Simplicius: On Aristotle On the Heavens 1.3-4 9781472552235, 9780715640630

This is the first English translation of Simplicius “responses to Philoponus” Against Aristotle on the Eternity of the W

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Simplicius: On Aristotle On the Heavens 1.3-4
 9781472552235, 9780715640630

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Abbreviations In most cases works are referred to by author or editor’s name and date of publication, full information being provided in the Bibliography. However, the following abbreviations are used: Against Proclus = Hugo Rabe (ed.), Ioannes Philoponus, De Aeternitate Mundi contra Proclum, Leipzig: Teubner, 1899. CAG = Commentaria in Aristotelem Graeca, 23 vols, Berlin: G. Reimer, 1882-1909. DK = Hermann Diels and Walther Kranz (ed. and tr.), Die Fragmente der Vorsokratiker, 6th edn, 3 vols, Berlin: Weidmann, 1954. LSJ = George Henry Liddell and Robert Scott (comps), Henry StuartJones (rev.), A Greek-English Lexicon, Oxford: Clarendon Press and New York: Oxford University Press, 1966. RE = Paulys Realencyclopaedie der Classischen Altertumswissenschaft, 51 vols, Stuttgart: J.B. Metzler, 1893-1997. In addition the following names are used without dates: Bessarion for emendations by the Renaissance humanist recorded in Heiberg’s apparatus. Hankinson for Hankinson (2002). Heiberg for Heiberg (1894) Karsten for Karsten (1865). Moerbeke for Latin readings found in Bossier (2004). Moraux for Moraux (1965). Rescigno for Rescigno (2004). Rivaud for Rivaud (1925). Ross for Ross (1936).

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Introduction This volume translates the second half of Simplicius of Cilicia’s commentary on Aristotle’s De Caelo 1.2-4, in which Aristotle argues that the world is everlasting;1 the first half is in Mueller (2010). Approximately 29% of this material is commentary in the ordinary sense, that is passage-by-passage explication of what Aristotle is saying. Another 11% (20,1-25,22 and 92,22-109,15) is more general philosophical discussion and treatment of some alternative views. The explications and general discussions, roughly 40% of 1.2-4, have already been translated into English in Hankinson (2002), a work to which I am much indebted. The other 60% is Simplicius’ discussion of the objections raised by his Christian contemporary John Philoponus2 (in a lost work which I shall call Against Aristotle) to Aristotle’s attempt to prove the everlastingness of the world. About 40% of that material containing Philoponus’ objections (roughly a fourth of 1.2-4) is translated in Wildberg (1987), another work to which I am much indebted. So what is new in this translation, somewhat more than one third of the whole, could be characterised as Simplicius’ responses to Philoponus. Since the debate between Simplicius and Philoponus is an extremely important item in the late stages of the transition from paganism to Christianity in the Byzantine Empire, it seemed desirable to include Simplicius’ responses in the Ancient Commentators on Aristotle series. But to print them in isolation did not seem reasonable since they obviously have to be read in connection with what they are responses to. Moreover, it is clear that a considerable portion of the material translated by Hankinson, e.g., the long excursus on coming to be at 92,22-109,15, is introduced by Simplicius in anticipation of his attack on Philoponus. The possibility of incorporating the two earlier translations into this one was considered, but it was decided that this was not feasible because of (hardly unexpected or surprising) differences in predilections between the two previous translators and between them and myself. Hence the decision to make a new translation which could rely on its predecessors for discussions of many issues3 and give readers direct access to a historically and philosophically important document in its entirety.

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Introduction 1. The disputes between Simplicius and Philoponus

Aristotle begins chapter 2 by asserting that all motions are either simple, that is rectilinear or circular, or composed of simple motions because the only simple magnitudes are straight and circular lines. He characterises circular motion as motion around the centre, rectilinear motion as motion up or down, up being away from the centre, down to the centre. He then introduces a distinction between ‘simple’4 bodies and compounds of them, and says that the simple bodies necessarily have simple motions and that it is necessary that there be a simple body which moves naturally in a circle by its own nature. This simple body is heaven, the world above the moon, the substance of which is a fifth element or aithêr, and for Simplicius Aristotle’s principal goal in 1.2-4 is to establish the difference between heaven, the only change in which is uniform motion in a circle, and the sublunary world which is composed of the four simple bodies or elements which move in a straight line, earth and water, which move down, and air and fire, which move up.5 For Simplicius the motions of the four simple bodies are inseparably connected with their continual change into one another, their acting on and being acted on by one another, a kind of change from which heaven is free. For Simplicius and Aristotle both heaven and the sublunary world are everlasting, but for Philoponus both came into existence in roughly 5500 BC when god created them and will end when god in some sense destroys them, an event thought to be imminent by Philoponus and his Christian contemporaries. However, the focus of the debate between Philoponus and Simplicius is heaven since that is the focus of 1.2-4, and one might say that they take for granted that the universe or cosmos is eternal if and only if heaven is. Simplicius takes it that prior to the texts which are commented on in this volume Aristotle has established not only the distinction between heaven and the sublunary world, but also the fact that heaven is more complete or perfect than the sublunary world, prior to it, and without weight or lightness. Although Philoponus would accept that there is a sense in which heaven is more complete than, better than, and prior to the sublunary world, he does not accept these assertions in the strong sense in which Aristotle and Simplicius intend them, and he raises explicit objections6 to Aristotle’s arguments against heaven being without weight or lightness. However, although Philoponus is ultimately interested in defending a Christian cosmological picture in opposition to Aristotle’s, his concern in Against Aristotle is, as this appellation suggests, merely to argue that Aristotle’s own arguments are inconclusive. To put this another way Philoponus’ concerns are eristic, and one cannot assume that an argument he makes represents a position to which he subscribes as

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opposed to a flourish he hopes will be persuasive. Since we don’t have anything like the full text of Against Aristotle we cannot be certain about its overall character, but Philoponus’ parallel work Against Proclus suggests that my characterisation is correct. If what I have said is true of Philoponus, it is even more true of Simplicius, whose argumentation is frequently both eristic and ad hominem. In responding to Philoponus’ arguments he freely casts aspersions on his opponent’s intelligence and motivation, and makes whatever counterarguments he can think of, whether or not they represent a consistent position. In this sense one might say that the dispute between Simplicius and Philoponus is a combat between rhetoricians rather than a philosophical, cosmological, or theological debate. There are, to be sure, philosophical, cosmological, and theological issues in the debate, but the overlay of rhetoric cannot and should not be disregarded. The structure of the part of De Caelo treated here is relatively simple, and can be seen by looking at ‘The text commented on’ section below. Aristotle argues first that heaven does not come to be or perish (270a12-22), from which he infers that it does not increase or decrease in size (270a22-5) or change in quality (270a25-35). If we can trust to Simplicius’ silence, Philoponus did not even discuss these further inferences, perhaps because he was only concerned to defend his Christian view that the world came to be (and will perish). Simplicius summarises the argument that heaven does not come to be or perish briefly at 92,4-7: I. The body which moves in a circle, i.e. heaven, does not have a contrary; II. what comes to be or perishes has a contrary from which it comes to be and into which it perishes; III. therefore, the body which moves in a circle does not come to be or perish. At 270a17-20 Aristotle suggests an argument for I, the premisses of which Simplicius presents as follows at 92,12-17: IV. There is no contrary to circular motion; V. ‘what has a contrary also has a motion which is contrary to its natural motion, namely the motion with which its contrary moves naturally’. For Simplicius the rather contorted V is clearly true (enargês) since, as he puts it rather opaquely, ‘since the natures of contrary natural forms are contrary, their motions are as well because nature is a starting point of motion’.7 Given V as ‘clearly true’, I follows from IV, the proof of which takes up chapter 4. It remains only to establish II, which Aristotle formulates in the following remark:

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Introduction Everything which comes to be comes to be from a contrary and some substratum and it likewise perishes by the action of a contrary and into a contrary with something underlying, as was said in our first discussions. (270a14-17)

The first discussions are undoubtedly the discussion of the principles of coming to be in the first book of the Physics. Simplicius tells us at 121,4-8 that Philoponus argued against both IV and II, and later, at 157,21-5, that he also objected to V. I shall consider these propositions in the order in which Simplicius discusses them, first II, then V, then IV. The issues involved with II are not so much the truth or falsity of a clearly understood Aristotelian doctrine as an interpretation of what he says on the question of coming to be and perishing and whether what he says entitles him to the premiss he needs for his argument. On the question of interpretation Philoponus is concerned with what the Aristotelian commentators Alexander and Themistius have to say as well as with Aristotle’s pronouncements. His discussion depends upon a distinction between what are called contraries in the strict sense (kuriôs), which I will call ordinary contraries, and cases of the contrasting pair form/privation. A simple and representative case of coming to be and perishing involving ordinary contraries is an ordinary object or piece of material (an ordinary substratum) coming to be warm from being cold. Philoponus implies that Aristotle and Alexander only recognise this kind of coming to be and perishing, and he accepts that if this were the only kind of coming to be and perishing, the cosmos as a substratum undergoing changes between ordinary contraries would be everlasting. Philoponus argues that if Aristotle had acknowledged coming to be and perishing involving forms and their privations he could not infer that the cosmos does not come to be or perish. One of the strong points of Philoponus’ argumentation is the fact that Aristotle mentions only contraries and not form and privation in his formulation of II. Simplicius, however, has no interest in defending the view that the cosmos does not come to be by restricting coming to be to cases involving ordinary contraries. He argues, with extensive quotation, that Aristotle does not believe that all coming to be involves ordinary contraries. He even claims (125,20-2) that Aristotle posits form and privation as principles of coming to be and perishing ‘more than’ (mallon hêper) contraries. At 128,16-129,3 he attempts to explain why Aristotle formulated II using the word ‘contrary’ rather than speaking of form and privation, when in Simplicius’ view he clearly intends to include the latter.8 We will see that this conception introduces other difficulties for Simplicius, but now I wish to look at the arguments of Philoponus designed to force acceptance of the view that there is coming to be involving form and privation as well as9

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other cases in which ordinary contraries are involved, a position which Simplicius, of course, accepts. I list here Philoponus’ arguments (123,11-124,17) with Simplicius’ responses (129,4-131,17) in parentheses: 1. Substances come to be, but, according to Aristotle in the Categories, substance has no contrary (Simplicius quotes two passages from Physics 1 to show that Aristotle says that substances do come to be.) 2. Irrational souls come to be, but they have no contrary. (Simplicius expresses agnosticism on the question whether irrational souls come to be, but, he says, if they do their doing so is a matter of a body taking on a form which it did not have previously.) 3. Geometrical figures come to be, but Aristotle holds that figures are not contrary to one another. (Simplicius argues both that Aristotle recognises contrariety among figures and that he can get along with figures and their privations.) 4. Left comes to be from right, but these are relatives, not contraries. (Simplicius insists that left and right are contraries (as well as relatives).) 5. Individuals in any of the categories in which there are no contraries do not come to be from contraries. (Simplicius says that even in such cases there is the opposition of form and privation.) 6. Air has no colour or flavour, but things with colour or flavour, e.g. water, come to be from it. (Simplicius insists that air does have some colour, but also finds nothing problematic in the idea that something without a quality in one range, e.g. colour, might come to be something which does have such a quality.) 7. Light comes to be from dark, which is the privation of light. (Simplicius sees no difficulty here.) Philoponus goes on to argue that if (as Simplicius thinks) Aristotle himself intends to include form and privation as contraries, then he cannot maintain the view that the cosmos did not come to be. Philoponus would be in a stronger position if he restricted himself to this negative formulation (‘cannot maintain’), but in Simplicius’ representation he appears to slip into the positive claim that Aristotle must accept that the cosmos came to be, although Philoponus is in no position to establish this:10 For every natural form which has its being in a substratum and matter there is always an opposite privation, from which it has come to be and into which it is resolved when it perishes. But both heaven and the whole cosmos have been given form by a

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Introduction natural form, so that they, too, will have a privation from which they have come to be and into which they perish. For just as human being comes to be from not human being and house from not house and, to speak generally, each natural or manufactured form comes to be from not such and such, so too heaven, since it is also a natural form, has come to be from not heaven and the cosmos has come to be from not cosmos. But this argument presumably requires that before the cosmos came to be there existed some substratum and matter in which the privation of heaven and cosmos existed and from which, when it had changed, heaven and the cosmos came to be, but it would not necessitate that heaven have no beginning and not come to be, as the Philosopher proposed to prove, but rather the contrary, that it comes to be and has a beginning of existence. (132,4-17)

Simplicius’ rejoinder to this argument seems rather weak. He claims that Aristotle does not hold that ‘for every natural form which has its being in a substratum or matter there is always an opposite privation’ but only that this is true of every natural form which comes to be, and Aristotle obviously holds that the cosmos does not come to be, since he argues in Physics 8 that heavenly motion is eternal. Simplicius agrees with Philoponus that the cosmos is a natural form existing in matter. This might seem to commit him to the view that the cosmos could conceivably come to be in the way Philoponus describes, but, according to Simplicius, there simply is no privation from which the cosmos might come to be. Where, he asks, does Aristotle say that every natural form has an opposite privation? ‘Would Aristotle be so superficial as to think that there is a privation opposed to heaven and nevertheless to try to demonstrate that it is everlasting and to demonstrate this from its not having an opposite?’ (133,1-311). But, of course, the real issue is not whether Aristotle believed the cosmos came to be, but whether his doctrine of coming to be leaves open the possibility that it might have. Simplicius gives at least some indications that he is aware of the weakness of his position. At 122,29 he says that even if there were a privation of heaven and the whole cosmos, one would need a further demonstration that it came to be and will perish. And at the end of his discussion of chapter 4 (200,14-18) he admits that Aristotle might have done better to ‘argue’ for the everlastingness of the cosmos on the basis of Neoplatonic ideas about the dependence of heavenly motion on Soul, Mind or Being, and ultimately the One, ideas of which he gives a thorough exposition at 93,23-98,15 and which he associates with the argument in Physics 8 that heavenly motion is everlasting. When Philoponus says that heaven and the whole cosmos have also been given form by a natural form, he means or implies that the

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cosmos or heaven is a compound of matter and form. Simplicius accepts this characterisation, and says it is ‘not at all disputed’ (133,25), but he proposes to look at what Philoponus says in support of this truth. The discussion is mainly of interest because it touches on the difficult question of the nature of matter. For Simplicius the ultimate substratum of everything in the cosmos is what he would call prime matter. He tells us that Philoponus thinks that what the Peripatetics call the second substratum is the ultimate substratum. Philoponus himself explains the difference between Aristotle’s conception of prime matter and the second substratum at 83,14-18 of his commentary on the Categories (CAG 13.1): ‘Prime matter ... is incorporeal and without form or shape before it is filled out and receives the three dimensions and becomes three-dimensional (what Aristotle calls second substratum), and then it receives qualities and produces the elements ....’ The second substratum or three-dimensional is also called qualityless body, but for Philoponus it is the true ultimate substratum and a substratum common to all things, heavenly and sublunary, the ‘prime matter’ of the Peripatetics (and Simplicius) being an incomprehensible fantasy.12 Simplicius quotes Philoponus as deriding those who say that heaven is immaterial, assuming that they mean it is an intelligible object. Simplicius responds that what these people mean is that the matter of heaven is superior to the matter of the sublunary world in which things come to be and perish. He cites Aristotle’s suggestion that everlasting natural substances either have no matter or have matter which can only change place but does not come to be or change in quality or in size (Metaphysics 8.4.1044b6-8). Thus we have a situation in which Philoponus insists that there is an ultimate matter which is the common substratum of everything material and Simplicius responds that there are two such matters, one for the heavens, the other for the sublunary world.13 To Philoponus’ suggestion that if there are two such matters they ought to have both something in common which makes them matters and some differentiating characteristics, Simplicius responds that the two matters should not be thought of as two species of a genus, but as two stages in the declination of things from the One in which heaven has a priority over the sublunary world. Clearly Philoponus’ identification of a single universal substratum is a fundamental part of his claim that heaven is as perishable as things in the sublunary world. Simplicius insists that there cannot be one common matter because there are no interchanges between the two domains, a fact which he says in a rhetorical remark14 Philoponus could not possibly deny. In the last passage quoted Philoponus concedes that his argumentation would imply that the cosmos comes to be from a pre-existing substratum. But that is not a conclusion acceptable to Philoponus, who at 136,17 refers to his Against Proclus for arguments against it.

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If one can trust Simplicius’ representation, in Against Aristotle Philoponus did not repeat the arguments of Against Proclus, but only argued against what he took to be a misunderstanding of the Christian doctrine that the cosmos came to be from what is not as the view that what is not is an enduring substratum for the cosmos in the way that wood is an enduring substratum from which a wooden ship is created. Simplicius denies the existence of this misunderstanding. For him the important point is the requirement that coming to be must be from a substratum and have an efficient cause. Simplicius also tells us that Philoponus gave many arguments that divine creation involves the simultaneous creation of form and substratum, but he does not describe them or answer them directly.15 Instead he gives his own account of eternal creation as the only way of avoiding a question to which the Christians have no satisfactory answer: why was the cosmos created at one time rather than another? Starting at 270b4 Aristotle gives what Simplicius calls three corroborations (marturiai) or confirmations (pisteis) of his view of the character of heaven: the fact that people always assign heaven to the divine (270b4-11), the fact that no changes have ever been observed in heaven (270b11-16), the use of the word aithêr, allegedly derived from aei thein (‘always running’),16 to refer to heaven. Simplicius does not report any comment by Philoponus on the third of these considerations, but it appears from Simplicius’ discussion at 139,23-141,11 that Philoponus took the opportunity to point out, citing Aristotle as an authority, that important Greek thinkers did not think that the cosmos was everlasting: Plato said that it came to be (although it will not perish because of the will of god), Empedocles and Heraclitus that it alternates between existence and non-existence through time. Simplicius cannot deny that Aristotle says these things, but he insists that Philoponus misconstrues their meaning. Aristotle is stating the superficial sense of what these people said, while being aware that their true doctrine was the same as his own: the cosmos is everlasting and dependent on a timeless reality for its existence. Philoponus also denies the significance of people’s assigning heaven to the divine and of the fact that no change has been observed in heaven. Even if people do assign heaven to the divine, they also think that gods inhabit sacred places on earth, but they do not assume such places to be everlasting. Simplicius replies that considering these places to be sacred is not incompatible with assigning heaven to the divine, and he cites the prophet David as making such an assignment and for the belief that the cosmos is everlasting. Against Aristotle’s remark that heaven has never been observed to change, Philoponus says that many things in the sublunary world exist for a long time without being observed to change, and that heaven is subject to destruction if god wills it since it is a finite body

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with finite power. Simplicius appears to adopt a kind of Heracliteanism, according to which anything which is subject to change is changing all the time, so that if anything goes without changing for an hour it is everlasting. Moreover, although the cosmos is a finite body with finite power, it is held in everlasting existence by an unchanging and eternal creator. In chapter 4 Aristotle turns to the proof of IV: there is no contrary to circular motion.17 But, as we have seen, Aristotle also needs V, which I shall now formulate as ‘if two things are contrary they have contrary motions’ or, since the relevant things are substances: V. If two substances are contrary they have contrary motions. Simplicius gives his own presentation of the arguments for IV at 144,5-156,24 before turning to Philoponus, where, after belittling him for objecting to the arguments for either IV or V when he is willing to concede the conclusion Aristotle wants to get from them, namely I (heaven or the cosmos has no contrary), he turns at 157,26 to Philoponus’ objections to V. The discussion is made complicated by the fact that several independent points are intertwined. First, Philoponus weakens his rhetorical position by formulating V as: V’. If two substances have contrary motions they are contrary (157,26-7). Second, Philoponus argues that Aristotle should have taken into account other kinds of change in addition to change of place, so that the relevant principles should be: V*. If two substances are contrary they admit of contrary changes, or, in Philoponus’ formulation: V*’. If two substances admit of contrary changes they are contraries. Philoponus invokes Aristotle’s dictum in the Categories that: A. The same substance can admit contraries to argue that V’ or V*’ imply that the same substance will be contrary to itself, which is not only itself impossible, but also incompatible with another dictum of the Categories: B. Substance has no contrary.

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In the course of his discussion Philoponus mentions both qualitative and quantitative change (a substance can become hotter or colder, larger or smaller) and change of place (air rises and sinks). Simplicius does not get around to pointing out Philoponus’ logical mistake in substituting V’ or V*’ for V or V* until 162,20 (cf. 163,34164,27), and he himself is sometimes somewhat cavalier about the difference between them.18 Blocking the substitution would by itself eliminate Philoponus’ argument, but Simplicius chooses to explain why A and V’ or V*’ are both true, that is why the same substance can admit contraries and not be contrary to itself. He does this by invoking a distinction between active and passive changes. Active changes include the natural motions of the elements, which are due to the nature inherent in them, and, e.g., fire heating other things; passive changes include constrained motion and being heated by fire. Simplicius first says (159,34-160,9) that any of V, V’, V*, V*’ are to be understood in terms of active changes, but that the changes relevant to A are all passive. But since he, like Philoponus, is convinced that Aristotle is only thinking about change of place, he ultimately decides (160,21-30) that Aristotle intends V only to apply to motion and not to, e.g., causing something to get warmer. Simplicius’ position means that he has to deny the relevance of Philoponus’ claim (158,13-10) that air moves both up and down naturally, a claim which Philoponus supports by saying that in either case air moves to fill a void. Simplicius responds (160,31-161,21; 161,28-162,14) by claiming that the motion of air up to fill a void is natural, but its motion down is due to the need to fill the void. At 163,14 Philoponus considers the possibility of escaping the difficulty he has adduced by replacing V’ with: V**’. If two substances have contrary motions they have contrary qualities. Philoponus concedes that V**’ would entail that if something has no contrary qualities (as Aristotle is taken to have believed of heaven), then there would be no contrary to its motion, but he denies (correctly) that V**’ would be entitled to assert: V**. If two substances have contrary qualities they have contrary motions. Philoponus points out that this proposition should be false for Aristotle since he believes that the hupekkauma moves in a circle and so should, according to Aristotle (IV), have no contrary to its motion, but, being fire, it does have contrary qualities. Simplicius responds by saying that the motion of the hupekkauma is irrelevant because its motion is not natural (as Philoponus believes) but ‘hypernatural’.

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Simplicius takes Philoponus’ proposal to consider V**’ in place of V’ as an indication that he thinks that for substances having contrary qualities, in particular contrary ‘substantial’ qualities, is incompatible with being themselves contraries. This claim, which is repeated at 165,21-3, seems unjustified, since all Philoponus looks to be doing is considering an alternative interpretation without suggesting that it is or is not compatible with another alternative.19 However, Simplicius sees his main task as countering Philoponus’ ‘misapprehension’ by explaining why Aristotle can call substances, such as fire and water, with contrary qualities contraries (as he does most explicitly at 2.3, 331a3-6 of On Coming to be and Perishing) while maintaining in the Categories that substance has no contrary (B). Unfortunately, Simplicius’ exposition starting at 166,14 does not make any reference to Philoponus, so that we have no idea of what features in it he might have objected to. And what Simplicius says is a variation on common themes in the commentary tradition, and the position he adopts is hardly distinguishable from the one expressed by Philoponus in his commentary on the passage in On Coming to be and Perishing just referred to. Simplicius begins by explaining that in the Categories primary substance20 is a composite of form and matter, which itself is taken as a substratum. He distinguishes sharply between this substratum and the ‘accidental’ contraries which belong to it, contraries which underlie Aristotle’s A. And B is true because substance is being taken as a substratum: The statement in the Categories that there is no contrary to substance is true. For there is no contrary with respect to matter, which is only a substratum. And there is none with respect to form  (for is also substance, even if it is in matter); rather, together with matter, underlies contraries. And much more is it true that there is no contrary with respect to the composite of form and matter, since this is still more a substratum for contraries. (166,24-30) However, form itself has contraries as components, e.g., the form of fire includes heat, dryness, and lightness. Simplicius makes, but does not explain, a distinction between these ‘substantial’ contraries in the form and the accidental contraries invoked to explain A. It is the substantial contraries which Aristotle has in mind when in On the Heavens he speaks (implicitly) of contrary substances: But here he has taken the differentiae which belong substantially, each contrary contributing to the filling out of a different substance and the differentiae belonging per se and not accidentally to the sub-

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Introduction stances. And he said that substances are contrary to each other with respect to those differentiae which belong per se to the different substances. For differentiae which belong accidentally exist in the same substance in turn. And so, when he says ‘the motions of contrary things are contrary’, he is calling substances which have substantial differentiae which are contrary to one another contrary substances, but he is not doing so insofar as they are substances and exist per se, but insofar as they are constituted by the contrary differentiae from which contrary motions follow; for upward motion is conjoined with heat and lightness, downward motion with coldness and heaviness. (167,14-24)

I turn finally to Aristotle’s arguments in chapter 4 for IV, which, despite their mathematical overlay, are really quite nebulous. I shall content myself with stating Simplicius’ understanding of them, the most important of Philoponus’ objections to them, which sometimes invoke Alexander and Themistius, and Simplicius’ replies. According to argument 1 (270b32-271a5), the most obvious candidate to be the contrary of motion in a circle is motion in a straight line. ‘But the motions in a straight line are opposed to one another by places, since up/down is a differentiation and contrariety with respect to place.’ For Simplicius Aristotle is here invoking the principle that a thing can have at most one contrary and the fact that for him the only simple rectilinear motions are from above to below and from below to above, and those two motions are contrary. Equally important for Simplicius’ understanding of Aristotle’s reasoning is the idea that ‘above and below are contrarieties of place, and the motions from those regions have contrariety most of all; for the motions which go from contrary places into contrary places are contrary’ (146,4-7), an idea which he bases on 271a27-8 (‘the contrarieties of motion are derived from the contrarieties of places’). In responding to this argument Philoponus first21 says that even if motions up and down and circular motion do not ‘conflict’ (makhetai) with respect to contrariety of places, they do conflict in other ways: In the case of the motions in a straight line motion is from one point to another and is unbroken in all its parts, but in the case of motion in a circle it is from and into the same thing with not even a chance part remaining unbroken. And motion in a circle conflicts with motion in a straight line because it is impossible for a motion on the same straight line to occur twice without having stopped, but motion in a circle can go around the same line infinitely many times without stopping. (171,27-31) In response Simplicius points out that (according to Aristotle) ‘con-

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trariety of places’ is fundamental to the idea of contrariety of motion, and he insists on the connection between this kind of contrariety of motion and the conflict among the sublunary bodies which produces their coming to be and perishing: Things which naturally go to places which are contrary to one another are always given form by contrary qualities, heat and coldness, lightness and heaviness; and things which are given form by these contrary qualities, which cause different impulsions, go to contrary places. These, and not ‘unbroken’ and ‘broken’, are the contraries which come to be from one another. For a circle does not change into a straight line, nor does what moves in a circle change into what moves in a straight line, nor does what moves from and to the same point change into what moves from one point to another, nor does what is separated by rest change into what moves continuously.22 For these are not contrarieties relating to qualities which act and are acted on, and they do not have the same substratum, since if they did it would result that sublunary things change into heavenly ones and heavenly things into sublunary ones. (172,7-18) Simplicius’ association of rectilinear motion with the kind of contraries involved in coming to be and perishing enables him to set aside Philoponus’ invocation of the contrariety convex/concave, which is found in heaven, as irrelevant to the unchangingness of heaven, which also exhibits many other contrarieties such as motion/rest, odd/even, same/different, one/many. Aristotle’s second argument (271a5-10) is very obscure. I quote it in full: Moreover, if someone assumes that the same statement which holds of the straight line also holds of the circular one (namely that motion from A toward B is contrary to motion from B toward A), he is speaking about motion in a straight line, since such motion is finite, but the circular motions between the same points are infinite. Simplicius takes Aristotle to be arguing that motion from A to B on a circular arc greater or less than a semicircle is not contrary to motion from B to A on such an arc on the grounds that infinitely many such arcs can be drawn through two points. Prior to considering Philoponus’ objections he explains Aristotle’s reasoning as follows: From what he said before Aristotle has obtained that motions from contrary places are contrary, and that contrary places are those which are at the greatest distance, and that the greatest

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Introduction distance is determinate, just as the least is, and that every distance which has a determinate size is measured by the straight line between the distances; for that straight line is one and determinate because it is the least line having the same limits, but circular arcs which are joined to the same points are infinite and so indeterminate; and consequently these arcs do not determine the distance between A and B, and consequently the greatest distance itself is not derived from the circular arcs; and consequently the places of A and B are not contrary; and consequently the motions from A and B are not contraries if they occur on an arc and not on a straight line. (176,15-26)

Philoponus, perhaps with understandable exasperation, suggests that Aristotle’s argument is intended as a joke and turns to refuting the accounts of it given by Themistius and Alexander. Themistius construed the argument as saying that motions on the infinitely many arcs from A to B will be contrary to the one rectilinear motion from B to A, contradicting the dictum that a single thing has a single contrary. Philoponus replies by saying that the motion from A to B on a given arc will be contrary only to the motion from B to A on the same arc. Although not endorsing Themistius’ position as an interpretation of Aristotle, Simplicius insists that his position is correct. Philoponus raises a perhaps more interesting issue when he points out that the same difficulty should arise for rectilinear motion since there are infinitely many upward motions from centre to periphery and infinitely many downward ones. He also claims that these upward or downward motions are not of the same kind whereas the circular motions between two points are of the same kind because they all have the same pair of end points, so that all the motions from A to B on circular arcs treated as one can be taken as contrary to all the motions from B to A taken as one. Simplicius responds: In the case of straight lines from the centre, all of which are equal, the interval between up and down, which is the greatest in this extension, is determinate, so that all the points on the periphery of the upper region, taken as one, are opposite to what is down.23 But, since the arcs between A and B are unequal and make the intervals between A and B unequal, they do not make the place A be at the greatest distance from the place B in terms of all the arcs. Consequently the places are not contrary, since they do not have the greatest distance between them one and determinate. ... But it is clear from what has been said that in the case of the straight lines everything which is up, taken as one, being at the same distance from what is down, is opposite to what is down taken as one, but that in the case of arcs, in which the kinds of distances are different, there is neither one

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15

kind, as he thinks, nor a contrariety of A to B with respect to these arcs at all. (177,25-178,7) Alexander appears to have given an exegesis similar to Simplicius’. In response Philoponus invokes a contrast between what is true in mathematics and what is true in nature. In mathematics it is true that there is no greatest circle on which two points lie, but in reality there is a greatest circle, e.g., the celestial equator. Philoponus goes on to argue that the inner limit of the sphere of the fixed stars and the outer limit of the sphere of the planets move in contrary directions. Simplicius does not address this claim until 194,21-198,6, but here he responds to Philoponus’ attempt to make something a determinate circular distance between two points: what Philoponus says is perhaps an adequate riposte to the claim that there is no greatest circle through two points, but it does not suffice to rule out there being infinitely many circular arcs through the points, even if the arcs are mathematical or conceptual and not physical things. As Simplicius puts it: Even if it is not possible to take a greater arc drawn on the same points than the one this person mentions, it would still always be possible to take a lesser one in the inner spheres. And even if such arcs drawn in the heavenly body are not natural things, the distances between the points would be different - conceptualisation is also sufficient to determine this. For when the points fall outside the straight line between them, the distance between them remains indefinite, so that they are not at the greatest distance from each other, their places are not contrary to one another, and the motions from them are not contrary, and the bodies moving with them are not contrary. (179,14-22) In the third argument (271a10-13) Aristotle considers the case in which the arc with endpoints A and B is a semicircle and therefore unique. He claims that motion on this arc is the same as motion on the straight line AB since ‘we always suppose that each thing is distant by a straight line’. Simplicius realises that this argument could have been used in the previous case, and he seems to think of it as in some sense the real argument in both cases. As he puts it: If contrary motions are contrary because they are from places which are most widely distant from one another, and the greatest distance is determinate, and we judge a determinate distance by reference to the least line of those having the same limits, and this is the straight line, it is clear that also on this hypothesis the contrary motions will occur as on a straight line. (148,1-5) Simplicius’ confrontation of Philoponus on the third argument, start-

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ing at 179,24, is long and difficult. He first tells us that Philoponus took Aristotle to be claiming that the straight line is the measure of the length of an arc and argued against this claim. Simplicius simply denies that Aristotle made such a claim; he only said that the distance between two points is measured by the straight line between them. As he puts it now: The person who takes the motions from C and D as contrary takes them as occurring on the diameter, since the determinate distance is determined by the diameter, the greatest distance is determinate, and the contrary distance is greatest. (181,4-7) At 181,20 we are told that Philoponus went on to argue that even if it is granted that the distance between two points is measured by the straight line between them, it remains the case that we can define the greatest distance between two points on an arc in terms of the arc. Philoponus’ argument invokes the signs of the zodiac, but it can be understood in terms of the hours on a clock face. According to Philoponus the most distant hours are the diametrically opposed ones such as 9 and 3 o’clock. It may be the case that 2 is at a greater distance from 9 in terms of the arc through 6, but it is at a lesser distance in terms of the arc through 12. ‘Therefore only points which divide a circle into two equal parts are separated by the greatest distance in every direction.’ No doubt Philoponus is right that we could define the greatest distance between points on a circle in this way, but there would not seem to be any compelling reason to do so. Simplicius’ response is that, if Philoponus is taking the distance between points in terms of the circumference, then contiguous points such as 8 and 9 are at the greatest distance, but if he is taking the distance between points in terms of the straight line joining them, he is in agreement with Aristotle. And if he wants to take them in both ways, he is adding a way which has nothing to do with the determination of contrary places. At 182,17 the discussion turns to an argument of Alexander’s, which, Simplicius tells us, is accurately recorded by Philoponus: Every interval is measured by what is least; in every case the interval on a straight line is least; therefore, the straight line and the on the straight line are the measure of every interval; however, it is for the measure to find what is most distant and contrary; therefore, the contrary in intervals is with the straight line and on it;

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and so is not on an arc. (182,31183,2) Philoponus objects to Alexander’s addition of the words ‘and on it’ in the next-to-last proposition of the argument. Simplicius, who paraphrases this proposition as ‘What is at a greatest distance in intervals and contrary is found with the straight line and the interval on it’, first responds to Philoponus with an argument which would seem to be aimed at showing that Alexander does not need the addition: But if is found with , it is clear that contrary intervals are defined in terms of and are by reference to it; and a thing is defined in terms of that from which it is found, and a thing is by reference to what it is defined in terms of. (183,12-14) But it turns out that Philoponus really wants to argue against a claim which might be formulated as ‘the points which are at the greatest distance in a measured interval are in the stick which does the measuring’. Simplicius responds (correctly it would seem) that the points are in the distance which is measured not in the measuring stick. This leads Simplicius into a disquisition on the way measurement and the application of criteria in general works. I move on to 185,2324 where the interpretation of Alexander is again the issue. As we have seen, in Simplicius’ understanding the third argument only concerns the motions in reverse directions on one semicircle. However, Alexander, presumably interested in arguing generally against the idea that the distance between two points might be specified in terms of an arc, pointed out that one might draw a greater arc between two close points and a lesser one between two points further apart. Philoponus, adhering to his position that points at the limits of a semicircle can be taken to be at a greatest distance, takes Alexander’s statement to be trivially true and irrelevant. Simplicius concedes that Alexander’s statement is of no use for the third argument, which concerns only two given points and a semicircle connecting them, but insists, again correctly, that Alexander shows that the distance between two points is not specified in a determinate way in terms of arcs. The fourth argument (271a13-19) is, in fact, two for Simplicius. In the first, which is really a repetition of the third, Aristotle asserts that ‘similarly’ in a circle ACBD with diameter AB a motion from A to B through C is not contrary to a motion from B to A through D. In the second Aristotle points to what, for Simplicius, is the real concern of the whole of chapter 4 when he says that even if the motions on the two semicircles are contraries, still the motions in reverse directions

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on one circle are not contrary. Philoponus does not appear to have had much to say about this passage. At 188,3 he says that if the argument is the same as the third argument there is no need for him to say any more. However, he really thinks that the two arguments are different and censures Themistius for taking them to be the same, as Simplicius also does. Philoponus’ grounds are that the arguments concern different cases and, more significantly, he thinks that Aristotle’s conclusion in the fourth argument is correct since, for example, the sun’s motion above the earth from an eastern point to a western point is not contrary to its motion under the earth from the western point back to the eastern one. Simplicius agrees that these motions are not contrary, but he thinks that Aristotle is considering the case of two separate motions on the two semicircles, and for that case the reasoning of the third argument suffices: The arcs do not define the greatest distance in terms of which contraries are characterised; but rather the greatest distance is defined in terms of the diameter ... . And consequently again if the motions are taken as contraries, they are taken as moving the distance on the straight line, not the distance on the arc. (149,6-10) Hence, for Simplicius, Philoponus’ acceptance of the fourth argument is wrong-headed because based on a misunderstanding. In the fifth argument (271a19-22) Aristotle proves what for Simplicius is the only essential point: reverse motions on the same circle are not contraries ‘since these motions are from and into the same thing, but contrary motion is defined as from a contrary into a contrary’. Alexander explains why this argument is different from its predecessors: It would have been possible to use this argument also in the case of the motions previously discussed. For none of them was from a contrary into a contrary. But this is more evident in the case of the circle, motion on which is not just not from a contrary into a contrary, but not even from one thing into another, but from and into the same thing. And that is why he also has set out the argument for this case. (150,15-19) Before considering Philoponus’ response to this argument it is necessary to look at the final passage in chapter 4 (271a23-33) because, whereas Philoponus treats it as a sixth argument, Simplicius considers it a ‘part’ (194,8) of the fifth argument, another way of proving the same thing. For simplicity I shall refer to it as the sixth argument. The argument is very problematic textually.25 Here I quote the version of the text I use.

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But also if a motion in a circle were contrary to another motion in a circle, one of them would be pointless because it is necessary that what moves in a circle, wherever it begins from, reach all the contrary places in the same way; but the contrarieties of place are above and below, front and back, and right and left, and the contrarieties of motion are derived from the contrarieties of places. For if they were equal, they would not move, and if one of the motions were dominant, the other would not exist. Consequently, if both were, one of the bodies would be pointless, because not moving with its motion. For we say that a sandal which is not worn is pointless. But god and nature do nothing pointless. For Simplicius this passage is a reductio ad absurdum of the assumption that reverse motions on a circle are contrary. For if they were they would be from contrary places, and so things moving with them would have ‘contrary natures’ and so come into conflict when they meet. But then the two things would either cancel each other so that both would be pointless or one would dominate the other, in which case the other would be pointless. 26 After his discussion of the sixth argument at 154,18, Simplicius, thinking specifically of the sphere of the planets and the sphere of the fixed stars, raises the question whether motions on two different circles might be contrary. He says that one might think so on the grounds that the two spheres move from contrary places, the sphere of the fixed stars from the east, that of the planets from the west. Simplicius does his best to refute this argument, which is obviously specious since ‘from the east’ and ‘from the west’ as applied here specify directions not places of origin. Simplicius also claims that if the two motions were contrary the things moving with them ought to be contrary in nature, meet with one another, and change into one another, something which is, of course, not true of the fixed stars and the planets. In this passage Simplicius looks forward to an objection of Philoponus at 195,14-17 that Aristotle ought to have considered the question whether the two spheres move in contrary ways. Simplicius responds there that it is perfectly obvious that the spheres do not move in contrary ways in the relevant respect since they don’t affect one another, and he repeats the arguments he has already used. In connection with the fifth argument Philoponus raises objections to the definition of contrary motion as from and into a contrary, although Simplicius insists that Aristotle has been relying on the definition all along. Philoponus’ position is that, although this definition does apply to rectilinear motion and ordinary changes, there is no reason why it should apply to circular motion, for which another definition might be appropriate. He argues by trying to show that the

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Aristotelian definition leads to impossibilities. Simplicius’ responses are inadequate because he ignores the fact that Philoponus’ immediate goal is refutation of Aristotle’s claims, not establishing an alternative to them.27 Ultimately Simplicius is in the position of saying that Aristotle is not willing to call the opposition clockwise/counterclockwise a contrariety (192,10-11; 196,2-4). In connection with the sixth argument Philoponus asks at 197,10 why it is not true in the case of two contrary rectilinear motions on the same straight line that either one or both is pointless. Simplicius acknowledges the force of this objection, while implying that Philoponus borrowed it from someone else. His response is, however, rather weak: sublunary things, unlike heavenly ones, are naturally constituted to conflict and overpower one another, and the result is a good for the universe as a whole. 2. The text This translation is based on Heiberg’s edition of Simplicius’ commentary (Heiberg (1894)), 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)). They relate only to book 1. For Heiberg the most important manuscript is: A Mutinensis III E 8, thirteenth-fourteenth century, in the Este Library in Modena (Wartelle (1963), no. 1052). Heiberg ((1892), p. 71) singles out A for its correctness and purity. But he admits that it is badly deficient and hastily written, with frequent incorrect divisions of words, misunderstandings of abbreviations, arbitrary use of accents and breathing marks, extremely many omissions, and frequent insertions in a wrong place of words occurring in the vicinity. A glance at the apparatus on almost any page of Heiberg’s edition makes clear how often he feels forced to depart from A. On the whole these departures seem justified, but there are some cases where he follows A and produces a text which seems to me impossible or at least very difficult. Heiberg thought that A and another text derived independently from a lost archetype. That other text is: B Ottobonianus gr. 83, sixteenth century, in the Vatican Library (Wartelle (1963), no. 1896). B stops in book 1 (at 292,25 in Heiberg’s text), the remaining pages

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being torn out. Heiberg stresses its defective quality. Among the other manuscripts which Heiberg cites are:28 C Coislinianus 169, fifteenth century, in the National Library in Paris (Wartelle (1963), no. 1560). D Coislinianus 166, fourteenth century, in the National Library in Paris (Wartelle (1963), no. 1558). E Marcianus 491, thirteenth century, in the library of San Marco in Venice (Mioni (1985), pp. 299-300; not in Wartelle (1963)). 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 De Caelo 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 also cites three printed versions of the commentary in his apparatus: (a) The editio princeps of the Greek text. Simplicii Commentarii in Quatuor Libros de Coelo, cum Textu Ejusdem, Venice: Aldus Romanus and Andrea Asulani, 1526. (b) The editio princeps of the Latin translation of William Moerbeke. Simplicii philosophi acutissimi, Commentaria in Quatuor Libros De coelo Aristotelis. Venice: Hieronymus Scotus, 1540. (c) Karsten (1865). Citations of (a) are rare because Heiberg ((1892), 75) realised that it was a translation back into Greek of Moerbeke’s Latin translation.29 However, he did not realise that (b) was ‘corrected’ in the light of (a). In my reports on what is in Heiberg’s apparatus criticus I omit what he says about (b), but, when it seems to me useful, I do cite as ‘Moerbeke’ the readings in the recent edition of Moerbeke’s translation of Simplicius’ commentary on book 1 (Bossier (2004)). Karsten’s edition was published one year after his death. It includes no critical apparatus, and has no preface by Karsten.

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Throughout it is based on single manuscripts. For 1-94,16 Karsten relied on a ms. Heiberg took to be descended from B: Taurinensis C.I.13, sixteenth century, in the National Library in Turin (Wartelle (1963), no. 2086). And for the rest of book 1 he relied on a ms. Heiberg took to be derived from E: Parasinus, gr. 1910, fifteenth century, in the National Library in Paris (Wartelle (1963), no. 1396). In the absence of a critical apparatus or inspection of these manuscripts, it is impossible to tell what alterations of his source Karsten made, but there is little doubt that he made ‘improvements’.30 I have sometimes thought it desirable to adopt them rather than what Heiberg prints. For Karsten’s readings I have relied on Heiberg’s apparatus, which includes an extensive, although not complete, record of Karsten’s text. My departures from Heiberg’s text are recorded in the footnotes and in the ‘Textual Questions’. For the text of De Caelo itself I have relied on Moraux. 3. Brackets and parentheses Square brackets are placed around lower case Roman numerals which I have inserted for clarification. Angle brackets are used to set off major and possibly debatable insertions made for clarification. (Many minor insertions such as the substitution of a noun for a pronoun are made without remark when they are judged to be relatively certain; in particular I have frequently inserted a proper name where Simplicius has only a ‘he’ or a third person singular verb.) If an insertion represents an addition to the Greek text a footnote explaining this is attached. Parentheses are used as punctuation marks and to enclose Greek words inserted as information. Occasionally they are used to mark an insertion by Simplicius in a quotation. Notes 1. That is, has no temporal beginning or end. For the most part discussion focuses on the question of whether the cosmos had a temporal beginning. 2. There is some discussion of Philoponus and Simplicius with references in the Introduction to Mueller (2010). 3. In particular I refer the reader to Hankinson’s translation for discussion of the philosophical meaning and merits of what is said by both Aristotle and Simplicius. The notes in Wildberg’s translation are largely textual, but Wildberg (1988) is essentially a philosophical commentary on the fragments

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of Against Aristotle; to facilitate the reader’s use of this material I have provided an index to the fragments found in the text translated in this volume as Appendix 1. I would also like to record here my indebtedness to Rescigno (2004), which provides a text, Italian translation, and analysis of the fragments of Alexander’s commentary on book 1 of De Caelo. In Appendix 2 I give an index to those fragments found in the text translated in this volume. 4. I use the quotation marks here because Simplicius holds that what we (and Aristotle) call simple bodies are really composites the motions of which are determined by their dominant component; see Appendix 3 on the purity of the elements. 5. This description is rendered much more complex by considering the ‘entireties’ of the four elements, which form concentric layers, with a spherical earth at the centre of the cosmos, followed by water, air (divided into a stagnant air beneath the mountain tops and a pure air above them, and fire). For Simplicius (and at least for the sake of argument Philoponus) and (according to Simplicius) Aristotle, the entireties of earth, water, and stagnant air are at rest, whereas the entireties of pure air and fire (both together or sometimes fire alone being called the hupekkauma) revolve along with the dominant east-west motion of heaven. 6. See 66,17-70,33 in the commentary on chapter 3. 7. 92,18-20; cf. 108,5-6. 8. Simplicius is here in agreement with Themistius, whom Philoponus cites (131,20-4) as correcting rather than explaining Aristotle’s position. 9. Simplicius sometimes represents Philoponus as claiming that there is no coming to be involving contraries; see, e.g., 123,11-14. This seems unlikely. 10. cf. Wildberg (1988), p. 193. 11. cf. also 133,11-19. When Simplicius first introduces the question whether there is a contrary to the cosmos or heaven at 121,25 he gives a citation from Philoponus according to which, even if the motion of heaven does not have a contrary, it does have a privation. Simplicius responds to the objection in the same weak way: since Aristotle believes the motion of heaven is eternal he cannot believe it has a privation. 12. See especially chapter 11.1-9 of Philoponus’ Against Proclus. Simplicius indicates (136,9-10) that many arguments have been given against the doctrine that the ultimate substratum is the three-dimensional but contents himself with one (136,1-7) according to which, since it is matter, the three-dimensional should be formless, without shape, size, number, or colour but also since it is three-dimensional, it is finite and should have form, shape, size, number, and colour. Philoponus would presumably accept that the three-dimensional is formless, except in the sense of being three-dimensional, but deny that this entails that it has form, shape, size, number, or colour. 13. For an argument that Simplicius is mistaken in this interpretation of Aristotle, see Sorabji (1988), 14-15. At one point (156,13-14) Simplicius suggests that the matters of the different heavenly spheres are different. 14. 134,26-32; cf. 142,24-5, where Philoponus concedes that heaven has never been observed to undergo ‘any of the things which lead to perishing’. 15. For Philoponus the simultaneous divine creation of matter and form is a consequence of the fact that god created without a pre-existing substratum and that form cannot exist without a substratum. For statements of the

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simultaneous creation of form and matter in Against Proclus; see, e.g., 6.11, 158,10-23 and 164,20-165,2; 11.1, 409,8-18; 12.6, 476,11-21. 16. Simplicius adds (118,20-2) without explanation that the word aithêr indicates that heaven ‘is highest and superior to the things beneath it and is finest and purest’. 17. For Simplicius’ rather weak attempt to explain the final words of chapter 3 (270b26-31) as a preliminary to the proof of IV see 144,17-29; Longo ((1961) ad loc.) considers the Aristotelian passage to be out of place. 18. Simplicius asserts what amounts to V’ at 157,3-6; cf. 161,21-3 and 167,25-7. 19. There is a similar apparent misrepresentation at 164,15-19. 20. It is necessary to keep in mind that in the disagreement between Philoponus and Simplicius the important cases of primary substance are the simple bodies and the cosmos or heaven. 21. I pass over what seems to me an insignificant discussion (170,22171,17) of whether Aristotle is talking about contrariety of lines or contrariety of motions on lines. 22. Simplicius’ point is that, e.g., a circle does not change into a straight line as a result of the being acted on by the straight line. 23. i.e., the centre. 24. Passing over disagreements about the meaning of Aristotle’s remark (271a12-13) that motion on a semicircle ‘is the same as motion on the diameter’ (185,3-13), and about an obscure phrase of Alexander’s (185,1322). 25. See the notes on 152,3 and 32. 26. After giving his interpretation of the passage Simplicius quotes and disagrees with a number of interpretive claims of Alexander (152,2-153,16). He then gives Alexander’s version of the whole argument that there is no contrary to motion in a circle, a version which is independent of this sixth argument. 27. To give one example Simplicius objects (190,15-191,5) to Philoponus’ arguing both that rectilinear motions are more contrary to each other than to circular motion and that there are different kinds of contrariety for rectilinear and circular motions. But Philoponus makes these claims in connection with different Aristotelian arguments. 28. I mention only the mss. cited in my footnotes. 29. A fact first noticed by Peyron (1810). 30. cf. Bergk (1883), p. 143, n.1 and p. 148.

Translation of the text commented on (On the Heavens 1.3, 270a12-4); outline of the commentary Since in this work the ratio of commentary to text commented on is unusually high I give here the text of Aristotle broken down in accordance with the lemmas in Simplicius. I indicate the pages in the commentary where the lemma is discussed directly and in Simplicius’ diatribes against Philoponus. The figures inserted for chapter 4 are taken from Heiberg. I. Heaven does not come to be or perish, change in size, or change in quality. Chapter 3.270a12-b25 (91,21-109,15) 3, 270a12-22 Similarly it is reasonable to suppose that also does not come to be or perish or increase or alter because everything which comes to be comes to be from a contrary and some substratum and it likewise perishes by the action of a contrary and into a contrary with something underlying, as was said in our first discussions. But the motions of contrary things are contrary. And so if there can be no contrary to because there is also no motion contrary to motion in a circle, it seems that nature was right to exempt what was not going to come to be or perish from contraries; for coming to be and perishing are found in contraries. (91,21-109,15, including a lengthy excursus on the devolution of the cosmos from the One and the notions of coming to be and perishing; cf. 119,13-136,12) 3, 270a22-5 Moreover, everything which increases is caused to increase by something of the same kind which accrues to it and is resolved into the matter; but there is nothing from which this has come to be. (109,16-110,32) 3, 270a25-35 But if it does not grow or perish, it is possible to accept by the same reasoning that it does not alter. For alteration is change with respect to quality, and the states and conditions of quality (such as health and illness) do not come to be without changes in affection. But we see that every natural body which changes in affection, for example the bodies of animals and their parts and similarly those of 25

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plants and those of the elements, grows and decays. Consequently, since the body which moves in a circle cannot grow or decay, it is reasonable that it also does not alter. (111,1-115,20) 3, 270b1-4 That the first body is everlasting and does not admit either growth or decay, but is without aging or alteration or affection is evident from what has been said – if one trusts our assumptions. (115,21-116,2) 3, 270b4-9 It seems that this theory corroborates the phenomena and that the phenomena corroborate the theory. For all people have a conception of the gods, and all of them, Greeks and non-Greeks – if, indeed, they believe in gods – assign the highest region to the divine, obviously because what is immortal is linked with what is immortal. For it cannot be any other way. (116,3-117,5; cf. 139,27-142,7) 3, 270b10-11 So if (eiper) there is something divine, as there is, what we have just said about the first substance of bodies is correct. (117,6-19) 3, 270b11-16 This also follows sufficiently from perception, at least if we speak in relation to human confidence. For, according to the record handed down from one person to another in all past time, nothing is observed to have changed either in the whole of the last heaven or in any of its proper parts. (117,20-118,13; cf. 142,7-143,31) 3, 270b16-25 It seems that also the name has been transmitted until the present time by the ancients, who understand matters in the way in which we do. For one should believe that the same opinions occur to us not just once or twice but infinitely often. And so, thinking that the first body was different from earth, fire, air, and water, they called the highest region aithêr, determining its name from its ‘always running’ (thein aei) through time everlasting. (However, Anaxagoras badly misuses the name aithêr, since he uses it to mean ‘fire’.) (118,14-119,6) 119,7-144,4 Against Philoponus (with a lengthy discussion of coming to be and perishing and of contrariety and privation). II. Premiss needed for I: there is no contrary to motion in a circle Chapter 3, 270b26-Chapter 4, end (144,5-201,10) 3, 270b26-31 It is also evident from what has been said why it is impossible for the number of so-called simple bodies to be greater. For it is necessary that a simple body have a simple motion, and we

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say that the only simple motions are in a circle and in a straight line, and of the latter there are two parts, motion from the centre and motion to the centre. (144,5-145,9) 4, 270b32-271a5 One can gain confidence that no other motion is contrary to motion in a circle from several considerations. In the first place we suppose that a straight line is most of all opposite to a circular one. For concave and convex are not only thought to be opposite to one another, but also, taken together and as a pair, they are thought to be opposite to the straight. So if something is contrary to motion in a circle, it is most necessary that it be motion in a straight line. But the motions in a straight line are opposed to one another by places, since up/down is a differentiation and contrariety with respect to place. (145,10-146,16; cf. 170,11-176,12) 4, 271a5-10 Moreover, if someone assumes that the same statement which holds of the straight line also holds of the circular one (namely that motion from A toward B is contrary to motion from B toward A), he is speaking about motion in a straight line, since such motion is finite, but the circular motions between the same points are infinite. (146,17-147,21; cf. 176,13-179,23)

Figure for 271a5-101

4, 271a10-13 Similarly in the case of the motion on a single semicircle, for example, that from C to D and from D to C. For it is the same as the motion on the diameter. For we always suppose that each thing is distant by a straight line. (147,22-148,26; cf. 179,24-187,27)

Figure for 271a10-13

4, 271a13-19 Similarly, even if someone were to draw a circle and lay it down that motion on one semicircle is contrary to that on the other, for example, that in the whole circle the motion from E to F on the

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semicircle G is contrary to the motion from F to E on the semicircle H. And even if these are contraries, nevertheless the motions on the whole circle are not thereby contrary to one another. (148,27-149,28; cf. 187,28-189,21)

Figure for 271a13-19

4, 271a19-22 However, the motion in a circle from A to B is not contrary to that from A to C either, since these motions are from and into the same thing, but contrary motion is defined2 as from a contrary into a contrary. (150,1-19; cf. 189,22-194,5)

Figure for 271a19-22

4, 271a22-33 But also if a motion in a circle were contrary to another motion in a circle, one of them would be pointless3 because it is necessary that what moves in a circle, wherever it begins from, reach all the contrary places in the same way; but the contrarieties of place are above and below, front and back, and right and left, and the contrarieties of motion are derived from the contrarieties of places. For if they were equal, they would not move, and if one of the motions were dominant, the other would not exist. Consequently, if both were, one of the bodies would be pointless, because not moving with its motion. For we say that a sandal which is not worn is pointless. But

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god and nature do nothing pointless. (150,20-156,24, including an excursus on whether the sphere of the fixed stars and the sphere of the planets move in contrary ways; cf. 194,6-198,6) 156,25-201,10 Against Philoponus. Notes 1. This figure is taken from Heiberg’s text at 146,23; the next are taken from 147,29, 149,5, and 150,8. 2. cf. Physics 5.2, 229b21-2. 3. Following Allen (1936), I bracket the words epi to auto gar (‘For they are to the same thing’); see the notes on 152,3 and 32.

SIMPLICIUS On Aristotle On the Heavens 1.3-4 Translation

Simplicius on the first book of Aristotle’s On the Heavens

270a12 Similarly it is reasonable to suppose that also does not come to be or perish ... . 1 He has proved that the body which moves in a circle is something different from sublunary things, more complete than they and prior to them, having neither weight nor lightness. He next proves that it ‘does not come to be or perish or increase or alter’ with the consequence that it does not undergo any change except change of place and of such change motion in a circle. Just as in the preceding he derived2 the transcendence of what moves in a circle over sublunary things from the difference in their motions, so now he derives from the form of circular motion both the ungeneratedness of heaven by comparison with the way we say sublunary things are generated3 and the fact that it does not increase or alter. And first he proves that it does not come to be or perish by giving, I believe, the following syllogism in the second figure: [i] The body which moves in a circle does not have a contrary; [ii] what comes to be or perishes has a contrary from which it comes to be and into which it perishes; and the conclusion is [iii] ‘therefore, the body which moves in a circle does not come to be or perish’. Of these two premisses he now proves the minor [i], which says that the body which moves in a circle does not have a contrary. For the demonstration of the major premiss [ii] he refers to the first book of the Physics; he calls them ‘our first discussions’ because they deal with the first principles of nature. He proves in turn that the body which moves in a circle does not have a contrary with the same kind of argument as follows: [iv] What moves in a circle does not have a motion which is contrary to its own natural motion; [v] what has a contrary also has a motion which is contrary to its natural motion, namely the motion with which its contrary moves naturally (he has posited this with the words ‘But the motions of contrary things (obviously natural things) are contrary’); 33

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Translation and the conclusion is [i] ‘what moves in a circle does not have a contrary’.

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Here again he has taken the major premiss [v] as something clearly true. For since the natures of contrary natural forms4 are contrary, their motions are as well because nature is a starting point of motion. He demonstrates the minor premiss [iv], which says that there is no motion contrary to the motion of the body which moves in a circle, that is to motion in a circle, later,5 having said more things in between. The whole argument depends on these two things, one that if something is going to come to be or perish there must always be something underlying and a contrary from which it comes to be and into which it perishes, the other that there is no motion contrary to motion in a circle; he will pursue the demonstration of the latter in several ways a little later, and he now assumes the former without demonstration since it was proved in the Physics. Accordingly we should now recall what he said there and, after having first distinguished the meanings of ‘comes to be’, we should clarify in which sense Aristotle is now making his argument and in which one he denies that heaven comes to be so that we may learn in what senses Plato says the universe comes to be and Aristotle says that it does not without contradicting one another.6 Now in general something is said to come to be if it receives its existence from some cause. For certainly what is made is made by a maker and what is generated is generated by a generator, and, as Plato says,7 it is impossible for anything to come to be apart from a cause. And it is clear that in this sense the only thing which does not come to be is the first cause of everything, and this cause is both one and absolutely simple since everything participates in the One and what doesn’t participate in it is nothing. However, the One does not even participate in plurality, and so everything which comes to be is pluralised. For plurality is given existence directly by the One, since it is also necessary for plurality to participate in the One in order that it not be infinitely many times infinite. However, the One is without trace of plurality since it is one in the strict sense. Because the first plurality which proceeds from the One participates directly in the One it is unified and remains in the One; and to the extent, however slight, to which it proceeds from the One, it does to that extent come to be. And as a result of this divine men have handed down to us theogonies, the plurality of gods which remains in the One and, as some would say, processes forth by the multiplication of the One; and these men make hymns to the coming to be of this plurality insofar as it has gotten its existence from the One, in just the way that we see progression from the monad as the coming to be of numbers. However, insofar as plurality re-

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mains in the One it is unified by the highest unification, no division (in which what is not is first produced) yet appearing. And that is Being in the primary sense, and it is also the first principle of beings, and not only something derived from a principle. But, as the Socrates of the Phaedrus8 shows, a first principle does not come to be. For this thing, which is self-substantiating in every way, is first and is Being in the strict sense.9 For the absolutely One, which is the cause of Being, is superior to what is self-substantiating and reveals something which is double and both gives and is given existence. And the first plurality is ruled by the One and is able to give existence because of the One and to receive existence because of plurality, and, as a result, it is not absolutely one because the One which is the cause of all things is above it. The very first and most authoritative being is a whole which exists simultaneously both in terms of being and of the extendedness10 of being, and so the time of our world is given its ‘always’ by Being.11 But since this time also remains in the One, its always, which is forever, is a restricted . For, being a unified plurality or rather a pluralised one, does not reveal either an extension in substance or an extendedness in being in the strict sense, and therefore, it is also what it is, genuine Being. Next, what is given existence directly by12 is given existence directly; it moves from Being and becomes different from it and is given substance in terms of this motion. And just as is self-substantiating, so too this has come to be self-moving. For insofar as it moves from13 Being, it is given existence because of motion, but, insofar as it is proximate to Being and not yet separating from itself, it has become self-moving just as what is prior to it14 is self-substantiating; and it has what moves and what is moved as the same thing because it is still filled with the One and ruled by it. But something pluralised proceeds from this, something which also participates in the One in a way but does not remain in the One and is not ruled by it; and therefore, because it is divided into parts, it is no longer either self-substantiating or self-moving because it no longer contains in itself the cause of existence connected to the One in the way that what is unified15 and what comes after it do. This thing immediately undergoes extension in substance and extendedness with respect to being16 because, departing and separating from the One in every respect, it has become body and things of the same kind as body. And time proceeds together with this from that eternity, measuring the extendedness of its being and receiving the always of time. But in this case there is no longer a simultaneous whole with respect to either substance or extendedness of being or (as some might say) with respect to life. And so, since this participates in much which is not, it is not a being in the strict sense; for a particular part of its substance is not exactly what it is (hoper todi),17

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nor is its being the same, but rather, as time flows, it is different at different times, so that it also does not receive its generation from its cause as a whole simultaneously (since if it did it too would be Being), but it receives its generation piece by piece in the way that it can. Departing entirely from the One and participating in it as something entering from outside, the plurality in it has become a composite18 rather than a unified thing, and therefore it also gets its existence entirely from an external source. For a plurality which is unified contains the One in itself, and since the One is what gives existence to all things and gives it in the strict sense, even if a unified plurality moves down from the only thing which gives existence, nevertheless it holds what gives existence in itself and it has become self-substantiating. But a composite plurality receives the one of composition from outside, and, coming to be in the indefiniteness and extension of this sort of plurality, it immediately becomes the one form which is in matter, just as what is self-moving is intermediate between the two.19 And so what participates by composition in the One as form in matter does not exist simultaneously as a whole either in terms of substance or in terms of the extendedness of being, and it is not at all the cause of being for itself because of being divided, as a result of which it no longer contains in itself the One. For what is divided exists part by part and is no longer a whole or self-substantiating in the strict sense, just as what causes motion part by part is not self-moving in the strict sense; for what is self-substantiating or self-moving in the strict sense must be without parts and unextended and coincident with itself as a whole, but what has parts and is extended only has its being from outside. So as a result and because it is composite and is not what it is as a simultaneous whole but has its being in coming to be, what has parts is what comes to be in the strict sense as distinguished from what is in the strict sense, namely what gets its being from itself and is simultaneously as a whole what it is. This sort of generated thing acquires both change and motion directly from Being because it does not remain in Being in the strict sense, and therefore it does not remain entirely in the same condition, since, if it did, it would remain in the One, just as genuine Being does. But it is always changing and moving out of its previous state, and so time moves along with it, measuring and ordering its unfolding, just as something else, whether it is place or something else which has this power, orders the divided extension of its substance and its corporeal nature. And so for the reasons given this is what comes to be in the strict sense. Because Being is unmoving and always in the same condition with respect to substance and power and activity, it is necessary that what is given existence directly from Being20 always continue to come to be, since Being in the strict sense has entered into what comes to be and the always of eternity has entered into the always of time. For

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receives the completeness and entirety of Being, which exists as a simultaneous whole, part-bypart as it is able, imitating its infinite power by means of this ‘to infinity’. The much-honoured heaven shows itself to us as this sort of thing, existing in corporeal nature as the first thing after the intelligible order, a most beautiful image in relation to the best of paradigms, since what comes to be moves down from unity and sameness into similarity to Being and becomes an image because it then is connected to Being by resemblance rather than by being. Because it is moved in a motionless way and causes change in an unchanging way, heaven has only those kinds of change which can exist together with stability. Therefore it has change with respect to place, the kind of change which can occur while the substance and substantial constitution of a thing remain, since of the kinds of change, it has the least connection with the substance and constitution of things. And of the kinds of change of place heaven has received the one with which, although it changes place, it does not depart from its place, but rather it remains in the same while moving, whereas, of things which move in a straight line, even one which moves a very short distance does not remain in the same place. Consequently motion in a circle is more rest than motion since in an amazing way things which move in a circle remain fixed as a whole but revolve in their parts. Being everlasting because of being given existence directly by what is unmoving, heaven is superior to change from not being into being or from being into not being, which it is customary to call coming to be and perishing. For if it came to be at some time not having previously been, it would be necessary that its cause make something at some time, not having made it previously, and that this cause no longer be preserved as unmoving and always the same; and if it perished it would lose its similarity to the unmoving cause, and that cause would no longer be the immediate cause or what21 makes exist the things which are directly given existence by it. Since increase and diminution are a kind of coming to be and perishing, they stand as completely alien to the generated thing22 which is introduced directly by the unmoving cause. But in a way which we will perhaps understand as we proceed23 one can in a sense observe qualitative change in that thing. And so the very first and most perfect generator of corporeal existence gave existence to this sort of thing, which does exist but it is not entirely unchanging; for even if, as Plato says in the Statesman,24 it participated in many blessed good things coming from its generator, nevertheless it shared in body – that is, it was extended and divided and underwent unfolding from being – and therefore it was impossible for it to endure with absolutely no participation in change. And so, changing its place and configurations and standing in different states at different times

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because of its different ways of participating in the goodness accruing to it from its causes, it introduces the things under it, but no longer without motion in the way in which it was introduced but rather giving existence to these things by moving. Here then substantial change first appears and the coming to be and perishing of substance take their start. But coming to be is not from what is not in any way and perishing is not into what is not in any way25 because the causes, changing from one state into another, give existence to the differences of the things which are introduced here.26 Perhaps one should state matters more clearly as follows. The intelligible plurality27 is also unified with respect to the division of itself, which is understood as taking place in the intelligible because everything which genuinely is remains in the One. And therefore, not only do the different forms exist together simultaneously in that substance, but so do their contraries, and they participate in one another and are unified with one another in such a way that their participation is not something extraneous; nor does acting and being acted on have any place there. And so those things transcend coming to be in the strict sense.28 Extension, division, and change make their appearance in the first things29 which come to be in the strict sense, but their likeness to what has no parts is preserved in its purity. The parts and forms which fill out that substance are distinguished from one another; they act on and are acted on by one another because they are separated from one another, but nevertheless, what acts acts and what is acted on is acted on while the substance endures and their activity with respect to one another brings about a completion; for by participating in one another the forms in what comes to be are images of the unity in what genuinely is. However, the things which are in what is given existence directly by Being act perfectively, but the things30 which are subsequently given existence from these move down from the ‘always’ of time to the ‘somewhere in a part of time’ 31 because they are given existence in terms of the conditions of heavenly things which come to be different at different times so that they are one way when the sun happens to be in such and such a sign of the zodiac and another way when it happens to be in another. And so when the separation in the last plurality has become great and sublunary substances are composed32 from things separated in this way, all things do not participate in all things nor are all things in all things,33 but those different things which have come together in one form can exist together with one another, and they participate in one another without conflict, and contraries which endure the whole separation in our world are all combined into the same thing,34 and most of all the more generic of these, such as heat, cold, dryness, moistness, and the things which accompany these and are apprehended by each of the senses, such as whiteness, blackness, acuteness, heaviness,

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sweetness, bitterness, roughness, smoothness, and the antitheses related to smell. These things are not combined on their own, but rather they are combined together with the bodies which underlie them in which they have their existence. These bodies are the first elements, fire, air, water, and earth, from which other things, animals and plants, are composed. But when a combining of something harmonious and balanced deriving from heavenly things occurs, a combining which has a suitability for this35 or that one of the composite forms, then that form shines out and holds together the coincidence of the contraries and is held together by it. But when contrary things such as fire and water, because they are naturally difficult to mix, remain in conflict with respect to their contrary qualities, then it is necessary that at some time one of them dominate and increase from the diminishing of its opposite and at that time that composite form, such as that of cow or horse, which is of a nature to attach to that sort of balance of the elements, perishes; but when another form of balance and a different suitability comes to the elements because of overbearing and being overborne among the elements, bees come to be from a cow, wasps from a horse and different worms from different animals and plants.36 There are times when a great overbearingness of the elements has occurred among composites, and , having then gotten weaker or37 having gotten older, become unsuitable for receiving a composite form; they are dissolved and then move into their own entireties, and there they are renewed and rejuvenated, and then they again move toward combination. These things are most of all made clear by water, which is most suitable for coming to be and nourishment when it has become pure and is separated from its own entirety, as is seen in the case of springs. And it is clear that in our world coming to be and perishing are changes which come to be by the action of a contrary, changes which are from one contrary state into another; in the case of the elements water, for example, is changed by fire into a structure which is contrary to water, a fiery structure, and in this way fire comes to be from what is contrary to itself in terms of contrary qualities,38 namely water, by the action of a contrary of water, namely fire; for it is necessary that what perishes be contrary to what makes it perish, and that the result of coming to be be the same as what acts. For the production of the elements is a change into themselves which is from things which are acted on and produced by39 things which act, where obviously the substrata are suitable for each of what acts and what is acted on. And again, the perishing of a contrary comes about by the action of a contrary; for water perishes into fire by the action of fire. Consequently the perishing of one thing is the coming to be of another and the coming to be of one thing is the perishing of another, with qualities being destroyed into what is not; for when fire comes to be

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from water the cold and moist quality departs from a corporeal substance, which takes on the qualities of fire. And this happens when the change is from one substance, that of water, into another substance, that of fire. But when the elements act on and are acted on by each other with respect to qualities more faintly so that they implant in one another from themselves a condition, water becoming warmer while remaining water, fire becoming cooler or moister while remaining fire, then there is said to be a qualitative change and the result is said to be an affection, since one substance has not come to be from another, but a substance has only come to be differently qualified. And it is clear that not just any condition comes to be from any condition, but a contrary condition comes to be from its contrary; for what is cooled is not cooled by dryness, but by coldness; for what is affected is affected by what acts and acts with respect to its own nature and by being what it is. For what acts naturally acts in this way, and is affected with the sort of affection which the producer had, that is, the affection with respect to which the producer acted; and what acts naturally and by itself implants the kind of affection which the producer had as a quality and with respect to which it acts. For what acts naturally wants to change what is acted on into itself, but a contrary is changed into a contrary, the heat in what is cooled into the coldness in what cools. But, as I said, when there is a qualitative change, what comes to be comes to be these things incompletely, and what was previously warm becomes cooler, but not in such a way to be cooled completely and change into the nature of what does the cooling: this is what happens in the case of things which come to be and perish . However, in every case a contrary acts on a contrary and destroys it, wanting to change what it acts on into itself. For example, if fire acts on air, wanting to change it into itself and make it fiery, then, since air is also assumed to be hot, fire does not want to change the heat of the air; for heat can also exist in the fire. However, since it is impossible for moistness to exist together with fire, fire destroys this, not with heat by itself but with dryness, and the heat coincidentally cooperates with the dryness. And so one might also give the following syllogism. Sublunary bodies which act naturally act with the desire to multiply themselves. Things which act for the sake of multiplying themselves change what they act on into themselves. Things which change what they act on into themselves make the things in what they act on which cannot exist together with themselves perish. Things which cannot exist together are contraries, and contraries are destroyed by their contraries; for things which can exist together in a common substratum do not destroy one another. And so when the contraries in what is acted on are destroyed by their contraries in what acts and the substratum takes on the qualities or quantities of what acts in place

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of their contraries which it previously possessed, it changes into the nature of what acts, and what was previously water becomes fire by the action of fire via air as an intermediate: the heat, being more active, first casts out the cold from the water and then the dryness casts out the moistness. And any magnitudes or figures which cannot exist together are changed into their contraries, and in this way the corporeal extension of water (or something else40 in the water which is more material), accepting the qualities contrary to the ones it had, changes from water into fire, with the qualities it has in common with fire and which could exist together with each of the qualities enduring. whether the corporeal nature itself41 has some qualities which are common at some time or prime matter has them; for when a change occurs it is necessary that something remain which is the subject of the change, and in the strict sense it is the thing which changes with respect to the departing quality. And so, some of these qualities themselves perish and others come to be, but the substratum changes with respect to them, and this is not just true in the case of coming to be but also in the case of qualitative change. For it was also said42 about the latter that when the change of what is acted on with respect to contrary qualities is not complete but is only a slight alteration43 of different things from different things, as in the case of water which is heated, then what is acted on does not become different, but only differently qualified. Now this is not just true in the case of qualitative changes in the way I have said, but it is also true in the case of natural increase and diminution; for what increases naturally, for example what is nourished, changes the contrary conditions in the nourishment toward itself and makes the nourishment similar , and in this way it attaches the nourishment to itself and grows. And even if the capacity to take in nutrition involves something related to soul, it nevertheless accomplishes what it does in terms of natural changes.44 But also things which change place change from one place to another with the thing which changes enduring. And so every sublunary transformation is a change, with the changing thing enduring in some respect. Therefore what comes to be in time does not come to be from what is not but from what is; for, just as the time at which these things come to be is preceded by another time after which it exists, so too what comes to be is preceded by something else after which and from which what has come to be has come to be.45 And so it was reasonable for Aristotle to posit change as the genus of all sublunary transformation in the Physics.46 And it is also reasonable that this change is everlasting, not just because it is given existence by the everlasting change in heaven, which is a change of place with respect to the different configurations47 but also because the perishing of one thing is always the

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coming to be of another. And it is reasonable that the simple bodies in our world endure forever in their own entireties, but undergo coming to be and perishing in their parts. For even if the change of compounds comes to be primarily with respect to these parts, and when are dissolved move naturally into their proper regions and entireties, the entireties endure and send away parts of themselves and again receive back parts, and this happens forever because of the everlastingness of change. And it is reasonable that, since coming to be is a change, things that come to be and perish or increase and diminish or alter or change in place – and in general what undergoes change – change from a contrary state into a contrary by the action of a cause which is contrary to it. And that is why in the first book of the Physics48 Aristotle, seeking the principles of natural things which come to be and perish, says that they are contraries and what underlies them. And it is clear that things which come to be or perish with respect to qualities, such as heat or dryness, have contrary qualities and change from them. However, things which change with respect to substance, such as fire insofar as it is fire or a human being insofar as it is a human being, also change because of the change of qualities into one another. But they are substances insofar as they are fire or a human being, and there is no form contrary to a substance. So from what do they come to be, not as hot or cold, but as a human being? It is clear that they come to be from what is not a human being but is naturally constituted to become a human being. The seed and the katamênia are things of this sort, not insofar as they are just seed or katamênia, but insofar as they are not a human being but are of a nature to become a human being. For it would not become a human being if it were a human being, since what is does not become what it is. Nor would it become a human being if it were neither a human being nor of a nature to become one. So what single word do we use to refer to this insofar as it is not something but is of a nature to become it? It is customary to refer to it as a privation or lack (sterêsis) and to say that what does not have the form which it is said to lack but is of a nature to possess it, is lacking. And so a new-born puppy lacks eyes because it is of a nature to have them, but what has been made completely blind is said to lack eyes with respect to some other privation but not this one, since this privation cannot make a turn (anakamptei), but the privation involved in coming to be, from which things which are said to come to be change into the form, does make a turn into the form. Now when something comes to be cold from being hot, it comes to be from what is not cold but is of a nature to come to be cold and therefore from what is hot; for what is dry is not of a nature to change into what is cold by the action of what is cold because it is possible for dry to exist together with cold. So if it is not true of everything which comes to be, that it comes to be from a

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contrary form which exists together for a while with the substratum in the way hot comes to be from cold (for first of all it is not true of substances, since substance has no contrary), but it is true of everything which comes to be, including what changes from contrary forms, that it comes to be from what is not so and so but is of a nature to be so and so, it is reasonable for Aristotle to call49 the general common principles of coming to be form, privation, and substratum. But when he calls50 form and privation contraries, he is not doing so in terms of the strict meaning of ‘contrary’ since both of two contraries are forms. Rather he is doing so in terms of opposition (antithesis) since form and privation are opposed to one another. I have set these things out at length in the desire to articulate my own thought about them most of all but – with reason – also that of those who will read them carefully. I think that on the basis of what has been said, everything for the sake of which this whole discussion was started has become clear: how what comes to be comes to be from some contrary and a substratum and how what perishes perishes from a substratum and into a contrary by the action of a contrary. This is now posited by Aristotle without demonstration because it has been proved in the ‘first discussions’, as he says.51 However, it is necessary to remember that even if a substance does not primarily come to be from or perish into a contrary in the strict sense (because substance is not contrary to substance), first of all it does come to be from its proper privation, and second it, too, does come to be through the coming to be of contraries from contraries, and again, conversely, it perishes through the perishing of contraries into a contrary. For when the qualities and quantities in the seed and the katamênia change into the contraries of themselves into which they are of a nature , that is, the qualities and quantities of a human being, then the form of human being supervenes; and conversely, when some elements overbear and their contraries are diminished and the substratum is carried down into disharmony, the substance perishes, but not otherwise. But since this is enough of these matters, let us next see in what sense of ‘comes to be’ Aristotle denies that heaven comes to be and tries to demonstrate that it does not come to be, and in what sense Plato says that both heaven and the whole cosmos come to be. Now it is clear that Aristotle calls only one thing coming to be: the change in time from not being into being, a change which is always followed by perishing. On this basis he will demonstrate52 that heaven not only does not come to be but also does not perish, and is even clearer when he clearly demonstrates53 that what comes to be always perishes and what perishes comes to be. For it is clear that he takes as coming to be and perishing those cases which occur in a segment of time and attach to sublunary things. And so, having demonstrated that there is a fifth

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substance apart from sublunary things, namely the substance of the heavenly body, which is prior to them in nature and more perfect, just as he denies that the fifth substance has weight or lightness or moves in a straight line (these being propria of sublunary things), so too he denies that it54 comes to be or perishes . I think this is indisputable both because he says that coming to be and perishing are a sort of change with one thing coming to be and perishing after another and because, speaking against those who say that the cosmos comes to be but does not perish, he proves55 that what comes to be always perishes as well. And it is not at all surprising that Aristotle, who always wants to take as assumptions things which are immediately clear to everyone, says that what comes to be is what shares in all coming to be56 and is seen clearly to come to be and perish in a segment of time. Plato, too, certainly knows this kind of coming to be of sublunary things which is the opposite of perishing, since in the tenth book of the Laws he writes:57 And the coming to be of anything results when what affection occurs? It is clear that it is when a starting point grows and comes into the second transition and then into the neighbouring one, and, coming as far as three, it takes on being perceived by perceivers. So everything comes to be by transforming and changing in this way. And it genuinely is whenever it endures, but if it changes into another state it is completely destroyed. However, Plato also knows the other kind of coming to be in which what has moved down into corporeal extension and is not further able to give itself existence but is only given existence by some other cause is said to come to be as distinguished from that which genuinely is and which is its immediate cause.58 For it is necessary that what comes to be and gets its existence from elsewhere get its existence from Being, which is self-substantiating; otherwise one proceeds to infinity, always positing one thing which comes to be prior to another. Having defined this kind of coming to be after this kind of Being in the Timaeus, Plato says that the cosmos comes to be in this sense. And the definition of both, which is based on our cognitive powers, is something like this: 59

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What is it which always is but does not come to be, and what is it which60 comes to be but never is? The one is grasped by thought with reason and is always the same,61 but the other is opined by opinion with irrational perception and it comes to be and is destroyed, but does not ever genuinely exist.

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And Plato says that the cosmos also comes to be in this sense of ‘come

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to be’, being given existence directly by the god who genuinely is. He writes the following about the cosmos:62 Was it always without having any starting point of coming to be or did it come to be?63 It has come to be, since it is visible and tangible, and it has a body. But everything of this sort has obviously come to be and does come to be. For what is self-substantiating must have no parts and be coincident with itself as a whole. But what is extended and has parts cannot be coincident with itself as a whole, and consequently, since it is not self-substantiating, it always gets its existence by the action of something else and is therefore said to come to be.64 However, some people interpret the term ‘is destroyed’ in the definition of ‘come to be’ carelessly and think that Plato obviously sentenced the cosmos and heaven to perishing. Therefore it is necessary to say what this term ‘is destroyed’ means. Since immediately after the words ‘comes to be and is destroyed’ Plato adds ‘but does not ever (oudepote) genuinely exist’, he is, I think, clearly indicating to those without preconceptions that existing forever transcends existing at some time (pote), since ‘not ever’ is said in the strict sense of everlasting things.65 However, exists forever because it is produced directly from what genuinely is and is unchanging; and conversely because it is not self-substantiating, does not genuinely exist, and is not simultaneously a whole and simultaneously everything which it is, changes in some way; and it receives a different completeness for itself at different times, but it receives it forever because of the directly productive cause, which is unchanging, and because of its own suitability, which it has because it is derived directly from what is genuinely existent. And I believe it is easy to see from what is written in the Statesman that Plato thinks that change attaches to not because it comes to be or perishes in some segment of time, but rather because of its corporeal nature because of which it does not have all its blessedness simultaneously, as what genuinely exists does. As I recall, what is written is sort of like this:66 What we call heaven or cosmos shares in many blessed things because of what generated it. Nevertheless it also shares in body, so that it would be completely impossible for it to remain without a share in change. Now suppose that it were to perish: if it perished into another cosmos, it would be possible to use the word ‘change’; but if it perished into what is not, it would not be said to change because what transforms

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from one thing into another changes.67 But why does he say ‘ without a share in change’ unless it also contains something which does not change? It is also clear from what is written in the Timaeus that Plato thinks that the cosmos neither has come to be in a segment of time nor perishes in a segment of time. First of all he says that time has come to be together with heaven when he says68 clearly, ‘So time has come to be together with heaven’. And so it is impossible for there to be a time before there is heaven. But if this is so, heaven did not begin to come to be after some time, since, if it did, time would have preceded it, and when the time at which the cosmos came to be was present, any preceding time would be entirely past. But it is also not possible for it to perish in a segment of time either. For again, after the present time at which it perishes there will be some future time. But if Plato said,69 ‘so that having been generated simultaneously they should also be dissolved simultaneously if some dissolution of them ever occurred’, he was using these very words to indicate their indissolubility. For if it is necessary that the cosmos be dissolved together with time (if, indeed, it were dissolved), but time is indissoluble (since what is dissolved at some time (pote) has time after it since ‘some time’ is a part of time), it is clear that the cosmos is indissoluble. And accordingly Plato added70 this to what had been said: And in accordance with the paradigm of the eternal nature in such a way that it would be as like it as possible; for the paradigm exists for all eternity, but it has come to be, is, and will be forever through all time.

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Now how could a thing of this sort, which ‘has come to be, is, and will be for all time’ have come to be after some time, say, for example, six thousand years ago,71 or perish at some time? However, these people, who are unable to distinguish the forever of time from the always of eternity and say that time comes to be and perishes in a segment of time, have no shame and they call as a witness Plato when he says,72 ‘so that it be as similar as possible to the perfect Intelligible Living Thing in imitating the eternal nature’. But how could what exists in a segment of time (and – as these people say – a very short one) be as similar as possible to eternity, especially if it is compared with what is forever? And what need is there to say very much when Plato has said clearly that because of their own nature, which is corporeal and extended, both heavenly and sublunary things (both earth – for he speaks clearly about earth73 – and obviously the entireties of the other elements) are not completely immortal since they participate in some change, but that because of the goodness of what directly creates them, which always bestows the

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appropriate goods upon them, they are indissoluble and will not meet ‘a fate of death’?74 But I think it is better to hear the words of Plato himself, or rather the words of the creator of all things, whose thoughts and deeds Plato, acting as a prophet, has proclaimed to us when he said,75 Now when all the gods, both those who revolve invisibly76 and those who are visible to the extent they wish, had come to be, the generator of this universe said the following to them: ‘Gods, of gods whereof I am the creator and of works the father, those which are my own handiwork are indissoluble save with my will.77 Now everything which is bound is dissoluble, but to will to dissolve what is well harmonised and in good condition is the work of someone bad. Therefore, also, since you have been generated you are not completely immortal or indissoluble, but78 you will not be dissolved or meet a fate of death since with my will you have attained79 a greater and more authoritative bond than those with which you were bound together when you were born. So now learn what I have to say to you. There remain80 three kinds of mortals which have not been generated, and if these are not generated, heaven will be incomplete since it will not contain all the kinds of living things, but it ought81 to contain them if it is going to be sufficiently complete. But if these things were generated and shared in life because of me, they would be equal to the gods. In order that they be mortal and this universe be genuinely everything, you must turn in accordance with nature to the creation of living things, imitating my power which was involved in your generation. And as far as concerns the part of them which it is appropriate to call by the same name as the immortals, the part which is called divine, and has command in those of them who always wish to follow justice and you, I will give it birth and existence and hand it over to you. And then, weaving what is mortal together with what is immortal, you must fashion and generate living things and give them nourishment82 and make them grow.83 And when they decay you must receive them again’. What could show more clearly than this passage that Plato thinks that the things84 which are given existence directly by the creator of the universe are indissoluble and immortal because of the creator’s goodness, even if, insofar as it was up to them, that is, up to their own division and separation from Being, they would be dissoluble because they get their unity (which Plato calls a ‘bond’) from outside themselves? And what could be clearer than the words ‘not completely immortal’ (that is not unchangeable in every way like I am), ‘but you will not be dissolved or meet a fate of death’?85 And who is so

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shameless or mindless as to think after hearing these words that Plato considers heaven to be perishable? And it is no less clear when he says that three mortal kinds still remain (the gods obviously not being mortal) and he orders the everlasting to use their own natural transformation86 and motion to weave together everything mortal with what had been made everlasting by the creator. For it would not be possible for them to be made mortal unless what gives them existence were changing. And so he also says this: ‘In order that they be mortal and this universe be genuinely everything, you must turn in accordance with nature to the creation of living things’. How then can heavenly things be mortal when they are brought into existence by a creator who acts without moving and eternally? I think that the words ‘you must fashion and generate living things and give them nourishment and make them grow, and when they decay you must receive them again’ are also appropriately addressed to the gods who rule the elements87 and preside over their entireties insofar as those gods also contain something everlasting; for particular living things are generated and nourished and grow directly from these sublunary elements, and when they decay they are again resolved into the entireties of the elements.88 I myself am not unaware that saying this much might be thought to go beyond the measure with respect to explaining what Aristotle says , but because I proposed to dissolve the objections of those who dispute the view that heaven does not come to be or perish and bring forward Plato as someone who provides support for them against Aristotle,89 I think it is not unsuitable to have recorded Plato’s views on these matters. But we should return to Aristotle’s words. Similarly it is reasonable to suppose that also does not come to be or perish ....90

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It was said earlier91 that, having proved that the body which moves in a circle is prior in nature to and more perfect than sublunary things and transcends motion in a straight line, he is now proposing to remove from it all the other changes as well, coming to be and perishing, increase and diminution and the qualitative change co-ordinate with these,92 so that it would only have the change which is least connected to substance, change of place, and only change of place in a circle, which is appropriate to everlasting things. And it was also said that he first gives an argument that it does not come to be or perish, and the analysis of the syllogisms was set out. And it was said that Aristotle demonstrated the other premisses in these syllogisms. He demonstrated the one which says that the body which moves in a circle has no contrary using the assertion that ‘the motions of contrary things are contrary’; for if things which have

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contrary starting points of motion are contrary in nature, it is clear that the motions of contrary things are contrary. So if there is no natural motion contrary to the natural motion of the body which moves in a circle – the discussion is about natural motions –, that is motion in a circle, it is clear that the body which moves in a circle has no contrary. (Alexander constructs a syllogism93 in the first figure as follows: if there is no motion contrary to the motion of a natural body, there is nothing contrary to the body; there is no motion contrary to the natural motion of the body which moves in a circle; therefore there is no contrary to the body which moves naturally with this motion.) Now Aristotle assumes two premisses of the whole argument without demonstration, one which says that what comes to be and perishes comes to be from a contrary and perishes into a contrary with some substratum underlying, the other that there is no contrary to motion in a circle. But, having assumed the second premiss now, he demonstrates it using many proofs later, and therefore he postponed bringing in the demonstration of it. He refers the demonstration of the other premiss to what is said in the first book of the Physics, things which I have also articulated94 at length as well as I could. These two premisses being assumed, he infers the body which moves in a circle will not come to be or perish, there being nothing from which it could come to be or into which it could perish. In this connection Alexander asserts that since things which have contrary motions are natural contraries most of all, earth is naturally more contrary to fire than water is. However, water, being cold and moist, is opposed to fire, which is hot and dry, in both qualities, but earth, being cold and dry, is opposed to it in one only, cold. And Alexander asserts that Aristotle, by saying95 that ‘nature was right to exempt what was not going to come to be ... from contraries’, is indicating that heavenly things must be naturally without generation, and that it is not the way it is thought to be by some people96 who make heaven perishable in its own nature and ask for certain postulates in their desire to make it not perish; and Aristotle does seem to reject Plato’s statement97 (written as if spoken by the creator) ‘you are not completely immortal, but you will not be dissolved because of my will’. But Plato is here indicating that heavenly things are not completely immortal insofar as concerns their nature, which is extended and corporeal and derived from what genuinely is, and is therefore not capable of possessing all everlastingness simultaneously, but that they do endure without dissolution because of the existence which they are given directly by the unmoving cause and which makes their changing unchanging, and because of their freedom from extension,98 which they receive99 at the start from the stronger bond of unification. And I think that the words ‘not completely immortal’

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are added to show that heavenly things do not get their immortality both from themselves and from their cause in the way self-substantiating things do, but only from their cause from which alone they are brought into existence. And I also affirm that Plato thinks100 that the heavenly body transcends contraries – not absolutely the pre-eminent101 contraries, which exist together and combine with one another but, unlike sublunary contraries, do not destroy one another or change into one another,102 – but rather the contraries which change into one another and cannot exist together with each other, the kind of contraries found in sublunary things. For it is immediately clear that the heavenly body participates in motion and rest simultaneously, since it revolves in the same place, and that it participates in sameness and difference and unity and plurality. 270a22 Moreover, everything which increases is caused to increase by something of the same kind which accrues to it ... .103

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He has inferred104 that the heavenly body does not come to be or perish, taking as a hypothesis that there is no natural motion contrary to motion in a circle. But he is going to demonstrate105 this hypothesis, and he now uses what is inferred from it, namely that the heavenly body does not come to be or perish, as if it were demonstrated. And, using this in addition, he proves that the heavenly body does not increase or diminish, making the assumption that increase is a kind of coming to be and that, just as nothing comes to be without having something contrary to it from which it can come to be, so too it does not increase or diminish without such a contrary; for diminishing is also a kind of perishing. And so he again syllogises106 in this way: What increases increases from a contrary from which it also comes to be; the body which moves in a circle does not have a contrary from which it comes to be;

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But it is clear that increase is a kind of coming to be, and that what increases increases from a contrary; for what is added to what increases becomes similar to it and is thus added to it and nourishes it and causes what it is added to to increase. But what becomes similar to what it is added to comes to be similar from what is dissimilar to it and contrary. And so it is not possible for what does not have a contrary to become something similar, because everything which comes to be comes to be from a contrary. But the same thing is contrary to similar things, so that the contrary to what is added is also contrary to the similar thing to which there is an addition.

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Aristotle indicates something even more precise with the words ‘but there is nothing from which this has come to be’. For something is nourished and caused to grow, either directly or from a distance, by that from which it comes to be. For an animal comes to be from seed and katamênia, but seed and katamênia come to be from the things by which the animal is nourished and caused to grow, and so the animal is nourished and caused to grow by the things from which it comes to be. And so what does not have anything from which it comes to be cannot have anything by which it is nourished and caused to grow either. For there will no longer be anything which is added since what is added also comes to be from that from which the thing to which it is added comes to be. Alexander says:

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If what is added becomes something similar to the body which moves in a circle and causes it to increase, it will also move in a circle, since motion of parts and of the whole are in the same direction. But if this were so, the whole would also come to be. But it has been proved that it does not come to be.107 Aristotle says that what is added ‘is resolved into the matter’ of that to which it is added, that is, into flesh and bones and the other homoiomerous parts. For these are the things which are nourished directly, and they play the role of matter in relation to the organic parts and the whole animal. It can be proved with the same argument that the heavenly body does not diminish either. For what diminishes diminishes when some part in it departs. But what departs becomes dissimilar and changes into its contrary, so that, no longer existing together with it, it departs. Consequently what diminishes must have a contrary from which it both increases and comes to be. But the body which moves in a circle does not increase or come to be or have a contrary. But in general what is not of a nature to increase perishes if it diminishes, but what is heavenly has been proved to also be imperishable. But why does Aristotle not, like us, give an argument about increase on the basis of nourishment, but rather says directly that what causes increase must be of the same kind as what it causes to increase? Is it because of his absolute precision? For it seems that he believes that the simple bodies also increase naturally by the addition of things similar to them (as he makes clear shortly when he says108 that we see that the elements grow and decay), but that organs are not nourished naturally, but by the nutritive soul. But it is clear that even if this is the way things are, the demonstration which we have given is not undermined, since a thing comes to be from that by which it is caused to increase when that becomes of the same kind and is added.

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Translation 270a25-35 But if it does not grow or perish, it is possible to accept by the same reasoning that it does not alter. ...

Just as he proved that it does not increase because it does not come to be (‘For’, he says,109 ‘there is nothing from which this has come to be’), so now he proves that it does not alter because it does not increase or diminish (I think that here he calls diminishing perishing110). And he argues as follows: What alters changes with respect to quality; what changes with respect to quality changes in affection;

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(For there are three kinds of corporeal qualities:111 those related to a perceptible affection (pathos) only, as when someone is warmed on the surface; those related to a condition (diathesis), as when someone is deeply changed (diatethêi) with respect to heat so as also to be called hot; those related to a state (hexis), when a condition becomes stable. But affection is seen in all these cases, and so Aristotle says that they ‘do not come to be without changes in affection’. For even if state and condition are different in species they are also brought to completion together with an affection, since they come to be when something is affected.) consequently, things which alter change in affection.

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But we see that all natural bodies which change in affection – the bodies of animals and the plants and the simple bodies and absolutely everything which changes in affection – increase and diminish. So, if what alters corporeally increases and diminishes, then what does not increase or diminish does not alter, since it doesn’t change in affection either. And this argument may be put categorically as follows:

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What alters in affection increases and diminishes; the body which moves in a circle does not increase or diminish; therefore, the body which moves in a circle does not alter in affection. It seems to me that it is rather in this way that Aristotle argues, and he infers the conclusion that it does not alter with the sense that it does not alter in affection.112 Alexander says:

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It should be signalled that the text is not expressed in terms of necessity but in terms of reasonableness.113 For it is not the case that if states involving an affection are found in things which

Translation are of such a nature as to be affected, then a fortiori it is necessary that they also be found in things not subject to affection. Nor is it the case that if we see that the things around us which alter also increase and diminish, that it is reasonable and universal that if something alters it increases. The reasoning is necessary if a thing alters in the same respect in which it increases or diminishes, but not otherwise. But also in the Categories114 Aristotle himself says that ‘it is not necessary for what changes in affection to either increase or diminish’. If for a thing there is some contrary to its formal substance and also some contrary to its affections, it is at the same time subject to coming to be and perishing and to increase and diminution because of the contrariety in substance, but it is subject to alteration because of the contrariety in affection. But in the case of things which have no contrariety in substance but are in qualities which have a contrariety115 and which do not come to be and increase nothing prevents these things, which do not come to be or increase, from altering and being affected in this way.

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And he says: It should also be signalled that Aristotle does not prove that these things do not alter because there is no contrary to their accidental quality. However, if he thought that there is no contrary, he would have used this, just as he proved116 that they do not come to be because they have no contrary. And from this consideration it should be proved to those who assert117 that Aristotle says that the fifth body is qualityless that they do not know what they are asserting. For if he said that it was qualityless, it would have been easy for him to prove on this basis that it does not alter, since what doesn’t have qualities at all could not change with respect to quality either. I have signalled this in order to prove that, even if the body which moves in a circle under the sun happened to be heated by the revolution of the sun and transmitted the heat coming from the motion of the sun to the body under it, nothing absurd is implied for the substance of the body which moves in a circle.118 For what alters is not always perishable; only things which can change in substance are, and such are things for which there is some contrary to their substance and form. For, as Aristotle says,119 it is ‘not affected by any of the difficulties to which mortals are subject’, but he does not say that it is absolutely not affected. For if there is a contrary to an accident of something, it is not the case that thereby it is necessary that there also be something contrary to the thing itself. For the stars do have a colour, and if every

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Translation colour is light or dark or a mixture of these, then there would be a contrary to the colour itself of the stars or their colour would be composed from contraries. However, the stars are not perishable because the colour is not contained in their substance.

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These are more or less Alexander’s very words, and I think it is worth noting first whether Aristotle would reason so unsoundly and fallaciously in a treatise of this sort – even if out of shame this person says that has been taken in a reasonable way. And next I think it should be said that Aristotle does not deny that there is any alteration in heavenly things, since he does not deny that there is also a perfective bequeathing to and reception from one another. He only denies change in affection, which, even when it is accidental, is nevertheless frequently the cause of increase and diminution; for what is dried and undergoes the affection of dryness is diminished very much in condition and even more in state,120 and what is moistened because moisture accrues to it increases, and in this way too what is condensed diminishes and what is made rarer increases. But even if these things are not seen as causes, nevertheless increase and diminution always accompany the affections which cause alteration. However, they do not accompany every alteration. For it is clear, I think, that the heavenly bodies act on one another and exchange with one another different proper goods at different times in accordance with their different configurations. For just as the moon is observed at different times receiving the solar light in a different part of itself in accordance with its different positions relative to the sun, so too everything interacts with everything, even if such alterations are not perceptible by us. This is also clear, I think, from their influences on things in our world; for at different times they become the causes of different things in accordance with their different configurations and combinations. And also in the case of the moon increase and diminution are not observed to be accompanied by this sort of alteration121 even though this sort of alteration is clear; nor are observed in the case of the other stars, except when they reach apogee or perigee; for then they are perceived as having a different size because of their different distance from us. For these exchanges do not involve being affected; rather they are perfective. For in heaven contraries can also exist together.122 But in our world contraries, not being of a nature to exist together with one another because of their separation from one another, do away with each other, and accordingly act by affecting one another. For when iron has been heated by fire and altered in affection it can no longer cool, even though it is naturally cold, because it acts in accordance with its affection. However, even if the moon is in a way altered by solar rays and transmits the light of the sun to us, it does

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so with its proper specificity, since the alteration does not change anything of its substance123 but only brings its inherent powers to perfection. For Melissus, too, is right to say,124 ‘What becomes different (in substance obviously) by a single hair in ten thousand years would be destroyed in the entirety of time’. Consequently, if someone says that heavenly things are also altered by one another, let him say that this alteration is not a matter of being affected but of perfecting, just as the soul might also be said to be altered when it is divinely inspired. For an affection comes about because of a change of something substantial, and so the form of alteration with respect to affection is different from that of alteration with respect to power.125 As a result I think that Aristotle was right to deny to heavenly things not alteration of every kind without qualification, but only alteration in affection, the kind of alteration which always accompanies increase and diminution and coming to be and perishing. Because of this he changed the alterations which he was going to deny into affection by saying that ‘the states and conditions of quality ... do not come to be without changes in affection’ – but change in affection directly involves affection. And in proceeding he makes clear that he says that heaven does not alter in the sense that it is not affected by saying126 that ‘the first body is without ... alteration or affection’. Consequently one should agree with Alexander that Aristotle leaves alteration in the domain of heavenly things since quality also exists there, but one should not agree that Aristotle thinks the alteration involves being affected, since if he thought that he would not try to demonstrate that it does not alter because it is not affected. And one should also understand this in connection with its demonstration and see the necessity of the demonstration. For natural bodies which are affected in being changed increase and diminish and come to be and perish, but they do not increase or diminish by altering, but both exist in perishable things and each has its own principle (logos). And that is why Aristotle says127 in the Categories that it is not necessary for what changes in affection to either increase or diminish; for they do not increase or diminish by the principle of affection even if increasing and diminishing always attach to things which are affected and have a changeable nature. But how can Alexander say128 that things which have a contrariety in substance increase and diminish and come to be and perish? For there is no contrary to substance except its privation, and the privation has no effectiveness but only presents a suitability , and what comes to be from the privation does not come to be from it as something productive but as coming after it and from something suitable toward it. So, if coming to be is not just from a contrary, but also by the action of a contrary, and contrariety is found in qualities, it is clear that coming to be and perishing, increase and

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diminution occur with respect to qualities which are affections, since coming to be and perishing, increase and diminution occur when the elements change into one another with respect to their qualities and they change by acting on and being affected by one another. So in a certain sense, change in substance is accidental because it is consequent on qualitative change, since it is necessary that direct change in the strict sense be by the action of a contrary, but there is no contrary to substance, although there are contraries to the qualities which fill out the substance. And change is substantial in this way: it involves things that belong substantially. So it is correct and precise for Aristotle to say that these things which alter in affection are also affected in substance, since when an affection is intensified it always produces a change in the elements which constitute the substance. But he is correct to deny that there is alteration in affection in heavenly things, what he has already demonstrated being sufficient for this. For if things which alter in affection are also affected in substance and come to be and perish and increase and diminish, it is clear that things which transcend these things are also superior to alteration in affection.129 Consequently130 one should listen attentively to what Alexander says131 about the spheres after the sun being heated by it and transmitting the heat to things here, never agreeing that there is some affective heat in heaven, since, if there were, change in substance would always be a consequence. But one should say that what is transmitted by the sun is something perfective and creative of life and exists together with the natural states of , but it does not change them in the way affective alteration does. For in our world the air receives the heat which generates life from the sun by being affected and it heats things here by affecting them; for things here receive not only the emanations from the sun but also those from other heavenly bodies by being affected. But if what is heavenly is ‘not affected by any of the difficulties to which mortals are subject’,132 it is clear that it also refuses every affection which belongs to mortal things, and so it refuses that the affective heat which intensifies and dissolves substance and in general the form which is involved in coming to be in this way attach to it. Consequently if only this kind of affection is being talked about, namely affection involved in coming to be, every affection is denied of heaven because it is of this sort. But if there is also something called a perfective affection, which also attaches to heaven, there will be a different story about that. And even if someone were to hypothesise contrary colours or other qualities in heavenly things, those things would not be perishable because contraries exist together harmoniously there, as has been said frequently,133 without conflicting. Therefore they do not act on one another by affecting and they are not acted on by being affected, because they don’t want to change one another.

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270b1 From ‘That ... everlasting and does not admit either growth or decay’ to ‘is evident from what has been said ...’ He recalls what has just been demonstrated about the body which moves in a circle, that it is everlasting because it does not come to be or perish, and does not increase or diminish; and being like this, it is ‘without aging’ and indeed ‘without alteration’ and without alteration in the sense that it is ‘without affection’. It does not seem to me that he adds ‘without affection’ pointlessly at the end but because all these things134 occur because of affections. With the words ‘if one trusts our assumptions’ he might be referring to the first hypotheses from which the demonstrations were carried out.135 Plotinus says of these that ‘‘There would be no issue for Aristotle if one accepted from him136 the hypotheses about the fifth body’, taking this from there, I think. But he might also be calling hypotheses all the lemmas from which the demonstrations were carried out. However, perhaps it is more appropriate to understand as a hypothesis the one which says that there is no contrary to motion in a circle and that things which come to be and perish come to be from contraries and perish into contraries. Aristotle has assumed137 these as hypotheses and inferred everything from them. He is going to demonstrate one of them here,138 and the other was demonstrated in the Physics. 270b4 From ‘It seems that this theory corroborates the phenomena’ to ‘For it cannot be any other way’.139 These two things contribute to our confidence in the truth of something: demonstrative argument and common human preconception or clear truth derived from perception. If these harmonise, especially in the case of natural things, which get their demonstration from perception, our confidence admits of no question; but if they conflict, some degree of puzzlement remains. So it is reasonable for Aristotle to also introduce after the demonstrations the confirmation derived from the phenomena, which is sufficient for some people, and indeed for most, to believe these things. He adduces three corroborations from the phenomena, first that based on people’s conception of heavenly things, second that based on the perception and record of them, and third that based on a word, since people call aithêr.140 Alexander divides the first consideration into two: that all people believe there are gods; and that they accept that the divine is in the upper region. He says: The argument has proved that both things are true. And first that there is something divine; for, this argument proving that there is some body which does not come to be or perish or increase and is not affected and is prior to all other bodies and

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Translation more perfect than they, has established and demonstrated that there are gods. But also the argument which proved that this body is what moves in a circle around the centre of the universe has established that it is in the upper .

Alexander says these things. But perhaps Aristotle is now invoking as evidence all people’s conception that there are gods because all people ...141 he adds ‘if they believe in gods’ because of the Hippons and of Diagoras142 and people who may live in places unknown to us and are ill-fated in this way, but all those who believe in gods assign the upper region to the divine. However, Aristotle did not establish that there are gods on the basis of the fact that there is a body of this sort, unless it is in the sense of there being vehicles of the gods (since he proved that there are eternal intellectual gods in the eighth book of the Physics and in the Metaphysics).143 And Alexander understands the words ‘what is immortal is linked with what is immortal’ as referring to the heavenly body and the region , the heavenly body being god; and he understands ‘for it cannot be any other way’ as saying that it is impossible for the upper region to be divine if there is no god there. And that is certainly true, but what Aristotle is saying is that what is immortal – the heavenly body and not the region – is linked with what is immortal – god.144 And when he says that ‘it cannot be any other way’ he means that it cannot be any other way than that what is immortal is linked with what is immortal. And he proves that all people (and not Greeks only but also non-Greeks) have145 a conception of this sort as something natural in their souls. 270b10 From ‘So if (eiper) there is something divine, as there is’ to ‘is correct’. In this connection Alexander puts forward the syllogism in this way:

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If (ei) there is something divine – that is, if there are gods – what we have said about the body which moves in a circle is also correct; but there are everlasting gods, and they are in the upper region (and all the things we have said); therefore, what we have said about the first substance is correct. But perhaps Aristotle is saying that ‘if (ei) there is some divine body’, that is, the body which moves in a circle (and not ‘if there are gods’), then what we have said about it is correct. Alexander correctly notes that the word ‘if’ (eiper) is like a causal connective146 because what is said is clearly true. For if (ei) there are

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gods inside the cosmos (he has left out ‘inside the cosmos’ because it has been proved and is clearly true), there is some divine body which is attached to them. So if (eiper) there is some divine body, what was said about the body which moves in a circle is correct because this is the divine , as is also made clear by the common preconception of people. 270b11 This also follows sufficiently from perception ... . He adds this second confirmation to what has been demonstrated about the body which moves in a circle not coming to be and perishing and being without affection. It is based on perception, both our own and that which has been transmitted to us from earlier, on the basis of which records of such things have been transmitted. I have heard that the Egyptians have in writing observations of the stars from no less than six hundred and thirty thousand years, the Babylonians ones from no less than one million four hundred and forty thousand.147 In all this time from which accounts are transmitted, nothing has been reported about heaven being different from what it is now, either in the number of stars or in their magnitude or colour or in the motions which bring them back to the same point. How is it possible that what in so many years has never varied but always been at its own acme, should, while being at its acme, perish? For these people148 say that these days are already the last for the cosmos. However, I believe that it is clear that what remains in unvarying sameness for even one hour transcends coming to be and perishing.149 For we see that everything which has come to be starts from incompleteness at the beginning of some period of time and advances into its own completeness and acme and then moves down from its acme into its decline and perishes. However, it is clear that what has remained in sameness during all the time known to people is free from coming to be and perishing and neither comes to be nor perishes. Aristotle calls the body which moves in a circle the ‘last heaven’, contrasting it with the whole cosmos, which is also called ‘heaven’. And notice that what another person might use as the clearest of demonstrations, he uses as confirmations which come after the demonstrations. 270b16 From ‘It seems that also the name has been transmitted ... by the ancients’ to ‘ since he uses it to mean “fire”‘. He brings in a third confirmation in support of everlastingness which is based on the name which has been transmitted from the ancients up to the present. On the basis of the name he shows us two ideas about it held by those who determined the name. For they

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called it aithêr as being highest and seated above all the sublunary elements, each of which they called by its own name, honouring heaven especially with the name of aithêr, which indicates that it is highest and superior to the things beneath it and also finest and purest. The name also indicates always running, which is indicative of its everlasting motion150 and at the same time the everlastingness of its existence. Wanting to show that it is not only the descendants of those who determined the name who have held this opinion up until the present, he says that the same opinions occur to people many times, even if sometimes gaps occur between them. And it is clear that one should think that it is the same true opinions which occur many times. For the nature of things endures and leads those who briefly stray from it back to it again. But I do not think that the same false opinions are always recycled, since they are indeterminate and occur when souls are moved in an indeterminate way. Aristotle censures Anaxagoras for incorrectly deriving the word aithêr from aithein, that is ‘burn’, and consequently applying it to fire.151 For if this were the natural understanding of the word we would also have called fire aithêr. Now what is the point of using two words with one meaning and leaving what is meant by one of them in the dark?152 But again this person, who signs himself ‘grammarian’, proposes the clear goal of persuading those who are like him to accept that the cosmos is perishable and comes to be at some time, and consequently shows scorn for those who demonstrate that heaven does not come to be or perish; and he stirs up a sewerful of arguments against what Aristotle says here. So let us call upon the great Heracles as a co-worker and descend to clean up the crap in his arguments.153 He starts by setting out the distinction among the senses of ‘does not come to be’ and ‘comes to be’ which Aristotle makes154 toward the end of this book and asks, ‘In which of these senses is Aristotle now demonstrating that heaven does not come to be?’ And he writes: Heaven or the cosmos could not be said to not come to be in the sense that it is, in fact, impossible for it to come to be, since it clearly exists and has taken on the completeness of its own nature. So, if it is not possible for it to come to be in the sense of having a beginning of its existence, even if it has not been brought into existence by a process of coming to be, there is only one further hypothesis left.155 Since Aristotle wanted to deny that the cosmos comes to be in this sense and made use of an axiom according to which everything which comes to be comes to be from a contrary, it should be asked whether everything which comes to be in time always comes to be from a contrary.

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Here he denies the third sense of ‘does not come to be’, namely, ‘cannot come to be’, since, as he says, it exists and has taken on completeness. But Aristotle certainly knows that it exists, but it exists neither as something which came to be nor as something which is at one time and not at another. This person says that if it does not come to be in the sense in which contact, lightning, and, in general, what occurs in an instant come to be (this is what is meant by ‘having a beginning of its existence, even if it has not been brought into existence by a process of coming to be’), then there is one hypothesis left concerning its not coming to be. So which of the three senses of ‘does not come to be’ enumerated by Aristotle is now being asked about? If it is neither the sense in which what is instantaneous does not come to be nor the sense of ‘is possible to have come to be but has not yet come to be’ nor the sense of ‘is impossible to have come to be’ (and this person says clearly that it is not the sense of ‘is, in fact, impossible to come to be’),156 then he proposes in a ‘pointless’ way157 (to use his word) to ask, in which of the senses of ‘does not come to be’ which he has distinguished does Aristotle say the cosmos does not come to be? And notice what hypothesis he says is left if it is not true that the cosmos comes to be in the way an instantaneous thing does (that is, if it does not come to be in this way – for Aristotle has included instantaneous things among things which do not come to be). And it is clear that Aristotle does say that heaven does not come to be in the sense of ‘cannot have come to be’ and not in the sense in which things cannot possibly exist in any way, as this person thinks, that is, in the sense that two and two cannot have come to be three. For it is not because this cannot arise through a process of coming to be that it is true to say that it cannot have come to be; rather it is true because it is something which cannot exist at all. Notice158 what a sound mind this man has: he is unable to decide such things and yet dares to speak against Aristotle; he is unable to see the sense of ‘does not come to be’ which Aristotle has proposed and yet fights against it. And you surely see that he thinks that Aristotle does away with the idea that the cosmos comes to be in the sense of ‘having had a beginning of existence, even if it has not been brought into existence by a process of coming to be’. This is what one can see in the case of instantaneous things; and such a thing surely has a beginning of existence even if it did not come into existence through a process of coming to be. And Aristotle counted this not only as not coming to be in the first sense of ‘not coming to be’ but also as coming to be in the first sense of ‘coming to be’ when he said159 ‘being at one time and not at another either with or without a process of coming to be’. So, even if this person is ignorant about what he is arguing against, one should understand that Aristotle says that heaven does not come to be or perish in the sense that it is everlast-

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ing. Aristotle mentioned this as the third sense of not coming to be when he said,160 ‘In one sense something is said to not come to be if it is entirely impossible for it to have come to be in such a way that it is at one time and not at another’, and he meant impossible in the sense that ‘it is not true to say that it might come to be’. Of this sort is that of which it is not true that it was not previously and later is and again later is not, but rather true to say that it always is. Having specified161 ‘comes to be’ in a first way by saying ‘if something previously is not and later is’ or in general can have come to be – whether by changing from not being into being over a course of time or instantaneously (‘previously’ and ‘later’ indicating parts of time) – and again having specified what is similar to this as perishing (namely what is earlier and later is not or is possibly not whether it changes into not being over a course of time or instantaneously), Aristotle says that heaven does not come to be and does not perish in the sense that it is superior to this kind of coming to be and perishing. And, as has been said before,162 Aristotle uses two premisses for the demonstration of this, one which says that what comes to be comes to be from a contrary and perishes into a contrary, the other that there is no motion contrary to motion in a circle. This person proposes to argue against both of them, and he first argues against the first. I have already said163 all that I was able to say for understanding Aristotle’s conception of these matters, and I think that it is easy to dissolve the objections of this man on the basis of what I have said. He says that Aristotle and his commentator Alexander think it is true in the case of contraries in the strict sense that contraries come to be from contraries, but others say that the hypothesis is sound in the case of privation and form. He makes clear that he does not understand what Aristotle says in this case either since Aristotle himself says164 that ‘musical comes to be from not musical, but not from every not musical but from unmusical’, and that ‘ the tuned come to be from the untuned and the untuned from the tuned, and that the tuned perish into the untuned, not just any untuned but the one which is opposite. And it does not make any difference whether one says this of harmony or of order or of composition’. How then can this person say that even in the first book of the Physics, on the basis of which I have set out these things, Aristotle discusses coming to be in the case of contraries in the strict sense? However, it is clear that Aristotle also discussed coming to be on the basis of contraries in the strict sense, and it was not necessary for this person to discuss it at length or to bring in things more mindless than the foregoing, even though none of them was needed. For he proposes to prove that Aristotle says that heaven has no contrary in the strict sense of contrary, and he tries to prove this on the basis of the assertion that heaven does have an opposite privation. For, he says, Aristotle would not have said that

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heaven does not have a contrary if he were calling privation a contrary. Again it is necessary to quote what he says because people who cannot believe that anyone ever wrote such mindless things. He says, Even if it were to be agreed that there is no motion contrary to the motion of heaven, it is certainly not impossible that there be a privation of this kind of motion. For there is an opposite privation to every natural thing which exists in a substratum. But motion is also a natural thing (since the absence of motion prior to a motion and after its cessation is a privation of this kind of motion). So if it is not impossible for there to be a privation opposite to the motion of heaven, it follows that Aristotle did not make use of relating to form and privation but in the sense of contraries. In connection with this the first question is why he does not understand that Aristotle would not have agreed that there is a privation of the heavenly motion, since he believes that he has proved in the eighth book of the Physics165 that motion in a circle is everlasting. But if there were – as this person says there is – an absence of motion before and after this motion, how would the motion be everlasting? And secondly, isn’t he taking what is in question as if it were agreed upon? For it is now being asked whether heaven and its motion are everlasting or whether, having come to be at the beginning of some time, it will also have an end of existence at some time. And this person assumes that Aristotle also accepts it as agreed that there is a privation of the motion both before it and after it. Here he is either ignorant of what the word ‘privation’ means, or, if he knows that it means an absence of a form in something which is naturally constituted to possess it, it is amazing that, whether maliciously or ignorantly, this person, who is asking about the everlastingness of something, takes it as agreed that there is a privation of it before it exists and following its existence; for I do not think that even he is unaware that, since privation is an absence of form, it cannot exist together with form. And Aristotle says clearly in the Physics,166 ‘Being a human being and being unmusical are not the same thing; and one endures, but the other does not endure; what is not an opposite endures (for the human being endures), but the not musical and the unmusical do not endure’. How then can Aristotle, who thinks is everlasting, have assumed it has a privation? And how can this person, who is asking whether it is everlasting, take it as agreed that it has a privation? And if this person believed this is true, he would still need another demonstration to show what he is striving to show, namely that in the same way as himself, heaven and the whole cosmos have come to be at the beginning of some time and will perish in a part of time.

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I am constrained to draw out these sorts of mistakes of his at even greater length, not because it takes much discussion to dissolve them (for what is said is clear167 even to a blind person), but so that those who have been impressed by him because of the large size of his books (even before reading them) will learn the sorts of things this person doesn’t know and the sorts of quarrels he gets himself ready for. And so he says a little later: White and black and in general opposites between which there is something are always, I suppose, contraries. For there is nothing between a form and its privation, since each of these exists in matter, and matter is not between them. What say? White and black do not exist in matter? What? Matter is between white and black? And why, if there is some path and duration from privation into form and from form into privation, will there not also be something in between them, even if it doesn’t have a name?168 After saying many things of this sort he proposes to prove first that it is not true that coming to be is from contraries in the strict sense169 and then that there is no coming to be from a privation.170 And he thinks he proves that coming to be is not from contraries in the strict sense through many considerations, of which the first is this: If not only accidents but also individual substances come to be and if, as Aristotle himself teaches in the Categories,171 there is no contrary to substance, how can everything which comes to be come to be from a contrary? He continues,

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Secondly, if irrational souls also come to be and not every kind of soul does not come to be and perish,172 let someone tell us from what contrary the soul of a horse or an ox or any of the other irrational animals has come to be, or again into what opposite they are resolved when they perish. Moreover, it will appear more clearly that the doctrine is false, if one investigates the kinds of soul. For what is the contrary of the kind related to spirit or to reproduction, nutrition, growth, and desire? Thirdly, Aristotle’s hypothesis is obviously not true not just in the case of substances but also in the case of accidents themselves. For a triangle or circle or the other figures come to be, and it is clear that none of these comes to be from a contrary, since figure is not contrary to figure, as Aristotle also thinks.173 And fourthly, left comes to be from right, but these are relatives and not contraries.174

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And in general it is clear that the individuals in any of the categories in which there are no contraries do not come to be from contraries (he also adds this as a fifth consideration). Sixthly, even in the case of of quality itself, in which there are most of all contraries, such as hot and cold, dry and moist, it is not universally true (as says it is) that contraries come to be from contraries, since it is not necessary that these always come to be from contraries. For if air has neither colour nor flavour (as is clear from the fact that it cannot be seen or tasted), but it changes into water, which does have both colour and flavour, from what kind of contrary colour and flavour in the air do the colour and flavour in the water come to be? And if air changes into earth or fire, the same thing should be said. But also living things with variegated colours and differences of flavours come to be because of the putrefaction of air.175 So from what sort of contraries in the air do they come to be, when air does not have ?

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But this person agrees that the colour comes to be from its proper privation, that is, from the colourlessness in the air. But in the case of fire he asks about its colour, that is about light,176 and says, Either there is a contrary to light or there is not. If there is not, light could not come to be from a contrary. But if there is, what would it be other than darkness? But darkness is the privation of light (he claims to have proved this elsewhere177) and not a contrary. But if someone were to agree that darkness is the contrary of light,178 Aristotle’s doctrine is refuted just as much if not more. For when fire comes to be from the illuminated air of day which is rubbed179 it clearly does not come to be from it as illuminated but from it as air, and, accordingly, it also comes to be from night air. So the light in the which has come to be has not come to be from a contrary. These are the things which this man brings forward in many lines as overturning Aristotelian doctrine, and I need only to say again a few things I have already said;180 these will, I think, dissolve both what he has said and what he is going to say. If I quote some of the things which Aristotle wrote in the first book of the Physics, to which Aristotle refers181 in the present argument, it is possible to see that he does not think that all coming to be is from things which are called contraries in the strict sense, but most of all from the opposites related to form and privation: First it is necessary to assume that, among everything which there is, not just anything is of a nature to be acted on by just

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anything, nor does anything come to be from anything whatsoever, unless one takes this in an accidental sense. For how could white come to be from musical unless musical were accidentally attached to white182 or black? But white comes to be from not white183 and not from every not white but from black or from intermediates ; and musical comes to be from not musical, but not from every not musical but from unmusical or an intermediate (if there is one). And nothing perishes into the first chance thing; for example white does not perish into musical – if it184 ever does, it is in an accidental sense –, but it perishes into not white, but185 not just any not white, but into black or what is intermediate. In the same way too186 musical perishes into not musical, and not just any not musical, but into unmusical or an intermediate (if there is one). It is the same in the case of all other things, since things which are not simple but composite conform to the same principle, but we overlook that this happens because the opposite conditions do not have names. For it is necessary that everything tuned come to be from untuned, and the untuned from the tuned, and that the tuned perish into the untuned, not just any untuned but the one which is opposite. And it does not make any difference whether one says this of harmony or of order or of composition, since it is evident that the account is the same. Indeed, a house or a statue or anything else whatsoever comes to be in the same way. For a house comes to be from some things not being put together but being divided in some way, and a statue and anything which has been given shape comes to be from shapelessness, some of these being an ordering, others a composition. Now if this is true, everything which comes to be would come to be from contraries, and everything which perishes would perish into contraries or intermediates. But intermediates are composed of contraries,187 so that everything which comes to be naturally comes to be from contraries or things composed of contraries.188

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I think that these words also suffice to prove that Aristotle posits as principles of what comes to be or perishes form and privation more than what are called contraries in the strict sense and takes most of his examples from form and privation – and many things in the next part of the Physics make this same thing clear. Let me add something briefly and, I think, shame this completely shameless person: 189

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So we have said how many principles of the things involved in coming to be190 there are and why.191 It is clear that there must be192 contraries and some substratum for them. In another way this is not necessary since one of the contraries will be sufficient to produce the change by its absence and presence.

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It is clear that the absence of form is privation, which he shortly after refers to with this word and opposes to form. For, having said that one principle is the substratum, he adds,193 ‘And one is194 the logos’ (that is, the form) ‘and, moreover, the contrary of this, the privation’. That he is bringing all the contrarieties or antitheses under the heading of the antithesis between form and privation as something which is present everywhere is clear from these words and from other things which he has said in this part of the Physics, which it would be long to quote. Since this is the case, this man is first of all obviously completely ignorant of what Aristotle says, because he thinks he has demonstrated that Aristotle says that coming to be and perishing come about only in terms of the antithesis between contraries in the strict sense; and second all his objections, which he has made on the basis of this kind of guesswork, are empty because they are beside the point and do not touch Aristotle’s demonstration. For, although he is not at all reliable as a witness since he is ignorant of the subject under discussion, even he bears witness that coming to be is from privation,195 as Aristotle also believes. For he says, Insofar as fire which comes to be from air has become coloured, it has not taken on its coming to be from a contrary, but only from the appropriate privation. It is not sufficient to show the unsoundness of this, but one should also establish the doctrine itself how coming to be is from contraries and what these contraries are and in addition dissolve the objections of this man one by one. And so, after I have reminded us of a few of things said previously, I will turn to dissolving them. This much should be said first: what comes to be is one thing, what it comes to be is another, but both come to be because something acts. For what acts and what comes to be are relative to one another, so that what acts produces coming to be and everything which comes to be and what it comes to be come to be because something acts. For, as Plato, too, says,196 ‘It is impossible for a thing to come to be without a cause’, and obviously a cause which is different from itself. For it is necessary that the whole of what is self-substantiating be simultaneously a whole which gives and is given existence, but what comes to be does not exist simultaneously as a whole. For if it did it would not have come to be. What comes to be is that in which the activity of what acts is fixed, that is, it is the substratum, for example, the stone which is carved into Hermes. What something comes to be is the form or shape which is brought to completion by the activity. And notice that the stone which is carved is carved by the carver who carves, because the stone is what comes to be, the shape is what it comes to

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be. Everything which comes to be because something acts is arranged in terms of the form on the basis of which what acts acts; the stone, for example, is arranged in terms of the form of Hermes in the carver, the wood in terms of the form of the ship in the shipbuilder, and the seed and katamênia in terms of the form of the animal in nature. Everything which is arranged in terms of some arrangement which it did not have previously is arranged in terms of that arrangement (otherwise it would not be said to be arranged); it did not have the arrangement previously, but it was suitable for being so arranged, and therefore it possesses the absence of that form which is naturally constituted to come to be in it. But the absence of what is naturally constituted to come to be in something is a privation. Therefore, what comes to be possesses the privation of the form which it is going to receive; and it is necessary that the privation depart if the form is going to be present, since it is not possible for the absence and the presence of the form to exist together. And this doctrine starts with substantial coming to be and spreads to all coming to be. For in the case of accidents it is also true to say that what becomes white was not white previously but possessed the absence of whiteness and was suitable for whiteness and was made white by the cause which produces whiteness. In the case of what are called contraries in the strict sense, it is always true that if what is naturally constituted in relation to an antithesis does not possess one of the contraries, it possesses the other or an intermediate. For what becomes white possesses the absence of whiteness and is either black or something intermediate which is a blending of both white and black and has the relation of opposite to each of the extremes. Grey has this relation to white and black, and lukewarm has it to hot and cold. Similarly in the case of opposites which are relatives, what comes to be to the right comes to be so from being to the left (that is from having been previously to the left) or from being somewhere in between. And if an affirmation were to come to be it would come to be from a denial, and a denial would come to be from an affirmation (these things have no intermediate). And the antithesis of form and privation is common to all these cases. For what comes to be white from being black or to the right from being to the left comes to be from what is not black or to the left and from the absence of what it is naturally constituted to be; and so it is necessary that everything which comes to be cast off its previous way of being arranged and take on in its place that form with respect to which it is said to come to be. And this is reasonable since it is necessary that what cannot exist together with the form which arrives depart; and the opposites involved in any antithesis cannot exist together. In every case, before the form with respect to which the thing which comes to be is said to come to be has arrived, its opposites inhered in what comes to be, that is, in the substratum; and in all cases the privation of the form which

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arrives, whether the form is substantial or accidental, inhered, but in the cases of accidental forms, in addition to the privation, there also inhered the opposites of those forms related to the other antitheses.197 If I am correct in saying these things, then I can produce a syllogism from what I have said as follows: Everything which comes to be comes to be because something acts; what comes to be because something acts is arranged in terms of the form in terms of which what acts acts; what is arranged by some form previously possessed the absence of that form and a suitability for it, that is, it previously possessed the privation of the form, and so was arranged in terms of it; what possesses the privation of the form which it is going to come to be (either it alone in the case of substances or also other things which are antithetical to the form which is going to supervene in the case of accidents) first casts off the privation and perhaps also the antithetical things because they cannot exist together with the form which is said to come to be, and then is arranged in terms of that form; what casts off opposites and then comes to be what it is said to come to be changes from the opposites into the opposite form; therefore, everything which comes to be what it comes to be comes to be from the opposite (Q.E.D., as the geometers say); and coming to be is from opposites and perishing is into opposites – the form departs, and the substratum takes on things opposite to it, the privation in every case, and in some cases also other antithetical things in addition. But why does Aristotle say198 that what comes to be comes to be from contraries and not from opposites? Is it because he has called all opposites contraries, characterising them in terms of not being able to exist together, a feature which belongs to things as opposites, and so he sometimes calls the things from which there is coming to be contraries and sometimes opposites? For he does say,199 ‘ ‘either a substratum or an opposite. And I call human being a substratum and the unmusical an opposite’. And frequently he calls opposites contraries and contraries opposites, characterising them in terms of not enduring. And so he says,200 ‘what is not an opposite endures; for the human being endures but the not musical and the unmusical do not endure’. However, in the Categories,201 having proposed to do this very thing – that is, to present the differences found in opposites –, he distinguished contraries from the other opposites by saying that in the case of contraries the two opposite things are forms; in the same way right and left also satisfy the common definition of opposites because they cannot exist to-

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gether and they satisfy the common definition of contraries because both are forms), but he bound them with another difference, that of being relatives, by which they go beyond ; and he maintained that form and privation deserved their own antithesis since they differ from the other opposites because they are not both forms; and he distinguished affirmation and denial insofar as when the denial does away with one thing there is nothing to prevent introducing the others.202 Although all this person’s objections have been dissolved as a batch by what has been said as being beside the point, there is nothing to prevent briefly going through them individually.203 For if there is not only coming to be from contraries in the strict sense, as has been proved, but also form comes to be from privation and this mode of coming to be is common to everything which comes to be, obviously nothing prevents substance from also coming to be. And Aristotle, who says that a house or an animal comes to be, also says that a plant and a substance come to be. I do not infer this from some syllogism, but listen to him saying clearly,204 It will be evident to a person who does an investigation that substances and everything else205 which is without qualification comes to be from a substratum, since there is always some206 substratum from which what comes to be comes to be;207 for example, plants and animals come to be from the208 seed (and obviously from the opposite, such as shapelessness or formlessness or disorder). And in another passage he says,209 A house or a statue or anything else whatsoever comes to be in the same way. For a house comes to be from some things not being put together but being divided in some way, and a statue and anything which has been given shape comes to be from shapelessness, some of these being an ordering, others a composition.

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And even if irrational souls come to be and perish, as this person says, they are obviously the form of bodies with souls which come to have souls from lacking them (just as bodies come to have form from lacking it), and, conversely, they come to be without soul from having had one, when the soul perishes, if, indeed, it does perish. And it is clear that the kinds of soul come to be in the same way. For coming to be from a privation is common to all such things, and nothing absurd will follow. And in response to the third objection, which argues on the basis of figure, it suffices to invoke the shapelessness which Aristotle

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frequently mentions. For even if a figure comes to be from another figure the substratum is without shape in relation to the shape which is going to accrue to it (or without angles, if it is a circle and turns into a figure with angles). But to see that Aristotle recognised antithesis in the case of shape, listen to what he says in the first book of the Physics210 about Democritus:

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And Democritus solid and void, of which he says the one is being, the other not being, and he speaks of in position, shape, and order. But these are genera of contraries: of position up and down and front and back, of shape angle, straight, and circular. However, if this person had any love of learning he should have investigated why Aristotle says in the Categories ...211 indeed having angles and being circular cannot exist together with one another in the same substratum. And if left comes to be from right, it also comes to be from a contrary. For both are relative forms and contraries, but they differ from other contraries because they are also said in relation to something else, and they are characterised by this difference. But coming to be from an opposite attaches to relatives and to other things. For the antithesis of form and privation attaches to all the categories, even those which do not contain contraries in the strict sense. In this way his fourth and fifth criticisms are dissolved. The sixth, about which he is clearly puffed up, can be dissolved in the same way. For this air , which is a composite and shares in fire and has a surface, always has some colour, just as glass does, but because it is the most transparent of all bodies and passes through vision without offering resistance, it is thought to be invisible and have no colour. Furthermore, the other qualities exist together with the primary qualities which give substance to the four elements; but not every other quality exists together with every primary quality or in every kind of mixture of them; I mean that not all of the other qualities related to colour or sound or flavour or odour or resistance exist together with each of heat and coldness and dryness and moistness or with any kind of mixture of them. Rather colour blossoms forth because of the heat and dryness which constitute fire, and so all colours are fiery; and sound accrues to heat and moistness, which give form to air and similarly in other cases. And so when water or fire comes to be from air, the qualities which are first principles change into their contraries, and the qualities proper to these elements, such as colour or flavour, grow out of their own privations. For even if air in itself is without colour or flavour, nevertheless it is suited to change into fire and water, and colours and flavours appear together with them.

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So too it is agreed that light – whether it is the colour of fire (as this person says212) or it is a form of fire (as Plato, the explainer of the truth, says213) – comes to be from the absence of light and is produced by it. But what else is the unlightened than the darkened, if, indeed, darkness is an absence of light (as this person also thinks – and he says he has demonstrated it, I know not where)?214 So too, since change is a transformation from one thing into another, it is possible for a change to have come to be when fire is ignited from the rubbing of air which is illuminated in the day and obviously has been illuminated from having been darkened in accordance with the nature of air itself (but not from a tree or a stone215 or from what is not in any way, as this person thinks). And when he says that living things with variegated colours and differences of flavours come to be because of the putrefaction of air and asks from what sort of contraries they come to be, when air does not have contraries, how much is he worth when he is not even able to understand that simple and pure air by itself cannot become putrefied nor can it alone generate living things of this sort? Rather, when air has been made full of the four elements which arise from exhalations blended together near the earth, then from these things there also arises putrefaction in that region and living things of this sort come to be. Let these considerations be sufficient for dissolving his objections! But perhaps there was no need of my arguments since he clearly agrees in his own words that Aristotle’s doctrine according to which things which come to be come to be from contraries can be true of the most generic antithesis, that between form and privation, but is not always true of the remaining kinds of contrariety. But what he says next mischievously brings Themistius into conflict with Aristotle. He says, When Themistius216 changes the term ‘contraries’ into ‘opposites in the sense of form and privation’ he himself in a way quietly teaches us that Aristotle’s hypothesis is not correct.

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However, Themistius certainly knows the things said in the Physics to which Aristotle also refers this argument, and he says reasonably that Aristotle takes the words ‘from a contrary’ and ‘into a contrary’217 universally, taking them as referring to the most generic opposition, that between form and privation. But this person realised he was writing for students of the trivium218 and so, I believe, either he did not read or, if he did, he did not understand what is said in the Physics about coming to be and therefore spit out so much nonsense about the word ‘contraries’ in the belief that quantity would suffice to dumbfound his listeners. But since he says, ‘Let it be agreed that Aristotle is here calling

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form and privation contraries and that everything which comes to be comes to be from an appropriate privation, just as what perishes turns back from form to privation’ from empty-headedness rather than love of learning, and having said this he thinks he can use it to prove that, according to Aristotle, too, heaven will be seen to come to be and perish, let us also inspect these remarkable proposals of his and see from what clearly true axioms219 he infers the things he is striving to prove. He says, For every natural form which has its being in a substratum and matter there is always an opposite privation, from which it has come to be and into which it is resolved when it perishes. But both heaven and the whole cosmos have been given form by a natural form, so that they, too, will have a privation from which they have come to be and into which they perish. For just as human being comes to be from not human being and house from not house and, to speak generally, each natural or manufactured form comes to be from not such and such, so too heaven, since it is also a natural form, has come to be from not heaven and the cosmos has come to be from not cosmos. But this argument presumably requires that before the cosmos came to be there existed some substratum and matter in which the privation of heaven and cosmos existed and from which, when it had changed, heaven and the cosmos came to be,220 but it would not necessitate that heaven have no beginning and not come to be, as the Philosopher proposed to prove, but rather the contrary, that it comes to be and has a beginning of existence. He says these things in these very words, and it is worth asking him, since he says he is expressing the views of Aristotle, how he shows that Aristotle says that for every natural form there is always an opposite privation from which it comes to be and into which it perishes. It is completely clear that Aristotle says that heaven is a natural body and moves in a circle naturally, since he says,221 We say that all natural bodies and magnitudes can change place on their own, since we say that nature is a starting point of motion in222 them. For every change of place – we call change of place motion – is either straight or in a circle or mixed from these. And I do not need to go on at length about the confirmation of this since this person also accepts it. However, to see that, although heaven is a natural thing, Aristotle does not think that it has an opposite privation from which it comes to be and into which it

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perishes, listen to him saying that nature has freed it from contraries. He says,223 30

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It seems that nature was right to exempt what was not going to come to be ...224 from contraries; for coming to be and perishing are found in contraries. But this person makes clear that he thinks that the coming to be and perishing follows from Aristotle’s doctrines when he says, ‘But this argument ... requires that before the cosmos came to be there existed some substratum and matter ..., but it would not necessitate that heaven have no beginning and not come to be, ... but rather the contrary, that it comes to be and perishes’. Now would Aristotle be so superficial as to think that there is a privation opposed to heaven and nevertheless to try to demonstrate that it is everlasting and to demonstrate this from its not having an opposite? And why do I say these things when Aristotle has demonstrated that the circular motion is everlasting, and nevertheless this person thinks225 that Aristotle hypothesises that that there is a privation of motion in a circle? But suppose that someone does not understand < this person > as speaking against Aristotle but as himself proposing a syllogism with the premisses: Heaven is something natural; what is natural has an opposite privation.

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Let someone who says this be required to prove that every natural form which exists in matter as a substratum always has an opposite privation. For obviously what comes to be and perishes has an opposite privation. But where does the idea that everything which is natural has an opposite privation come from? Doesn’t Aristotle also clearly say in the first book of the Physics that form and privation are principles not of all natural things but only of those which come to be? For he writes,226 ‘ how many principles of the natural things involved in coming to be there are’, and throughout his whole discussion of things which come to be and perish and in general change he posits these principles. And in the second book of the same treatise he says,227 We must seek the first causes both in the case of coming to be and perishing and also of every natural change, so that, knowing their principles, we can try to reduce each case of coming to be .

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But notice also the knavery or mindlessness of what this person says. And here I am uncertain whether one should blame his mindlessness

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or his knavery. Perhaps one should rather blame both. In any case, he has introduced two premisses, one which says that heaven has been given form by a natural form which is in matter, the other that what has been given form by a natural form has an opposing privation. He passes over as clear this second premiss, which is a false assumption, but he invokes many arguments in the attempt to establish the first, which says that heaven is a natural form in matter. However, this premiss is not at all disputed, and so, because of an excess of cleverness, he is casting doubt on things which are agreed upon. But perhaps there is nothing to prevent looking into what he says in this connexion as well. He says, ‘It is completely ridiculous to say that heaven is immaterial, since it is perceptible, not intelligible’. But it is clear that those who say heaven is immaterial228 do not say it is immaterial in the sense of intelligible, but in the sense of being superior to the matter which is involved in coming to be and perishing and receives and casts off forms. Indeed, in book 8 of the Metaphysics Aristotle says:229 If one is to investigate correctly, it is necessary to investigate natural substances which come to be in this way. For230 these are the causes and they are this many, and it is necessary to know the causes. But there is a different account in the case of natural substances which are everlasting, since perhaps some do not have matter or at least not this sort of matter but only matter which can change place. For since Aristotle always investigates matter on the basis of change, but he knows only change of place in heaven, it is reasonable for him to have left it only this kind of matter. This person, who thinks that the body which the Peripatetics call the second substratum is matter,231 seems to waste a lot of words in his eagerness to prove that heaven has a body and therefore also matter. But who would doubt that heaven has a body? However, if this body is its matter, it is not necessary that it have a privation opposed to it (as this person thinks) and that it come to be and perish, since privation co-exists with that matter which underlies things which come to be and perish. It is, then, perhaps superfluous to speak against these arguments of his, except for the fact that he obviously thinks that, since both heavenly things and sublunary ones are three-dimensional, they do not differ from one another at all. Here he badly misuses the fact that the same words are used in both cases. For who would say that the heavenly body has the same nature as things in our world? He writes, Why is it surprising that, just as it is agreed that one and the same matter underlies the multitude of kinds (ideai) of sublu-

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Translation nary things and is suited for all forms – as is proved by the fact that all sublunary things change into one another –, so too the same matter is naturally constituted to receive the kinds of heavenly things?

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Why does he not understand that, if the matter of heavenly and sublunary things were the same and received the same forms, then they would certainly also have to change into one another? However, even though he has sounded off with all these things in a rash and thoughtless way, I do not think he would say that heavenly and sublunary things change into one another. If he were speaking while imagining things above to be below, he would reasonably be considered to be a drunken man among the sober. For heavenly and sublunary things ought to have interchanged many times already, if the matter, being the same, were similar on either side as far as not holding onto the forms which come to it for even a short time. To what great thick-headedness in reasoning does it belong to think that what is three-dimensional in heavenly things does not differ from what is three-dimensional in our world in any way because each is three-dimensional? For on this kind of reasoning substance would not differ from substance insofar as it is substance, nor would the light of the sun differ from light here insofar as it is light. But it seems that I am forgetful and dull-witted, having forgotten that this person said earlier232 ‘with head uncovered’233 that the light of the sun is the same as that of a firefly. So how can I set out these things before him as absurdities? I do not even know how he will react to the statement that the most unworthy substance in this world does not differ at all from the substance of the creator insofar as it is substance or the statement that being in this world does not differ from being there. Or will the person who mashes divine and human things together into one mush234 be embarrassed at this? But since he is striving to prove that also according to Aristotle heaven is material, expecting to demonstrate from that that heaven comes to be and perishes, let him hear the things I set out a little while ago235 in which Aristotle says that heaven does not have the same sort of matter as things which come to be but only matter for change of place. And it seems that Aristotle knew in advance the misunderstandings of these sorts of superficial people since a little after the text I set out before he wrote this:236 Not everything has matter, but all things which come to be and change into one another do. Those things which, without ever changing, are or are not have no matter. And even if he says in On the Heavens237 that heaven is material, he says it because it is an individual and perceptible thing, but he does

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not say it because it has the matter which underlies things which come to be and perish, but only because it has matter for change of place. For he has made this distinction clearly. This person says,

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But if heavenly matter differs from sublunary matter the two matters will be composites of the nature which is common to them and its differentiae. When he says this, he is thinking that the differences are only differences of species; he is not aware of difference by declination in terms of which things which proceed from the One differ.238 However, the procession of every specific feature in and of itself is brought to completion in terms of this declination. But since he is obviously scornful of incorporeal matter,239 he says that he has also demonstrated in the eleventh discourse of his refutations of Proclus240 that it is impossible for the mythic (mutheuomenos) incorporeal and formless matter to exist, but rather bodies are ultimately to be resolved into the three-dimensional. However, I have not come across his boastings there nor would I be pleased to come across his loose nonsense when even now I do not know how, having proposed to elucidate Aristotle’s On the Heavens, I have fallen into the dung of Augeas.241 Nevertheless I also say against his wilful denial on the subject of matter that if the first matter is the three-dimensional, then, insofar as it is matter, no natural forms belong to it substantially, no shape, no size, no number, no colour; but, insofar as it is three-dimensional it is obviously also finite (since it is not infinite), and it has a determinate size and shape and colour on its surface and is ordered by forms and numbers. How then is it possible for contraries to be true together of matter? Let him say, and let him not amaze the ignorant by signing his name to lots of discourses. And it would be possible to give many arguments, old and new, against this doctrine, which has already produced many criticisms, but even what I have said suffices for this person if he could get serious and seek what is true in the more difficult arguments rather than to declare what comes into his head242 in a thoughtless way. But thus far – he says – he has refuted the arguments of Aristotle which try to establish that the cosmos does not come to be, as if he refuted anything with this sort of babble. However, he agrees243 that with what he has said he has not refuted the claim that the cosmos comes to be from a pre-existing substratum. And so he wants to prove that the cosmos receives its existence from what is not. He briefly refers to his Against Proclus244 for the proof of this, but he puts forward the argument objecting and tries to dissolve it. He says:

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Translation They say that if something were to come to be from what is not in any way, it would result that what is not is, since what is not has been changed into what is. Now if someone says that what comes to be comes to be from what is not in the way that a ship comes to be from wood (that is, with what is not being a substratum for what comes to be and changing into it), it would truly follow that what is not is. But I do not think that there is anyone so lacking in brains as to hypothesise that there is coming to be from what is not in this way; rather, insofar as anything comes to be without previously existing in any way, it is brought into existence.

Here either I do not understand what this person is saying at all or he has obviously heard the ancient discourses without understanding them. For no one reduced the idea that there is coming to be from what is not into the absurdity that what is not is, but into the impossibility of anything coming to be from what is not because what is not lacks efficacy. For, thinking that what comes to be comes to be from a substratum and is produced by an efficient cause, they said with reason that nothing comes to be from what is not, with what is not serving either as an element or as an efficient cause. For Parmenides is the first person we know by hearing to have asked this question, and he has written this in his verses on the fact that being does not come to be.245 For what origin will you seek for it? How and from where did it grow? I will not allow you to say or think from what is not. For it cannot be said or thought that it is not. And Aristotle sets out the difficulty in this way:246

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They say that nothing which is247 comes to be or perishes because it is necessary that what comes to be come to be either from what is or from what is not, but it is impossible that it come to be from either of these. For what is cannot come to be since it is already, and nothing can have come to be from what is not, since it is necessary248 that there be a substratum. So who is it who makes a reduction into the absurdity that what is not has been changed into what is?249 And in general, if, as this person says, ‘insofar as anything comes to be without previously existing in any way, it is brought into existence’, what is to prevent the following being true? Even if it is not in the respect in which it comes to be (it comes to be with respect to shape), nevertheless it is with respect to a substratum, just as with respect to shape the stone

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Hermes is not before it has come to be but it is with respect to the stone.250 But he tries to prove with many arguments that things which are produced immediately by god do not come to be from some pre-existing substratum, but that the form comes to be together with the substratum. If only he knew what it means to be produced immediately by the creator-god! For then, I think, he would not have fallen into these blasphemies about heaven. For we also say that the substratum was constructed (paraskeuasthênai) by the creator neither spontaneously nor as a result of some other cause, but we say that the creator-god immediately introduces the substratum of heaven – if there ever is such a thing251 – simultaneously with its form; and we do not say that this happens through coming to be or in the sense of having come to be later after previously not existing, but rather we say that this happens through god’s goodness, being introduced by god through his very being, and not through his choosing and doing different things at different times; and we say that is dependent on his goodness and the eternal permanence of his existence, just as those people are accustomed to say about the ‘son’.252 For it is not possible for a generative creator-god to ever be quiescent without doing anything, just as the sun cannot not give light and fire cannot not heat; and coming to be and perishing do not yet show themselves in this existence (hupostasis).253 In the case in which what has no prior suitability was not previously and later is, why would it come forth at one time but not at another?254 In fact, just as there is a time which is prior to the time of a thing’s manifestation in being, and the time of its manifestation is continuous with the prior time and ordered after it (and if someone were to ask why today manifested itself at this time it is easy to say, ‘because it has received this position, in which some days precede it, others follow it, in the whole of time’), so too what is coming to be at the present time has antecedents from which it comes to be and consequents into which it changes.255 For the motion of heavenly things by which are brought to completion directly also has a motion prior to it and one which follows it; and as a result such things do not come to be or perish earlier or later but they do so now.256 So I think that if received existence from what is not and perished into what is not, no one could give the reason why this happened now but not earlier. However, because what always exists is not given existence because of a change, it does not raise the question why now and not earlier. Rather what always exists is introduced directly by the creator because of the creator’s unchanging and eternal goodness, all of which exists simultaneously; and it exists forever because it was introduced by an unmoving cause which acts directly by being; and it has received an existence which is descended from its cause; and it extends around itself in the most

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perfect of shapes, sphericity; and it moves in a circle because among natural motions only circular motion is unceasing. For it was necessary that the first thing separated from what is unextended and the first moving thing deriving from what is unmoving be extended with the most perfect shape, and also move with the unceasing motion which is capable of existing together with everlasting substance. But,257 since it was necessary, in order that the universe genuinely be a universe, that the goodness of the creator not stop with everlasting things but that things which receive their being in a part of time also exist to the limits of the universe, the things which come to be immediately because of the creator himself were also everlasting because of his changeless activity. For this reason he orders all sublunary things by means of the everlasting motion which he bestowed upon heavenly things and by means of their configurations, which vary from time to time. This person also agrees with this since he says: It has been agreed that as a whole and in its parts heaven is the most authoritative part of the cosmos, and it most holds the parts of the cosmos together, since all bodies inside heaven are guided naturally by its motion. Among sublunary things there is coming to be and perishing and the other things asserted by Aristotle to be there. For here transformation is through change, and things which come to be come to be from a substratum and from opposites, and the perishing of one thing is the coming to be of another because not even in the extremities258 of the universe is a substance entirely destroyed, but in a way change here is only alteration and substance is not destroyed. Accordingly one should not transfer what holds of the coming to be of sublunary things to heaven, which Aristotle proposed to demonstrate completely transcends the whole nature of sublunary things and their coming to be. And so to avoid misunderstandings Aristotle says that heaven is immaterial (although Aristotle clearly says that, because it changes place, it also has some substratum for change of place, although not a substratum for substantial change in the way sublunary things have).259 Let this person compare these things with what he himself has said, if he wishes, and consider what seems to harmonise more with the greatness of god and the nature of things; and Aristotle’s rules (kanonôn) having been assumed for sublunary things, let him hear what are the only things which Aristotle says come to be and perish, even though he too thinks that heaven is brought into existence by god, as this person agrees. However, running together words, this person says that heaven comes to be because it is produced by god, and immediately transfers what is appropriate to the coming to be of sublunary things, that is coming

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to be from a substratum and a privation, to the coming to be of heaven. However, as I have said, although Aristotle maintains these things in the case of sublunary coming to be, he demonstrates that heaven completely transcends this kind of coming to be from opposites. However, let these things suffice since we have also discussed them previously.260 But since this person has overcome the ‘more forceful’ (as he thinks) of Aristotle’s arguments about the cosmos not coming to be, and he next proposes to undermine confidence derived from the shared belief of humans and from perception, let us take a look at his siege engine against those ideas. Aristotle has said261 that all people, Greek and non-Greek, assign the upper region to the divine because what is immortal is linked with what is immortal, and a little later, recounting the views of his predecessors on the construction of the cosmos, he says, ‘Everyone says that it has come to be, but ... some say it is everlasting, others that it perishes ..., and others, for example Empedocles of Acragas and Heraclitus of Ephesus, that there is an alteration with it sometimes being one way and sometimes another ...262 and this goes on forever’. And this person has thought that Aristotle’s using the witness of ordinary people and a little later bringing in those renowned in philosophy as providing evidence for the contrary view of heaven offered him a feast.263 However, if, in the case of the doctrine that being is one Aristotle cited as evidence the common conception according to which there are many things, and proposed to correct the view of Parmenides and Melissus, I think it would be possible for anyone, even late learners, to say that, thinking the common conception to be true, he raised objections against the apparent meaning of those men in order that those who attach themselves in a superficial way to the doctrine of those men and are not able to grasp their depth, not be disturbed concerning the views which are clearly true in this way.264 Now then, is Aristotle unaware that Plato did not say that the cosmos came to be in some part of time, when Plato says265 that time has come to be with heaven and clearly adds the reason why he says that the cosmos has come to be, the reason being not that so and so many years ago it came into existence, but that it is visible and tangible and has a body? These are features which indicate not having anything which is self-substantiating but being reasonably said to have come to be because of being given existence only by something external. For what is self-substantiating must have no parts and coincide with itself as a whole with a whole, but body is extended and has parts and therefore has its existence only from something else and is said to come to be. But it is not said to come to be in the Aristotelian sense of the term in which ‘coming to be’ indicates a change from one thing into another and which is another sense of coming to be.266 And even if this person was not able to satisfactorily understand the words of Plato, and even if he was not

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able to understand the words of Aristotle which have been set out, he ought to understand when Aristotle says267 that according to Plato ‘heaven came to be but nevertheless will be for all time’. For who, hearing Aristotle say these things would suppose that he thinks that Plato says heaven has come to be in that sense of coming to be which Aristotle himself denies of heaven?268 Similarly Empedocles, too, presents the intelligible cosmos, which is united under Love in an enigmatic way (as was the Pythagorean custom) and the perceptible cosmos, which is separated from it by Strife, but he says that they neither come to be nor perish in time, but that the intelligible cosmos stands as something that is and the perceptible cosmos as something which comes to be, and he says that the perceptible cosmos recycles in succession forever. And so that I do not seem to some people to be fabricating ‘empty blessings’269 I will set out a few lines of Empedocles:270 ... at one time all things coming together into one because of Love, at another again all271 being carried272 apart by the hate of Strife, ... and insofar as many are brought to completion from one when it in turn has divided, they come to be and there is no abiding life for them; but insofar as they never cease their thorough interchanging, they are always unchanging in a circle. Consequently, instead of being eternally, what is separated from the intelligible cosmos by Strife comes to be and has ‘no abiding life’, but recycles forever. And Aristotle did not fail to understand these things, which are clearly expressed as enigmas, but he also argues against them by dealing with their apparent meaning. And even if, as this person says, people disagree with one another on other matters, nevertheless they all agree in assigning the upper region to the divine, and, accordingly, this belief would be fixed, implanted in human souls as a common conception. But he says,

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Even if everyone assigns the upper region to the divine, this is not evidence that they suppose heaven to be imperishable. For they raise their hands to holy places and temples, thinking they are full of gods, and no one thinks that they are without beginning or perishing; rather they think that one place is more appropriate for a god than another.273

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This person says these things again without heeding the difference between heavenly things and things in our world, and he puts both in the same rank. So he is clearly injured in the eyes of his soul.

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Nevertheless it should also be said in response to this remark that people have fashioned temples and holy places and statues on earth as imitations of heavenly things, and they have constructed receptacles of divine illuminations in them, receptacles which are more symmetric with and nearer to themselves . And why do I speak of the sacred worship which comes into existence with the cosmos? Even David, whom the Jews take as a prophet, says about god,274 ‘He has set his tabernacle in the sun’. And David makes clear that he does not think that god settled in at a certain time when he says,275 ‘, who establishes the earth so that it will not be moved for all eternity’. It is clear that, even if he frequently uses the phrase ‘eternity’ to mean ‘for a long time’, he is nevertheless taking ‘for all eternity’ to mean ‘unceasing’. But if the earth is unceasing, it is clear that heaven and the sun are so too. Furthermore, if people see their temples as bereft of divine light at some time and go to different temples at different times, they all still dedicate heaven, from which the race of men is derived, to god, and it follows that those who are not corrupted by pointless conceptions consider this close relation to be everlasting. This person says, However, one also should not think that the fact that heaven has not been observed to have changed either as a whole or in its parts in all past time is a demonstration that heaven is completely imperishable and has not come to be.276 For some animals live for a longer time than others. And parts of the earth, such as mountains, and stones, such as adamant, last for practically the whole of time. And there is no record of a beginning of existence or an increase or diminution of Mount Olympus. And in the case of mortal animals, it is necessary that their most authoritative parts endure in their own nature as long as the animals should be preserved, and so it is also necessary that the most authoritative parts of the cosmos themselves be preserved for as long as god wishes the cosmos to exist. It has been agreed277 that as a whole and in its parts heaven is the most authoritative part of the cosmos and it most holds the parts of the cosmos together, since all the bodies inside heaven are guided naturally by its motion. Therefore, it is necessary that heaven, both as a whole and in its parts, not depart at all from its proper nature as long as the cosmos should be preserved. But if Aristotle has correctly proved278 that every body has finite power, and heaven is a body, it is clear that it admits of perishing since it satisfies the definition of perishing, even if until this time it has not been observed to undergo any of the things which lead to perishing.

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I have quoted these things which, like those people who – as the saying goes – carry around the strange Eurycles,279 contain their own refutation at rather great length, so that I can speak briefly against all of them ‘Which of the things which come to be and perish do not have a beginning of their own existence and power, and an acme and a decline’? The gulls and the crows and Mount Olympus change somewhat every day and every hour, and after some time this change is perceptible, since some parts of Olympus are always breaking off, and it changes shape, and animals and their more authoritative parts reach their acme and decline from it. So if something remains completely the same for one hour, why can’t it do so for the next hour and the one after that and for an infinite time?280 So if heaven, of which some record is handed down and which is, as they281 say, already coming to the end of the last days of its own existence, is observed not to have varied at all either in substance or in size or in the number of the parts which fill it out or (what is amazing) in the speed of its motion, how is it possible that, if, as this person says, heaven is at its acme in terms of the proper definition of its nature, heaven has not also perished by constraint? But if, as this person says, all bodies inside heaven are guided naturally by its motion, then it is clear that, since the motion always has its own proper completeness, the things guided by it will also remain and undergo nothing which makes them worse. But if Aristotle has demonstrated that by its own nature a finite body has finite power (and not just Aristotle but Plato before him282), and since in addition to this Aristotle has also demonstrated that the circular motion is everlasting and that heaven neither comes to be nor perishes, and Plato says283 that heavenly things are indissoluble because of the will of god, how much better would it be for this person to set aside his contentious empty-headedness and ask how statements of wise men, which seem to those who attend to them carelessly to be in conflict, show their own harmony to those who are more attentive? For, although the corporeal nature of heaven is inseparable from the unchanging, eternal, goodness of the creator, each of these philosophers separated them in discourse because he wanted to see the power of each in itself. Plato did this more clearly in the Statesman284 when he separated in discourse the providential goodness of the creator from the natural existence of the cosmos. And it is clear that even if heaven has a ‘restored immortality’285 nevertheless, because it is brought into existence directly by the unchanging and eternal creator to which it is akin in substance, it is suited to unceasing participation in the goodness which is furnished by the creator and to an inborn dependence on his power for all time, so that the power of the creator is never incomplete, and his goodness is not transient, and the creation is not carried down to non-existence because of its unsuitability. But, in order that I do not go on at length

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and write the same things twice, it is necessary in this connection to recall286 the words spoken by the creator to the heavenly beings, according to Plato. I thought that for those who are attending closely to the things said by Aristotle I should dissolve the arguments against them. And the objections and dissolutions relating to the texts already set out have proceeded this far. So come, let us return and set out the texts which come immediately after the ones already discussed, and elucidate them. 270b26 It is also evident from what has been said why it is impossible for the number of so-called simple bodies to be greater. ... He has proved that heaven does not come to be or perish. And from this he has proved that it does not increase or diminish or alter. And in the proof that heaven does not come to be or perish he used two premisses, one saying that what comes to be comes to be from a contrary (he referred the demonstration of this to the beginning of the Physics), the other that there is no contrary to the body which moves in a circle. When he has proved the latter from the assertion that if there is a contrary to the body which moves in a circle, there must be a motion contrary to circular motion (a conditional which he expressed with the words287 ‘the motions of contrary things are contrary’), he has by conversion that if there is not some other motion contrary to motion in a circle, there is nothing contrary to the body which moves in a circle. Consequently the whole proof still depends on the assertion that there is not some other motion contrary to motion in a circle. Wanting to demonstrate this premiss, he mentions again the simple bodies and the simple motions. He needed to bring these things forward because, since motion in a circle is simple, if there were a motion contrary to it, that would be one of the simple motions. And he mentions the simple bodies because the body which moves in a circle is simple, and if it had a contrary, the contrary would be one of these simple bodies. Each of these is used to establish the other: for if simple bodies are the ones which move with simple motions, then if only these five bodies are simple, then also only these three motions are simple motions; and if there are three simple motions, in a circle, up, and down, then also only these five bodies are simple. He has introduced these subjects again so that we do not seek the contrariety of the body which moves in a circle and of motion in a circle among indefinite things,288 but among definite ones, the simple bodies and motions. The reason that there are three simple motions but five simple bodies is that in the case of things moving in a straight line there is something absolutely heavy and something absolutely light, and

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these are contrary to one another; but there are also two intermediates; they share in both, but each shares more in one.289 And so these intermediates move with the same motion as the things in which they share more, since they move in accordance with what predominates. But they don’t move in the same way as what they share in more, since earth moves as far as the centre, and fire moves up to heaven, but the intermediates move as far as the extreme (akros) elements because air is not perfectly (akrôs) light, and water is not perfectly heavy. Consequently it was possible to divide the motions into five. But if it has been proved290 that there is no contrary to motion in a circle, it is reasonable that motion in a circle remain undivided; for there is nothing which moves less in a circle as there is something less light or less heavy. For being less attaches to these intermediates because of the mixture of the contrary.

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270b32 One can gain confidence that no other motion is contrary to motion in a circle from several considerations. ... He proves with several arguments that no other motion is contrary to motion in a circle. In my opinion he carries out the reasoning on the basis of a division.291 For since motion in a circle and the two motions in a straight line are the simple motions, if there is a contrary to motion in a circle, it must be either some motion in a straight line or else motions on a circular arc must be contrary, either those on some segment of a single circle which is either greater or less than a semicircle, or those on one semicircle or those on two semicircles of a single circle or those on a single circle. But if none of these are contrary, there is no contrary motion at all. The first of these arguments is the following: [i] If some motion is contrary to motion in a circle, it would most of all be a motion in a straight line; [ii] but motion in a straight line is not contrary to motion in a circle; [iii] therefore, no other motion is contrary to motion in a circle. And he gives the following tacit proof of the conditional [i]:

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If a straight line is thought to be most of all opposite to a circular one (as an unbroken line is thought to be contrary to one which is broken everywhere),292 then motion in a straight line should also be thought to be most opposite to motion in a circle; but the antecedent; therefore the consequent.

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In the middle he dissolves an objection which is brought against this additional assumption [ii]; it says that the concave in a circular arc is most of all opposed to the convex. He says that the concave and the convex are the same in substratum and differ only relatively,293 and even if they are opposite to one another relatively, nevertheless, when they are taken as a pair and combined into one arc, they are opposite to a straight line; but the difference of motions is not determined by relations.294 Consequently, the original assertion is true: a circular arc is opposite to a straight line; and the previous conditional [i] is true: if there is a contrary to motion in a circle it is most of all motion in a straight line. He proves that the additional assumption [ii] of the original syllogism, which says ‘but motion in a straight line is not contrary to motion in a circle’, is also true on the basis of the fact that motions in a straight line are contrary to one another, upward motion to downward; for above and below are contrarieties of place, and the motions from those regions have contrariety most of all; for the motions which go from contrary places into contrary places are contrary. So if the motions in a straight line are contrary to one another, and for a single thing there is a single contrary (he omits to say this now because it is clear since it has been said many times), and there are two motions in a straight line and no more (and that is why he set out the differences of the simple motions earlier295), motion in a straight line will not be contrary to motion in a circle. One should try to understand whether this argument is an argument from more and less, as Alexander says, or whether argument from the most and its opposite is not at all a demonstration from the genus of more and less, because in my opinion less is opposite to more and not to most – unless is now using ‘most’ to mean ‘more’.296

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271a5 Moreover, if someone assumes that the same statement ... . Since he has said297 that motions in a straight line from contrary places are contrary, it is easy to make the assumption that in the case of an arc which is greater or less than a semicircle, motions from opposites to opposites are contrary, for example that the motion from A toward B is contrary to that from B toward A.298 And so he says that even if this sort of assumption seems to be true of an arc, in fact, it is taken as if it were about a straight line, if it is taken as about motion from a contrary place to a contrary place. And he adds the reason in a remarkable way when he says, ‘such motion is finite, but circular arcs299 between the same points are infinite’. By ‘finite’ he means ‘one’, since it is impossible to join more than one straight line from a point to a point because a straight line is the least line having the

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same limits, and the least is unique. And that he means that the straight line is finite in number, not magnitude, is made clear by his saying that the circular arcs are infinite, since the arcs are infinite in number, not magnitude; for it is possible to draw infinitely many circular . For if the motions from A and from B are contrary, and contrary motions are from contrary places, and motions from contrary places are from places which are most widely separated, and motions from places which are most widely separated are from places which are separated by a determinate distance (since the greatest distance is determinate), and what is at determinate distances is at things having a straight line between them (since what determines and measures distances is a straight line; for it alone is determinate because it alone is the least line having the same limits), and the motions which come from distances300 which have the distance between them as a straight line occur as on a straight line, then, if the motions from A and from B are taken as contraries, they are taken as in a straight line. But circular arcs which are drawn between (epi) the same points are indefinitely or infinitely many. So since motions from contrary places are contrary, the motion from A on the least301 arc will be no more contrary to the motion from B on the same arc than to the motion from B on the greatest arc. For B is equally contrary to A on the greatest arc. And the argument is the same in the case of infinitely many . For in the case of arcs it is not possible to take either a greatest or a determinate one since for any arc which is drawn it is possible to take a greater one and a lesser one. Furthermore, if the motion from A takes place on the straight line between A and B, and the motion from B on the arc , then, if the motion from A is contrary to the motion from B, motion in a straight line will be contrary to motion in a circle.302 271a10 Similarly in the case of the motion on a single semicircle ... .

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In destroying the view that motions along an arc greater than a semicircle or less than one are contrary on the basis of the fact that the arcs are infinitely or indeterminately many, he gave the impression that what he said followed because of the number of those arcs and not because of the nature of the circular arc and of the straight line. And so now he proves the same thing again in the case of a single semicircle, which obviously has one arc. For also in the case of the semicircle drawn on CD,303 if the motions on the arc from C and from D are taken as contraries, they are the same as the motion on the diameter. For, again, if contrary motions are contrary because they are from places which are most widely distant from one another, and the greatest distance is determinate, and we judge a determinate distance by reference to the least line of those having the same limits,

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and this is the straight line, it is clear that also on this hypothesis the contrary motions will occur as on a straight line. And the demonstration holds no less when it takes place for a single semicircle . And the situation is the same in this case as in that:304 if motion from A is contrary to motion from B and one occurs on a straight line, the other on an arc, motion in a straight line will be contrary to motion in a circle. And it is clear that the contrariety of things moving on an arc is taken as in the case of things moving in a straight line because the motions are taken in terms of the greatest distance, and the greatest distance is determined in terms of the straight line; for it is possible to draw different arcs, greater and smaller ones, of different circles between the same points, and to draw a greater segment305 of a circle between less distant points and a smaller segment between more distant points. Alexander says:306 If someone, having specified the contraries up and down and joined the straight line CD, drew a semicircle around it, and then thought that up and down were not defined by the straight line , then, first of all, nothing which moves naturally would move either up or down on the semicircle, but it would move on a straight line, since it would move on a least line. For Diogenes307 says that even donkeys go after food and drink on a straight line. Moreover, motion on a semicircle of this kind which has above and below as limits is not simple, since it is not just circular but at the same time upward or downward. For even if you were to draw a whole circle around a straight line from earth to heaven, something moving on this would not be moving with a simple motion either, but at the same time it would be moving with a motion up or down along with a circular motion, since only the motion around the centre is simple and in a circle.

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271a13 Similarly, even if someone were to draw a circle ... . He has proved that in the case of a single semicircle the motions on it from the limits of the diameter are also not contrary because the greatest distance, which gives form to contraries, is not defined by an arc but by a straight line. Now he proves in the case of two semicircles G and H joined to make a single circle that308 even if I cause one thing to move on semicircle G from E to F and another to move on semicircle H from F toward E, even so the motions are not contrary, and for the same reason. For the arcs do not define the greatest distance in terms of which contraries are characterised; but rather the greatest distance is defined in terms of the diameter EF. And consequently again

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if the motions are taken as contraries, they are taken as moving the distance on the straight line, not the distance on the arc. Having proved in the case of an arc greater or less than a semicircle and in the case of a single semicircle and in the case of two semicircles joined together that the motions on them are not contraries even if they seem to take place from opposites, he adds, ‘And even if these are contraries, nevertheless the motions on the whole circle are not thereby contrary to one another’, using an indirect counterargument.309 For the person who has proved that the motions on the semicircles are contrary has not thereby proved that those on the circle are, the case for which the demonstration is now being proposed to us. For in the case of arcs and semicircles, the motions from their limits are thought to be contrary because the limits of the arcs from and to which they move are opposite, but in the case of motions on a whole circle, if two things move in reverse directions to one another, there are not any opposite starting points of motion since each is from a point to itself. He will make the difference between motions on a semicircle and motions on a circle clearer when he proves next that motions which occur on a whole circle are not contraries. Consequently he has used the demonstrations for arcs and semicircles superfluously but not to no purpose; rather he proves through them that the nature of an arc does not admit opposition with respect to motion at all. 271a19 However, the motion in a circle from A to B is not contrary to that from A to C either ... . Now he directly proves the very thing which was proposed for proof, that not even the motions which occur in reverse directions on a whole circle are contrary to one another. And he proves it from the definition of contrary motions (motions which come about from contrary places and into contrary places are contrary) and from the definition of motion in a circle. For if ABC were a circle and something,310 beginning from A, were to move on the B side of the circle as far as A and something else (or even the same thing), beginning from A and proceeding in the reverse direction through the C side of the circle, were also to reach A, both of these motions are from A and to A, that is, from and to the same thing; for to have moved in a circle is to have moved around the whole of it. However, contrary motions are from contrary places to contrary places, not from and to the same thing. So the motions in a circle are not contrary. The inference is in the second figure. Alexander says, It would have been possible to use this argument also in the case of the motions previously discussed. For none of them was from

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a contrary into a contrary. But this is more evident in the case of the circle, motion on which is not just not from a contrary into a contrary, but not even from one thing into another, but from and into the same thing. And that is why he also has set out the argument for this case. 271a23 From ‘But also if a motion in a circle were contrary to another motion in a circle, one of them would be pointless’ to ‘But god and nature do nothing pointless’. Having proved that motions to the same thing which proceed in directions reverse to one another are not contrary, he now proves the same thing by reductio ad impossibile with the following syllogism: [i] If motion on a circle were contrary to motion in the reverse direction on the same circle, one of them would be pointless; [ii] but it is impossible that what is pointless exist; [iii] therefore, a motion in a circle is not contrary to a motion in a circle.

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And he proves the conditional [i] in the following way: Wherever they begin, each of two things which move in reverse directions on the same circle reach all the places on the circle; and if these motions themselves are contrary, as they are being assumed to be, and the contrarieties of motion are derived from the contrarieties of places, both things will reach all the contrary places in the circle in the same way; but the contrarieties of place are above and below, front and back, and right and left, and if there is contrariety of place in a circle, all the contrarieties are simultaneously, since one is no more than another; and so, moving in reverse directions through the whole circle, they meet one another, and because they are from contrary places everywhere and have contrary natures (since they would not move in contrary ways if they did not have contrary starting points of motion), they conflict with one another; and if they were equally strong (this is what ‘equal’ means), ‘they would not move’, since things which are equally strong, moving from contraries, stop each other, so that, remaining motionless, both would be pointless; but if one of the motions were dominant, the thing dominated by the dominant one would be carried around with the motion of the dominant thing, and in this way the motion in a circle would be single, and the dominated motion would not complete the circle;

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Translation and in this way, one of the motions would be pointless, being unable to reach the end of its proper activity; for we call something pointless if it does not supply what it is used for, as in the case of a sandal; consequently, if both are equally strong, they will remain motionless and both will be pointless, but if one is dominant, what is dominated will be pointless.

And in this way the conditional [i] in the syllogism is demonstrated. For that these things meet with one another follows from their moving in reverse directions on the same circle, and that they clash when they meet follows from the assumption that they are contrary in nature and proceed from contrary places. I think it is for this reason that Aristotle has hypothesised contrary places and given their names, indicating that, if the motions in a circle are contrary, there are also contrary places everywhere in the circle, since they are not more in one place than another, and also indicating that since the moving things reach all the contrary places in the same way, they always have their contrariety to one another renewed, and therefore they conflict. What follows from their conflict is that either they stop each other or one dominates and carries what it dominates around with itself, in which case it is necessary that either both or at least one is pointless. He proves the additional assumption [ii], which says, ‘But it is impossible that anything natural be pointless’ by also assuming another premiss, namely that nothing of which god and nature are causes is pointless because they do nothing pointless, and tacitly making the following inference:311 God and nature are the causes of natural things; nothing of which god and nature are causes is pointless; therefore nothing natural is pointless. I myself think it is necessary to analyse Aristotle’s demonstration in this way and for the reasons given. However, Alexander says:312

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But I think , proceeding in a better way, is pointing out313 that if there are contrary motions on a circle, there must be contrary

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places too, since contrary changes of place occur in accordance with contrarieties of places. However, says that from there being contrary motions on the circle that there are contrary places on the circle and that there is an above and below, and the other antitheses, on the circumference. But even if this is absurd, he obviously does not infer it as simply absurd as much as as a consequence of the hypothesis,314 their taking their start from contrary places contributing to the the things moving in reverse directions come into conflict. I give as evidence the fact that this absurdity does follow from there being contrary places, and that he also uses the assertion that, from wherever it begins, what moves ‘reaches all the contrary places in the same way’, from which it follows that they are always renewed in the contrariety of their power. Alexander says: But it is also possible that two arguments are expressed in this text. One of these is that one of the motions is pointless; having asserted this, he later gives the explanation for it after the other argument, when he adds, ‘For if they were equal, they would not move ... .’ For these words prove that one of the motions is pointless. However, the words ‘they would not move’ indicate that both would be pointless, and Aristotle has asserted that ‘one of the bodies would be pointless’ with respect to the other hypothesis, according to which one thing dominates and the other is dominated, but he has asserted that ‘God and nature do nothing pointless’ with respect to both hypotheses. Alexander says: The words in the middle of this passage would be a different argument. For in some manuscripts, what is written is not ‘because, it is necessary that what moves in a circle’ but ‘Furthermore,315 it is necessary that what moves in a circle’, as if he were adding something different to what has already been said. And what is added would be that if there were contrary motions on the same circle, they would necessarily pass through all the contrarieties of place in the circle; and he adds what the contrarieties of place are. Consequently it is necessary that there be contrarieties of place on the circumference. For the contrary motion occurs on the circle either because the motion is in the direction of contrary things316 (as it is when motion occurs on a straight line), or, if not, because it occurs through contrary places, which motion in a circle would do if it had contrariety; for it is not able to occur in the direction of contrary places, at

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Translation least if it is toward the same place. Having said this, Aristotle does not further add that it is absurd to say that there are contrary places – above and below or the other antitheses or even all of them – on a single circular circumference which is continuous; rather, taking up the argument again, he shows why he said initially that ‘one of them would be pointless’.

So Alexander. But perhaps the person who wrote ‘furthermore’ did not apprehend the continuity of the one argument nor that it is out of keeping with Aristotle’s customary style to use these sorts of hyperbatons. But why does Alexander say that motion in a circle ‘is not able to occur in the direction of contrary places, at least if it is toward the same place’? For, in general, if the circle is hypothesised to have contrary places, the motion, I think, is entirely through contrary places and also in the direction of contrary places. Alexander sets out in a concise way and, as he says, in accordance with his master Aristotle,317 the demonstration that there is no motion contrary to motion in a circle and no contrary to the body which moves in a circle as follows: If there is a motion contrary to motion in a circle, either it is in a straight line or it is circular. But, as will be proved, it is neither, and so there is none at all. There is no motion in a straight line contrary to circular motion. For what sort of motion in a straight line will be contrary to it? And why one rather than another? Furthermore, motions in a straight line are contrary to one another, and for a single thing there is a single contrary. But if we are able to prove318 that no motion in a straight line is contrary to motion in a circle, then, in general, motion in a straight line will not be contrary to motion in a circle. But neither is motion in a circle contrary, since contrary motions are from contraries and into contraries. For the contrarieties in motion are derivative from the contrarieties of places, but things that move circularly and on a circle move from and to the same place even if they move in reverse directions to one another. But nothing is contrary to itself. Consequently, motions in a circle will not be contrary to one another. For the things which move in directions reverse to one another in this way do undergo something contrary (hupenantion), but their motions are not contrary, since the definition of contrary 319 does not apply to them. But if neither motion in a straight line nor motion on a circle is contrary to motion in a circle, there will not be any contrary to what moves in a circle naturally. And it is clear that things which move on a semicircle and

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things which move on a circle are not said to move in the same way because things which move in a circle move continuously from and to the same thing, but motions on a diameter320 are not continuous because what moves must turn, and what turns must first stand still. Let these things suffice for the clarification of what Aristotle says. And let me add that one should bring forward what is said here for those who believe that Aristotle does not say that god is an efficient cause but only a final one. For it says here clearly that ‘god and nature do nothing pointless’. However, some people also do violence to this statement. Some of them understand ‘god’ to mean ‘heaven’, on the grounds that its motion is the cause of the nature of things here. And they are correct if they add the word ‘direct’, since god on his own gives existence to heavenly things and through their motion also creates the sublunary things, which come to be and perish. For, as Plato321 also says, the unmoving cause makes whatever it makes on its own everlasting and equal to the gods. However, some others of these people say that in assigning the same rank to god and nature in this passage Aristotle makes a mistake because of the axiom.322 However, since with what he says here, which is expressed in terms of the motion being on a single circle, Aristotle has given a proof that even if things move in directions reverse to one another on the same circle, there is no motion contrary to motion in a circle (for either both will be pointless, if both are brought to a stop by force, or one will be, when it is carried around by the stronger), it is worth asking why the motion of the sphere of the planets is not contrary to the motion of the sphere of the fixed stars;323 for these do not just move in reverse directions; they also seem to move from opposite places to opposite places, if, indeed, the sphere of the fixed stars moves from east to west, and the spheres of the planets move from west to east. For the fact that this motion does not occur on the same circle does not seem to prevent there being a contrariety, since it is not necessary that everything which moves from the centre or to the centre move on the same straight line or that they always meet each other. And in general the motions on one circle which are thought to be contrary do have an apparent contrariety because they are in reverse directions but not because they are from contrary places. And this is most of all the specific feature of contrary motions. However, the sphere of the fixed stars and that of the planets are thought to move from contrary places. Now it should be said that the contrary motions about which we are now enquiring ought to be from and into contrary places, since this is the definition of contrary motions.324 However, things which move in accordance with them ought to be equally strong in power with one another, if the contrariety is not going to give out quickly

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because one of them dominates. But the things which move with these motions also ought to meet with one another and be contrary in nature (if we are going to call the motions of natural contraries contrary) and change into one another, having a common substratum. For things which come to be from one another are contraries in this sense –this I think has been proved in a reasonable way. Let us then see if the motion of the sphere of planets and the motion of the sphere of the fixed stars have any of these features which have been distinguished. First of all east and west, from which, as opposites, the planets and the fixed stars are thought to move, have their being in relation to us and not to the universe. For what is east to some people is west to others. Secondly, each of these spheres could be said to move both from the east and from the west at the same time.325 For just as the hemisphere of the sphere of the fixed stars which is above earth obviously moves from east to west, so the hemisphere under earth obviously moves in the reverse direction from west to east; for otherwise the stars which have set would not rise again. And the hemisphere of the sphere of the planets which is above earth seems to move from west to east, that under the earth in the reverse direction, but both move by revolving from and to the same things. And if you conceive some point outside of each of the spheres, every part of either which begins from it ends up again at it, and similarly both depart from it naturally and proceed toward it naturally. In general how can they be said to move from contraries into contraries when each of them is always in every place, albeit with different parts at different times, and they move naturally from every place and to every place equally? Moreover, if the sublunary elements, which move in a straight line, made continuous reversals in their motion and naturally rose and sank equally, and most of all in a different place so that they did not meet one another, but some moved to the right, some to the left, no one, I think, would say that either their motions or the moving things themselves, being similarly related to all places, were contrary. For each of the elements which move in contrary ways moves from a contrary place toward a contrary place and is related in a suitable way to the one and in an alien way to the other. However, the motions of the two spheres are not equally strong either, if, indeed, the sphere of the fixed stars carries the sphere of the planets around with it. However, the dominant sphere does not constrain the dominated one or eliminate its natural motion, as happens in the case of contrary motions. It is clear that there is no constraint because the sphere of the planets is filled with (koresthen) the motion of the sphere of the fixed stars, but nevertheless preserves its own natural motion, always counterrevolving in the same measures. However, if it were constrained by a contrary and thus stronger motion, it would certainly also have completely ceased its own proper

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motion long ago, and if it did not, nevertheless, being constrained, it would not have preserved the sameness of its motion for all time. Consequently the things which move in this way are not contrary either. And even if these motions themselves were contrary because in reverse directions, the motions and the things having them are not at all contraries in the sense that they change into one another, if, indeed, the things having them are distinguished by proper places and are not of a nature to meet one another either as whole or in their parts; for even if they touch one another, they do not do so as things proceeding from contrary places and having contrary natures, but as things which are always together and familiar with one another and in agreement. In general the things which change one another have a common substratum and are not able to exist together with one another in it and so conflict in relation to the substratum and change one another. But these do not have a common substratum but each has a substratum by itself, and they are of a nature to exist together, touching one another in a friendly way. However, the entireties of the sublunary do not change one another either; only detached parts of them do so. So if no part of these becomes detached, the parts are not of a nature to change into one another either; but if changed as wholes, then, if the whole endured, the cosmos would become different; and if the whole perished, the cosmos would no longer change, but perish along with the whole.326 What then! someone might say, does the motion in reverse directions of the spheres have no power? And does its being one way or the other make no difference? Rather the motion has the greatest power, since it harmonises the whole cosmos and furnishes the cause of sublunary coming to be and perishing. But it does not do so in such a way that one motion is changed by the other, which is what was asked about, but in such a way that there arises a harmonious ordering of secondary things in relation to prior ones. Let these things be said with respect to our investigation. But since, to quote the lyric poet Alcaeus,327 ‘the pig is worked up328 again’, it is necessary to turn away again to this grammarian, who in his discussions displays a great deal of badness of character as well as mindlessness. Having said in this connection that Aristotle shows that heaven does not come to be or perish using two hypotheses, one which says that everything which comes to be comes to be from a contrary, the other which hypothesises that there is no contrary to the heavenly body, he says (speaking in this way with these very words), ‘We have accepted the second hypothesis – I mean that there is no contrary to the heavenly body – since there is no contrary to substance in general,329 but we have refuted the first, which is false’.330

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The person who says these things spends a whole book, the fifth, seeking victory by refuting the arguments which demonstrate that there is no motion contrary to motion in a circle. And he does not understand that, since nature is a starting point of motion, if there is no natural structure which is contrary to the substance of heaven, that is to the natural structure of heaven, there is also no natural motion contrary to its natural motion. But this person concedes that nothing is contrary to heaven – something which, because Aristotle accepts it, he would no longer have to demonstrate using the fact that there is no contrary to motion in a circle – and does battle with this demonstration, obviously because of his empty-headedness. For if a person who pays attention to truth concedes what is to be demonstrated, why would he disagree about the way it is demonstrated? Let this be an indication of this person’s mindless desire for victory. Meanwhile we should point out that since, as I think, the premiss in question, that what comes to be comes to be from a contrary, has been firmly established, because the things said against it have been proved331 to be beside the point and spoken mindlessly, and the minor premiss which says that there is no contrary to heaven has been accepted by this person, it follows directly in the second figure that heaven does not come to be, and we no longer need to demonstrate that heaven has no contrary from the assertion that there is no motion contrary to motion in a circle. However, since, even though he thinks that this demonstration contributes nothing to the proposed conclusion, he strives for victory by trying to overturn it, let us ring the bells of these arguments of his too and hear the way they sound cracked. Aristotle having proposed to prove that there is nothing contrary to the body which moves in a circle because the motions of contraries are also contrary but no motion is contrary to motion in a circle, this person raises objections to both of these assertions, first to the assertion that the motions of contraries are also contrary. He asks: Does Aristotle think that the substances of things of which he says the motions are contrary are contrary? Or does he think that even though the substances themselves of bodies are not contraries they do at least always share in contrary qualities in the way that fire and water move in contrary ways but one shares in the hot quality, the other in the cold and, for example, the flesh of an Ethiopian and the flesh of a Scythian share in contrary colours even if they are not contrary in substance?332 And if Aristotle is saying that the substances themselves of the bodies, the substances which move with contrary motions, are contraries, then he himself will be caught contradicting himself, since he taught us in the Categories333 that substance has no contrary and most of all substance which is a composite

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of matter and form. There he taught that ‘it is a proprium of substance to be one and the same in number and receptive of contraries’. How then can things which change334 in contrary ways be contrary? For then a substance which is the subject of contrary changes (so that it will become light and dark, hot and cold, larger and smaller) will be contrary to itself. For it is arbitrary to say that things which change place in contrary ways are contrary, but things which change with respect to quality or increase and diminish are not. For nature is a starting point of change and rest not just with respect to place, but also with respect to quality and quantity (and clearly also with respect to substance, although this person does not add this; for change with respect to coming to be and perishing is natural). And things which change with respect to quality and coming to be335 are bodies which are more contrary than those which change place if, indeed, change of place is only something accidental. And it is not only in the case of the other kinds of change that we see bodies which are the same in number changing naturally in contrary ways, but also in the case of change of place itself. For air has a starting point not only of movement upward, but also of movement downward, since if some of the earth or water lying under air is taken away, it immediately fills that space, just as, if something lying above it is taken away, it moves upward. But if someone makes the force of the void rather than a natural starting point responsible for the downward motion, what is to prevent one from saying that in the case of the upward motion of the air there is the same cause, since it moves up if there happens to be an empty space, and otherwise it does not? And perhaps it is not just possible but also necessary that what holds in the case of the other contrary changes also holds in the case of change of place; and motion is one genus of change, and air is one substratum. Consequently it does not follow that things which change in contrary ways are contrary in substance, since nothing is contrary to itself. Now if this person were perplexed about these matters and making enquiry and raised the question how the statements of a wise man which seem to conflict are in fact harmonious, he would rightly be considered a lover of learning. (I mean the statements in the Categories that there is no contrary to substance, and that a substance which is one and the same in number can admit contraries, and what is said here, namely that the motions of contraries are contrary.) For if things which have contrary motions are contrary (as Alexander and not Aristotle said336), substance itself would seem to be contrary to itself, and it would not just have a contrary, it would have itself as

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contrary. But if when he says, ‘Therefore it is entirely necessary that either what is shown in the Categories or what is shown here be rejected as false, and if what is shown in the Categories is true and in agreement with the nature of things, it is false that bodies which move with contrary motions are contrary in substance’, he speaks rashly without making enquiry, then, I think, he will be rightly judged as a late learner rather than a lover of learning. For when those who have been trained in argument from childhood hear something which seems to be contradictory and has not been challenged, especially if they hear it from men like this one,337 they investigate whether they can somehow harmonise these kinds of things with one another because they have already come across many apparently conflicting things which actually harmonised. But because late learners only look at a few cases, they are struck by the apparent conflict and, inclining by chance toward one of the apparently discordant texts, they condemn the other. I think that this is what has befallen this person in this case too. But it should be said that, if, indeed, nature is a starting point of motion and rest, what person with a mind would doubt that the motions of things which are natural contraries are contrary? That would be similar to someone doubting a person who says that the activities of naturally good are good. But we should next investigate why it is true that a substance which is one and the same in number is the subject of contrary changes so that it will become light and dark, hot and cold, larger and smaller, and move up and down, as happens in the case of air. Why won’t the substance itself which moves with contrary motions be contrary to itself even though we say that one substance is not contrary to another? One should notice first that the things which are said in the Categories which this person says are ‘true and in agreement with the nature of things’, namely that there is no contrary to substance and that a substance which is one and the same in number is of a nature to move and change in contrary ways, also seem to superficial people to be in conflict with and contrary to one another because of the same objections. For if a substance which is the same in number is disposed in contrary ways because it becomes light and becomes dark, but things which are disposed in contrary ways are contrary to one another, why won’t the substance itself be contrary to itself? For the dissolution of these matters, it should be noted that some natural changes are active and some are passive, active being those with respect to which natural bodies are said to act, to heat or cool, to make light or dark, to cause to increase or diminish; passive those with respect to which what is acted on undergoes something naturally by the action of what produces these things naturally, for example, being heated or cooled and or being affected in the other ways. But change of place is only active, so that nothing is made to

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change place naturally by another thing in the way that it is heated or made dark; it is only moved by the nature which is inside it. Since this is the way things are, when Aristotle says here that ‘the motions of contrary things are contrary’,338 he is talking about active changes. For in their case nature is the starting point of motion in the sense that it causes motion rather than being moved and acts rather than being acted on. And so fire and water are said to be contrary in the sense that they activate contrary changes, that is, contrary activities: one makes things hot and dry, the other makes them cold and moist; and the one goes upward, the other downward. For, as I have said, these changes are also activities. But when Aristotle says that a substance which is one and the same in number is receptive of contraries, he is taking the contraries to be passive, since what receives is acted on, just as what gives acts. And so the same underlying substance is lightened or darkened, increased or diminished, but the same substance in and of itself does not make things both light and dark; for what acts with respect to its own substance which is already complete cannot activate contrary activities both of which are projected from the substance, and this most of all when what acts is something natural and simple. But what is acted on with respect to its own incompleteness and is able to be acted on and is naturally related to both opposites is reasonably said to undergo contraries in turn. And in its case it is not absurd that a thing be contrary to itself, but not in the same respect, but rather insofar as it is disposed in contrary ways at different times, as in the case of a body which is heated at one time and cooled at another whether substantially (as when it becomes fire at one time and water at another) or accidentally; but fire cannot heat at one time and cool at another, nor can it go up naturally at one time and down at another. And therefore it was not pointless for Aristotle to trace the differences between natural substances back to their changes of place and not to the other changes; for only changes of place are active because what changes place acts with respect to the nature within it. But when the other changes, which are both naturally active and naturally passive, are taken as passive they make the underlying substance itself appear to be contrary to itself. However, as I said, change of place is active; and so nothing is moved naturally by the action of anything else, but it is made warm and light and comes to be and increases and undergoes the contraries of these by the action of something else. For these bodies naturally act on and are acted on by one another. But since this person says that air also has a contrariety with respect to changes of place, it is amazing that he does not realise what he himself said,339 namely that in the fourth book of this treatise Aristotle says340 that what sinks to the bottom of everything, as earth does, is absolutely heavy, what rises to the top of everything, as fire does, is absolutely light, and what is intermediate between these, I

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mean water and air, which rise above some things and sink below others, are both heavy and light. And also Aristotle frequently says341 that these things are not simple in the strict sense. So what is surprising, if air sometimes moves up and sometimes down in accordance with what is dominant in it at any time, not having both of these contrary active powers in the same respect, but putting them forward in accordance with its own varying qualitative change? For it has a downward impulsion when it is thickened and an upward one when it is thinned. However, when some space below it is emptied and air is drawn down into it, this happens because of the emptying, since the universe always contracts itself and admits no empty space, but rather pushes finer and more mobile things into the spaces which are in danger of being made empty. Since air, at least in its own nature, is lighter, it is of a nature to move upward, and if nothing above makes room for the rising air, some bodies are necessarily made denser or they mutually replace one another, so that the region can receive air which has come to be from water.342 So it is not correct for this person to say that air changes position up and down in the same way so that if it moves down because there cannot be a void, it moves up for same reason. This is made clear by the air which comes to be from water: although it is more moist it nevertheless runs upward and also constrains what lies above it to become denser. So it is clear from what has been said that it is not strange even if what underlies contrary changes in a passive way becomes contrary to itself, but what is active does not activate contrary motions, and it cannot become contrary to itself. Nor is it arbitrary that things which change place naturally with contrary motions are contrary, but those which change in quality or increase or diminish in contrary ways are not;343 if, indeed, only natural changes of place are active, and it is not possible for the same substance to naturally activate contrary activities (because the activities are attached to an active nature), but contrary passive changes do arise in the same subject. And one should not view contrary changes in this indeterminate and confused way and attribute what happens in the case of passive changes to active ones. But since this person is prolix344 and thinks that air moves up and down naturally in the same way, he should be asked whether he says that air has both weight and lightness in the way Aristotle says, that is, not in relation to the same thing, but having lightness in relation to water and heaviness in relation to fire, or whether it has both of them in and of itself. And if he thinks the latter he should be asked whether it is said to have weight because of some other thicker thing in it and lightness because of some other finer thing in it or whether it has both in every part of itself. And it is clear that this is impossible since air would be completely motionless if each power on its own dragged it in accordance with this alterna-

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tive.345 But if it is light because of one of its parts and heavy because of another (in the way that we are light because of the fire in us and heavy because of the earth), air would be a composite, and it would be true to say of it, as it is true to say of us, that the natural changes of the contrary substances which are naturally in it are contrary. And there would be nothing absurd if you wanted to say that air is contrary to itself because it is composed of contrary parts. But if he says that air has both motions because it is light relative to one thing and heavy relative to another, it is clear that because of the two motions it will move to the same place, which lies under fire and above water; and, again, there will be a single natural motion for a single thing, and the motions of air will not be contrary in reality, but only relatively speaking, and what moves will not be contrary to itself. In general Aristotle says that ‘the motions of contrary things are contrary’ in order to affirm the truth of its conversion with antithesis, which says that there is no contrary to something the motion of which has no contrary. If he proves that there is no other motion contrary to motion in a circle, he will have proved that there is no contrary to the body which moves in a circle, a proposition which, as he says, this person accepts without demonstration, but nevertheless he has stretched out this many words.346 This is Aristotle’s view, but the grammarian says that it is arbitrary to say that bodies which change place with contrary motions are contrary while saying that things which make contrary changes with respect to quality or increase are not contraries. It seems that he believes that if the motions of contrary things are contrary, then also things of which the motions are contrary are contrary. However, unless these two are equivalent, it is not correct to posit the antecedent when the consequent is posited. Nor does it follow from what Aristotle says that, as this person says, things which change in contrary ways with respect to quality or place are contrary to themselves, unless this equivalence is proved first. But if these are equivalent to one another (that is ‘the motions of contrary things are contrary’ and ‘things of which the motions are contrary are contrary’), it is clear that what follows is not absurd.347 However, I think I have already explained in detail how matters stand, but I have set out these things now in order to make clear that this person, who has no understanding of the entailments among propositions, is deceiving himself in thinking that he and those who make mindless presuppositions say anything. And, forgetting, as it seems, that the subject of discussion is simple, natural motions, he says that since the soul changes or is able to change to virtue and vice and also to false and true understanding, it will then be contrary to itself with respect to the same thing. However, having had this idea, he ought to have raised the difficulty

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why the soul acts both from virtue and from vice, but fire never acts as a cooling agent. And, having raised this difficulty, he ought to have found as a solution that simple natural things act because of what they are and so, as long as they exist, they activate the same uniform activities; but that, although the soul gives life because of what it is and therefore is always ready to perform this activity, it does not act from virtue or vice or falsehood or truth because of what it is, but because it puts forward opinions and choices differently at different times. But let’s go on to what comes next and see whether these things sound more coherent than what has preceded them. He writes the following (again it is necessary for me to quote more of what this man says to avoid appearing like a bribed witness for the prosecution (sukophantês) to those who do not believe me):

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These things are true348 if they say that things which move with contrary motions are bodies which are contrary in substance. But if someone were to say that they are not contrary in substance because of the universal truth that there is no contrary to substance but, rather, things which move in contrary ways always share in contrary qualities,349 as in the case of fire and earth (since fire is hot, earth cold, and fire is light, earth heavy), then it would follow from this by conversion with antithesis that things which do not share in contrary qualities do not move with contrary motions, and that there is no motion contrary to the motion of such things at all. But it is not true that if there is no motion contrary to the motion of some body, the body does not share in a contrary quality, since conversion from the antecedent is not sound.350 But if someone says that these are equivalent, so that things which have a motion to which there is a contrary motion also share in contrary qualities and things which share in contrary qualities always also have a motion to which there is a contrary motion, he is demanding that an undemonstrated thesis be granted to him. But he is, nevertheless, refuted by the facts themselves. For the entireties of the elements clearly share in contrary qualities, but there is no motion contrary to the motion of at least the hupekkauma and the air, since their motion is circular, seeing that Aristotle himself thinks that there is no motion contrary to motion in a circle.

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In this connection I first signal that this person thinks that things which share substantially351 in contrary qualities, as fire and earth do, are not contraries in substance. For if substantial contrariety is not due to these qualities, the remaining possibility is that it is due to matter itself. And I don’t think that even this person would say

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that, but nevertheless he assumes that Aristotle would speak in this way. And I think that what comes next is filled with utter mindlessness and stupidity. For, although Aristotle has said that the motions of contraries are contrary, this person makes a conversion and hypothesises that things which move in contrary ways are contraries in the sense that they share in contrary qualities. And if he has converted the proposition thinking that the terms are not equivalent, let him tell us what things he should assume when he does not even know that it is not possible to convert terms which are not equivalent or to present them indifferently in one order or another. But if he proceeded in this way in the belief that they are equivalent, why does he say that they are not equivalent and consequently that it is not possible to convert from the antecedent and say that if some body does not have a contrary motion, it does not share in a contrary quality? Notice how he says that the person who believes that the terms are equivalent is demanding that an undemonstrated thesis be granted to him and has converted the terms posited by Aristotle as if taking them to be equivalent. He makes clear that he has converted them when he says that things which move in contrary ways share in contrary qualities and, using the conversion with antithesis of this, that what does not share in contrary qualities does not move with contrary motions (motions being the antecedent, contraries the consequent).352 He starts from these things and the conversion, not understanding, as I said before, that Aristotle wants to prove that there is no contrary to what moves in a circle on the basis of the fact that there is no motion contrary to motion in a circle. But this person, having converted the terms, has inferred353 that there is no motion contrary to motion in a circle, but will prove this using a proper demonstration with the goal of inferring from it that there is no contrary to the substance of heaven, since this was needed for proving that heaven does not come to be. But this person, striving for victory, continues to try to prove from the ‘facts’, as he says, that the terms are not equivalent and cannot convert. And here again he makes the conversion, but even more mindlessly. He says, For the air and the hupekkauma have contrary qualities and both move with a circular motion; therefore, if motion in a circle is not contrary to motion in a circle, these things which have contrary qualities will not have contrary motions. And here . First of all fire and air do not have as contraries those qualities from which their change of place follows, since both are hot and both are light, even if one is more light because of dryness, the other less light because of moistness.354 And secondly it has been proved earlier355 and I think reasonably on the basis of the

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fact that the air and the hupekkauma move along with the sphere of the fixed stars that motion in a circle is not a proprium of the nature of fire and air, but rather they share in the motion in a better way because they are obviously suited to share in it. That they do move along with the sphere of the fixed stars is made clear by the comets which arise in them as well as the other appearances which rise and set with the fixed stars. And it is not just these things356 which move along with the sphere of the fixed stars but also the sphere of the planets; but whereas the sphere of the planets also has its own motion, the sublunary spheres357 are moved in their entireties in accordance with a better participation. Let this much which I have said be sufficient so that no one who despises the unsoundness of this person’s arguments charges us with taking too much trouble. A person who makes such a charge should realise that I too have not endured this trouble for the sake of his arguments but for the sake of those who are deceived by their quantity and this very speaking against Aristotle. So I am not unaware that those who come after us will consider not just this person’s words but also mine superfluous and not worth attending to. But it is necessary to take the measure of the next thing Charybdis358 says. In this material which I have set out he has frequently alleged that there is no contrary to substance, and he thinks that Aristotle contradicts himself because he says this clearly in the Categories but here he says that the motions of things contrary in substance are contrary.359 I think he completely misunderstands what is meant by saying that there is no contrary to substance. I give as evidence the division on the basis of which he made his response. It is at the beginning of the passage which has just been set out and reveals how he thinks, where he writes:360 These things are true if they say that things which move with contrary motions are bodies which are contrary in substance. But if someone were to say that they are not contrary in substance because of the universal truth that there is no contrary to substance, but rather things which move in contrary ways always share in contrary qualities, as in the case of fire and earth (since fire is hot, earth cold, and fire is light, earth heavy)... . You see that he has contrasted things which are contrary in quality with those which are contrary in substance, and that, obviously thinking that the former are different from the latter and that are not opposed because of just any qualities but because of substantial ones,361 he says, ‘as in the case of fire and earth since fire is hot, earth cold, and fire is light,

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earth heavy’. Now if he does not believe that fire and earth and things like them are contrary in substance, then, since every composite substance (and he thinks that these most of all have no contrary) is composed of matter and substantial qualities, what other natural composite substance is left of which he thinks it is true that there is no contrary to substance?362 He has written clearly that he believes that this is said of composite substance in the Categories, since in the third chapter of his fifth book he writes the following:363 If Aristotle is saying that the substances themselves of the bodies, the substances which move with contrary motions, are contraries, then he himself will be caught contradicting himself, since he taught us in the Categories that substance has no contrary and most of all substance which is a composite of matter and form. So what sort of natural body composed of matter and form is it which is not given form by opposite qualities? For even if someone takes it to be the three-dimensional itself – and matter is the three-dimensional according to this grammarian364 –, then this becomes a natural body and composite substance when it has been given form by antithetical qualities, and the which is given form by contrary qualities is nothing other than this . But also if the body in question365 is not matter but a composite of matter and form, its form also has antithetical differentiae; for Aristotle says that ‘there is a matter for body and the same matter for a great body and a small one’.366 So what sort of substance composed of matter and form is there besides that which is given form by the antithetical qualities, hot and cold, light and heavy, of which he thinks it is true that substance has no contrary? He seems to agree that it is not true of this substance.367 And so he tries to pursue the argument in another direction, attacking368 the figure of conversion, itself something which he has also shown himself to be ignorant of. But this person will also show his ‘ability’ in argumentation in what follows. It would be good to explain to myself first, and thereby also to those who are eager to learn, what it means in and of itself that there is no contrary to substance. Aristotle, having taken what in the Categories is substance in the strict sense, the individual thing, the substance composed of form and matter, has taken it as a substratum, and so he says it is neither in a substratum nor said of a substratum so that he indicates in every way that it is a substratum. But contraries qua contraries are accidents, since they are differentiae and differentiae are qualities and accidents.369 And differentiae are not contrary to substance, but they have their own contrary existence in substance. And therefore Aristotle says both that there is no contrary to substance and that substance can receive contraries while being one and

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the same in number. Consequently the statement in the Categories that there is no contrary to substance is true. For there is no contrary with respect to matter, which is only a substratum. And there is none with respect to form, the composite of genus and differentiae (for is also substance, even if it is in matter); rather, together with matter, underlies contraries. And much more is it true that there is no contrary with respect to the composite of form and matter, since this is still more a substratum for contraries. (A substratum cannot be a contrary; for it cannot be both members of a contrary pair, since they are in a substratum; nor can it be one member of the contrary pair both because that member is not a substratum, but is in a substratum, and because if the substratum were a contrary it could not receive its opposite.) Substance in the strict sense according to Aristotle, individual substance, which both comes to be and perishes, is composed of matter and form. But form, of which we give a definition, is composed of a genus and differentiae, and differentiae are qualities which are antithetical to other qualities; for differentiae are divided out from their appropriate genera by antithesis. And so substances are said to be contrary with respect to these differentiae, not insofar as they exist independently and are substances and substrata, but insofar as they are given existence and form from contrary differentiae; for example, fire qua fire and water qua water are not contraries because they are substances which underlie contrary accidents ...,370 but they are contrary to each other and conflict with each other and change into each other insofar as one is hot and dry, the other cold and moist, and one is light, the other heavy, and not insofar as they are substances and substrata, but rather insofar as they have contrary qualities. And so in the Categories Aristotle took the kind of substance which is a composite of matter and form as a substratum and said that the same substance is receptive at different times of contraries, but contraries which exist as accidents,371 and he said that there is no contrary to this kind of substance. But here he has taken the differentiae which belong substantially, each contrary contributing to the filling out of a different substance and the differentiae belonging per se and not accidentally to the substances. And he said that substances are contrary to each other with respect to those differentiae which belong per se to the different substances. For differentiae which belong accidentally exist in the same substance in turn. And so, when he says ‘the motions of contrary things are contrary’, he is calling substances which have substantial differentiae which are contrary to one another contrary substances, but he is not doing so insofar as they are substances and exist per se, but insofar as they are constituted by the contrary differentiae from which contrary motions follow; for upward motion

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is conjoined with heat and lightness, downward motion with coldness and heaviness. And these things do not contradict what is said in the Categories; nor is it necessary, as this person says, to eliminate the view that the motions of contrary things are contrary because one thinks that what is said in the Categories is true.372 Rather373 one should understand that in the first book of the Physics Aristotle said that the privation of the form which is in matter, and is constituted from qualities which are contraries, is contrary to the form; and he says that the form comes to be from this privation because there is not always a contrary form for every form; for there is no form contrary to human or musical. But there is always a privation. And sometimes the privation involves a complete form which has complete qualities constituting it; for example, the privation of fire in water exists together with the form of water, which is complete and possesses the qualities in it, coldness and moistness (the contraries of the qualities of fire) complete, and, as a result, fire is said to come to be not just from its own privation but also from the form which is contrary to it. But when the privation does not exist together with a complete form, but with something material which is suitably disposed to receive the form which is opposite to the privation, as in the case of the privation of human in seed, then what comes to be is said to come to be not from a contrary form but from a privation. This is not because the seed is not also a kind of form, but because it is an incomplete form and has the role of matter in relation to the existence of the complete form and is entirely derivative from it. Accordingly, a human being does not come to be from seed as from a contrary form. And it is clear that there are also in the seed some qualities which have contrariety to one another, but the qualities are also incomplete and not like the complete qualities of complete forms. Therefore, whatever qualities there are in the seed which are contrary to human qualities change into human qualities when the moist in the seed is dried and the spherical is stretched out. And whichever qualities are of the same kind as human qualities change from being incomplete to being complete. And so because the condition of the substratum is incomplete, when an animal comes to be from seed or musical comes to be from unmusical, it is said to come to be from the privation of the form and not from a contrary form. that I am not writing these ideas as my own but that they are also accepted by the most reputable commentators and expressed by Aristotle himself, listen to what Alexander has written in his commentary on the Categories. Having first set out the text which says, ‘It is a feature of substances that they have no contrary’,374 he adds the following: He in turn shows another concomitant of substance which, as he himself says,375 is not peculiar to substance, namely, there is

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no contrary to substance. And, accordingly, there is no contrary to the substances which he has set out. However, he will say in the Physics376 that the privation is contrary to substance as form, and also more generally that a privation is said to be a contrary; for it is his custom also to call things which are assumed contrary by privation contraries. But in the case of the elements, their forms, because of which they are fire or air or water or earth, are contraries, as he also says in On Coming to be and Perishing;377 for this is why they change into one another. So he would be saying that there is no contrary to those substances which he has set out , and since he proved in the second book of On Coming to be that, because dryness, moistness, heat, and coldness give form to the simple, primary bodies, these bodies themselves are also contrarieties. From this alone it is clear that he does not say that a differentia of substance is substance since a differentia was not among the substances set out .378 But also the divine Iamblichus has written the following in his commentary on the Categories:

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So it is a feature of substances that they have no contrary. For contraries are always subsumed under a single genus, but there is no single higher genus under which substance can be ordered; and contraries are relative to one another, but substance is not relative and has no additional need of the relation of contrariety. Furthermore contraries are directed to (aponeuei) one another, but substance is determined in and of itself.379 establishes that substance has no contrary by induction on the basis of primary and secondary substances. Shortly after this has written: Some people raise as a difficulty the question why rational animal is not contrary to irrational animal. And we say that the inherent differentia is contrary to a differentia , but the whole is not contrary to the whole . The reason for this is the following. What receives contraries is not itself a contrary. For if it were occupied by one contrary, it could not have the structure suitable for receiving the other contrary. Consider, for example, soul, body, individual substances, and secondary substances: if they did indeed receive contraries, they would not themselves be contraries. But also, if something, such as animal, is divided into contraries, even so it will not be a contrary, at least if it embraces together the division of the contraries. Consequently,

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none of these things will be a contrary. One could also realise this from the definition of contraries since we define them to be what is most separated from one other; however, in the way in which they are being spoken of now, they exist together in the same substance, that of animal.380 But why does Aristotle say381 that fire is contrary to water, and air to earth? We will answer that obviously they are contrary with respect to the differentiae which give them form, and these are not substances. Cold and hot, dry and moist are contrary to one another, but the substances as wholes are not contrary to the substances as wholes, and they have been constituted together on the same matter. And what need is there to drag things out by quoting the lengthy discourses of the commentators when it is possible to bring in Aristotle himself? He clearly reveals his own view shortly after the beginning of the second book of On Coming to be and Perishing, when he writes:382 There are four simple bodies and two of each belong to each of the two regions;383 for384 fire and air move toward the boundary, earth and water toward the centre. Earth and fire385 are the extremes and purest, water and air are intermediate and more mixed. And each is contrary to each since water is contrary to fire, earth to air, since these are constructed from contrary affections. Now notice that he also says substances are contrary to substances, water to fire and earth to air, and notice in what respect he has made clear that they are contraries, not insofar as they are substances and substrata, but insofar as they are constructed from contrary qualities and so are able to act on and be acted on by one another. I think that these things have proceeded far enough to this point. And I think it has also become evident to those who are reasonably perceptive about logical entailment how this person has been overthrown in this disagreement about the proposition that the motions of contrary things are contrary. But this good fellow, who accuses Aristotle of speaking cleverly but does not even understand some of the things Aristotle says and uses others as an indication of Aristotle’s cleverness,386 after having made a lot of objections out of pride, seems to accept the arguments he has overturn and has next written the following: Even if we were to agree that it is true that a body is contrary to a body and also that the motions of contrary bodies are contrary and consequently that if there is no motion contrary to the motion of a body, then the body has no contrary, it obviously

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still must be proved that there is no motion contrary to motion in a circle. Consequently if we set out each of the arguments through which Aristotle tried to establish this and give a refutation,387 it will be clear that, since it has not been proved that there is no motion contrary to motion in a circle, it has also not been proved that there is no body contrary to the body which moves in a circle. Now notice how the person who threatens things of this sort obviously does not even understand what Aristotle has written. For, having set out Aristotle’s statement of the first argument388 and Alexander’s exegesis, he has set Aristotle aside and passed over to Alexander, and said that although Alexander announced that he would prove that a straight line is not contrary to a circular one, he obviously has not proved anything. But neither Aristotle nor Alexander announced that they would prove this. But this person does not understand the development of the argument, which is the following:389 If there is a contrary to motion in a circle, it is motion in a straight line; but motion in a straight line is not contrary to motion in a circle; therefore, there is no contrary to motion in a circle. And he proves the conditional on the basis of the fact that a straight line is thought to be opposite to a circular arc. But even if these are opposites, the motions on them are not contraries because there is not one motion in a straight line but two; each of them is opposite to the other; and, as has been said many times, for a single thing there is a single contrary. Alexander390 is comparing rectilinear motion with motion in a circle when he says: Straight (hê eutheia) is thought to be contrary to circular (têi kuklôi ) because the latter is thought to be broken everywhere, but straight is the very most unbroken of all lines. So if it is not contrary to circular, nothing else which is thought to be less opposite to circular will be.

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But this person thought that the straight was being compared with the circle (tôi kuklôi) and was bold enough to change what Alexander wrote by writing, ‘Straight is most of all thought to be opposite to circle’, whereas Alexander wrote ‘to circular’, as is also made clear by what follows. For even if the argument is based on lines, nevertheless it is expressed for motions, and Alexander applies both ‘unbroken’ and ‘broken’ to motions on the basis of lines, as is

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made clear by what is added, namely, ‘So if it is not contrary to circular ...’. However, Alexander also does not think that the demonstration can be accomplished from the premiss that the straight line is not contrary to the linear circle, and so he did 391 announce that he would prove this. For, even if the lines are contrary, the motions cannot be contrary because motion in a straight line is opposite to motion in straight line and for a single thing there is a single contrary. Next this person tries to prove that motion in a straight line is contrary to both motion in a straight line and motion in a circle in different respects, just as excess is contrary to deficiency and to balance, and having more than one’s share is contrary to having less and to a just distribution, and in general the cases in which things on each side of balance, as unbalanced, are opposed to one another and to balance.392 He says, And both air and earth are in conflict with fire, but in different respects; and the false and ignorance are in conflict with truth, but the first is in conflict as a contrary, the second as a privation. And so in this case motion up conflicts with motion down with respect to a contrariety of places, but motion in a circle conflicts with each of the motions in a straight line not with respect to a contrariety of places but with respect to the very form of the motion;393 for in the case of the motions in a straight line motion is from one point to another and is unbroken in all its parts, but in the case of motion in a circle it is from and into the same thing with not even a chance part remaining unbroken. And motion in a circle conflicts with motion in a straight line because it is impossible for a motion on the same straight line to occur twice without having stopped, but motion in a circle can go around the same line infinitely many times without stopping. So if the motions are characterised by contraries, it is clear that they would also be contraries. You see how he does not understand the point of what has been said. Aristotle, in demonstrating that there is no change of place contrary to change of place in a circle, has said in these very words394 that ‘the contrarieties of motion are derived from the contrarieties of places’. But this person, who himself says literally, ‘Each of the motions in a straight line conflicts with motion in a circle not with respect to a contrariety of the places to which motions in accordance with them go but with respect to the very form of the motion’, nevertheless thinks that he can prove that motion in a circle is contrary to motion in a straight line in terms of the contrariety which Aristotle says does not apply,395 namely the contrariety with respect to places with respect to which it is possible for contrary things to conflict with one

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another and to change into one another; for things which naturally go to places which are contrary to one another are always given form by contrary qualities, heat and coldness, lightness and heaviness; and things which are given form by these contrary qualities, which cause different impulsions, go to contrary places. These, and not ‘unbroken’ and ‘broken’, are the contraries which come to be from one another. For a circle does not change into a straight line, nor does what moves in a circle change into what moves in a straight line, nor does what moves from and to the same point change into what moves from one point to another, nor does what is separated by rest change into what moves continuously.396 For these are not contrarieties relating to qualities which act and are acted on, and they do not have the same substratum, since if they did it would result that sublunary things change into heavenly ones and heavenly things into sublunary ones. I do not believe that even this person accepts this, since he clearly says that heaven is of a superior nature when he says,397 ‘It has been agreed that as a whole and in its parts heaven is the most authoritative part of the cosmos, and it most holds together the parts of the cosmos, since all bodies inside heaven are ... guided by its motion’. How then are these things going to change into one another? But if contraries of this sort, contraries which change into one another, must be understood in terms of contrariety of places, then it was pointless for this person to go on to spend many arguments contentiously proving that, even if motion in a straight line and motion in a circle are not contrary with respect to places, they are contrary in some other ways, and that it would be more reasonable to say that motion in a circle is contrary to motion in a straight line because it is opposed to motion in a straight line in many respects than to say that motion up is contrary to motion down when it is contrary only with respect to places. For things which come to be and perish are akin to one another, and they are opposite in many ways to things which do not come to be and perish; and they are said to have a contrariety in relation to one another with respect to which they change into one another, but they do not have this contrariety in relation to things which do not come to be and perish. But since he said earlier398 that two contraries conflict with one thing, as earth and air conflict with fire, earth as something cold to something hot, air as something moist to something dry, the excess of his stupidity seems amazing to me. For he has contended many times399 that these things are not contraries as earth and as air and fire, and in general as substances. Why then does he not understand that if hot is contrary to cold and dry to moist, two things are not contrary to one, one thing is, and the elements also change into one another with respect to those contraries? In general, if, as this person says, two things are contrary to one not in the same respect but in different ones, and in the case of excess and deficiency and his many

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other examples of this kind both conflict with equality with respect to inequality, which is common to them, and both conflict with balance with respect to imbalance, which is common to them, but they conflict with each other in some other respect, why – again – are two things and not one contrary to one thing? For imbalance400 is one thing and so is inequality. He says, But if the upper region to which things which move upward move is the concave periphery of the lunar sphere, and the upper region is contrary to the lower, heaven shares in one of the contrary places and is contrary to something with respect to that, just as fire is contrary to water, even if they are not contrary with respect to being bodies or substances but with respect to contrary qualities.

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Again this person has forgotten the form of the contrariety with respect to which the change of the contraries into one another occurs. For even if the upper region is contrary to the lower, they are not contrary in the sense that they change into one another, since the upper region never becomes the lower one or vice versa; rather the things which are in these regions or move to them are the things which are contrary in the sense of also changing into one another. Therefore, even if the upper region is in heaven and the lower one is in earth, earth and heaven are not contrary in the sense that they change into one another. Nor does heaven have any contrariety of this kind since this person himself knows that Aristotle’s account of place, which says that place is the limit of the containing thing, is not a complete account because Aristotle was the first person to enquire about place.401 Next he says,402

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Convex and the concave are opposed as contraries.403 For they are not opposed in the way relatives are since they do not always exist together; for there is convexity on the surface of a sphere, but there is no concavity when the sphere is solid, and there is concavity in the case of roofs which are concave inside and flat outside. But convex and concave are not opposed as state (hexis) and privation either since each is a quality.

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It seems that this rash person is unaware that privation is one species of quality.404 For if he were not, how could he say that convex and concave are not opposed as state and privation because they are qualities? He says, But they are not opposed as affirmation and denial either. And so it remains that concave and convex are opposed as contrar-

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ies.405 So if these two are certain qualities or affections of the heavenly body, the heavenly body is receptive of contraries and so of perishing and coming to be. 5

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Isn’t this person here obviously departing completely from the point of what Aristotle is saying? First because, where Aristotle applies the words ‘concave’ and ‘convex’ to a line on which motion in a circle occurs (since every motion comes about on a line), this person took them as applying to a solid, saying that it is not possible for a line to exist on its own without a body, but every natural line has its being in a body; and in fact concave and convex exist in different limits of a spherical body. And as a result of this he also censures Alexander for saying that if, considered in connection with one line, concave were contrary to convex, the line itself would be contrary to itself. However, if Aristotle applied the words ‘concave’ and ‘convex’ to the extension on which motion in a circle occurs and the extension has no breadth, it is clear that Alexander also has spoken correctly. For neither Alexander nor Aristotle has spoken about the concave and the convex which exist in different limits of a spherical body, but about those which exist in the linear distance on which a motion in a circle occurs. And,406 even if heaven does have concavity and convexity in different limits of its spherical body and contains these as contrary to one another, it also contains many other contrarieties in itself,407 since it contains motion and rest in itself, and odd and even, and sameness and difference, and one and many, and a multitude of other things of this kind. But, first of all, how can concavity and convexity, which exist in different limits, meet one another or act on one another or be acted on by one another in such a way that by changing into one another they become causes of coming to be and perishing? Secondly one should understand that although it is necessary that where there is coming to be and perishing there are always contraries from which coming to be occurs and into which perishing occurs, it is not necessary that where there are contraries there is always coming to be and perishing. For it is not the case that all contraries are of a nature to act on and be acted on by one another in such a way as to also change into one another; rather it is only those which are studied in terms of active and passive qualities, that is heat, coldness, dryness, moistness, and the things linked with these, light colour, dark colour, sweetness, bitterness, lightness, heaviness, and such. It is because of the change of these things into one another that other contraries, like, say, concave and convex, odd and even, change into one another, and the same is true of substances themselves, as was said earlier.408 So if heaven transcends that contrariety which involves active and passive qualities, it is reasonable that it also transcend coming to be and perishing.

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And it is also worth noting that if heaven had a contrary into which it changes, that contrary would be external to the substance of heaven, not in it, since, if the contrary were in heaven it would be constitutive of it and not destroy it; and so too the contraries which are parts of the sublunary world conflict with one another and change each another into themselves, but the whole which comes to be is everlasting because the perishing of one thing is always the coming to be of another. So, let the person who wishes to refute the doctrine of Aristotle prove that heaven has some contrary external to it, even if it is not contrary in terms of substance but in terms of the qualities in it in the way that fire has water as its contrary because it has contrary qualities. And this person does not infer anything sensible when he says: If they say universally that sharing in one or both of two contraries of any kind is a demonstration that what shares comes to be and perishes, then, since the heavenly body also admits the contrariety relating to concavity and convexity (and further the concavity of the lunar sphere is one of the contrary places), they should also say that heaven comes to be and perishes. But if not every contrariety is a cause for bodies of coming to be and perishing, then, just as it is not the case that changing place up and down in contrary directions is coming to be and perishing, so too it is not the case that something is exempted from coming to be and perishing just because it is exempted from contrary changes of place. For sharing in two contraries simultaneously in the way heaven shares in concave and convex does not prove coming to be and perishing. For contraries which can exist together do not conflict with or destroy one another and therefore are not causes of coming to be and perishing. Rather what possesses one of a pair of contraries and a substratum in common with what shares in the other contrary is receptive of coming to be and perishing, the contraries changing one another in a single substratum. Changing place up or down is not itself coming to be or perishing, but they are propria of things which do come to be and perish. For one thing is light and another heavy, and these things are hot and cold and dry and moist, and coming to be and perishing result from because of their change into one another in the same substratum. But perhaps these motions upward and downward themselves are also in a way cases of coming to be and perishing, if, indeed, fire moves upward and earth moves downward in the desire to take on their own pure form. And so if what is given form by contrary active and passive qualities always has a natural motion which is a contrary because lightness and heaviness are always apportioned substantially together with those qualities, it is true to say that what is superior to contrary

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changes of place always also transcends coming to be and perishing because it also transcends this kind of contrariety which involves those qualities. And therefore Aristotle has said409 that the motions of things contrary in this way are contrary and that, if there is no motion contrary to motion in a circle, there is also no contrary to what moves in a circle, and he has added that ‘it seems that nature was right to exempt what was not going to come to be ... from contraries; for coming to be and perishing are found in contraries’ – obviously the kind of contraries which conflict in a single substratum. So in this way this good fellow has pointlessly written down many arguments directed against the first of Aristotle’s arguments. Let’s see how he deals with the second argument.410 From what he said before, Aristotle has obtained that motions from contrary places are contrary, and that contrary places are those which are at the greatest distance, and that the greatest distance is determinate, just as the least is, and that every distance which has a determinate size is measured by the straight line between the distances;411 for that straight line is one and determinate because it is the least line having the same limits, but circular arcs which are joined to the same points are infinite and so indeterminate; and consequently these arcs do not determine the distance between A and B, and consequently the greatest distance itself is not derived from the circular arcs; and consequently the places of A and B are not contrary; and consequently the motions from A and B are not contraries if they occur on an arc and not on a straight line. Aristotle has inferred these things in this way from indisputable lemmas, but this person does not understand what he says, and says, ‘I wonder very much if the philosopher has made use of these sorts of arguments in jest rather than seriously’. And it is clear that because he considers this rigorous development of the arguments as jest, but his own arguments (which we will hear) as serious, he might appear to be very worthy. For having first set out Themistius’ paraphrase of Aristotle’s words and then the exegesis of Alexander of Aphrodisias (trying to appear wise in this way as well), he proposes to refute Aristotle’s view in terms of each. Themistius says that those who say that the motions on the circumference are contrary are led into the absurdity that infinitely many things are antithetical to one because the arcs drawn through A, B are infinitely many.412 And this person makes a joke of the argument by saying that there are infinitely many contraries to the infinitely many motions; for he says that there are two motions which are contrary to one another for each of the infinitely many arcs. He does not yet understand that since motions from contrary places are contrary, each of the infinitely many motions from B will be contrary to one motion from A. So there will be infinitely many contrary motions, and the argument of Themistius is correct.

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Secondly, he adduces against the argument that even if the arcs through A, B are infinitely many, nevertheless they are of the same kind as one another and therefore all the motions from A taken as one are opposite to the motions from B taken as one.413 And then, after superfluously setting out examples, he says: I am amazed that did he not see that the same thing also happens in the case of motions in a straight line; for the centre of the universe, to which all heavy things move, is one, but light things moving from the centre to the periphery do not end up at one point but at infinitely many. And in this connection he does not shrink from tastelessly drawing diagrams depicting the centre of the universe, the peripheral circle, and the lines from the centre, again not being able to understand the same thing which previously had also been the cause of his misunderstanding, namely that motions from contrary places are contrary, contrary places are those at the greatest distance from one another, and these places are determinate and have a determinate distance between them. For if this person understood these things he would not have been ‘amazed’ that Aristotle, who previously maintained these things, which are very clear, did not see that ‘the same thing’ happens in the case of motions in a straight line as happens in the case of arcs. For, in fact, the same thing does not happen since in the case of straight lines from the centre, all of which are equal, the interval between up and down, which is the greatest in this extension, is determinate, so that all the points on the periphery of the upper region, taken as one, are opposite to what is down.414 But, since the arcs between A and B are unequal and make the intervals between A and B unequal, they do not make the place A be at the greatest distance from the place B in terms of all the arcs. Consequently the places are not contrary, since they do not have the greatest distance between them one and determinate. But this person does not understand these things and says that the absurdity follows much more reasonably in the case of straight lines than in the case of arcs because the motions on the arcs are from the same point and to the same point and therefore are akin and of the same kind, but those on straight lines, even if they all start from the same point are not to the same point. Consequently it is true in the case of straight lines more than in the case of arcs that infinitely many things are contrary to one thing. But it is clear from what has been said that in the case of the straight lines everything which is up, taken as one, being at the same distance from what is down, is opposite to what is down taken as one, but that in the case of arcs, in which the kinds of distances are different, there is neither one kind, as he thinks, nor a contrariety of A to B with respect to these arcs at all.

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Alexander more suitably reduces this argument to the assertion that motions on an arc are not contrary at all because there is no greatest distance separating A from B along an arc, as is made clear by the fact that it is possible to draw to the points A and B infinitely many arcs which have different lengths (diastêmata). And this person again speaks a lot of nonsense in objecting to trying to demonstrate things about nature on the basis of geometrical principles. He says, It is true to say of mathematical things,415 which are abstractions, that it is possible to draw arcs through the same points to infinity so that one cannot take a greatest,416 but it is impossible in the case of natural things, which are apprehended with affections and matter. And therefore it is possible to take the greatest natural circumference in the universe, and so things which move in contrary ways from the limits of a diameter of the universe on the greatest arc of the universe move with contrary motions, since the points from which they have moved are also at the greatest distance from each other with respect to the arc; for it is impossible for there to be an arc greater than the outermost circumference of the universe. So if the two peripheries417 move in contrary ways to one another from the points of the diameter at which the limits (that is the concave limit of the sphere of the fixed stars and the convex limit of the sphere of the planets) of the outer spheres fit together with one another, the inner and the outer peripheries move with contrary motions; consequently their bodies418 themselves are contraries. For the sake of brevity I have gathered together these things he has written, in most cases in succession but in a few cases scattered here and there. It is also necessary in this case to show his stupid desire for victory.419 For first of all he says that it is true of mathematical things that it is possible to draw arcs from the same points to infinity so that one cannot take a greatest,420 but it is impossible in the case of natural things. So does he not know that every natural body has a surface because it is limited and that every surface is continuous and that everything which is continuous is divisible to infinity,421 since this is the definition422 of continuity? And it is clear that anything which is of a nature to be divided is divisible to infinity (although not into infinitely many things423), in such a way that it is not possible to take a magnitude which is itself extended, but is not divided by what is unextended by comparison with it (as body is divided by plane, plane by line, and line by point). Things which, like those in heaven, are indivisible naturally are also extended and are divisible conceptually (kat’ epinoian), and the distance between the

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points on them which are thought to be opposite is only determined by the determinate straight line joining them. And it is not possible to take one arc between the points. For an arc on the concave surface of the sphere of the fixed stars and the convex surface in the sphere of the planets is conceptual, not natural. So why isn’t it also possible to draw conceptually in the depth of each sphere arcs from the same points, greater ones in the sphere of the fixed stars, lesser ones in the sphere of the planets? For, in general, how can he think that he can say that there is no greater arc in heaven than the circumference in the concave of the sphere of the fixed stars?424 For the circumference in the convex limit of that sphere would be greater than this, if, indeed, the bodies of the spheres have depth and are not just surfaces and if the points in the convex surface move on greater circles . However, even if it is not possible to take a greater arc drawn on the same points than the one this person mentions,425 it would still always be possible to take a lesser one in the inner spheres. And even if such arcs drawn in the heavenly body are not natural things, the distances between the points would be different – conceptualisation is also sufficient to determine this. For when the points fall outside the straight line between them,426 the distance between them remains indefinite, so that they are not at the greatest distance from each other, their places are not contrary to one another, and the motions from them are not contrary, and the bodies moving with them are not contrary. However, this ignorant person has lumped together in a pointless way everything that Aristotle and his commentators have said. This person also puts forward counterarguments against Aristotle’s third argument,427 which says that even if the motion in the reverse direction is not taken to be along an indeterminate arc (it being possible to draw infinitely many arcs around the same points) but along one determinate arc, for example, the semicircle, even so the distance of C from D will be measured in terms of a straight line. Not understanding the arguments of either Aristotle or his exegetes, this person puts forward many arguments in an attempt to prove that it is not necessary that the straight line is the measure of every magnitude or even of every line; rather it is only the measure of lines of the same kind as it with which it can coincide, but it does not coincide with an arc. And so he constructs all his arguments as if Aristotle and his commentators were saying that the interval on an arc is measured by a straight line. But perhaps it is again necessary to quote some things he says for those who do not believe me: if the straight line is in fact the least of those drawn through the same points, it is not thereby necessary that it be the measure

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of every line and every magnitude; but clearly it is the measure of things which are of the same kind as it, with which it can coincide. But it does not coincide with an arc and it is not of the same kind as it. And therefore it cannot be the measure of it. Now isn’t it immediately clear that he thinks that they are saying that an arc is measured by a straight line? But if these words aren’t sufficient to prove his stupidity, listen also to what comes next:

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Even if craftsmen frequently measure some round artifacts with a straight line, for example, with a cubit,428 they do not measure the curved line as such with the cubit in the way that in the case of rectilinear artifacts the cubit is fitted to the straight edge itself of the artifact. In the case of an arc they do not fit the cubit to the arc itself, since that is impossible. Rather they take the rectilinear intervals on the circumference and measure them with a straight line,429 so that again what is measured is like what measures it. But suppose someone were to maintain that since by learning the size of the diameter of a circle, the size of the perimeter of the circle is also learned, a straight line is the measure of an arc. Then, since it is also possible to learn the diameter from learning the perimeter, he should also say that an arc is the measure of a straight line. In addition, we do not learn that the three straight lines of an equilateral triangle are equal to one another in any other way than on the basis of the circles drawn on one of the sides of the triangle as diameter.430 Why then is an arc more to be assessed on the basis of a straight line than a straight line is on the basis of an arc? Let no one who is refined (kathariôteros) blame me for pursuing inappropriate leisure if I choose to quote so much of this sort of thing from this person. Rather let him blame those who attach themselves uncritically to what this person says and those who sometimes do not believe that a person who writes such things dares to speak against someone so shamelessly. Where did Aristotle or one of his commentators say that the circumference is measured by the straight line? But this person does not understand that they say that the distance between limits, such as those Aristotle calls C and D, is measured by the straight line which joins them but not by an arc drawn around them, and they certainly do not say that an arc is measured by a straight line. For even if this were true, it would have nothing whatsoever to do with the argument. For it was proposed to prove that things which move in reverse directions on a semicircle do not move with contrary motions because the limits, C and D, of the semicircle are not contrary places because they are not at the great-

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est distance from each other in terms of the circumference of the semicircle; for it is also possible to draw an arc greater than the semicircle on the points in terms of which they would be at a greater distance from each other than they would be in terms of the arc of the semicircle. However, the person who takes the motions from C and D as431 contrary takes them as occurring on the diameter, since the determinate distance is determined by the diameter, the greatest distance is determinate, and the contrary distance is greatest. Accordingly Aristotle also says432 in this way that we suppose that things which are separated by a determinate distance (and the greatest distance, by which contrary places are separated, is determinate) are distant by a straight line. For this is the determinate between the limits which is least, and therefore the interval is measured by it. And Alexander in explaining the passage says:

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However, it is for the measure to find what is most distant and contrary. Therefore the contrary is with the straight line and on it. Therefore the contrary motions on the interval CD are not on the arc or the semicircle. So, did one of these people say that a straight line is the measure of the arc but not of the distance between C and D? But this person doesn’t understand the point of what is being put forward because, for what he thinks is the refutation of it he has introduced the fact that those who measure the circumferences of artifacts take the rectilinear intervals of the circumference and measure them with a straight line, not noticing that this is exactly what Aristotle says: 433 ‘We always suppose that each thing is distant ‘. However, as is his custom, he in turn grants that it is true that the straight line is the measure of every interval, and says that, even so, the argument will not move them any closer to proving that the motions in contrary directions from the limits of the semicircle are not contraries. He says,434

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Since a circle is a magnitude, parts of it are more or less distant from each other. Gemini is more distant from the beginning of Aries than Taurus is, and Cancer is more distant than these. Therefore there are in the some things which are most distant, as are Aries and Libra, since the distance of these on each semicircle is equal. Consider Aries and Scorpio. Even if they are at a greater distance in terms of one part of the circle, since they are separated from each other by seven signs, they are closer to one another in terms of the other part, since they are distant by five signs. Therefore, only Aries and Libra and in general the signs which divide the circle into two equal parts are separated by the greatest distance in every direction.

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Since he has said these things it is fair to ask whether he is taking the distance of the parts of the circle in terms of the circumference or in terms of the straight line between them which joins them. For if it is in terms of the circumference it is clear that in terms of the greater circumference Taurus is more distant from the beginning of Aries than Gemini is, and, also in terms of the greater circumference, the location of Aries is more contrary to that of Sagittarius than to that of Libra, because in terms of this it is more distant and places which are most distant from each other are contrary. For, in general, if he has taken the distance on the circumference, how does he dare to say that Aries and Libra are separated by the greatest distance in every direction? For it is true to say that they are separated by an equal distance in every direction, but it is not possible to say that they are separated by the greatest distance in any direction. For the signs which are next to one another are at the greatest distance in terms of the other arc. But if he is not defining the distance of the parts in the circle in terms of the circumference, but in terms of the straight line joining them, he is saying the same thing as Aristotle even if he is not aware of it. For Aristotle says435 that if the from C and the from D are taken as contrary, their distance is the same as the distance on the diameter. This person accepts that there is a greatest distance between C and D in terms of the diameter, but he says that there is also one in terms of the circumference because C and D are equally distant in every direction. But what does this have to do with the greatest distance by which contrary places are separated and from which contrary motions ?436 And next,437 following up in his combination of mindlessness and rashness, he says, This became for Alexander a cause of deception. For he assumed that the straight line is the measure and that it is for the measure to find the things which are at the greatest distance from each other and contraries, from which there follows the conclusion which says, ‘therefore, it is for the straight line to find the things in intervals which are at the greatest distance from each other and contraries’. But he maliciously added the words ‘and on it’ when he said, ‘Therefore, the contrary in intervals is with the straight line and on it’ when he did not have ‘and on it’ in the premisses. Here again one should first notice that, having said that Alexander was deceived, he immediately afterward says that Alexander was being malicious on the same matter on which he himself says that Alexander was deceived, not understanding that the person who says

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something because of being deceived is not being malicious since the deception is caused by ignorance, but that the person who acts maliciously in arguments knows the truth and tries hard to twist it. Second, how can he say that Alexander does not assume ‘on the straight line’ in the premisses when Alexander, as this person himself has recorded, set out the argument as follows: Every interval is measured by what is least; in every case the interval on a straight line is least; therefore, the straight line and the on the straight line are the measure of every interval; however, it is for the measure to find what is most distant and contrary; therefore, the contrary in intervals is with the straight line and on it; and so is not on an arc.438

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Is it not immediately clear that Alexander has also included ‘on a straight line’ in the premiss and syllogised as follows?439 Every interval is measured by a least interval because this is determinate; what is measured by a least interval is measured by a straight line and the interval on the straight line, since it the least of the lines or distances having the same limits; and the conclusion remains that for any interval the straight line and the interval on the straight line is the measure. And adds another premiss to this which says, ‘It is for the measure to find what is most distant and contrary’, and he infers that what is at a greatest distance in intervals and contrary is found with the straight line and the interval on it. But if it is found with this, it is clear that contrary intervals are defined in terms of (kata) this and are by reference to (kata) this; and a thing is defined in terms of (kata) that from (kata) which it is found, and a thing is by reference to (kata) what it is defined in terms of (kata). So which of these people is it fair to say is either deceived or malicious? Is it the one who syllogises coherently in this way? Or is it the one who charges the other with deception and malice on the grounds that he has inferred (as this person says) that it is possible to find the things which are most distant and contrary with the straight line and added to the conclusion that it is possible what is contrary in intervals on a straight line, that is, the one who also does not understand that places are distant from each other with respect to (kata) the interval from (kata) which their contrariety is found?440

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But this person, who understands nothing which has been said, wastes a lot of arguments proving again that, if we are measuring with a cubit, the points which are most distant from each other are not in the cubit used to make the measurement nor are they at the greatest distance in that cubit. He could not even understand that if the distance were only a cubit long, the things at the distance would be in the limits of a cubit – not the limits of the wooden or bronze cubit, but the limits of the intervening straight line; and the greatest distance for the limits would be relative to (kata) this straight line which measures as a determinate interval (because it is least), but is measured as an indefinite interval.441 The wooden cubit does not add the measure, but it makes the measure which inheres in the distance clear. But he is so out of tune with the meaning of what is said that he writes (in these very words), ‘In general it is completely naïve and absurd to say that the things in what is measured which are apprehended by means of the measure are also in the measure’, not understanding the way in which the interval determined by a straight line is both the measure of the greatest distance and something measured. Instead he mindlessly assembled a large number of standards (kritêria) to prove that the distance and contrariety of what is judged are not in the standards. He says, ‘For the distance between true and false is not in the demonstration nor is that between good and bad,442 nor is light and dark or running and standing still in the faculty of vision, nor is high and low sound in the faculty of hearing, nor is being twisted in the straightedge, and neither does the straightedge possess the straightness which exists, for example, in wood, although we learn about the straightness by means of the straightedge.’ It is clear that it was pointless for him to digress into these things, if one takes as the measure relating to the straight line not the one which comes from outside (such as the bronze cubit), but rather the one relating to the interval between separated things, which, as an indefinite interval, is measured and, as something straight and least and determinate, measures the distance from each other of separated things (because of this the distance relating to the straight line is not at all similar to external standards, but the bronze cubit is analogous to them). But he obviously does not know the specific character of the very things which he has dragged in either. For if the standards do not possess the logoi of what is judged, they cannot make a judgment. For how can the faculty of vision distinguish dark and light if it has not previously received an impression of them? But it does not possess the impression in the sense of being light or dark but in the sense of being a judge. In the same way, too, demonstration, which distinguishes truth and falsity, applies truth to what is judged, judging

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truth in terms of fitting, falsehood in terms of deviation, and the straightedge, which tests straight and twisted, applies straightness to them in the same way. And clearly he has set out his examples in droves because he is also unaware that the faculty of vision judges in one way, demonstration and the straightedge in another: the faculty of vision judges both light and dark as forms by a formal awareness, having previously received the forms in perception, either actually or potentially, but demonstration judges truth and the straightedge straight by the fitting of the form which they contain, and they judge falsehood and twistedness by deviation from this; for it is false to say that a human being is not an animal. And be assured that I am ashamed to be spending time with things of this sort, but it is necessary to expose their unsoundness to help those who listen to him superficially since with these things he is trying to do away with the blessed everlastingness of heaven and the unchanging goodness of its creator. For I know well that those who judge443 reasonably will loathe not only what this person says but also my arguments, which they will judge as jousting with shadows and take as the work of an unfortunate leisure. And so now it is also necessary to listen to what comes next. In what way is it not the act of a person who completely despises arguments to say that the antithesis of motions on a semicircle is the same as the antithesis of motions on the diameter because the semicircle and the diameter are limited by the same points? You see how he does not notice that Aristotle does not say without qualification that motions on the semicircle are the same as those on the diameter. Rather he says444 that they are the same when they are taken as contraries (that is, as coming from contrary places, that is places which are at the greatest distance, that is places the distance between which is determinate – since the greatest is determinate –, that is a distance which is measured by what is least – for this is what a determinate distance is). But if this person doesn’t know that a straight line is the least line of those having the same limits, he should learn it. Alexander says that even if things which move on a semicircle as from contrary places do not move in a straight line, nevertheless they do move with a contrary motion (that is, a motion from places which are at a greatest distance) because they move through the interval between them to the extent that (tosouton ... hoson) they are distant from each other by a straight line.445 In response this person says that ‘even in this way Alexander will not escape agreeing that the reverse motions which occur on a semicircle are contrary whether they are contrary because of the circle or whether they are contrary because of its diameter’. However, if it is because of the diameter,446 the motions are not contraries as occurring on the semicircle; for C, D are not at the greatest distance from each other because they are limits of the semicircle but because they are on the straight line.

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Alexander goes on to say that if every interval were not measured by a straight line but by an arc, it would not be possible to take anything at a greatest distance because it is possible to make both a very great arc between things which are close by drawing a very convex circumference and a smaller one between points which are very distant. And again447 this person stretches out long arguments in a contentious way to prove that also on a circumference the greatest distance is the one which is equally long448 in every direction, as is the interval from Aries to Libra. He does not understand that there is a difference between being equal in every direction and being greatest, and that the distance which moves from Aries through Libra up to Sagittarius, taken on the circumference, is greater than the distance which moves from Aries up to Libra. However, if the distances are taken on the straight lines between the limits, the distance from Aries to Libra is greatest because the diameter is greater than all straight lines drawn through a circle. But if the distance is taken on arcs, it is possible, as Alexander says, for more than one arc to be drawn on the same points so that, if the distance of the points from one another is taken in terms of a different arc at a different time, what is greatest will no longer be determinate. And again this person does not understand what Alexander is saying, and says, I do not know whether to say that the assertion449 that it is possible to draw a smaller arc from widely separated things and a greater one from close ones is the assertion of someone who wants to be fraudulent or of someone who does not know that it is not amazing if in different circles points which are close in one of the circles (suppose the circle has a perimeter which is one foot long and the points are half a foot apart ) are said to be at a greatest distance whereas points which are 25 feet apart from each other in a circle which has a perimeter of 100 feet are not at a greatest distance from each other. Again he speaks the same nonsense about straight lines in saying that the limits of a cubit-long straight line are at the greatest distance since they are distant by the whole line, but in a straight line of one hundred cubits the distance of the centre from an extreme is not the greatest, since it isn’t distant by the whole but by the half. And this person writes these things in the belief that Alexander is taking a greatest and a not greatest distance in the case of different points because Alexander says450 ‘because it is possible to make both a greatest arc between things which are close’ ... and a smaller one between points which are not close. He does not understand that Alexander has not advanced by making this hy-

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pothesis since Aristotle has proposed to prove also that if the motions in reverse directions between the limits of semicircle are taken as contrary, that is, as proceeding from places at a greatest distance, they are taken as on the diameter. However, although Alexander wants to prove that it is possible to draw greater and smaller arcs on the same points, he has superfluously done the argument as applying to different limits by saying that it is possible to make a greatest arc between limits which are close and a smaller one between limits which are very distant. But if this is possible in the case of different limits, it is clear that it is much more possible in the case of the same limits. But this person, not understanding this, stretches out lots of arguments, proving that in the case of different magnitudes, it is not at all amazing that closer ones are at a greatest distance from each other and further apart ones are not. He says, Even if we draw both a greatest arc and a least through the same points, say A, B, it will not follow that the points A, B are both at a greatest distance because of the greater arc and at a lesser one because of the smaller arc. For451 if we fill out the remaining arcs of the two circles, the points A, B will be potentially four, not two, since they have a different relation to each other in each of the circles. This is what he says, in these very words, and is it not clear that he does not understand what is said and is only spouting out empty words? What is the point of this word ‘potentially’ here? For the distances between the points A, B remain related to each other in the same way actually, the distance of the greater arc being one thing, that of the smaller another, and that of the straight line between A, B being a third and always determinate because it is measured by the straight line, which is determinate because the452 line which has the same limits is one and least. But the distances relating to the arcs are indefinite because many unequal arcs can have the same limits; and because of this it is not possible for a greatest distance for contraries which is definite to be defined by arcs; it can only be done by a straight line. But this person does not understand453 what is meant by saying that the interval is measured by a straight line, namely that it is determined to be in a straight line in such a way that what is in the middle covers the extremes.454 Rather he thinks that is said to be in a straight line because a straight line added to the distance from outside makes it straight. He says, On what basis does Alexander say455 that in a circle there are no points which are at a greatest distance from each other unless every interval is measured by a straight line? For every meas-

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ure only makes what is measured known; it does not make what is measured be such as it is known to be by nature because of the measure. For it is clear that a straight measure fits because the distance is a straight line. 25

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However, Alexander is not considering a measure introduced from outside. Rather he is considering the fact that sometimes the distance is made determinate by a straight determination (thesis), and sometimes, when the distance is curved, it is indefinite. And this person sets out the fourth argument456 which proves that even if one takes two motions on one circle, that from E to F through the semicircle G and that from F to E through the semicircle H, these motions too are not contrary because they do not come from contrary places, since the places do not have a determinate distance. This good fellow is so emboldened by his vacuously spoken words as to say: If this conclusion is reached by means of the same arguments as its predecessor, there is no need for us to speak against it since we have already confronted the predecessor to the best of our ability. And next he censures Themistius for saying457 that one should say the same things as were said about the preceding argument concerning things moving on just one semicircle. And he says that this argument does not reach its conclusion from the same hypotheses as its predecessor, since that one hypothesised motions reverse to one another occurring on one and the same semicircle whereas this one does not take motions on the same semicircle but it takes one motion on a circle, the motion being divided in terms of the division of the semicircles. He says, It is reasonable that these motions are not contrary, since on a circle both are a single thing if they are unified; for the motion from east to west on one of the hemispheres, say that above the earth, is not contrary to the motion from west to east on the remaining hemisphere, that under earth. So this argument is not the same as the preceding. He was able to see that motions which occur as on one circle are not contrary. that there are two arguments.458 One hypothesises two semicircles which are joined and similarly to the previous theorem says that the motions on them are contrary only when they are considered as occurring on the diameter by which the points E and F are separated from each other. But the other argument proceeds by agreeing to concede as a hypothesis that these motions on the semicircles are also contrary, but not conceding that

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this means that the motions on the whole circle are contrary. But this person thinks that only this first argument, the one which says that the motions on a circle are not contrary, is sound. And I do not see how he has agreed to even this argument without self-contradiction! Perhaps he was satisfied with speaking against Themistius’ statement that one should say the same things as in the case of the preceding argument even though, in my view, by using the word ‘similarly’459 Aristotle clearly shows that this argument about the two semicircles proceeds in accordance with the argument before it, and even though Themistius, having divided the arguments in his paraphrase, does say with respect to the first argument that one should say the same thing as in the case of its predecessor, but with respect to the second he says that,460 ‘Even if someone were to agree that the motions on a semicircle are contraries, he should not agree that motion on the whole circle, which is the subject of discussion, is divided into contrary motions’. In the case of the hypothesis of these two semicircles I have said in my exegeses of the arguments how the argument proceeds for Aristotle, but it would not be a bad thing to now recall this.461 The first argument of those proving that there is no motion contrary to motion in a circle argues more universally from the more;462 it says, ‘So if something is contrary to motion in a circle, it is most necessary that it be motion in a straight line. But the motions in a straight line are opposed to one another by places ... .’ The second argument proves that the motions in reverse directions on an arbitrary arc are not contrary because there are infinitely many arcs around the same limits. The third argument infers the same thing, having made its hypothesis for the case of a determinate arc, that of a semicircle. And next this fourth argument hypothesises two semicircles which are joined and Aristotle says that the same things follow in their case, but, accepting that these things are external to the problem, he thinks it worthwhile to make an investigation in the case of the circle; for the problem was to show that there is no motion contrary to motion in a circle. If what I am saying is true, it is, I think, entirely463 possible to comprehend what follows, namely that this man does not perceive the point of Aristotle’s discussion and does not understand the discussions of his commentators. But he has also armed himself for the fifth argument,464 which proves that two motions which occur on the same circle and come from and to the same point, but in reverse directions, because one thing moves from A through the semicircle B back to A, the other from A through the other semicircle C and again to the same thing, A, are not contrary on the grounds that these motions are from and into the same thing, but contrary motions are from a contrary and into a contrary; and having, it would seem, used up his own counterarguments and being pressed, he now objects to the assertion that

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those motions which are from contrary places are always contrary, even though Aristotle has used this axiom in the other arguments and consequently thought that there is no motion contrary to motion in a circle because in a circle there are no places at a greatest distance from each other unless the places are defined in terms of the diameter. And so this person says that contrarieties of things of different kinds are also different, and consequently, if contrary rectilinear motions are from contrary places, it is not thereby necessary that motions in a circle be contrary in this way. He says, If they demand that whatever things attach to rectilinear motions also attach to circular motions, it will result that there isn’t any motion in a circle at all. For every rectilinear motion is a change from something to something, and the natural simple motions are from a contrary into a contrary. For the motion upward of light things such as fire is from below to above, and above is contrary to below; and the motion of heavy things such as earth is in the reverse direction. And also in the case of change in quantity or quality, what changes always transforms from one thing into a different one. So if every change is from one contrary into another or simply from one thing into another, but no motion in a circle is from one thing into another but is rather from and into the same thing, then circular motion is not even motion. But what need is there for me to set out a lot of what this person says and infect myself with the nonsense in it? But in the case of these things and also in what he says later, one should notice first that he is clearly agreeing that there is no motion contrary to motion in a circle, contrary in the sense that the motions are from contrary places. And clearly contrary places are those at the greatest distance, but even so he stretches out so many arguments to prove that in a circle the segments which are most distant from each other are the ones separated by a diameter.465 And he writes the following in the 25th chapter of the fifth book (these are his very words): ‘Since the limits of a semicircle are at the greatest distance, it is necessary that the motions which occur contrarily from them be contrary because of the definition of contrary ’. Now you see how well those words agree with these: ‘So if every change is from one contrary into another or simply from one thing into another, but no motion in a circle is from one thing into another but is rather from and into the same thing, then circular motion is not even motion’.466 Secondly we should notice that it is even more superfluous for this person to try to prove what Aristotle proposes,467 namely that there is no motion contrary to a motion in a circle, when he himself put forward all his counter argumentation against it, saying,468 ‘Let us

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undertake to demonstrate that none of the arguments establishing that there is no motion contrary to motion in a circle is sound’. For if, as he says, no motion in a circle is from a contrary into a contrary, and none is from one thing into another (and this is jumping over the pit,469 as the saying goes, since what is not even from one thing into another is a fortiori not from a contrary into a contrary), it is clear that if someone hypothesises that a contrary motion is one from contrary places – and he agreed to this earlier when he said, ‘because of the definition of contrary ‘470 – then it follows necessarily that there is no motion contrary to motion in a circle. There is a third thing worthy of attention, namely how amateurishly he puts it forward that in motion in a circle there is no transformation from one thing into another because a revolution is from and into the same thing. However, if always approaching471 is not transforming from one thing to another, it is not a motion either. But one might also be amazed by this piece of his stupidity: how he adduces against Aristotle as an absurdity that there is no motion in a circle at all if, as he says,472 ‘every change is from one contrary into another’. Moreover, he objects to the argument of Aristotle proving that there is no motion contrary to motion in a circle, in which Aristotle defines a contrary motion as one from contrary places. But how can the person who says these things473 say that every change is from one contrary into another? But has agreed clearly that motion from contrary places is not contrary to motion in a circle and stated the reason when he said474 that motion in a circle is from and into the same thing – for he says that this is the specific feature of every circular motion. This person does not understand that anyone who says that in terms of another kind of contrariety there is a contrary to motion in a circle is not objecting to Aristotle’s argument, but he also does not seem to remember why Aristotle proposed to prove that there is no motion contrary to motion in a circle. And so it should be recalled475 that two premisses were accepted for establishing that heaven does not come to be or perish, the major saying that there must be a contrary to what comes to be from which it comes to be and to what perishes into which it perishes, the other that heaven – which is the same as to say the body which moves in a circle – does not have a contrary. For the demonstration of the second premiss another proposition476 of the following sort was accepted: if the motions of contrary things are also contrary, then if the motion of something does not have a contrary, it itself does not have any contrary. As a result of this it became necessary to prove that there is no contrary to motion in a circle. And Aristotle made clear the kind of contrariety which he is denying when he said477 in the fifth argument that ‘the contrarieties of motion are derived from the contrarieties of places’. And this

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is reasonable because things which come from contrary places have contrary impulsions, some being heavy, others light; and the active and passive qualities, heat, coldness, dryness and all the qualities in terms of which the changes of bodies into one another and their coming to be and perishing are brought about accompany these qualities. Consequently motions which are antithetical in some other way than being from contrary places and only occur in reverse directions, as is the case with the motions of the sphere of the planets and that of the fixed stars (this person thinks it right to also call these motions contraries478) are of no relevance to the argument because they are not from contrary places, as this person also agrees when he says,479 ‘no motion in a circle is from one thing into another but is rather from and into the same thing’. However, Aristotle does not think it at all right to call these sorts of motion contrary; rather he distinguishes them from contrary motions when he says in the fifth argument:480 ‘However, the motion in a circle from A to B is not contrary to that from A to C either, since these motions are from and into the same thing, but contrary motion is defined as from a contrary into a contrary’. And this person says that there is one kind of contrariety for motions in a circle and another for motions in a straight line both in the words which I have set out481 and at the beginning of his dissolution of what he calls the sixth argument,482 where he writes, ‘It has been said that since it is agreed that rectilinear motion and motion in a circle are different, it is necessary that their contrarieties also be different’. In general if you want to see the crudeness (allokotia) of the things which this person says and that he is only out to speak against everything that is said, whatever it might be, listen to what he says here and what he says against the first argument.483 Here he says that there is one kind of contrariety for rectilinear motions and another for motions in a circle. There he maintains that motion in a circle is more opposed to rectilinear motion than the motions in a straight line are to each other. However, if the kinds of contrariety were different, motion in a circle would not be opposite to motion in a straight line at all. But there he wrote this: ‘But perhaps it would be more reasonable for one to agree that motion in a circle is more contrary to motion in a straight line than motion up and motion down are to each other.’ But here he has written this: ‘Therefore, it is not the case that whatever attach to contrary rectilinear motions also attach to contrary motions in a circle; for since the species of motion are different, it is also necessary that the contrarieties for each species, whatever they might be, be different; in the same way a colour and a flavour are both certainly qualities, but since their species are different, the contrarieties applicable to these species are different’. However, if motion in a circle is contrary to motion in a straight line (as he said before), it is necessary that there

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be one and the same contrariety between both. And again, forgetting what he says here,484 he goes on to say , ‘What is there to prevent motion in a straight line from being contrary in genus to motion in a circle’? And he would say that white is contrary to sweet in this way since he says that motion in a circle differs from motion in a straight line in the same way as flavour differs from colour. And he adds this kind of nonsense: As in the case of contrary rectilinear motions the conflict of the contraries occurs because they use the limits in alternation (for what is the starting point for light things is the limit for heavy ones), so too in the case of circular motions it is common to all that they are from and into the same thing, but there is conflict for the contrary motions because the limit of one is where the other starts from.485 For of the two motions which start from Aries the outer one moves toward the west (epi ta hêgoumena) of Aries, to Pisces and Aquarius and the rest, and the inner one moves toward the east (epi ta hepomena), I mean toward Taurus and Gemini. And what the outer motion has made as a beginning of motion for itself after Aries, namely, Pisces, the sphere of the planets makes as a limit, and what the sphere of the planets had as a beginning after Aries, I mean Taurus, attaches to the sphere of the fixed stars as limit. You should notice first that having said that the two motions start from Aries, he next proposes that the one starts as if from Pisces, the other as if from Taurus. And secondly that, although he has said many times that it is common to all motions in a circle to proceed from and into the same thing, he does not understand that, since the motion is continuous, either it is not possible to take either a beginning or a limit for it or every point is both its beginning and its end. How then will either Pisces or Taurus be either a beginning of one motion or a limit of the other when are related in the same way to each ? And what kind of conflict is there between these motions? For because things which move in reverse directions in a straight line proceed from contrary places and encounter one another in accordance with their contrary qualities they, striving for victory, fight to change their opposites into themselves and to make their path easy for themselves. But what conflict would there be between the sphere of the fixed stars and that of the planets, since they don’t encounter one another at all, they don’t put up obstacles to each other’s motions, they don’t have those active and passive qualities, and they are not of a nature to change into one another? But if someone yearns to learn the reason why this motion in reverse directions of the heavenly circles is necessary, Aristotle himself gives it later,486 and I say how

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I understand it in the elucidation of these passages. Here I would say this much: the reverse motion sustains the harmony of the whole cosmos and provides the cause for the unceasing coming to be and perishing of everything beneath the moon.487 However, if it seems appropriate, we will also sound out what this person says against what he calls the sixth argument,488 and say first that he does not even understand that this passage is part of the fifth argument (although Alexander said that it is a superfluous additional argument). And although in explaining Aristotle’s text, I have already clarified the whole meaning of the argument to the best of my ability, it is also necessary now to recall some of the things I said there: after proving that motions in reverse directions which occur on an arc or on one semicircle or on two semicircles are not contrary, he next proceeded to the very thing which was set out for proof, and proposed to prove that the motions which occur in reverse directions on a whole circle are not contrary either; and having proved this first on the basis of the definition of contrary motions he now proves the same thing by reductio ad impossibile. It is not necessary to say these things, which were said a little while ago, twice except so that those who encounter them learn that this person did not understand the development of the argument and consequently considered it a sixth argument for the fifth hypothesis, which considers motions in reverse directions occurring on one circle, although it is a different way of demonstrating the same hypothesis.489 This person raises an objection by asking why, even though enquiring about heaven,490 Aristotle hypothesised the motion in reverse direction to be on one circle and not on two, as is the case with the spheres of the fixed stars and the planets. And he says that Alexander perceives the unsoundness491 of the present argument and, thinking it right to try to help it, he492 says that motions in a straight line are contrary because they come from and go into contrary places even if they do not occur on one and the same straight line, but if motions in a circle in reverse directions were contrary they would occur on one circle. ‘For’, says, ‘it would be extremely unreasonable that a motion occurring on one circle be contrary to a motion occurring on another’; but he does not add or establish a reason why this is so. And it is clear, to begin with, that this person’s accusation493 of Alexander is incorrect if we maintain the definition of contrary motions which says that contrary motions are those which come from contrary places. But if this person is saying that this is the definition for contrary motions in a straight line, but there is another one for circular motions, he is again forgetting the point of the demonstration, because it says that things which conflict with each other and change into one another move in contrary ways. But these are the things which are opposed with respect to the active and passive

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qualities from which weight and lightness follow, and the contrary changes of place of natural bodies occur with respect to weight and lightness. And so the heavy is contrary to the light and the hot is contrary to the cold, and they start from contrary places, and even if they move on different straight lines, they are still contrary in form. For what is cold here where we are is contrary to what is hot in Rome because they are of such a nature that they would conflict and change into one another if they were in the same place. However, if the contrariety of motions appears more clearly when they are taken on the same straight line, one would do better to accept Aristotle’s taking the things moving in reverse directions to be on one circle, since if there were contrariety between things moving in reverse directions it would be more evident in the case of things moving on a single circle; consequently if he had attempted his proof in terms of two circles, he would have been more under suspicion. But this person says, Since the present investigation of heaven concerns nature, should have proved for the spheres of the fixed stars and the planets that their motions are not contrary. Consequently he has thrown awry and missed the point in demonstrating something else and not what is being sought. And again it is worth noticing with what lack of understanding this person demands that Aristotle prove things that are perfectly clear even to a blind person (as they say). For that the motions of the spheres of the fixed stars and of the planets are not contrary, especially in terms of this form of contrariety, according to which things which move in contrary ways are contrary and of a nature to change into one another, is immediately clear from the very things we see. For the bodies of these things are seen not to have changed into one another in the whole of time even though they do touch one another. Moreover the motions of these things are not from or into contrary places, as even this person agrees; for if every circular motion is from and into the same thing494 and every point is both a beginning and end of the motion, what contrariety would there be between places in different circles? Furthermore, things are said to move in contrary ways when one of them ends in the place from which the other begins and when each of the places is natural for one of them and unnatural for the other. But the sphere of the fixed stars does not move from the place of the sphere of the planets to its place, nor does the sphere of the planets move from the place of the sphere of the fixed stars to its place; nor is there some place which is natural for the one and unnatural for the other; and in general a hemisphere of each of them which is above earth moves in the same way as the hemisphere under earth of the other.495

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But if someone wants to call this496 itself a contrariety, then for Aristotle, this is not the subject of discussion, which is rather the motion of things which change into one another. For these are the things which are contrary to one another because of the active and passive qualities from which follow the contrary impulsions of bodies, impulsions which are distinguished together with the contrarieties of places. And so Aristotle also frequently gives demonstrations on the basis of the definition of the changes of place of things which are contrary in this way. But how can someone say that the motion of what is said to wander is contrary497 to the motion of the sphere of the fixed stars if it is necessary that contrary motions be as equally strong as possible, and that the motion which is natural for one thing is unnatural for the other, but the sphere of the fixed stars dominates that of the planets in such a way that the sphere of the planets, insofar as it makes its own apparent motion a single motion (although are498 very many), is carried around with the sphere of the fixed stars? Also, however, the sphere of the planets is not carried around with the sphere of the fixed stars unnaturally, since what moves unnaturally for all time would not endure in its own perfection. Rather it is endowed with this motion beyond its own nature, and the motion fills it with a more perfect life and a more concise participation in the Good. In general the motion which is opposite to the motion which is naturally co-ordinate with a thing and belongs naturally to something which is co-ordinate with what is contrary to the thing is said to be unnatural for the thing. And so upward motion is unnatural for earth because it belongs naturally to its contrary, fire. So I think it is clear from what has been said that Aristotle was right not to give his proof that there is no motion contrary to motion in a circle in relation to these things499 for which it was clear that there is never any change into one another. But if there were some motion completely contrary to heaven’s motion in a circle in such a way that the things moving with them had to change into one another, it would be necessary that they sometime meet one another and do so by moving on the same circle and not on different ones. For even if they were on a different circle at some time, then, as is also the case with things moving on different straight lines, there is nothing to prevent them from moving in ways which are contrary in form, since they are contraries. But just as contrariety is revealed better by things moving on the same straight line, so too, if there were some motion contrary to motion in a circle, it would be revealed better using the same circle. For if it were proved that things moving in reverse directions on one circle are not moving with contrary motions, it would have been proved much more and more clearly that motions in reverse directions which occur on different circles are not contrary.

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But this person has also made the superficial statement500 that, just as in the case of things which move in a straight line the upper point is the limit for light things and the starting point for heavy ones and conversely for the lower point, so too in the case of things which move in a circle: even if they use the same point as both starting point and limit, nevertheless they use it in different relations, since the point is the starting point for one thing as moving toward the west, and the limit for another as moving toward the east.501 Now what does he mean by this? For the same point, the eastern one for example, is the starting point for both the sphere of the fixed stars and that of the planets, since both move from this point and both move to the western point, except that in the case of the former the hemisphere above earth moves in this way, in the case of the latter the hemisphere beneath earth does so. But when Aristotle says,502 ‘But also if a motion in a circle were contrary to another motion in a circle, one of them would be pointless’ (because, since the things in motion proceed from contrary places and are disposed to conflict, they are related, so that what dominates makes the motion of what is dominated cease), this person objects to what Aristotle has said by saying, Why doesn’t the same absurdity, that if one motion dominates, the other is pointless, follow in the case of things moving in reverse directions on a straight line? But if they are equally strong, they stop each other and both will be pointless, since we say that what does not activate its own activity is pointless. But this is absurd because neither god nor nature does anything pointless. Now the person who first introduced this as a difficulty was reasonable to raise it. But one should understand that even if things which move in a straight line are brought to a stop by one another, this is not pointless because these things are of a nature to stand still. For earth and water and air are of a nature to move and to stand still; and fire is thought to be always in motion, but, since it moves up from below at one time and down503 from above at another, and contrary motions are separated by rest, it is clear that fire too stands still between its contrary motions. But the things which move in a circle are of a nature to make their motion continuously, and if they stood still it would be pointless. And in addition things which move in reverse directions in a straight line and have contrary natural impulsions because they contain contrary active and passive qualities are of a nature to act on and be acted on by one another and to come to be from one another when they meet. But the things which move in a circle and do not have either lightness or weight obviously don’t have the active and passive qualities, heat and cold, dryness and

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moistness, either, since, if they did, they would also have lightness and heaviness. But since they do not act on and are not acted on by one another, they are not of a nature to change into one another. Consequently if a stronger thing encounters a weaker one and carries it around into its own motion, then, in the case of things which move in a straight line, what is carried around is changed into what carries it around and becomes an addition to it, and increasing it would not be pointless both because it produced something useful and because it is no longer; but in the case of things moving in a circle, what is carried around is not of a nature to change into what carries it around nor would it be pointless to exercise its own activity.504 And this is why Aristotle also used505 the example of a sandal which exists, but does not display its own activity – that’s what it is to be pointless. But what changes into something else is no longer and its very non-being brings a benefit to the universe. But this person is not satisfied with arguing against details and so he sets out some general arguments about the motion of the heavenly bodies, trying hard to show that their motions are of different kinds and consequently so are their substances. Here then it is also necessary to write some general things against the whole purpose of his refutation and also to investigate in particular each of the things which he has said badly. I say generally against his whole purpose that Aristotle, having proposed to prove that everything which moves in a circle taken as one thing transcends everything which moves in a straight line and has a different nature from it, proved that motion in a straight line is divided into contraries, but motion in a circle has no contrary. Having previously demonstrated in the Physics that coming to be is from contraries and perishing is into contraries, he reasonably inferred that because sublunary things move in a straight line it is necessary that they come to be and perish, but that heavenly things, which move in a circle, endure without coming to be or perishing. And so even if there is a difference in heavenly things involving their motions, the differences do not go so far as contrariety. For the motion of the sphere of the fixed stars is not contrary to the motion of the things which are said to wander, as I think has been proved506 with many arguments. Nor is a faster motion contrary to a slower one of the same kind; for in our world a greater chunk of earth moves faster than a smaller one, but it is not said to have a contrary motion. And so even if the substances are different from one another in some way, nevertheless they are not disposed as contraries in such a way as to come to be from one another. And so it would not be necessary for someone who thinks to refute Aristotle’s views to prove that their motions and their substances are different, but necessary to prove that they have differences which are contrary. But also, if there is some substantial difference among heavenly things, it is not necessary that they not

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be simple in terms of the simplicity which is ascribed to them. For, if nothing prevents the sublunary elements, which are not only different from one another but also disposed in contrary ways (hupenantiôs), from being simple, all having moving in a straight line as a common feature, what prevents heavenly things, which all move in a circle, from also being simple in nature and having both one common specific character (which Aristotle has called the fifth substance) derived from their common feature of moving in a circle and transcending coming to be, and also a difference from one another which does not proceed into contrariety? For who would not say that there is a difference between the bodies of the stars and the heavenly bodies507 or between the sun, which illuminates, and the moon, which is illuminated? But they all move in a circle, they all are simple, they all are superior to coming to be, and consequently they all are distinguished by one substance, the fifth. For it is not now being proposed to investigate the difference in kind between heavenly things but to investigate their common superiority to sublunary things, which it was necessary to distinguish by means of the contrariety involved in rectilinear motion. Accordingly, Aristotle divided the sublunary simple bodies into two when he said,508 ‘I mean by simple bodies those which have a starting point of motion naturally, for example, fire and earth and their species and the things which are akin ...’. And in book 3 of this treatise, contracting the four elements into the light and heavy, he says,509 ‘It remains to speak about the two’. So if he contracts the species of these things and what is akin to them into the pair given by the contrariety, what would be absurd about his also taking what transcends this contrariety as one of the simple bodies? If what I am saying is true, all the nonsense this person utters in what he calls the ‘common arguments’ would be pointless; and it would also be pointless if someone noticed that these arguments of his are also based on things he said previously and called irrefutable even though they are unsound in this way and, as I think, proved unintelligible. Since in his discussions of particular points he takes it as agreed that the sphere of Saturn moves more slowly than the spheres under it, let him learn that this is not necessarily so. For, if the excess of the magnitude510 were great, then, even if it moved faster than the things under it, it would be possible for it make its return to the same point more slowly. But since he has also added something like the assertion that if the heavenly body does not move in a circle naturally but because of soul (as in the case of animals) or because of some other superior power (and as evidence he brings in Aristotle’s saying in the eighth book of the Physics511 that heaven is moved by a superior cause), it would not be possible to infer that heaven comes to be or that it does not from its motion, he clearly does not understand that it is possible for the

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same motion to be brought about by different causes and that the heavenly body as natural is moved in a circle by Nature in one way, and as ensouled it is moved in another way by Soul, and again as possessing mind it is moved in another way by Mind. And it receives the unchangingness and unceasingness and perpetually uniform completeness of its motion from Mind, which is unchanging; and it enjoys its changing motion differently512 at different times from Soul because of Soul’s changing thoughts about what is always complete; and because of its own nature heaven both possesses the power to perform and does perform the activities which are appropriate to a substance of this sort, one of which is the circular motion appropriate to simplicity. And it is clear that the goods from both Mind and Soul accrue to it because of its natural suitability, since it is not possible to have mind unless one first has soul. For Plato says513 that it is not possible for mind to accrue to anything without soul. Nor is it possible to have soul without nature. And so Aristotle says514 that soul is the actuality of – not just any body but – a natural body. Consequently, even if heaven possesses soul and mind, it is not prevented from also being natural; rather it is necessary that, while being natural, it shares in soul and mind with the result that, even if it has its circular motion from Soul and Mind, it has it in a still prior sense from Nature. And I think it would be possible and perhaps easier to have proved the everlastingness of heaven from its circular motion, since the motion is derived from Soul and Mind, and accordingly in the eighth book of the Physics515 the circular motion has been proved everlasting because it is imparted by the unmoving cause. But here Aristotle proposed to prove that it is everlasting from its natural motion because he wanted to prove the everlastingness and superiority of heaven from the way its existence transcends sublunary things. But this person thinks that he has dissolved these arguments proving that there is no motion contrary to motion in a circle as well as those in the Physics which say that things which come to be come to be from contraries and things which perish perish into contraries, and that he has set up this laughable book against the everlastingness of heaven as some kind of trophy. But if he has been seen many times not to be understanding what is said by Aristotle and his commentators and everywhere to be thinking that he can preserve his own really empty and pointless belief from refutation by those who are renowned in philosophy, let him lie with the fish, swimming in the sea of irrationality, and let him lie with the person who, they say, being rejected and wanting somehow to become famous, set the temple of Ephesian Artemis on fire.516 For anyone who tries by every means to establish that heaven perishes or rather desires to establish it in order to become famous would probably join in even the destruction of heaven in order to achieve his aim if he had such a power.

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However we should now cleanse away this bitter talk with sweet words, and turn to what Aristotle says next. But since this person also tries to refute the arguments in the eighth book of the Physics proving that the circular motion is everlasting and to deal with arguments for the everlastingness of the cosmos which he says are anonymous (adespotos), let them be passed over for now. For, wanting to show to those who are eager to learn that the things which Aristotle demonstrated in On the Heavens also remain unaffected by this new nonsense, I was diverted into this business. But if it ever seems right to test out the rest of the things this person has said, I will make the examination on the basis of another starting point.517

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Notes 1. For the whole text on which Simplicius will now comment see pp. 25-9. 2. In 1.2, 269a18-30. 3. Heaven is generated in the sense that it is derived from higher eternal causes, but it does not come to be and perish in the way sublunary things do. 4. That is, the natures associated with contrary natural forms, such as fire and earth. 5. In the next chapter. 6. Simplicius resumes direct discussion of the lemma at 107,25. 7. Timaeus 28A5-6. 8. 245D1-3. 9. Simplicius follows Proclus’ doctrine that the One does not furnish its own existence (is not self-substantiating (authupostatos)), but Being, which derives its existence from the One is authupostatos; on this doctrine see Whittaker (1974), 217-22. Simplicius will stress that our cosmos does not furnish its own existence but rather comes to be in his sense of being the product of higher things. 10. Simplicius uses paratasis (which I translate ‘extendedness’) here and three lines below to refer to a temporal extension. He refers to spatial extension here simply as being and below as extension (diastasis, also translated ‘dimension’, ‘distance’ and ‘separation’ where appropriate) of substance. Accordingly Simplicius is saying in this passage that Being has no spatial or temporal extension. 11. That is, the everlasting duration of our world is derived from intelligible Being and its ‘all at once’, eternal existence. 12. Inserting hupo with E. What is given existence by Being is Soul. 13. Inserting apo with Hankinson; Karsten inserts hupo, and Moerbeke has ab. 14. Being. 15. Being; what comes after Being is Soul. 16. cf. 93,29-30 with the note on 93,27. 17. This difficult phrase is perhaps meant to distinguish the parts of the cosmos from the ‘parts’ of the world of Forms (Being), each of which is hoper todi. 18. The most important sense of composition here is composition from form and matter. 19. What is self-moving should be Soul, which is intermediate between Being and the world of form-matter composites; in the same way, Simplicius says, form-matter composites are intermediate between the unified form and the indefinite matter which is their substratum. 20. I have not translated autou de toutou in l7 because I do not know to what they refer. Hankinson renders the equivalent of ‘the Being of this thing itself’. 21. Agreeing with Hankinson in accepting Karsten’s to where Heiberg prints tôi. 22. Heaven. 23. See the discussion of 270a25-35 starting at 111,3. 24. cf. 269D7-E2.

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25. Simplicius presumably brings in this point because of Philoponus’ belief that god created the cosmos from what is not; see 136,16ff. 26. Simplicius refers to the way in which changes in heaven effect changes in the sublunary world; cf. 97,15-17. 27. Being, the world of Forms. 28. i.e., the kind of coming to be found in sublunary things, which act on and are acted on by one another; see 111,3-115,20. 29. Heaven. 30. In the sublunary world. 31. The words in angle brackets translate the proskeitai en allois genesiourgôs which occurs in the margin of D and are not printed by Heiberg. They are accepted by Hankinson, and the context seems to require some such addition grammatically. 32. Reading suntithemenôn for the suntithenenês printed by Heiberg; Moerbeke has compositis. Simplicius is describing the formation of ordinary things out of contrary qualities. 33. As happens in the world of Forms. 34. Reading tauto with D and Karsten for the touto printed by Heiberg. 35. Bracketing the ti printed by Heiberg but missing in A and B. 36. Hankinson ad loc. gives some references for this claim. 37. Reading ê with A and B for the kai printed by Heiberg. 38. This clause is added to explain that fire and water are not contraries in the strict sense, but are called contraries because they have qualities which are contrary in the strict sense; see, e.g., 167,14-24. 39. Inserting hupo as suggested by Hankinson. 40. i.e., prime matter understood as something prior to corporeal extension. The phrase ‘corporeal extension’ suggests that Simplicius is thinking of Philoponus’ characterisation of first matter as the three-dimensional or qualityless body (see the Introduction, p. 7). 41. Reading autê for the autês printed by Heiberg; Moerbeke has hec (= haec). Here Simplicius apparently contrasts cases in which some qualities endure in a change, e.g., when water changes into air, with cases in which none do, e.g., when water changes into fire. In the former case the substratum can be thought of as moist matter, but in the latter it is prime matter. 42. At 98,30-99,4 and 99,13-17. 43. parakhrôsis. 8 of the 9 occurrences of this term listed on the TLG are in Simplicius. The one which is most clearly related to this one is at 1064,3 of his commentary on the Physics (CAG 10). 44. Simplicius, unlike Aristotle, is hesitant about treating nutrition as a fullfledged activity of soul; cf. 110,26-30. 45. cf. 96,27-9 with the note on 96,28. 46. Simplicius is thinking of 5.1; see 801,6-9 of his commentary on the Physics (CAG 10). 47. i.e., it is the motion of the sun through the zodiac. 48. See, e.g., chapter 7, 191a3-7, quoted below at 125,25-8, and for this whole paragraph see 123,11-129,3. 49. cf. Physics 1.7, 191a3-7, quoted below at 125,15-8. 50. cf. Physics 1.7, 191a13-14, cited below at 125,30-126,2. The question whether when Aristotle refers to contraries at 270a14-17 he means to include form and privation is central to Simplicius’ disagreement with Philoponus; see 123,11131,17.

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51. See 270a17 with 92,8-11. 52. Simplicius refers to 1.10-12. 53. In 1.12. 54. Translating autês instead of the autôn printed by Heiberg. With the latter we would have to supply something like ‘heavenly things’. 55. Again the primary reference is to 1.12. 56. This presumably means all kinds of change, substantial, qualitative, quantitative, and local. 57. 894A1-8. 58. cf. 92,32-95,17. 59. Simplicius quotes Timaeus 27D6-28A4. 60. Simplicius omits a controversial aei (‘always’), printed by Rivaud; see Whittaker (1969) and (1973), 387-8. 61. Simplicius adds a kai hôsautôs to Plato’s kata tauta. 62. Timaeus 28B6-8. 63. Simplicius omits Plato’s words ‘beginning from some starting point’. 64. cf. 94,8-95,17. 65. Simplicius tendentiously attempts to read into Plato’s words the idea that the perceived world does not just exist for a particular time period. 66. Simplicius gives a quite approximate rendering of Statesman 269D7-E2. In particular he writes menein (‘remain’) where Plato has gignesthai (‘be’). 67. And what is not is not another thing. 68. Timaeus 38B6. Simplicius quotes the continuation of these words just below at 105,15-16 and 20-23. 69. Timaeus 38B6-7. 70. Timaeus 38B7-C3. 71. Simplicius’ mention of 6,000 years undoubtedly reflects standard Christian estimates of the age of the world, which would have made the world approximately 6,000 years old in 500 AD; see, e.g., the entries ‘Alexandrian Era’ and ‘Byzantine Era’ in Kazhdan (1991). And of course the Christians did not expect the world to last much longer; cf., e.g., 143,1-2. 72. Timaeus 39E1-2, at the end of the description of the heavenly bodies and time. Presumably these people thought that if the cosmos only imitated the eternal nature it could not be everlasting. But for Simplicius the everlasting is an imitation of the eternal or timeless. 73. On Plato’s account of the four elements only earth does not interchange with the other three, as he says very explicitly at Timaeus 56D5-6. Simplicius is obviously straining to read anything about the immortality of the entireties of the four elements into Plato’s text; see also 107,14-19. 74. Timaeus 41B4, quoted just below. Hankinson quite rightly changes Heiberg’s period to a question mark here. 75. Timaeus 41A3-D3. 76. Simplicius has aphanôs where Rivaud prints phanerôs. The anonymous vetter of the first 21 CAG pages of this translation, to whom I am much indebted, points out that Philoponus uses the same word in a citation of this passage at 93,23 of Against Proclus. 77. I have taken text and translation (with one minor change) of this first difficult sentence from Cornford (1937); see pp. 367-71. Simplicius’ quotation agrees with Rivaud’s text in its first eight words but then has aluta emou ge ethelontos, where Rivaud prints di’ emou genomena aluta emou ge mê ethelontos. 78. Heiberg prints ou mên where Rivaud has outi men dê.

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79. Simplicius has tukhontes where Rivaud prints lakhontes. 80. Heiberg prints esti loipa where Rivaud has eti genê loipa, which is also found in Moerbeke (adhuc reliqua genera), a Bessarion correction, and Karsten. Simplicius uses the word genê in a paraphrase at 107,7. 81. Simplicius has edei where Rivaud prints dei. 82. Simplicius has the plural trophas where Rivaud has the singular. 83. Simplicius has auxete where Rivaud prints auxanete. 84. That is, the heavenly bodies. It is important to bear in mind that for Simplicius these are the audience to whom the creator is speaking. 85. Simplicius does not here include the god’s reference to his will as the reason why heaven will not perish. According to Philoponus Plato held the false view that the cosmos would not perish because of the will of god; see, e.g., Against Proclus, 144,6-15. For Simplicius’ explanation of Plato’s meaning see below 108,34-109,8. 86. tropê. Where Plato mentions ‘turning in accordance with nature’ (trepesthe kata phusin) Simplicius paraphrases ‘using your natural transformation and motion’ (dia tês phusikês heautôn tropês kai kinêseôs). 87. stoikheiokratoras, a hapax. With this sentence cf. 105,32-106,4. 88. Simplicius comments further on the speech of the demiurge at 108,28109,15. 89. It seems certain that Simplicius has at least Philoponus in mind here. For Philoponus’ invocation of Plato as a person who believes that the cosmos has come to be see chapter 6 of his Against Proclus. 90. 270a12-13. 91. With the exception of the lines on Alexander (108,9-14) the next two paragraphs restate what was said at 91,23-92,21, the notes on which should be consulted. 92. As opposed to the kind of ‘perfective’ qualitative changes seen in heaven. 93. Alexander’s formulation is more tortuous than my translation conveys because he is trying to make the argument appear categorical. 94. Hankinson makes the chronologically difficult suggestion that Simplicius is here referring to his commentary on the Physics, but it seems more likely that he is referring to 98,15-102,31 above; see 102,15-21. 95. 270a20-1. The quotation omits a kai aphtharton found in our text of Aristotle; see also 132,30. At this point Simplicius enters on the interpretation of the creator’s statement in Plato’s Timaeus (see 106,10-14) that heaven is imperishable only because he wills it to be so, a statement which obviously implies that heaven would be perishable if the creator chose it to be so. Alexander is perfectly happy to contrast Aristotle and Plato on this point, apparently taking it that for Aristotle heaven is everlasting by nature. Simplicius tries to eliminate this contrast by saying that Plato only intends to contrast the everlastingness of heaven and its dependence on a higher cause with the timeless eternity of Being, which is ‘self-substantiating’. 96. Alexander is presumably referring to those, such as Plutarch of Chaironea (c. 100 AD), Atticus (second century AD) and his pupil Harpocration, and Severus (date uncertain), who held that for Plato the world was generated in time and therefore is perishable ‘in its own nature’, but imperishable because of the will of god; for references see Baltes (1998), 115-18, 417-19. By ‘postulates’ Alexander probably means the will of god, but the plural is puzzling; see Rescigno, p. 258. 97. Simplicius gives an approximate version of Timaeus 41B3-5, included in the passage quoted above at 106,9-25. Simplicius means that Aristotle seems to reject

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this statement because he holds that nothing which comes to be lasts forever, and he (apparently) ascribes to Plato the view that heaven has come to be. 98. i.e., they are freed from the coming to be and perishing which is associated with all other extended things. 99. Reading prolambanomenên for Heiberg’s prolambanousan. 100. In agreement with Aristotle. 101. kata idiotêta. I do not understand the force of this expression, but Simplicius is clearly using it to mark out the kinds of general contraries, such as sameness and difference, which belong to all things, and ordinary contraries, such as hot and cold, which cannot co-exist. 102. I have transposed sunuparkhontôn ... allêla from 13-15 to after enantiôn in line 10. This requires dropping the alla in line 13. 103. In reading the discussion of this text it is important to realise that forms of the same verb (auxein) are translated using forms of both ‘increase’ and ‘grow’. 104. In the previous lemma (270a12-22). 105. In chapter 4. 106. Heiberg’s sullogizesthai should probably be sullogizetai here. Moerbeke has sillogizetur. 107. This argument, on which Simplicius does not comment, seems to presuppose that heaven could only be nourished by something subject to generation, so that, if it could be nourished, it, too, would be subject to generation; see Rescigno, p. 260. 108. In the next lemma (270a25-35) Simplicius suggests that Aristotle may not have invoked the growth of living things because he thinks that growth is a function of the nutritive soul, whereas the elements grow naturally with soul playing no role. Simplicius is inclined to think that the growth of living things also does not involve soul and so feels free to bring such growth into Aristotle’s argument; cf. 100,23-6. 109. At 270a25 in the preceding lemma. 110. To be more precise (at the suggestion of a vetter): in the lemma Aristotle says that the body which moves in a circle is without growth or perishing (anauxêton kai aphtharton), and Simplicius says that he thinks Aristotle is here calling ‘without diminishing’ (ameiôton) ‘without perishing’. 111. The distinction Simplicius makes here is a standard one and traces back to Aristotle’s discussion of quality in chapter 7 of the Categories; see, for example, 132,12-19 of Porphyry’s commentary on the Categories (CAG 4.1). 112. Simplicius is constrained to admit that heaven does alter in some ways, e.g., the moon appears to have a different colour at different times, but he wants to insist that it is not the kind of alteration which sublunary things undergo when they are affected by something. 113. to eulogon. Alexander pushes hard on Aristotle’s phrase ‘it is possible to accept by the same reasoning’ (tês autês dianoias estin hupolabein). 114. 14, 15a22-4. At 114,12-14 Simplicius offers a tortured reading of this passage as part of his own account of Aristotle’s position. 115. i.e., have qualities to which there are contraries. 116. At 270a12-22. 117. Although there appear to be no other extant texts in which the heavenly body is described as qualityless for Aristotle, Rescigno (p. 268) quite appropriately refers to fragment 5 of Atticus (des Places (1977)) in which Atticus charges Aristotle with saying that ‘there is a body which is neither heavy nor light, neither soft nor hard, neither moist nor dry, and practically saying that there is a body which is not a body’ (sôma ou sôma).

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118. Simplicius responds to this sentence and the remainder of the quotation at 114,35-115,20. 119. At 2.1, 284a14. 120. For the contrast between condition (diathesis) and state (hexis) see 111,713. 121. Alteration involving affection. Simplicius is arguing that the waxing and waning of the moon does not involve affection although such affection would be observable if it occurred. He goes on to argue that the changes in the apparent sizes of heavenly bodies are due to changes in their distance from us, not to the increase and diminution he believes is associated with affection. 122. I am not sure what Simplicius has in mind here. At 109,8-15 he has said that Plato (and so Simplicius himself) thinks that the heavenly body transcends contraries, while conceding that it does admit certain ‘pre-eminent’ contraries such as motion and rest. But those contraries would seem irrelevant here. Perhaps all Simplicius means is that if there are contrary properties in heaven as a whole, they do not act on one another in the way sublunary contraries do; cf. 115,16-20. 123. Here and in the rest of this paragraph Simplicius seems to move closer to Alexander’s position that the alterations in heaven are only accidental, but Simplicius never abandons his claim that the alterations are not matters of being affected; the closest he comes is at 115,14-15. 124. Simplicius gives a version of DK30B7, 7-8. He cites it in a different way at 111,23-4 (the source for the whole fragment) and 113,8-9 of his commentary on the Physics (CAG 9). 125. i.e., perfective alteration. Simplicius’ train of thought is a little loose here; he should have said only that affective alteration sometimes brings about substantial change but perfective alteration never does. 126. In the next lemma, 270b1-4. 127. See 111,29-31 with the note. 128. cf. 111,31-112,3. Simplicius’ disagreement with Alexander here seems mainly a matter of formulation. Both presumably agree that substantial change, e.g., from water to fire, involves a substratum changing contrary substantial qualities. Simplicius picks up on Alexander’s talking about contrariety in substance on the grounds that in the Categories Aristotle says there is no contrary to substance. But elsewhere (167,2-10) he says that substances can be called contrary insofar as they are given form by contrary differentia, and his position hardly seems different from Alexander’s, whom Simplicius even cites (168,20-169,2) on this issue. 129. With this paragraph see also 166,14-169,2. 130. With this paragraph cf. 112,12-24. 131. At 112,12-24. 132. See 112,18-19 with the note. 133. See 113,13 with the note 134. That is, coming to be, growth, etc. For the importance of affections in Simplicius’ interpretation see the discussion of the preceding lemma. 135. In this sentence and the next two Simplicius canvasses some alternative interpretations of Aristotle’s word ‘assumptions’ (hupokeimena). The first takes them as the preliminary assumptions (prolambanomena) listed by Simplicius at 12,6-11 in the commentary on chapter 2. There, as here, Simplicius tells us that Plotinus refers to these as hypotheses, and he cites Ennead 2.1, 12-14. The words ‘taking this from there’ (enteuthen ... labôn auto) seem to me too obscure to interpret. The next sentence is also obscure and may mean that he (Aristotle?

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Plotinus?) took the assumptions or hypotheses to be all the premisses of all the arguments up to this point. Finally Simplicius gives his own interpretation according to which the assumptions are the premisses [ii] and [iv] of p. 92. 136. Here Simplicius writes autôi instead of the autou of 12,14, which is in our text of Plotinus. 137. At 270a12-22; with what Simplicius says here cf. 92,2-21 with the notes. 138. In the next chapter. 139. Simplicius’ discussions of this lemma and the next should be read together; for Simplicius the two constitute one confirmation of what Aristotle has said based on people’s ideas. Alexander apparently believed that there were two ideas in question, the existence of the divine or gods and its or their occupation of the upper region. Aristotle is clearly concerned with the latter, but Simplicius disputes Alexander’s suggestion that Aristotle is concerned with the former, I suspect, because Aristotle has been talking only about a single divine body, not a plurality of them. 140. Simplicius is summarising the present lemma and the next three lemmas. 141. The sentence is anacoluthic, but the meaning is clear. 142. Hippon and Diagoras are labeled atheists in some sources. For the sources for Hippon see DK38; for Diagoras, Winiarczyk (1981). 143. The sentence is difficult. I take Simplicius to be pointing out against Alexander that, although Aristotle has established that there is a divine body (heaven), he has not established that there is a plurality of gods except in 12.6-9 of the Metaphysics (and by a doubtful extension in 8.6 of the Physics), where Aristotle argues for a multiplicity of divine prime movers corresponding to the spheres of his astronomical theory. 144. The issue here seems insignificant. Whereas Alexander understands Aristotle to be asserting that the divine (heavenly) body, which he associates with god, is linked with the upper region, Simplicius understands him to be saying that the heavenly body, which, of course, is in the upper region, is linked with god. 145. Inserting ekhein with Karsten. 146. The issue raised here is whether Aristotle is speaking hypothetically or taking it as established that there is something divine (so that the lemma should start ‘So since there is ...’; cf. 18,9-15 in the commentary on 1.2. 147. The numbers are, of course, absurd, and there is also no good evidence that the early Egyptians, unlike the Babylonians, even kept astronomical records. I have not been able to locate a source or analogue for Simplicius’ particular numbers, but the idea that the Babylonians and Egyptians were of enormous antiquity was common. 148. i.e., the Christians such as Philoponus. 149. cf. 142,33-5 where Simplicius implies that there is no reason why what is completely unchanging for one hour will not remain unchanging forever. 150. Reading the autou kinêsin of B, D, a correction of A, and Karsten for the autokinêsin of A and E printed by Heiberg. Heaven is not self-moving for Simplicius. 151. cf. [Aristotle], De Mundo 1, 392a4-8. 152. i.e., if two words with two distinct references are applied to the reference of one of them, the other will be unnamed. Simplicius now embarks on a lengthy disputation with Philoponus on the material he has just been discussing. He picks up with a brief discussion of the remainder of chapter 2 (270b26-31) at 144,5. 153. cf. 135,31-136,1 with the note. 154. Aristotle gives three senses of ‘does not come to be’ (agenêtos) and three of

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Notes to pages 60-64

‘comes to be’ (genêtos) in chapter 11 at 280b6-20. Aristotle’s exposition is notoriously unsatisfactory, but Simplicius is clearly right to insist that when Aristotle says that heaven is agenêtos he should be understood as denying that it is genêtos in the first sense specified at 280b14-16, which Simplicius paraphrases at 120,29121,1. One might say that the denial that heaven is genêtos in this sense is tantamount to saying that it is agenêtos in the third sense specified at 280b11-12 which holds of something when ‘it is entirely impossible for it to come to be so that it is at one time and not at another’. In Simplicius’ representation Philoponus discarded this sense as irrelevant on the grounds that to say it applies to heaven would entail that heaven does not exist. We seem to be faced with the option of taking Philoponus to be arguing tendentiously (cf. Wildberg (1988), 188-9) or taking Simplicius to be misrepresenting his position (cf. Davidson (1969), 358 n. 8). 155. We are not told what the remaining hypothesis is, but, as the sequel starting at 121,4 shows, Philoponus is mainly interested in the question he now raises: does everything which comes to be in time come to be from a contrary? 156. Moving Heiberg’s right parenthesis behind tugkhanontos, in agreement with Bossier in his edition of Moerbeke’s translation. This requires changing the question mark in line 5 to a full stop. 157. Simplicius apparently accuses Philoponus of ruling out all three of Aristotle’s senses of agenêtos and then asking in which of these senses Aristotle claims that heaven is agenêtos. 158. Reading hora with Karsten and eliminating the an inserted by Heiberg, who prints the âra which signals a question, whereas the manuscripts he reports all have the ara which means, among other things, ‘therefore’. Without Heiberg’s âra the question mark in line 15 goes. 159. De Caelo 1.11, 280b15-16. Simplicius here points to one of the awkwardnesses in Aristotle’s divisions in 1.11: something which comes into existence instantaneously counts as both agenêtos and genêtos. 160. De Caelo 1.11, 280b11-12. The specification of what ‘impossible’ means is quoted from 280b13. 161. Simplicius now paraphrases 1.11, 280b14-16 and then 20-23. Aristotle declares that heaven is everlasting at 2.1, 283b26-30. 162. See, e.g., 92,22-32. 163. See 98,15-102,14. 164. Simplicius quotes Physics 1.5, 188b1-2 and 12-16. He gives an extensive quotation of their context below at 124,25-125,20. 165. In chapter 6. 166. 1.6, 190a17-20, translating Ross’s text. This means inserting to after tauton in line 25, dropping Heiberg’s gar in line 26, placing parentheses around ho gar anthrôpos hupomenei, followed by a comma, followed by to mê mousikon de kai to amouson oukh hupomenei. 167. Reading dêlon with Karsten and D rather than the dêla printed by Heiberg; Moerbeke has palam, his standard translation of dêlon. 168. The two sentences of Philoponus quoted here may be a feeble attempt to explain the difference between form/privation and contraries in the strict sense, and, of course, Simplicius believes that Aristotle uses the word ‘contrary’ to cover both. But surely Simplicius would have to agree that the distinction is an important one which should be explained. 169. It is, I think, certain (see, e.g., line 17 below) that Philoponus really only argued that not all coming to be is from contraries in the strict sense. Philoponus gives the same sort of arguments in 8.3 of Against Proclus (307,14-309,12), where

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the final conclusion is that not everything which comes to be comes to be from a contrary. 170. It is difficult to know what to make of this assertion, which is certainly false. Philoponus’ view is that there is a coming to be of form from privation and that in the coming to be of the world the privation is what is not in any way; see, e.g., 131,17-20. 171. 5, 3b24-7. 172. For some discussion of later views of the immortality of parts of the soul, see Sorabji (2004), vol. 1, pp. 264-8. 173. cf. De Caelo 3.8, 307b8-9 and De Sensu 4, 442b19-20. 174. Aristotle does not discuss left and right in the Categories, but he does say at 7, 6b15-19 that some relatives have contraries, and some do not. At 127,19-21 Simplicius treats right and left as relatives which are contrary (or at least opposite). 175. Philoponus makes this same kind of claim in On the Creation of the World (Reichardt (1897)), 5.5, 216,22-3. Simplicius accepts it at 131, 9-17; cf. [Aristotle], On Plants 2.4, 825b14-18. 176. At 130,31-131,2 Simplicius ascribes the identification of light as the colour of fire to Philoponus but seems to dissociate himself from it; see also 89,4-7. 177. That darkness is a privation of light is standard Aristotelian doctrine, associated particularly with De Anima 2.7, 418b3-20. But the doctrine was contested in later antiquity. In his Paraphrase of Theophrastus (Bywater (1886), 8, 15-16) Priscian of Lydus says bluntly, ‘Darkness is not the privation of light, but it, too, is an actuality (energeia)’. Wildberg ((1987), 84 n. 95) refers to Philoponus’ commentary on the De Anima (CAG 15, 341,10-342,16) for Philoponus’ justification of the claim that darkness is the privation of light, but Philoponus, who is mainly concerned to deny that light is a body, considers the possibilities that darkness is or is not a privation; cf. also the treatment of the same Aristotle passage in the commentary on De Anima sometimes ascribed to Simplicius (CAG 11, 133,7-21), where the alternatives are that darkness is a privation of light or an energeia of earth. In his commentary on the Categories (CAG 13.1, 179,18-21) Philoponus says he has proved that darkness is the privation of light ‘elsewhere’; for a suggestion as to where elsewhere might be see Évrard (1985), 43. Finally I mention that in the later On the Creation of the World (Reichardt (1897), 2.6) Philoponus offers extensive argumentation for the claim that darkness is the privation of light, the denial of which he associates with the Manichaeans. 178. And so not the privation of light. 179. For the idea of air becoming fiery because of rubbing see De Caelo 2.6, 289a19-28 with Simplicius’ comments at 438,30-439,13. 180. Simplicius’ first response to Philoponus’ arguments is a general discussion of coming to be and perishing, contraries, and form and privation, repeating much he said at 98,15-102,31. He responds to the arguments in a more specific way starting at 129,4. 181. See 270a17. 182. Ross prints ‘not white’. 183. Heiberg prints ouk ek leukou, where Ross has ex ou leukou; but see Ross’s note on 188b1. Karsten also prints ex ou leukou. 184. Ross, without citing any positive evidence, inserts a mê here. 185. Heiberg’s text has an eis mê leukon, which is not in the text of Aristotle. 186. Heiberg’s text omits a to printed by Ross and by Karsten. 187. Except in Karsten’s addition Simplicius omits Aristotle’s example which says that colours are composites of black (dark) and white (light).

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Notes to pages 66-72

188. Physics 1.5, 188a31-b26. 189. Physics 1.7, 191a3-7. 190. Translating Heiberg’s tôn peri genesin. Ross’s text adds a phusikôn, and he remarks that peri genesin should perhaps be excluded. See also 133,13-14, where Simplicius includes phusikôn while stressing the significance of peri genesin. 191. Heiberg prints pôs, Ross pôs posai. And Ross begins the next sentence with a kai, which is not in Heiberg. 192. Of the manuscripts reported by Heiberg only D has the word ‘two’, which is in our mss. of Aristotle. 193. Physics 1.7, 191a13-14. 194. Heiberg omits a problematic hê, which is found in D and in many mss. of Aristotle and was read by Simplicius (see 233,3-10 of his commentary on the Physics (CAG 9)). Ross prints an unconvincing (to me) hês; see his note ad loc. 195. Of course, Philoponus believes that there is coming to be from a privation; he is only trying to refute what he takes to be Aristotle’s assumption that coming to be is only from a contrary; cf. 131,17-20. 196. cf. Timaeus 28A5-6. 197. That is, in every case of coming to be a form comes to be from a privation, but in the case of the coming to be of an accidental ‘form’ in addition to the privation there are positive characteristics from which it comes to be: black comes to be from both not black and from white or grey or ... ; cf. 128,7-8 and 13-16 below. 198. At 270a22. 199. Simplicius gives a rough paraphrase of Physics 1.7, 190b12-14. 200. Physics 1.7, 190a18-20; for the text see the note on 122,25. 201. Simplicius is referring to chapter 10, where Aristotle makes his standard division of opposites into relatives, contraries, state and privation, and affirmation and denial and discusses each species in turn. What Simplicius goes on to say is not found in that chapter, where Aristotle never mentions forms. But, taking for granted that a privation is not a form, Simplicius only wants to point out that in the case of opposite relatives and contraries both opposites are ‘forms’. 202. That is, simply to deny something can leave open many possibilities. Aristotle does not make this point in the Categories, only the point that one or the other of an affirmation and its denial must be true. 203. Simplicius now responds to each of the objections of Philoponus introduced at 123,11-124,171. 204. Physics 1.7, 190b1-5. 205. Simplicius includes the alla which Ross brackets on philosophical grounds; see Ross’s note ad loc. 206. Simplicius includes a ti not in our text of Aristotle. 207. Simplicius includes a ginetai not in our text of Aristotle. 208. Simplicius includes a tou not in our text of Aristotle. 209. Physics 1.5, 188b16-21, the context of which is quoted in full at 124,25125,20. 210. 1.5, 188a22-6. Simplicius’ text, which I have translated, deviates considerably from Ross’s. He has: stereon where Ross prints to plêres; to men on where Ross prints to men hôs on; gônia where Ross prints gegôniômenon agônion; and to euthu where Ross prints euthu. Simplicius also omits an einai before phêsin. 211. I have translated the text as it stands, but assume that something has dropped out. Aristotle does not use the words ‘having angles’ (gegôniômenos) or ‘being circular’ (peripherês) in the Categories. 212. cf. 89,4-7.

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213. At Timaeus 58C5-8. 214. cf. 124,11-12 with the note. Heiberg’s comma after hopou should be a question mark. 215. cf. Homer, Iliad (West (2000)), 22, 26 and Odyssey (Van Thiel (1991)), 19, 163. 216. In commenting on 270a12-22 Themistius says (CAG 5.4, 14,23-6) that although Aristotle speaks of contraries he wants one to understand the generic contrariety between form and privation: et in universum dum a contrario et in contrarium dicit eam contrarietatem intellegi vult quae est secundum genus, quaeque forma et privatio est ..., a passage which Simplicius paraphrases closely in his response to Philoponus. 217. At 270a15-17. 218. Grammar, logic, rhetoric, subjects of low esteem for those who considered themselves philosophers. 219. The ‘axioms’ which Simplicius has in mind are [i] that heaven is a natural entity and [ii] that what is natural has an opposite privation. He agrees that Aristotle holds [i] but denies that he holds [ii] as a general truth, since it is not true of everlasting natural entities such as heaven or the cosmos. 220. For Philoponus’ denial that there is such a substratum, see 136,14-16. 221. 2, 268b14-18. 222. Simplicius inserts an en which is not in our texts of Aristotle; he does the same thing at 27,28 in the commentary on chapter 2. 223. 270a20-2. 224. Simplicius omits a kai aphtharton found in our text of Aristotle; see also 108,29. 225. cf. 122,2-33. 226. 1.7, 191a3-4. Simplicius quotes these words somewhat differently at 125,25, on which see the notes. 227. Simplicius closely paraphrases Physics 2.3, 194b20-3. 228. Alexander of Aphrodisias denies that heaven has matter several times in his commentary on the Metaphysics (CAG 1, 22,2-3, 169,18-19, 375,37-376,1). For other examples see 5.4. of Iamblichus’ On the Mysteries (des Places (1966), 159-60) and 1.19 of Proclus’ Platonic Theology 1 (Saffrey and Westerink (1968), 91,2792,1). Other references to heaven as immaterial include 3.9 of Hierocles of Alexandria’s commentary on the Pythagorean golden verses (Koehler (1974), 120,6-8) and 111,25-6 of Hermeias of Alexandria’s commentary on Plato’s Phaedrus (Couvreur (1901)). 229. 4, 1044b3-8. 230. Simplicius has kai gar where our texts of Aristotle have eiper ara. 231. See the Introduction, p. 7. 232. See 89,4-7. 233. gumnêi kephalêi. I take Simplicius to be referring to Philoponus’ alleged impiety in a sarcastic way. Normally one would address the gods with head uncovered.; see, e.g., Plato, Phaedrus 243B6. 234. Reading Mukonon with Karsten; Heiberg prints Mukônon, noting that A and B have Mikônon. According to Strabo (Radt (2002-9)) 10.5.9 the phrase hupo mian Mukonon was proverbially applied to those who use one name to refer to things which are different by nature; cf. LSJ, s.v. Mukonos. 235. 134,3-7. 236. Metaphysics 8.5, 1044b27-9. 237. At 1.9, 278b3-4 and 279a7-9.

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Notes to pages 77-81

238. Simplicius has attempted to explain this declination at 92,33-98,15. 239. i.e., prime matter in the most common interpretation of it, an interpretation accepted by Simplicius; cf. the Introduction, p. 7. 240. Against Proclus, where the phrase ‘mythic incorporeal and formless matter’ occurs at 406,8-9. 241. One of Heracles’ labours was to clean the stables of Augeas; see, for example, Gantz (1993), 392-3, and cf. above, 119,12-13. 242. to epion; cf., e.g., Plato, Phaedrus 264B6. 243. cf. 132,12-14. 244. In chapter 9 of that work Philoponus argues that everything which comes to be in the strict sense comes to be from what is not. 245. DK28B8, 6-9. 246. Physics 1.8, 191a27-31. 247. Simplicius has ti tôn ontôn where Aristotle has tôn ontôn ouden. 248. Simplicius has dei. Ross prints dein, following Bonitz ((1862), 41) and two citations of the passage by Simplicius (1140,24 and 1144,7 in his commentary on the Physics (CAG 10)). 249. In the way that wood is changed into a ship. 250. Simplicius insists (but hardly proves) that in all coming to be there is an enduring substratum. 251. ei ti pote esti. Simplicius’ point is that there never was a separate substratum for the cosmos, as there is in the case of the stone statue. 252. It seems impossible to know exactly what, if any, Christian account of the relation of God the Father to Jesus Christ, his son, Simplicius has in mind, but certainly Simplicius’ characterisation would apply to the monophysitism dominant at Alexandria and subscribed to by Philoponus. 253. i.e., at the level of the creator god. 254. A standard argument against the creation of the world in time. 255. I have changed Heiberg’s punctuation here, dropping the question mark after ekeinon and putting a left parenthesis after it and replacing the full stop after hepomenôn with a right parenthesis and a comma; cf. Bossier’s punctuation of Moerbeke’s translation. 256. That is, at the appropriate now. 257. In the rest of this paragraph Simplicius gives an abstract paraphrase of the speech to the created gods at Timaeus 41A7-D3, quoted above at 106,9. 258. Here the lower levels. 259. cf. 133,28-134,9 and 135,10-18. 260. Simplicius now turns to Philoponus’ criticism of 270b4-16. 261. Simplicius paraphrases 270b5-9 and then more or less quotes 1.10, 279b12-17. In connection with the material which follows one should also consult Simplicius’ commentary on 279b12-21 at 293,11-301,28. As has already been mentioned, Philoponus devotes book 6 of Against Proclus to arguing against the view that Plato held the world to be everlasting. 262. I have not translated the word phtheiromenon, which is difficult and bracketed by Moraux at 279b15. 263. In this and the next sentence Simplicius plays with 256A6-7 of Plato’s Sophist, where the Eleatic guest speaks of having prepared a feast for young people and the late learners among the old. 264. In this complex sentence Simplicius expresses his standard view of Aristotle’s criticisms of Plato and others, in this case the Eleatics: Aristotle knows the true meaning of what the people he criticises say and that it is compatible with

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ordinary true beliefs. But he worries about people who understand what these people say in a false, superficial way and believe that it is true, and so he argues against the superficial meaning to prevent people from accepting it. 265. Simplicius refers to Timaeus 38B6 and 31B5-6. 266. Translating Bessarion’s correction of E, which is adopted by Karsten: ho tên ex allou eis allo metabolên sêmainei kai hoper allo geneseôs sêmainomenon esti. Heiberg’s text runs to metabolên ex allou eis allo dêloun. kai hoti allo touto tês geneseôs sêmainomenon, all of which is omitted in E, leaving a text which is perfectly clear, but is inexplicit about the Aristotelian sense of coming to be. 267. Simplicius quotes 1.10, 280a31-2, but he leaves out the word loipon, which gives the sense ‘for all the rest of time’. I suspect the omission is deliberate, since Simplicius cites the text with loipon in his commentary on the passage at 311,25-7. On the history of the passage see Moraux (1954), 173-4. 268. Simplicius’ point is perhaps that for Aristotle anything which comes to be perishes, so if he says that for Plato heaven comes to be but does not perish he is not using ‘come to be’ in his standard sense. 269. Imagined or dreamt good things; see Scholia on Lucian (Rabe (1906)), 246,15. 270. DK31B17, 7-8, 20-13. These lines or close variants of them are also DK31B26, 5-6, 9-12, so that the textual situation is quite complicated; see Wright (1981), 96-8 and 102. The principal text for B17 is 158,1-159,4 of Simplicius’ commentary on the Physics (CAG 9), where Simplicius omits the line ‘and insofar as one thing has learned to come from many’, as he does here, but he has it at 33,26 of the Physics commentary, the principal source for B26. And Aristotle (Physics 8.1, 250b30-251a3) has the line in a quotation of it and the following four lines in a form which corresponds to B26. 271. Heiberg prints dikha panta where Wright (1981) prints dikh’ hekasta. 272. Heiberg prints phoroumena from the principal text for DK31B26; Wright (1981) prints phoreumena, following the principal text for DK31B17. Since this is the reading of Heiberg’s ms. D (and Karsten), and A and B have nothing, one should print phoreumena here. 273. With this quotation one should compare text 79 (pp. 89-90) of Wildberg (1988), a quotation of the tenth-century philosopher Abu Sulayman al-Sijistani which suggests that Philoponus said that all things are filled with god, so that heaven differs from other things only in degree, not in kind. The anonymous vetter of CAG pp. 135-56, to whom I am indebted for very many corrections, has called my attention to 188,14-27 of Philoponus’ commentary on De Anima (CAG 15), in which Philoponus says, ‘... It is absurd and contrary to reason to suppose that god is everywhere spatially, at least if god cannot even be a body ..., but it is necessary that god be everywhere in his activities, at least if it has been demonstrated that he is the cause of all things.’ 274. Simplicius cites Psalm 18.5 in the Septuagint version (Rahlfs (1935)): en tôi hêliôi etheto to skhênôma autou (Heiberg prints hautou, noting that A, D, and E have the autou printed by Rahlfs). In the Hebrew and in modern versions of the Psalms this is 19.5, and a standard English translation is ‘In them (sc. the heavens) he has set a tabernacle for the sun.’ 275. Psalm 104.5 Septuagint (Rahlfs (1935) = 105.5 in Hebrew and modern versions). The words translated ‘for all eternity’ are eis ton aiôna tôn aiônôn. For Simplicius Being is eternal (aionios), whereas the earth is everlasting (aidios) or unceasing (anekleiptos). 276. cf. 270b11-16.

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277. cf. 73,12-15, and especially 138,32-3. 278. In Physics 8.10. 279. Eurycles was a ventriloquist/prophet first mentioned in line 1019 of Aristophanes’ Wasps (Wilson (2007)), whose prophecies seemed to come from the bellies of others. Simplicius is here picking up on Plato’s Sophist 252C6-9, where the Stranger compares people whose speech contradicts their doctrines with people who carry around the strange Eurycles. 280. cf. 118,4-5 where Simplicius affirms that anything which goes an hour without changing transcends coming to be and perishing. 281. The Christians. 282. I do not know what in Plato is being referred to here. Richard Sorabji has suggested to me that it is Timaeus 41A3-B6 (quoted at 106,6-14 and referred to immediately hereafter). Philoponus makes the same claim about Plato at 6.29, 235,4-8 of Against Proclus. 283. Timaeus 41A7-B6, quoted above at 106,9-14. 284. Starting at 269C4. 285. Statesman 270A5. 286. See 106,4-25. 287. 270a17-18. In this paragraph Simplicius is again summarising 270a12-35 and indicating where the argument stands at this point. 288. i.e., composite bodies and motions. 289. i.e., air and water are both heavier than something and lighter than something, but water is heavier than air, air lighter than water. 290. As will be done in the next chapter. 291. Simplicius is describing the reasoning of the whole chapter. The alternatives which he goes on to mention are taken up in the successive lemmas. 292. Simplicius takes this idea from Alexander; see 170,34-171,4. 293. To an observer. From the outside, a circle or sphere is convex, from the inside, concave. 294. Simplicius’ point is perhaps that the relational opposition of convex and concave has no bearing on the question of contrary motions. 295. At 2, 268b20-2, but Simplicius could also be referring to 3, 270b29-31. 296. Alexander apparently construed Aristotle’s main argument to be something like: a. Rectilinear motion is more contrary to circular motion than any other motion; but it is not contrary; therefore no other motion is contrary to circular motion. Simplicius makes the trivial formal point that Aristotle uses the word malista rather than mallon. On arguments from more and less see Aristotle, Topics 2.10, 114b37-115a14. 297. In the previous lemma at 271a3-4. 298. Heiberg’s text has a figure here, for which see p. 27. 299. peripheriai, where Moraux prints periphereis (one main ms. has peripheriai). Karsten ‘corrects’ Simplicius to periphereis. 300. diastaseôn, ‘distant points ‘in Hankinson’s translation; cf. 176,19. 301. Of course, as Simplicius goes on to say, there is no least or greatest circular arc with A and B as end points. 302. Contradicting what is established at 270b32-271a5. 303. Heiberg’s text has a figure here, for which see p. 27. 304. cf. 147,19-21 with the note.

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305. tmêma, presumably an arc. 306. Heiberg’s text has a figure here, like the figure for 271a10-13 on p. 27, but rotated 90o. 307. This Diogenes is standardly taken to be the Cynic, but his identity is not certain; see, e.g., Giannantoni (1990), V.B.185 and Hankinson’s note ad loc. 308. Heiberg’s text has a figure here, for which see p. 28. 309. Reading, instead of the antiperistasin of A, D, and E printed by Heiberg, antiparastasin with B, Moerbeke (antiparastasim), Bessarion, Karsten, and Hankinson. Aristotle is arguing that he is right about motions in reverse directions on one circle, even if the hypothesis that the motions on two semicircles are contraries is correct; see the note on 13,29 in Mueller (2010). 310. Heiberg’s text has a figure here, for which see p. 28. 311. Reading sunagagôn with E and Karsten, instead of the sunagô printed by Heiberg; Moerbeke has concludens. 312. Simplicius has given his reading of the lemma as one coherent argument. He now turns to Alexander’s alternative reading and dissents from it. Lines 23-8 of the lemma (from ‘[For they are to the same thing] because’ to ‘derived from the contrarieties of places’) are very problematic, and various emendations and excisions have been proposed. Moraux’s suggestion that the lines have been misplaced from the end of 271a13-19 is adopted by Leggatt (1995) . Following Allan (1936), I have bracketed the words ‘For they are to the same thing’ after ‘one of them would be pointless’; see also the note on line 32. 313. My understanding of these words is in line with Hankinson’s. Rescigno (pp. 285-6) takes the subject to be Alexander and takes Simplicius to be saying that Alexander later did better to point out that etc. 314. That two things moving in reverse directions on the same circle are moving in contrary ways. 315. Alexander’s other text has eti in place of hoti. It would also appear that Alexander (and presumably Simplicius) did not have the words epi to auto gar, which I have eliminated in the translation of the lemma. See Rescigno, pp. 292-3. 316. ep’ enantia, which I take to be synonymous with the ‘in the direction of contrary places’ (ep’ enantious topous) which occurs two lines below. Alexander dismisses this alternative because it has been ruled out by the preceding arguments, leaving the alternative ‘through (dia) contrary places’, which he goes on to rule out on the grounds that there are no contrary places on a circle. 317. Aristotle of Mytilene; see Moraux (1984), 399-425. 318. As we just have. 319. Being from contraries and into contraries (271b21). It is not clear to me what Alexander means by saying that things which move in reverse directions on a circle ‘undergo something hupenantios’. 320. Presumably motions on a semicircle with the diameter. This distinction between motion on a circle and motion on a semicircle is certainly justified on Aristotelian grounds (see Physics 8.8, 261b28-262a17), but it is not clear why Alexander wishes to make it. 321. cf. Timaeus 41A3-D3, quoted at 105,28-106,25. 322. dia to axiôma katakhrômenon, an obscure phrase. Hankinson translates the sentence, ‘But some say that Aristotle loosely equates God with nature in this passage by means of this phrase.’ I, following the anonymous vetter of these pages, take the ‘axiom’ to be the assertion that god and nature do nothing in vain. 323. Aristotle’s argument has purportedly eliminated the claim that two things moving naturally in reverse directions on the same circle have contrary motions;

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Notes to pages 95-104

Simplicius now asks about the planets and the fixed stars, which might be thought to move in reverse directions on different (concentric) circles, and tries to explain why those motions are not contraries. Simplicius is looking forward to an objection of Philoponus introduced at 193,3, the response to which at 193,19-194,5 echoes what Simplicius goes on to say here; see also 195,14-196,34. 324. cf. 271a21. 325. kata tauton. I have imported the word ‘time’ from Moerbeke, who has secundum idem tempus; Hankinson translates ‘in the same way’. 326. This sentence is obscure, but it does not express real possibilities for Simplicius. 327. Fragment 393 (Campbell (1982)), a proverbial expression applied to violent, eristic people. 328. The parorinei of B, D, and Karsten seems more likely to be right than the parorinnei of A and E printed by Heiberg. 329. cf., e.g., 123,15-17. 330. See 123,13-124,17. 331. See 124,17-131,17. 332. Replacing Heiberg’s full stop with a question mark, as in Bossier’s edition of Moerbeke. 333. 5, 3b24-7. Philoponus goes on to quote 5, 4a10-11. 334. At this point translation becomes difficult because Philoponus uses forms of kineisthai and related words to refer to change in general and specifically to change of place. 335. i.e., substance. 336. Simplicius here contrasts what he reports Alexander as saying at 108,23-4 and Aristotle’s assertion at 3, 270a17-18 that contrary things have contrary motions. He attacks Philoponus for thinking they are equivalent at 162,20-33 and again at 163,35-164,18. Simplicius himself affirms not only Aristotle’s assertion but also Alexander’s; see 157,3-6. 337. Aristotle. 338. At 270a17-18. 339. cf. 74,16-20. 340. 4.4, 311a16-29. 341. Aristotle does not ‘frequently’ say this, but Simplicius is quite convinced he believes it. See Appendix 3 on the purity of the elements. 342. These last words show that Simplicius is thinking specifically about water evaporating. 343. cf. 158,3-5. 344. polus; the translation is Moerbeke’s (prolixus). 345. kata touton is difficult. I read kata touto. 346. cf. 156,28-157,12. 347. Simplicius perhaps means that since nothing problematic follows from the first statement, nothing problematic would follow from the second if they were equivalent (as they are not). 348. That is, Philoponus’ objections hold. 349. Philoponus now considers the second alternative mooted at 157,27-31: saying that things with contrary motions have contrary qualities rather than saying that they are contrary in substance. 350. So, even if there is no motion contrary to motion in a circle, heaven may still have contrary qualities. 351. Simplicius supplies this word, but I see no reason to think he is unjustified

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in doing so. Elsewhere Philoponus speaks of substantial qualities in much the same way as Simplicius; see, e.g., 11.5, 423,13-424,4 of Against Proclus. Simplicius’ ultimate concern is to harmonise the idea that a substance such as fire has no contrary with the idea that the form of fire is specified in terms of the (substantial) qualities, hot and dry, which do have contraries; see especially 166,14-170,7. 352. This formulation is hasty. Presumably the antecedent should be contrary motions, the consequent contrary qualities. 353. sunêgage. This charge looks unfair since Philoponus argues against the doctrine that there is no contrary to motion in a circle and only uses the fact that Aristotle believes there is none in an attempt to convict him of an inconsistency. 354. I take Simplicius to be saying that the circular motion of the hupekkauma and upper air is not associated with those qualities of fire and air which are associated with their rectilinear motion. 355. see, e.g., 21,14-25, 34,13-21, 35,12-20 in the commentary on chapter 2. Simplicius’ point here is that the motion of the upper air and the hupekkauma is hypernatural and not natural, and therefore not relevant to what Aristotle is talking about in chapter 4. 356. Heiberg prints hautai monai, noting that B has auta mona and A autai. It is difficult to understand the feminine, and I would prefer the reading of B or perhaps tauta mona. 357. i.e., the hupekkauma and the upper air. 358. Mythological sea monster, traditionally associated with the Sicilian bank of the Straits of Messina, where as a whirlpool she, together with Scylla on the opposite bank, made the safe passage of ships very difficult. Since Simplicius has referred several times to Heracles and his labours, he may here be thinking of the story according to which Charybdis, as the wife of Heracles, stole his cattle, for which she was thrown in the sea by a thunderbolt from Zeus. 359. See, e.g. 157,34-158,1. On the question of whether substance has a contrary one should read the commentaries on the Categories of Philoponus (CAG 13.1, 74,13-27), Dexippus (CAG 4.1, 51,23-53,25), and Simplicius (CAG 8, 105,24110,25). 360. Simplicius repeats 163,12-17. 361. See the note on 163,31. 362. Simplicius wants to put Philoponus in the position of denying that, e.g., fire has a contrary and then to argue that in a sense fire does have one. 363. Simplicius repeats 157,32-5. 364. See the Introduction, p. 7. Simplicius here argues that it makes no difference to his position if the matter of a natural body is Philoponus’ three-dimensional or whether, as Simplicius believes, the three-dimensional is a composite of more fundamental matter and three-dimensionality. 365. i.e., the three-dimensional. 366. Simplicius quotes Physics 4.9, 217a26-7, on which see 689,16-690,17 of Simplicius’ commentary on the Physics (CAG 9). 367. ‘This substance’ presumably refers to the four elements, but it is hard to see how Simplicius can say that Philoponus agrees that this substance has a contrary. At most Philoponus has claimed that Aristotle puts himself in the position of accepting that such substance has a contrary even though this contradicts his general claim in the Categories. 368. aitiômenos. Simplicius has, of course, explained how Philoponus misunderstands ‘conversion’, but nothing that he has said or will say makes clear what he has in mind here.

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369. Simplicius is here working with a standard theory according to which differentiae are qualities (see, e.g., Metaphysics 5.14, 1020a32-b2) and qualities, like all items in categories other than substance, are ‘accidents’; on this view, since substance has no contrary, contraries will themselves be accidents. Of course, in this discussion the relevant contrary qualities which differentiate substances are hot/cold, wet/dry, and light/heavy, the differentiae of the four elements, which Simplicius and others call ‘substantial’ qualities. The ancient commentaries on the Categories all include discussions of the status of differentiae; particularly useful here are Simplicius (CAG 8, 97,24-102,10) and Philoponus (CAG 13.1, 64,9-68,9). 370. Omitting the words kata tauta, which may be a dittograph since the same words occur in the next line. 371. Here accidents are non-substantial qualities rather than differentiae. 372. cf. 157, 32-158,1. 373. The discussion in the rest of this paragraph is not directly relevant to the issue of whether substances have contraries, but rather bears more on the question whether coming to be is from contraries, a question which was addressed earlier (123,11-132,31). 374. A version of 5, 3b24-5. 375. Categories 5, 3b27. 376. 1.7, 191a13-14. 377. cf. 2.3-4, especially 3, 331a1-3, quoted below at 169,30-170,4; however, Aristotle does not speak about forms in this context. 378. cf. the note on 166,21. On what Alexander says here see Moraux (2001), 10-11. 379. This passage is essentially the same as 105,27-106,2 of Simplicius’ commentary on the Categories (CAG 8), but there Iamblichus is not mentioned. The two passages are also followed by essentially the same sentence, but in the Categories the sentence has Aristotle as explicit subject; this is appropriate since Aristotle does justify his claim by reference to primary and secondary substances. 380. The quotation to this point should be compared with 106,28-107,3 of Simplicius’ commentary on the Categories (CAG 8) where Iamblichus is mentioned and Simplicius goes on to criticise what he says. For the remainder of the passage see 107,25-30, where again Iamblichus is not mentioned. 381. See the quotation immediately below. 382. 2.3, 330b30-331a3, with which one should consult the apparatus in Joachim (1922); see also 229,22-230,7 of Philoponus’ commentary on On Coming to be and Perishing (CAG 14.2), where Philoponus states what amounts to Simplicius’ understanding of the sense in which substances are and are not contrary; see also 74,13-27 of Philoponus’ commentary on the Categories (CAG 13.1). 383. Reading the topôn printed by Joachim (1922) and by Karsten, rather than the prôtôn printed by Heiberg. 384. Reading the gar of Aristotle, printed by Karsten, rather than the oun printed by Heiberg. 385. Simplicius reverses the order of the two terms. 386. cf. 26,23-8 in the commentary on chapter 2. 387. We now turn to the discussion of chapter 4. 388. At 270b32-271a5, which Simplicius has discussed at 145,12-146,16. 389. For Simplicius’ more precise formulation of the argument and a slight disagreement with Alexander, see 145,12-146,16. In the present discussion Simplicius is only concerned with the fact that Philoponus takes what for Simplicius is an argument about motions as an argument about lines. The difference seems

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insignificant since Aristotle’s argument about motions depends importantly on a claim about lines. 390. Simplicius’ criticism of Philoponus’ construal of Alexander’s understanding cannot be conveyed in English, a problem which is made worse by the ambiguity of Alexander’s formulation itself, an ambiguity which stems from forms of the Greek expressions hê eutheia and hê kuklôi. The former usually means ‘straight line’ but can mean ‘rectilinear ‘; the latter would normally mean in De Caelo ‘ in a circle’, but perhaps could mean ‘circular ‘, although I have not found an occurrence of hê kuklôi with this sense – rather one finds hê kuklikê. In any case Philoponus substituted hôi kuklôi (circle) for Alexander’s hêi kuklôi ( in a circle), and so, much to Simplicius’ outrage, took Alexander to be talking about lines rather than motions. Simplicius (Alexander?) is willing to concede that straight and circular lines might be contrary, but insists that motion in a straight line and motion in a circle are not. 391. The insertion of ouk would seem to be required by which Simplicius has said; see especially 170,26-8. 392. cf. 55,25ff. 393. This remark is quoted somewhat differently at 172,1-4. 394. 271a27-8. 395. This seems a misleading formulation. In the passage quoted Philoponus concedes that rectilinear and circular motion are not contrary ‘with respect to places’, but claims they are contrary in other respects. Of course, he does want to connect these kinds of contrariety with perishability, a connection which Simplicius denies. 396. Simplicius’ point is that, e.g., a circle does not change into a straight line as a result of being acted on by the straight line. 397. cf. 138,32-4 and 142,17-20. 398. cf. 171,22-3. 399. cf., e.g., 165,32-5. 400. Following Wildberg (1987) in accepting the asummetria of D (and Moerbeke, who has incommensuratio) in place of Heiberg’s summetria. Simplicius’ claim is that if, e.g., both excess and deficiency are contrary to due measure because they both lack due measure, then there is really only one thing which is contrary to due measure, namely lack of due measure. 401. Simplicius takes the trouble to note that in saying that the concave periphery of the lunar sphere is the upper topos Philoponus is relying on Aristotle’s account of place, which both he and Philoponus find inadequate, but, of course, Philoponus is entitled to make use of Aristotle’s own views in criticising him. For Philoponus’ criticisms of Aristotle’s account of place (apparently known to Simplicius) see 557,8-589,26 of his commentary on the Physics (CAG 17), and for Simplicius’ criticisms see 601,1-645,19 of his commentary on the same text (CAG 9). 402. The points Philoponus makes from here to 174,13 relate to Aristotle’s obscure remark at 270b34-271a2, which Philoponus takes to be an attempt to rule out the idea that concave and convex are contraries; for Simplicius’ understanding of Aristotle’s remark, which includes the suggestion that concave and convex differ as relatives, see 145,26-146,1. 403. The argument from here to 174,4 relies on the division in Categories 10 of opposites into relatives, contraries, states and privations, affirmations and denials. 404. States are the first kind of quality mentioned by Aristotle in the Categories (8, 8b26-7). It is the view of Simplicius that the privation of any item in a category

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is also in the category; see, e.g., 65,2-13 of his commentary on the Categories (CAG 8). Philoponus’ position in his commentary on that dialogue (CAG 13.1) is less clear. At 48,7-27 he says that privations should not fall under any category because they are indefinite, while mentioning that others say that they should because privation and possession are contraries. But at 144,2-14 he restricts himself to saying that if a privation and a state are contraries they should be included in the same category. 405. For reasons which are not clear to me this sentence is not treated as part of the quotation by Heiberg or Wildberg (1987); it is so treated by Bossier. 406. Simplicius has first rejected Philoponus’ claim that Aristotle is talking about spheres rather than circles, but he now goes on to develop the claim in which he puts much more at stake: even if heaven is both concave and convex, and concave and convex are contraries, they are not the kind of contraries involved in coming to be and perishing. 407. For this point see also 109,8-15. 408. See, e.g., 99,24-102,14. 409. 3, 270a17-22. 410. 271a5-10. What Simplicius goes on to say is presumably intended as a summary of his explication of that passage at 146,18-147,21, which should be consulted. 411. diastaseôn; cf. 147,6. 412. cf. 19,20-3 of Themistius’ paraphrase of De Caelo (CAG 5.4). Philoponus responds that only motions from A to B and B to A on the same arc are contrary and is willing to accept that there are infinitely many contrary motions between A and B, while maintaining the principle that for a single thing there is a single contrary. Simplicius insists that since contrary motions involve contrary places, one motion from A to B will have infinitely many contraries. 413. For Simplicius’ response to this suggestion see 177,32-178,7. 414. i.e., the centre. 415. mathêmatôn, emended here by Karsten to mathêmatikôn, but not at 178,30, where the same considerations would apply. 416. The text here says ‘greater’ (meizona), but it should say megistên, which is what I have translated; see also 178,30. 417. Here peripheries are spherical surfaces, the inner surface of the sphere of the fixed stars, which moves from east to west, and the outer surface of the sphere of the planets, which moves from west to east. This sudden shift probably reflects the fact that, as Simplicius goes on to say, he has brought together separate passages in Philoponus. In any case Simplicius says nothing here about the remaining part of this quotation, but see 154,18-156,24 and 194,21-198,6. 418. Apparently the sphere of the fixed stars and the sphere of the planets. 419. In the first part of the passage quoted (178,7-21) Philoponus is concerned with Aristotle’s apparent (or alleged) view that because there is no longest circular arc through points A and B there is no longest ‘circular distance’ between A and B, so that the two motions between A and B on that greatest distance cannot be called contraries. Philoponus first concedes that this is true mathematically speaking, but if A and B are two diametrically opposed points on the surface of the universe the great circle through them determines a greatest circular interval and so the two motions between A and B on that circle can be considered contraries. Simplicius apparently thinks that if he accepts Philoponus’ use of the distinction between mathematical spheres or circles and physical ones he will be lost. So he argues that the arcs on heavenly spheres invoked by Philoponus are themselves

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conceptual, and this opens the possibility for conceptual argument. Simplicius ends up focusing more on the possibility of drawing multiple arcs of different lengths than on the question of the possibility of greatest arcs, and so avoids having to talk about arcs which extend outside the universe. 420. Reading megistên for the meizona of Heiberg’s text; cf. 178,14. 421. It is not clear why Simplicius brings in divisibility at this point since his real concern should be the possibility of taking greater and greater circular arcs through two points. 422. cf., e.g., De Caelo 1.1, 268a6-7 with Simplicius’ comment at 8,12-14. 423. That is, there is no limit on the number of times something continuous can be divided, but it cannot be actually divided infinitely many times. 424. Simplicius appears to grossly misrepresent what he has quoted Philoponus as saying, since one would suppose that by ‘outermost circumference of the universe’ Philoponus means the convex limit of the universe. Simplicius may acknowledge this indirectly with his hypothetical concession at lines 14-15 (‘Even if it is not possible ...’). 425. What Simplicius says could apply to either the special arc mentioned by Philoponus or an arc of a cosmic great circle, but what follows is Simplicius’ only argument against Philoponus’ use of the fact that the latter is a greatest arc. 426. An opaque formulation, which should mean something like ‘when the interval between the points is not determined by the straight line between them’. 427. 271a10-13. 428. pêkhus, forearm, known as the cubitum in Latin. Translation is sometimes difficult because the word is used both for a measuring implement and for its length. 429. Philoponus imagines measuring the circumference of a hoop by dividing it into short segments and measuring the straight lines connecting the end points of the segments. 430. As Wildberg ((1987), 108) says, ‘This does not seem to be right. In order to find out by means of a compass whether all sides of a triangle are equal, one has to draw two circles with one side as the radius’. The sentence is definitely improved (and made clearer) by bracketing diametron (‘as diameter’). For the construction Philoponus has in mind see 1.1 of Euclid’s Elements (Heiberg (1883)). 431. Reading hôs with D rather than the tas printed by Heiberg. 432. cf. 271a13. 433. Simplicius quotes 271a13, which hardly says what he claims it does. Aristotle’s words ‘by a straight line’ are only in D and not printed by Heiberg. 434. The reader may find it useful to consult the figure in Appendix 4 here, but even so it is difficult to see why Philoponus thought that what he says advances his case. 435. Simplicius gives a loose citation of 271a10-13. 436. There is a brief discussion similar to the preceding at 185,27-186,7. 437. From here until 183,21 there is a discussion of an argument of Alexander’s, which is apparently quoted at 181,11-14 and accurately represented at 182,31183,2. From these two passages and what Simplicius says it would appear that Philoponus did misrepresent Alexander. I have translated and made insertions accordingly. 438. These last three lines are very close to 181,11-14. 439. Simplicius paraphrases the first three lines of the preceding argument and then goes on to the rest of it. 440. I have inserted the names ‘Philoponus’ and ‘Alexander’ for clarification at

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the suggestion of the anonymous vetter of the last 20 CAG pages of this translation, to whom I am grateful for many useful suggestions. 441. That is, the distance between two points is determined by the straight line between them. That straight line is determinate, but if we ask how long the distance is, we are treating the distance as indeterminate; cf. 184,7-12. 442. Perhaps a reference to some standard of good and bad has dropped out here; Simplicius does not mention good and bad in his criticism of this material at 184,16-27. 443. Reading hêgoumenoi with A, B, and D rather than the êgmenoi of E printed by Heiberg; Moerbeke has qui ... intelligunt. 444. Whereas Philoponus takes Aristotle’s remark that motion on a semicircle is the same as motion on its diameter (271a12-13) as an unqualified assertion, Simplicius takes it as resting on the false hypothesis that reverse motions on a semicircle are contraries; cf. 147,28-148,6. 445. Alexander’s meaning is not transparent, but his explanation of why reverse motions on a semicircle might be called contrary is presumably intended to ward off rather than support the kind of move Philoponus makes. 446. As Simplicius believes it is. 447. cf. 181,24-182,17; and for a diagrammatic representation of the zodiac see Appendix 4. 448. Reading aphestôsa with Bessarion and Karsten for the aphestanai printed by Heiberg. 449. cf. 185,25-7. 450. cf. 185,25-7. 451. In the absence of further development the force of Philoponus’ reasoning here is not apparent, and Simplicius’ criticism seems sound. 452. Reading estin hê with A, B, C, D, and Karsten rather than the esti printed by Heiberg. 453. Reading ennoêsas with Wildberg (1987) for the misprint ennoêtas in Heiberg. 454. For this definition of ‘straight’ cf. 137E3-5 of Plato’s Parmenides, 6.11, 148b27 of Aristotle’s Topics, and 109,21 of Proclus’ commentary on book 1 of Euclid’s Elements (Friedlein (1873)). 455. cf. 185,23-4. Philoponus insists that the length of an arc is intrinsic to it, and not given by the measure. Simplicius agrees with this, but insists that only a rectilinear distance is determinate. 456. 271a13-19. 457. See 20,4-6 of Themistius’ paraphrase of De Caelo (CAG 5.4). 458. At 271a13-17 and 271a17-19. 459. At 271a13. 460. Themistius, paraphrase of De Caelo (CAG 5.4), 20,8-11. 461. Simplicius now summarises his discussion of all of 270b33-271a19 at 145,10-149,28. 462. cf. 146,11-16 with the note. 463. Reading pantôs with D and E rather than the pantos of A and B printed by Heiberg; Moerbeke has semper. 464. 271a19-22. 465. cf. 181,20-33 and 185,27-186,7. 466. 190,12-15. Simplicius writes only ‘So if every change is from one contrary, and so on’. Here and in the next paragraph he chooses to overlook the fact that Philoponus is only trying to refute Aristotle, not build a positive theory.

Notes to pages 132-138

167

467. Simplicius now takes 190,4-15 as an argument implying that there is no motion contrary to motion in a circle in Aristotle’s sense. 468. cf. 170,14-22. 469. huper ta eskammena pêdan, roughly going excessively or unnecessarily far. For the saying see Gardiner (1904). 470. 190,24. 471. i.e., moving toward but never reaching. Simplicius is right that one could attach this conclusion to the argument at 190,12-15, but again Philoponus is trying to show that Aristotelian premisses, if extended in a not implausible way, lead to an absurd conclusion. 472. 190,12-13. Simplicius presumably is objecting that some changes are not between contraries. 473. Aristotle. Simplicius insists that for Aristotle there are kinêseis, e.g., circular motion, which are not between contraries. 474. cf. 190,13-14. 475. Simplicius summarises his analysis of 3, 270a12-22 at 91,23-92,27. 476. In this formulation a logical truth. 477. 271a27-8. 478. cf. 194,21-197,7. 479. 190,12-13. 480. 271a19-22. 481. cf. 190,2-4. 482. 271a22-33; for the dispute about whether this is a genuine ‘sixth’ argument see 194,6-9. 483. Particularly relevant to the rest of this paragraph is 172,23-33. 484. i.e., that contrariety is different for rectilinear and circular motion. 485. For what follows the reader might find the depiction of the zodiac in Appendix 4 helpful. 486. In 2.3; for Simplicius’ discussion of this question see 395,19-405,27 of this commentary. 487. With 193,8-194,5 cf. 154,18-156,24. 488. 271a22-33; Simplicius goes on to briefly summarise 145,10-156,24. 489. The contrast Simplicius makes in this sentence does not seem significant. 490. Following Wildberg (1987) in moving the raised dot after planômenês to after zêtôn. 491. That is, its failure to take into account motions on two different circles. 492. In agreement with Rescigno (p. 294) I take ‘he’ to be Alexander and the remainder of this paragraph to be derived from Philoponus’ account of Alexander. Wildberg (1987) places a full stop after ‘help it’ and (apparently) takes the remainder of this sentence to report Philoponus’ own view, and the last sentence to be Philoponus talking about Alexander. See also the next note. 493. The accusation is presumably that Alexander is wrong to say that contrary circular motions must be on a single circle. Simplicius goes on from here to 196,34 to give his own explanation of why Aristotle is justified in considering only single circles. 494. For Philoponus’ ‘acceptance’ of this claim, cf. 190,12-15. 495. cf., e.g., 155,12-20. 496. i.e., the motions of the heavenly spheres in reverse directions. 497. Reading enantian with Moerbeke (contrarium, in agreement with motum) and Karsten rather than the enantias printed by Heiberg. 498. Reading ousas with A, B, and Karsten for the hosas of D and E printed by Heiberg.

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499. The planets and the fixed stars. 500. cf. 193,8-19. 501. Reading hê arkhê with A and B in place of the arkhê hê printed by Heiberg, and dropping the hê in line 3 with A. Wildberg (1987) marks 196,35-197,3 as a quotation and puts 197,10-15 in indirect discourse. My reversal of his decision follows Bossier’s edition of Moerbeke. 502. 271a22-3. 503. Translating the katô of Bessarion and Karsten, which is not printed by Heiberg. 504. Reading the energein of D, E, Moerbeke (agere) Karsten for the energoun of A and B printed by Heiberg. 505. At 271a32-3. 506. See 154,18-156,24 with 193,19-194,5 and 195,14-196,34. 507. i.e., the spheres. 508. 2, 268b27-9. 509. 3.1, 298b7-8. 510. i.e., the length of Saturn’s orbit. Philoponus apparently said that Saturn moved more slowly than the other planets because its sidereal period was longer; Simplicius points out that despite this fact Saturn’s linear velocity might be greater than that of other planets. 511. In chapter 6. 512. Reading allôs with D and Karsten rather than the allôi of A and E printed by Heiberg; B and a second hand of A have allo. But the sentence is difficult in any case. 513. A close paraphrase of Timaeus 30B3-4. 514. cf. De Anima 2.1, 412a11-21. 515. 6, 259b32-260a19. 516. Like many of the authors who refer to this incident, Simplicius does not mention its perpetrator, Herostratus, on whom see RE, 8.1.1145-65. Many authors refer to the alleged coincidence of the burning with the birth of Alexander the Great, which sets its date in 356 BC. According to Valerius Maximus (Shackleton Bailey (2000)), 8.14.ext. 5, the Ephesians decreed that the memory of the (by him unnamed) perpetrator should be abolished, and his name was preserved only by the fourth-century BC historian Theopompus. 517. For Simplicius’ subsequent criticism of Philoponus’ discussion of Physics 8, see 1129,29-1152,19, 1156,28-1169,9, 1171,30-1182,39, and 1326,38-1336,34 of Simplicius’ commentary on the Physics (CAG 10).

Appendix 1 The ‘fragments’ of Philoponus, Against Aristotle I give here the correlation between passages translated in Wildberg (1987) and their location in the text translated here. Wildberg attaches an asterisk to indicate that the ‘fragment’ includes no direct citation or paraphrase of an argument in Against Aristotle. I also indicate where a fragment is discussed in Wildberg (1988). For a survey of these fragments and Simplicius’ responses see section 1 of the Introduction to this volume. Simplicius, in Cael. 119,7-120,12 121,4-14 121,25-122,9 123,4-7 123,11-124,17 126,5-16 131,17-132,17 133,21-9 134,9-28 135,21-136,1 136,12-26 137,16-19 138,32-139,6 139,23-7 141,11-19 142,7-25 156,25-157,6 157,21-159,3 162,20-163,3 163,11-30 164,21-7 165,10-166,13 170,11-171,9 171,17-32 172,23-173,15

Wildberg (1987) fragment 63 64* 65 66 67 68 69 70 71 72 73 74* 75 77* 78 80 81 82 83* 84 85 86 87 88 89

169

Wildberg (1988) discussion 188-9 189-90 190 — 189-92 192 192 194-5 194-5, 219 194 195-8 198-201 155, 169 — 203 203-4 187 221-2 223 223-4 223-4 225 224-5 225-6 —

170

Appendix 1 173,25-174,13 175,13-22 176,13-177,22 178,7-26 179,24-180,23 181,16-33 182,14-25 183,21-184,7 185,3-186,15 186,24-187,6 187,16-25 187,28-188,25 189,22-190,31 192,5-14 192,15-193,19 194,6-30 195,9-17 196,34-197,15 199,27-35

90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 50*

226 226-7 227-8 228-9 229 229 — — — — — 230 230 — 230-1 231 231 231 165

Appendix 2 The ‘fragments’ of Alexander’s commentary on De Caelo I give here the correlation between passages translated in Rescigno (2004) and their location in the text translated here. Simplicius Rescigno Aristotle text in Cael. fragment where relevant 108,9-14 28 (p. 256) 270a12-22 Alexander gives a syllogistic representation of Aristotle’s argument. 108,23-34 29 (257-8) 270a12-22 Alexander uses the statement that the motions of contrary things are contrary (see also below 41, 158,29) to argue that earth is more contrary to fire than water is. He also criticises ‘some people’ for making heaven perishable but keeping it from perishing by invoking ‘certain postulates’. Simplicius denies that heaven is perishable for Plato. 110,11-14 30a (259-261) 270a22-5 Alexander explains why what doesn’t come to be doesn’t increase in size. 111,24-112,24 31a (262-70) 270a25-35 Alexander says that Aristotle’s argument has to be refined so as not to imply that heaven suffers no alteration in quality or affection whatsoever. Heaven can change with respect to accidental qualities or affections, but not with respect to substantial ones, and so it cannot come to be or perish, increase or diminish. Alexander applies this point to heat coming from the sun to this world and qualitative contrarieties in heaven; such things do not concern substance and so do not entail coming to be or perishing, increase or diminution. Simplicius replies to Alexander in the next three passages, insisting that one should not talk about affection in connection with heaven, since affection does entail coming to be and perishing, increase and diminution. 114,1-6 31c (265-70) 270a25-35 Recurring to the previous passage, Simplicius says that one should agree

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Appendix 2

with Alexander that there is alteration in the heaven, but disagree with his belief that this alteration involves affection. 114,14-19 31d (265-70) 270a25-35 Simplicius takes issue with Alexander’s use of the phrase ‘contrariety in substance’ when Aristotle denies that substance has a contrary; see the note on 114,14. 114,35-115,2 31e (266-70) 270a25-35 Simplicius picks up on Alexander’s discussion of the heat of the sun and the qualitative contrarieties in heaven. Things in our world are affected by the heat of the sun, but the sun’s heat is perfective and creative and does not act on things in this world in the ordinary sense. Similarly, contrary qualities in heaven do not conflict with one another and so produce coming to be and perishing. 116,15-22 32 (270-2) 270b4-9 Alexander takes Aristotle to have proved two things at this point: that there are gods and that the divine is in the upper region. Simplicius denies that Aristotle has established that there are gods; cf. 34, 117,8. 116,30-117,2 33 (272-3) 270b8-9 Alexander and Simplicius disagree in a minor way about the meaning of Aristotle’s assertion that ‘what is immortal is linked with what is immortal’. 117,8-19 34 (274-5) 270b10-11 Cf. 32, 116,15. Alexander takes the expression ti theion to refer to the gods, while Simplicius takes it to refer to heaven. Alexander also says that the word eiper here should be understood as causal (‘since’) rather than hypothetical (‘if’). Simplicius apparently agrees. 121,11-14 27 (253-6) 270a14-17 According to Philoponus, Alexander and Aristotle think that the statement that ‘everything which comes to be comes to be from a contrary and some substratum’ is true of contraries in the strict sense, but others think it holds for privation and form. Simplicius believes that Aristotle intends to include form and privation among contraries in the statement. 146,11-16 35a (275-6) 270b32-271a5 Alexander thinks Aristotle is arguing from the more and the less. Simplicius is sceptical because of Aristotle’s use of the word ‘most’ at 270b34. 148,14-26 36 (282-3) 271a13 Alexander’s explanation and justification of Aristotle’s statement that ‘we always suppose that each thing is distant by a straight line’.

Appendix 2

173

150,15-19 37 (284-5) 271a5-22 Alexander says that the crucial premiss in the argument of 271a19-22 (‘contrary motion is defined as from a contrary into a contrary’) could have been used in the three previous arguments. 152,4-15 38 (285-6) 271a22-33 152,21-153,11 39a (287-94) 271a22-33 After giving his own interpretation of 271a23-33 as a single argument, Simplicius explains and rejects Alexander’s interpretation. In the first passage Alexander explains away Aristotle’s statement that something moving in a circle reaches all the ‘contrary places’ on it as meaning only that such a thing goes through every point on a circle (because there are no contrary points on a circle). Simplicius thinks that Aristotle’s argument is a reductio of the assumption that motions in reverse direction on a circle are contrary, an assumption which implies that there would be contrary points on a circle. In the second passage Alexander claims that there are two arguments in 271a23-33, one in 271a22-3 and 29-33, the other in 271a23-8. 153,16-154,5 40 (294-8) 271a5-33 Following his teacher, Alexander of Mytilene, Simplicius gives a representation of the argument that there is no contrary to motion in a circle. 158,29-32 41 (298-9) 270a17-18 Simplicius points out that whereas Aristotle said ‘the motions of contrary things are contrary’ Alexander invoked the claim (see above 29,108) that ‘things with contrary motions are contrary’, a statement frequently used (with variations) by Philoponus. 170,23-171,14 35c (277-81) 270b32-271a5 Simplicius defends Alexander against what he takes to be (apparently correctly) Philoponus’ misconstrual of Alexander’s construal of Aristotle’s argument, the issue being whether Alexander illegitimately took Aristotle to be talking about lines rather than motions. 174,11-19 42a (299-301) 270b34-271a2 Philoponus (incorrectly) censured Alexander for taking the notions of convexity and concavity to apply to lines rather than surfaces. 176,32-177,1 43a (301-4) 271a5-10 Philoponus set out Themistius’ paraphrase and Alexander’s exegesis of this passage in order to refute Aristotle. 178,7-13 43c (302-4) 271a5-10 Against Alexander’s exegesis of this argument Philoponus invoked the

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distinction between mathematical and natural things. Simplicius defends Alexander. 181,10-14 44a (304-11) 271a10-13 Alexander invoked as a proponent of the view that the straight line is the measure of the distance between two points and not of the length of a line connecting them when Philoponus took Alexander and Aristotle to be saying it was the measure of the length. 182,17-183,9 44b (304-11) 271a10-13 Alexander, accused by Philoponus of an illegitimate inference in his analysis of Aristotle’s argument, is defended by Simplicius. 185,13-186,7 186,18-30 187,20-7 Philoponus’ disagreement with be measured by straight lines.

44c (306-11) 271a10-13 44d (308-11) 271a10-13 44e (308-11) 271a10-13 Alexander’s claim that distances have to

194,6-9 39c (287-94) 271a22-33 Alexander’s characterisation of this argument as superfluous is invoked by Simplicius against Philoponus’ treatment of it as an additional argument. 194,23-33 39d (287-94) According to Philoponus, Alexander was aware that Aristotle failed to raise the question whether the motions on two different circles (notably the ecliptic and the equator) were contrary and dismissed the claim that such motions might be contrary as ‘extremely unreasonable’. Simplicius defends Alexander. Addendum At 168,19-169,2 Simplicius quotes from Alexander’s lost commentary on the Categories to support his own account of substance and contrariety.

Appendix 3 On the purity of the elements In his Supplement to On the Soul (Sharples (2008), 125,7-13) Alexander gives an argument against those who say that none of the four elements can exist on its own, an argument which he rejects. The argument is based on Plato’s statement (Timaeus 31B6-8) that nothing can be visible if it is separated from fire or tangible without being solid or solid without earth, a claim which was later extended to the other elements in terms of unspecified properties holding of all ordinary things. So far as I know we do not find this argument in Simplicius, although he obviously accepts its conclusion, and insists (see, e.g., 161,1-2) that Aristotle accepts it as well. Aristotle’s most explicit statement on the subject is at 2.3, 330b21-5 of On Coming to be and Perishing, where he says that the elements are not simple but mixed (mikta), the simple body corresponding to fire, for example, being ‘fiery’ (puroeides). In his commentary on this passage (CAG 14, 227,26-228,25) Philoponus interprets Aristotle as saying not that the simple bodies are composites in the ordinary sense accepted by Simplicius but that they are form/matter composites, ‘fiery’ being a way of referring to the form of fire. Philoponus is clearly responding to the argument based on the Timaeus, which he mentions and attempts to disarm by saying that there is no need to ‘characterise’ fire and earth in terms of visibility and tangibility since they can be characterised in terms of other, Aristotelian qualities. (It is conceivable that Philoponus is here following Alexander’s commentary on On Coming to be and Perishing; see Gannagé (2005), 45-9.) As far as I can see, nothing in Simplicius’ altercation with Philoponus turns importantly on the question whether the elements exist in unmixed states, although Simplicius’ conception of the elements as always composites does play an important role in his interpretation of Aristotle’s theory of the elements.

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Appendix 4 The signs of the zodiac

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Wartelle, André (1963), Inventaire des Manuscrits Grecs d’Aristote et de ses Commentateurs, Paris: Belles Lettres. West, M.L. (ed.) (2000), Homeri Ilias, vol. 2, Stuttgart and Leipzig: Teubner. Whittaker, John (1969), ‘Timaeus 27d5 sq.’, Phoenix 23, 181-5; reprinted in Whittaker (1984). Whittaker, John (1973), ‘Textual comments on Timaeus 27c-d’, Phoenix 27, 387-91; reprinted in Whittaker (1984). Whittaker, John (1974), ‘The historical background of Proclus’ doctrine of the AUTHUPOSTATA’, De Jamblique à Proclus (Entretiens sur l’Antiquité Classique 21), Geneva: Fondation Hardt, 193-237; reprinted in Whittaker (1984). Whittaker, John (1984), Studies in Platonism and Patristic Thought, London: Variorum Reprints. Wilberding, James (2006), Plotinus’ Cosmology, Oxford: Oxford University Press. Wildberg, Christian (1987) (tr.), Philoponus: Against Aristotle on the Eternity of the World, London: Duckworth. Wildberg, Christian (1988), John Philoponus’ Criticism of Aristotle’s Theory of Aether, Berlin and New York: De Gruyter. Wilson, N.G. (ed.) (2007), Aristophanis Fabulae, Oxford: Clarendon. Winiarczyk, Marek (ed.) (1981), Diagorae Melii et Theodori Cyrenaei Reliquae, Leipzig: Teubner. Wright, M.R. (1981), Empedocles: The Extant Fragments, New Haven and London: Yale University Press.

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. For Simplicius’ quotations of other authors see section b. 94,1 94,5 95,17 96,11 97,15 97,18 97,22 97,30 98,10 98,22 100,13 103,14 109,4 109,10-15 109,25 117,5 118,23 120,3 120,5 120,12 120,15 121,16 123,2 131,4 135,9 138,6-8

Insert hupo after to with E. Insert apo before tou with Hankinson. Bracket autou de toutou. Read to with Karsten and Hankinson for Heiberg’s tôi. Insert proskeitai en allois genesiourgôs from the margin of D after hupelthonta with Hankinson. Read suntithemenôn for Heiberg’s suntithenenês. Read tauto with D and Karsten for Heiberg’s touto. Bracket Heiberg’s ti, which is missing in A and B. Read ê with A and B for Heiberg’s kai. Insert hupo after metabolê with Hankinson. Read autê for Heiberg’s autês. Read autês for Heiberg’s autôn. Read prolambanomenên for Heiberg’s prolambanousan. Move the words alla ... allêla from lines 13-15 to line 10 to replace the alla. Read sullogizetai with Moerbeke for Heiberg’s sullogizesthai. Insert ekhein after tina with Karsten. Read the autou kinêsin of B, D, a correction of A, and Karsten for the autokinêsin of A and E printed by Heiberg. Move Heiberg’s right parenthesis from after zêtein to after tunkhanontos. Change Heiberg’s question mark to a full stop. Read hora for Heiberg’s ara with Karsten, and drop Heiberg’s inserted an. Change Heiberg’s question mark to a full stop. For the ouk ek of A, B, D, and E printed by Heiberg read ex ou with Karsten and an insertion in D by its scribe. Read dêlon with D, Moerbeke, and Karsten for Heiberg’s dêla. Replace Heiberg’s comma after hopou with a question mark. For Heiberg’s Mukônon read Mukonon with Karsten. Drop Heiberg’s question mark after ekeinon in line 6. Enclose kan ... hepomenôn (lines 6-8) in parentheses followed by a comma. Drop the full stop after hepomenôn.

181

182 140,18-19

149,15 151,35 157,31 162,3 164,35 167,5 171, 14 173,9 178,14 178,30 181,4 184,31 185,29 187,12 187,16 189,19 194,23 196,9 196,13 197,2 197,3 197,20 198,2 200,4

Textual Questions For Heiberg’s to metabolên ex allou eis allo dêloun. kai hoti allo touto tês geneseôs sêmainomenon read ho tên ex allou eis allo metabolên sêmainei kai hoper allo geneseôs sêmainomenon esti, a correction of Bessarion adopted by Karsten. For the antiperistasin of A, D, and E printed by Heiberg read antiparastasin with B, Moerbeke, Bessarion, Karsten, and Hankinson. Read sunagagôn with E, Moerbeke, and Karsten for Heiberg’s sunagô. Replace Heiberg’s full stop after metekhousin with a question mark. Read touto for Heiberg’s touton. Read auta mona with B for the hautai monai of A printed by Heiberg. Bracket the words kata tauta. Insert an ouk before epêngeilato. For Heiberg’s summetria read asummetria with D, Moerbeke, and Wildberg. For Heiberg’s meizona read megistên. For Heiberg’s meizona read megistên. Read hôs for the first occurrence of tas with D For the êgmenoi of E printed by Heiberg read hêgoumenoi with A, B, D, and Moerbeke. Read aphestôsa with Bessarion and Karsten for the aphestanai printed by Heiberg. For the esti printed by Heiberg read estin hê with A, B, C, D, and Karsten. Read ennoêsas for the misprint ennoêtas in Heiberg, noted by Wildberg. Read pantôs with D and E for the pantos of A and B printed by Heiberg. Move the raised dot after planômenês behind zêtôn with Wildberg. Read enantian with Moerbeke and Karsten for Heiberg’s enantias. Read ousas with A, B, and Karsten for the hosas of D and E printed by Heiberg. For Heiberg’s arkhê hê read hê arkhê with A and B. Drop the hê with A. Insert katô after anôthen with Bessarion and Karsten. For the energoun of A and B printed by Heiberg read energein with D, E, and Karsten. For the allôi of A and E printed by Heiberg read allôs with D and Karsten; B and a second hand of A have allo.

(b) Simplicius’ quotation of other texts Here I bring together places where a quotation by Simplicius of a passage from a text other than De Caelo 1.3.270a11-4 as printed by Heiberg differs from the passage in a standard edition of the text. I have paid no attention to the numerous differences regarding elision (e.g. de v. d’) or minor variations in spelling (e.g., hauton vs. heauton or teleiotaton vs. teleôtaton).

Textual Questions ARISTOTLE

De Caelo Moraux 268b16 phamen autois 280a31 loipon

Heiberg 132,24 phamen en autois 140,22 omit

Metaphysics Ross (1953) 1044b4 eiper ara

Heiberg 134,4 kai gar

On Coming to be and Perishing Joachim (1922) 330b31-2 topôn

Heiberg 169,31-2 prôtôn

Physics Ross 188a22 to plêres 188a23 to men hôs on 188a23 einai 188a25 gegôniômenon agônion 188a25 euthu 188a36 tôi mê leukôi 188a37 ex ou leukou 188b4 ei mê pote 188b5 kai ouk 188b6 kai to mousikon 188b24-5 hoion khrômata ek leukou kai melanos 190a18 to men mê 190a19-20 (ho gar anthrôpos hupomenei), to mê mousikon de kai to amouson oukh hupomenei. 190b2 hosa [alla] 190b3 ho hupokeitai 190b4 ex hou to gignomenon 190b4-5 ek spermatos 191a4-5 peri genesin phusikôn 191a4 pôs posai 191a4 kai dêlon 191a5 tanantia duo 191a13 hês ho logos 191a27 tôn ontôn ouden 191a31 dein

Heiberg 130,1 stereon 130,1 to men on 130,2 omit 130,3 gônia 130,3 to euthu 124,29 tôi leukôi 124,30 ouk ek leukou 125,3 ei pote 125,4 kai eis mê leukon ouk 25,5 kai mousikon 125,19 omit 122,26 to men gar mê 122,27 ho gar anthrôpos hupomenei to mousikon, to de amouson oukh hupomenei. (also 128,24-5) 129,11 hosa alla 129,13 ti ho hupokeitai 129,13 ex hou ginetai to ginomenon 129,14 ek tou spermatos 125,25 peri genesin 125,26 pôs 125,26 dêlon 126,27-8 tanantia 126,1 ho logos 137,7 ti tôn ontôn 137,11 dei

EMPEDOCLES

DK31B17 Wright (1981) line 8 dikh’ hekasta phoreumena

Heiberg 141,2 dikha panta phoroumena

183

184

Textual Questions

PLATO

Timaeus Rivaud 28A1 aei 28A2 omit 28B7-8 ap’ arkhês tinos arxamenos 41A4 phanerôs 41A7-8 di’ emou genomena aluta emou ge mê ethelontos (41A7-8) 41B3-4 outi men dê 41B6 lakhontes 41B7-8 eti genê loipa 41C1 dei 41D2 trophên 41D3 auxanete

Heiberg 104,5 omit 104,7 kai hôsautôs 104,11 omit 106,7 aphanôs 106,9-10 aluta emou ge ethelontos 106,12 ou mên (also 107,4) 106,14 tukhontes 106,15 esti loipa 106,17 edei 106,24 trophas (also 107,14) 106,25 auxete (also 107,14)

PLOTINUS

Enneads Wilberding (2006) 2.1.14 autou

Heiberg 115,31 autôi

SEPTUAGINT

Psalms Rahlfs (1935) 18.5 autou

Heiberg 141,27 hautou

English-Greek Glossary This glossary is derived from the Greek-English Indices for this volume and for Mueller (2010) and gives standard Greek equivalents for many nouns, verbs, adjectives, adverbs, and a few prepositions in the translation. It does not include equivalents for words which have no relatively simple equivalent in English, and it does not always attend to the difference in meaning between active, middle, and passive forms of a verb. 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. The letter ‘n’ indicates that an English word is a noun or nominalisation, ‘v’ that it is a verb or deverbative. There is a separate Index of Names. abiding (n.): aiôn abode (n.): hedra above: anô absolutely: haplôs abstraction (n.): aphairesis absurd: atopos absurdity (n.): atopia accept (v.): apodekhomai, eisdekhomai, homologeô, hupodekhomai, hupolambanô, paradekhomai, paralambanô, prosiêmi, sunginôskô, sunkheô accidental: sumbebêkôs accompany (v.); sunedreuô account (n.): apodosis, historia, logos accrue (v.): epiballô, epiginomai, paraginomai, proseimi, prosginomai accurate: akribês accuse (v.): enkaleô, episkêptô acme (n.): akmê act (n.): poiêsis act (v.): draô, energeô, poieô act as a prophet (v.): propheteuô act childlishly (v.): neanieuomai acting (n.): drasis activate (v.): energeô active: drastikos, energêtikos activity (n.): energeia actual: energeiai actualisation (n.): entelekheia acuteness (n.): oxutês adamant (n.): adamas add (v.) epagô, epipherô, prostithêmi

add nonsense (v.): prosphluareô addition (n.): prosthêkê, prosthesis additional assumption (n.): proslêpsis adduce (v.): epagô adhere to (v.): proiskhô admire (v.): timaô admit (v.): dekhomai, epidekhomai admitting: dektikos advance (v.): prokhôreô, prokoptô affection (n.): pathos affirm (v.): episêmainô affirmation (n.): kataphasis again: authis, palin age (v.): gêraskô agree (v.): homognômoneô, homologeô, sumphôneô, sunaidô, sunkheô, suntithêmi agreeing: sumphônos agreement (n.): sunkhôrêsis air (n.): aêr aithêr (n.): aithêr akin: sunêthês alien: allotrios allege (v.): proiskhô alone: monos already: hêdê alter (v.): alloioô alterable: alloiôtos alteration (n.): alloiôsis alternate (v.): enallassô alternately: enallax always: aei always moving: aeikinêtos always: pantakhou, pantôs

185

186

English-Greek Glossary

amateurish: idiôtikos amazing: thaumastos analysis (n.): analusis analyse (v.): analuô ancient: arkhaios, palaios angle (n.): gônia angleless: agônios animal (n.): zôion announce (v.): epangellô anonymous: adespotos antecedent (n.): hêgoumenon antithesis (n.): antithesis antithetical: antithetos apogee, at: apogeios appear (v.): anaphainô, phainô appear together (v.): sunekphainô appearance (n.): phasma apply (v.): epharmottô apportion with (v.): sundiaireô apprehend (v.): katalambanô apprehended: antilêptos approach (v.): plêsiazô appropriate: oikeios arbitrary: apoklêrôtikos arc (n.): periphereia argue (v.): epikheireô, sullogizô argue against (v.): antepikheirô, antilegô argument (n.): epikheirêma, epikheirêsis, kataskeuê, logos, sullogismos arm (n.): kheir arm oneself (v.): anazônnumi arrange (v.): diatattô, diatithêmi articulate (v.): diarthroô articulation (n.): diarthrôsis artifact (n.): kataskeusama artificial: tekhnêtos ask (v.): erôtaô, zêteô ask for (v.): aiteô assert (v.): episêmainô assign (v.): anieroô, apodidômi, didômai, klêroô assign the same rank (v.): suntassô assume (v.): hupolambanô, lambanô assume in addition (v.): proslambanô, prosupotithêmi assume in advance (v.): prolambanô assumption (n.): lêpsis astound (v.): kataplêttô astronomer (n.): astronomos attach (v.): exaptô, huparkhô, prosphuô, prosêkô attach oneself to (v.): prosekhô

attain (v.): tunkhanô attend (v.): blepô, apoblepô attention (n.): epistasis attentive: prosektikos auditory: akoustikos authentic: gnêsios authoritative: kurios awareness (n.): sunaisthêsis axiom (n.): axiôma axis (n.): axôn babble (n.): phlênaphos babble utter nonsense (v.): lêreô back: opisthen, opisthios backward: opisthen bad: kakos badness of character (n.): kakotropia balance (n.): summetria banquet (n.): thoinê be (v.): huparkhô, eimi, tunkhanô bear witness (v.): martureô beautiful: kalos begin (v.): arkhô beginning (n.): arkhê beginningless: anarkhos belief (n.): dogma, doxa believe (v.): hêgeomai, nomizô, pisteuô belong (v.): huparkhô below: katô bending (n.): kampsis beneficial: epôphelês bereave (v.): erêmoô beside the point: para thuras best: aristos bestow (v.): endidômi, epinaô better: ameinôn, kreittôn between: metaxu binding: sunektikos bitterness (n.): pikrotês black: melas blame (v.): aitiasthai blasphemy (n.): blasphêmia blend together (v.): sumphurô blessed: makarios blessedness (n.): makariotês blind (v.): ektuphlô blind: tuphlos blossom forth (v.): epantheô boast (v.): kompazô body (n.): sôma bond (n.): desmos bone (n.): osteon book (n.): biblion, biblos both: amphô, amphoteros

English-Greek Glossary bother (v.): enokhleô boundary (n.): horos brag childishly (v.): neanieuomai breadthless: aplatês break (v.): klaô, periklaô break off (v.): aporrêgnumi brevity (n.): suntomia bribed witness (n.): sukophantês brief: brakhus, suntomos bright: lampros, phôteinos bring (v.): suneisagô bring about (v.): epiteleô bring down (v.): hupopherô bring forward (v.): parapherô, proagô bring in (v.): epagô, epeisagô, paragô, paremballô, prosagô bring into conflict (v.): sunkrouô bring into existence (v.): paragô bring to completion (v.): epiteleô bring under the heading (v.): apokoruphoô bringing completion: teleiôtikos bronze (n.): khalkos burn (v.): aithô, kaiô burning: kaustikos business (n.): askholia call (v.): kaleô, onomazô call upon (v.): parakaleô care (n.): epistasis, eulabeia careful: epimelês careless: atalaiporos carry around (v.): periagô, peripherô, sumperiagô, sumperipherô carry down (v.): hupopherô carry out (v.): proagô carry up (v.): anapherô carve (v.): gluphô carver (n.): hermogluphos cast off (v.): apoballô cast out (v.): ekballô categorical: katêgorikos category (n.): katêgoria causal: parasunaptikos cause (n.): aitia, aition causing alteration: alloiôtikos caution (n.): eulabeia cease (v.): lêgô, pauô censure (v.): memphomai centre (n.): kentron, meson certainly: amelei, pantôs certainty (n.): enargeia cessation (n.): paula chance: apoklêrôtikos

187

change (n.): kinêsis, metabolê change (v.): ameibô, metaballô, metalambanein change (form) (v.); allassô change a text (v.): metagraphô change in quality (v.): alloioô change position (v.): methistêmi change the shape of (v.): metaskhêmatizô changeable: metabolikos changing: kinêtos, metabatikos chapter (n.): kephalaion characterise (v.): kharaktêrizô charge (v.): enkaleô child (n.): pais choice (n.): proairesis choose (v.): haireô, proaireô chunk of earth (n.): bôlos circle (n.): kuklos circuit (n.): periagôgê circular arc (n.): periphereia circular: diallêlos, enkuklios, kuklikos, peripherês circumference (n.): periphereia cite as evidence (v.): martureô clarification (n.); saphêneia clarify (v.): diasapheô, saphênizô cleaning up (n.): katharsis cleanse away (v.): apokluzô clear: dêlos, enargês, saphês clearly: dêlonoti clever: deinos cleverness (n.): deinotês, phronêsis close: engus close to earth: perigeios coals (n.): anthrax cognition (n.): gnôsis cognitive: gnôstikos coincide (v.): epharmottô coincidence (n.): sundromê cold (n.): psuxis, psukhros coldness (n.): psukhrotês, psuxis collect (v.): sustrephô collect together (v.): sunagô colour (n.): khrôma colour (v.): khrôizô colourless: akhrômatos combination (n.); sunthesis combine (v.): sunkrinô, suntassô, suntithêmi combining (n.): sunagôgê come (v.): erkhomai come (into existence) (v.): parekhô come across (v.): empiptô, entunkhanô

188

English-Greek Glossary

come from (v.): exerkhomai come to be (v.): ginomai come together (v.): suntrekhô comet (n.): komêtês coming to be (n.): genesis coming to be: genêtos commentator (n.): exêgêtês common feature (n.): koinotêta common: koinos commonality (n.): koinotêta compare (v.): sunkrinô comparison (n.): parexetasis, sunkrasis complain (v.): memphomai complete (v.): apoteleô, sumplêroô, sunteleô, teleô, teleiô complete: teleios, telikos completely: pampan, pantelôs, panu, pantapasi completeness (n.): teleiotês compose (v.): sunistêmi composite: sunthetos composition (n.): sunthesis concave: koilos concede (v.): didômai, endidômi, sunkheô conceive (v.): epinoeô, noeô concentrate (v.): sunneuô concept (n.): epinoia conception (n.) ennoia, hupolêpsis, prolêpsis conclude (v.): sumperainô conclusion (n.): sumperasma condensation (n.): puknôsis condense (v.): puknoô condition (n.): diathesis, katastasis confidence (n.): pistis configuration (n.): skhêmatismos configure (v.): skhêmatizô confirmation (n.): marturia, pistis conflict (n.): diaphônia conflict (v.): diaphôneô, stasiazô conflictless: astasiastos confront (v.): apantaô confuse (v.): sunkheô connect (v.): sunaptô consequent (n.): hepomenon, lêgon consider (v.): apeidon, episkopeô, exetazô, hêgeomai, theôreô constitute (v.): sunistêmi constitution (n.): diathesis, sustasis constitutive: sustatikos constrain (v.): anankazô, biazô, prosanankazô constrained: biaios

constraint (n.): bia construct (v.): kataskeuazô, mêkhanaomai, paraskeuô contact (n.): haphê contain (v.): periekhô, perilambanô containing: periektikos contend (v.): diateinô contentious: philoneikos contentiousness (n.): philoneikia continue (v.): epimenô continuity (n.): sunekheia, sunokhê continuous: sunekhês contract (v.): perisphingô, sunaireô contradict (v.): enantioomai contradiction (n.): enantiologia, enantiologos contradictory: diaphônos contrariety (n.): enantiôsis, enantiotês contrary: enantios, hupenantios contrast (v.): antidiastellô contribute (v.): epiballô, sumballô, sunteleô converge (v.): sunneuô conversion (n.): antistrophê convert (v.): anastrephô, antistrephô convex: kurtos cool (v.): psukhô co-operate (v.): sunergeô co-ordinate: isostoikhos, sustoikhos co-ordination (n.): epharmogê correct (v.): euthunô correct: alêthês, hugiês, kalos, orthos corroborate (v.): martureô corrupt (v.): diaphtheirô cosmos (n.): kosmos count (v.): aparithmeô counterargument (n.): antilogia counterrevolve (v.): anelittô courage (n.): andreia cover (v.); epiprostheô cow (n.): bous cowardice (n.): deilia craftsman (n.): tekhnitês crap (n.): kopros create (life) (v.): zôipoieô create (v.): dêmiourgeô creation (n.): dêmiourgêma, dêmiourgia creator (n.): dêmiourgos criticism (n.): enklêma, euthuna crow (n.): korax crudeness (n.): allokotia cube (n.): kubos cubit (n.): pêkhus

English-Greek Glossary curved: peripherês custom (n.): ethos, sunêtheia customary: sunêthês cut (v.): temnô cylinder (n.): kulindros cylindrical: kulindrikos dark colour (n.): melanotês dark: melas darken (v.): melainô, skotizô darkening (n.): melansis darkness (n.): skotos day (n.): hêmera decline (n.): parakmê deal with (v.): hupantaô, pragmateuomai decay (n.) phthisis decay (v.): aporreô, phthinô deceive (v.): apataô deception (n.): apatê declare (v.): apophainô declination (n.): huphesis decline (v.): parakmazô defend (v.): apologeomai defend (oneself) (v.): amunô deficiency (n.): elleipsis deficient: ellipês define (v.): diorizô, horizô definition (n.): horismos, horos demand (v.): apaiteô, axioô demiurgic: dêmiourgikos demonstrate (v.): apodeiknumi demonstrate previously (v.): proapodeiknumi demonstration (n.): apodeixis demonstrative: apodeiktikos denial (n.): apophasis deny (v.): anaireô, apophaskô, paraiteomai depart (v.): apeimi, apophoitaô, exeimi, exerkhomai, existêmi, oikhomai depend upon (v.): exartaô depict (v.): tupoô depth (n.): bathos derivation (n.): anaphora derive (a word) (v.) etumologeô descend (v.): huphiêmi, katabainô desiderative: orektikos, thumikos desire (n.): ephesis, hormê desire (v.): ephiêmi, epithumeô, hormaô desire for victory (n.): philoneikia desired: ephetos

189

despise (v.): epêreazô, kataphroneô destroy (v.): anaireô, apollumi, diaphtheirô, phtheirô destroy along with (v.): sumphtheirô detach (v.): apospaô determine (v.): horizô, tithêmi development (n.): agôgê deviation (n.): parallaxis diagram (n.): diagramma diameter (n.): diametros differ (v.): diapherô difference (n.): diaphora, heterotês, parallaxis different: alloios, allos, diaphoros, heteros different in kind: heteroeidês differentia (n.): diaphora differently qualified: alloios difficult: aporos difficult to mix: dusmiktos difficulty (n.): aporia dig (v.): skaptô digress (v.): pareiskukleô dimension (n.): diastasis diminish (v.): hêssaomai, meioô, phthinô diminishing (n.): meiôsis, phthisis diminution (n.): meiôsis direct (v.): apoteinô direct: prosekhês directly: autothen disagree (v.): diapherô, diaphôneô disagreement (n.): antirrêsis disciple (n.): akroatês discuss (v.), dialegô discuss at length (v.): makrologeô discussion (n.): logos disdain (n.): kataphronêsis disharmony (n.): anarmostia disorder (n.): ataxia dispose (v.): diatithêmi disposition (n.): diathesis dispute (v.): amphisbêteô disregard (v.): pareidon dissimilar: anomoios dissoluble: lutos dissolution (n.): dialusis, lusis dissolve (v.): dialuô, luô dissolve simultaneously (v.): sulluoô distance (n.): apostasis, diastasis distinction (n.): diairesis distinguish (v.): antidiaireô, aphorizô, diaireô, diakrinô, diorizô distinguish together (v.): sundiaireô

190

English-Greek Glossary

disturb (v.): tarattô divert (v.): perispaô divide (v.): diaireô divide (into parts) (v.): merizô divided: meristos divine: theios division (n.): diairesis, diakrisis, merismos, logos dodecahedron (n.): dôdekaedron doctrine (n.): dogma dominate (v.): krateô donkey (n.): onos doubt (v.): amphiballô doubtful: amphibolos down: katô drag (v.): helkô drag down (v.): kataspaô, kathelkô drag up (v.): anelkô draw (v.): agô, graphô, helkô, perigraphô draw down (v.): kathelkô draw things out (v.): mêkunô draw through (v.): diagô draw up (v.): anelkô dry (v.): xêrainô dry: xêros dryness (n.): xerotês due measure (n.): summetria dumbfounding (n.): kataplêxis dung (n.): kopros duration (n.): paratasis eager to learn: philomathês earlier: emprosthen early: arkhaios earth (n.): gê earthen: geôdês east (n.): anatolê eastern: anatolikos easy: eulutos, hetoimos, prokheiros, rhaidios eccentric: ekkentros educate (v.): paideuô effective: drastêrios efficient: poiêtikos element (n.): stoikheion elevation (n.): hupsos eliminate (v.): aphanizô, diagraphô elucidate (v.): saphênizô elucidation (n.): dieukrinêsis emanation (n.): aporroia embrace (v.): periekhô, peripiptô embracing: periektikos emplant (v.): empoieô, enspeirô

empty (v.): kenoô empty: kenos empty-headed: kenodoxos empty-headedness (n.): kenodoxia emptying (n.): kenôsis encounter (v.): entunkhanô, hupantaô end (n.) teleutê, telos end (v.): katalêgô end up (v.): teleutaô endless: diôlugios endure (v.): anekhô, diateleô, hupomenô, menô enigma (n.): ainigma enigmatic: ainigmatôdos enjoy (v.): apolauô enough: halis enquire (v.): zêteô enquiring: zêtêtikos entailment (n.): akolouthia entangle in (v.): periballô entire: holos entirely: pampan, pantelôs, pantapasi entirety (n.): holotês enumerate (v.): aparithmeô epicycle (n.): epikuklos equality (n.): isotês equally: homoiôs equally strong: isosthenês equivalence (n.): exisasmos err (v.): hamartanô escape (v.): ekpheugô escape notice (v.): lanthanô especially: malista establish (v.): bebaioô, kataskeuazô, themelioô establish together (v.): sunkataskeuazô establishing: kataskeuastikos eternal: aiônios, diaiônios eternity (n.): aiôn even: artios everlasting: aidios everlastingness (n.): aidiotêta everywhere: pantakhothen, pantakhou evidence (n.): marturia, tekmêrion evident: phaneros, prophanês examination (n.): exetasis examine (v.): basanizô example (n.): hupodeigma, paradeigma exceed (v.): huperballô excess (n.): huperbolê, huperokhê exchange (n.): metadosis exchange (v.): metadidômi excuse (v.): sunginôskô exegesis (n.): exêgêsis

English-Greek Glossary exegetical: exêgêtikos exercise (v.): gumnazein exhalation (n.): anathumiasis exist (v.): huparkhô, eimi, huphistêmi exist before (v.): prouparkhô exist together (v.) suneimi, sunuparkhô, sunuphistêmi existence (n.): hupostasis expect (v.): prosdokeô explain (v.): apologeomai, diarthroô, exêgeomai explain in detail (v.): dierkhomai explainer (n.): exêgêtês explanation (n.): aitia, exêgêsis expose (v.): dielenkhô express (v.): paramutheomai extend (v.): prosauxanô extend along with (v.): sumparateinô extended: diastatos extendedness (n.): paratasis extension (n.): diastasis, ektasis external: ektos, exô, exôthen, heterôthen extreme: akros, eskhatos eye (n.): omma, ophthalmos fabricate (v.): anaplattô fact (n.): pragma faculty (n.): dunamis faint: amudros fair: dikaios fall (v.): piptô fall away (v.): apopiptô fall down (v.): apopiptô fall from (v.): ekpiptô fall into (v.): empiptô fallacious: paralogos false: pseudos famous: onomastos far away: prosô fashion (v.): apotupoô fast: takhus fate (n.): moira few: oligos fiery: purios fight (v.): makhomai figure (n.): skhêma figure out (v.): anikhneuô fill (v.): korennumi, pimplêmi, plêroô fill out (v.): anaplêroô, sumplêroô filling out: sumplêrôtikos final: teleutaios, telikos find (v.): heuriskô find a solution (v.): euporeô find fault (v.): memphomai

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fine: leptos fine-parted: leptomerês fire (n.): pur fire-fly (n.): pugolampis firm: bebaios first: prôtos fish (n.): ikhthus fit (v.): epharmottô fit together (v.): harmozô fitting (n.): epharmogê fixed: aplanês flame (n.): phlox flat: epipedos flavour (n.): khumos flavourless: akhumos flesh (n.): sarx float (v.): epinêkhomai flow (v.): khôreô, rheô flow out (v.): aporreô, ekkheô flowing: rheustos follow (v.): akoloutheô, diadekhomai, epakoloutheô, hepomai, sumbainô following: akolouthos, ephexês foot (n.): pous force (n.): bia force (v.): biazô forceful: biaios foreign: xenos forever: aei, aidios forget (v.): epilanthanô forgetful: epilêsmôn form (n.): eidos, idea form (v.): eidopoieô form into a sphere (v.): sphairoô formal: eidêtikos forming: eidopoios formless: aneideos formlessness (n.): amorphia fortunate: eutukhês forward: emprosthen frequently: pollakhou, pollakis friendly: philikos frivolous: kakoskholos front: emprosthen, prosthen, prosthios full: plêrês furnish (v.): khorêgeô, parekhô furthest down: katôtatô gap (n.): dialeimma gather together (v.): sullambanô general: katholikos generate (v.): apogennaô, gennaô generated: genêtos generating life: zôigonos

192

English-Greek Glossary

generative: gonimos generic: genikos genesis (n.): genesis gentle: êremaios genuinely: ontôs genus (n.): genos geometer (n.): geômetrês geometrical: geômetrikos get ready (v.): parapoduomai get weaker (v.): kamnô give (v.): apodidômi, didômai give as evidence (v.): tekmairomai give existence (v.): huphistêmi, sunistêmi give life (v.): zôipoieô give light (v.): phôtizô give out (v.): ekleipô give shape (v.): skhêmatizô, morphoô give substance (v.): ousioô giving existence: hupostatikos glass (n.): hualos go (v.): bainô, eimi go after (v.): apeimi go beyond (v.): pleonazô go on (v.): diateleô go on at length (v.): mêkunô go past (v.): parekhô go through (v.): dierkhomai, eperkhomai goal (n.): skopos god (n.): theos good: agathos, kalos good fellow (n.): khrêstos good sir!: beltiste goodheartedness (n.): euêtheia goodness: agathotêtos governing: arkhikos grammarian (n.): grammatikos grand: diôlugios grant (v.): didômai, sunkheô, grasp (v.): haireô great: megas greater: meizôn greatness (n.): megaleiotês grey: phaios grow (v.): anaphuô, auxanô, prosauxanô grow together (v.); sumphuô growth (n.): auxêsis guesswork (n.): huponoia guide (v.): ithunô gull (n.): korônê hair (n.): thrix

half a foot (n.): hêmipodion half: hêmisus hand (n.): kheir hand down (v.): diadidomai, paradidômi happen (v.) sumbainô happen to be (v.): tunkhanô hardness (n.): sklêrotês harm (n.): blabê harm (v.): blaptô harmful: blaberos harmonious: enarmonios, homonoêtikos harmonize (v.): harmozô, sumphôneô, sunaidô, sunarmozô harmonising: sumphônos harmony (n.): harmonia, sumphônia have (v.): epekhein, iskhô, ekhô have the strength to (v.): iskhuô head (n.): kephalê hear (v.): akouô hearing (n.): akoê heart (n.): kardia heat (n.): thermê, thermotês heat (v.): thermainô heaven (n.): ouranos heavenly: ouranios heavens (n.): ouranos heaviness (n.): barutês heavy: barus helix (n.): helix help (v.): boêtheô, sunergeô hemisphere (n.): hêmisphairion high: oxus higher: anôterô highest: akros, anôtatô hold (v.): huparkhô hold oneself up: (v.) anekhô hold onto (v.): stegô hold together (v.): sunekhô holding together: sunektikos hollow: koilos holy: hieros homocentric: homokentros homoiomerous: homoiomerês honour (v.): timaô honourable: timios horse: hippos hot: thermos hour (n.): hôra house (n.): oikia human (n.); anthrôpos human: anthrôpinos hupekkauma (n.): hupekkauma

English-Greek Glossary hyperbaton: huperbaton hypernatural: huper phusin, huperphuês hypothesis (n.): hupothesis hypothesise (v.): hupotithêmi hypothetical: hupothetikos ice (n.): krustallos idea (n.): ennoia, epibolê, epinoia, idea ignite (v.): exaptô ignorance (n.): agnoia ignorant: anoêtos illuminate (v.): phôtizô illumination (n.): ellampsis image (n.): eikôn imagination (n.): phantasia imagine (v.): phantazô imagining (n.): phantasia imbalance (n.): asummetria imitate (v.): mimeomai imitation (n.): mimêsis immaterial: aülos immediate: amesos, prosekhês immediately clear: prodêlos immortal: athanatos immortality (n.): athanasia imperishable: aphthartos impious: asebês impossible: adunatos impression (n.): tupos impulsion (n.): rhopê in droves: khudên inanimate: apsukhos inappropriate: akairos inborn: sumphuês incline (v.): apoklinô include (v.): perilambanô, sullambanô incomplete: atelês inconsistent: anakolouthos incorporeal: asômatos incorrect: kakos increase (n.): auxêsis increase (v.): auxanô, epiteinô, prosauxanô indefinite: aoristos indefiniteness (n.): aoristia indeterminate: aoristos indicate (v.): dêloô, emphainô, endeiknumi, sêmainô indicate also (v.): sunemphainô indication (n.): epideixis, tekmêrion indifferent: adiaphoros indisputable: anamphilektos indivisible: adiairetos

193

induction (n.): epagôgê inefficacy (n.): adraneia inequality (n.): anisotês infect (v.): anapimplêmi infer (v.): epagô, sullogizô, sumperainô, sunagô, tekmairomai inference (n.): akolouthia, sunagôgê infinite: apeiros infinitely many: apeiros infinity (n.): apeiria influence (n.): apotelesma inhere (v.): enuparkhein injure (v.): blaptô inner: endoterô, entos inseparable: akhôristos inside: endothen, entos inside the cosmos: enkosmios instantaneous: exaiphnês intellectual: noeros intelligible: noêtos intense: sphodros intensify (v.): epiteinô intermediate: mesos, metaxu interpretation (n.): exêgêsis interval (n.): apostêma introduce (v.): eisagô, epeisagô, paragô, proagô, prosagô investigate (v.): anazêteô, episkeptomai, episkopeô, meteimi, skopeô investigation (n.): theôria, zêtêsis invisible: aoratos, aphanês iron (n.): sidêros irrational: alogistos, alogos irrationality (n.): alogia irrefutable: anelenktos issue (n.): pragma jaw (n.): genus jest (n.): paidia jest (v.): paizô join (v.): epizeugnumi, sunaptô join in (v.): sunephaptomai joke (v.): diapaizei jousting with shadows (n.): skiamakhia judge (v.): hêgeomai, krinô judging: kritikos just distribution (n.): dikaiosunê just: dikaios justice (n.): dikê knavery (n.): panourgia katamênia (n.): katamênion kind (n.): eidos, idea

194

English-Greek Glossary

know (v.): ginôskô, gnôrizô, noeô, oida know in advance (v.): progignôskô lack (n.): sterêsis lack (v.): atukheô, elleipô, stasis lacking due measure: asummetros lacking form: amorphos last (v.): diamenô last: eskhatos lasting: monimos later: husteros lay down in advance (v.): proupotithêmi lead (v.): agô lead back (v.): epanagô learn (v.): ginôskô, gnôrizô, manthanô learning late: opsimathês least: elakhistos, hêkistos leave (v.): apoleipô, eaô, existêmi leave in the dark (v.); episkiazô leave out (v.) aphaireô, pariêmi left: aristeros leisure (n.): skholê lemma (n.): lêmma length (n.): mêkos lengthy: makros less: elattôn, hêttôn let out (v.): aporriptô lie (v.): keimai lie above (v.): epipolazô, huperkeimai lie at the top (v.): epipolazô lie together (v.): parakeimai lie under (v.): hupokeimai life (n.): bios, zôê light (in colour): leukos light (n.): phôs light (not heavy): kouphos light colour (n.): leukotês lighten (in colour) (v.): leukainô lightening (in colour) (n.): leukansis lightness (n.): kouphotês lightning (n.): astrapê like: homoios limb (n.): kôlon limit (n.): peras limit (v.): peratoô line (n.): grammê line (of poetry) (n.): epos line (of writing) (n.): stikhos linear: grammikos link with (v.): sunartaô listener (n.): akroatês literate: grammatikos living a long time: makrobios living: zôos

living thing (n.): zôion long: makros long ago: palai look (v.): eidon look at (v.): blepô look into (v.): epeidon look to (v.): apeidon look!: idou loose: platus lose (v.): apollumi Love (n.): Philia loving learning: philomathês lower: katô, katôterô lowest: katôtatô lowly: eutelês lukewarm: khliaros luminous: euagês lunar: selêniakos lyric poet (n.): melopoios magnitude (n.): megethos maintain (v.): axioô, phulattô maintain previously (v.): proaxioô major (premiss): meizôn make (v.): poieô make cold (v.): psukhô make fiery (v.): ekphlogoô make room (v.): hupexistêmi make similar (v.): exomoiôoô malice (n.): kakourgia malicious: kakourgos man (n.): anêr manifestation (n.): ekphansis manuscript (n.): antigraphon many: polus mass (n.): onkos master (n.): didaskalos master (v.): krateô material: enulos, hulikos mathematical thing (n.): mathêma mathematical: mathêmatikos matter (n.): hulê mean (n.): mesotês mean (v.): sêmainô meaning (n.): ennoia, sêmasia measure (n.): metron measure (v.): anametreô, katametreô, metreô measuring: metrêtikos meet (v.): hupantaô, sumballô, sunantaô mention (v.): erô, hupomimnêskô, mnêmoneuô, onomazô middle (n.): mesotês

English-Greek Glossary mind (n.): noos mindless: anoêtos mindlessness (n.): anoia minor (premiss): elattôn mischief (n.): panourgia mischievous: kakoskholos misinterpret (v.): parakouô mistake (n.): parorama misunderstanding (n.): agnoia, parakoê mix (v.): kerannumi, mignumi mixed: miktos mixture (n.): krasis, mixis mobile: eukinêtos mode (n.): tropos moist: hugros moisten (v.): hugrainô moistness (n.): hugrotês monad (n.): monas moon (n.): selênê mortal: thnêtos most of all: malista motion (n.): kinêsis, phora motion in a circle (n.): kuklophoria motion in a reverese direction (n.): antiphora motion in reverse directions: antikinêsis mountain (n.): oros move (v.): erkhomai, hiêmi, khôreô, kineô, pherô move along with (v.): sumparatheô, sunkineô move closer (v.): prokoptô move down (v.): huperkhomai move in a circle (v.): kuklophoreomai move in a straight line (v.): euthuporeô move in both directions (v.): epamphoterizô move in reverse directions (v.): antikineô, antipherô move in the opposite direction (v.): parapherô move together (v.): suneimi moving in a circle: kuklophorêtikos moving: kinêtos much-honoured: polutimêtos multiplication (n.): pollaplasiasmos multiply (v.): pollaplasiazô mush (n.): Mukônos mush together (v.): sunkukaô mutual replacement (n.): antiperistasis naïve: euêthês

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name (n.): onoma name (v.): onomazô natural: phusikos, kata phusin nature: phusis near: plêsios necessitate (v.): anankazô necessity (n.): anankê necesssary: anankaios need (n.): khreia need in addition (v.): prosdeô devise in addition (v.): prosexeuriskô negating: arnêtikos negative: apophatikos new: neos newborn: neogenês next: ephexês, hexês, loipos night: nukterinos no longer: mêketi, ouketi nonsense (n.): phlênaphos, phluaria note (v.); ephistêmi notice (v.): ephistêmi, suniêmi nourish (v.): trephô nourishment (n.) trophê novel: xenos number (n.): arithmos, plêthos nutritive: threptikos object (v.): enistêmi, enkaleô, memphomai objection (n.): antirrêsis, enstasis oblique: loxos obscure (v.): suskiazô observation (n.): têrêsis observe (v.): theaomai obviously: dêlonoti occupy (v.): epekhô, katekhô touch (v.): kathaptô occur (v.): aphikneomai, ginomai, sumbainô odd: perittos odour (n.) atmos old: palaios omit (v.): pariêmi one foot long: podiaios only: monos opinion (n.): dogma, doxa oppose (v.): antitithêmi order (n.): diakosmêsis, taxis order (v.): diakosmeô, euthetizô, keleuô ordering (n.): suntaxis ordinary: sunêthês ordinary use (n.): sunêtheia organic: organikos other: allos, heteros, loipos

196

English-Greek Glossary

outer: ektos, exôterô outermost: exôtatô outside: ektos, exô overbear (v.): pleonekteô overbearingness (n.): pleonexia overpower (v.): krateô overtake (v.): hupertrekhô overthrow (v.): anastrephô, anatrepô overturn (v.): anatrepô overturning: anatreptikos paltry: eutelês paradigm (n.): paradeigma parallel: parallêlos parallelogram (n.): parallêlogrammon paraphrase (n.): paraphrasis part (n.): meros, morion partial: merikos participate in (v.): metekhô participation (n.): metalêpsis, methexis, metokhê particular: merikos pass (v.): metabainô pass over (v.): eaô pass through (v.): diaporthmeuô passage (n.): khôrion, lexis, rhêsis passive: pathêtikos perceive (v.): aisthanomai, sunaisthanomai perceptible: aisthêtos perception (n.): aisthêsis, sunaisthêsis perfection (n.): teleiotês perfective: telesiourgos perhaps: isôs, mêpote, takha perimeter (n.): perimetros peripheral: perix perishable: epikêros, phroudos perishing (n.): phthora perishing: phroudos permanence (n.): diamonê persuade (v.): peithô philosopher (n.): philosophos philosophical: philosophos philosophy (n.): philosophia place (n.): khôra, topos plane: epipedos plant (n.): phuton please (v.): areskô plurality (n.): plêthos point (n.): sêmeion, skopos pointless: mataios, matên portion (n.): moira, morion posit (v.): tithêmi position (n.): thesis

possess in addition (v.): prosktaomai possible: dunatos posterior: husteros postpone (v.): anaballô postulate (n.): aitêma postulate (v.): aiteô potentiality (n.): dunamis power (n.): dunamis practically: skhedon precede (v.): phthanô, proêgeomai, prouparkhô preceding: prosthen precise: akribês preconception (n.): prolêpsis predicate (n.): hatêgoroumenon predominance (n.): epikrateia predominate (v.): epikrateô pre-exist (v.): prouparkhô premiss (n.): lêmma, protasis prepare (v.): paraskeuô presence (n.): parousia present (v.): paradidômi, proagô present as one’s own progeny (v.): hupoballô preserve (v.): diasôzô, peripoieô, sôzô, phulattô preside over (v.): epibainô press (v.): stenokhôreô prevent (v.): kôluô previous: prosthen, proteros pride (n.): philotimia primary: prôtos principle (n.): arkhê, logos prior: proteros, prôtos privation (n.): sterêsis privative: sterêtikos probable: eikos problem (n.): problêma proceed (v.): eimi, proeimi, proerkhomai proceed together with (v.): sumproerkhomai procession (n.): proodos, propodismos proclaim (v.): ekphôneô produce (v.): apergazomai, paragô, poieô producing motion: poiêtikos production (n.): poiêsis progression (n.): propodismos proof (n.): deixis proper: idios, oikeios prophet (n.): prophêtês proposal (n.): epibolê, problêma propose (v.): propherô, protithêmi

English-Greek Glossary proposition (n.): logos, protasis proprium (n.): idion prove (v.): deiknumi prove first (v.): prodeiknumi provide (v.): parekhô providential: pronoêtikos proving: deiktikos proximity (n.): plêsiasis punishment (n.): dikê puppy (n.): skulakion pure: eilikrinês, katharos purpose (n.): skopos pursue (v.): meteimi, meterkhomai push (v.): ôtheô, sunôtheô put around (v.): periballô put forward (v.): diateinô, proballô, propherô, proteinô putrefaction (n.): sêpedôn, sêpsis putrefy (v.): sêpô qualitative change (n.): alloiôsis quality (n.): poion, poiotês qualityless: apoios quantity (n.): plêthos, poson, posotês quarrel (n.): agôn quick: takhus quiescent: apraktos quietly: êrema quote (v.): paragraphô raise (v.): anateinô, meteôrizô rank (n.): taxis rarefy (v.): manoô rash: propetês, tolmêros rashness (n.): propeteia, thrasutês ratio (n.): logos rational: logikos ray (n.): akros reach (v.): aphikneomai, katalambanô reach a conclusion (v.): perainô read (v.): anagignôskô, entunkhanô ready: eukolos, prokheiros reality (n.): huparxis realise (v.): ennoeô, ginôskô reason (n.): aitia, aition reasonable: eikos, eulogos, metriôs reasonably: eikotôs reasoning (n.): dianoia, logismos recall (v.): hupomimnêskô, mimnêsko receive (v.): apolambanô, dekhomai, epidekhomai, hupodekhomai, lankhanô receive in advance (v.): prolambanô receiving (n.): katadokhê

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receptacle (n.): hupodokhê reception (n.): metalêpsis receptive: dektikos reckless: atarakhos recognise (v.): ennoeô record (n.): mnêmê record (v.): anagraphô recount (v.): historeô rectilinear: euthugrammos recycle (v.): anakukleô reduce (to an absurdity): apagôgê reductio ad impossibile (n.): apagôgê eis adunaton refer (v.): anapempô refined: katharos refutation (n.): antilogia, elenkhos refute (v.) apelenkhô, dielenkhô, elenkhô region (n.): khôra, topos reject (v.): anainomai, apeipon, aporriptô relation (n.): skhesis release (v.): aphiêmi reliable: axiokhreôs remain (v.): epimenô, leipô, menô, perileipomai remaining: loipos remarkable: thaumasios, thaumastos remember (v.): mimnêsko remind (v.): hupomimnêskô remove (v.): aphaireô, exaireô renew (v.): ekneazô renown (n.): eukleia renowned: kleinos replace mutually (v.): antiperiistêmi report (v.): historeô reproach (n.): enklêma reputable: dokimos reputation (n.): doxa require (v.): anankazô, apaiteô resist (v.): antereidô resistance (n.): antitupia resolve (v.): analuô respond (v.): hupantaô response (n.): hupantêsis rest (n.): êremia, monê, stasis rest (v.): êremeô, menô restrict (v.): sunaireô result (v.); sumbainô resume (v.): epanalambanô retrogression (n.): hupopodismos return (v.): apokathistêmi reveal (v.): apokaluptô, diaphainô, emphainô

198

English-Greek Glossary

reverse: anapalin, apenantios, empalin revolution (n.): periagôgê, periodos, periphora revolve (v.): anakukleô, peridineô ridiculous: geloios right: dexios, dikaios, kalos, orthos rigorous: akribês rise (v.): anabainô, anatellô rise above (v.): epipolazô rise to the top (v.): epipolazô rise together with (v.): sunanatellô risible: gelastikos role (n.): logos roof (n.): orophos room (n.): khôra roughness (n.): trakhutês rub (v.): paratribô rule (n.): kanôn rule (v.): krateô ruler of the elements (n.): stoikheiokratôr run (v.): theô, trekhô run together (v.) sunkheô sacred: hieros said previously: proeirêmenos sameness (n.): tautotês sandal (n.): hupodêma say (v.): eipon, erô, legô saying (n.): paroimia scale (of a fish) (n.): lepis scatterdly: sporadên scorn (v.): duskherainô sea (n.): thalatta season (n.): hôra seat (n.): hedra seat above (v.): huperidruô see (v.): eidon, horaô, katamanthanô, sunêgoreô, theaomai, theôreô see in (v.): entheôreô seed (n.): sperma sphere (n.): sphaira seek (v.) zêteô seem (v.): dokeô, eoika segment (n.): tithêmi self-moving: autokinêtos self-satisfied: eukolos self-substantiating: authupostatos semicircle (n.): hêmikuklion send away (v.): pempô separate (v.): apomerizô, diakrinô, dialambanô, khôrizô separation (n.): diakrisis, diastasis service (n.): hupêresia set (v.): duô

set aside (v.): apotithêmi, eaô set out (v.): ektithêmi, paratithêmi, proektithêmi, protithêmi set out at length (v.): mêkunô set on fire (v.): empimprêmi set together (v.) sundunô set up (v.): anôrthoô setting out (n.): parathesis settle in (v.) eisoikizô sewer (n.): borboros shake (v.): saleuô shameless: anaidês shape (n.): morphê, skhêma shapeless: askhêmatistos shapelessness (n.): askhêmosunê share in (v.): koinôneô, metekhô shine out (v.): ellampô shining: phôteinos ship (n.): naus shipbuilder (n.): naupêgos short: brakhus show (v.): deiknumi, dêloô, ekphainô, epideiknumi show oneself (v.): anaphainô showing (n.): parastasis shrink from (v.): okneô side (n.): pleura siege engine (n.): paraskeuê sign (n.): tekmêrion sign (of the zodiac) (n.): zôidion sign (v.): epigraphô signal (v.): episêmainô similar: homoios, paraplêsios similarity (n.): homoiotês similarly: homoiôs simple: haplous simplicity (n.): haplotês simply: haplôs simultaneous: hama sink (v.); katabainô size (n.): megethos, poson slight alteration (n.): parakhrôsis slow: bradus small: mikros smaller: elattôn smell (n.): osmê smoothness (n.): leiotês, malakotês solar: hêliakos solid: nastos, sterros, stereos solidity (n.): sterrotês sometimes: eniote soul (n.): psukhê sound: hugiês sound (n.): phônê, psophos

English-Greek Glossary sound (off) (v.): phthengomai sound out (v.): perikrouô space (n.): khôra space (n.): topos spatial: topikos speak against (v.): anteipon, anterô, antilegô speak nonsense (v.): phluareô species (n.): eidos specific feature (n.): idion speech (n.): logos speed (n.): takhutês spend (v.): dapanaô spend time (v.): endiatribô spherical: sphairikos spit out (v.): exeptuô spit upon (v.): periptuô spontaneous: automatos spout out (v.): ekphusaô spread (v.): khôreô spread around (v.): perikheô stable: monimos stand (v.): bainô, kathistêmi stand in the way (v.): empodizô stand still (v.): histêmi standard (n.): kritêrion star (n.): astêr, astron start (v.): arkhô, hormaô starting point (n.): arkhê state (n.): hexis statement (n.): logos statue (n.): agalma stir up (v.): anakineô stone (n.): lithos stop (v.): histêmi stopping (n.): stasis straight: euthus, ithutenês straightedge (n.): kanôn strange: atopos stray (v.): apoplanaô stretch out (v.): apoteinô, ekteinô, katateinô stretching (n.): ektasis strict: kurios Strife (n.): Neikos strike (v.): plessô strike into perplexity (v.): kataplêttô strive (v.): spoudazô strive for victory (v.): philoneikeô strong: iskhuros structure (n.): sustasis stupid: anepistatos stupidity (n.): anepistasia, asunesia subject to diminution: meiôtos

199

subject to increase: auxêtos sublunary: hupo selênên substance (n.): ousia substantial: ousiôdês subsume (v.): hupotattô succession (n.): diadokhê suffer (v.): eaô suffering: pathêtos suffice (v.): arkeô sufficient: hikanos suitability (n.): epitêdeiotês suitable: epitêdeios, prosphuês suited: epitêdeios summer (n.): theros sun (n.): hêlios superficial: epipolaios superfluity (n.): periousia superfluous: perittos superior: huperteros superiority (n.): huperokhê supervene (v.): epiginomai, paraginomai supply (v.): parekhô support (v.): sunêgoreô suppose (v.): hupolambanô, huponoeô, tithêmi surface (n.): epiphaneia surprising: thaumastos surround (v.): periekhô surrounding: perix sustain (v.): sunekhô sweet: glukus, potimos sweetness (n.): glukutês swim (v.): nêkhô syllogism (n.): sullogismos symmetric: summetros symmetry (n.): summetria sympathy (n.): sumpatheia synthesis (n.): sunthesis tabernacle (n.): skênoma take (v.): lambanô, paralambanô take as a pair (v.): sunduazô take away (v.): aphaireô, aphiêmi take away from under (v.): hupospaô take on (v.): apolambanô, metalambanein take on in addition (v.): proslambanô taking (n.): lêpsis tangible: haptos tasteless: apeirokalos teach (v.): didaskô teacher (n.): didaskalos teaching (n.): didaskalia

200

English-Greek Glossary

temple (n.): naos term (n.): horos test (v.): basanizô text (n.): lexis, rhêsis theogony (n.): theogonia theorem (n.): theôrêma theory (n.): logos thereby: hêdê thesis (n.): thesis thick: pakhus thicken (v.): pakhunô thickness (n.): pakhutês thin (v.): leptunô thing (n.): pragma think (v.): boulomai, dianoeô, doxazein, epinoeô, noeô, nomizô, oiomai think of (v.): mnêmoneuô think of in addition (v.): prosennoeô thinking (n.): phronêsis thought (n.): epinoia, noêsis thoughtless: aperiskeptos threaten (v.): anateinô three-dimensional: trikhê diastatos throw (v.): rhiptô time (n.): aiôn, hôra, khronos today: sêmeron together: hama, homou tongue (n.): glôtta tool (n.): organon touch (v.): ephaptô, haptô trace back (v.): anikhneuô traceless: aneideos train (v.): gumnazein transcend (v.): exaireô transcendence (n.): exairesis transcendent: exairetos transfer (v.): metapherô transform (v.): metabainô transformation (n.): metabasis, tropê transient: proskairos transition (n.): metabasis transmission (n.): metadosis transmit (v.): diadidomai, diapempô, metadidômi, paradidômi transparent: diaphanês traverse (v.): diexeimi, perieimi treatise (n.): logos treatise (n.): pragmateia tree (n.): drus triangle (n.):trigônon trivium (n.): triodos trophy (n.): tropaion trouble (n.): askholia

trouble (v.): enokhleô true: alêthês trust (v.): pisteuô truth (n.): alêtheia try (v.): epikheireô, peiraô try hard (v.): spoudazô tune (v.): harmozô turn (v.): anakamptô, meteimi, strephô, trepô turn away (v.): apoklinô twist (v.): diastrephô twisted: diastrophos unaffected: apathês, asaleutos unbroken: aklastos unceasing: anekleiptos unchanging: akinêtos, ametablêtos uncovered: gumnos uncritical: akritos undemonstrated: anapodeiktos under suspicion: hupoptos undergo (v.): hupomenô, paskhô underlie (v.): hupokeimai undermine (v.): parapodizô, saleuô understand (v.): akouô, apodekhomai, ennoeô, ephistêmi, ginôskô, parakoloutheô, sunaisthanomai, sunêgoreô, suniêmi, sunneuô understand in addition (v.): prosennoeô understanding (n.): gnôsis, noêsis, sunaisthêsis undivided: adiairetos uneducated: apaideutos unequal: anisos unextended: adiastatos unification (n.): henôsis uniform: homalês, monoeidês unify (v.): hênoô unintelligible: asunetos unity (n.): henôsis universal: katholikos, katholou unknown: agnôstos unmoving: akinêtos unmusical: amousos unnatural: para phusin unreasonable: alogos unreasonably: apeikotôs unrefuted: anelenktos unshakable: asphalês, bebaios unsound: sathros unsoundness (n.): sathrotês unsuitability (n.) anepitêdeiotês unsuitable: anepitêdeios unvarying: aparallaktos

English-Greek Glossary unworthy: atimos up: anô upper: anô use (n.): khreia use (v.): apokhraomai, khraomai, paralambanô, proskhraomai valuable: timios value (n.): axiôma vanishing: phroudos variegated: poikilos vary (v.): paralattô vehicle (n.): okhêma verse (n.): epos vice (n.): kakia victory-loving: philoneikos view (n.): doxa, gnômê virtue (n.): aretê visible: horatos vision (n.): opsis visual: optikos vital: zôtikos void: kenos wander (v.): planaô want (v.): boulomai, ethelô warm: thermos warm (v.): thermainô wasp (n.): sphêx waste (v.): dapanaô water (n.): hudôr watery: hudatinos way (n.): tropos weak: asthenês wear out (v.): kamnô weave together (v.): prosuphainô weigh (v.) helkô weigh down (v.): bareô weight (n.): baros west (n.): dusis, dusmai

white: leukos whiteness (n.): leukotês whole: holos whole (n.): holotês whiten (v.): leukainô will (n.): boulêsis will (v.): ethelô willful: authadês winter (n.): kheimôn wisdom (n.): phronêsis wise: sophos wish (v.): boulomai, ethelô with pleasure: hêdeôs withdraw (v.): hupexerkhomai without qualification: haplôs witness (n.): martus wonder (v.): thaumazô wood (n.): xulon wooden: xulinos word (n.): onoma words (n.): lexis, logos, rhêmata work (n.): ergon, poiêsis work together (v.): suntrekhô working together: sunergos worm (n.): skôlêx worse: kheirôn worship (n.): thrêskeia worth: axios write (v.): graphô write against (v.): antigraphô write down (v.): sungraphô write in addition (v.): epigraphô writing (n.): graphê written: anagraptos year (n.): etos yearn (v.): epipotheô yield (v.): hupeikô young: neos

201

Greek-English Index This index, which is based on Heiberg’s text with my emendations and covers all of the commentary on 1.2-4, indicates the English translations of those nouns, verbs, adjectives, and some adverbs used by Simplicius only once. Words which occur only in quotations (or apparent quotations) of Aristotle and earlier authors are omitted. For the most part Greek words are given in the form which serves as the basis of an entry in LSJ. A similar index for words used more than once is included in Mueller (2010) The expression ‘m/p’ indicates that a verb occurs in the middle or passive tense. adamas, adamant, 142,12 adespotos, anonymous, 201,4 adikos, unjust, 19,18 adioristos, in the same way, 161,27 (adioristôs) adraneia, inefficacy, 136,30 aeikinêtos, always in motion, 197,19 agalma, statue, 141,22 agenêsia, not coming to be, 139,24 agnômôn, ignorant, 57,14 agnômosunê, ignorance, 56,27 agnôstos, unknown, 116,25 agôn, quarrel, 123,4 agônios, without angles, 129,28 ainigma, enigma, 141,9 ainigmatôdos, enigmatic, 140,26 (ainigmatôdôs) aisthêtikos, having perception, 73,22 aitêma, postulate, 108,31 aithô, to burn, 119,3 akairos, inappropriate, 180,24 akharis, distasteful, 46,12 akhlus, mist, 26,26 akhôristos, inseparable, 143,17 akhumos, without flavour, 130,29 akoustikos, involving hearing, 184,5 akribeia, precision, 15,29 akritos, uncritical, 180,25 (akritôs) alloiôtikos, causing alteration, 112,35 alloiôtos, subject to alteration, 112,3 allokotia, crudeness, 192,20; and 270a2 alogia, irrationality, 200,29 ameinôn, better, 106,4 amelei, certainly, 192,33

amethodos, unsystematic, 29,36 (amethodôs) ametria, unmeasuredness, 39,33 ammôdês, sandy, 16,19 amorphia, formlessness, 129,15 amorphos, lacking form, 129,21 amphibolos, doubtful, 133,26 amudros, faint, 98,30 anabasis, motion up, 36,31 anadunô, to emerge, 25,25 anágôgos, badly educated, 82,12 anagôgós, elevating, 55,18 anagraptos, in writing, 117,26 anainomai, to reject, 115,10 anaklaô, to be reflected back, 88,22 (m/p) anaklasis, reflection back, 83,8 analogeô, to be analogous, 184,13 analogia, proportion, 81,24 analogos, proportional, 81,33 analusis, analysis, 108,2 anametreô, to be measured, 165,9 (m/p) anangellô, to declare, 90,17 anapaula, rest, 78,24 anapauô, to rest, 53,16 anapausis, rest period, 53,15 anapherô, to move up, 158,20 anaphora, derivation, 168,6 anapimplêmi, to infect, 190,16 anaplattô (anaplassô in LSJ), to fabricate, 140,31 anaplêroô, to fill out, 187,3 anatasis, elevation, 54,9 anathumiasis, exhalation, 131,14 anatolikos, eastern, 197,4

203

204

Greek-English Index

anatreptikos, overturning, 124,18 anazêteô, to investigate, 159,6 anazônnumi, to arm oneself, 189,22 anazôpureô, to burn, 85,18 anêbaô, to be rejuvenated, 98,12 anedên, without restraint. 88,28 aneideos, formless, 135,29 aneimi, to go up, 36,12 anemphatos, without a trace, 93,8 anepikritos, unexamined, 25,32 anepitêdeios, unsuitable, 98,10 anepitêdeiotês, unsuitability, 143,28 aneuphêmeô, to be proclaimed, 85,15 (m/p) aniêmi, to be dedicated to, 85,3 anieroô, to dedicate, 142,6 ankôn, elbow, 48,2 anoêtainô, be ignorant, 122,21 anômalia, anomaly, 32,21 anôrthoô to set up, 200,24 anteisagô, to replace with, 77,30 antepikheirô, to put forward counterarguments, 179,24 antereidô, to offer resistance, 130,17 antereisis, pressure, 78,24 antheô, to blossom, 25,35 anthrôpeios, human, 48,27 anthrôpiskos, humanoid, 86,4 antibainô, to come against, 76,10 antidiastellô, to contrast, 118,10 antigraphon (see antigraphos in LSJ), manuscript, 152,31 antikoptô, to strike, 15,17 antilêptos, apprehended, 97,24 antiphora, motion in a reverse direction, 156,20 antitupoô, to have resistance, 12,30 anumneô, to hymn the praises of, 91,10 aoratos, invisible, 130,17 apantaô, to confront, 188,5 aparallaktos, unvarying, 118,4 apartaô, to make depend, 25,13 apaugasma, efflux, 86,14 apaxioô, to decline, 12,32 apeikonizô, to be an image, 97,12 (m/p) apeikotôs, unreasonably, 107,23 apeipon, to reject, 172,5 apeiria, unfamiliarity, 36,27 apeirodunamia, infinite power, 44,26 apeirodunamos, infinitely powerful, 79,5

apeirokalos, tasteless, 177,17 (apeirokalôs) apeiroplasiôn, infinitely many times, 82,4 apekoruphoô, to bring under the heading, 126,3 apelenkhô, to be refuted, 124,14 (m/p) apemphainô, to be incongruous, 35,10 apenantios, reverse, 188,9 aperilêptos, impossible to grasp, 49,21 aperriptô, to reject, 200,30 aperuthriaô, to not be embarrassed, 135,9 aphidruma, icon, 26,24 aphuktos, inescapable, 52,26 aplatês, without breadth, 174,15 apogennaô, to generate, 131,13 apokhê, distance, 148,2,3 apokhôreô, to depart, 69,33 apoklêrôsis, arbitrary chatter, 27,6 apokluzô, to be cleansed away, 201,2 (m/p) apokoruphoô, to bring under a heading, 126,3 apokrinô, to be chosen, 84,20 (m/p) apokruptô, to obscure, 89,12 apolausis, enjoyment, 72,20 aponeueô, to be directed to, 169,8 aponoia, rebellion, 86,4 aponos, without difficulty, 53,12 (aponôs) apophoitaô, to depart, 94,14 apoplanaô, to stray, 118,29 aporêma, difficulty, 43,26 aporrapizô, to reject, 69,13 aporrêgnumi, to break off, 142,31 aporroia, emanation, 115,7 aposbennumi, to die, 25,36 (m/p) aposkeuazô, to argue against, 79,14 apotelesma, influence, 113,6 apôtheô, to be thrust away, 55,23 (m/p) apotithêmi, to set aside, 143,15 apotrepô,to turn away, 25,30 apotupoô, to fashion, 141,23 apraktos, quiescent, 137,29 arkhegonos, original, 85,30 arrepês, transcending impulsion, 70,14 artiakis, even times (even), 29,32 artiperissos, even times odd, 29,29 asaleutos, unaffected, 201,7

Greek-English Index asebeô, to sin, 84,30 askhêmatistos, without shape, 129,27 askhetos, not relative, 169,7 askhistos, undivided, 31,29 askholos, without leisure, 79,19 askos, bag, 74,20 astasiastos, without conflict, 97,20 (astasiastôs) astrapê, lightning, 119,29 astronomia, astronomy, 81,16 astronomikos, astronomical, 36,27 asullogistos, not following, 62,14 asummetros, unbalanced, 171,20 asunesia, stupidity, 180,7 atar, nevertheless, 105,1 atarakhos, reckless, 159,5 (atarakhôs) ataxia, disorder, 129,15 ateleia, incomplete condition, 54,31 atheteô, to do away with, 70,3 athroizô, to assemble, 25,24 athroos, in a batch, 129,4 (athroôs) atimos, unworthy, 135,7 atmos, odour, 130,22 atropheô, to be undernourished, 54,8 atukheô, to be lacking in, 136,24 authadês, willful, 136,1 authis, again, 120,28 automatos, spontaneously, 137,21 (ek tautomatou) auxêtikos, related to growth, 123,23 auxêtos, subject to increase 112,2 axiokhreôs, reliable, 126,12 barunô, to be burdened, 26,4 (m/p) bebaiôsis, warrant, 55,15 biblos (see bublos in LSJ), book, 200,25 blabê, harm, 76,20 blasphêmeô, to blapsheme, 88,29 blasphêmia, blasphemy, 137,20 boaô, to shout, 88,31 boêthos (see boêthoos in LSJ), helping, 68,7 borborôdês, filthy, 66,9 borboros, sewer, 119,11 daktulos, finger, 48,2 deigma, showing, 25,7 diaballô, to pass over, 89,29 diaboaô, to be celebrated, 90,24 (m/p) diadekhomai, to follow, 103,6 diadokhê, succession, 140,30 diagô, to be drawn through, 186,3 (m/p)

205

diagramma, diagram, 177,16 diagraphô, to eliminate, 167,26 diairetikos, relating to the method of division, 52,25 diaittôn (see diaissô in LSJ), shooting star,17,7 diakoptô, to be interrupted, 46,19 (m/p) diakorês, full, 80,14 diakosmêsis, order, 95,25 dialeimma, gap, 118,27 dialektikos, dialectical, 28,20 diamartanô, to misunderstand entirely, 59,10 diamonê, permanence, 137,28 dianoêtikos, intellectual, 59,27 diapaizei, to make a joke, 177,4 diaperainô, to be concluded, 11,10 (m/p) diaperainô, to be concluded, 11,10 (m/p) diaphainô, to be revealed, 196,31 (m/p) diaporthmeuô, to pass through, 130,16 diarkeô, to be sufficient, 78,6 diarthrôsis, articulation, 108,21 diasaleuô, to undermine, 62,2 diaspaô, to distort, 37,16 diazôgrapheô, to be figured, 12,18 (m/p) diêgeomai, to proclaim, 90,16 diêkô, to extend, 83,32 diêrthrômenôs, explicitly, 34,14 dieukrinêsis, elucidation, 194,2 diexeimi, to traverse,14,17 dikaiosunê, just distribution, 171,20 dikanikos, lawyer-like, 48,28 diolou, always, 44,21 diorismos, determination, 47,16 dipêkhus: two-cubit, 47,9 dokimos, reputable, 168,16 drastêrios, effective, 114,17 drimakos, drimakos, 59,11 (on which see the note) drus, tree, 131,7 dusaisthêtos, not able to perceive, 73,23 dusmiktos, difficult to mix, 98,1 dusôpeô, to be constrained, 57,17 (m/p) dussunesia, dull wittedness, 56,26 dustukheô, to be ill-fated, 116,25 dustukhês, unfortnate, 82,11

206

Greek-English Index

eidêsis, knowledge, 55,8 eidêtikos, formal, 184,23 eikosaedron, icosahedron, 12,19 eisagô, to introduce, 129,3 eisdekhomai, to accept, 100,11 eisoikizô, to settle in, 141,28 (m/p) ekbainô, to deviate, 53,7 ekballô, to cast out, 100,7 ekdekhomai, to understand, 23,22 ekleipô, to give out, 155,3 ekneazô, to be renewed, 98,11 (m/p) ekpheugô, to escape, 185,19 ekphlogoô, to make fiery, 99,19 ekphôneô, to proclaim, 106,6 ekphusaô, to spout out, 187,7 ekteinô, to be stretched out, 168,11 (m/p) ektrepô, to turn aside, 66,10 elaion, olive oil, 66,24 eleeinos, to be pitied, 46,13 eleutheros, free, 76,29 ellampô, to shine out, 97,30 ellampsis, illumination, 141,24 elpizô, to hope, 25,30 emmelês, appropriate, 26,19 empimprêmi, to set on fire, 200,31 enallassô, to alternate, 193,9 enallax, alternately, 139,32 endeô, to bind, 128,15 endoterô, inner, 179,16 enegeirô (not in LSJ; cf. egeirô), to awaken, 55,18 eneimi, to be in, 48,29 eneimi, to be possible, 150,15 enkephalos, brain, 73,18 enkosmios, inside the cosmos, 117,16 enspeirô, to be emplanted, 141,13 (m/p) entelekheia, actualisation, 22,22 enteuxis, reading, 25,32 entheazô, to be divinely inspired, 113,25 enthousiaô, to be divinely inspired, 34,19 epagôgê, induction, 169,9 epalêtheuô, to be true of, 58,13 epanalambanô, to resume, 153,10 epanapauô, to be based on, 199,21 (m/p) epanerkhomai, to go up again, 72,14 epanô, above, 53,20 epantheô, to blossom forth, 130,24 epaphê, contact, 66,2 epaporeô, to ask also, 51,15

epathlon, prize, 25,26 epauxanô, to increase, 81,24 (m/p) epeidon, to look into, 133,28 epeiseimi, to impinge, 81,31 epêreazô, to despise, 185,4 ephikneomai, to touch, 47,14 ephodos, argument, 63,6 epibainô, to preside over, 107,16 epideixis, indication, 170,12 epididômi, to increase, 47,19 epiginôskô (epigignôskô in LSJ), to witness, 45,9 epikeimai, to lie on top, 66,21 epikêros, perishable, 114,10 epilambanô, to occupy, 22,2 epilêsmôn, forgetful, 135,3 epilogos, epilogue, 48,29 epimelês, careful, 102,16 epinaô, to bestow, 106,3 epipan, for the most part, 24,17 epiphanês, well-known, 67,23 epiphora, conclusion, 30,19 epipotheô, to yearn, 193,33 epiprostheô, to cover, 187,18 episkêptô, to accuse, 194,31 episkhô, to occupy, 22,8 episkiazô, to leave in the dark, 119,6 epistamai, to understand, 28,15 epistêmonikos, scientific, 55,8 epitasis, increase, 74,8 epitekhnêsis, artifice, 56,2 epitithêmi, to impose, 26,20 epizêteô, to seek, 34,28 epokhê, position, 83,2 êrema, quietly, 131,23 ergazomai, to make, 76,12 erêmoô, to be bereaved, 142,4 (m/p) erôs, Love, 55,18 eruthrainomai, to blush, 88,18 etumologeô, to derive a word, 119,2 etumologia, etymology, 49,11 euarmostos, harmonious, 84,8 eudiairetos, easy to divide, 76,10 eudiakritos, discriminating, 75,1 euêthês, naïve, 183,32 eukairos, apropos, 90,19 eukinêtos, mobile, 161,9 eukraês, temperate, 84,17 eulutos, easy, 193,29 euporeô, to find a solution, 163,5 eusunkritos, synthesising, 75,2 euthugrammos, rectilinear, 180,10 euthuna, criticism, 136,9 euthunô, to correct, 140,5

Greek-English Index euthuporos, moving in a straight line, 65,31 eutukhês, fortunate, 185,2 exairô, to be raised, 65,32 (m/p) exaitheroô, to be made bright, 65,21 (m/p) exakontizô, to be thrown, 36,17 (m/p) exallassô, to differ, 31,11 (m/p) exêgêtikos, exegetical, 179,29 exeimi, to depart, 100,15 exeptuô, to spit out, 131,30 exesti, it is possible, 124,24 exetasis, examination, 201,10 exetazô, to consider, 194,20 exisasmos, equivalence, 162,28 exomoiôoô, to make similar, 100,24 exôterô, outer, 178,22 geloios, ridiculous, 133,28 gennadas, gentleman, 48,14 gennêtikos, related to reproduction, 123,23 geômetrês, geometer, 128,12 geômetrikos, geometrical, 178,12 gêraskô, to get older, 98,10 gigantikos, gigantesque, 86,4 glaphuros, elegant, 56,17 glukus, sweet, 193,6 gnêsios, authentic, 12,22 gnômê, view, 169,29 gnôstikos, cognitive, 104,4 gnôstos, knowable, 55,17 gônia, angle, 130,3 gramma, something written, 28,12 graphê, what is written, 152,32 gumnasia, exercise, 46,11 gumnos, uncovered, 135,4 haphê, contact, 119,29 hêdeôs, with pleasure, 135,31 hedrazô, to be seated, 65,18 (m/p) hekaterôthi, on either side, 134,31 hekatontapêkhus, of one hundred cubits, 186,16 hêmipodion, half a foot, 186,19 hêmisus, half, 186,18 hermêneuô, to explain, 66,32 hêssaomai, to be diminished, 102,30 heteroeidês, of a different kind, 198,9 heterokinêtos, moved by something else, 53,18 hidruô, to settle, 65,2 (m/p) hidrusis, foundation, 55,20 historia, account, 117,27

207

hololampês, shining everywhere, 85,14 homogenês, of the same genus, 30,4 homognômoneô, to agree, 141,12 homoiôsis, likeness, 97,7 homonoêtikos, harmonious, 115,17 hopêi, how, 157,21 hopôsdêpote (see hopôs dê in LSJ), in any way, 120,9 hugiainô, to be sound, 121,14 humnô, to make hymns to, 93,13 hupagô, to be led, 26,30 (m/p) hupargoreuô, to refer to, 12,11 huperbainô, to be too much, 67,15 huperbaton, hyperbaton, 153,13 huperedrazô (not in LSJ; cf. edrazô), to place above, 86,8 huperidruô, to be seated above, 118,19 (m/p) hupexistêmi, to make room for, 161,12 huphaireô, to take away, 34,26 huphesis, declination, 135,24 huphiêmi, to descend, 138,19 huphizô, to lie at the bottom, 22,23 hupodeigma, example, 198,3 hupodeiknumi, to indicate, 80,29 hupomnêma, commentary, 26,16 huponoia, guesswork, 126,10 hupoptos, under suspicion, 195,13 hupotattô (hupotassô in LSJ), to be subsumed (Iamblichus), 169,5 (m/p) idiôtês, uneducated amateur, 73,25 idiôtikos, amateurish, 191,6 isarithmos, equal in number, 31,15 isêmerinos (kuklos), equator, 25,2 iskhus, strength, 77,32 isodunameô, to mean the same thing, 18,13 isodunamos, having an equal power, 84,6 isokhronios, of the same age, 78,11 isomegethês, equal in size, 84,7 isotakhês, moving with equal speed, 24,23 ithutenês, straight, 180,10 kainoprepês, novel, 59,9 kakotropia, badness of character, 156,27 kakourgia, malice, 183,16 kakourgos, malicious, 182,22 kallos, beauty, 55,18

208

Greek-English Index

katabasis, moving down, 36,31 katadokhê, receiving, 169,16 katakhraomai, to misuse, 28,6 katakrinô, to be judged, 31,6 (m/p) katalêgô, to end, 195,29 katalêptos, capable of being apprehended, 33,13 katamanthanô, to see, 104,32 kataphroneô, to despise, 165,4 kataplêxis, dumbfounding, 131,31 katapsêphizomai, to condemn, 159,8 katapsukhô, to be cooled down, 83,33 (m/p) kataptustos, worthy to be spit upon, 26,30 katathrauô, to be broken into pieces, 85,17 (m/p) katêgoros, prosecutor, 25,25 kateimi, to go down, 36,12 katekhô, to occupy, 169,14 (Iamblichus) (m/p) kathaptô, to touch, 126,11 katharotês, purity, 72,21 katharsis, cleaning up, 119,12 kathêkô, to reach, 48,13 kathôs, seeing that, 163,29 katorthoô, to set straight, 59,6 keleuô, to order, 107,8 kenôsis, emptying, 161,8 kentrikos, central, 65,20 kerannumi, to mix, 130,19 keratoeidês khitôn, cornea, 47,12 khairô, to rejoice, 26,3 kharaktêr, characteristic, 48,33 kheiragôgeô, to be guided, 66,28 (m/p) khiôn, snow, 76,25 khitôn, see keratoeidês khitôn khliaros, lukewarm, 127,19 khôrêtikos, receptive, 76,7 khrêsimos, useful, 67,27 khronios, for a long time, 78,4 khudên, in droves, 184,22 khuma, mass, 84,10 khusis, flow, 40,1 kinduneuô, to be in danger, 161,10 koinônia, commonality, 15,30 koloios, jackdaw, 42,17 (said of Philoponus) kolumbêthra, pool, 66,9 kompazô, to boast, 135,30 korônê, gull, 142,29 koruphê, zenith, 83,9 kosmikos, cosmic, 39,31

krasis, mixture, 130,19 kritikos, being a judge, 184,18 krokodeilos (see krokodilos in LSJ), crocodile, 29,16 kuathos, cup, 81,26 lamprotêta, brightness, 89,8 leptomereia, having fine parts, 30,36 leptotês, fineness, 72,22 lêrêma, absurdity, 75,15 lian, excessively, 75,13 lithôdês, stony, 16,19 logikos, rational, 169,11 (Iamblichus) logismos, reasoning, 135,2 logizomai, to take into account, 82,10 lutta (lussa in LSJ), frenzy, 58,15 makrobios, living a long time, 142,11 makrologeô, to discuss at length, 121,24 maniôdês, mad, 88,28 manôsis, rarefaction, 37,5 marainô, to waste away, 73,30 (m/p) mathêsis, learning, 59,27 megaleiotês, greatness, 139,13 megalorrêmôn, magniloquent, 42,18 meiôtos, subject to diminution, 112,2 mêkhanaomai, to construct, 141,25 mêkhanêma, arrangement, 84,28 mêkunô, to set out at length, 102,15 melania, blackness, 97,24 melanotês, dark colour, 174,33 melitta (melissa in LSJ), bee, 98,7 melopoios, lyric poet, 156,26 mesêmbria, noon, 83,7 metabolikos, changeable, 114,14 metagraphô, to change a text, 171,6 metamelomai, to regret, 46,4 metaskhêmatizô, to change shape, 142,32 (m/p) metastasis, change, 91,16 meteôros, high, 65,33 meterkhomai, to pursue, 92,26 methuô, to be drunk, 134,29 metokhê, participation, 97,11 morphoô, to receive shape, 129,21 (m/p) Mukônos, mush, 135,9 (on which see the note) mutheuô, to be mythical, 135,29 (m/p) nastos, solid, 173,28 naupêgos, shipbuilder, 127,2 nearos, young, 42,17

Greek-English Index nemesaô, to take offence, 26,18 neogenês, new-born, 101,31 nêphô, to be sober, 134,29 neuron, sinew, 78,4 nomos, rule, 28,20 nomotheteô, to decree, 49,21 nukterinos, night, 124,16 oikêma, house, 81,29 oikhomai, to depart, 98,28 okhêma, vehicle, 116,28 okheô, to ride, 27,16 (m/p) oktahedron, octahedron, 12,19 onos, donkey, 148,19 ophelos, use, 72,30 oregô, to desire, 71,14 (m/p) orektikos, desiderative, 123,24 orophos, roof, 173,29 osmê, smell, 97,25 oudamothen, in no direction, 182,8 oxus, high, 184,5 oxutês, acuteness, 97,24 paidia, jest, 176,30 pais, child, 159,3 paizô, to jest, 176,28 pakhunô, to be thickened, 161,6 (m/p) pakhus, thick, 162,1 panteleios, absolutely complete, 39,20 paradosis, teaching, 87,18 paraineô, to espouse, 55,14 parakaleô, to call upon, 119,12 parakharattô (parakharassô in LSJ), to debase, 35,14 parakhôreô, to cede, 66,24 parakhrôsis, slight alteration, 100,20 paraleipô, to leave out, 32,26 paralogismos, fallacy, 26,26 paralogizomai, to be fraudulent, 186,10 paralogos, fallacious, 112,26 paramutheomai, to express, 144,13 parangellô, to urge, 78,9 paraphtheirô, to debase, 26,33 paraplekô, to be woven in, 37,31 (m/p) parapoduomai, to get ready for, 123,4 paraskeuê, siege engine, 139,27 parastasis, showing, 106,26 paratrekhô, to pass over, 42,16 paratripsis, rubbing, 88,20 pareisdusis, entrance, 85,20 pareiskukleô, to digress, 184,8

209

parekduomai, to sneak out, 42,19 paremballô, to bring in, 108,18 parepomai, to accompany, 89,5 paristêmi, to call on, 68,6 parorama, mistake, 122,33 paula, cessation, 122,6 peithô, to persuade, 119,8 pêkhuaios, being a cubit long, 186,15 pelagos, sea, 66,8 pempô, to send away, 101,10 pera, beyond, 107,20 perieimi, to go around, 171,31 perikaluptô, to envelop, 80,5 perinosteô, to wander about, 67,21 periphuô, to grow around, 27,14 (m/p) peripiptô, to fall into, 137,21 peripoieô, to preserve, 200,28 periptuô, to loathe, 185,1 perirreô, to flow around, 65,19 perispaô, to be diverted, 201,8 (m/p) perisphingô, to contract, 161,8 perissartios, odd times even, 29,29 peristrephô, to revolve, 14,16 (m/p) phantazô, to imagine, 134,28 (m/p) phasis, phase, 36,32 Philia, Love, 140,25 (referring to Empedocles) philikos, friendly, 156,14 philosopheô, to be a philosopher, 59,9 philotimia, pride, 170,13 phleps, vein, 78,4 phthanô, to precede, 91,28 phusaô, to be inflated, 74,20 (m/p) phusiologia, study of nature, 31,30 pimplêmi, to be made full, 131,14 (m/p) piston (see pistos in LSJ), trustworthiness, 59,30 pistoô, to confirm, 64,32 (m/p) plagios, lateral, 15,12 plastinx, disk of a balance, 68,15 platos, breadth, 48,12 platus, loose, 135,31 pleonakis, many times, 118,26 pleonekteô, to overbear, 102,29 plêsiasmos, nearness, 72,19 plessô, to strike, 159,8 plinthinos, made of clay, 50,25 pneuma, wind, 36,17 podiaios, one foot long, 186,12 pollaplasiasmos, multiplication, 93,13 polukhronios, lasting a long time, 78,1

210

Greek-English Index

polustikhos, of many pages, 25,29 polutimêtos, much-honoured, 95,24 pôpote, ever, 26,19 porizô, to furnish oneself with, 72,11 (m/p) potimos, sweet, 201,1 pragmateuomai, to deal with, 92,11 prepô, to belong, 23,10 presbus, early, 32,15 proaireô, to choose, 137,27 proaphôneô, to announce previously, 61,6 (aorist) proaxioô (not in LSJ; see Lampe (1961)), to maintain previously, 177,23 (aorist) probainô, to move forward, 66,16 prodeiknumi, to prove first, 162,28 (aorist passive) proeipon, to have said initially, 153,10 proekkeimai, to be set out, 165,10 proektithêmi, to set out, 146,9 progignôskô, to know in advance, 135,14 prokatekhô, to be occupied previously, 22,2 (m/p) prokhôreô, to advance, 186,22 promanteuomai, to foresee, 86,4 pronoêtikos, providential, 143,22 pronoia, foresight, 73,21 prooimion, prologue, 48,29 proomologeô, to be agreed in advance, 64,12 (m/p) prophainô, to emerge, 52,13 (m/p) prophêtês, prophet, 141,26 propheteuô, to act as a prophet, 106,6 prophtheirô, to perish already, 73,19 (m/p) prorrêteon, should be said first, 126,20 prosanankazô, to constrain, 161,17 prosauxêsis, further increase, 43,12 prosdeô, to need in addition, 169,7 prosêgoros, in agreement, 156,10 prosekteon, one should pay attention, 11,15 prosexeuriskô, to devise in addition, 59,13 proskairos, transient, 143,28 proskrinô, to be assimilated, 47,3 (m/p) proslogizomai, to factor in, 79,23 prosphluareô (a hapax not in LSJ), to add nonsense, 193,8

prosphuês, suitable, 178,7 prosthaphairesis, addition and subtraction, 36,30 prothumia, desire, 25,28 proupokeimai, to be laid down in advance, 59,29 ptênos, winged, 79,11 ptêsis, flight, 79,11 puknos, dense, 54,13 puramis, pyramid, 12,19 puretos, fever, 73,20 sathrotês, unsoundness, 165,4 sebomai, to reverence, 74,15 selis, a papyrus column (translated ‘page’), 25,33 sêmasia, meaning, 119,6 sêmeron, today, 138,6 semnunô, to glorify, 57,19 sêpedôn, putrefaction, 131,15 sêpô, to putrefy, 131,12 (m/p) sidêros, iron, 113,15 skaptô, to be dug, 191,1 (m/p) skedastos, prone to scatter, 65,12 skênoma, tabernacle, 141,27 (Septuagint) skiamakhia, jousting with shadows, 185,2 skôlêx, worm, 98,17 skopeô, to investigate, 189,18 skulakion, puppy, 101,31 sophia, wisdom, 25,33 sôphroneô, to be of sound mind, 89,7 speudô, to strive, 65,14 sphallô, to make fall down, 35,18 sphêx, wasp, 98,7 sphodra, very, 185,26 sporadên, scatteredly, 178,27 stasiazô, to conflict, 115,18 stegô, to hold onto, 134,31 stenokhôreô, to be pressed, 189,29 (m/p) stereôma, firmament (Septuagint), 90,17 sternon, chest, 48,28 stikhos, line (of writing), 124,18 stoikheiôdês, of an element, 85,21 stoikheiokratôr, ruler of the elements, 107,15 stratêgos, general, 87,6 stratopedon, army, 87,7 sukê, fig-tree, 30,2 sukophantês, bribed witness, 163,12 sullegô, to gather, 67,21

Greek-English Index sulluoô, to be dissolved simultaneously, 105,17 (m/p) summartureô, to also give support, 71,20 summenô, to endure together, 83,30 sumparatheô, to move along with, 95,13 sumperipoleô, to revolve with, 20,25 sumpherô, to be carried along with, 42,24 (m/p) sumphônia, harmony, 143,16 sumphtheirô, to perish along with, 156,19 (m/p) sumphuês, inborn, 143,26 sumphurô, to be blended together, 131,14 (m/p) sumphusis, blending, 85,31 sumpleonazô (not in LSJ), to be magnified along with, 81,28 (m/p) sumplêrôtikos, filling out, 167,15 sumplokê, combination, 26,26 sumproerkhomai, to proceed together with, 94,15 sunalatheuô, to be true together, 136,7 sunanakerannumai, to be mixed together, 85,27 sunanakineô, to be stirred up together with, 55,10 (m/p) sunantaô, to meet, 197,25 sunapelenkhô (not in LSJ; see Lampe (1961)), to be refuted as well, 66,14 (m/p) sunapodeiknumi, to demonstrate together, 41,32 sunapokatastasis, keeping pace together, 37,35 sunarmozô, to harmonise, 156,21 sunauxanô, to expand along with, 82,1 (m/p) sundesis, binding, 84,32 sundromê, coincidence, 97,31 sunêgoria, support, 72,11 sunêgoros, providing support, 67,24 suneisagô, to bring, 198,67 sunekphainô, to appear together, 130,30 (m/p) sunektrekhô, move along with, 87,10 sunemphainô, to also indicate, 118,24 sunephaptomai, to join in, 201,1 sunergos, working together, 119,12 sungeneia, kinship, 43,25 sungramma, work, 49,11

211

sungraphê, book, 67,15 sungraphô, to write down, 176,14 sunkataskeuazô, to be established together with, 38,21 (m/p) sunkhôrêsis, agreement, 188,21 sunkhraomai, to use, 45,16 sunkrasis, comparison, 113,8 sunkrima, composition, 84,20 sunkrisis, comparison, 17,28 sunkritikos, comparative, 74,8 sunkrouô, to bring into conflict, 131,21 sunkukaô, to mush together, 135,9 sunneusis, convergence, 65,24 sunophruoomai, to frown, 88,19 sunôtheô, to push, 161,10 suntaxis, ordering, 156,24 sunteleia, completion, 88,3 suntomia, brevity, 178,27 susphinxis (not in LSJ; see Lampe (1961)), being held together, 46,3 sustasiôtês, member of the same sect, 91,18 sustrephô, to get serious, 136,11 (m/p) takhos, speed, 31,12 takhutês, speed, 143,4 tapeinos, low, 37,23 tarattô (tarasssô in LSJ), to be disturbed, 140,9 (m/p) tegos, roof, 40,18 tekhnitês, craftsman, 180,8 teleiôtikos, bringing completion, 97,10 telmation (cf. telma in LSJ), swamp, 66,9 temnô, to cut, 181,33 têrêsis, observation, 117,25 tetragônon (see tetragônos in LSJ), rectangle, 14,14 themelioô, to establish, 141,29 (Septuagint) theogonia, theogony, 93,11 theôrêma, theorem, 188,19 theôria, investigation, 195,14 theosebeô, to honour god, 26,4 theosebês, reverential, 26,13 thêratês, searcher, 25,23 thermasia, heat, 83,5 thermê, heat, 115,2 thôlôdês, turbid, 65,21 thrêskeia, worship, 141,25 thruleô, to chatter, 26,10 thumikos, relating to desire, 123,23

212 timê, esteem, 26,8 timiotês, value, 55,22 timôria, retribution, 84,29 tolmêma, adventure, 25,34 tolmêros, rash, 134,26 trakhus, rough, 26,17 trekhô, to run, 184,4 triodos, trivium, 131,28 tripêkhus, three-cubit, 47,9 trokhos, wheel, 15,2 tropaion, trophy, 200,24

Greek-English Index trugê, sludge, 84,24 trugôdês, sludgy, 84,21 tupoô, to depict, 177,18 tupos, impression, 184,17 zêtêtikos, making enquiry, 158,32 zô, to live, 67,25 zôidiakos (ho), zodiac, 14,25 zôigonos, (no iota subscript in LSJ), generating life, 115,6 zôikos, animal, 53,17

Index of Passages (a) Passages quoted by Simplicius For Philoponus and Alexander see Appendices 1 and 2. In section (b) of Textual Questions I indicate places where Heiberg’s text of a quotation deviates from standard versions. ALCAEUS

Fragment 393 (Campbell (1982)): 156,26 ARISTOTLE

Categories 5, 3b27: 168,21; 5, 4a10-11: 157,26-158,1; 14, 15a22-4: 111,30 De Caelo (outside of 1.3, 270a11-4) 1.2, 268b14-18: 132,22-5; 1.10, 280a31-2: 140,21; 1.11, 280b11-12: 120,25-6; 1.11, 280b13: 120,27; 1.11, 280b15-16: 120,21-2; 2.1, 284a14: 112,18-19; 4.4, 311a16-29: 160,34 Metaphysics 8.4, 1044b3-8: 134,3-7; 8.5, 1044b27-9: 135,16-18 On Coming to be and Perishing 2.3, 330b30-331a3: 169,30-170,4 Physics 1.5, 188a22-6: 130,1-4; 1.5, 188a31-b26: 124,25-125,20; 1.5, 188b1-2: 121,16-17; 1.5, 188b12-16: 121,17-20; 1.5, 188b16-21: 129, 15-19; 1.7, 190a17-20: 122,25-7; 1.7, 190a18-20: 128,23-5; 1.7, 190b1-5:

129,11-14; 1.7, 191a3-4: 133,13-14; 1.7, 191a3-7: 125,25-8; 1.7, 191a13-14: 126,1-2; 1.8, 191a27-31: 137,7-11; 4.9, 217a26-7: 166,7-8 EMPEDOCLES (DK31) B17,7-8, 10-13: 141,1-6 MELISSUS (DK30) B7, 7-8: 113,21 PARMENIDES (DK28) B8, 6-9: 137,3-7 PLATO

Laws 8, 894A1-8: 103,23-8 Timaeus 27D6-28A4: 104,5-8; 28B6-8: 104,10-12; 38B6: 105,9; 38B6-7: 105,15-16; 38B7-C3: 105,20-3; 39E1-2: 105,28-30; 41A3-D3: 106,6-25; 41B2-4: 107,2-4; 41B4: 106,4; 41C3-5: 107,11-12; 41D2-3: 107,14-15 PLOTINUS

Ennead 2 (Wilberding (2006)) 1,12-14: 115,30-1 SEPTUAGINT (Rahlfs (1935)) Psalms 18.5: 141,27; 104.5: 141,29-142,1

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

In Metaph. (CAG 1) 22,2-3: 133,29; 169,18-19: 133,29; 375,37-376,1: 133,29 ARISTOPHANES

Wasps (Wilson (2007)), 1019: 145,26

ARISTOTLE

Categories 5, 3b24-5: 168,19: 5, 3b24-7: 123,16; 157,34; 5, 3b27: 168,21; 7, 6b15-19: 123,29; 8, 8b26-7: 173,31; 10: 128,25; 173,26; 14, 15a22-4: 111,20; 114,11

213

214

Index of Passages

De Anima 2.1, 412a11-21: 200,11; 2.7, 318b3-20: 124,12 De Caelo (outside of 1.3.270a11-14) 1.1, 268a6-7: 178,33; 1.2, 268b20-2: 146,10; 1.2, 269a18-30: 91,29; 1.9, 278b3-4: 135,18; 1.9, 279a7-9: 135,18; 1.10, 279b12-17: 139,27; 1.10-12: 103,7; 1.11, 280b6-20: 119,14; 1.11, 280b14-16: 120,29; 1.11, 280b20-23: 120,29; 1.12: 103,8; 2.1, 283b26-30: 120,29; 2.6, 289a19-28: 124,15; 3.8, 307b8-9: 123,28 De Sensu 4, 442b19-20: 123,28 Metaphysics 5.14, 1020a32-b2: 166,21; 12.6-9: 116,29 On Coming to be and Perishing 2.3-4: 168,28; 2.3, 331a1-3: 168,28 Physics 1.7, 190b12-14: 128,20; 1.7, 191a3-7: 101,15; 102,11; 1.7, 191a13-14: 102,12; 168,23; 5.1: 101,2; 8.1, 250b30-251a3: 140,32; 8.6: 116,29; 8.6, 259b32-260a19: 200,17; 8.8, 261b28-262a17: 151,4; 8.10: 142,22 Topics 2.10, 114b37-115a14: 146,16; 6.11, 148b27: 187,18 [ARISTOTLE]

De Mundo 1, 392a4-8: 119,4 On Plants 2.4, 825b14-18: 124,5 ATTICUS

Fragments (des Places (1977)) 5: 112,8 DEXIPPUS

in Cat. (CAG 4.1) 51,23-53,25: 165,13 EUCLID

Elements 1 (Heiberg (1883)), prop. 1: 180,22 HERMEIAS OF ALEXANDRIA

Commentary on the Phaedrus (Couvreur (1901)) 111,25-6: 133,29 HIEROCLES OF ALEXANDRIA

Commentary on the Golden Verses (Koehler (1974)) 120,6-8: 133,29 HOMER

Iliad (West (2000)) 22, 26: 131,8 Odyssey (Van Thiel (1991)) 19, 163: 131,8 IAMBLICHUS

On The Mysteries (des Places (1966)) 159-60: 133,29 JOHN PHILOPONUS

Against Proclus 4.14, 93,23: 106,7; 6: 107,23; 139,27; 6.7. 144,6-15: 107,4; 6.29, 235,4-8: 143,11; 8.3,

307,14-309,12: 123,12; 9: 136,17; 11: 135,28; 11.5, 423,13-424,4: 163,31 in Cat. (CAG 13.1) 48,7-27: 173,31; 64,9-68,9: 166,21; 74,13-27: 165,13; 169,30; 144,2-14: 173,31; 179,18-21: 124,12 in De An. (CAG 15) 341,10-342,16: 124,12 in GC (CAG 14.2) 229,22-230,7: 169,30 in Phys. (CAG 17) 557,8-589,26: 173,25 On the Creation of the World (Reichardt (1897)) 2.6: 124,12; 5.5, 216,22-3: 124,5 PLATO

Parmenides 137E3-5: 187,18 Phaedrus 243B6: 135,4; 245D1-3: 93,19; 264B6: 136,12 Sophist 252C6-9: 145,26; 256A6-7: 139,34 Statesman 269C4 ff.: 143,20; 269D7-E2: 96,19; 104,32; 270A5: 143,23 Timaeus 28A5-6: 93,1; 126,24; 30B3-4: 200,10; 31B5-6: 140,10: 38B6:140,10; 41A3-B6: 143,11; 41A3-D3: 154,16; 41A7-B6: 108,28; 143,13; 41A7-D3: 138,25; 143,30; 41B3-5: 108,32; 56D5-6: 105,34; 58C5-8: 131,1 PORPHYRY

in Cat. (CAG 4.10) 132,12-19: 111,8 PRISCIAN OF LYDIA

Paraphrase of Theophrastus (Bywater (1886)) 8,15-16: 124,12

PROCLUS

in Euc. (Friedlein (1873)) 109,21: 187,18 Platonic Theology 1 (Saffrey and Westerink (1968)) 91,27-92,1: 133,29 SCHOLIA ON LUCIAN (Rabe (1906)) 246,15: 140,31 SIMPLICIUS

in Cael. (other than the text translated here): 8,12-14; 178,33; 18,9-15: 117,15; 21,14-25: 164,32; 26,23-8: 170,12; 34,13-21: 164,32; 35,12-20: 164,32; 55,25 ff.: 171,22; 73,12-15: 142,19; 89,4-7: 124,9; 293,11-301,28: 139,27; 438,30-439,13: 124,15 in Cat. (CAG 8) 65,2-13: 173,31;

Index of Passages 87,24-102,10: 166,21; 105,24-110,25: 165,13; 105,27-106,2: 169,9; 106,28-107,3: 169,22; 107,25-30: 169,22 in Phys. (CAG 9 and 10): 53,26: 140,32; 111,23-4: 113,21; 113,8-9: 113,21; 158,1-159,4: 140,32; 233,3-10: 126,1; 601,1-645,19: 173,25; 686,19-690,17: 166,8; 801,6-9: 101,2; 1064,3: 100,20; 1129,29-1152,19: 201,10; 1140,24: 137,11; 1144,7: 137,11; 1156,28-1169,9: 201,10; 1171,30-1182,39: 201,10; 1326,38-1336,34: 201,10; 1360,24-1363,24: 154,9

SIMPLICIUS(?)

215

in de An. (CAG 11) 133,7-21: 124,12 STRABO

Geography (Radt (2002-9)) 10.5.9: 135,9 THEMISTIUS

in Cael. (CAG 5.4) 14,23-6: 131,22; 19,20-3: 177,4; 20,4-6: 188,6; 20,8-11: 189,2 VALERIUS MAXIMUS

Memorable Doings and Sayings (Shackleton Bailey (2000)) 8.14.ext. 5: 200,32

Index of Names (a) Names mentioned by Simplicius In many cases information on an item 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. Alcaeus: 156,26 (his words ‘the pig is worked up again’ referred to Philoponus) Alexander (of Aphrodisias): 52 occurrences; see Appendix 2 Anaxagoras: 119,2; 270b24 (calls fire aithêr) Aquarius (Hudrokhoos, sign of the zodiac): 193,15 Aries (Krios, sign of the zodiac): 181,26.28.29.32; 182,2.3.7; 185,29.30; 186,3; 193,13.14.16.18.20 Aristotle: 92,31 (does not contradict Plato on the everlastingness of the cosmos); 101,1 makes metabolê the genus of all sublunary tropê); 102,12 (says that the general principles of coming to be are form, privation, and substratum); 103,4 (the only thing he calls coming to be is the change in time from not being into being); 103,19 (always wants to use as assumptions things which are clear to everyone); 110,24 (does not invoke nourishment and growth in arguing that the cosmos does not increase in size); 111,11.22.30; 112,27; 113,27; 114,4.11.29 (when he says that heaven does not alter he means that it does not alter in affection); 112,8.25 (Alexander argues against those who say Aristotle holds that heaven is without qualities); 115,30 (Plotinus on his belief in a fifth element); 116,27 (Alexander is wrong to think that in chapters 2 and 3 Aristotle establishes that there are gods); 119,11.14.16.22.26.31;

217

120,5.7.14.16.20.24 (dispute with Philoponus over Aristotle’s distinction among senses of genêtos); 121,9.11.15.16.20.25.28; 122,10.18.24.28; 123,16.25; 124,14.18.22.24; 125,22; 126,7.8.11.14; 129,9.26.29;130,5; 131,18 (dispute with Philoponus about whether Aristotle believes all coming to be involves contraries in the strict sense, as opposed to form and privation); 128,16 (the meaning of ‘contraries’ at 270a22); 131,21.24.26(2) (dispute with Philoponus about whether Themistius corrected or correctly interpreted Aristotle); 131,33; 132,3.18.19.31; 133,1.6.11 (dispute with Philoponus on the question whether for Aristotle there is a privation corresponding to every form); 134,2; 135,10.14.32 (discussion of the matter of heaven); 136,14; 137,7; 139,1.14.20 (dispute about whether coming to be always requires a substratum); 139,24.27; 140,9.18.20.23; 141,10; 142,22; 143,10(2).11.12; 143,31 (dispute with Philoponus about whether all the earlier philosophers agree that the cosmos is everlasting); 151,26; 152,3.27; 153,12 (dispute with Alexander of Aphrodisias over the interpretation of 271a22-33); 154,8 (believes that god is an efficient cause); 157,27.33; 158,30; 159,35; 160,7.22.33; 161,2.31; 162,14.20.26 (dispute with Philoponus over whether Aristotle is correct to say

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Index of Names

that the kinêseis of contrary things are contrary); 163,29.34; 164,1.11.17; 165,7.11.33; 166,8; 168,17; 169,23.28 (dispute with Philoponus over Aristotle’s implicit speaking about contraries of substance in De Caelo and his claim in the Categories that substance has no contrary); 170,23.25.27 (dispute with Philoponus over whether in 270b32-271a5 Aristotle is talking about contrariety of lines or of motions on lines); 171,33; 172,5; 173,24; 174,6.14.17; 175,10; 176,7; 191,19; 192,11; 199,3 (dispute with Philoponus over the relevance of various forms of contrariety to Aristotle’s claim that circular motion has no contrary); 177,23 (discussion of whether one motion toward the centre is contrary to the infinitely many motions away from the center); 179,29.33; 180,27(2).30; 181,7.20 (dispute over whether Aristotle claimed that the straight line is the measure of every length, as opposed to every distance); 188,28 (dispute, involving Themistius, over whether the argument of 271a13-19 is new); 194,1 (gives argument for the necessity of the sun’s motion on the ecliptic later); 195,11.18; 196,3.7.21; 197,7; 198,3.27 (discussion of whether motions on two circles, notably the zodiac and the ecliptic, are contrary); 199,31 (says in Physics 8 that heaven is moved by a higher cause); 200,10 (says that soul is the actuality of a natural body, not just of a body); 200,18 (proposed in De Caelo to prove that heaven is everlasting on the basis of its natural motion); 92,29; 101,15; 102,20; 103,2; 107,20.22.25; 108,3; 154,16.18; 156,29; 157,7.22; 170,11.19; 176,15.27.33; 177,1; 179,22.24; 182,11; 185,8; 186,22; 189,6.20.31; 190,27; 191,10.12.21; 194,10; 198,14; 200,26; 201,2.6 (other mentions of less interest) Aristotle of Mytilene (teacher of

Alexander of Aphrodisias): 153,17 (his formulation of the argument that there is no contrary to motion in a circle as presented by Alexander) Artemis, Ephesian: 200,31 (Philoponus compared to the person who set the temple of Artemis on fire in an attempt to become famous) Augeus, dung of: 136,1 (metaphor for Philoponus’ arguments) Babylonians: 117,27 (kept records of astronomical observations for no less than 1,440,000 years!) Cancer (Karkinos, sign of the zodiac): 181,27 Categories (Katêgoriai): 111,30;114,10;123,16; 128,25; 130,4; 157,34; 158,26.33; 159,19; 165,12.30.34; 166,17.25; 167,10.25; 168,18; 169,3 Charybdis: 165,9 (Philoponus called by this name) David: 141,26 (a prophet according to the Jews) Democritus: 129,30; 130,1 (Physics 1.5, 188a22-6 quoted to show that Aristotle thought shapes could be contrary) Diagoras of Melos: 116,25 (example of atheist) Diogenes: 148,19 (says that donkeys go after food and drink in a straight line) Empedocles of Acragas: 139,3 (mentioned by Aristotle (De Caelo 1.10, 279b16) as a person who believed in alternating worlds); 140,25 (according to Simplicius made the distinction between the intelligible and the perceptible world); 140,31 (quotation of DK31B17, 7-8, 10-13) Heraclitus of Ephesus: 139,34 (mentioned by Aristotle (De Caelo 1.10, 279b16) as a person who believed in alternating worlds) Hippon (in plural): 116,24 (example of atheist) Egyptians: 117,25 (kept records of astronomical observations for no less than 630,000 years!) Ethiopian: 157,30 (example)

Index of Names Eurycles: 142,26 (Philoponus’ arguments compared to people who carry Eurycles in their stomachs) Gemini (Didumoi, sign of the zodiac): 181,26; 182,2; 193,16) Greeks: 117,4; 139,29; 270b7 (all have a conception of the gods and assign heaven to the divine) Heracles: 119,12 (called upon for aid in the combat with Philoponus) Hermes: 126,28; 127,1; 137,15 (in all three cases mentioned in connection with the carving of a stone statue) Iamblichus: 169,2 (his commentary on the Categories quoted) Jews: 141,26 (regard David as a prophet) John Philoponus: never referred to by name; see Appendix 1 Laws (Plato’s dialogue): 103,23 (cited to show that Plato knows the ordinary sense of ‘come to be’ as well as the sense in which things come to be from the One) Libra (Zugos, sign of the zodiac): 181,28.33; 182,4.7; 185,29.31; 186,1.3 Melissus: 113,21 (a version of DK30B7, 7-8 quoted to support the view that what alters in any way will eventually perish); 140,4 (Aristotle’s interpretation of him) Metaphysics (Meta ta phusika): 116,29; 134,2 Olympus (mountain): 142,13.30.32 (Philoponus’ claim that it has never changed size disputed by Simplicius) On Coming to be and Perishing: (i) Peri geneseôs kai phthora: 168,27; 169,30; (ii) Peri geneseôs: 168,30 On the Heavens (Peri ouranou): 135,18.32; 201,6 Parmenides: 137,1 (the first person we know by hearing to have held that what is does not come to be from what is not; DK28B8, 6-9 quoted) ; 140,4 (Aristotle’s interpretation of him) Peripatetics: 134,10 (Philoponus thinks that what they call the second substratum is matter) Phaedrus (Plato’s dialogue): 93,19

219

(cited for the doctrine that a first principle does not come to be) Physics: (i) Phusikê akroasis, 92,9.26; 101,15; 108,20; 116,29; 122,12; 124,23; 131,25; 133,11; 144,10; 167,27; 168,23; 199,31; 201,3; (ii) Physika, 101,2; 116,2; 122,25; 129,30; 131,29; 198,16; (iii) Physikê, 121,22; 200,17.23 Pisces (Ikhthues, sign of the zodiac): 139,15.17.20.25 Plato: 93,2; 126,24 (says it is impossible for anything to come to be without a cause at Timaeus 28A); 103,21 (knows of coming to be in the ordinary sense); 104,18 (the meaning of ‘is destroyed’ at Timaeus 28A3); 104,29 (thinks that there is change in the cosmos because it is corporeal); 105,7.28.32; 106,26; 107,5 (thinks the cosmos is everlasting); 108,32.34 (what he means when the creator says at Timaeus 41B3 that the gods will not be destroyed because of his will); 131,1 (thinks light is a form of fire); 140,10.20.21.24 (Aristotle understands that he thinks that the cosmos is everlasting); 143,11 (Like Aristotle, thinks that a finite body has finite power); 143,13 (says that heavenly things are indissoluble because of the will of god); 143,30 (separated in discourse the goodness of the creator from the natural existence of the cosmos in the Statesman); 154,16 (says that the unmoving cause makes what it makes on its own everlasting); 200,10 (says that what has mind must have soul); 92,30; 96,19; 103,3; 106,4.6; 107,22.24; 143,39 (other mentions of less interest) Plotinus: 115,30 (Enneads 2.1, 12-14 cited in connection with Aristotle’s reference to assumptions at 270b3) Proclus: 135,28; 136,17 (two mentions of Philoponus’ Against Proclus) Pythagoreans: 140,26 (Like them, Empedocles wrote in an enigmatic way) Rome: 195,8 (what is cold in

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Index of Names

Alexandria is contrary to what is hot in Rome) Sagittarius (Toxotês, sign of the zodiac): 182,3; 185,31 Saturn (Kronos, planet): 199,24 (Philoponus believes that its sphere moves more slowly than the planetary spheres under it) Scorpio (Skorpios, sign of the zodiac): 181,29 Socrates in the Phaedrus: 93,19 (shows that a first principle does not come to be (245D1-3)) Son, the: 137,28 (Christians say that he is dependent upon god’s goodness and the eternal permanence of god’s existence) Statesman (Plato’s dialogue): 96,8; 104,31; 143,20

Scythian: 157,31 (example) Taurus (Tauros, sign of the zodiac: 181,26; 182,2; 193,16.18.21.25 Themistius: 131,21.22.24 (said by Philoponus to have corrected Aristotle, whereas Simplicius thinks he has correctly understood Aristotle); 176,32; 177,1.9 (Philoponus’ response to his interpretation of 271a5-10 rejected by Simplicius); 188,6.26.30 (Philoponus’ denial of Themistius’ claim that the argument of 271a13-19 is the same as that of 271a10-13 rejected by Simplicius) Timaeus (Plato’s dialogue): 104,3; 105,8

(b) Scholars cited in the Introduction and in the notes to the Translation This index does not include editors or translators of texts unless they are mentioned for their position on an editorial or interpretive issue; reference to a page and line of the text translated indicates the place of a note in which the scholar in question is mentioned. 126,1; 131,4; 135,9; 138,10; 140,19; 141,2(2).27; 149,16; 152,1; 156,26; Allan, D.J., The text commented on, n. 157,31; 165,35; 169,31.32; 173,9; 3; 152,4 174,2; 178,14.30; 181,4.20; Baltes, Matthias: 108,30 185,2.29; 187,12; 189,19; 196,9.13; Bergk, Theodor: Introduction, n. 28 197,3.20; 198,2; 200,4 Bessarion, Basilius: Introduction, p. Joachim, Harold H.: 169,30.31.32 21; 106,15; 140,19; 149,16; 185,29; Karsten, Simon: Introduction, pp. 21, 197,20 22; 94,5: 96,11; 97,22; 106,15; Boniz, H.: 137,11 117,8; 118,23; 120,12; 123,2; Bossier, F., Introduction, p. 21; 120,3; 124,30; 125,4.19; 135,9; 140,19; 138,10; 157,31; 174,2; 197,3 141,2; 146,25; 149,16; 152,1; Cornford, F.M.: 106,10 156,26; 169,31.32; 178,15; 185,29; Davidson, Herbert A.: 119,14 187,12; 196,9.13; 197,20; 198,2; Évrard, Étienne: 124,12 200,4 Gantz, Timothy: 136,1 Kazhdan, Alexander P.: 105,24 Giannantoni, Gabriele: 148,19 Leggatt, Stuart: 152,4 Hankinson, R.J.: Introduction, p. 21, Longo, Oddone: Introduction, n. 17 n. 3; 94,5; 95,17; 96,11; 97,15; Moraux, Paul: Introduction, p. 22; 98,8.22; 106,4; 108,21; 147,9; 139,33; 140,23; 146,25; 152,4; 148,19; 149,16; 152,10; 154,17; 153,17; 169,2 155,12 Mioni, Elpidio: Introduction, p. 21 Heiberg, J.L.: Introduction, pp. 20, 21, Peyron, Amadeo: Introduction, n. 95 22; 96,11; 97,15.18; 97,22.30; 98,10; Rahlfs, Alfred: 141,27.28 100,13; Rivaud, Albert: 104,5; 106,4.7.10.12.14.15.17.24.25; 106,7.10.12.14.15.17.24.25 109,5.25; 118,23; 120,3.12; 122,25; Rescigno, Andrea: Introduction, n. 3; 123,2; 124,30; 125,4.5.25.26.27;

Index of Names 108,30; 110,14; 112,8; 152,10.32; 194,25 Ross, W.D.: 122,25; 124,29.30; 125,3.4.5.25.26; 126,1; 129,11.30; 137,11 Sorabji, Richard: Introduction, n. 13; 123,18; 143,11 Wartelle, André: Introduction, pp. 20, 21, 22

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Whittaker, John: 93,20; 104,5 Wildberg, Christian: Introduction, p. 22 n. 3, also n. 3(2), n. 10; 119,14; 124,12; 141,19; 173,9; 174,2; 180,22; 187,16; 194,23.24; 197,3 Wright, M.R.: 140,32; 141,2(2)

Subject Index aithêr: 118,16-24; 119,2-6 changes, active and passive: 159,26-162,14 coming to be (and perishing): the senses of: 92,27-107,19; the senses distinguished by Aristotle: 119,13-121,4; coming to be of Being, heaven, and the cosmos from the One: 92,33-98,15; 137,16-138,31; 199,27-200,21; its place in the sublunary world: 98,15-102,31; does all coming to be involve contraries in the strict sense or does some involve form and privation? 121,4-131,31 concavity and convexity: 145,26-146,1; 173,25-176,12 confidence, confirmation (pistis): 116,5-15; 118,11-13 consensus among philosophers: 139,23-142,7 contraries: 97,17-100,15; 101,11-102,14; 109,8-15; 123,11-124,17; 128,16-129,3; 173,10-25; 175,4-176,12; 177,1-179,23; 185,23-187,16; contrary motions: 145,12-16; 146,1-11; 146,18-147,21; 147,23-148,14; 148,28-149,28; 150,3-19; 150,23-154,5; 171,17-172, 33; 185,3-22; 187,28-189,4; 189,28-194,5; 196,34-198,6; is planetary motion contrary to the motion of the sphere of the fixed stars? 154,18-156,24; 194,21-196,34; do contrary things have contrary changes (motions)? 157,26-170,7 criteria and measures: 183,21-184.27; 187,16-27 eternity and time or everlastingness: 93,25-94,1; 94,8-95,17; 97,12-17; 105,25-106,4 god, an efficient cause: 154,6-17

heaven: does not come to be or perish: 91,25-92,21; 107,26-108,14; does not increase or diminish: 109,18-110,32; the sense in which heaven changes in quality and the sense in which it does not: 97,5-17; 111,3-115,20; Aristotle’s view that heaven and the cosmos are everlasting: 103,4-21; the sense in which Plato says heaven comes to be and the sense in which he denies it: 103,21-107,19; 108,28109,8; long-time observation confirms its everlastingness: 117,21-118,9; 142,7-143,9 hupekkauma: 164,24-165,2 infinite and finite: 146,18-147,21 lines and motions: 170,22-171,17 mathematics and physics: 178,7-179,23 matter: 133,21-136,12; 139,9-12 privation and form: 101,19-102,14; is there a privation corresponding to the form of heaven (or the cosmos)? 122,2-14; 132,4-133,19 simple motions and simple bodies: 144,29-145,9 straight line as measure of length or of distance: 179,24-181,20; 182,17-183,21 substance: has no contrary: 102,23; 123,11-17; 157,32-158,11; 159,13-16; 165,10-170,7; in what sense substance comes to be: 98,15-30; 101,11-102,31; 126,20-127,9; 129,6-19; substance and quality: 157,32-158,11; 163,10-170,10; 172,33-173,10 substratum and coming to be or change: 99,24-101,2; does the cosmos come to be from what is not? 136,12-138,31 zodiacal motions and distances: 181,20-182,17; 185,23-186,7; 193,7-26

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