 19 and 22 below. 383. Heiberg prints the plural with A, where F and Karsten have a singular. 384. Simplicius supplies this reason, relying perhaps on the doctrine that air is hot and moist, water cold and moist. 385. The lemma here is ‘“Since some continuous things are easily divided” until the end’. 386. On this closing prayer as an index of the religious orientation of Simplicius’ commentary see Hoffmann (1987), pp. 72-6.

Bibliography Adler, Ada (ed.) (1930), Suidae Lexicon, pt. 4, Leipzig: Teubner. Allan, D.J. (1936), Aristotelis De Caelo Libri Quattuor, Oxford: Clarendon Press. Bergk, Theodor (1883), Fünf Abhandlungen zur Geschichte der Griechischen Philosophie und Astronomie, Leipzig: Fues’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 2.2), Berlin: Reimer. Cherniss, Harold (1935), Aristotle’s Criticism of Presocratic Philosophy, Baltimore: Johns Hopkins. Cherniss, Harold (1944), Aristotle’s Criticism of Plato and the Academy, Baltimore: Johns Hopkins. Cherniss, Harold (1954), ‘A much misread passage of the Timaeus’, American Journal of Philology, 75, 113-30, reproduced in Tarán (1977), pp. 346-63. Cooper, John (2004), ‘A note on Aristotle on mixture’, in De Haas and Mansfeld (2004), pp. 315-26. Cornford, Francis MacDonald (1937), Plato’s Cosmology, London: Routledge and Kegan Paul. De Haas, Frans and Mansfeld, Jaap (eds) (2004), Aristotle: On Generation and Corruption, Book I, Oxford: Clarendon Press. Diehl, Ernst (ed.) (1903-6), Procli Diadochi in Platonis Timaeum Commentaria, 3 vols, Leipzig: Teubner. Edelstein, L. and Kidd, I.G. (eds) (1989), Posidonius, vol. 1, 2nd edn, Cambridge: Cambridge University Press. Friedlein, Gottfried (ed.) (1873), Procli Diadochi in Primum Euclidis Elementorum Librum Commentarii, Leipzig: Teubner. Gulley, Norman (1960), ‘The interpretation of Plato, Timaeus, 49D-E’, American Journal of Philology 81, pp. 53-64. Hadot, Ilsetraut (1990), ‘The life and work of Simplicius in Greek and Arabic sources’, in Sorabji (1990), pp. 275-303. Hadot, Ilsetraut (2002), ‘Simplicius or Priscianus?’, Mnemosyne 4.55, pp. 159-99 Hankinson, R.J. (trans.) (2002), Simplicius: On Aristotle On the Heavens 1.1-4, London: Duckworth. Hankinson, R.J. (trans.) (2004), Simplicius: On Aristotle On the Heavens 1.5-9, London: Duckworth. Hankinson, R.J. (trans.) (2006), Simplicius: On Aristotle On the Heavens 1.10-12, London: Duckworth. Heath, Thomas (1949), Mathematics in Aristotle, Oxford: Clarendon Press.

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Heiberg, J.L. (ed.) (1883), Euclidis Elementa, vol. 1, Leipzig: Teubner. Heiberg, J.L. (1892), ‘Handschriftliches zum Commentar des Simplicius zu Aristoteles de caelo’, Sitzungsberichte der königlich preussischen Akademie der Wissenschaften zu Berlin, Berlin: Reimer, pp. 59-66. Heiberg, J.L. (ed.) (1907), Claudii Ptolemaei Opera Quae Exstant Omnia, vol. 2, Leipzig: Teubner. Hoffmann, Philippe (1987), ‘Simplicius’ Polemics’, in Sorabji (1987), pp. 57-83. Huby, Pamela and Steel, Carlos (trans.) (1997), Priscian: On Theophrastus On Sense-Perception and ‘Simplicius’: On Aristotle On the Soul 2.5-12, London: Duckworth. Joachim, Harold H. (ed.) (1922), Aristotle, On Coming-to-be and Passing-away, Oxford: Clarendon Press. Kneale, William and Kneale, Martha (1962), The Development of Logic, Oxford: Clarendon Press. Krivushina, Anastasia and Fusaro, Diego (trans.) (2007), Democrito: Raccolta dei Frammenti, Interpretazione, e Commentario di Salomon Luria, Milan: Bompiani. Leinkauf, Thomas and Steel, Carlos (eds) (2005), Plato’s Timaeus and the Foundations of Cosmology in Late Antiquity, The Middle Ages, and Renaissance, Leiden: Leiden University Press. Longo, Oddone (ed. and trans.) (1961), Aristotele, De Caelo, Florence: Sansoni. Luria, S. (1933), ‘Die Infinitesimaltheorie der antiken Atomisten’, Quellen und Studien zur Geschichte der Mathematik, Astronomie und Physik, B.2, pp. 106-85. Marcovich, Miroslav (ed.) (1999), Diogenes Laertii Vitae Philosophorum, Stuttgart and Leipzig: Teubner. Marg, Walter (ed. and trans.) (1972), Timaeus Locrus, De Natura Mundi et Animae, Leiden: E.J. Brill. Martin, Th. Henri (1841), Études sur le Timée de Platon, 2 vols, Paris: Ladrange. Mioni, Elpidio (1981), Bibliothecae Divi Marci Venetiarum Codices Graeci Manuscripti, vol. 1, Rome: Istituto Poligrafico dello Stato. Moraux, Paul (1973-2001), Der Aristotelismus bei den Griechen, 3 vols (Peripatoi, 5, 6, and 7.1), Berlin and New York: Walter De Gruyter, Mueller, Ian (trans.) (2004), Simplicius: On Aristotle On the Heavens 2.1-9, London: Duckworth. Mueller, Ian (trans.) (2005), Simplicius: On Aristotle On the Heavens 2.10-14, London: Duckworth. Mueller, Ian (trans.) (2009), Simplicius: On Aristotle On the Heavens 3.1-7, London: Duckworth. Mueller, Ian (forthcoming), ‘Plato asserts, Aristotle objects, Alexander, Proclus, and Simplicius respond’, to appear in the proceedings of a conference on Neoplatonism and Science organised by Christoph Horn and James Wilberding in Bonn, September, 2007. O’Brien, D. (1981), Theories of Weight in the Ancient World, vol. 1 (Democritus: Weight and Size), Paris: Les Belles Lettres and Leiden: E.J. Brill. Perkams, Matthias (2005), ‘Priscian of Lydia, commentator on the “de Anima” in the tradition of Iamblichus’, Mnemosyne 4.58, pp. 510-30. Peyron, Amedeo (1810), Empedoclis et Parmenidis Fragmenta, Leipzig: I.A.G. Weigl. Rabe, Hugo (ed.) (1899), De aeternitate mundi contra Proclum, Leipzig: Teubner. Rashed, Marwan (2007), L’Héritage Aristotelicien, Paris: Les Belles Lettres.

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Rescigno, Andrea (2001), ‘Potamone, interprete del De Caelo di Aristotele’, Lexis 19, pp. 267-82 Sharples, R.W. (1998), Theophrastus of Eresus: Sources for his Life, Influence, and Writings, Commentary, vol. 3.1, Leiden: Brill. Siorvanes, Lucas (1996), Proclus: Neo-Platonic Philosophy and Science, New Haven: Yale University Press. Sorabji, Richard (ed.) (1987), Philoponus and the Rejection of Aristotelian Science, London: Duckworth. Sorabji, Richard (ed.) (1990), Aristotle Transformed: The Ancient Commentators and Their Influence, London: Duckworth. Steel, Carlos (2005), ‘Proclus’ defence of the Timaeus against Aristotle’s objections’, in Leinkauf and Steel, pp. 163-93. Tarán, Leonardo (ed.) (1997), Harold Cherniss: Selected Papers, Leiden: Brill. Taylor, C.C.W (trans.) (1999), The Atomists, Leucippus and Democritus (Phoenix, supplementary vol. 36), Toronto, Buffalo, and London: University of Toronto Press. Verbeke, G. (1945), L’evolution de la doctrine du pneuma du Stoicisme à S. Augustin, Paris: Desclée de Brouwer and Louvain: Editions de l’Institut Supérieur de Philosophie. Vlastos, Gregory (1975), Plato’s Universe, Seattle: University of Washington Press. Wartelle, André (1963), Inventaire des Manuscrits Grecs d’Aristote et de ses Commentateurs, Paris: Belles Lettres. Wildberg, Christian (trans.) (1987), Philoponus: Against Aristotle on the Eternity of the World, London: Duckworth. Wright, M.R. (1981), Empedocles: The Extant Fragments, New Haven and London: Yale University Press. Zeyl, Donald J. (1975), ‘Plato and talk of a world in flux’, Harvard Studies in Classical Philology, 79, pp. 125-48

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. abandon: existanai able: dunatos able, be: dunasthai, eutonein above: anô above, from: anôthen absolute: haplous absolutely: haplôs, pantôs absurd: atopos, apemphainôn absurdity: atopia accept: apodekhesthai, dekhesthai, endidonai accidental: kata sumbebêkos accidentally: kata sumbebêkos account, offer an: apologizesthai account, take into: logizesthai accrue: paragignesthai achieve: tunkhanein act (n.): ergon act (v.): energein acted on, be: paskhein active: energêtikos activity: energeia actual: energeiai (dat.) actuality: energeia, entelekheia actually: energeiai (dat.) add: epagein, prostithenai adduce: epagein, paragein adequate: hikanos adjacent: ephexês admit: dekhesthai, didonai advance: erkhesthai, khôrein affected, be: paskhein affected easily: eupathês affection: pathos affective: pathêtikos agree: homologein, sumphônein agree with: sumphthengesthai agreement, be in: sunaidein

air: aêr akin: sungenês alien: allotrios alike: homoios, sungenês alterable: alloiôtos alteration, causing: alloiôtikos alteration, subject to: alloiôtos alteration: alloiôsis altered, be: alloiousthai always: aei, katholou, pantakhou, pantôs amount: plêthos analogous: analogos analogous, be: analogein angle: gônia angles, having: gegôniômenos animal: zôion animate thing: zôion answer (v.): hupantan antecedent: hêgoumenon antithesis: antithesis apex: koruphê apparent, be: phainesthai appear: phainesthai appear in: epiphainesthai appropriate: oikeios appropriate, be: prosêkein appropriate time: kairos argue: dialegein argue against: antilegein argument: epikheirêma, epikheirêsis art: tekhnê ask: erôtan, zêtein assign: apodidonai, dianemein, didonai assimilate: exomoioun assume: lambanein assume to start: prolambanein assumption: hupolêpsis

174

English-Greek Glossary

atom: hê atomos attack: empiptein balance (n.): zugon base (n.): basis, hedra, puthmên be: einai, huparkhein beautiful: kalos begin: arkhesthai beginning: arkhê belong: huparkhein belong to: prosêkein below: katô below, from: katôthen bend: sunkamptesthai bestow: endidonai between: metaxu bigger, getting (n.): auxêsis black: melas blend (v.): sunkrinein, kerannunai blending (adj.): sunkritikos blending (n.): krasis, sunkrisis blood: haima blunt: amblus body: sôma bone: ostoun book: biblion boundary: horos break apart: diaspan break up: katathrauein, luein brief: brakhus briefly: suntomôs bring: prospherein bring against: hupopherein bring in: paragein bring together: sunagein, sunorizein bronze: khalkos bulk: onkos burn: kaiein burn, able to: kaustikos call (v.): kalein, onomazein, proseirêkein careful: asphalês causal: aitiôdês cause: aitia, aition cease: pauesthai censure: aitiasthai, episkêptein central: mesos centre: kentron, meson certainly: pantôs chance thing: tukhon chance, by: eikê change (intrans.) kineisthai, metabainein, metaballein, metapiptein

change (n.): hupallagê, metabasis, metabolê change (trans.): kinein, methistanai change qualitatively (intrans.): alloiousthai change qualitatively, cause to: alloioun change, causing: kinêtikos change, subject to: kinêtos changed easily: eukinêtos changed, be: kineisthai changing (adj.): kinêtos characterise: kharaktêrizein circle: kuklos circle, moving in a: kuklophorêtikos claim (v.): boulesthai clarify: saphênizein clear: dêlos, enargês, epidêlos, saphês clear, make: dêloun clear, prima facie: prodêlos clearly true: enargês cloak: himation close: engus co-exist: sunuparkhein cold (adj.): psukhros cold (n.): psuxis colder, make: psukhein coldness: psukhrotês collect: athroizein colour: khrôma combine: suntithenai combining (n.): sunthesis come to be: gignesthai come to be in: engignesthai come together: sunelthein, sunerkhesthai, sunienai coming to be (adj.): genêtos coming to be (n.): genesis coming to be, not (adj.): agenêtos coming together (n.): sunodos common character: koinônia common: koinos communion: koinônia compare: paraballein, sunkrinein comparison: sunkrisis compel: anankazein complete (adj.): holoklêros, teleios complete (v.): apotelein, sumplêroun, sumperainesthai completeness: teleiotês completion: teleiôsis completion, come to a: teleioun compose: sunistanai, suntithenai composite (adj.): sunthetos composition: sunthesis

English-Greek Glossary compound (n.) sunthesis compound (v.): suntithenai concede: endidonai conception: ennoia, hupolêpsis conclude: sumperainesthai condensation: puknôsis condense: puknoun condense into liquid: exudatousthai condition: diathesis condition which makes ready: paraskeuê confident, be: tharrein confirm: pistousthai conflict with: makhesthai, sumballein conjoin: suntithenai consequence, be a: hepesthai consequently: akolouthôs consider: ennoein, logizesthai consistently: akolouthôs constituted, be: pephukenai constraint: bia construct: histanai, sunistanai construction: sustasis contact (n.): aphê contain: emperilambanein, periekhein containing: periektikos continuity: sunekheia continuous: sunekhês continuous, make: sunekhizein contract (v.): sustellein contraction: sunairesis contradict: enantia legein, enantiousthai contrariety: enantiôsis contrary: enantios contribute: sunergein converge: sunneuein convex, make: kurtoun cool (v.): psukhein copper: khalkos copy of a text: antigraphê coordinate (adj.): sustoikhos correctly: kalôs cosmos: kosmos craft: tekhnê credible, make: pistousthai criticism: enklêma criticise: euthunein cube: kubos cultured: mousikos cupping glass: sikua cured, able to be: hugiastos custom: ethos cut (v.): temnein cut off (adj.): apolelumenos cut, able to: tmêtikos

175

cutting (adj.): tmêtikos cutting (n.): tomê dark: melas define: horizein definite, be: hôrizesthai demand (v.): apaitein, axioun demonstrate: apodeiknunai demonstration: apodeixis dense: puknos denseness: puknotês denser, make: puknoun depth: bathos depth, without: abathês desire (n.): ephesis desire (v.): ephiesthai, oregesthai, prothumeisthai destroy: aphanizein destruction: phthora determinate, be: hôrizesthai determine: diorizein, horizein develop: sunagein development: ephodos, sunagôgê diagram: katagraphê differ: diapherein difference: diaphora difference, without: adiaphoros different: allos, diaphoros, heteros differentia: diaphora difficult: duskolos difficult to move: duskinêtos difficulty: aporia, duskhereia difficulty, raise a: aporein difficulty, resolve a: euporein difficulty, with: mogis dimension: diastasis direct prosekhês directly: euthus discard: apotithesthai discover: heuriskein discuss: prokheirizesthai disperse: diakheisthai, diaspeirein disposed, be: diakeisthai dissimilar: anomoios dissimilarity: anomoiotês dissolution: dialusis dissolve: dialuein, luein, sunkhôneuein distance: diastêma distant: aphestôs distinction: diakrisis, diorismos distinguish: diairein, diastellein, diorizein distribute: dianemein dive: kataduein

176

English-Greek Glossary

divide: diairein, diakrinein, diistanai divided easily: eudiairetos dividing (adj.): diairetikos divine: theios divisible: diairetos division: diairesis, tomê do away with: aphanizein double: diplasios down: katô drag: helkein drag down: kataspan draw: diagein, graphein, helkein, katagraphein, span draw in: epispan draw together: sunairein draw up: span draw with: sunelkein drive out: exairein dryness: xêrotês earlier (adj.): palaios early: arkhaios earth: gê earth, made of: geêros, geôdês earthen: geôdês ease of motion: eukinêsia easily: eukolôs easy: rhadios edge: peras element: stoikheion elemental: stoikheiôdês eliminate: anairein elongated: makros empty: kenos encounter (v.): entunkhanein end (n.): telos, peras end, reach an: teleioun endow: endidonai endure: diamenein, hupomenein, menein enduring: monimos enflame: puroun enquire: zêtein enter: eisdunein entire: holos entirely: holôs, pantêi entirety: holotês enunciation: protasis equal in bulk: isonkos equal: isos equally: homoiôs equiangular: isogônios equilateral: isopleuros equivalent: isos

escape: diapheugein, pheugein establish: kataskeuazein eternal: aidios evaporate: exaeroun everywhere: pantakhou, pantakhothen, pantêi everywhere, from: pantakhothen evidence: tekmêrion evident: phaneros example: hupodeigma, paradeigma exceed: huperballein, huperekhein, pleonazein excess: huperokhê exercise: energein exert oneself: prothumeisthai exhibit: endeiknusthai experiment (v.): peirasthai explain: aitiasthai, aitiologein, apodidonai, didaskein, exêgeisthai, hupodeiknunai explanation: aitia, apodosis explanation, offer an: kataskeuazein explanation, without: anaitios extend: ekballein extend up: anateinesthai external: exôthen extreme: akros, eskhatos fabricate: plassein fall prey to: enekhesthai fall short: apoleipein false: pseudos fast: takhus faster: thattôn feeble: malakos few: oligos fewer: elattôn fewness: oligotês fight: makhesthai figure: skhêma figure, assign a: skhêmatizein fill: plêroun, sumplêroun fill out: anaplêroun, ekplêroun, sumplêroun fill up: anaplêroun find: heuriskein fine: leptos fine parts, having (adj.): leptomerês fine, make: leptunein fineness: leptotês finite: peperasmenos finitely many: peperasmenos fire: pur fire, be turned into: ekphlogousthai

English-Greek Glossary first: prôtos fit (v.): epharmozein, harmozein flame: phlox flat: platus flee: pheugein flesh: sarx float: epokheisthai float in: epiplein float on: epiplein flow together: surrein follow: akolouthein, hepesthai, paraxein, sunepesthai following: akolouthos foot: pous force (n.): bia force (v.): anankazein, biazein form: eidos, morphê form, give: eidopoiein form, giving (adj.): eidopoios form, without: amorphôtos formal: eidikos frequently: pollakhou, pollakis full: plêrês fundamental: arkhoeidês fuse: sumphuein gap: dialeimma general: koinos general, in: holôs generate: gennân generation: genesis genus: genos give: didonai given boundaries easily: euoristos go: ienai, khôrein go through: epexienai gold: khrusos good: kalos great: megas greater: meizôn greatness: megethos grow: auxesthai grow, able to: auxêtos grow, cause to: auxein growth: auxêsis growth, causing: auxêtikos growth, subject to: auxêtos half-triangle: hêmitrigônon happen: sumbainein, tunkhanein harmonise: sumphônein harmony, out of: asumphônos health: hugeia, hugieia healthy, make: hugiazein

177

hear: akouein heat (n.): thermasia, thermotês heat (v.): puroun, thermainein heat, able to: thermantikos heating (adj.): thermantikos heating (n.): thermansis heaven: ouranos heavenly: ouranios heavens: ouranos heaviness: barutês heavy: barus heavy, be: brithein heavy, equally: isobarês hexagon: hexagônon higher: anôteros hint: ainissesthai hold: katekhein hold up: anekhein hollow: kolpos homogeneous: homogenês hot: thermos house: oikos human: anthrôpeios, anthrôpinos human being: anthrôpos hypothesis: hupothesis hypothesise: hupotithenai hypothetical: hupothetikos icosahedron: eikosaedron ignite: exhaptein ignore: katanôtizesthai ill, be: nosein illness: nosos illness, susceptible to: noseros immediately: amesôs, ephexês, euthus impassive: apathês impede: empodizein imperceptible: anaisthêtos imperishable: aphthartos impose: empoiein impossible: adunatos impulsion: rhopê impulsion, have an: rhepein impulsion, having an: epirrepôn in itself: kath’ hauto, kath’ hautên incline (v.): rhepein include: perilambanein incomplete: atelês incorporeal: asômatos increment: huperokhê indeterminate: aoristos indicate: dêloun, epideiknunai, hupodeiknunai, paradeiknunai, sêmainein

178

English-Greek Glossary

indicate in an obscure way: ainissesthai indication: sêmeion indirectly: kata sumbebêkos indissolvable: adialutos indivisible: adiairetos, atomos infer: sunagein inference: sunagôgê inferior: kheirôn infinite: apeiros infinity, to: ep’ apeiron inflate: phusan inhere: enhuparkhein innovative: kainos insert: paremballein insist: episkêptein insofar as: kath’ ho, kath’ hoson instrument: organon intend: boulesthai intermediate between: metaxu intermediate: mesos interpret: exêgeisthai, hermêneuein intersection: tomê interval: diastasis, diastêma intervene: parempiptein interweaving (n.): paremplokê investigate: skopein, theôrein iron: sidêros isosceles: isoskelês join: sunaptein, suntattein join together: sumpêgnunai judge (v.): krinein just anything: tukhon juxtapose: paratithenai juxtaposition: parathesis keep: phulattein keep contained: katheirgnusthai kind: eidos, genos, tropos kind, of a different: allophulos kind, of the same: homoeidês, homogenês, homophulos, sungenês kinds, of different: anomoeidês knife: makhaira know: eidenai large: megas large parts, having: megalomerês largeness: megethos larger: meizôn last (adj.): eskhatos, teleutaios later: husteros lay together: paraballein

lead (n.): molibdos least (adj.): elakhistos least (adv.): hêkista leave: kataleipein leave out: apoleipein, paralimpanein leave over: apoleipein, enapoleipein left over, be: hupoleipesthai length: mêkos lesser: elattôn letter: stoikheion lie: keisthai lie at the bottom: huphistasthai lie below: huphistasthai, hupokeisthai lie on: epikeisthai lie over: huperkeisthai lie under: hupokeisthai life: hêlikia, zôê light: kouphos, leukos lighter, make: kouphizein lightness: kouphotês lightness, giving: kouphistikos like: homoios like, be: eoikenai likely: eikos limit: peras line: grammê liquefy: khein literate: grammatikos little: brakhus long: makros look at: apidein, blepein, idein, theôrein loose-textured: araios lose: apoballein, apollunai lower (v.): kathiesthai lower (adv.): katô magnitude: megethos maintain: axioun make pure: kathairein many times: pollakis mark: sêmeion mass: onkos material (adj.): hulikos mathematical: mathêmatikos matter: hulê matter, involving: enhulos mean (adj.): mesos mean (v.): sêmainein meaning: ennoia meet together: sumpiptein method: ephodos methodical: emmethodos mina, weighing a: mnaïaios mix (v.): mignunai

English-Greek Glossary mixed: miktos mixture: mixis mobile: eukinêtos mode: tropos moist: hugros moisture: hugrotês monad: monas motion: kinêsis, phora motion up: anodos motion, causing: kinêtikos motion, subject to: kinêtos mould: plassein moulded easily: euplastos mouth: stoma move (intrans.): khôrein, kineisthai, pheresthai move (trans.): kinein move up: anapheresthai moved easily: eukinêtos moved, be: kineisthai movement: hodos moving easily: eukinêtos moving equally quickly: isotakhês multitude: plêthos name (n.): onoma name (v.): onomazein natural: kata phusin, phusei, phusikos naturally: kata phusin naturally constituted, be: pephukenai nature: phusis nature, by: phusei nature, concerning: phusikos nature, student of: ho phusikos nature, study of: phusikê near, be: plêsiazein near, come: plêsiazein necessary: anankaios necessity: anankê need (n.): khreia need (v.): dein, deisthai next: ephexês, loipon notice: ephistanein nourishment: trophê number: arithmos, plêthos object (v.): enistanai, enkalein, hupantan objection: enstasis objections, raise: episêmainein obligated, be: opheilein obvious: enargês obvious, be: phainesthai obviously: dêlonoti occupy: epekhein, katekhein

179

occur: empiptein octahedron: oktaedron offer: paragein, prospherein often: pollakis oldest: presbutatos one (n.): monas one’s own: idios, oikeios only: monos, psilos opinion: doxa opposite: kata koruphên opposite, to be: antikeisthai outside, from: exôthen overtake: prolambanein parallel: parallêlos part: meros, morion, tmêma pass on: diadidonai pass over: parerkhesthai, parienai pass through: diienai passage: rhêsis passive: pathêtikos path: hodos penetrate: eisdunein pentagon: pentagônon per se: kath’ hauto, kath’ hautên perceive: aisthanesthai perceptible: aisthêtos perception: aisthêsis perhaps: isôs periphery: perix perish: phtheiresthai perishable: phthartos perishing (adj.): phthartos perishing (n.): phthora perpendicular: kathetos phenomena: phainomena philosopher: (ho) philosophos piece: morion place (n.): hedra, topos place (v.): tithenai plane: epipedon plausible: eikos plausibly: eikotôs pneuma: pneuma point: sêmeion, stigmê point out: ephistanein portion: meros, morion posit (v.): tithenai position: thesis possible: dunatos possible, be: dunasthai, endekhesthai, exeinai posterior: husteros postpone: hupertithesthai

180

English-Greek Glossary

potentially: dunamei power: dunamis precede: proêgeisthai preceding: proteros precise: akribês precisely: antikrus precision: akribeia predecessors: hoi proteroi predicate: katêgorein present (v.): apodidonai present, be: prokeisthai preserve: diasôzein, phulattein, sôzein press together: sumpilein, sunthlibein prevent: kôluein previous: proteros primary: prôtos principle: arkhê prior: proteros privation: sterêsis problem, make something a: proballein problematic: aporos proceed: proerkhesthai, proienai produce: apergazesthai, sunistanai product: ergon productive: poiêtikos proper: axios, oikeios proportion: analogia proportional: analogos propose: protithenai proposition: protasis prove: deiknunai prove previously: prodeiknusthai proximate: prosekhês proximately: prosekhôs pull: sunelkein pull away: apospan pure: eilikrinês, katharos purpose: skopos put forward: proballein, protithenai put together: sunarmozein pyramid: puramis qua: hêi qualification: diorismos qualitative change: alloiôsis quality: poion, poiotês quantity: megethos, plêthos, poson quicker: thattôn raise the question: ephistanein rarefaction: manôsis rarefy: khein rareness: manotês reach: erkhesthai eis

reason: aitia, aition reasonable: eikos, eulogos reasonably: eikotôs, metriôs recall: anamimnêiskein, hupomimnêskein receive: dekhesthai reckon: logizesthai recognise: eidenai, ennoein, noein reconfiguration: metaplasis recount: historein reduce: apagein refer: apoteinesthai refute: anaskeuazein, antilegein, dielenkhein, elenkhein region: khôra, topos relation: analogia relevant: prosekhês remain: hupoleipesthai, leipein, menein remain fixed: menein remain together: summenein remaining: loipos remove: hupospan report: historein require: apaitein, deisthai required, be: opheilein reshape: metaplattein, metarruthmizein reshaping (n.): metaplasmos, metaskhêmatisis, metaskhêmatismos resist: makhesthai resistance: antereisis resistant: asphalês resolution: analusis, lusis resolve: analuein, luein respect, in every: pantêi responsible, make: aitiasthai rest (n.): monê rest (v.): êremein, menein rest, be at: hêsukhazein rest, cause to: hedrazein restrain: epekhein result (n.): telos result (v.): apobainein, sumbainein right: orthos rise above: epipolazein rise to the top of: epipolazein rise up: anadidosthai rolling easily: eumetakulistos safe: asphalês same way, in the: homoiôs saw: priôn

English-Greek Glossary scalene: skalênos science: epistêmê seat (v.): hedrazein section: kephalaion see: horan, idein, sunidein, theôrein seed: sperma seek: zêtein seek after: anikhneuein seem: dokein, eoikenai seen, be: phainesthai segment: tmêma separate (v.): diakhôrizein, diakrinein, diistanai, khôrizein separate out: ekkrinein separating (adj.): diakritikos separation: diakrisis, diastasis separation out: ekkrisis set: hedrazein set alongside: paratithenai set down: tithenai set out: ektithesthai, paradidonai, paratithenai several times as much: pollaplasios shape (n.): morphê, skhêma shape (v.): skhêmatizein, suskhêmatizein shape, give a: skhêmatizein shape, without: askhêmatistos share in: metekhein sharp: oxus sharp angles, having (adj.): oxugônios sharpness: oxutês show (v.): deiknunai, dêloun side: pleura silver: arguros similar: homoios similarity: homoiotês similarly: homoiôs simple: haplous sink: brithein, kataduein sink below: huphistasthai sink down: huphizanein, katô pheresthai sink to the bottom: huphistasthai size: megethos slow: bradus small: brakhus, mikros, oligos small parts, having: mikromerês smaller: elattôn smallest: elakhistos smallness: brakhutês, mikrotês soft: malakos softness: malakotês solid: stereos

181

space: khôra, topos spark: zôpuros spatial: topikos speak against: anteipein specific: idios specific feature: idiotês specificity: idiotês specify: diorizein sphere: sphaira spherical: sphairikos, sphairoeidês, strongulos square: tetragônon squeeze out: ekthlibein stable, be: bebêkenai stand: histanai starting point: arkhê steady: monimos stone: lithos straight line: eutheia straight line, move in a: euthuporein straightforwardly: antikrus, euthus strength: iskhus strict sense, in the: kuriôs Strife: Neikos strike: empiptein, hupantan strike against: antikrouein strive: hienai, horman stronger: kreittôn study (n.): pragmateia, theôria study (v.): theôrein subject to, be: enekhesthai subject, be a: hupokeisthai sublunary: hupo selênên submit to: hupomenein substance: ousia substance, give: ousioun substratum, be a: hupokeisthai subtract: aphairein succinctly: suntomôs suffice: arkein sufficient: hikanos suggest: hupodeiknunai, hupopherein suitability: epitêdeiotês suitable: epitêdeios, prepôn superiority: huperokhê supervene: epigignesthai support (v.): apologizesthai, stêrizein suppose: hupolambanein, nomizein surface: epipedon, epiphaneia surprising: thaumastos surround: periekhein suspended, be: paraiôreisthai sweet: glukus syllogism, give a: sullogizesthai

182

English-Greek Glossary

syllogism, make a: sullogizesthai systematic: emmethodos take: lambanein, paralambanein take away: apolambanein, anairein, aphairein, huphairein take on: apolambanein, dekhesthai, epidekhesthai, katadekhesthai take to start: prolambanein talent, weighing a: talantiaios teach: didaskein termination: horos text: graphê, lexis thesis: thesis thick: pakhus thick parts, having (adj.): pakhumerês thick parts, having (n.): pakhumereia thickness: pakhutês think: hupolambanein, logizesthai, noein, nomizein, oiesthai think right: axioun thought, be: dokein, phainesthai time: khronos together, be: sumpiptein tool: organon torch: lampas touch (n.): haphê touch (v.): ephaptesthai, haptesthai, sunaptein transfer: metatithenai transferred, be: metapiptein treatise: pragmateia, sungramma triangle: trigônon true: alêthês truly, speak: alêtheuein truth: alêtheia try: peirasthai turn (v.): metabainein, trepesthai turn into air: exaeroun turn to: metienai turning easily: euperitreptos unaffected: apathês unchangeable: ametablêtos unchanging: akinêtos unclear: asaphês undemonstrated: anapodeiktos undergo: paskhein underlie, hupoballesthai, hupokeisthai understand: akouein, apodekhesthai, eidenai, ekdekhesthai, ephistanein,

gignôskein, gnôrizein, hupolambanein, noein unification: henôsis unify: henoun uninflated: aphusêtos unite: henoun unity: henôsis universally: katholou universe: to pan, to holon unlike: anomoios unmoving: akinêtos unnatural: para phusin unnaturally: para phusin unreasonable: alogos up: anô upper: anô use (n.): khreia use (v.): khrasthai use also: proskhrêsthai useful: khrêsimos vacant: diakenos vertex: koruphê vessel: angeion view: doxa view, point of: epibolê visible: horatos void: kenos wall: toikhos want (v.): boulesthai water: hudôr way: tropos weigh: helkein weighed down, be: bareisthai weight: baros weight, giving: baruntikos well: kalôs white: leukos whiteness: leukotês whole: holikos, holos wind: pneuma wish (v.): boulesthai wood: xulon wool: erion word: onoma, rhêma work (n.): ergon worse: kheirôn worthy: axios write: graphein yield to: sunepesthai

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, and 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, 685,8 abathês, without depth, 648,20 (Proclus); 659,29 adiairetos, indivisible, 637,29; 649,2.7 (both with 306a32); see also atomos adialutos, indissolvable, 644,23-31 (4 with 306a19,20) adiaphoros, without difference, 698,25 (with 310b5) adunatos, impossible, 16 occurrences in Simplicius (1 Proclus), 6 in Aristotle aei, always, 39 occurrences in Simplicius (7 Plato), 21 in Aristotle aêr, air, 215 occurrences in Simplicius (12 Proclus, 8 Plato, 7 Alexander, 2 TL) 42 in Aristotle agenêtos, not coming to be, 672,29 agôgê, leading, 681,1 aidios, eternal, 642,21(2); 642,25 (all 3 with 306a10(2)); 672,27; 673,7; 674,10 ainigma, enigma, 655,31 ainigmatôdês, hinting at more obscure matters, 646,12 ainissesthai, to hint, indicate in an obscure way 703,13; 721,26 airesthai, to be removed, 705,26 aisthanesthai, to perceive, 664,16 (Plato); 710,18.21.24; 711,15

aisthêsis, perception, 642,10.24; 643,12 (all 3 with 306a4,17); 655,26 (Potamon); 664,1 (Proclus); aisthêseis translated ‘senses’ at 667,26 (Proclus) aisthêtos, perceptible, 11 occurrences in Simplicius (1 Proclus), 3 in Aristotle aithêr, ether, 646,11 aitia (feminine), reason, cause, explanation, 39 occurrences in Simplicius (3 Alexander, 2 Proclus), 7 in Aristotle aitiasthai, to censure, make responsible, explain, 22 occurrences in Simplicius (1 Plato, 1 Alexander), 1 in Aristotle aitiologein, to explain, 641,5; 670,4 aition, reason, cause, 23 occurrences in Simplicius, 11 in Aristotle aitiôdês, causal, 658,4 akinêtos, unchanging, unmoving, 643,14; 669,24 (Plato) akoinônêtos, not sharing in, 712,22 akolouthein, to follow, 16 occurrences in Simplicius (1 Proclus), 1 in Aristotle akolouthia, sequence, 675,15 akolouthos, following, 702,4; 711,12 akolouthôs, consequently, consistently, 665,18; 678,12; 685,12; 709,18

184

Greek-English Index

akouein, to hear, understand, 640,30; 641,8; 666,24; 692,8; 715,28; 717,2 akribeia, precision, 710,29; 712,16 akribês, precise, 638,26; 649,8 (with 306a27); 675,9.12 (Aristotle); 676,14; 712,13; 718,10; 722,27 akroatês, listener, 706,11 akros, extreme, 21 occurrences in Simplicius, 1 in Aristotle alêtheia, truth, 636,25 (Plato); 643,11.12; 679,19; 724,20 alêthês, true, 14 occurrences in Simplicius (1 Proclus), 1 in Aristotle alêtheuein, to speak truly, 642,31; 643,2 alloiôsis, qualitative change, alteration, 666,5; 695,28; 704,19 alloiôtikos, causing alteration, 696,31; 697,1 (both with 310a29) alloiôtos, alterable, subject to alteration, 696,30 (with 310a28); 701,11 (with 310b19). alloioun, to cause qualitative change, 702,24 alloiousthai, to be altered, to change qualitatively, 696,31; 697,1; 702,13.17.26; 703,22; 704,7 allophulos, of a different kind, 668,3 allotrios, alien, 13 occurrences in Simplicius (1 Proclus), 3 in Aristotle alogos, unreasonable, 637,25; 662,2 (2, with 307a29); 690,5 (with 309b24); also 306b4 amblus, blunt, 668,31 (Proclus); 669,11; 670,24.25.26 (all 3 Proclus) amesos, having nothing between, 721,21 amesôs, immediately, 646,20 ametablêtos, unchanging, unchangeable, 643,17 (Proclus); 644,6.11.16; 645,18 (Proclus) amorphôtos, without form, 644,17; 648,6 (Proclus) amphidoxein, to be in doubt, 676,16 amphoterizein, to have both of two properties, 708,11 anadidosthai, to rise up, 730,19 anaduein, to climb up, 711,13 anagein hupo, to place under, 715,9 anagein pros, to lead back to, 642,25 (with 306a9) anagignôskein, to read, 702,6 anairein, to eliminate, take away,

636,3; 659,16; 660,2 (both with 306b28); 672,29; 679,14; 723,8.13 (with 312b8) anaisthêtos, imperceptible, 650,31 anaitios, without explanation, 665,11 analêpsin ekhein, to pick up on, 686,11 analogein, to be analogous, 718,25.28 analogia, proportion, relation, 16 occurrences in Simplicius (2 Plato), 1 in Aristotle analogos, proportional, analogous, 661,5; 688,28 (with 309b8); 700,1 analuein, to resolve, 633,22; 639,11; 645,14; 648,2.3; 666,11 (all 3 Proclus) analusis, resolution, 644,16; 645,30; 648,1; 674,13 anamimnêiskein, to recall, 638,25; 664,20 (Plato) anankaios, necessary, 676,15; 677,26 (with 308a6); 687,12 (with 309a27); 709,28 (with 311b7); 711,19; 728,14; also 309b25, 310a8, and 312b20 anankazein, to force, compel, 649,3; 680,8; 705,21; 712,2; 722,13 anankê, necessity (usually translated using ‘necessary’), 49 occurrences in Simplicius (4 Plato, 2 Alexander), 16 in Aristotle anapheresthai, to move up, 723,9.17.19; 730,10.24 (both with 313a23) anaplêroun, to fill up or out, 643,17 (Proclus); 651,7; 654,5.10; 655,20 (2; all 4 Potamon); 656,10 (Proclus). 16.18.25 (all 9 with 306b5) anapnoê, breath, 711,14 anapodeiktos, undemonstrated, 642,16.31 anaskeuazein, to refute, 657,12 anateinesthai, to extend up, 646,12 anathumiasis, rising vapour, 701,26 anatithenai, to ascribe, 711,14 anekhein, to hold up, 730,13.19.22 anêr, man,712,12 (referring to Aristotle) angeion, vessel, 657,22; 659,1 (Proclus); 724,4-16 (5 with 312b13) anikhneuein, to seek after, 674,20 anô, up, above, upper, 164 occurrences in Simplicius (7 Plato, 1 Alexander), 45 in Aristotle

Greek-English Index anodos, motion up, 699,29 anômalia, irregularity, 657,5 anomoeidês, of different kinds, 682,27; 683,4 anomoios, dissimilar, unlike, 662,4; 681,19.25.27 (all 3 Plato); 715,10; 717,7 (Plato).12 anomoiotês, dissimilarity, 662,7; 663,6; 671,1 (both Proclus) anôteros, higher, 700,23.26 (both with 310b14); 714,3(2); 724,35; 725,2.12; also 313a9 anôthen, from above, 656,7 (Proclus); 683,13 (with 308b20); 715,18.19.27 anteipein, to speak against, 683,14; 672,32; 673,6 anteirêkein, to have responded, spoken against, 640,24; 690,19 antereisis, resistance, 730,14 anthrôpeios, human, 712,14 anthrôpinos, human, 731,28 anthrôpos, human being, 713,5; 714,28 antidiastolê, contrast, 688,4 antigraphê, copy of a text, 686,1; 698,11 antikeisthai, to be opposite, 672,1.10; 687,27; 716,24.27; 717,23.25; 721,20; 725,1 antikrouein, to strike against, 730,11 (with 313b2) antikrus, precisely, straightforwardly, 658,15; 665,7 antilegein, to argue against, refute, 636,19; 640,31; 679,2; 688,10; 710,28 antilogia, refutation, 694,4 antirropos, balancing, 662,5 antistrephein, to convert, 688,23 antithesis, antithesis, 718,28.29; 727,16 antitithenai, to respond, 663,3 aoristos, indeterminate, 718,31 apagein, to reduce, 644,21; 648,28; 664,26 apaiôroumenos, suspended, 647,24 apaitein, to demand, require, 665,17; 668,20.30 (both Proclus); 695,24; 727,21 apantan, to confront, 663,2 apartasthai, to be detached, 705,21 apathês, impassive, unaffected, 643,19 (2, both Proclus); 665,6 apaxioun, to deny, 703,21 apeiros, infinite, 657,2 (Plato);

185

673,3.4; 674,9; 676,12; 679,4.5; 690,8; see also ep’ apeiron apemphainôn, absurd, 666,7 apergazesthai, to produce, 639,3; 669,25 (Plato) aphairein, to subtract, take away, 638,7.8; 681,18; 717,6 (both Plato); 723,14 aphairesis, abstraction, 649,6 aphanizein, to destroy, do away with, 645,22 (Proclus); 661,6; 667,4 aphestôs, distant, 680,13.15 (both Plato); 716,10 aphikneisthai, to arrive, 703,26 aphthartos, imperishable, 644,24(2); 645,1.9.11 (all with 306a19(2)) aphusêtos, uninflated, 710,13.27; 711,1.11.32; 712,1; 722,31 apidein, to look at, 700,23 aplanês, fixed, 716,20 apobainein, to result, 643,5 (with 306a5) apoballein, to lose, 657,25.28; 658,26 apodeiknunai, to demonstrate,11 occurrences in Simplicius, 0 in Aristotle apodeixis, demonstration, 695,21 apodekhesthai, to accept, understand, 659,13 (with 306b8); 698,19 apodidonai, to assign, explain, present, 39 occurrences in Simplicius (2 Proclus), 5 in Aristotle. apodosis, explanation, 641,6 apoios, qualityless, 665,6 apokathairein, to extract by smelting, 667,16 apolambanein, to take on, take away from, 19 occurrences in Simplicius (2 Potamon), 1 in Aristotle apoleipein, to leave (out or over), to fall short, 10 occurrences in Simplicius (3 Potamon, 1 Proclus), 0 in Aristotle apolelumenos, cut off, 704,5.7.21 (all with 310b34) apollunai, to lose, 661,1 apologizesthai, to offer an account, to support, 691,26; 693,6; 730,26 apopallomenos, rebounding, 706,24 apopêdan, to bounce off, 706,24 (with 311a11)

186

Greek-English Index

apophainesthai, to assert, 678,21 apophaskein, to deny, 680,12 aporein, to raise a difficulty, 656,19; 659,6 (Proclus); 669,4; 694,6.10 (Alexander); 695,3 (all 3 with 310a17); 706,17; 729,28.32 (both with 313a16) aporia, difficulty, 646,19; 677,22; 688,28 (with 309b10); 692,30 (with 310a7); 709,17; 730,7.9.15 aporos, problematic, 712,9 apospasthai, to be pulled away, 681,4.6; 715,9 apotelein, to bring to completion, 639,2.4.22 (Plato); 669,13 apotelesma, finished thing, 643,7 apoteinesthai pros, to refer to, 665,5; 679,7 apotexis, giving birth, 704,11 apothesis, loss (of weight), 711,15 apotithesthai, to discard, 705,18; 711,13 apsukhos, inanimate, 704,16 araios, loose-textured, 678,14.15 arguros, silver, 667,15; 668,4; 717,2 arithmos, number, 639,22 (Plato); 642,25; 647,7; 651,17; 653,2 (Potamon); 656,31 (Plato); 673,3 arkein, to suffice, 680,9; 715,31; see also arkeisthai arkeisthai, to content oneself, 728,6 arkhaioprepôs, in an old-fashioned way, 698,13 arkhaios, early, 684,22 (with 308b31); also 310b2 arkhê, starting point, principle, beginning, 36 occurrences in Simplicius, (2 Plato, 1 TL, 1 Alexander), 5 in Aristotle; ex arkhês, translated ‘original’, ‘initial’, ‘first’ at: 652,20 (Potamon); 656,27; 706,20 (with 311a10); 721,8; 728,14; 730,14 arkhesthai, to begin, 715,16.18 arkhoeidês, fundamental, 638,27; 641,14.16.21 arrepês, without impulsion, 711,5 asaphôs, in an unclear way, 639,13 (Plato); 640,4 (Alexander quoting Plato); 703,13 askhêmatistos, without shape, 658,3 asômatos, incorporeal, 648,16.22 (Proclus); 673,8; 674,11 asphalês, careful, resistant, safe,

636,25 (Plato); 649,24; 692,31 (with 310a6); 716,18 asthenês, weak, 731,17 (with 313b21) astron, star, 674,7 astronomos, astronomer, 641,23 asumphônos, out of harmony, 661,20 (with 306b30); 727,8 ataktos, disordered, 650,4 atelês, incomplete, 703,11.18; 704,10.13; 705,23 athroizesthai, to be collected, 681,16 (Plato); 693,21; 717,4 (Plato) atomos, indivisible; 19 occurrences in Simplicius (5 Alexander), 2 in Aristotle; the feminine hê atomos, used by Simplicius (from the Epicurean hê atomos phusis) is usually translated ‘atom’. atopia, absurdity, 664,26 atopos, absurd, 40 occurrences in Simplicius (1 Alexander), 4 in Aristotle autophuôs, spontaneously, 713,7 auxêsis, growth, getting bigger, 695,26; 704,20; 718,27 auxesthai, to grow, to be caused to grow, 696,31.32; 702,16.26.27.31; 703,22; 704,7 auxêtikos, causing growth, 696,32 (2, both with 310a29); 702,28 auxêtos, able to grow, subject to growth, 696,30 (with 310a28); 701,11.12 (both with 310b20(2)); also 310b26. axios, worthy, proper, 637,5; 662,31; 731,27 axioun, to maintain, think right, demand, 666,3 (with 307a30); 679,7.30 (with 308a18); 709,2 bareisthai, to be weighed down, 710,22 baros, weight, 78 occurrences in Simplicius (2 Alexander), 25 in Aristotle baruntikos, giving weight, 697,13.17; 698,12 (all with 310a34) barus, heavy, 278 occurrences in Simplicius (5 Plato, 4 Alexander, 1 Aristotle), 61 in Aristotle barutês, heaviness, 47 occurrences in Simplicius, 0 in Aristotle basis, base, 638,30; 646,9 (TL); 655,15 (Potamon); 663,6.9.13 (all 3 Proclus); 680,5

Greek-English Index bathmos, stage, 718,35 bathos, depth, 646,23; 648,21 (Proclus); 656,22 (2, both Plato); 656,24; 710,19 bebaiôs, firmly, 715,13 bebêkenai, to be stable, 662,4-32 (4 with 307a1 and 8) belonê, needle, 730,3 (with 313a19) bia, force, constraint, 11 occurrences in Simplicius (3 Plato), 1 in Aristotle biazesthai, to force, to be forced, 16 occurrences in Simplicius (6 Plato, 1 Proclus), 1 in Aristotle biblion, book, 14 occurrences in Simplicius, 0 in Aristotle blepein, to look at, 643,6; 661,19.28 (both with 306b31); 707,15.22 (both with 311a18); 722,8 boêthein, to help, 664,29 bôlos, clod of earth, 695,5 boulesthai, to intend, wish, want, claim, 17 occurrences in Simplicius (1 Proclus), 3 in Aristotle braduteron, more slowly, 625,27.30; 678,32; also 308b21 and 313a15 brakhus, small, little, brief, 638,9; 656,26(2).27; 703,1; 712,16 brakhutês, smallness, 671,30 brithein, to be heavy, to sink, 712,10; 726,16.17 deiknunai, to show, prove, 77 occurrences in Simplicius (1 Plato, 1 Alexander), 1 in Aristotle dein, to need, 702,27; 703,1 deisthai, to need, require, 669,15; 702,6.31; 703,30 dekhesthai, to receive, take on, accept, admit, 12 occurrences in Simplicius (4 Plato, 1 Alexander), 0 in Aristotle dektikos, receptive, 703,2 (with 310b29) dêlonoti, obviously, 643,5; 664,18; 687,25 dêlos, clear, 39 occurrences in Simplicius (1 Alexander, 3 Plato), 11 in Aristotle dêloun, to make clear, show, indicate, 18 occurrences in Simplicius, 0 in Aristotle dêmiourgia, creation, 695,6 dêmiourgos, Creator, 731,26 despotês, Lord, 731,25

187

diadidonai, to pass on, 642,15 (Plato); 660,27 diadokhos, succeeding, 640,25 diagesthai, to be drawn, 651,8.15 diairein, to divide, distinguish, 46 occurrences in Simplicius (10 Proclus, 1 Plato), 5 in Aristotle diairesis, division, 11 occurrences in Simplicius (3 Proclus), 1 in Aristotle diairetikos, dividing, 10 occurrences in Simplicius (1 Proclus), 1 in Aristotle diairetos, divisible, 643,25.26 (both Proclus); 649,3.6.23 (all 3 with 306a26b2(3)); 666,21; 731,11; also 305b33 diakeisthai, to be disposed, 705,20.22 diakenos, vacant, 650,23; 655,1; 657,3 diakheisthai, to disperse, 657,23 diakhôrizein, to separate, 667,15 diakrinein, to separate, divide, 12 occurrences in Simplicius (2 Plato, 2 Proclus), 2 in Aristotle diakrisis, separation, distinction, 664,15 (Plato); 667,17 (with 307b3); 673,12; 704,29 diakritikos, separating, 667,26 (Proclus); 668,1; 669,3 (Proclus) dialegein, to argue, take issue with, 673,9; 727,22; 729,11 dialeimma, gap, 687,3.4 (Plato) dialuein, to dissolve, 36 occurrences in Simplicius (3 Alexander, 2 Plato, 1 Proclus), 1 in Aristotle dialusis, dissolution, 636,10 (with 305b30); 650,10; 673,13; also 306a1 diamartanein, to be mistaken, 662,14 (with 307a4) diamenein, to endure, 646,8 (TL); 657,15.16.17.27 (all 4 with 306b11) (hê) diametros, diameter, 679,36 dianemein, to distribute, assign, 639,5; 661,28 (with 306b31) diapherein, to differ, 20 occurrences in Simplicius (1 Proclus), 5 in Aristotle. diapheugein, to escape, 642,23 diaphônein, to disagree, 644,7 diaphônia, disagreement, 640,28 diaphora, difference, differentia, 55 occurrences in Simplicius, 9 in Aristotle diaphoros, different, 16 occurrences

188

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in Simplicius (2 Plato), 0 in Aristotle diaphulattein, to protect, 642,30 (with 306a13) diaplasis, formation, 704,11 diasôzein, to preserve, 657,3 diaspan, to break apart, 731,8-16 (5 with 313b11,13, and 18) diaspeiresthai, to be dispersed, 639,21 (Plato); 730,21 diastasis, dimension, interval, separation, 655,31 (Alexander); 656,2; 679,6; 680,1.2; 715,21; translated ‘contrast’ at 312a14 diastellein, to distinguish, 719,19 diastêma, interval, distance, 651,6; 716,1 diathesis, condition, 669,13 diatithesthai, to be arranged, 657,9 didaskein, to teach, explain, 672,21.28; 674,3; 711,22; 721,10 didonai, to admit, assign, give, 647,24; 664,5 (Proclus); 689,27; 699,26 dielenkhein, to refute, 673,9; 729,11 diienai, to pass through, 670,5.7 (with 307b13 and 14) diistanai, to separate, divide, 648,21 (Proclus); 679,36; 681,24 (Plato); 684,1; 689,31 (with 309b23); 691,8 dikhôs, in two ways, 636,7 (with 305b29); 642,7 diorismos, distinction, qualification, 669,15; 688,10.25; 717,17 diorizein, to determine, distinguish, specify, 41 occurrences in Simplicius (2 Plato, 2 Proclus), 16 in Aristotle dipêkhus, two feet long, 705,8 diplasios, double, 651,17.20; 683,22 dogma, belief, 680,26 dokein, to seem, to be thought, 40 occurrences in Simplicius (2 Plato), 7 in Aristotle doxa, view, opinion, 642,24.27 (both with 306a8); 675,15; 679,4; 682,15.16; 690,18; 694,3; 710,35 drosos, dew, 701,28 dunamei, potentially, 37 occurrences in Simplicius, 3 in Aristotle dunamis, power, 32 occurrences in Simplicius (10 Proclus, 2 Plato, 2 Alexander), 1 in Aristotle; see also dunamei

dunasthai, to be possible, able, 41 occurrences in Simplicius (5 Alexander, 2 Plato), 3 in Aristotle dunatos, possible, able, 10 occurrences in Simplicius (1 Plato), 0 in Aristotle duskhereia, difficulty, 687,13 (with 309a29) duskinêtos, difficult to move, 669,10; 670,27; 671,17 (2; last 3 Proclus) duskolos, difficult, 683,15 eidenai, to know, understand, recognise, 662,31; 675,9; 679,23; 686,23; 691,25; 692,16; 717,17; 719,29 eidikos, formal, 700,4.10.12 (Alexander) eidopoiein, to give form, 640,9 (Alexander); 650,8 (Proclus); 657,14; 673,15; 675,1; 676,5; 700,2; 718,14 eidopoios, giving form, 640,11 (Alexander); 673,15; 700,1.16.29; 722,1 eidos, form, kind, 89 occurrences in Simplicius (5 Plato, 4 Proclus 2 Alexander, 1 TL), 6 in Aristotle eikê, by chance, 667,1 eikôn, image, 717,1 eikos, likely, plausible, reasonable, 639,24 (Plato); 641,22; 657,3; 710,24; 724,27 eikosaedron, icosahedron, 20 occurrences in Simplicius (1 Proclus), 0 in Aristotle eikotôs, reasonably, plausibly, 10 occurrences in Simplicius (2 Proclus, 1 Plato), 0 in Aristotle eilikrinês, pure, 657,3.7 eisdunein, to enter, penetrate, 656,10; 664,8 (both Proclus); 668,2 eispempesthai, to be introduced, 712,13 eisphusômenos, blown in, 712,15 eisrein, to flow into, 724,6 ei tukhoi, for example, 704,11; 705,8 (2) ekballein, to extend, 10 occurrences in Simplicius (9 Potamon), 0 in Aristotle ekdekhesthai, to understand, 663,2; 672,7 ekkrinesthai, to be separated out, 636,5; 673,11

Greek-English Index ekkrisis, separation out, 636,3; 673,11.12 ekphainein, to proclaim, 731,27 ekphlogousthai, to be turned into fire, 661,3 ekplêroun, to fill out, 652,18; 653,6 (both Potamon); 655,5.7.8 (all 3 Alexander); 655,9.11.12.22.25 (all 5 Potamon); 659,24 (Alexander); 660,14 ekstênai, to rise, 724,35 ekthlibomenos, squeezed out, 693,17 (with 310a10); 712,29; 713,16 ektithesthai, to set out, 654,13; 670,6; 677,30; 681,11; 682,16; 694,4; 729,30; 730,7 ektrepein, to divert, 650,7 elakhistos, smallest, least, 662,2.3.16 (all 3 with 306b34); 711,3 elattôn, lesser, smaller, fewer, 73 occurrences in Simplicius (5 Plato, 5 Proclus, 1 Alexander), 13 in Aristotle elenkhein, to refute, 638,6; 643,9; 661,17; 673,4 ellampein, to outshine, 717,3 elleipês, elliptical, 719,30 embruon, embryo, 704,11 emmesos, having something between, 721,21(2) emmethodos, methodical, systematic, 654,12; 656,5 emperilambanesthai, to be contained, 685,18 (with 309a6) emphainein, to produce an appearance, 661,10 emphusêsis, what is blown in, 712,15 empiptein, to attack, strike, occur, 638,17; 643,20; 648,20 (both Proclus) empodizein, to impede, 705,11.15.25 (all 3 with 311a8); 708,1 empoiein, to impose, 660,24; 666,28 (Plato); 672,5 (Alexander) empsukhos, living, 703,9 empureuma, ember, 677,11 enantios, contrary, 91 occurrences in Simplicius (9 Proclus, 6 Plato), 12 in Aristotle; enantia legein translated ‘contradict’ enantiôsis, contrariety, 669,12.17.18; 672,8,11; 722,1 enantiousthai, to contradict, 684,29

189

enapoleipesthai, to be left over in, 651,2 enargeia, what is clear or clearly true, 642,16; 678,18 enargês, clear, clearly true, obvious, 11 occurrences in Simplicius (1 Potamon), 0 in Aristotle endeiknusthai, to indicate, exhibit, 641,27 (Plato); 658,17; 699,21 endeiktikos, capable of being exhibited, 641,27 endekhesthai, to be possible, 659,16.18 (both with 306b22); 685,10 (with 309a2); also 310a5 and 311b11 and 31 endidonai, to bestow, endow, accept, concede, 645,16; 658,7; 660,18; 700,3.29 enekhesthai, to fall prey to, be subject to, 687,13 (with 309a29); 693,11(2) energeia, activity, actuality, 21 occurrences in Simplicius, 1 in Aristotle; see also energeiai energeiai (dat.), actually, actual, 35 occurrences in Simplicius, 0 in Aristotle; to energeiai, translated ‘actuality’ energein, to act, exercise, 667,20; 702,28.30; 706,1 energêtikos, active, 674,14; 703,22 engignesthai, to come to be in, 636,26 (Plato); 637,7 (Plato); 672,16; 674,15; 719,12 engus, close, 667,4; 700,14 (Alexander); 703,13.19.29; 704,3 (all 4 with 310b32) enhulos, involving matter, 665,19.22 enhuparkhein, to inhere, 660,31; 685,22 (with 309a11); 699,11 enistanai, to object, 638,15; 640,8; 647,4; 658,25; 667,22; 674,3; 730,8.15.17 (all 3 with 313b3 and 4) enkalein, to object, 656,17 enklêma, criticism, 686,11.20 ennoein, to recognise, consider, 659,34; 664,16 (Plato) ennoia, meaning, conception, 637,3; 686,2; 689,28; 698,10 enstasis, objection, 21 occurrences in Simplicius, 0 in Aristotle entelekheia, actuality, 703,26; 705,3.5.6.7 (all 4 with 311a4 and 5)

190

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entunkhanein, to encounter, 643,21 (Proclus); 653,9 eoikenai, to seem, to be like, 15 occurrences in Simplicius (1 Proclus), 3 in Aristotle epagein, to adduce, add, say, 41 occurrences in Simplicius, 0 in Aristotle epallattesthai, to be interchanged, 658,23 epamphoterizein, to be both heavy and light, to go in both directions, 695,23; 719,25; 720,8; 727,1 ep’ apeiron, to infinity, 714,15.24.25 epeigesthai, to move rapidly, 705,24 epekhein, to occupy (652,3); to restrain (311a9) epexienai, to go through, 722,27 ephaptesthai, to touch, 710,22 epharmozein, to fit, 658,34; 659,3.7 (all 3 Proclus); 662,12; 682,14.26 (both with 308b3) ephesis, desire, 681,1; 711,7 ephexês, next, adjacent, immediately, 18 occurrences in Simplicius, 2 in Aristotle ephiesthai, to desire, 684,17; 711,8 ephistanein, to point out, raise the question, notice, understand, 11 occurrences in Simplicius, 0 in Aristotle ephodos, method (653,7); development (672,25) epiblêtikos, insightful, 684,25 epibolê, point of view, 661,27; 672,4 (Alexander) epideiknunai, to indicate, 702,25 epidekhesthai, to take on, 720,13 epidêlos, clear, 682,8 epidiarthrôsis, further articulation, 686,12 epigignesthai, to supervene, 660,23; 704,20; 720,11 epikheirêma, argument, 15 occurrences in Simplicius, 0 in Aristotle epikheirêsis, argument, 663,3 epikeisthai, to lie on, 710,18.20.24; 731,22 epikheisthai, to be poured over, 724,7 epimimnêskesthai, to mention, 686,18 (with 309a25) epipedon, plane, surface, 90 occurrences in Simplicius (8

Proclus, 4 Potamon, 4 Alexander, 1 TL, 1 Plato), 8 in Aristotle epiphainesthai, to appear in, 660,25 epiphaneia, surface, 656,21; 659,5 (Proclus); 723,35; 724,12 epiphora, introduction, 725,31 epiplein, to float on or in, 730,1.4 (with 313a17 and 20) epipolaiôs, superficially, 640,30 epipolastikos, able to rise, 701,17 epipolazein, to rise (above or to the top of), 65 occurrences in Simplicius, 16 in Aristotle epiprepeia, appearance, 661,10 epirrepôn, having an impulsion, 724,28 episêmainein, to raise objections, 701,30 episkêptein, to insist, censure, 685,25; 729,7 epispasthai, to be drawn in, 724,18 epistasthai, to be erected, 651,13 epistêmê, science, 643,7 (with 306a6); 649,4.8 (both with 306a27) epitêdeios, suitable, 667,7.8; 719,14.17 epitêdeiotês, suitability, 667,3; 703,14.20.29 epiteleisthai, to come about, 681,1 epokhê, holding (of breath), 711,14 epokheisthai, to float, 712,6; 730,16 epopteuein, to behold, 731,27 êremein, to rest, 699,31 ergon, act, product, work, 643,7.11 (both with 306a16); 671,25.29 (both with 307b21 and 22); 731,27 erion, wool, 643,10; 684,28; 685,16 (both with 309a5) erkhesthai, to advance (erkhesthai eis sometimes translated ‘to reach’), 12 occurrences in Simplicius (1 Plato), 6 in Aristotle erôtan, to ask, 636,24 (Plato); 657,6 eskhatos, extreme, last, 52 occurrences in Simplicius (4 Plato), 10 in Aristotle esterêmenos, deprived, 690,6 ethein, to be one’s custom, 640,27 ethizesthai, to become accustomed, 681,14 ethos, custom, 677,28 eudiairetos, easily divided, 731,1-24 (7 with 313b6-16(4)) euêthês, naive, 642,15

Greek-English Index eukinêsia, ease of motion, 662,20; 670,18 (Proclus) eukinêtos, moving easily, easily moved or changed, mobile, 12 occurrences in Simplicius (4 Proclus), 6 in Aristotle eukolôs, easily, 646,2; 662,6 eukrasia aerôn, moderate climate, 702,32 eulogos, reasonable, 642,8 (with 306a3); 665,31; 711,16; 716,25 (with 312a7); also 306a22 eumetakulistos, easily rolling, 662,19 euoristos, easily given boundaries, 731,3.5.6 (all with 313b9) eupathês, easily affected, 731,8 euperitreptos, turning easily, 662,19 euplastos, easily moulded, 659,9 euporein, to resolve a difficulty, 685,23 eutheia, straight line, 24 occurrences in Simplicius (8 Potamon), 1 in Aristotle euthunein, to criticise, 686,8 euthuporein, to move in a straight line, 672,28; 674,8; see also euthuporoumenos euthuporoumenos, moving in straight line, 672,28; 674,8 euthus, directly, immediately, straightforwardly, 645,29; 669,20; 689,26; 694,16 (Alexander) eutonein, to be able, 730,26 exaeroun, to evaporate, turn into air, 647,23; 661,3 exairein, to drive out, 667,18.24 (Proclus) (both with 307b4); see also exêirêmenos exaptein, to ignite, 646,8 (TL); 705,14 exêirêmenos, transcendent, 676,12 exêgeisthai, to interpret, explain, 644,29; 686,4; 692,8; 707,14 exêgêtês, exegete, 700,9 exeinai, to be possible, 690,9 existanai, to abandon, 681,5; 696,13; 711,34 exomoiousthai, to be assimilated, 650,9 (Proclus); 724,23 exôthen, external, from outside, 660,10 (Proclus); 702,34; 703,1 (both with 310b26) exudatousthai, to condense into liquid, 701,27 exumnein, to hymn, 646,11

191

gê, earth, 360 occurrences in Simplicius (12 Alexander, 11 Proclus, 5 Plato, 3 TL), 38 in Aristotle geêros, made of earth, 713,11 (with 311b20); also 308b14 gegôniômenos, having angles, 665,21 genesis, coming to be, generation, 47 occurrences in Simplicius (4 Plato, 2 Proclus), 5 in Aristotle genêtos, coming to be (adjective), 638,17; 672,28; 673,1.7; 674,10; 675,2 gennân, to generate, 637,20; 640,10 (Alexander); 642,3 (with 306a2); 646,7 (TL); 659,30 (with 306b26); 687,9; 690,28; 691,13; 704,12 genos, genus, kind, 24 occurrences in Simplicius (11 Plato), 2 in Aristotle geôdês, earthen, made of earth, 681,24 (Plato); 712,4.7.11; also 313a20 gignesthai, to come to be, 195 occurrences in Simplicius (12 Plato, 11 Alexander, 6 Proclus, 3 Potamon, 1 TL), 12 in Aristotle gignôskein, to understand, 673,2; 674,17; 709,4 glukus, sweet, 713,29(2) gnôrizein, to understand, 672,18 gônia, angle, 77 occurrences in Simplicius (14 Potamon, 12 Proclus, 3 Alexander, 2 Plato), 7 in Aristotle grammatikê, ability to read, 706,1 grammatikos, literate, 695,10(2); 696,4.21.22; 705,31 grammê, line, 656,1.7; 676,7 graphê, text, 686,3; 701,30; 719,29.30 graphein, to write, draw, 13 occurrences in Simplicius (1 Potamon), 0 in Aristotle haima, blood, 723,21-724,19(4) haphê, contact, touch, 659,1 (Alexander); 660,17; 661,4; 667,26 (Proclus) haplôs, absolutely, 197 occurrences in Simplicius (2 Alexander, 1 Proclus), 26 in Aristotle haplous, simple, absolute, 29 occurrences in Simplicius (2 Proclus), 2 in Aristotle; see also haplôs

192

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haptesthai, to touch, 657,18 (with 306b12); 660,16; 661,32; 662,16 (both with 306b34); 723,26; 724,22 haptos, tangible, 722,14 harmozein, to fit, 690,25.30 hedra, base, place, 662,3; 669,23 (Plato) hedrazein, to set, seat, cause to rest, 645,19 (Proclus); 646,10; 712,8; 715,14 hêgoumenon, antecedent (of a conditional), 663,25; 697,16 hêkista, least (adverb), 662,4.16 (both with 306b34) hêlikia, life, 684,22 (with 308b31) helkein, to drag, draw, weigh, 11 occurrences in Simplicius (3 Plato), 1 in Aristotle hêmisphairion, hemisphere, 679,20 (with 308a26) hêmitetragônon, half-square (the word used in TL for the isosceles right triangle), 638,31 hêmitrigônon, half-triangle (the word used in TL for the right triangle with angles of 30 and 60 degrees), 11 occurrences henôsis, unity, unification, 660,7 (Proclus).23; 723,31; 724,18 henousthai, to be united, be unified, 660,18.21.29; 723,35; 724,1.3.10.12; also 307b2 hepesthai, to follow, be a consequence. 12 occurrences in Simplicius (1 Proclus), 0 in Aristotle hermêneuesthai, to be interpreted, 698,14 hêsukhazein, to be at rest, 713,14.15 (both with 311b23) heuriskein, to find, discover, 15 occurrences in Simplicius, 0 in Aristotle hexagônon, hexagon, 20 occurrences in Simplicius (8 Potamon, 4 Alexander), all with 306b7) hienai, to strive, 703,20 hikanos, sufficient, adequate, 675,11 (Aristotle); 688,27 (with 309b9); also 308a24, 308b30,33 himation, cloak, 643,8.9; 660,25 histanai, to stand, construct, 650,19; 651,12; 680,24 (Plato); 681,18 (Plato); 715,13; 717,6 (Plato)

historein, to report, recount, 641,7; 652,9; 655,28; 675,16 hodos, path, movement, 641,26; 682,2; 684,5 (all 3 Plato); 695,13 holikos, whole, 674,5 holoklêros, complete, 704,5 holoskherôs, in a rough and ready way, 665,11 holos, whole, entire, 34 occurrences in Simplicius (4 Alexander, 4 Proclus, 1 Plato), 3 in Aristotle; to holon translated ‘universe’ at 681,12 (Plato) and 306b5; see also holôs holôs, in general, entirely, at all, 27 occurrences in Simplicius (2 Alexander), 5 in Aristotle holotês, entirety, 658,27 (Proclus); 660,31; 710,25 homoeidês, of the same kind, 682,24.27; 684,14 (all 3 with 308b8); 729,11 homogenês, homogeneous, of the same kind, 642,20 (with 306a11); 684,14 (with 308b22) homoios, similar, like, alike, 44 occurrences in Simplicius (5 Plato, 5 Proclus, 3 Alexander), 9 in Aristotle; see also homoiôs homoiôs, similarly, equally, in the same way, 38 occurrences in Simplicius (2 Plato, 2 Alexander, 1 Potamon), 11 in Aristotle homoiotês, similarity, 14 occurrences in Simplicius (2 Proclus, 1 Plato), 1 in Aristotle homologein, to agree, 642,18 (with 306a6); 648,9 (Proclus); 657,5; 663,21; 686,19 (with 309a26); 711,7 homologêma, agreement, 678,20 homophulos, of the same kind, 667,15.16.18 (all with 307b1-4(3)) horan, to see, 14 occurrences in Simplicius (3 Plato, 2 Proclus), 5 in Aristotle horatos, visible, 664,12 (Proclus); 722,13 horizein, to define, determine, 673,3; 683,16; 718,31; 729,3; 731,4; see also hôrizesthai hôrizesthai, to be determinate or definite, 31 occurrences in Simplicius, 4 in Aristotle

Greek-English Index horman, to strive, 730,21 (with 313b4) horos, boundary, termination, 679,5; 714,18 hudôr, water, 201 occurrences in Simplicius (12 Proclus, 7 Alexander, 4 Plato, 2 TL), 45 in Aristotle hugeia/hugieia, health, 701,10.12; 702,33; 703,3 (all 4 with 310b18-30(4)); 707,3; 719,5 hugiainein, to be healthy, 719,7.9 hugiastos, able to be cured, 10 occurrences in Simplicius, 7 in Aristotle hugiazein, to make healthy, 702,27.32(2) hugros, moist, 643,18 (Proclus); 646,8 (2, both TL); 669,22 (Plato); 712,14; 724,22; 731,3.6 hugrotês, moisture, 636,18; 641,2; 672,1; 719,13; 720,13; 722,2 hulê, matter, 107 occurrences in Simplicius (5 Alexander, 2 TL), 16 in Aristotle hulikos, material, 643,9; 672,2; 700,4,10.12.14.15 (last 3 Alexander) humnos, hymn, 731,26 hupallagê, change, 702,5 hupallattesthai, to be exchanged, 658,19 hupantan, to object, answer, strike, 640,29; 645,15; 647,4; 649,28; 656,6; 665,16; 670,4; 682,17; 730,13 huparkhein, to belong, to be, 18 occurrences in Simplicius, 4 in Aristotle huperballein, to exceed, 651,29; 654,11 (Potamon); 655,6 (Alexander); 731,13 (with 313b9); also 309a31; see also huperekhein huperekhein, to exceed, 651,5; 685,28 (with 309a14); 727,11 (with 312b32); 728,26 (with 313a12); see also huperballein huperkeisthai, to lie over, 675,29; 699,7.9.22; 707,18; 724,33; 730,22 huperokhê, increment, excess, superiority, 685,32; 701,13 (with 310b21); 731,29 huperthetikos, superlative, 713,28 hupertithesthai, to postpone, 675,13; 676,15

193

huphaireisthai, to be taken away, 723,18 (with 312b15); 725,5 huphantikê, weaving, 643,7.9 huphistanai, to establish, 701,18; see also huphistasthai huphistasthai, to lie below or on the bottom, to sink below or to the bottom, to be constituted, 51 occurrences in Simplicius, 14 in Aristotle huphizanein, to sink down, 678,13; 680,28 hupoballesthai, to underlie, 721,11 hupodeigma, example, 719,5 hupodeiknunai, to suggest, indicate, explain, 688,26; 689,16; 721,12 hupokeisthai, to lie under or below, underlie, be a substratum or subject, 54 occurrences in Simplicius (2 Alexander, 1 TL), 2 in Aristotle hupolambanein, to suppose, think, understand, 681,10; 697,5 (with 310a22,30); 698,21 (with 310b1) hupoleipesthai, to remain, be left over, 651,6; 656,11 (Proclus) hupolêpsis, conception, assumption, 642,31; 707,10; also 303a30 hupomenein, to endure, submit to, 636,29; 643,1 (with 306a13); 643,30; 649,22 hupomimnêskein, to recall, 669,17; 712,24; 714,26; 720,27 huponoia, deeper understanding, 642,27 hupopherein, to suggest, to bring against, 687,24; 692,31 hupo selênên, sublunary, 645,20 (Proclus); 674,7; 675,1,8; 676,21; 716,21 hupospan, to remove, 706,22 (with 311a10); 723,7-724,29 (6 with 312b6 and 17); 729,19 hupostasis, reality, 704,8 hupostatikos, able to sink, 701,18 hupotassein, to append, 640,27 hupothesis, hypothesis, 16 occurrences in Simplicius (1 Alexander), 1 in Aristotle hupothetikos, hypothetical, 668,14; 714,13 hupotithenai, to hypothesise, 32 occurrences in Simplicius (1 Plato, 1 Aristotle), 0 in Aristotle

194

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husterizein, to fall more slowly, 693,16 (with 310a10) husteros, later, posterior, 11 occurrences in Simplicius, 0 in Aristotle iatrikê, art of medicine, 723,23 iatrikos, medical, 723,23 idein, to see, look at, 641,29; 643,15 (Proclus); 660,25; 663,3; 664,14 (Plato); 677,28 (with 308a4); 729,28 (with 313a6) idios, specific, one’s own, 11 occurrences in Simplicius, 0 in Aristotle idiotês, specific feature, specificity, 644,12; 658,31; 670,27 (both Proclus); 671,16; 717,32 idiôtikôs, in an amateurish way, 641,6 ienai, to go, 680,6; 705,3-6 (3 with 311a4) illesthai, to be wound, 662,33 isarithmos, equal in number, 725,27 iskhus, strength, 731,10.13.14 (all with 313b16 and 19) isobarês, equally heavy, 684,30; 685,2 (both with 308b34) isogônios, equiangular, 650,24; 651,3.30; 652,1; 654,20 (Alexander) isonkos, equal in bulk, 685,1.2; 691,35 isopleuros, equilateral, 14 occurrences in Simplicius (1 Potamon, 1 Alexander), 0 in Aristotle isorropos, having equal impulsion, 685,1 isos, equal, equivalent, 57 occurrences in Simplicius (8 Potamon, 2 Alexander, 1 Plato, 1 Proclus), 6 in Aristotle; see also isôs isôs, perhaps, 642,22 (with 306a9); 656,15; 657,9; 659,28; 688,4; 695,27; 730,24; also 307a15 isoskelês, isosceles, 638,27.31; 639,17 (Plato); 644,10.12.14 isotakhês, moving equally quickly, 689,2.8; 729,13 isousthai, to be made equal, 726,2 kaiein, to burn, 11 occurrences in Simplicius (1 Proclus), 6 in Aristotle kainos, innovative, 684,23.25 (both with 308b31)

kairos, appropriate time, 640,27; 676,15; 694,4; 709,18 kalein, to call, 18 occurrences in Simplicius (1 Plato), 1 in Aristotle kalos, good, beautiful, 641,17; 666,23; 669,20; 717,1; ; see also kalôs kalôs, correctly, well, 12 occurrences in Simplicius (1 Plato, 1 Proclus) katadeês, deficient, 718,28 katadekhesthai, to take on, 667,8 kataduein, to sink, dive, 710,7.17.18.20 katagraphê, diagram, 652,10; 654,13 katagraphein, to draw, 653,7 katalambanein, to grasp, 672,19 kataleipein, to leave, 650,23; 651,4; 655,1 (Alexander); 673,10; 694,22 (Alexander) katamênion, katamenia, 704,11 katanoêsis, understanding, 638,26 katanôtizesthai, to ignore, 644,5; 712,13 kataphainesthai, to be made manifest, 644,16 katapuknousthai, to be pressed together, 651,7 kataskeuazein, to offer an explanation, establish, 690,30 (with 309b31); 710,15 kataspasthai, to be dragged down, 683,13 kata sumbebêkos, accidental, accidentally, indirectly, 666,13 (Proclus); 667,18.21.23 (last 2 Proclus; all 3 with 307b3); 706,23; 716,4 katathrauein, to break up, 644,13; 645,24 katêgoreisthai, to be predicated, 720,6.7 katekhein, to occupy, hold, 646,16.18 (both Alexander).23.24; 705,1.19; 712,3; 717,20 (Plato); 724,12 kathairesthai, to be made pure, 667,6 katharos, pure, 646,10; 657,20; 667,5 katheirgnusthai, to keep contained, 657,22 kathetos, perpendicular, 638,30; 655,17 (Potamon); 715,17 kath’ hauta, in themselves, per se, 647,28; 693,3; 694,21 (Alexander); 704,7

Greek-English Index kath’ hauto, kath’ hautên (or heautên), per se, in itself, 12 occurrences in Simplicius (1 Proclus), 1 in Aristotle kath’ ho, insofar as, 677,11; 701,9.12.19; 703,2.3.24; 707,2; 718,37; see also kath’ hoson kath’ hoson, insofar as, to the degree that, 643,16; 681,4; 708,29; see also kath’ ho kathiesthai, to lower, 724,5.7 katholou, universally, always, 12 occurrences in Simplicius, 0 in Aristotle katô, down, below, lower, 155 occurrences in Simplicius (4 Alexander, 9 Plato), 45 in Aristotle katôrthômenos, successful, 643,12 katôthen, from below, 715,19 (2) kaustikos, able to burn, 661,30 (with 306b32); 662,7 (with 307a1) keisthai, to lie, exist, be placed, 637,17; 644,1 (both Plato); 656,7 (Proclus); 677,5 (with 307b33); 699,26; 700,1; 709,18 kenos, void, empty, 117 occurrences in Simplicius (8 Potamon, 4 Alexander, 3 Proclus), 30 in Aristotle kentron, centre, 646,2; 649,13; 655,22 (Potamon); 679,32; 680,27; 715,20; see also mesos kephalaion, section, 675,18.20 kephalê, head, 679,12 kêros, wax, 636,8 (with 305b30) khalepos, difficult, 729,18 (with 313a16) khalkos, bronze, copper, 11 occurrences in Simplicius (1 Plato), 4 in Aristotle kharaktêristikos, characteristic, 713,24 kharaktêrizein, to characterise, 667,13; 698,9; 707,16.24 khein, to liquefy, rarefy, 668,4; 724,11 kheirôn, worse, inferior, 640,29; 644,22; 664,13 khôra, region, space, 23 occurrences in Simplicius, 8 in Aristotle; see also topos khôrein, to move, go, advance, 11 occurrences in Simplicius (2 Proclus), 0 in Aristotle khôrizesthai, to be separated, be

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lost, 658,13.15 (both with 306b21); 660,30; 661,7; 665,4; 679,35; 690,4 (2); 723,31 khrasthai, to use, 12 occurrences in Simplicius, 1 in Aristotle khreia, need, use, point, 650,10; 664,4 (Proclus); 675,4 (Aristotle); 676,18 khrêsimos, useful, 677,27; 713,32.35 khrôma, colour, 660,24.26; 721,16.17 (both with 312b1) khronos, time, 645,32; 646,21; 647,24; 704,12.23 khrusos, gold, 12 occurrences in Simplicius (2 Plato, 1 Alexander), 2 in Aristotle kinein, to cause motion or change, to move or change (transitive), 643,14 (Proclus); 695,16; 696,31; 697,4.29; 706,16.24 (both with 311a9 and 12); see also kineisthai kineisthai, to be moved or changed, to move or change (intransitive), 111 occurrences in Simplicius (4 Alexander, 3 Plato, 1 Proclus), 7 in Aristotle kinêsis, motion, change, 99 occurrences in Simplicius (5 Proclus), 14 in Aristotle kinêtikos, causing change or motion, 696,28 (with 310a27); 697,13; 698,12.25 (all 3 with 310a32); also 310a30 kinêtos, changing, subject to change or movement, 695,18 (with 310a30); 697,14 (with 310a33) koinônia, common character, communion, 721,11; 722,5 koinopoiein, to generalise, 718,22 koinos, common, general, 24 occurrences in Simplicius (1 Potamon, 1 in Aristotle kolla, glue, 661,5 kollasthai, to be glued, 661,6 kolpos, hollow, 645,19 (Proclus); 646,9 kôluein, to prevent, 15 occurrences in Simplicius (1 Proclus), 5 in Aristotle kômôidia, comedy, 664,26 koniortos, dust, 730,5 (with koniortôdês at 313a20) korennusthai, to be satiated, 711,9 koruphê, apex, vertex, 638,30; 649,14.25; 655,22.26 (both Potamon); 663,6.9.12 (all 3

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Proclus); 680,5; kata koruphên translated ‘opposite’ at 651,13; 652,15; 653,13 (last 2 Potamon) kosmos, cosmos, 14 occurrences in Simplicius (1 Plato), 0 in Aristotle kouphistikos, giving lightness, 697,13 (with 310a32) kouphizein, to make lighter, 685,18 (with 309a7) kouphos, light, 284 occurrences in Simplicius (2 Plato, 1 Aristotle, 1 Alexander), 73 in Aristotle kouphotês, lightness, 62 occurrences in Simplicius, 8 in Aristotle krasis, blending, 661,13; 723,28 kreittôn, stronger, 658,31 (Proclus); 666,30 (Plato); 718,27 krinein, to judge, 643,5 (with 306a15); 692,1 krisis, judgement, 712,13 krokê, woof, 660,26 kubikos, cubical, 638,7 kubos, cube, 29 occurrences in Simplicius (13 Potamon, 1 Proclus), 6 in Aristotle kuklophorêtikos, moving in a circle, 672,27; 674,4.20; 699,18 kuklos, circle, 642,15 (Plato); 652,20 (Potamon); 658,32 (Proclus); 679,21 (with 308a27); 680,24 (Plato); 716,31.32; also 307a7 kulisis, rolling, 662,19 (with 307a7) kurios, important, 673,15 (with 307b20); see also kuriôs kuriôs, in the strict sense, 12 occurrences in Simplicius, 1 in Aristotle kurtousthai, to be made convex, 658,34 (Proclus); 659,10 lambanein, to take, assume, 31 occurrences in Simplicius (3 Plato, 2 Alexander, 2 Proclus), 4 in Aristotle lampas, torch, 661,6.8 lêgon, consequent, 697,18; see also hepesthai leipein, to remain, 636,3 (with 305b28); 649,14 (with 306a33; 654,2 (Potamon) leptomereia, having fine parts (noun), 692,27 leptomerês, having fine parts (adjective), 656,8 (Proclus); 662,9;

667,31; 670,7-9 (3, all with 307b14); 690,25; 693,19 leptos, fine, 645,26 (Proclus); 669,9; 671,4.5 (both Proclus); 730,20 leptotês, fineness, 664,2-9 (3, all Proclus); 664,17 (Plato); 668,24.27 (both Proclus); 670,17 (Proclus); 693,1; 726,11 leptunein, to make fine, 664,4; 665,22 (both Proclus); 667,6; 724,11 leukos, white, light, 15 occurrences in Simplicius (1 Plato), 0 in Aristotle leukotês, whiteness, 648,20 (Proclus); 701,10 (with 310b18); 707,3 lexis, text, 641,29; 664,14; 684,1; 698,10; 702,6 limnazein, to be stagnant, 646,10 lithos, stone, 642,12 (Plato); 657,21; 705,14; 706,23 logizesthai, to take into account, consider, reckon, think, 664,19; 666,25 (both Plato); 685,32; 716,35; 731,28 logos, argument, discussion, account, statement, words, theory, doctrine, reason, role, ratio, 80 occurrences in Simplicius, (4 Potamon, 2 Proclus, 1 TL, 1 Plato), 9 in Aristotle loimôdês, pestilential, 650,6 loipos, remaining, other, next, 28 occurrences in Simplicius (1 Potamon, 1 Alexander, 1 Proclus), 0 in Aristotle luein, to resolve, dissolve, break up, 15 occurrences in Simplicius (3 Plato), 2 in Aristotle lusis, resolution, 640,27; 730,7.18.25 makhaira, knife, 666,3(2).10 (Proclus) (all with 307a30(2)) makhesthai, to be in conflict with, fight, resist, 649,3.8 (both with 303a21); 666,21.30 (Plato); 669,26 (Plato) makros, long, elongated, 636,25 (Plato); 637,2; 730,2 (with 313a18); 731,22 malakos, soft, feeble, 660,10 (Proclus); 730,9 (with 313b4).25 malakotês, softness, 671,26; 672,10 manos, rare, 691,6 manôsis, rarefaction, 675,4; 692,27 manotês, rareness, 671,26; 690,27.28.31

Greek-English Index manthanein, to learn, 701,23 mataios, empty, 644,17 matên, in an empty way (647,13); for no reason (699,20) mathêmata, mathematics, 642,29 mathêmatikos, mathematical, 14 occurrences in Simplicius, 2 in Aristotle; ho mathêmatikos translated ‘mathematician’ at 710,14 megalomerês, having large parts, 14 occurrences in Simplicius (5 Proclus, 1 Plato), 1 in Aristotle megas, large, great, 11 occurrences in Simplicius (3 Plato, 3 Proclus, 1 Alexander), 2 in Aristotle; see also meizon megethos, size, magnitude, quantity, largeness, greatness, 37 occurrences in Simplicius (4 Proclus, 2 Plato), 9 in Aristotle meizôn, greater, larger, 41 occurrences in Simplicius (6 Plato, 5 Proclus, 3 Alexander), 5 in Aristotle mêkos, length, 638,28; 648,18; 679,35 melas, black, dark, 696,23(2); 718,25; 722,18 memphesthai, to censure, complain, 649,28; 667,12 menein, to remain (fixed), rest, endure, 26 occurrences in Simplicius (4 Proclus), 2 in Aristotle merikos, particular, 674,6 meros, part, portion, 45 occurrences in Simplicius (9 Proclus, 5 Plato, 3 Alexander), 4 in Aristotle mesos, intermediate, mean, central, 115 occurrences in Simplicius (7 Plato, 4 Proclus), 23 in Aristotle; to meson often translated ‘centre’; see also kentron metabainein, to turn, change, 634,11; 658,17; 694,5 metaballein, to change, 81 occurrences in Simplicius (7 Proclus, 2 Alexander), 8 in Aristotle metabasis, change, 696,4; also 306a4,23 metabolê, change, 29 in Simplicius (1 Plato, 1 Proclus); 4 in Aristotle metadidonai, to give a share, 700,21 metallon, metal, 668,5 metapiptein, to change, be

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transferred, 636,27 (Plato); 637,5; 681,7 metaplasis, reconfiguration, 636,19.27 metaplasmos, reshaping, 638,19 metaplattein, to reshape, 636,9,13.23 (Plato) metarruthmizesthai, to be reshaped, 657,17.25 (both with 306b13) metaskhêmatisis, reshaping, 636,8 (with 305b29 and 32); Simplicius prefers metaskhêmatismos metaskhêmatismos, reshaping, 636,13.19; 637,12.18; 673,13; 674,12 metasuntithemenos, combined together, 636,14 metatithenai, to transfer, 694,26 (Alexander); 695,4; 698,22 (with 310b3) metaxu, (intermediate) between, 53 occurrences in Simplicius (1 Plato, 1 Alexander, 1 Proclus), 3 in Aristotle; to metaxu usually translated ‘intermediate’ metekhein, to share in, have, 641,26 (Plato); 677,4; 691,26; 705,17; 709,9; 710,8.10.11; 728,3 methexis, participation, 693,1 methistanai, to change (trans.), 667,4 metienai, to turn to, 673,5; 684,20; 692,25 metriôs, reasonably, 660,13 mignunai, to mix, 661,7; 690,1.3 mikromeres/smikromerês, having small parts, 660,5 (Proclus); 669,9.23 (Plato); 670,21 (Proclus); 671,8; 693,21.22 mikros/smikros, small, 24 occurrences in Simplicius (8 Plato, 2 Alexander, 2 Proclus), 5 in Aristotle mikrotês/smikrotês, smallness, 16 occurrences in Simplicius (2 Plato, 2 Proclus), 4 in Aristotle miktos, mixed, 660,25 mixis, mixture, 657,6; 720,15; 725,29; 726,33 mnaïaios, weighing a mina, 688,25; 709,12.16; 710,9 (all 3 with 311b4) mogis, with difficulty, 645,33 molibdos, lead, 11 occurrences in Simplicius, 6 in Aristotle monas, monad, one, 642,26; 651,19

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monê, rest, 681,2 monimos, steady, enduring, 658,26; 662,22.31 monos, only, 76 occurrences in Simplicius (8 Proclus, 4 Plato), 12 in Aristotle morion, portion, part, piece, 13 occurrences in Simplicius (1 Plato), 6 in Aristotle morphê, shape, form, 637,12.14.16 (Plato); 641,12 (TL); 643,31 (Plato); 644,18; 658,6 (Plato) mousikos, cultured, 695,11(2) muthikos, mythical, 646,12 muthos, myth, 646,13 nastotês, solidity, 684,21 Neikos, Strife (Empedocles), 586,29; 587,13-21(4); 590,20.27; 591,7 (hoi) neôteroi, more recent thinkers, 715,10 nephos, cloud, 705,14 noein, to think, understand, recognise, 640,29; 680,3; 684,23; 709,10 noêtos, intelligible, 649,5 (2 with 306a28) nomizein, to think, suppose, 16 occurrences in Simplicius (1 Plato), 3 in Aristotle nosein, to be ill, 719,7.9 noseros, susceptible to illness, 703,3 (with 310b31); 719,6.8 (both with 312a19) nosos, illness, 703,2.3 (both with 310b29, 31); 719,5 notheuein, to declare spurious, 675,6 oiesthai, to think, 14 occurrences in Simplicius (1 Proclus), 4 in Aristotle oikeios, proper, appropriate, one’s own, 93 occurrences in Simplicius (9 Alexander, 2 Proclus), 1 in Aristotle oikhesthai, to vanish, 691,14 oikodomêsis, building a house, 677,6 oikodomikê, house building, 677,6 oikos, house, 636,12(2) oktaedron, octahedron, 25 occurrences in Simplicius (4 Proclus), 1 in Aristotle oligôrein, to disregard, 683,20 oligos, few, small in amount, 55 occurrences in Simplicius (4

Alexander, 1 Plato), 13 in Aristotle; also used in various temporal expressions: met’ oliga or met’ oligon or oligon husteron (‘shortly hereafter’), oligon pro or pro oligou (‘shortly before’), and pros oligon (‘for a short time’); also kat’ oligon (‘little by little’) oligotês, fewness, 15 occurrences in Simplicius, 2 in Aristotle onkos, bulk, mass, 19 occurrences in Simplicius (3 Plato), 5 in Aristotle onoma, name, word, 10 occurrences in Simplicius (5 Plato), 1 in Aristotle onomazein, to name, call, 642,12 (Plato); 680,4.7; 681,13 (Plato); 690,31 opê, hole, 710,21 opheilein, to be obligated, required, 647,19 (Alexander); 685,25; 688,27; 689,2; 696,13; 722,15; 729,14 ophelos, contribution, 662,20 oregesthai, to desire, 711,6 organon, instrument, tool, 664,3 (Proclus); 665,20 orouein, to strive, 680,5 orthios, in a straight line, 680,3 orthogônios, right (said of a triangle), 638,27 orthos, right (said of an angle), 36 occurrences in Simplicius (10 Potamon, 3 Alexander), 0 in Aristotle ostoun, bone, 659,16; 660,15.23 (all with 306b23) ouranios, heavenly, 674,4; 675,9; 676,22 ouranos, heaven or heavens, 17 occurrences in Simplicius (7 Proclus, 2 Plato, 1 TL), 3 in Aristotle ousia, substance, 24 occurrences in Simplicius (3 Proclus, 1 Aristotle), 3 in Aristotle ousiousthai, to be given substance, 646,3; 657,27; 672,22 oxugônios, having sharp angles, 662,10 (with 307a2); 665,21.31 oxus, sharp, 663,29 (Proclus); 664,19 (Plato).30; 669,10; 670,24.25.26 (all 3 Proclus) oxutês, sharpness, 639,25 (Plato); 645,26 (Proclus); 664,1-9 (3, all

Greek-English Index Proclus); 664,16.17 (both Plato).29; 666,26 (Plato); 668,23.26; 670,18 (all 3 Proclus) pais, child, 705,31 pakhnê, frost, 701,28 pakhumereia, having thick parts, 692,26 pakhumerês, with thick parts, 670,8 pakhus, thick, 645,27; 656,8 (both Proclus); 667,4; 668,32 (Proclus); 669,9; 671,5 (2, both Proclus); 730,22 pakhutês, thickness, 668,28; 670,17 (both Proclus); 693,1; 726,10 palaios, earlier, 698,19; 715,8 pankalos, extremely beautiful, 656,4 pantakhêi, at all points, 657,18 (with 306b12) pantakhou, everywhere, always, 700,8; 707,9; 709,10.14.28 (all 3 with 311b1,6, and 7); 713,29; 722,25.26; 726,24 (with 312b26) pantakhothen, (from) everywhere, 649,12; 658,31 (Proclus); 710,22.23; 715,25.26; 716,10; also 308a20 pantêi, in every respect, entirely, everywhere, 12 occurrences in Simplicius (2 Plato, 1 Proclus), 2 in Aristotle pantelôs, completely, 666,2 (with 307a29) pantôs, always, absolutely, certainly, 14 occurrences in Simplicius (1 Alexander), 2 in Aristotle paraballein, to lay together, compare, 655,10; 711,20 parabolê, comparison, 680,7 paradeigma, example, 637,11; 726,7.22 paradeiknunai, to indicate, 702,2 paradidonai, to set out, 652,10; 661,28; 675,15.20; 700,10; 702,21; 704,29; 718,13 paradoxos, paradoxical, 642,30 paragein, to bring in, offer, adduce, 636,28; 637,11; 704,4; 730,7; 731,29 paragignesthai, to accrue, 704,16.24 paragraphein, to quote, 637,2 paraiôreisthai, to be suspended, 647,9.12 (both with paraiôrêsis at 306a21) parakeisthai, to be juxtaposed, lie

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alongside, 660,9 (Proclus).24.27; 661,10.13(2) parakeleuesthai, to call for, 676,24 paralambanein, to take, 726,7 paralimpanein, to leave out, 665,23; 685,31 parallassein, to crisscross, 715,24 parallêlos, parallel, 649,12; 656,6 (Proclus); 715,19; 728,23 paraskeuê, condition which makes ready, 661,24; 672,14 parathesis, juxtaposition, 660,7 (Proclus); 661,12; 666,3 paratithenai, to set out or alongside, 637,12; 644,5; 650,33; 664,13; 669,19; 680,11; 684,10; 686,26 paraxein, to follow, 646,6 parekhesthai, to provide, 723,7 paremballein, to insert, 663,21; 723,4 parempiptôn, intervening, 634,12.15 paremplekesthai, to be interwoven, 660,22 paremplokê, interweaving, 684,22; 689,13 parerkhesthai, to pass over, 644,29; 718,36 parienai, to pass over, 702,14 (ek) parodou, casually, 659,33 (with 306b27) paskhein, to be affected, be acted on, undergo, 645,22.24 (both Proclus).32.33; 666,23.29 (Plato); 672,5 (Alexander); 672,16; 674,16; also 312b12 pathêtikos, affective, passive, 661,21; 663,19; 668,10; 671,29; 672,2.3.9.33 pathos, affection, 30 occurrences in Simplicius (3 Plato, 3 Proclus, 2 Alexander), 4 in Aristotle; kata ta pathê translated ‘qualitative’ pauesthai, to cease, 636,23 (Plato); 666,22(2).27.30 (both Plato); 720,5 peirasthai, to try, experiment, 678,21; 710,15.29; 711,2.4; also 306b3 and 307b11 pentagônon, pentagon, 651,21; 655,3,7 (both Alexander) peperasmenos, finite, finitely many, 673,3.7.10 pephukenai, to be (naturally) constituted, 34 occurrences in Simplicius (5 Plato, 1 Proclus), 1 in Aristotle

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peras, limit, end, edge, 22 occurrences in Simplicius (1 Alexander, 1 Proclus), 1 in Aristotle periaireisthai, to be taken off on the outside, 649,13 periekhein, to contain, surround, 46 occurrences in Simplicius (8 Proclus, 3 Alexander, 1 Potamon), 8 in Aristotle periektikos, containing, 699,22; 718,14.33 perikhoreuein, process around, 679,32 perilambanein, to contain, include, 656,23 (Plato); 691,5; also 313b12 and 14 (to) perix, periphery, 679,31(2); 680,1.9.19 (Plato); 713,4; 717,18 phainesthai, to appear, be thought, be apparent, be seen, be obvious, 26 occurrences in Simplicius (3 Plato), 16 in Aristotle; see also phainomena phainomena, phenomena, 11 occurrences in Simplicius (1 Proclus), 3 in Aristotle phaios, grey, 722,18 phaneros, evident, 655,26 (Potamon); 705,2 (with 311a4); 713,31 (with 311b14); also 306b14, 307a19, and 307b19 pheidô, paying attention, 640,30 pheresthai, to move (intransitive), 199 occurrences in Simplicius (11 Alexander, 10 Plato, 2 Proclus), 65 in Aristotle; katô pheresthai translated ‘sink down’ between 729,16 and 731,23; see also kineisthai pheugein, to flee, escape, 649,9; 679,34 philia, love, 642,29 (with 306a12) philokalos, elegant, 656,4 philosophos, philosophical, 711,26 (ho) philosophos, philosopher, 640,28; 643,27; 645,15.28; 648,1; 660,18 phlox, flame, 661,7-8(3) phoinix, purple, 722,19 phora, motion, 23 occurrences in Simplicius (1 Plato, 1 Alexander, 1 Proclus), 7 in Aristotle phthartos, perishing, perishable, 638,17; 642,21 (2 with 306a19(2))

phtheiresthai, to perish, 645,1.11 phthora, perishing, destruction, 638,11; 675,7; 695,29 phulattein, to keep, preserve, 643,4.28; 644,11; 649,26; 657,30(2); 709,30 phusasthai, to be inflated, 11 occurrences in Simplicius, 1 in Aristotle phusei, natural, by nature, 16 occurrences in Simplicius (1 Plato, 1 Proclus), 3 in Aristotle; see also (kata) phusin (hê) phusikê, study of nature, 677,9.23.24 phusikos, natural, concerning nature, 25 occurrences in Simplicius (1 Proclus), 2 in Aristotle; see also (hê) phusikê and (ho) phusikos (ho) phusikos, student of nature, 674,21; 676,16; 677,13.25.26 (all 4 with 308a1) (kata) phusin, natural, naturally, 40 occurrences in Simplicius (3 Alexander, 1 Plato), 1 in Aristotle; see also phusei (para) phusin, unnatural, unnaturally, 650,6.9; 669,25 (Plato); 681,7.25 (Plato); 683,17; 705,19.22 phusis, nature 38 occurrences in Simplicius (5 Plato, 1 Alexander, 1 Proclus), 3 in Aristotle; see also phusei, (kata) phusin, (para) phusin phuton, plant, 704,13 pistousthai, to confirm, make credible, 697,9; 701,5; 702,2.17; 710,12 pithanôs, in a persuasive way, 730,25 (epi ta) plagia, to the side, 706,26 plasmatia, fabrication, 692,29 plassein, to fabricate, mould, 636,23 (Plato); 665,23; also 310a4 Platônikoi, Platonists, 640,23 Platônikos: Platonic, 649,29; see also Platônikoi platos, breadth, 648,19 platus, flat, 730,1-731,23 (8 with 313a17-b12(3)) pleon (pleôs), wholly, 728,16 pleonazein, to exceed, 647,14; 656,6 (Potamon) pleonektein, to surpass, 703,10

Greek-English Index plêrês, full, 39 occurrences in Simplicius, 10 in Aristotle plêroun, to fill, 655,14 (Potamon); 724,8 plêsiazein, to be or come near, 658,32 (Proclus); 718,6; 723,24; 724,13 plêsios, near, 699,23 plêthos, number, amount, multitude, quantity, 31 occurrences in Simplicius (2 Proclus, 1 Plato), 9 in Aristotle pleura, side, 23 occurrences in Simplicius (6 Potamon, 8 Proclus, 3 Plato, 1 Alexander), 0 in Aristotle pneuma, wind, pneuma, 642,13 (Plato); 723,27 (on which see the note) poiêtikos, productive, 643,7.10 (both with 306a16); 671,30.31; 672,3 poion, quality, 696,30; 697,1; 701,14; 702,7 (with 310b22); 705,7; 715,9; 718,24 (with 312a14) poiotês, quality, 31 occurrences in Simplicius (1 Alexander, 1 Proclus), 0 in Aristotle pollakhôs, in several ways, 671,25 pollakhou, frequently, 676,13 pollakis, often, frequently, many times, 640,27.29; 647,27; 648,9 (Proclus); 680,24 (Plato); 685,20.24 (both with 309a9); also 313a13 pollaplasios, several times as much, 685,35; 686,2.3.6 (Alexander, all 4 with 309a18); 692,2; 729,8.10 polueidôs, in many ways, 721,33 polugônon, polygon, 651,16 polupragmonein, to make a great fuss, 708,28 poros, pore, 670,6 (with 307b13) poson, quantity, 641,3; 666,12; 671,5 (both Proclus); 696,30; 697,2; 701,13; 702,7 (with 310b22); 705,6; 715,9; 718,26 (with 312a14) pous, foot, 662,1; 679,11 pragma, thing, 674,22 pragmateia, treatise, study, 669,18; 672,24.27; 674,2; 676,20.30; ; 677,9.23.25 (all 3 with 308a1) pragmateuomenos pros, dealing with, 706,18 pragmatikos, substantive, 640,28 prepôn, suitable, 643,28 presbutatos, oldest, 643,25; 645,18

201

(both Proclus); 646,4.6 (TL, presbistos) priôn, saw, 645,26 (Proclus), 666,4 (2, both with 307a31(2)) proanastellein, to open up, 570,3 proballesthai, to be put forward, be made a problem, 636,20; 672,12; 726,22 problêma, what is put forward, 726,4 prodeiknusthai, to be previously proved, 697,17; 701,32 prodêlos, prima facie clear, 641,4.22; 679,28 prodiakekrimenos, previously separated, 724,15 prodiarthroun, to articulate to start, 697,19 proêgeisthai, to precede, 704,10.19; see also proêgoumenos proêgoumenos, pre-eminent, 667,17 proeirêkein, to have said previously, 639,24 (Plato); 648,26; 651,27; 686,11; 728,25 proerkhesthai, to proceed, go on, 721,15; also 308b3 prohuparkhein, to exist already, 651,5 proienai, to proceed, 657,14; 703,13 prokeisthai, to be proposed, to be present, 684,23; 714,13; 721,8 prokekhumenos, previously diffused, 724,17 prokheirizesthai, to discuss, 672,20; 682,15 prokheiros, easy, 657,8 prokluzein, to wash out first, 724,7 prolambanein, to assume or take to start, to overtake, 640,20; 651,7.16.21; 693,16; 704,14; 714,2 prologizesthai, to take into account also, 686,6.7 prosairesthai, to choose to take over, 682,15 prosartan, to fasten together, 723,32 proseirêkein, to call, 645,17 (Proclus); 681,27 (Plato); 717,14 prosêkein, to be appropriate, to belong to, 11 occurrences in Simplicius (2 Plato, 1 Proclus), 1 in Aristotle prosekhein, to pay attention, 675,5 prosekhês, proximate, relevant, direct, 14 occurrences in Simplicius

202

Greek-English Index

(2 Alexander), 0 in Aristotle; see also prosekhôs prosekhôs, directly, proximately, just, 12 occurrences in Simplicius, 0 in Aristotle prosennoein, to think further, 679,21 proshupakouein, to understand also, 688,14 proskeisthai, to be added, 665,20; 685,35; see also prostithenai proskhrêsthai, to use also, 637,9 (Plato); 696,24 proskunein, to kneel down to, 731,29 proslêpsis, additional assumption, 714,19 prosparalambanein, to take into account also, 690,18 prospherein, to bring, offer, 640,23; 731,26 prostithenai, to add, 19 occurrences in Simplicius, 1 in Aristotle; see also proskeisthai protasis, enunciation, proposition, 651,11; 669,14 proteros, previous, preceding, prior, 45 occurrences in Simplicius (2 Alexander, 1 Plato), 5 in Aristotle prothumeisthai, to desire, exert oneself, 636,22 (Plato); 731,27 protithenai, to propose, put forward, 671,23; 672,25; 674,8.24; 692,31; 695,22; 706,27; 725,30 (protheô (b) in LSJ); 728,14 prôtos, first, primary, 62 occurrences in Simplicius (2 Plato, 1 Proclus), 16 in Aristotle psêgma, shavings, 730,5 (with 313a20) pseudesthai, to speak falsely, 643,2 pseudodoxia, false belief, 681,l0 pseudos, false 663,24.27.28 (both Proclus, all 3 with 307a18); 681,10 psilos, only, 657,22 psukhê, soul, 641,8 psukhein, to cool, make colder, 647,17 (Alexander); 663,25; 668,21 (Proclus); 670,13.14 psukhros, cold, 16 occurrences in Simplicius (1 Plato, 1 Proclus), 4 in Aristotle psukhrotês, coldness, 636,17; 668,24 (Proclus); 671,27; 672,1; 720,12 psuxis, cold, 661,21; 719,13; 722,2; 724,13

puknos, dense, 691,6; 726,18 puknôsis, condensation, 692,27 puknotês, denseness, 671,27; 690,27.31 puknousthai, to be condensed, made denser, 647,17 (Alexander); 724,14; 730,20.23 pur, fire, 239 occurrences in Simplicius (23 Proclus, 15 Alexander, 14 Plato, 2 TL), 44 in Aristotle puramis, pyramid, 96 occurrences in Simplicius (15 Proclus, 8 Potamon), 13 in Aristotle puroun, to enflame, heat, 665,28-666,15 (7, 1 Proclus, all with 307a25); 724,4 (with 312b13) Puthagorikos, Pythagorean (applied to the author of TL), 640,32 puthmên, base, 724,7 rhadios, easy, 16 occurrences in Simplicius (3 Plato), 3 in Aristotle; see also eukinêsia, eukinêtos, eukolos, eumetakulistos, euristos, eupathês, euplastos rhaistônê, relief, 711,14 rhêma, word, 666,24; 717,2 rhepein, to have an impulsion, incline, 12 occurrences in Simplicius, 1 in Aristotle rhêsis, passage (always referring to some part of Plato’s Timaeus), 637,1.2; 640,4; 669,19; 670,6; 680,11; 686,26 rhêteon, one should say, 640,12; 644,8; 656,24; 659,8 rhopê, impulsion, 33 occurrences in Simplicius (2 Proclus, 1 Alexander) 1 in Aristotle saphênizein, to clarify, 653,8; 719,4 saphês, clear, 13 occurrences in Simplicius (1 Plato), 0 in Aristotle sarx, flesh, 659,16; 660,15.23 (all 3 with 306b22); 705,28 sêmainein, to mean, indicate, 658,3 (with 306b16); 715,1; 716,35 sêmeion, point, indication, mark, 28 occurrences in Simplicius (4 Potamon, 2 Alexander, 1 Proclus), 2 in Aristotle; see also stigmê sidêros, iron, 667,16; 729,32 sikua, cupping glass, 723,23; 724,17

Greek-English Index skalênos, scalene, 638,27; 671,19; 682,19; 691,11; skedasmos, dispersion, 730,25 skemma, enquiry, 675,7 skhêma, shape, figure, 127 occurrences in Simplicius (11 Proclus, 4 Plato, 3 Alexander), 18 in Aristotle skhêmatizein, to assign a figure, 648,27; 649,22; 658,22; 661,20; 667,31; 729,24; also 306b4; see also skhêmatizesthai skhêmatizesthai, to be shaped, given a shape, assigned a figure, 10 occurrences in Simplicius (1 Alexander, 1 Proclus), 1 in Aristotle sklêrotês, hardness, 671,26 skopein, to investigate, 664,15 (Plato); 689,22 (with 309b21) skopos, purpose, 661,18.29; 662,14; 674,2; 726,4 skôptikos, jesting, 665,27 skôria, slag, 667,15 sôma, body, 203 occurrences in Simplicius (12 Alexander, 7 Proclus, 5 Plato, 3 TL), 24 in Aristotle sôzein, to preserve, 641,24; 657,7; 658,15; 689,28; 692,5; also 306a30 span, to draw (up), 17 occurrences in Simplicius, 3 in Aristotle sperma, seed, 649,30; 704,10; 730,10 sphaira, sphere, 31 occurrences in Simplicius (1 Potamon), 11 in Aristotle sphairikos, spherical, 659,4 (Proclus).8; 662,10; 679,29; 680,3; 693,26 (Alexander); 717,16 sphairoeidês, spherical, 680,13; 681,12 (both Plato); 686,22 stathmon, weight, 711,1.2 stenostomos, having a narrow mouth, 724,5 stereos, solid, 65 occurrences in Simplicius (6 Potamon, 2 Alexander, 1 Plato), 13 in Aristotle sterêsis, privation, 672,4; 696,17; 712,5; 718,29 stêrizein, to support, 710,21.23 stigmê, point, 63 occurrences in Simplicius, 14 in Aristotle; see also sêmeion stoikheiôdês, elemental, 637,22; 649,21

203

stoikheion, element, letter, 167 occurrences in Simplicius (18 Proclus, 1 Plato, 1 Alexander), 16 in Aristotle stoma, mouth, 712,14; 724,5.8 strongulos, spherical, 730,2 (with 313a18); 731,22 sullabê, syllable, 638,22 sullogizesthai, to give or make a syllogism, 697,12; 714,14.21 sumbainein, to follow, result, happen, 26 occurrences in Simplicius (1 Alexander), 23 in Aristotle; see also kata sumbebêkos sumballein, to come into conflict, 731,12 (with 313b8) sumbolon, token, 722,6 summenein, to remain together, 690,1 sumpêgnusthai, to be joined together, 639,2; 646,21; 667,5 sumperainesthai, to conclude, complete, 671,23; 673,6; 681,29; 694,3; 706,27 sumphônein, to harmonise, agree, 645,31; 663,18; 676,16 sumphthengesthai, to agree with, 711,4 sumphuein, to fuse, 650,15; 723,36; 724,10 sumpilein, to press together, 645,27 (Proclus); 656,25; 657,3.7 sumpiptein, to meet or be together, 712,4; 715,23.25 sumplêroun, to fill (out), complete, 20 occurrences in Simplicius (3 Proclus, 2 Potamon, 1 Alexander), 1 in Aristotle sunagein, to infer, develop (an argument), bring together, 639,1; 662,26; 666,18; 668,14; 669,26 (Plato); 673,14; 689,19; 703,4; 727,10; 728,7 sunagôgê, inference, 659,23; 668,13; 728,6; sunagôgê tou logou translated ‘development of the argument’ at 699,14 and 714,2 sunaidein, to be in agreement, 685,3 sunairein, to draw together, 695,21 sunairesis, contraction, 686,12 sunakolouthein, to be derived from, 636,18 sunalloiôsis, mutual qualitative change, 661,14

204

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sunalloioun, to change one another qualitatively, 661,10 sunaphê, context, 702,6 sunapodeiknunai, to demonstrate also, 714,12 sunapospasthai, to be separated along with, 661,8 sunaptein, to touch, join, 655,17 (Potamon); 661,4; 722,15; see also sunêmmenon sunarmogê, putting together, 656,5 sunarmozesthai, to be put together, 639,17.27 (both Plato); 647,28; 656,3 sunarsis, assistance, 703,1 sunêgorein, to support, 729,30 suneispherein, to bring in as well, 658,10 sunekheia, continuity, 645,22 (Proclus); 660,23; 710,19; 712,15 sunekhês, continuous, 23 occurrences in Simplicius (2 Alexander), 5 in Aristotle sunekhizein, to make continuous, 659,29; 723,27 sunelkein, to draw with, pull, 724,1.13 sunelthein, to come together, 658,29; 723,27 sunêmmenon, conditional, 714,17 sunepesthai, to yield to, follow, 641,27; 681,21.27; 717,9 (all 4 Plato); 717,13 sunergein, to contribute, 729,27.31 sunerkhesthai, to come together, 658,29 (Proclus); 723,27 sungeneia, likeness, 711,18 sungenês, of the same kind, akin, like, 10 occurrences in Simplicius (3 Plato), 0 in Aristotle sungramma, treatise, 646,5 sunidein, to see, 640,31 sunienai, to come together, 661,7 sunienai (suniêmi), to understand, 647,20 sunistanai, to construct, compose, produce, 33 occurrences in Simplicius (4 Plato, 1 Potamon), 7 in Aristotle sunkamptesthai, to be bent, 662,10.11 sunkeisthai, to be composed, conjoined, combined, compounded, 25 occurrences in Simplicius (1

Potamon, 1 Alexander, 1 Proclus), 2 in Aristotle; see also suntithenai sunkhôneuein, to dissolve, 724,10 sunkhôrein, to accept, 640,8; 648,7 (Proclus); 658,25; also 306a9 sunkoptesthai, to be chopped up, 660,22 sunkrinein, to blend, compare (12 occurrences in Simplicius (5 Proclus)), 4 in Aristotle) sunkrisis, comparison, blending, 673,12; 678,4.6.16; 684,16; 689,30; 706,12; 707,24; also 307b1 sunkritikos, blending, 668,2.26; 669,1.2 (last 3 Proclus) sunkroteisthai, to be driven together, 730,23 sunneuein, to converge, 12 occurrences in Simplicius (3 Potamon, 1 Proclus), 0 in Aristotle sunodos, coming together, 661,9; 667,24 (Proclus) sunorizein, to bring together, 667,14 (with 307a33); also 307b2 suntattesthai, to be joined, 656,2,3 sunthesis, combining, composition, compound, 10 occurrences in Simplicius (2 Proclus), 2 in Aristotle sunthetos, composite, 20 occurrences in Simplicius (1 Proclus), 3 in Aristotle sunthlibein, to press together, 670,5 (with 307b10) suntithenai, to compose, combine, 16 occurrences in Simplicius (2 Potamon, 1 Alexander), 1 in Aristotle; see also sunkeisthai suntomôs, briefly, succinctly, 640,26; 641,10; 644,29; 645,2; 652,9; 672,25; 705,6; 720,27; 728,25 sunuparkhein, to co-exist, 696,19 surrein, to flow together, 657,29; 723,11 suskhêmatizesthai, to be shaped, 657,21.23; 659,1 (Proclus) sustasis, construction, 647,14; 656,29 (Plato); 667,7; 712,4 sustellesthai, to be contracted, 724,13.15.18 sustoikhia, co-ordination, 643,28 sustoikhos, co-ordinate, 641,18; 642,8

Greek-English Index takhus, fast, 664,5 (Proclus); 729,26 (takhuteros); see also thattôn talantiaios, weighing a talent, 688,25; 709,11.15; 710,7.9 (all 4 with 311b3) taxis, rank, 638,22 tekhnê, art, craft, 645,26 (Proclus); 659,8; 661,5; 664,2 (Proclus) tekmêrion, evidence, 658,12; 710,26 teleios, complete, 27 occurrences in Simplicius, 0 in Aristotle teleiôsis, completion, 704,12 teleiotês, completeness, 21 occurrences in Simplicius, 0 in Aristotle teleiôthênai, to have come to completion, have reached an end, 704,16.17.21; 715,2 teleutaios, last, 665,24 telos, end, result, 10 occurrences in Simplicius, 0 in Aristotle temnein, to cut, 14 occurrences in Simplicius (4 Proclus, 3 Plato, 3 Potamon), 2 in Aristotle tetragônon, square, 18 occurrences in Simplicius (8 Potamon), 1 in Aristotle tetraplos, fourfold, 721,4 tharrein, to be confident, 643,3; 721,31 thattôn, faster, quicker, 18 occurrences in Simplicius (1 Proclus), 10 in Aristotle thaumastos, surprising, 648,6 (Proclus); 650,3; 659,9; 660,9 (Proclus) theios, divine, 658,31 (Proclus); 703,21; 722,12 theôrein, to study, see, look at, investigate, 672,13 (with 307b23); 673,16; 674,13; 677,10; 678,12; 682,10 theôrêma, theorem, 651,10 theôrêtikos, theoretical, 643,11 theôria, study, 676,18; 677,26 (both with 307b30) theos, god, 695,3 thermainein, to heat, 18 occurrences in Simplicius, 3 in Aristotle thermansis, heating, 661,26; 677,6 thermantikos, able to heat, heating, 661,30 (with 306b32); 662,7 (with 307a1); 663,20.23.28 (Proclus) (all

205

3 with 307a14); 665,21; 672,14; 697,20 thermasia, heat, 723,27 thermos, hot, 32 occurrences in Simplicius (3 Plato, 3 Proclus), 4 in Aristotle thermotês, heat, 16 occurrences in Simplicius (3 Proclus), 0 in Aristotle thesis, thesis, position, 642,30 (2 with 306a12); 679,16; 680,6 (both with 308a22) tholôdês, turbid, 667,4 threptikos, nutritive, 702,28 thruptesthai, to be broken into pieces, 724,1 tiktesthai, to be born, 704,12 tithenai, to posit, place, set down, 13 occurrences in Simplicius (5 Plato, 1 Proclus), 0 in Aristotle; see also keisthai tmêma, segment, part, 650,7 (Proclus); 673,10 tmêtikos, cutting, able to cut, 663,20.22; 664,2; 668,23.26 (all 3 Proclus) toikhos, wall, 706,24; 710,22-3(3); 715,12 tolman, to dare, 675,6 tomê, division, intersection, cutting, 649,26; 653,1 (Potamon); 664,15 (Plato) topikos, related to place or space, 703,19; 704,22.23; 705,5 topos, place, region, space, 227 occurrences in Simplicius (23 Alexander, 14 Potamon, 9 Plato, 9 Proclus), 16 in Aristotle; see also khôra trepesthai, to turn, 663,12 (Proclus); 707,8 trephein, to nourish, 705,28 trigônon, triangle, 92 occurrences in Simplicius (8 Potamon, 6 Plato, 4 Alexander, 4 Proclus, 1 TL), 9 in Aristotle; see also hêmitrigônon trophê, nourishment, 702,31; 705,26-9 (3 with 311a8); 711,9 tropos, way, kind, mode, 24 occurrences in Simplicius (1 Plato), 12 in Aristotle (to) tukhon, just anything, a chance thing, 20 occurrences in Simplicius, 8 in Aristotle tunkhanein, to happen, achieve,

206

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reach, 639,26 (Plato); 652,6; 661,18.29; 667,1; 704,1; 707,27 (with 311a20); 711,8; 725,12; also 307a9, 308b5, and 311a32; see also (to) tukhon and ei tukhoi xanthos, yellow, 722,19 xenizein, to dismiss, 679,28 xêrotês, dryness, 11 occurrences in Simplicius (1 Alexander), 0 in Aristotle xulon, wood, 678,5.6 (both with 308a9); 683,1 (with 308b10);

709,11.15.16; 710,7.9; 712,6 (all 6 with 311b4) zêtein, to enquire, ask, seek, 26 occurrences in Simplicius, 1 in Aristotle zôê, life, 677,11.12 zôion, animal, animate thing, 703,9; 704,10-22(6) zôpuros, spark, 677,19-24 (3 with 308a2) zugon, balance, 662,6; 681,18; 717,6 (both Plato); 717,12

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. (DK68) A61: 712,27-31 B154a: 662,10-12 POSIDONIUS (Edelstein and Kidd (1989)) 93a: 699,14-700,8 THEOPHRASTUS (Theophrastus: Sources) 171: 700,3-8 DEMOCRITUS

62C8-63A5: 680,12-25; 63A5-D4: 681,11-29; 63D4-6: 717,19-20; 63E4-7: 681,29-682,3; 684,4-6 [TIMAEUS OF LOCRI] (Marg (1972)) 215,9-12: 646,6-9; 215,13-16: 641,11-14 (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: 640,12

ARISTOTLE

(b) Passages quoted or paraphrased by Simplicius ARISTOTLE

Cael. (outside 3.7-4.6) 1.3, 269b20-3: 675,10-13; 2.14, 296b12-15, 16-18: 716,1-5 [There is a summary of 3.1-7 at 672,24-673,13 and of the whole of Cael. up to 3.7 at 674,2-12.]

EUCLID

Elements (Heiberg (1883)), 1, prop. 13: 651,11-12

PLATO

Tim. 49B7-C2: 642,11-14; 49C6-7: 642,15; 49D4-E4: 637,3-5; 49E6-50A4: 637,6-11; 50A4-B5: 636,22-7; 50B10-C6: 643,31-644,4; 50B10-C3: 637,15-18; 50B10-C1: 658,5-8; 53C2-4: 641,25-7; 53C5-56E8: 638,25-640,3; 53C6-8: 656,21-3; 54B6-D3: 639,12-22; 56B7-C3: 641,18-21; 56C8-E1: 639,23-640,3; 56D4-5: 647,25-6; 57C8-D5: 656,28-657,2; 57D1-2: 671,9-10; 56E8-57A7: 666,24-30; 59C1-3: 687,4-6; 61D6-62A5: 664,14-23; 62A5-B7: 669,21-8;

Cael. (outside 3.7-4.6) 1.3, 269b18-270a12: 676,11; 1.3, 269b18-26: 677,1; 681,8; 1.4: 669,18; 1.6, 273a22-274a18: 676,13; 2.3, 286a25-8: 672,4; 2.13, 293b30-2: 663,1; 3.1, 298b8-299a1: 638,17; 3.1, 299a2ff.: 638,14; 3.1, 299a2-6; 648,26; 3.1, 299a25-b23: 676,6; 3.1, 299b14-17: 685,9; 3.2, 301a22-b17: 676,9; 3.3, 302a10-14: 721,8; 3.3, 302a15-19: 638,1; 3.3, 303a12-14: 649,10; 3.4, 303a20-4: 648,26; 3.5: 727,14; 3.5, 303b22-30: 670,9; 3.5, 304b4-6: 638,3; 3.6, 305a16-22: 648,15; 3.6, 305a31-2: 720,31 Cat. 8, 9a35-b9: 672,6 GC 1.3, 318b14-8: 672,4; 1.6: 672,2; 2.1-4: 658,21; 721,10; 2.1, 329a24-b3; 721,10; 2.2-3: 718,11; 2.2, 329b19-31: 672,2; 2.2, 329b26-9: 667,10; 2.3, 330a30-b1: 722,3; 2.3, 330b1-6: 722,4; 2.3, 330b30-331a6: 722,8; 2.3, 330b33-331a1: 718,11; 2.4, 331a23-b2: 722,6; 2.8, 335a18-20: 700,8

208

Index of Passages

Metaph. 1.5, 986b27-34: 691,6; 1.6, 987b14-33: 665,5; 7.2, 1028b19-21: 665,5; 9.1, 1046a4-28: 672,6; 12.4, 1070b9-16: 672,4; 13.9, 1086a11-3: 665,5 Meteor. 4.1, 379a14-16: 700,8 Phys. 1.5, 188a20-2: 691,6; 4.6, 213a22-7: 686,14; 5.1, 225a12-16: 695,30; 5.1, 225a26-7: 695,30; 7.1, 241b24-242a49: 706,15; 8.1, 250b14-5: 677,13; 8.4, 254b33-256a3: 706,15 PA 2.3, 648b34-649a20: 672,4 Sens. 4, 442b17-21: 668,6 Top. 1.11, 104b19-20: 642,31 DIOGENES LAERTIUS (Marcovich (1999)) 1.21: 652,9 EMPEDOCLES (DK31) B13: 686,14 PHILOPONUS

Contra Proclum (Rabe (1899)), 29,2-8: 640,31

PLATO

Crat. 412B3-7: 729,16; 426C1-2: 665,21 Phaed. 109B4-C3: 646,13; 110B4: 646,13 Plt. 270A9: 662,1

Tim. 40B8-C3: 680,10; 48B3-C2: 638,22; 647,28; 49C7-50B5: 636,22; 50E3-4: 658,8; 56B3-5: 649,30; 56E5: 644,13; 56E6-8: 647,21; 57E7-58A1: 671,1; 58A5-B7: 656,11; 58C4-D4: 664,11; 62D11-63A7: 678,1; 66D2: 648,10; 79E5: 726,20 PROCLUS

in Tim. (Diehl (1903-6)) 2,37,33-41,14: 643,24 in Euc. (Friedlein (1873)) 291,20: 651,11; 381,23-382,21: 651,18

SIMPLICIUS

in Cael. (outside 636-731) 21,33-23,10: 706,3; 517,3-519,11: 663,1; 538,21-2: 715,11; 564,4-8: 641,11; 564,24-6: 641,7; 565,28-566,1: 641,25; 583,4-5: 714,21; 594,12-13: 714,21; 608,25-31: 641,28; 615,13-15: 691,1 in Phys. (CAG 9 and 10) 7,23-7: 641,11; 1036,17-1037,8: 706,16 SUDA pt. 4 (Adler (1930)) 2126: 652,9 [TIMAEUS OF LOCRI] (Marg (1972)) 215,13: 726,20; 215,17: 638,29; 216,2: 638,29; 217,15-16: 664,11; 219,10: 726,20

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. Alexander of Aphrodisias: 1. Cases in which Simplicius says nothing negative (9): 642,25 (says in connection with 306a7-9 that Plato wants to lead everything back to the eternal principles); 652,9 (sets out Potamon’s geometric arguments); 654,13 (gives his own geometric arguments); 671,25 (his distinctions among affections, acts, and powers); 692,16 (read haplôn at 310a3 although he knew of texts which had haplôs); 693,25 (an objection made by Aristotle at 310a7-13 might also be applied to the atomists); 695,21 (his formulation of the argument of 310a13-31); 696,12 (his explanation of why a change must be into a contrary); 719,29 (proposes to read peras for heteras at 312a23) 2. Cases of disagreement of some significance (5): Alexander, 640,5.20 (correctly sees that Plato is committed to make earth interchange with the other elements, but does not realise that Plato really does think this); 646,14 (objects to Plato that he is forced to acknowledge that a void arises when earth is dissolved into its triangles; Simplicius says that this can be generalised to the other simple bodies, but has no force because the triangles are natural, not mathematical); 647,15.20 (his charge that Plato arbitrarily made fire come to be to make certain transformations come out even rejected by Simplicius, who denies (correctly) that Plato did this); 660,13 (Proclus gives a good response to what Alexander says at 659,23-6); 720,9 (says that matters of the elements are characterised only as magnitudes which are heavy or light; Simplicius says they are instead characterised by hot or cold, dry or moist) 3. Cases of disagreement of less significance (11): 644,29; 645,2 (his analysis of objection 2, supplemented by Simplicius, but not rejected); 659,24 (in connection with 306b22-9 mentions that nether atoms nor Plato’s figures fill space; Simplicius responds that commitment to void is no absurdity for the atomists); 655,29 (his formulation of a criticism of Potamon criticised by Simplicius); 676,19 (the discussion of weight and lightness is appropriate to discussions of nature since nature is a starting point of motion; for Simplicius it is appropriate for finding out about the sublunary elements on the basis of their motions); 686,3 (interprets a text in which the mê of 309a18 is missing); 692,7 (understands the intermediates referred to at 310a1 as composites of void and full; Simplicius takes them to be water and air); 694,10 (a general statement of the difficulties involved in Aristotle’s conception of natural motion; Simplicius responds to the question where pieces of earth would move if the earth were moved elsewhere by invoking god); 698,13 (he reads anô kai katô instead of eis to ano kai to katô at 310a31-2); 700,9.22 (his position on the question of the formal and material aspects of the four elements rejected by Simplicius); 701,30 (thinks the text would be improved

210

Index of Names

by writing dê instead of de at 310b16; also two proposals for emending the text at 310b21-2) Anaxagoras: 673,4 (summary of book 3 referring to 3.4, 302b13-303a3); 686,14 (with 309a20; he and Empedocles, both of whom denied that there is a void, made no distinction between light and heavy) Anaximander: 679,4 (like Democritus believed that there is no above and below in the cosmos because the universe is infinite) Archelaus: 604,31 (he and Anaxagoras hypothesised the homoiomeries as elements) Democritus: 641,7 (said that qualitative explanations are amateurish (idiôtikos); 649,10 (said that fire is a sphere); 659,14.19.27 (atomism is incompatible with the existence of continuous compounds); 661,31 (made fire a sphere because it moves easily and can heat and burn); 665,6 (believed in indivisible, impassive, qualityless magnitudes); 679,4 (like Anaximander held that that there is no above and below in the cosmos because he thought the universe is infinite); 684,20 (makes the solidity of the atoms responsible for weight, and the interweaving of void responsible for lightness); 685,9 (says that the primary things are solids); 690,24 (said that fire is composed of small spheres (so that it has the finest parts), earth of larger atoms, and the intermediates (water and air) of intermediate atoms.); 693,29 (Alexander says that what Aristotle says at 310a7-13 could perhaps also be applied to him); 712,27 (thinks that everything has weight, but fire, because it has less weight, is squeezed out by things and moves up and consequently seems to be light); 726,8 (hypothesised the void and full, and also said that the void is the cause of lightness in bodies); 730,7-18 (5 with 312a21; his explanation of why e.g., lead sinks in water when it is a ball and floats when it is flattened out); also 648,28; 673,5,13; 307a16 (for Democritus the sphere, being a sort of angle, cuts because it moves easily) Empedocles: 673,2 (summary of book 3 referring to 3.7.305b1-5); 686,14 (with 309a21; he and Anaxagoras, both of whom denied that there is a void, made no distinction between light and heavy) Hesiod: 672,31 (summary of book 3 referring to 3.1, 298b26-9) Leucippus: 684,20 (he and Democritus made the solidity of the atoms responsible for weight and the interweaving of void responsible for lightness) Melissus: 672,30 (summary of book 3 referring to 3.1, 298b14-24) Parmenides: 672,30 (summary of book 3 referring to 3.1, 298b14-24); 691,6 (spoke of the contrary pair earth and fire as matter) Plato: 53 occurrences Poseidonius the Stoic: 700,7 (borrows the idea that heavy and cold things have the role of matter, hot and light things that of form from Aristotle and Theophrastus) Potamon: 652,9-655,28 (his arguments about space-filling figures as reported by Alexander) Proclus of Lycia: 640,24-670,16 (19 occurrences; his responses to Aristotle’s objections (3.7, 306a1-3.8, 307b18) to Plato’s geometrical chemistry) responses apparently accepted by Simplicius: 648,1 (objection 3); 648,19 (4); 663,3 (9); 663,27 (10); 667,22 (13) responses not accepted or at least modified in some way: 643,1.27 (both with objection 1); 645,15 (2); 649,28; 650,5 (both with 5); 656,6 (6); 658,24 (7); 660,4 (8); 665,16 (11); 666,9 (12); 668,20; 669,4 (both with 14); 670,16 (15) Ptolemy: 710,14-711,10 (5 occurrences; his disagreement with Aristotle’s assertion that an inflated askos weighs more than an uninflated one) Socrates: 641,25 (his statement at Tim. 53C2-4)

Index of Names

211

Syrianus: 711, 26 (his opinions about whether an inflated askos weighs more than an uninflated one) Theophrastus: 641,7 (reports that Democritus that the soul desires a principle more appropriate to body than the activity of heat); 700,6 (in his On the coming to be of the elements says that heavy and cold are material, light and hot formal) Timaeus: a (Plato’s dialogue Timaeus), 636,20; 647,16 (Alexander); 658,8 (with 306b19); 716,29; also 308b5 b (the ‘author’ of TL), 638,31; 640,32; 641,10; 646,5 c (the character in a), 641,25; 663,1,2.29 (all 3 Proclus); 664,11 (Proclus); 679,6; 682,16 (Proclus) d (either b or c), 659,14.19 Xenocrates: 665,7 (hypothesised indivisible lines) (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. Allan, D.J., 663,17, p. 23 Baltzly, Dirk, 643,24 Bergk, Theodor, p. 23 Bessarion, Basilius, 637,10; 639,12; 689,2; 693,17.29; 701,32; 720,17; 721,7 Bossier, Fernand, p. 23 Brennan, Tad, p. 22 Brittain, Charles, p. 22 Cherniss, Harold, p. 22, 636,22; 637,10; 691,6 Cooper, John, 660,24 Cornford, Francis MacDonald, p. 22 Coxeter, H.S.M., 650,17 Gulley, Norman, 636,22; 637,10 Guthrie, W.K.C., 702,3; 712,18 Hadot, Ilsetraut, p. 22 Heath, Thomas, 650,17 Heiberg, J.L., passim Hoffmann, Philippe, 731,25 Huby, Pamela, p. 22 Joachim, Harold H., 672,2.4 Karsten, Simon, passim Kneale, Martha, 659,23; 714,14

Kneale, William, 659,23; 714,14 Longo, Oddone, 720,23 Luria, S., 662,12 Marg, Walter, 641,11.13 Martin, Th. Henri, 664,23 Moraux, Paul, passim O’Brien, D., p. 22 Opsomer, Jan, 665,24 Perkams, Matthias, p. 22 Peyron, Amedeo, p. 23 Rashed, Marwan, 640,25; 643,27; 709,17 Rivaud, Albert, passim Sharples, R.W., 700,8 Siorvanes, Lucas, p. 22, 643,27 Steel, Carlos, p. 22, 640,25 Stocks, J.L., 692,17; 699,10; 702,3 Taylor, C.C.W., p. 22 Türker, Mubahat, 650,17 Verbeke, G., 723,27 Vlastos, Gregory, 638,26 Wright, M.R., 686,14 Zeller, Eduard, 652,9 Zeyl, Donald, J., 636,22

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. above and below in the cosmos, 679,1-680,26 book 4 an appropriate part of Cael., 675,5-32 causation, 706,10-26 continuity, 659,13-661,14 contrariety, 668,8-669,18 elemental change not by reshaping, 636,3-638,12 not in the way put forward by Plato in the Tim. 638,14-671,20 Plato’s theory of, 638,25-640,2; 666,15-667,9 Plato’s theory a hypothesis, 641,21-8 for Plato earth does interchange with the other three elements, 640,3-21; 643,27-644,18; 645,28-646,4 elements, arguments that there are four, 707,6-708,22; 712,20-716,17; 717,23-719,10; 725,4-728,10 GC, relation of Cael. to, 676,23-30; 718,9-11; 721,9-12; 721,25-722,12 formalisation of argument, 659,20-23 (second figure, i.e. the second hypothetical mode); 714,12-715,2 (second hypothetical mode)

harmony of Plato and Aristotle, 640,27-641,9 matter different for different elements, 719,10-722,12 Plato believed in prime matter, 640,3-21; 641,9-18 (TL); 658,11-24 Plato’s triangles are natural not mathematical things, 646,21-5; 648,13-23; 650,11-15; 664,26-665,23 natural motion and achievement of form, 697,9-698,9; 699,16-706,7; 718,12-719,10 shape and motion, 729,18-731,24 space-filling figures, 651,2-656,5 weight and location, 709,8-712,17; 722,22-725,21 weight, theories of Aristotelian, 694,3-698,9 atomist, 684,19-686,8; 687,9-690,14 Platonic, 680,26-682,3; 682,16-684,12; 686,20-687,6; 716,23-717,20 other 690,17-693,32 void, 646,14-25; 648,13-23; 650,18-651,2; 656,6-657,9

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 642,1-671,20, 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

640,3-12

212

508-11

642,24-7

213

511-12

644,26-645,3 646,14-25

214a 214b

512-15

647,3-20

215

515-18

652,9-656,5

216a

518-30

659,18-660,3 660,13-14

217a 217c

530-34

661,20-6*

218a

534-6

664,28-665,8*

219b

536-42

671,23-672,6

220a

542-5

676,17-20

221

549-50

684,19-22* 686,1-6

222a 222c

550-5

691,18-692,17

223

556-60

693,25-32

224

560-1

216

Addenda 694,10-695,21 696,12-27 698,10-14

225a 225b 225d

560-70

700,3-24

226

570-4

701,30-702,5

227

574-5

706,10-26*

228a

576-8

713,15-17*

229b

579-80

719,28-720,11

230a

580-5

723,17-724,16*

231a

585-97