Philoponus: On Aristotle Physics 4.10–14 9781472552006, 9780715640883

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Philoponus: On Aristotle Physics 4.10–14
 9781472552006, 9780715640883

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Preface Richard Sorabji This commentary by Philoponus, translated here by Sarah Broadie, discusses Aristotle’s treatment of time in his Physics Book 4, Chapters 10-14, and it creates a surprise. The other parts of Book 4 of Aristotle’s Physics concern place and vacuum, and the supposed impossibility of motion in a vacuum. On all these subjects Philoponus’ commentary offered innovative corrections of Aristotle which were a genuine contribution to science. These corrections were not all confined to the two digressive ‘Corollaries’ on place and vacuum, which interrupt the commentary. In those Corollaries Philoponus argued against Aristotle that a body’s place is not its immediate surroundings, much less the inner surface of its immediate surroundings, but is a three-dimensional extension that it occupies. This concept of place as space does not exclude place being an empty vacuum, even though extraneous reasons may require it always to be occupied.1 Nor, says Philoponus to the later acclaim of Galileo, would motion in a vacuum be impossible. The absence of resistance in a vacuum does not (absurdly) imply that movement would take no time, but only that it would not require extra time to overcome resistance.2 The heavens take time to rotate, according to Aristotle himself, even though they meet no external resistance.3 Philoponus attacked Aristotle’s explanation of the motion upwards and downwards of earth, air, fire and water in terms of their having a natural place.4 He recorded experiments anticipating Galileo with the dropping of different weights from a height, to establish that speed of fall is not proportional to weight.5 Pantelis Golitsis has rightly pointed out that when innovations in the Corollaries are not reflected in the main commentary, this need not imply a change of view

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by Philoponus, since he warns that he is saving criticisms for the Corollaries.6 But an enormous innovation does occur in the main commentary itself. The motion of projectiles after they have left the thrower’s hand depends, in Aristotle’s view, on the hand turning pockets of air into no-longer-moved movers of the projectile, and so requires air, not vacuum. But if that were the case, Philoponus complains, artillery could shoot projectiles by means of bellows blowing air at its projectiles. Instead, we should postulate impetus, that is, a force implanted by the thrower directly into the projectile, not into the air.7 Thomas Kuhn has called that a scientific revolution. After that, we turn with anticipation to Philoponus’ commentary on the last part of Aristotle’s Physics Book 4, concerning time. We have all the more reason to do so, because of the history of objections against Aristotle on time that were surely known to Philoponus. The doctor Galen had taken Aristotle to task for drawing the inference that time itself requires change from the premiss that our thoughts have to change when we notice time.8 He also charged Aristotle’s definition of time with circularity because of its reference to prior and posterior. Themistius had defended Aristotle against this charge,9 and Themistius was tacitly used in Philoponus’ own commentary on the Physics no less than 600 times, in the estimate of its editor, Vitelli.10 Further, the head of the Aristotelian school, Alexander, had written a separate treatise on time,11 and had defended Aristotle’s claim that time depends on consciousness,12 although Themistius in his commentary on Physics Book 4 was not to be satisfied with Alexander’s defence.13 Themistius’ objection is part of a series of arguments he gives against Aristotle’s treatment of time.14 In his treatise, Alexander put forward a view that goes beyond Aristotle, that the instants by which we divide time into past, present and future exist only in the mind.15 The surprise comes when we find that Philoponus’ commentary on the part of Physics Book 4 that concerns time is a straight exposition, with little objection or defence of Aristotle. This cannot be because it was too early in his career for him to have thought of criticisms, because the main part of Philoponus’ commentary on Book 4 on time is the one piece of commentary that allows us to date it precisely. A reference at the very beginning of the commentary on 4.10, at 703,16-

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17, dates the writing to 517 AD. His teacher, Ammonius, would then have been near the end of his life, and this commentary of Philoponus is not one of those that are described as being taken from the seminars of Ammonius. There would have been ample time for the brilliant Philoponus to think about the wealth of past criticisms and suggestions, and to work out his own position. One explanation would be provided by Verrycken’s controversial view that the commentary written in 517 represents a non-combative early strand, and that all revision came later as a result of religious conversion, and was added into parts of the early strand.16 But why was it not added into the comments on time? So far we might be drawn to a different explanation. Different commentaries reflect lectures to different levels of student. I suggested in the preface to Owen Goldin’s translation of the commentary on Posterior Analytics Book 2, that the difference from Philoponus’ commentary on Book 1 might be due not to its being by a different author, but to its reflecting Philoponus’ lectures to a more elementary level of student. Might the commentary on Aristotle’s treatment of time similarly reflect lectures to a more elementary group of students than those who were regaled with the lectures on Physics Book 4, Chapter 8, introducing impetus theory? It is the difference between these two parts of the main commentary on Book 4 that we need to explain. If the reason lies in the level of the audience, our expectations of the content of the commentary would have been pitched too high, although we would be getting clearer about the circumstances of Philoponus’ writing. But even if this explanation is correct, it does not provide the whole story, as is shown by two passages on which Sarah Broadie has commented and to which she has drawn my attention. Within the commentary on Physics 4.13, translated here, Philoponus makes one of three references17 to his still earlier commentary on Book 8 of Aristotle’s Physics. He tells us that he had there refuted Aristotle’s attempt to show that motion exists always – in the sense, that is, of having no beginning or end. This in turn has implications for a beginning or end of time, given the view, shared by Aristotle, that motion and time go together. It means that Aristotle should not argue, as he does at Physics 4.13, 222a29-30, that time will not end,

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since motion will not end. Nor need Aristotle’s opponents accept his further argument (222a33-b7) that an instant is the end of one time and the beginning of another, so that there can be no final instant of time. For those who disagree will not accept that an instant is always a beginning as well as an end. Evidently in the lectures reflected in the present commentary on Book 4 Philoponus does not repeat his arguments on motion from the earlier commentary on Book 8, but only alludes to them. The most obvious reason is that Aristotle does likewise, only mentioning in Book 4 the arguments on motion which he supplies in Book 8. On the other hand, Broadie draws attention to two arguments by Philoponus in Book 8 about time, including the one about an instant not needing to be both beginning and end. They have survived in an Arabic paraphrase of Philoponus’ commentary on Book 8, available in English translation.18 The important point is that objections to Aristotle were voiced both in the earlier commentary and, with references back, in our commentary written in 517 AD. On the view that these objections to Aristotle did not occur to Philoponus until some later conversion to Christianity, we should have to postulate that anti-Aristotelian afterthoughts were added into his commentaries on both 4 and 8. There is one more point to be made. The present commentary contains interesting claims not only against Aristotle, but also in supportive exposition of his views. The one to which Broadie has drawn my attention, and which she expounds, occurs at 771,20-8 and concerns motion. Aristotle supposes at Physics 4.13, 222b33-223a4 that one body cannot be compared as faster than another, if one is travelling straight and the other round a bend. Philoponus comments that speed round a bend may be faster than speed along a straight line, even if it takes more time to cover the same distance. The reason he gives is that motion round a circumference is impeded by the bend. This is presumably a response to the phenomenon that he and Aristotle will have sensed, that change of direction requires more effort than motion in a straight line. Motion in a straight line was later to be treated by Newton as the motion that, once started, would continue without requiring new forces, merely the absence of contrary forces – it is inertial motion. By contrast every change of direction would require a new force. Neither Aristotle nor Philoponus

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drew Newton’s conclusion, and indeed Philoponus’ impetus was not inertial, but would wear out in the absence of renewal, while the best example of inertial motion in Aristotle would be not straight, but circular movement supposedly executed by the stars. But both thinkers had sensed the impediment to motion round a bend, and Broadie suggests that Philoponus takes the actual speed on a bend to be the speed that a body would have attained if it had been running on a straight track. In correspondence with Broadie, Sylvia Berryman has pointed out that the pseudo-Aristotelian Mechanica considers motion round a circumference to be a product of two motions, one of which, a pull towards the centre, impedes the motion round the circumference. Notes 1. See David Sedley, ‘Philoponus’ conception of space’, ch. 7 in Richard Sorabji, ed., Philoponus and the Rejection of Aristotelian Science, 2nd edn, Supplement 103 to the Bulletin of the Institute of Classical Studies, London, 2010. 2. 678,24-684,10. 3. 690,34-691,5. 4. 581,8-31; 632,4-634,2 5. 683,5-25. 6. Pantelis Golitsis, Les commentaries de Simplicius et de Jean Philopon à la Physique d’Aristote, Berlin 2008, 31 and 36, is speaking against Koenraad Verrycken’s postulation of a change of mind. But Verrycken’s defence of his view, which I have not seen, is expected in Lloyd Gerson, ed., The Cambridge History of Philosophy in Late Antiquity, Cambridge University Press, announced for December 2010. 7. 641,13-642,20. 8. Galen ap. Simplicium in Phys. 708,22-709,13, translated in Richard Sorabji, The Philosophy of the Commentators, 200-600 AD, A Sourcebook, vol. 2, ch. 11 f1. 9. Galen and Themistius ap. Simplicium in Phys. 718,13-719,18, translated in Sourcebook, vol. 2, ch. 11 a1. 10. H. Vitelli, Commentaria in Aristotelem Graeca, vol. 17, index, p. 992, s.v. Themistios. 11. Translated by Robert W. Sharples with Fritz Zimmermann, Phronesis 27, 1982, 58-81. 12. In Alexander’s treatise on time and Simplicius’ report, in Phys. 759,20-760,3, translated in Sourcebook, vol. 2, ch. 11 d2-3. 13. Themistius in Phys. 163,1-7, in DA 120, 17-21, translated in Sourcebook, vol. 2, ch. 11 d6-7. 14. Themistius in Phys. 161,29-163,11. 15. Translated in Sourcebook, vol. 2, ch. 11 e7, 8, 9. 16. I have summarized Verrycken’s view and the objections to it to date in Richard Sorabji, ed., Philoponus and the Rejection of Aristotelian Science,

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2nd edn, Supplement 103 to the Bulletin of the Institute of Classical Studies, London, 2010, 14-17. His defence of his view is expected soon, see above n. 6. 17. The other references are at Philoponus in Phys. 3.5, 458,30-1 and 4.8, 639,7-9. 18. She cites the translation from 816,14 of the Arabic by Paul Lettinck, Philoponus: On Aristotle Physics 5-8, Duckworth, London, 1994, 135.

Translator’s Note The translation is from the edition of H. Vitelli, Berlin 1888. In reproducing Philoponus’ lemmata, I have occasionally filled out a lemma with words from Aristotle; these supplements appear in square brackets. Bold type in the translation indicates that Aristotle is being directly quoted. References to Aristotle in the notes are to the edition of Bekker, 1831. The present translation has had the benefit of comments from four anonymous referees for the CAG translation project.

Philoponus On Aristotle Physics 4.10-14 Translation

Philoponus on Aristotle, Physics 4.10-14 217b27 Next for discussion after the subjects mentioned is time. It is the natural philosopher’s task to examine time too, no less than any of the preceding subjects. For this too is one of the concomitants of all physical entities.1 again approaches this , too, by the same route,2 first asking whether it exists or does not exist and arguing against each of the two sides, and then next the subsequent questions: I mean, ‘What is it?’ and ‘What sort of thing is it?’. First he argues that time does not exist. Although it is obvious that time exists, nonetheless the grounds he gives on which he bases the attempt to show that time does not exist cannot be lightly dismissed. Of time, he says, one part has gone past and does not exist, and the other is future and does not yet exist [217b33-4] (for these are the two parts of time, the past and the future); but each of these two does not exist; hence time consists of things that do not exist; but if X consists of what does not exist, X itself, too, does not exist (for if X exists, the parts of it themselves exist too); hence time does not exist. Again, he says, everything that is extended and divisible into parts is implemented either by way of the totality of its parts together or by way of some of its parts: e.g., animals and plants by way of the totality, and the games by way of parts. For it is because the wrestling or the boxing is present that the games are said to be present. But time, although it is extended, subsists neither by way of the totality of its parts (for it is not the case that all time is together) nor yet by way of a part: for neither the past nor the future exists, since the one no exists and the other does

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not yet exist. So if time neither is by way of a totality, nor by way of parts, it indeed seems not to be at all. The now, he says, which alone seems to exist, is neither time nor a part of time. For the part measures the whole (it is a third or a tenth or a thousandth or some other by which the whole is measured out), but the now does not measure time. For the now is unextended. Nor does time consist of nows, since everything divisible consists of divisibles. So the now is not part of time. A fortiori, then, it is not time either. Nor, then, is it by way of the now that time subsists. Having made these he shows that the now too3 is in no way a thing that exists. Perhaps ‘now’ is only a word with no reality. He establishes this by taking two axioms. The first is that it is impossible for there to occur two times together unless one contains and the other is contained [218a11-14]. (For we say that a year and a month and a day are present now – year is the 233rd of Diocletian, month is Pachon, day is the 10th4 – so these three times occur together; the year, however, contains the month and this the day. But that there should occur two equal times together, e.g. two days or two months or two years, is impossible.) The second is that everything that existed before and now does not must have perished [218a14]. By using these axioms in his proof, he proves that the now does not exist. The reasoning will proceed from division: if (a) the now exists, he says, then either (a1) the prior is one and the same as the posterior and is as it were one now flowing (as it were) from eternity,5 being present, always the same, to everything: or (a2) it is other and other. And if it is other, then either (b1) the prior one stays on when the posterior one comes into being: or (b2) it does not stay on but perishes. And if it perishes, then (c1) it certainly perishes in something:6 therefore either (d1) in itself or (d2) in another. And if (d2) in another, it has perished either (e1) in the now that is next to it or (e2) in the one that is further away. So: since the division produces a total of five segmentations, if it is shown that none of them can stand, it would be evident that the now in no way exists. This is how he shows that the prior now is not other than the

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posterior (for it is this division7 that he formulates first): if the prior one were other than the posterior, then either the prior one stays on for the posterior one to arrive , or it does not stay on for it. If, then, it stays on, the result will be that two times equal to each other occur together; but this is impossible. For we said that it is impossible that two times should occur together unless one contains and the other is contained. So the prior now does not stay on as the posterior now comes to be. But if it does not stay on, and everything that previously was and now is not must have perished, it follows that the prior now has perished. But if it has perished, then it has perished either in itself or in another. Now, it cannot have perished in itself, since the same thing will at once be and not be: which is impossible. So in another. So: either in the next one or in the further off one. That in the next one is impossible, for in no way is a point next to a point. Let this, he says [218a18], be conceded by us at this stage (for he shows it in the last books of this work8), namely that point cannot be next to point, nor now to now, nor line to line, nor surface to surface. Yet it would certainly do no harm if we show now that this is impossible. If two nows or two points were next to each other, either they would coincide with each other or they would be as dots apart from each other, or they would be in contact in one respect and as dots apart in a different respect. But if they coincide, they will not be two but one; and if they are as dots apart they will not be next to each other. For, according to his own definition in the fifth book,9 things are next just when nothing of the same kind is between them. But for every two separate nows, the interval between them is time, and in any time the nows are infinitely many. So between the two separate nows there will be infinitely many nows of the same kind as they. So the separate nows are not next to each other. It follows that it is also impossible that if they are next they are separate. But if in one respect they are in contact, and in another are distinct dots, they will not be partless. So it is impossible for two nows to be next to each other. So if the now perishes, it does not perish in the next now – not if a next one does not even exist. But if it perishes in one that is further

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off and remote, necessarily the interval between these two nows is time, and in any time there are infinitely many nows. First, then, its perishing in this now, and not perishing in the infinitely many nows in between, would be an arbitrary thing. Secondly, if it perishes in the remote now, it will turn out to be in the intervening nows which are infinitely many – but it is taken for granted that the previous one does not stay on when the subsequent one comes to be. And at the same time the previous absurdity will follow too: that of two equal times occurring together.10 So it is impossible that the now is other and other. For all the assumptions have been refuted. But surely the now is not always one and the same? That is impossible, for, he says [218a22-4], nothing extended that is bounded is bounded by one boundary; instead, the smallest is two; e.g. the line is bounded by two points, while the now is the boundary of time, and it is the case both that time is extended and that one can take a bounded time, e.g. a day or a month. So if a given time, being extended, is bounded, and no bounded thing has just one boundary, and the now is a boundary: then it is not possible that the now is single. And, besides, if the things we say have happened at the same time are things which happen at the same now, and the now is single from eternity, it will follow that the Trojan wars have happened at the same time as events of our own day. Hence nothing will be older or younger than anything else: which is absurd. Hence it is not possible that the now is one and the same. Consequently, nor can in any way exist. For if it existed, either it would be one and the same, or it would be other and other; but it can be neither other and other nor one and the same. So in every way it seems just not to exist. If, then, time exists neither by way of the past, nor yet by way of the future, nor yet by way of the now, it seems just not to exist at all. 217b30 The best plan will be to begin by listing the difficulties connected with it, even making use of the exoteric arguments

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He says exoteric arguments in order to contrast the demonstrative

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arguments presented to academic audiences with ones based on received opinions and plausible considerations. It has also been stated in Categories11 that those arguments are exoteric that are not demonstrative, and are addressed not to the real in the audience but to ordinary people, and are based on plausible considerations. 218a2 One would naturally suppose that what is made up of non-beings have no share in reality.

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He says reality, i.e. existence and being. For how would what is be made up of non-beings? 218a3 Further, for every divisible thing, if it exists, it is necessary that when it exists all or some of its parts exist. another argument to show that time does not exist. Everything divisible into parts, he says, when it is, either has all its parts there together, as with animals and plants, or has some of them, as with the games; but in the case of time, which is divisible into parts, the parts are not there, neither all of them nor some of them (for the past is not and the future is not yet); hence time does not exist.

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218a6 The now is not a part: the part measures , and the whole must be made up of the parts. Since he said that time does not subsist by way of its parts – but, of the things that belong to time, only the now subsists – lest anyone should say ‘But time does subsist by way of the now’, first shows that the now is not part of time, (for, he says, the part measures the whole, and the parts make up the whole, whereas the now neither measures time nor is time composed of nows); next he will show that the now in no way exists, by using the division which has already been mentioned [703,23ff.]. 218a11 and none of the parts in time which are other and other are together (unless the one contains and the other is contained)

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one of the axioms, that it is impossible that two times or parts of time should occur together unless one contains and the other is contained. 218a14 that which is not but previously was must have perished at some time12 That is: there must be a moment of time when it passed into nonbeing, whether through perishing or not; for in my view this makes no difference: here he has used the expression ‘perished’ in place of ‘not been’.13

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218a15 the nows too cannot be together with each other, and the prior one must at each stage have ceased to be Having stated the axioms [218a11-14], he proceeds to introduce the proof; the sequence of thought in the text is as follows: if the now is always other and other; and it has been agreed that two parts of time cannot occur together unless one contains and the other is contained; and it has also been agreed that what previously was and now is not must have ceased to be at some point: it is obvious, I suppose, that these nows, too, cannot occur together with each other (because of the first axiom), and that the prior one must at each stage have perished (because of the second axiom). So since it perished, when did it perish, and in which now? Either in itself or in another, and if in another, either in another that is next to it or in another that is remote. But each alternative is impossible. 218a17 the prior now cannot have perished in another now.

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By in another now he means: in the one that is next and immediately in sequence. For it was because he was talking about that that he followed with: For let it be granted that nows cannot be in immediate sequence to one another [218a18-19]. It is also possible that perished in another now has been said with a more widely shared reference, meaning ‘neither in the next now nor in the remote one’, and that then goes on through the cases one

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by one, first next by saying For let it be granted that nows cannot be in immediate sequence to one another [218a18-19]. The reason he did not say that it is impossible that they are in immediate sequence to each other, but rather let it be granted is that he has not shown this yet; rather, he claims it as an assumption for the time being, but will demonstrate it .14

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218a19 If then it was not in the next one that it perished, but in another the now’s perishing is not only not possible in the next one (because there is no next one), but also not in any other one that is not next. For, he says, between two nows there must be time, and in every time there are infinitely many points. So if the now perishes in none of these, it is together with all of them. But this is impossible, for it has been stated that two parts of time cannot occur together unless one contains and the other is contained, and no now is capable of containing another now. 218a21 Yes, but neither is it possible for the now to remain always the same. Having refuted one segment of the division15 by the foregoing arguments, that now cannot be different and different, he thereupon means to refute the other one too, that the now cannot be one and the same either. For nothing divisible that is bounded has one boundary: so if the now is a boundary of time, and time is divisible (, since it is continuous), the now would not be single.

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218a23 [no determinate divisible thing has a single boundary,] whether it is continuous in one or in more than one dimension He says continuous because just above he said divisible, since the continuous is the divisible. So both: the divisible is in every case also continuous; and: the continuous is in every case also divisible. The

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line is a thing continuous in one dimension, along its length, and in just this respect it is also something divisible, while the surface and the solid are continuous in more than one dimension, the surface along two, and the solid along three; and in whatever way each has continuity, in those ways it has divisibility too. 218a25 Further, if being together in respect of time 15

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The second proof is that if the now is single, the Trojan wars would be contemporaneous with events now; for both would be in the same now – which describes the contemporaneous. So older and younger would be obliterated. 218a30 This may serve as a statement of the difficulties about the data concerning time. As to what time is or what is its nature, the traditional accounts give us as little light as the preliminary problems which we have worked through. Having said at the beginning that we must ask concerning time whether it exists or not and then what it is, he first argued that time does not exist, and having proved its non-existence very ingeniously from received opinions, he does not now argue in the opposite direction – I mean to the effect that time exists, since the self-evidence of this is more trustworthy than any demonstration (for he will presently resolve the difficulties about it). He will now go to ask what it is, and according to his usual he first clears out of the way the false views of the ancients concerning time. In all, he tables three views on time. Some, he says, thought that time is the revolution of the universe [to pan]; others that it is the sphere itself [218b1], i.e. the corporeal mass of the heaven;16 while yet others have said without qualification that movement is time. First he shows as follows that time is not the revolution: if the revolution were time, then, since the part of time is time, it will follow that the part of the revolution is a revolution. But this is impossible. For a revolution is a return from the same to the same. So it is not the case that the revolution is time. For if they said that the revolu-

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tion is a certain definite time, e.g. a day or month, it would have been possible for part of the revolution to be part of time; but since they say without qualification that time, insofar as it is time, is a revolution, it will follow that part of the revolution is not time (for part of the revolution is not a revolution): with the result that the revolution, too, will not be time. Furthermore, he says, if we suppose that there is a plurality of heavens, there would be a plurality of revolutions; but there would not be a plurality of times: rather, there would still be one and the same . For there would not be many days together, or many years, given that as things actually are the revolutions are many – since the spheres are many – whereas time is single. So, in the same way, even if there were other celestial and cosmic systems, there would have been a plurality of revolutions but a single time. For if all the celestial systems moved17 with equal velocity, one and the same time would have been their measure in similar fashion : for day and month and year would have been the same and equal for all of them; while if they were of unequal velocities the movements of the other celestial systems would have been measured by the swifter movement, just as, in the actual state of things, the movements of the other spheres are measured by the movement of the sphere of the fixed stars. For the greater is always measured by the lesser. E.g., the ten-cubit piece of wood is measured by the cubit, and the cubit by the inch. In the same way, then, the faster movement is measure of the others. So the same time that measures out this would be measure of all the other too. That is how he shows that the revolution is not time. As for showing that the sphere itself is not time either: he does not rate as even worth refuting. For this is simpleminded, and the syllogism by which they thought they established that the sphere is time is plainly invalid. For it depends on a combination of affirmative premisses in the second figure. All things are in time, they say; and all things are in the sphere; ergo the sphere is time.18 First, as I said, the combination is invalid; secondly, in something is not always a matter of in time.19 In one sense these things are in the sphere, and in another sense they are in time. For all things are in the sphere as in a place, but all things

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are not in time as in a place, but in a different manner. So strictly it would be concluded that the sphere is not time – precisely the opposite of what they wanted. All things are in the sphere as in a place, but all things are not in time as in a place: so the sphere is not time. In their argument the middle term does not function in the same way in connection with both extremes. Now, it is also possible to combine syllogistically in the third figure:20 all things are in the sphere; all things are in time; ergo the sphere is time. But again the middle term does not combine in the same way with extremes, as I said. Because the view itself and the effort to support it are transparently weak, Aristotle says nothing in response to its proponents. But one can make these points against them: time possesses past and future, but the sphere does not possess past and future; part of time is a time, but part of the sphere is not a sphere, so the sphere is not time; time is divided by the now, but the sphere is not divided by the now; time subsists part by part, whereas the sphere does not subsist part by part – so accordingly the sphere would not be time either. That it is not simply movement21 either, he shows as follows: movement, he says, is only in the subject of movement, and in the place in which the subject of movement is moved, whereas time is not in the subject of movement nor yet in the place in which the movement comes about, but accompanies everything everywhere in the same way, being one and the same. Hence movement is not time. For my movement is not in all things; nor is movement unqualified22 observed in all things, for some things are at rest. Second argument: faster and slower belong to movement and change in general (for we say that one movement is faster or slower than another; e.g. we say that the movement of the sphere of the fixed stars is fast, while that of Saturn is slow); but faster and slower do not belong to time; hence time is not movement. And that faster and slower belong to movement he does not even think it requisite to establish. (For this is clear, as I said. Who does not know that the movement of the sphere of the fixed stars is faster than the others, and after it comes the movement of the moon, and in this way one movement differs from another in respect of faster and slower? – and at the very least the eagle’s movement is faster than the

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jackdaw’s movement?23) On the other hand, he does establish that faster and slower do not belong to time by a third syllogism as follows: faster and slower, he says, are defined by time24 (for we say that a large movement taking place in a small time is faster, and a small movement taking place in a large time is slow; hence faster and slower are defined by time); time is not defined by time (for it would be ridiculous to say that time is defined by time); ergo faster and slower do not belong to time. For one cannot say that a year is faster or slower than a year, or a day than a day (if you understand ‘day’ as the day-and-night period). So once he has shown by these arguments that time is neither revolution nor sphere nor movement, he next states that although time is not movement, even so, it is not without movement. For together with the noting of time, movement is thereby noted too. If we take note of a duration of such and such length, we are thereby taking note of a correspondingly long movement of the universe; and conversely, if we note that the universe has moved by so much, we thereby concurrently note a corresponding amount of time. This is very clearly shown by something that happens to us every day. Often when we have read a lot, and because of absorption lose awareness of the amount, we thereby lose the time too. For often when we have spent most of the day , we do not yet believe that a short part of it has gone by; but later, when we register the quantity of our reading, we thereby register the length of the time; and conversely, if we first register the length of time, we thereby register the length of the movement; for we say that we have read a lot since most of the day has been used up. Conversely, we say that it seems that a lot of time has gone by because a large quantity of reading has taken place. So if movement and time get noted, and fail to be noted, together with each other, it looks, he says [219a8-10], as if time either is the same thing as movement or is something about movement. So, since it has been shown that it is not movement, it must be that time is something about movement. So we must ask: what about movement is it? With these things stated, he proceeds to the next stage of the question ‘What is time?’

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Translation 218a30 This may serve as a list of difficulties about the data concerning time.25

That is, the previous difficulties were developed from data about time: from its having past and future, from its being present by way of the now, etc. 5

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218a31 As to what time is or what is its nature, the traditional accounts give us as little light as the preliminary problems which we have worked through.26 What he is saying is that the views of the ancients put forward in the past will contribute nothing at all to our getting to know the essence of time; on the contrary, they in fact create in us great unclarity about it, every bit as much as the difficulties about it which we have just put forward. For just as the latter fill us with unclarity about its nature, so too do the sayings of the ancients. One of them declared its nature to be this, another one that; but time – on the basis of common notions – appears to be none of these things. So unclarity about the nature of time is generated in us equally from the sayings handed down from the ancients and from the difficulties we have just now detailed. He is referring to the that no part of time subsists – that it subsists only by way of the now – from which it was deduced that time in no way exists. So if the data concerning time bring us to the thought of its not even existing at all, they throw us into what is surely much deeper unclarity on the question ‘What would be the nature of time?’. 218b1 Yet part, too, of the revolution is a time, but it certainly is not a revolution.

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For if the part of time is time, and the revolution is time, the part of the revolution would be time too. But the part of the revolution is not a revolution. So time is not the revolution. 218b3 Besides, if there were a plurality of heavens, the movement of any of them would equally be time

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the second argument.27 If (he says) there were a plurality of heavens there would also be a plurality of revolutions. So there would also be a plurality of times. But that is impossible, for even given that condition time would have been single and the common accompaniment of all things, just as it is of the plurality of revolutions of the spheres.28 So time is not the revolution. 218b5 Those who said that time is the sphere of the whole thought so on the ground that all things are in time and all things are in the sphere of the whole. Since some held the sphere itself and the corporeal mass of the heaven to be time, he has also provided the explanation of their fallacy. (he says) because all things are equally said to be both in the sphere (since it contains all things) and in time; for on this basis they inferred invalidly (from two affirmatives in the second figure29) that time is the sphere. But it would be simple minded, he says [218b7-9], to consider the impossible consequences of this position. We, however, have stated its consequences just now.

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218b9 But as time is most usually supposed to be movement and a kind of change, we must consider this view. Having said that time is neither the revolution nor the sphere, he now says that since to most people movement seems most of all to be time, this precise question should be raised: whether is movement or not.

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218b10 Now the change and movement of each thing occurs only in the changing thing itself The first argument to show that movement is not time is that movement occurs only in the subject of movement and in whatever the place might be in which the movement occurs, whereas time is not only in the subject of movement but accompanies all things equally. Hence movement is not time.

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Translation 218b12 or wherever the moving thing itself happens to be

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I.e: ‘and in whatever place it is moved in’; for ‘or’ instead of the conjunction ‘and’. 218b13 Again, change is faster and slower the other argument: the faster and the slower belong to movement; the faster and the slower do not belong to time; therefore movement is not time.

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218b15 for the fast and slow are determined by reference to time that the faster and the slower are not in time.30 It is because the faster and the slower are determined by reference to time (since ‘faster’ is what we say of the large movement that takes place in a small time, and ‘slow’ of a small movement that takes place in a large time); but time does not get determined by reference to time. Therefore the faster and the slower are not in time. 218b17 but time is not determined by time; neither by being a sort of quantity of it nor by being a kind of it

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For movement is determined by time both in respect of quantity and in respect of quality: in respect of quantity, because we say ‘long movement’ of the movement that takes place in a large time, and ‘short’ of the one in a small time; and in respect of quality, because we say ‘faster’ of the large movement that takes place in a small time, and ‘slow’ of the small one that takes place in a large time. Time, however, is not determined by time either in respect of quantity (for we do not say that the year is determined by a year), nor yet is time determined by time in respect of quality. For in no way is time faster or slower. For a day is not faster or slower than a day.

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218b19 We need not distinguish at present between movement and change. Since we formulated the argument change, and not all change is movement, and it was not change that they claimed time to be, but movement – because of this he says that we should not let it make a difference whether movement and change are the same thing or not, but shall use the terms as if movement and change are the same thing. For in the next books31 he is going to show that change is wider than movement. For coming to be and perishing are change but not movement.

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218b21 But neither does time exist without change For although time is not movement and change, even so not without movement and change. 218b21 for when the state of our minds does not change at all, or we have not noticed its changing, we do not think that time has elapsed

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I.e., whenever we are moving but do not take note mentally that we are moving, we do not think that time has elapsed; but when we notice the movement we immediately become aware of time. 218b23 any more than to those who are fabled to sleep among the heroes in Sardinia, when they are awakened He takes a story as example. It used to be said that certain sick people would withdraw to the heroes in Sardinia and would be treated, and on withdrawing32 would sleep for five days on end, and then on being woken up would believe it to be the hour when they got to the heroes. So just as (he says) those people in the story in failing to register the revolutions of the universe by which it revolved33 also failed to perceive the time passing, and conversely in failing to perceive the time also failed to perceive the movement but instead thought that when they fell asleep and when they got up were

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one and the same now – just so, if the nows were not different but one and the same, there would not be time. For just as in the case of what seems to be one now there seems to be neither time nor movement, so in the case of what is really one there is neither time nor movement. But if that is so, either movement and time are simply identical with each other, or time is something about movement. If, then, it has been shown that it is not movement, time must be something about movement. 219a2 We must take this as our starting-point since we are trying to discover what time is: what about movement ? Since, he says, our purpose is to discover what time is, and reasoning has just now made it clear that time must be something about movement, let us, in pursuing that self-same inquiry, start from here and take up the question: time is what about movement? Is it a sort of attribute, or an incidental property, or something else? 219a3 we perceive movement and time together He takes up the same argument again, that movement and time are noticed along with each other.

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219a4 for even when it is dark and we are not being affected through the body, if any movement takes place in the soul we at once suppose that some time has indeed elapsed Not only by registering bodily movement do we immediately come to notice time, but even when we are not aware of any bodily movement, and all our senses are still and the soul moves only its imaginative part, time is (here too) immediately apprehended along with such a movement. And this an a fortiori argument: so true is it that time is apprehended together with movement that even if we do not externally perceive a single bodily movement – one that is certainly accompanied by time – but do perceive a psychological change, we immediately thereby become aware of time along with it.

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Thus time is in some way naturally akin to movement. Just as time is apprehended along with movement, so too conversely awareness of movement comes to us along with the awareness of time. For, as I said, if we become conscious of time’s having passed, we immediately register that we have read a great deal, or have slept a great deal, or have been subject to some other movement.

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219a10 That which moves, moves from something to something, and all magnitude is continuous. Therefore the movement corresponds to the magnitude. Having refuted the predecessors’ claims about time, he now means to lay out his own view. He first takes it as an assumption that movement is continuous, and he establishes this in this way: every moved thing is moved from something to something (for this is true of every movement, but whilst it is true of every movement he himself formulates the argument as if for movement in respect of place) – so: if movement is from something to something, then movement is over magnitude (for if it is from something to something, what is between must be magnitude; so that movement in respect of place is over magnitude); but every magnitude is continuous, so movement is over continuous; but what moves over the continuous is moved with a continuous movement; so movement in respect of place is continuous. Therefore the continuous exists primarily in magnitude, and because of magnitude in movement too. Again, since the prior and the posterior are in the continuous (for in the magnitude this is prior and that is second), because of this the prior and the second must occur in movement too. For as matters stand with magnitude so they stand with movement. So since the prior and posterior occurs in magnitude, this must occur in movement too. So the prior and the posterior are in movement. Now, since we come to awareness of time precisely by coming to awareness of movement, and in movement one is prior and one is posterior, it is clear that both in the prior movement and in the second one we come to awareness of time. For if time is introduced along with awareness of the movement, it is clear that both in the prior movement and in the second one time will be apprehended along with it. So the prior

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and the posterior belong to time too. For as matters stand with movement, so they must stand with time; for movement and time correspond to one another. But movement is not the same as the prior and the posterior; for in substrate the prior and posterior in movement is nothing other than movement, but in aspect it is one thing for movement to be movement and another for it to be prior and posterior . At any rate, the prior and the posterior exist not only in movement but also in certain other things, for instance number. For the one is prior to the two, and the preamble is prior to the narrative, and the letters prior to the syllables. So saying ‘movement in respect of place’ is not the same as ‘the prior and the posterior’. We come to awareness of time not simply whenever we become aware of movement – for it is not the case that if I simply note alteration or locomotion I immediately become aware of time too along with it; rather: whenever I become aware of the prior and the posterior in movement, then, along with this sort of awareness, the awareness of time is immediately introduced. For, he says [cf. 219a25-9], whenever we become aware of the prior and the posterior, then we say that what is between is time. For when we get to be aware of the beginning of the movement and of its end, we say that what is between is time. Consequently, he says, if it is just when we number34 the movement and say that one of it is prior and another one second, that we also say that time is, time seems to be the number of movement in accordance with the prior and the posterior. Time is not the number of every movement (for it is not the number of alteration or growth);35 instead, it is the number of with respect to place, and not of all but of regular . For time measures all movement,36 but primarily the regular , and through that it measures the others too. For day and hour and month and year are measured by the period of the sphere of the fixed stars, and thereby time measures all movement. Hence it is of that sort of movement that time is number. So, he says [cf. 219b1-2], it is not movement but the number of movement that is time. That time is this he also shows by a syllogism, as follows: every more and less is discriminated by number; a certain sort of more and less is discrimi-

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nated by time (movement is this sort); ergo time is a certain sort of number. But since number is in two senses, on the one hand as number that numbers and on the other hand as number that is numbered (since pint and bushel are also in two senses, on the one hand that which measures and on the other hand that which is measured37), which sort of number do we say time is: that which measures or that which is measured? Well, he says that it is not the one that measures but the one that is measured.38 For if number in the first sense is in our soul, and time is external to us, it follows that time is not the that numbers, but the that is numbered. 219a13 for the time [that has passed is always thought to be] as great as the movement If time is apprehended along with movement, it is reasonable that as matters stand with movement, so matters stand with time. So if the movement is large the time too must be large, and if small, small. Although he said earlier [218b15-17] that we call ‘faster’ the large movement in a small time, so that movement is large and time is small, he is not now saying the opposite. For it was not with reference to the movement that produces time39 that he was speaking in those passages, but to just any movement, whereas here it is with reference to the movement that produces time that that as the movement that occurs is greater or lesser, so, necessarily, the time that occurs is greater or lesser too.

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219a14 The distinction of prior and posterior holds primarily, then, in place; and there in virtue of position. The prior, he says, and the posterior is primarily in place, and by means of place it is also in movement. He calls ‘place’ the magnitude over which the movement occurs. For things in locomotion are moved over magnitude. But in the case of place, he says, the prior and the posterior is by way of the position of the parts. For magnitudes are composed of parts having position. In saying there in virtue of position, he has not stated the antithesis .40 Instead, he did

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say that in movement too there is the prior and the posterior corresponding to the magnitude41 [219a17-18]; but he did not say in what way the prior and the posterior in movement – but by his silence he left it to us to understand that it is not through position. For movement does not consist of parts having position. For what is prior does not remain for what is after to arrive – it is in passage, rather, that the prior and posterior occur. But by correspondence with those belonging to magnitude – I mean the prior and posterior – they occur in movement too, he says: because the movement that takes place over the first part of the magnitude is first, and that which takes place over the second part is second. That he said ‘place’ as a substitute for ‘magnitude’, he made clear too from what he went on to say. For he says since the prior and the posterior are in magnitude [219a16], here using in magnitude to express what he expressed above using in place, saying in effect: ‘the prior and the posterior occur primarily in place, i.e. in magnitude’. But why do we say that movement gets the prior and the posterior from magnitude and not the opposite, that magnitude has them from movement? For magnitude too has the prior and the posterior through movement, as is clear from the following: if two objects are moved along the same straight line, one starting from one end, the other from the other, they will not each occupy the same part of the magnitude first; instead, for each of the moving objects the part of the magnitude that is first is the one from which it started its movement. One can also see this in things that are naturally in movement. For if the stone is carried downwards and fire upwards through the same air, the part of the air that is first for one is last for the other. So for each the prior and posterior is determined on the basis of movement. So how is it that Aristotle says that the prior and the posterior occur primarily in magnitude? Well, I say that being in general, for movement, is based on magnitude, since if the magnitude is taken away the movement too must be taken away, whereas it is not the case that if the movement is taken away the magnitude is taken away. Just as the movement has being because of the magnitude, so, obviously, what belongs to movement will have being too because of the magnitude. But the prior and posterior belong to . So these too

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have being because of magnitude. So that, presumably, is why he says that the prior and the posterior occur first in magnitude. 219a18 But also in time the distinction of prior and posterior must hold

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Since, he says, time not only corresponds to movement, but movement also to time, it makes sense – given that in movement there is the prior and posterior – that in time too there should be the prior and the posterior. 219a19 The prior and the posterior42 is whatever it is by being which movement is The prior and the posterior, he says, which is found in movement and in time, in respect of substrate (for that is what he means by whatever it is by being which43) is nothing other than movement, but in respect of definition and meaning they are different. Just as the way up and the way down are, in respect of substrate, a ladder, but in respect of definition are different and are not a ladder: in the same way the prior as such is not movement, since it would not have also occurred in other things that are not movement, e.g. in numbers. Although we do not observe the prior and the posterior in the absence of movement (for in arithmetical calculation it is when we make a transition from this to this that we say that one is prior and one posterior; for unless we do make a transition from this to this , we are unaware of prior and posterior), still the prior and the posterior are different from movement. For the prior and posterior, in so far as both are movement do not differ at all, but they do differ in that the one is prior and the other is posterior. So they are something other and are not movement, but are a sort of attribute of movement. But if we consider the prior and the posterior not with reference to the parts themselves of the movement, but with reference to the limits and the stage-by-stage-arrivals,44 the point will be clearer, that both are in their substrate the movement although they are different from , just as the

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points too from the line, and the surface from the solid.

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219a25 we determine them by taking them in as other and other, and between as different from them In determining the prior and the posterior in movement, he says, we come to awareness of time. For the prior and posterior being in the same , as has been said, whenever we determine this, and say that there is one now at which the movement began and a different one at which it has ceased: that which is between these, being other than the extremes, is what we say is time, just as that which is between the stage-by-stage-arrivals, the one that is prior and the one that is posterior, is what we say is movement. For just as what is determined by points is a line, and what is determined by stages is movement: just so, what is determined by nows is time. 219a29 for what is determined by the now is thought to be time – we may assume this Since time does not consist of nows (for no two nows are next ), but is determined by them, with what is between being – not nows, but – time, he therefore says we may assume in the meantime that what is between any two nows is time. For he will show in the following discussions [Phys. VI, 231a21-232a22] that no magnitude consists of partless items: a line does not of points, nor a movement of stage-by-stage-arrivals, nor a time of nows, nor yet a plane of non-planes (I mean: surfaces of lines), nor a depth of non-depths (I mean: a solid does not consist of surfaces). 219a31 or as the same but in relation to something prior and posterior If, he says, we do not perceive two nows, or if we perceive a single one but not as occurring in something that is posterior and prior, it does not seem to us that time has gone by. Even if the now is single but

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we note it moving and coming to be once in something and once in something else, we are thereby aware of time. Thus when he says in relation to something prior and posterior, either this means ‘coming to be in something prior and in something posterior’ (for this interval, in whose different parts in turn the now comes to be, is time), or when we treat the same now as halted and yet as having taken on two descriptions, that of ‘end’ and that of ‘beginning’, so that it is end in relation to something prior and beginning posterior. For these , of which the same now is both end and beginning, are times. For in general whatever is determined by the now is time. So, he says, whether we perceive two nows, or one taking on another and another description (for it should make no difference whether the prior now and the posterior one are other and other numerically, or whether it is numerically the same but occurs in its flux in one thing at one point and in another at another) – in each of these two45 cases awareness of time is generated in us; whereas if we regard the now as in all respects one, both in substrate and in description, we then fail to receive awareness of time just like the sleepers in Sardinia. The reason, he says [219a32-3], why time seems not to have elapsed is that movement, also, . For no continuance, either,46 and all movement involves continuance.

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219b1 For time is just this: number of movement in respect of prior and posterior. He defines time by saying what it is. It is number of movement not numbering it; instead, the numbered prior and posterior of movement is time. 219b2 Hence time is not movement; rather, it is the way in which movement has number.47 rather, it is the way in which movement has number means: ‘rather, it is the way in which movement is numbered’. For time is what it is about movement that has been numbered, not in so far as

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it is movement, but in so far as it has been numbered according to prior and posterior.48 219b3 An indication of this: we discriminate the more and less by number, but more and less movement by time.

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That time is number of movement – numbered , of course, not numbering (as will be shown next) he proves in the third figure49 as follows: every sort of more and less is discriminated by number; a certain sort of more and less is discriminated by time – for we discriminate more and less movement by time; therefore time is a sort of number. 219b5 Since number is said in two ways – for we call number both what is numbered, and what is numerable, and that with which we number.

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Since he said that time is number of movement, and since number in several ways, he lists the number of ways and in which sense time is number of movement. Having said that number is said in two ways, he seems to speak of three senses: what is numbered, and what is numerable, and that with which we number. However, we say that he has put forward the first two under the heading of a single sense, except that one, i.e. what is numbered, refers to the actual, and the other, what is numerable, to the potential. Or: in order to show more clearly what what is numbered means, he introduced what is numerable the very object which is measured; e.g. the ten horses or ten dogs. So, since number is said in two ways, we assert that time is number in the sense of what is numbered. It is worth raising this difficulty: given that we say that time is continuous, how do we say, on the contrary, that it is number? For number is discrete quantity, and it is impossible for the same things to be both continuous and discrete. Well, we assert that if time were number that numbers,50 it would be impossible for it to be continuous; however, since it is not numbering but numbered , there is no reason why it should not be continuous in one

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respect and number in another. Insofar as it is measure of continuous movement, it is continuous; but insofar as it has the prior and the posterior, it is number. It is not impossible, nor for that matter unfamiliar, to apply number to continuous entities too. E.g. we say that the piece of wood is ten cubits and the road ten stades although they are continuous; but because they have the potential to be divided by us into parts we therefore also predicate some number of them. So in those cases, continuous is predicated by nature, but number by convention and on the basis of our conception. Again, it is worth pressing the question how he can assert that time is number not as measuring but as measured, although it is nothing other than time that measures movement. (At any rate, he asserts that time is measure of movement [220b14-15].) So, my response to this is that even though time is said to measure movement, still itself is measured too, by the soul. Primarily, it is measured, and through being measured it itself measures too; whereas the number that only measures and in no way is measured must be only discrete and in no way continuous. Thus even if time is said to measure movement, this has no absurd consequence for the argument. And in any case, there is an sense in which it is said that time measures. To illustrate: if one of two equal pieces of wood lying side by side with each other gets measured, one would say that the measured one itself also measures the one lying alongside; for whatever the size of the one, that is the size of the other. In this way, then, we say that time too measures movement, because they are together with, and stretch alongside, each other. So, necessarily, whatever the size of the one, that is the size of the other.51

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19b9 And just as movement is always other , so too is time That time is number of movement alone and not of anything else, he also shows as follows: just as movement is always different and different (he says), so too time, being the latter’s number, is always different and different; whereas with all other things, they are always the same, their number too is always the same.52 So if

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time is always other and other, and time is the number of a sort of continuance, time would be number of movement alone. 219b10 All time that is together is the same; for the now is the same whatever it was, although its being is different53

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All time that is together, taken anywhere , is one and the same. For it measures the prior and the posterior of every movement (not of alteration as such or of growth as such, however54); but the prior and posterior of movements that occur together are the same, so that the time too is the same. However, it is not correct to go on and say this of movement too, for movements that are together are not the same; rather, some differ not only in number but also in form, and others, although the same in form, e.g. a plurality of locomotions, are still not the same in number. Yet time everywhere is one and the same in number. So from this consideration too it is clear that time is not movement but number of movement. That time everywhere is one and the same he proves on the basis of the now. The now, he says, in respect of its own nature is everywhere one, but it differs in description. For it is taken in one way when taken as prior, and in another way when as posterior; yet as prior it is one and the same everywhere, and so also as posterior. So if the now is what generates time, and is one and the same everywhere, clearly time too that is together will be everywhere one, both in nature and in number. 219b12 The now in one way is the same, in another it is not the same.

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he therefore now sets forth what the division left out – the prior now is neither straightforwardly the same as nor straightforwardly different from the posterior now, but in a way is the same and in a way not the same. In the earlier passage he declines this so as to conceal the paralogism, but here he puts it so as to solve that difficulty. I.e., the prior now is the same in essence as the posterior, but not the same in aspect. For its being prior is one thing and its being posterior is another, just as (he says [219b20-21]) the sophists too claim that there is one Coriscus in the Lyceum and another in the market-place, and thus far they are right; since the same thing’s being here is not the same as there. So too for the now: if (this is one alternative) one lays down that it is one in number and the same, and that by its flow time is generated, it will not follow that what happened before is the same as what happened now. For even if they happen in the same now, it is not in the same state (since what happened in Coriscus when he was in the Lyceum and when in the market-place is not the same or together; e.g. here he was warming up, and there he was cooling down, or the like). So if numerically one and the same now were to be substrate none of the absurdities mentioned will follow, since it is not by being the same in aspect that it is substrate. If (this is the other alternative) the prior now were even of the same essence as the posterior now but not the same in number – which is closer to the truth – a fortiori none of those will follow.56 But as for how matters stand concerning the now’s coming into being and perishing, he will explain in the subsequent books [Phys. VIII, 217b16-20; cf. Metaph. XI, 1060b1719]57 that it and very many other items are and are not non-temporally,58 neither being brought to being through becoming, nor to non-being through perishing. The now in one way is the same, in another it is not the same [219b12-13]. Having said ‘The now is the same whatever it was, although its being is different’ – on the basis of which , as I said, he solves the stated difficulty, he now explains in what way it is both the same and not the same now. Insofar, he says, as it is taken in another and another, the prior and the posterior is different and different. It is taken in another and another portion of

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the movement, and this, he says [219b16], turns out to be the basis of its indeed being now.59 For the now is without parts, and being without parts it cannot be in several together; rather, when it is in this it is not in that. So it was rightly said that because of always being taken in another and another, not only in this way does it have being as now (for one cannot say that it is in this and in this together60), but also in this way the prior is different from the posterior – for its being in this is one thing, and its being in this is another. So in this way the prior now is different from the posterior . But whatever it is by being which it is, is the same, he says, i.e. in substrate.61 Next, with aim of proving this he added: for movement, as was said, corresponds to magnitude, and time, as we maintain, to movement. And62 similarly to the point the body in locomotion, by which we cognize the movement and the prior and the posterior involved in it [219b15-18]. For he said earlier [219a11-19] that movement corresponds to magnitude, and time too movement. For it is because the prior and the posterior, and the continuous as well, are in magnitude that the prior and posterior, and continuity, turn out to be in movement too: and, because of movement, in time too – with the difference that the prior and the posterior in magnitude means in position, since one can make a beginning from whichever part , but in the cases of movement and time this is not so. For in them it is not possible for what is prior to get to be posterior nor, conversely, what is posterior, prior. So, he says, just as these correspond to each other, so too between what so to speak generates and produces them. He has shown this by saying: And similarly to the point the body in locomotion, by which we cognize the movement. For the point is productive of magnitude, i.e. the point generates the line as it flows, and the line is the primary magnitude, and the body in locomotion is productive of the movement.63 For the body in locomotion is cause of the occurrence of the movement from Athens to Thebes, whether it is a man or whatever; and the cause of the occurrence of the movement from the Ram to the Bull64 is perhaps the sun or some other star that is moved in this way.

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And by this the movement is also cognized.65 Uncognizable in itself, it is cognized as belonging to that which is in motion. E.g. we cognize the completion of the heaven’s movement from the same to the same – its revolution – by nothing other than the heaven itself. For by seeing the same part of it appear twice at the same part of the horizon, we thereby cognize that a movement of a given quantity has come about. The now, too, is productive cause of time, since its flowing generates time. So if as the point stands to the magnitude and the moving body to the movement, so the now stands to time; and if the point being one and the same generates magnitude (for it is not by the juxtaposition of a plurality of points that the line is generated, but by the flowing of one point), and likewise the moving body, being one, generates the movement: it surely follows that the now, too, being one, generates time. For time is not generated by many nows lying side by side (since it is not constituted from nows), but by the flowing of one. For it is by the same now’s being taken as prior and posterior that time has being. So: just as the moving object is the same whatever it is by being which ; (i.e. it is a stone or a man or a star or something else), but through being taken in another and another it is different (since, as I said, for Socrates to be at home is one thing, and in the market-place another): so the now too is identical in substrate and in essence, the prior with the posterior, yet precisely through being prior and posterior it is different in description. To clarify things by an illustration so as to explain how we call the same in substrate but different in description, he mentioned what the sophists say. They seize on the point that for Coriscus to be in the Lyceum is one thing and in the market-place another, and carry this difference – which is incidental and descriptive – over to the substrate. They say: if for Coriscus it is one thing to be in the Lyceum and another in the market-place, it follows that Coriscus himself is a different from himself. But if something is different in description and incidentally, it need not be the case that it is therefore different in substrate too. For one and the same ladder is other and other in description, since its being a mode of ascent is one thing, of descent another. So in this way the now too is both the same and different: different in description when taken as prior and posterior, but identical in substrate.

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Translation 219b22 But the now corresponds to the body in locomotion, as time corresponds to the movement

Having said that ‘movement corresponds to magnitude, and time to movement, and similarly there corresponds to the point the body in locomotion’, and having interjected the sophists’ argument in between, in the present passage he supplies the missing part , i.e. that the now corresponds to the body in locomotion. For it is because the body in locomotion is taken in a certain prior and posterior, and its transitional stages get numbered, that the now has its subsistence. That the now corresponds to the body in locomotion he explained when he said: For it is by means of the body in locomotion that we cognize the prior and posterior involved in movement [219b23-4]. For just as, for every time and every movement, time accompanies movement and extends alongside it, so too the now the body in locomotion. For as the body in locomotion is to the movement, so, analogously, the now is to the time: from which it follows alternando that as the movement is to the time, so the body in locomotion is to the now. So: if the body in locomotion is one and the same whatever it is – whether a point or a stone or whatever it is – but differs in description through coming to be in another and another, the same kind of result will certainly hold for the now as well. 219b25 it is insofar as the prior and posterior is numerable that we get the now

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Having said ‘For it is by the body in locomotion that we cognize the prior and posterior involved in movement’ [219b23-4], he added: it is insofar as the prior and posterior is numerable that we get the now, implying by these words too that the now corresponds to the body in locomotion. For if the prior and the posterior in movement corresponds to the body in locomotion, and the prior and posterior in movement is the now (since insofar as the prior and posterior in movement is numerable, we get the now), the now will correspond to the body in locomotion.

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219b26 Hence in these also that, whatever it is, by being which it is now is the same (for it is the prior and posterior in movement), but its being is different: for it is insofar as the prior and posterior is numerable that we get the now. In this way he now draws the intended conclusion – namely, that the now is the same in substrate but other and other in description. (Hence in these also is instead of ‘ in the case of the nows’.) Just as the point too that is generative of the line is one and the same in substrate, and likewise the body in locomotion that is generative of the movement, so it is with the now that is generative of time. That, whatever it is, by being which it is now – i.e. whatever it is that is there at the level of substrate, and is now – is one and the same. He then follows up with what 66 is. , he says, the prior and posterior in movement. For the prior and posterior in movement are the same in substrate, since so too is the body in locomotion. But its being is different: i.e. in description. For the prior and posterior in movement, if not taken as numbered nor yet as prior and posterior, is the substrate of the nows; yet precisely this, whenever it is taken as prior and posterior and as occurring in accordance with the movement’s different ,67 is – then – other and other in description. For it is one thing for the prior itself to be, and another thing for the posterior.68

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219b28 And this is what is cognizable; for movement is cognised because of that which moves, and locomotion because of the body in locomotion. For the body in locomotion is a this, but the movement is not.

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He added this since his aim throughout has been to show the similarity of the now to the body in locomotion, and also because it is useful in itself for the study of time. It makes sense, he says, that the now is what is most cognizable about time, since the now is the only thing about time that is in existence. Movement too, being uncognizable in itself, is cognized by means of the body in locomotion, and the now corresponds to the body in locomotion; and as the body in locomotion is to movement, so the now is to time. So it makes sense

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that we also cognize time through the now, since we movement through what is in motion. And that locomotion is cognizable because of the body in locomotion he showed by saying: For the body in locomotion is a this, but the movement is not. For the body in motion is a substance and is there in existence, whereas movement is not there in existence but has its being in coming to be, since being, for movement, is in the passage of what moves. And besides: if the thing in motion is a substance, and the movement is an actuality, and in many cases substances are clearer to grasp than actualities, it is to be expected that movement should be cognizable through the object in motion. Having said: for movement is cognized because of that which moves, he added: and locomotion because of the body in locomotion, either make the same point in parallel fashion, or rather because he is passing from what is more general and less clear to what is more specific and clearer. For in the case of alteration too, the alteration is knowable because of what is being altered, and similarly with growth and diminution; but with locomotion the motion is known by means of the moving body, this being the most perspicuous case of all. 219b31 Thus the now in one way is69 the same, in another it is not the same; so too for the body in locomotion. This serves as conclusion of the preceding discussion. What he proved above he now asserts by way of conclusion. As the body in locomotion is the same in substrate but different in aspect and description, so too it is with the now.

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219b33 Clearly, too, if there were no time, there would be no now, and vice versa Having shown that time is number of the prior and posterior that is in movement, i.e. the now (since the now is the prior and posterior that is in movement), he has excellent reason to deduce that it is impossible for there to be one without the other. For if as the body in locomotion is to the locomotion, so too the now is to time, and

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there cannot be a thing in locomotion without locomotion, nor locomotion without something in locomotion, evidently time and the now too must be thus related: i.e. if one of them is posited the other is introduced too, and if one is taken away the other is taken away along with it. For this is how the point and the line are related too: they introduce each other and take away. 220a1 Just as the body in locomotion and its motion are together, so too are the number of the body in locomotion and the number of its motion. For the number of the locomotion is time, while the now corresponds to the body in locomotion, being like the unit of number. He speaks of the now as number of the object in locomotion, and of time as number of the locomotion. So just as the object in locomotion and the locomotion are, or are not,70 together, so it is too with the number of the object in locomotion and that of the locomotion, i.e. with the now and time: they are, or are not, together. But after saying for the number of the locomotion is time, he should have added: ‘and the now is the number of the object in locomotion’; but he said the now corresponds to the body in locomotion, and thereby in fact made his language more unclear. in what way the now is number of the object in locomotion, he added: being like the unit of number. For just as in the case of number the unit by being taken again and again produces the number of the objects being numbered, it itself being indivisible, so too the now, being indivisible and as a unit by being taken again and again, produces time. Therefore just as time which is being generated from the now measures the movement, so too the now measures the object in motion,71 and time is the number of the movement, and the now of the object in locomotion. He has already said in what way time is number of the locomotion: has its being not as numbering it, but in being numbered. But does number it: not insofar as it is locomotion, but insofar as the prior and the posterior in it. For time is not number of the movement itself: rather, it is the interval between the prior and posterior in it. And the now is number of the

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object in locomotion not insofar as is in locomotion, but insofar as is taken in a given prior and posterior. For the nows are what the taking of the prior and posterior accords with as it72 occurs. For the now in accordance with which73 the sun has come to be in the Ram, and again the now in accordance with which it has come to be in the Bull, would be the number of the sun itself as it comes to be in a given prior and posterior, comparable to units found in number. For just as it is the unit by which we number number or the numerable as such whatever it is (with the unit the ten horses and the ten stones; for we number each by counting up unit by unit), so too it is by the now that we number the object in locomotion, numbering its prior and posterior on the basis of which it continually comes to be at different places at different moments. For example, the sun comes to be in the Ram prior to the Bull, and in the Bull posterior to the Ram, and in the Bull prior to the Twins, and in the Twins posterior to the former; and so on. 220a4 Time, then, is both made continuous by the now and divided in virtue of the now. that the now is cause, for time, of both continuity and division, just as the object undergoing movement is for movement, and the point for the line. For here too the same analogy is again observed, except that the point when taken potentially is cause of the line’s continuity (that being continuous whose parts touch at a common boundary [Phys. V, 227a10-13; VI, 231a22]), and when taken potentially it is one; whereas if it is taken actually it both becomes cause of division of the line and is no longer one but two, with each of the two bounding one of the parts obtained by division. For is one by its own nature, and division comes about in accordance with that. For that which divides, insofar as it divides, must be one and without dimension. For this reason, that which is three-dimensional is divided by a surface, this being without the dimension of depth in respect of which the division takes place; and the surface is divided by a line, this being without the dimension of width (since the division is of a width); and the line by a point, this

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being in every respect without dimension. But when the point on the line is taken in actuality and divides it, it generates two points which are the division-ward boundaries of the two parts. Similarly, the object undergoing movement, too, is cause of both continuity and division for the movement. For it is because the object undergoing movement moves continuously and without break that the movement has the property of continuity; whereas if the object in locomotion interrupts it in the middle by halting, then it becomes a cause of division too for the movement. However, in the domain of coming to be and perishing, it is possible for the object undergoing movement to come to a halt in very actuality; for example, it is possible for the man walking from Athens to Thebes to halt in the middle and then finish the rest : in this way the object undergoing movement cut the movement from Athens to Thebes by halting. But in the domain of the heavenly bodies, the object in motion is cause solely of continuity for the movement; of division never in actuality but only in thought. Similarly, the now is cause of both continuity and division for time – but of continuity alone in every case, whereas of division solely in thought. For if it is not possible for the first movement, that of which time is primarily the measure, to come to a halt or be interrupted by rest, it is clear that it is not possible for time, either, to be cut in actuality; instead, we say that the now is cause of division in time only in thought. For by this we divide days into hours, and months into days, and years into months. The impossibility of time’s being divided in actuality is also clear from the following: movement too must come to a halt; but there is a demonstration showing that any two successive movements are always in every case separated by halting and rest, and that it is not possible for movements made two by division to be in continuous succession [cf. Phys. VIII, 262a12-263a3]. But if that is so, it follows that the two times that measure the two movements will have something between them that is not time.74 But whatever is between two nows is time. So there will be a time when there was no time: which is absurd. So it is not possible for time ever to be divided in actuality; but, as we said, only in thought is it divided by the now.

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Translation 220a6 For here too there is a correspondence with the locomotion and the object in locomotion.

Just as time and the now necessitate that time both is continuous because of the now and is divided in virtue of the now, so this same follows both for locomotion and for the object in locomotion, that the movement both is continuous because of the object in locomotion and is divided in accordance with it.75 And in similar fashion the same follows for the point and the line, as we have already said. 220a6 For movement too or locomotion is made one by the object in locomotion, because it is one – and not whatever it is by being which (for might intermit) – but in description.

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Having said that movement or locomotion is made one by the object in locomotion he followed up in what way it is one on account of the object in locomotion: because the object in locomotion is one, he says, – and not one whatever it is by being which (for in that case it might intermit) – but in description. I.e., if the object in locomotion is one, and not only in substrate (for whatever it is by being which signifies this), but also in description, then the movement is one.76 Since the moving object, which in itself is one, can also interrupt its motion, in that way the object in locomotion would be one, yet the movement would no longer be one and continuous but would be two movements arising from division. But is taken as one in description too, i.e. as moving (for if it intermits it will no longer be one in description, but two, since its being as a moving object is one thing and as an object at rest another) – if, then, it is taken as one in description too, then the movement is one and continuous, and this belongs to on account of the object in locomotion. In this way the point too makes the line one and the now the time one, on condition that the point is one and the now both in substrate and in description. For if the point is subject of two descriptions, and is end of this line and beginning of

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that, then the lines are two, and the point is cause not of continuity but of division; but if it is one in description, i.e. is taken only as common boundary of both the parts,77 then the line is one and continuous, and the point is cause of this. It is the same with time and the now.

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220a8 And this determines the movement as prior and posterior. Having said that ‘movement and locomotion are one through the object in locomotion’ and having explained in what way they are one, that whenever the object in locomotion is taken as one both in substrate and in description, he now states the way in which it is cause of division in movement: whenever the object in locomotion halts and then starts moving again, the earlier movement gets its end and the second one its beginning, and the movements are two, not one. So in this way, the object in locomotion is cause of division too.

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220a9 This corresponds in a way to the point. We have already said in what way the point is cause of both continuity and division for the line. But he added in a way because in the case of magnitudes the point does divide the line in actuality, whereas the now never divides time in actuality, as we said (and also in the celestial domain the object in locomotion does not the movement except for thought, as we have already said). So on this account would differ from each other, and he would be entitled to add in a way for this reason too. Aristotle himself, however, has provided the exegesis of why he added in a way by following up with: for the point too both holds together and demarcates78 the length – for it is beginning of this and end of that. But when you take it in this way, using the one point as two, it must stand still79 if the same point is to be both beginning and end. The now, on the other hand, since the body in locomotion is moving, is always different [220a10-14]. For in the case of the point and the magnitude, the same point taken twice and numbered, as beginning and end, and staying (for that is how it is

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taken twice), comes to be end of one line and beginning of the other, and in this way it numbers80 the magnitudes and marks them off. But the now does not like this, for the prior now does not stay for the posterior one. Instead: because corresponds to the object in locomotion – and the object in locomotion (through its coming to be in different places at different moments) cannot stay, so that it is not possible that it be taken as the same twice – the now (consequently) likewise does not stay (and is not taken twice together81), as happens with the point.82 However, nothing prevents it, though one and the same, from being subject of two descriptions. For the now that demarcates the day from the night is end of the one and beginning of the other, whenever (as I said) it is taken as dividing these times in thought, not in actuality. 220a14 Hence time is not number in the way in which there is of the same point because it is beginning and end, but rather as the extremities of the same are a number. What has been stated, he says, implies that when we call time number (it is called number because its prior and posterior – which are nows – are numbered), we do not speak of it, or of the nows in it, as number in the way in which we call the point number when we take the same one twice, i.e. as having the description ‘end’ and the ‘beginning’. For the point, since it has position and stays put and subsists in an object that has position and stays put, can be taken twice, for it will not escape our taking; but the now cannot be taken twice, both as beginning and as end. For because time, in which it subsists, has its being in becoming and in flowing, the same now cannot be taken twice, both as beginning and as end. For by doing that we would halt time. For if it is the end of this time and the beginning of that, time has been divided and the times and the movements are two: but it will be proved [Phys. VIII, 262a12263a3; cf. V, 228a20-b1] that two movements cannot be continuous: in all cases they are interrupted by rest. So if it is impossible for this to happen with time, it is also therefore impossible for the same now to be taken twice. In that way, then, it is impossible for nows, or the time marked off by them, to be number; however, it is possible in the

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way extremes of the bounded line . For the extremes of the line are two points lying in opposite directions, by which it is limited in each direction: and these have number. For the extremes of the bounded line are two, yet not two in the manner of the same point taken twice (I mean both as beginning and as end83), but with each being subject of one description, that of ‘limit’. So in this way the now, too, is number: not as the same item taken twice, but as other and other and in another and another part of time. (For it is in this way too that the on the line are two: as being in another and another of the line.) But is other and other not in respect of substrate (in this respect it was shown to be the same), but because that which is the same is taken in another and another, and as prior and posterior, just as the in the market place is one Coriscus and the one in the Lyceum another, but the same in substrate. 220a16 and not as the parts , both for the reason given (i.e. one will be treating the mid-point as two, so that in consequence will stand still), and further because obviously neither is time part of movement84 Having shown that time, i.e. the nows by which time is numbered, cannot be number in the same way as the same point taken twice both as end and as beginning – whereas in the way the ends of the bounded line are – he shows that it is also not number in the way the parts of the line are: i.e. if one were to divide the line either in actuality or in thought, and say that it is number as having two parts. So in this way too it is not possible to say that time is number, by its having the nows by which it is numbered as parts. For it is impossible, he says, for nows to be parts of time. The first reason is what has already been stated: i.e. if the prior and the posterior now are parts of time, then, since they are divided from each other, the one now occurring at sunrise, as it might be, and the other at sunset, there will be something in between that divides them; so again one will be treating this item as two just as we treat as two the point at which the division of the line occurs – as the end of one of the parts of the line and as the beginning of the

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other, or (in a word) as terminating two lines but with the end-points in each case having their own description.85 So again it will result that time is divided in actuality.86 So both for that reason (he says) it is impossible for nows to be parts of time, and also because nows cannot be parts of it any more than points can be of the line, it being impossible for partless entities to be parts of what is divisible into parts.87 The parts of the line are lines; similarly, then, the parts of time too are times. Where he should have said ‘and further it is obvious that neither are the nows part of time’, his words are  neither is time part of movement, meaning by time the nows. The nows cannot be parts either of the movement of which time is the number or of time itself, for the reasons stated. However, there is also the point that time itself cannot be a part of movement; for the ten (hê dekas) itself, too, which numbers the ten (deka) horses is not part of the ten horses, nor is the bushel (I mean the measure itself) part of the grain that is measured by it. But we can also interpret ‘movement’ as meaning not the movement of the heaven (or, speaking generally, the magnitude of which time is said to be the measure88), but the very flow of the now from which time . And since time is said to be number, and the number of time is in virtue of the nows, he said ‘time’ instead of ‘the nows’, and ‘movement (of the now)’ instead of ‘time’.89 220a21 In so far then as the now is a limit, it is not time but is incidental to it; but in so far as it numbers ;90 for limits belong only to that of which they are limits, but the number of these91 horses, ten (hê dekas), occurs elsewhere too. The now is both a limit of something, and now. Insofar as it is a limit, he says, it is not time but is incidental to time, just as the point is to the line (for the limit is incidental to that of which it is limit). However, taken as limit it is not in fact now, but the substrate of92 the now. For the now does not consist in being the limit of time, but in being numbered according to prior and posterior. Consequently, but is incidental can be understood as ‘but the now is incidentally related to this which is taken as limit’; whereas it is insofar as it is

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numbered, being taken again and again and as prior and posterior, that it is time. For the interval between repeatedly taken nows is time.93 This is how he shows that when the now is taken as limit, it is not time: limits are only in those entities of which they are limits, and they are limits of them alone, not of other things, whereas time one and the same is common to all things and is everywhere the same. Hence the nows are not time insofar as they are limits. For time is in every movement, since it can measure every movement. For just as the same number is in all things, not just in things of the same kind but also in heterogeneous things (for one and the same ten [dekas] is in the ten [deka] horses and ten asses and ten pieces of wood and however many other collections of ten [dekades] there might be, and although as ten [deka] they are not the same,94 as ten [dekas], it is one for all the cases), in this way, the nows too, being taken as number, are both time and one and the same everywhere; but in substrate they are limits of movement. That is why taken as limits they are not the same everywhere, for different movements have different limits. He seems also to be showing by means of these considerations that time is number not of some particular specified movement, but of all movement without distinction insofar as it is movement, even if differ in species – for they are numerable just the same. At any rate with movements that take place simultaneously [kata t’auto] and have their beginnings and their ends together, the prior and the posterior in them, insofar as it is limit, is not the same in all of them (for some limits are of growth and others are of alteration and others are of locomotion). But insofar as the prior and the posterior in them is numerable, it is one and the same in all of them, and the interval between is one and the same time, capable of measuring all . It is because of this that although many objects are together moving, and the movement of each is measured by time, still it is not the case that there are many times. This is because time has its role of numbering the prior and posterior in movement not insofar as is locomotion or insofar as it is alteration or growth or diminution, but simply in so far as it

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is movement. For, as he said, does not regard them as limits but simply insofar as they are the prior and the posterior of movement; and with movements that occur together, the prior and the posterior are one and the same,95 just as the many tens (dekades), even if heterogeneous in their substrates and at a distance from each other, have one and the same ten (dekas) as their measure. With reference to this passage Alexander asks: ‘What is but in so far as it numbers?’96 For time, he says, was not as numbering, but as numbered. He says that either the text is mistaken in giving it numbers rather than ‘it is numbered’, or (he says) ‘the nows are numbered in the movement, but they number time. For it is in virtue of the nows that the division of time occurs.’ Indeed, in what comes next, too, seems to be treating the now as number that numbers. For he says: the number of these horses, ten, occurs elsewhere too. It is number as numbering which can be elsewhere too, not number as numbered.97 Certainly, since time’s being consists in movement’s being numbered, and movement is numbered in accordance with the prior and posterior in it – which prior and posterior, when taken as prior and posterior and not simply as limits of this or that movement, turns out to be now – it is clear that movement is numbered in accordance with the nows. Since, then, time is not the nows, but is what is marked off and contained by the nows, and, as has already been stated, the division of time is in accordance with them, they would indeed have being as numbering time. So they are, on the one hand, numbered – insofar as they are observed in movement – and, on the other hand, they number time. 220a24 It is clear, then, that time is number of movement in respect of the prior and posterior, and is continuous since it is an attribute of what is continuous.

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movement in the sense of having its being in numbering that: for time is not number of movement itself, but of the prior and posterior in movement; for if it is taken as number of movement simply, it will not number the prior and posterior at all, as when I say that the number five is measure of the five movements just as it is of the five horses or human beings. This sort of number is of movement, but it is not time, since it is the number not of the prior and posterior in movements but of the movements themselves. He adds and is continuous, because is number of continuous, not of divided, movement. For it is through the movement’s being numbered in accordance with the prior and posterior, continuous that time subsists as a continuous reality, extending along with the continuity of the movement. For because the movement never breaks off, the prior and posterior in it likewise does not break off; and because this does not break off, time does not, either. For this is time: number of the prior and posterior in movement. Hence time too is continuous. 220a27 The smallest number, without qualification,98 is two; but a number qualified in a given way is in a way and in a way not Having said that time is number of movement, and having said that movement corresponds to magnitude and time to movement, so that, the magnitude being continuous, the movement must be continuous too, and because of it the time, he might have raised the difficulty of how time can be both continuous and number. For these are contraries of each other. Time is continuous, but number is not continuous: so time is not number. For if time is number, and the continuous is not number, it follows that time is not continuous. So one must assert one or other of two positions: either that time is not continuous or that it is not number. But time must be continuous. So time is not number. It is this difficulty that he solves in the present passage. Since number is twofold – the number with which we number, which is the one in the soul, and the number that itself is numbered, the numbering number is in no way continuous, for it has its being in our soul;

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so if the soul is not a magnitude, obviously it is not continuous; for every magnitude is continuous.99 Therefore the number in it is not continuous either. However, number that is numbered – i.e. that time is – is in one way continuous and in another way number. Insofar as it has the prior and the posterior it is number, whereas insofar as it is in a continuous substrate it itself is continuous too. By way of parallel, (he says), the smallest number of lines is two, so that insofar as the two lines participate in number they both are numbered and have the minimum in the domain of numbers, two, whereas insofar as they are lines they no longer have a minimum, since every line is infinitely divisible. That is how it is with time too: insofar as it is numbered by days and nights and the other segments of time it is number, whereas insofar as this number has its being in movement, the movement being continuous, it too must be continuous. So it is not at all impossible for the self-same to be both continuous and number. But given that number admits of large and small, whereas the continuous for a line admits of long and short, and for a surface broad and narrow, the number in the soul, not being continuous, only admits of large and small and not of long and short; whereas the number that is numbered admits qua number of large and small – for we say ‘a large days’ and ‘a large time’ – whereas qua continuous it also admits of long and short – for we say ‘in a short time’ and ‘in a long ’ [cf. 220a32-5]. But, he says, fast and slow are not in time. For fast and slow are simply in movement. Of movements, one is faster and another slower; but since time is number of uniform movement, it is appropriate that it does not have faster and slower. Next he says that present time is one and the same, whereas past time is other than future time.100 He means present in the broad sense, for example  [brief lacuna probably containing a phrase such as ‘the present day’]. For while today is one and the same, yesterday is other in relation to tomorrow, since their nows too are other. For the now from which yesterday began is other than the now from which tomorrow will begin, and similarly with the nows at which each ceases. The nows being different, then, the times contained by the nows

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are different too. For if time were the number that numbers,101 it would be one and the same (for the number in the soul, being one and the same, e.g. ten (hê dekas) numbers the ten (deka) horses or the ten human beings, and so on), whereas the ten (hê dekas) in the horses is another besides the ten in human beings or in stones, since the substrates are other.102 But since time is numbered, i.e. not numbering, number, past time is not the same as future time, nor are these the same as present time; instead they are other than each other, as has been stated. But are they in no way the same as each other? Well, his position is what he has already said: that they are the same in kind, but not in aspect and description [cf. 219b12-15]. In the way it is possible for the same movement to occur again and again, and many times over return from the same to the same, and these movements are the same in kind but not the same in number – in that way, it is possible for the times to be the same: spring, and again spring, and so on for the other . These too are not the same in number, but are the same in kind. Next [221a15ff.] he states that not only does time measure movement, but time is also reciprocally measured by movement. For we say that a large103 movement has occurred, measuring it by the time, because the time large, and conversely that a large time , measuring it by the movement, because a large movement has occurred. In the same way, not only is the amphora measured by the wine, but the wine, too, by the amphora. For we say that the amphora is large when we measure it by this-much wine, and conversely we say that the wine is this-much when we measure it by the amphora; and we apply the term ‘bushel’ to this-much grain by the measure, and similarly we that the measure is a bushel, determining it and measuring it by this-much grain. But perhaps the measure is only what measures the grain or the wine, and is not also reciprocally measured by it. For even if the wine measures the amphora and the grain the bushel, still they having been previously measured by another measure, so that that which measures principally is the measure. And if by means of the wine and the grain we do measure the amphora or the bushel, all the same we do so treating them as still indeterminate and as not yet functioning as measures. Hence even if these are measured immedi-

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ately by the grain and the wine, still that is when the latter have already been determined and measured by measures. Thus the measure is that which measures principally and primarily. However, I say that even if this bushel here is measured by the grain already measured by another bushel, still in simple terms and, as it were, in keeping with the first proposal, the bushel [sc. the one here] has been determined by this amount of grain, and this amount of grain has been measured by the [sc. prior] bushel.104 But with time one cannot say this. For it is not the case that first the movement is measured by the time and then it reciprocally measures the time. Instead, they are apprehended together with each other, like relatives. So just as together and by the same token the father owes being father to the son, and the son owes being son to the father, and similarly with the right and the left – just so are time and movement determined by each other. For if time is number, it obviously falls into the class of relatives, since number is of what is numerable. But movement is what is numerable by time. Thus it is both the case that movement owes its being this-much to time (since time is number of it), and the case that the time’s being this-much comes from no other source but movement. For if were not, time too would not be, just as, if time (by which I mean number of movement) were not, movement too would not be; for movement is something numerable. By ‘number’ I mean not simply the number that is measured by us, but the number that is present in things. As with the ten stones: even if no one is there to number them and say that they are ten, still being ten holds of them just as much; and in the same way I say of time too, by which I mean the number of movement, that even if no one is there to measure the movements, it belongs to them just the same to be of such and such quantities. For the revolution of the sun occurring ten times over from the same to the same is just as much a tenfold occurrence even if no one is there to count it. This is the sort of number of movement that time is. The smallest number in a way is and in a way is not105 With these words he introduces the solution (as if for an already acknowledged difficulty), without having posed the difficulty. The meaning of the in front of us is as follows. Since time is continuous, and he has said that time is number of movement, and in the continuous

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there is no minimum as it is infinitely divisible, whereas in number there is, namely two (hê duas) – and these , which are contraries, seem to belong to time which is one and the same (because time is both continuous and number) – he states in what way these attributes hold of it. He says that in a certain respect number has a smallest, and in a certain respect it does not. In respect of the substrate number does not have a smallest because it is number of continuous entities such as lines or movements; but in respect of definition, and insofar as it is number, it does have a smallest. For in respect of number the smallest is one or two (ho heis ê duo106) [220a31-2]. The point is not that one (hê monas) is a number; rather, the statement has been made hypothetically: if we thought that one is a number, one would be the smallest number. (According to one account at least, two is not a number either. For if number is the plurality that consists of ones, then two is indeed a number; but that two is a number is refuted by the following line of argument: every number when multiplied by itself is greater than when added to itself, e.g. three multiplied by itself makes nine, whereas added to itself it makes six, and so on for all cases; but two, when added to, and when multiplied by, itself, makes the same (since twice two is four, and two plus two is four). So in this way, two is not a number, and the smallest number is three.107)

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220b3 it is not fast and slow – for nor is any number with which we number fast and slow He seems to be saying that time does not admit of fast and slow because this is also true of the number by which we number time, i.e. the number in the soul. But, since things in the world are not determined by our thought, that is not what he asserts. Instead, ‘the number with which we number’ is what he is calling the number that has been numbered on the basis of which there is time: I mean the movement that has been numbered. For it is by means of this that we number time. For whatever the amount of the movement, that (we say) is the amount of time too. So since this [sc. the movement] does not admit of fast and slow,108 time too will not

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admit of fast and slow. However, it is also possible to take nor is  number with which we number as meaning the number in the soul. For since we determine time by the number in the soul, given that this does not admit of fast and slow it makes sense that what we determine by means of it does not admit of them either. For the number in the soul does admit of large and small, and time too admits of large and small. How, then, given that the number in the soul does not admit of long and short, is it that time admits of long and short? My answer is that it is through the substrate that time admits of long and short. Since it is number of something continuous, namely movement; and movement is continuous because the magnitude where the movement occurs is continuous; and long and short hold of the magnitude: it makes sense that long and short hold both of movement and of time. It is because of the substrate, then, that long and short belong to time, and not in so far as it is number. 220b5 And so109 the same is everywhere together. But prior and posterior are not the same110

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The same everywhere is the present. For the stretch of time present is one, whereas the prior stretch is not the same as the posterior one, as the limits of each are different. 220b8 Time is not number with which we number, but that is numbered

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For if time were number by which we number, past time and future time would be one, since the number in the soul is one. But as things are, is not numbering but numbered , so that past and future time are other and other. For numbering is the same, but the items numbered are not the same. 220b12 Further, as a movement can be one and the same again and again

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– in kind, of course – just as many movements can be the same in kind. 220b14 Not only do we measure the movement by the time that not only does time measure movement, but movement also measures time; and we have said in what way [cf. 741,21ff.]. 220b19 just as we the number by means of what is counted, e.g. the number of the horses by means of the one horse111 Just as (he says) we cognize the number of horses, e.g. ten horses, by the ten that is in them, and again we cognize this by means of the number of horses, so it is with time and movement: they can measure each other. 220b24 And this result makes sense. For movement corresponds to magnitude, and time to movement, because they are quanta and continuous and divisible. To prove that time and movement are measured reciprocally, he makes the point that movement corresponds to magnitude, and time to movement. For if what is true of magnitude is also true of movement, and what is true of movement is also true of time, it is clear that when there is much movement there must also be much time, and conversely that when there is much time also be much movement. For just as movement and time correspond to each other in respect of continuous and divisible, etc., so they also correspond in respect of much and little and long and short. Hence each is a measure of the other. For if one is much or little, or long or short, etc., the other must be so too. 220b32 Since112 time is measure of movement and of being moved

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Different identify the aim of this passage differently. Alexander says that proposes to show here in what way time is said to measure movement, and generally in what way movement is said to be in time, and in what way anything else (in a word) is said to be in time. However, others say that the aim of the passage is to show that time measures not only movement but also rest. Their evidence for this is the fact that in conclusion Aristotle says ‘since time is measure of movement, it will also be measure of rest’ [221b7-8]. But it would be closer to the truth to say that Aristotle’s aim concerns not one of these , but all of them: in what way movement is measured by time; in what way things are said to be in time; and that time is measure not only of movement but also of rest. That being the aim of the discussion, he first asks in what way time is measure of movement. gives rise to an understandable difficulty. The measure is supposed to be homogeneous with the object in motion.113 For we measure number by means of the unit: we measure the group of ten horses by the one horse, and the piece of wood by its part. So if time is not homogeneous with movement (since it has been shown that time is not movement), in what way do we say that movement is measured by time? Well, he says that if movement measures time 114 through measuring a certain movement by means of which one measures out the rest . E.g., perhaps it defines an hour-long movement, and by means of this it measures the day, and by means of the day, the year. For ‘year’ is what we call so many revolutions . For ‘measure’ is said in two ways: there is measure that is set apart115 and there is measure that is classified along with and is the same in kind. One can measure the piece of wood by means of the cubit,116 and one can also do so by as it were removing a portion of it and by means of this measuring out the rest. The cubit would be the measure set apart, and the portion would be that is the same in kind and classified along with ; and so it is with every measure. For instance, the pint pot would be a measure set apart, and a fortiori so would be the pint in the soul that also determines the external pint.117 However, if the pint of wine measured measures all the rest , it would be a measure that is classified along with . As it is in these cases, then, so it is with time: time is a measure set apart, and the part of movement by which the rest is measured is a measure classified along with. So what is the part of movement that is primarily determined by time to be measure of all the movement118 119 time does not measure primarily? So if it does indeed measure a certain movement primarily, on account of what does it not all ? Just how does it determine some movement by which it measures the rest, given that all the movement is single and continuous? Well, I say that just as one might with one’s hand measure and mark off the ten thousandth part of a schoinos,120 and then with that measure the rest of the schoinos, so it is with time. For the marked off part is by convention, not by nature, which is why different people choose different measures for hours and months and years.121 So once a part of the movement has been marked off, and has been given primary determination by [i.e. in terms of] time (I mean, by the number of the prior and the posterior of the movementpart), through this all the rest of the movement is measured as by a measure closer to it. So it is this movement that time primarily measures and determines, and by means of it the whole of the rest of the movement. This, then, is how movement is measured by time; and in this way, he says [221a5-7], movement is also said to be in time, because its being is measured by time. But movement is measured by time not insofar as it is everlasting,122 but because any given part of it is bounded; qua everlasting it is not measured by . In fact, he says [221a9-11] that what is in time is twofold:123 (1) that which co-exists with time, and is when time is; and (2) that which has a certain time by which one can measure its being is said to be in time. Just so, that which is in number is twofold, he says (221a11-13]: (a) that which is either a part or an attribute of number (e.g. we say that the unit is in number as being part of number, and we say that the odd and even are in number as attributes of number; and these are together with number, since as long as there is number there are these too); so that is one way in which we say that something is in number. According to the other way, (b) something is said to be in number if it is what has a certain

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number: e.g. we say that the ten horses are in number, i.e. there is a number of them. Since, then, that which is in number is two-fold, that which is in time is twofold too, as time too is a sort of number. When we say that the now is in time we mean that it is so as part in a whole,124 just as the unit is in number; but when we say that the prior and posterior are in time, we mean that they are so as attributes [cf. 221a11-16]. These are together with time, since nows and the prior and the posterior are together with time. Again, we say that things are in time in that a given time is measure of their being, just as we said that the second sense of ‘ in number’ is having a certain number: e.g. the ten horses have the number ten. At any rate the latter is the strict way of in time, since what is together with time is surely not in time in the strict way. For if what is together with time is in time, then since the soul and all divine beings are together with time (when time is, they are too) these things too would be in time. Thus just as it is not the case that what is together with movement is in movement, nor that what is together with place is in place [cf. 221a20-1] (for instance, all incorporeal beings – I mean, angels and God: for it is not the case that movement or place existed when these beings did not; yet nonetheless these beings are neither in movement nor in place): so too ‘together with time’ is not ‘in time’. For if what is together with something is in it, then since, he says [221a21-3], the celestial system is when the millet-seed is, the celestial system would be in the millet-seed. So it is also not the case that what is when time also is, is in time, just as it is not the case that what is when the millet-seed is, is in the millet-seed. Accordingly, it is not universally the case that what is when time is, is in time. For being in something in the strict way means being contained by it [cf. Phys. III, 210a24; 221a28-30]. So is in time in the strict way is that which has a certain time by which it can be measured, , e.g. ten or some other . But if this is in time, then for anything that is in time a greater time must be assigned, just as for that which is in this way in number a greater number must be assigned. It is, he says, for this reason, because what is in time in the strict way is what has a time greater

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than itself, that we say that all things grow old through time, and that time makes all things perish, whereas we do not say that they come into being through time [221a31-b2]. One might reasonably ask how it is that he asserts that we say that time is cause of perishing and not of coming to be. For we do say that things come to be in time: ‘Long and innumerable time’, says , ‘brings all That’s hidden to birth’126 and: ‘Time makes me know something’.127 How does he simply say that all things are made to perish by time? After all, he himself said in the first discourse that everything that perishes is made to perish by its contrary [Phys. I, 192a21-2];128 but time is not contrary to anything. For time is a sort of quantity, but nothing is contrary to quantity; and is together with all things that are, but nothing is together with its contrary. I say, then, in response to this: first, he did not actually say ‘we by no means say that things come into being through time’, but, instead, that we say that they perish rather than come to be (for, he says, time in itself is the cause rather of perishing). Secondly, what causes the coming to be of each thing is definite and evident, e.g. the progenitor of the animal and the teacher of the learner’s knowledge. So it is because we are able to attribute the coming to be to some definite cause that no one says that time generated, but instead that the father generated, nor that time taught, but instead that the teacher did. But with perishing and forgetfulness, when we cannot show any definite cause we attribute the causality to time – since when we have an obvious cause of the perishing, e.g. if the house is destroyed by fire, we call the fire, not time, cause of the destruction, and the shipwreck cause of the death, and we often say that illness is cause of forgetfulness, and toil of aging. So with perishing too, when the cause is definite, we assign the causation to it and not to time. So it is clear from this why we assign causation to time more for what perishes than for what comes to be. If the entities in time are those for which there is a time greater than theirs, reason suggests that everlasting ones and those that are

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throughout all time, are not in time; for there is no time greater than theirs. An indication of this, he says [221b5-7], is that time does not affect them. For if what is in time is affected by time, it follows that what is not affected by time is not in time; and what is throughout all time is not affected by time. So such entities are not in time. But since time is measure of movement and of being moved [220b32-221a1] Having said: of movement he has added: and of being moved. By being moved he either means what further on he speaks of as movement and its being [221a5], so that he says being moved is the being of movement; or, having mentioned movement, he added and being moved so as to draw us to the precise thought of its continuance. For ‘movement’ also signifies the very form of movement, whereas ‘being moved’ signifies precisely its continuance, of which time is measure. Thus being moved explains of movement. 221a4 and movement’s being in time is its being measured by time, both it and its being say that the conjunction ‘and’ (kai) is superfluous, on the ground that the apodosis of the subordinate clause But since time is measure of movement and of being moved [220b32221a1] is: movement’s being in time is its being measured by time, both it and its being. Others say that the apodosis is given in : it is clear that for other things too being in time is this [221a7-8]. I.e. since, as he says, time is measure of movement, and movement’s being in time is its being measured by time, it is clear that for other things too being in time is this. But on this the conjunction ‘and/but’ (de) in the and/but it is clear that129 is superfluous. Yet others say that the apodosis comes much later, ‘But since time is measure of movement, it is measure of rest too’ [221b7].130 That is why, according to them, he repeated But since is [221b7]: he did so in order to preserve the sequence given the length of the passage in between. We for our part say that he has given an apodosis that acknowledges all these , so that the sequence is: ‘But since time is measure of movement and of moving: movement’s being in time is its being

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measured by time, and for other things too this is being in time, being measured by it; and if time is measure of movement it is also measure of rest.’131 In what way it is measure of rest we shall find out when we get to the passage. being measured by time, both it and its being.132 In the case of composite entities, being X is one thing and what it is to be X is another, e.g. being animal and what it is to be animal are different, for ‘animal’ signifies the composite, and ‘what it is to be animal’ the form.133 But with simple entities being X and what it is to be X are the same. Anyway, being soul and what it is to be soul are the same, as are being angel and what it is to be angel. For this reason, then, being movement and what it is to be movement are also the same, as movement is something simple.

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221a9 To be in time is one of two things By this he means either: ‘in time’ is two-fold, or: ‘in time’ being said in two ways, only one of them is strictly in time. For he proposes two significations for ‘in time’, and selects just one as true while refuting the other. ‘In time’, he says, either what is there together with time (this is what he will object to, not that none of the entities that are in time is together with time, but that together with time is not in all cases in time, as we shall show in due course) – anyway, to resume: he says, ‘in time’ either to what co-exists with time or to what is contained by time (just as we say that some things are in number because they are contained by number). The latter is the strict ‘in time’. But this strict ‘in time’ he again divides into two: either as a part or attribute of time, or as measured by time (e.g. we say that the Trojan war happened in time because it occupied ten years). For ‘ in number’ too, to which he likens the strict ‘ in time’, is itself two-fold, denoting either a part and attribute of number, like the unit and the odd and the even, or numbered by number, as when we say that the ten horses are in number. Notice that one signification of strict ‘in time’ pertains to things whose subsistence is time. For the part of time and the attribute – I mean the now and the

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prior and the posterior, subsist with time. For there is no time at all in which there is not the now and the prior and the posterior, just as the unit and either the odd or the even subsist along with every case of number. What is strictly in something is so either as part in a whole or as in a substrate. It is in the latter way that the attribute is in that of which it is attribute. For the odd and the even are in number as in a substrate, just as the prior and posterior are in time as in a substrate. Thus I was right in saying that he asserts not that everything that co-subsists with time is not in time, but that being in time is not co-subsisting with time. For a certain class of what co-subsists with time is in time: the part and the attribute of , as I said. And he himself, at least, asserts that the movement of which time is measure, I mean that of the fixed , is in time. For he says: ‘And for movement to be in time is for it to be measured by time, both it and its being’ [221a4-5]. That it is the movement of the fixed that he here says is in time is clear from what precedes. For, he says, since time is measure of movement and of moving, for movement to be in time is for it to be measured by time. But time is measure of no other movement than that of the fixed .134 Hence he is also saying that the movement of fixed is in time, even though it gives subsistence to time. Thus the point is not that everything that co-subsists with time is not in time; rather, it is that not just everything that co-subsists with time is in time. For of course the point, too, co-subsists with the line, and the surface with the body (the line and the body being bounded ones, obviously), yet even so the point is in the line and the surface in the body. In this way, then, although time and movement co-subsist with each other, it is possible to say both that time is in movement as in a substrate, and that movement is in time as numerable objects are in number. For time is something numerable, and time is number. For, likewise, many things that are co-subsistent with place are said to be in place; for each of the spheres and of the total masses of the elements is co-subsistent with its own place, yet even so is in place; and each of the moving bodies, I mean the celestial ones, is co-subsistent with its own movement, and yet is in movement. In this way, then, the movement of the whole too,

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being co-subsistent with time, will be in time, as numbered things are in number. 221a19 Plainly, too, to be in time is not to be when time is Notice that he does not say that ‘that which is when time is, is not in time’, but: to be in time is not to be then when time too is. For being in movement, too, is not being together with movement.

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221a21 For if ‘to be in something’ is to mean this, then all things will be in anything whatever: even the heaven in a millet-seed. He shows that in time is not being then when time is. For in time is in something; on the contrary that in time is being then when itself is: it follows that being in something is being then when it is. But if this is in something is, and if this is distinctive of in something, namely being then when it is, i.e. co-existing and being together with , it is clear that the proposition will convert and that whatever co-subsists with something and is then when it, too, is, will be in it. Hence since when the millet-seed is, then the heaven too is, the heaven will be in the millet-seed. And since the amphora is then when the sea too is, the sea will be in the amphora. Consequently, if these are impossible, in something is not being co-existent with it. And let no one find fault with the conversion136 on the ground that we converted a universal affirmative proposition with itself. For in the first place it must be understood that unless we use the conversion, we should not deduce the absurdity of the heaven’s being in the millet-seed (for no one will grant this; , rather, that anything that is in X must also be then when X is, but not that what co-subsists with X is thereby also in it; hence the heaven, being when the millet-seed also is, will not be logically bound to be in the millet-seed). But given the conversion, the conclusion follows. For if in X is being then when X too is, then obviously that which is when something else is, is in it. But in that case, the heaven must be in the millet-seed. But we necessarily converted the universal proposition with itself, since for any given

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item, what is definitive of being it is convertible with it.137 For if what it is to be man is what it is to be rational mortal animal, then, too, what it is to be rational mortal animal is what it is to be man. In this way, then, since it is supposed that what is distinctive and definitive of in something is being then when that thing too is in which it is said to be, the converse, reasonably enough, will also , and that which is co-existent with something will be in it. 221a23 But this is incidental, whereas the other is necessarily involved; for that which is in time there is, , a given time when it is It is an incidental fact that the heaven is when the millet-seed also is, i.e. that they co-exist with each other. For it is possible that when one of them, e.g. the heaven, is, the other – the millet-seed – is not. Co-existence with each other belongs to them – I mean the heaven and the millet-seed – incidentally, whereas for something that is in time it is a necessary consequence that there is a given time when it too is. So if some items that are in a given thing co-exist with it of necessity, whereas some of its co-existents do not co-exist with it of necessity, it follows that not everything that co-exists with a given thing is in that very thing, and also that in something is not being then when it is, I mean co-existing with it. 221a26 Since what is in time is so in the same way as what is in number,138 a time greater than anything in time can be assigned.

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For everything that is in number, there is some greater number; so that for what is in time too there is some greater time. 221a30 A thing, then, is affected in a way by time

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For if for everything that is in time one can assign a larger time, it makes sense that they are all affected by time and made to age by it, for they all run past and pass away.

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221b1 For time in itself is cause rather of perishing, since it is number of movement, and movement shifts away what is currently given. Since time is number of movement, and all movement shifts away from something, it makes sense that time is cause of perishing rather than of coming to be. 221b5 An indication of this is that none is affected by time It is, he says, an indication that everlasting things are not in time that none is made to age by time. For if things in time are made to age by time, and everlasting things are not made to age by time, it follows that everlasting things are not in time.

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221b7 Since time is measure of movement, it is139 measure of rest too incidentally. We said earlier that it is his aim to show that time is measure not only of movement, but also of rest. And this makes sense, since every sort of cognition grasps not only forms but also privations. For the eye knows not only light but also darkness; but it knows light per se, and darkness by the negation of light. Similarly in other cases: the straight-edge discriminates the straight and the bent; but it discriminates the straight per se by conforming to it, and the bent by the negation of the straight. For in not conforming it discriminates – not directly nor affirmatively, but by denial and negatively. In this way, then, time is number not only of movement but also of rest: of movement through itself, by measuring its continuance140 and as it were being continuated along with it, but of rest, he says, incidentally; it would have been stricter to say ‘through something else’. For it is by measuring movement – since in the period when one thing is moving another thing can be at rest – that time that measures the movement thereby measures the rest too. For we speak of rest as lasting a day or a year because was at rest for as much time as some other took to carry out a

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movement, the continuance being observed not in the rest but through something else. For it is because something else comes to be in continuance that rest too is said to have continuance. We were right to say that time measures rest not incidentally but through something else, namely by measuring movement. For if it measured the rest incidentally while measuring the movement per se, the rest would have had to be incidental to the movement (since it was earlier explained [535,2ff.] that this is how it is with things to which something belongs incidentally);141 but as things are, rest is not incidental to movement; hence does not measure rest incidentally. Yet it does not measure it per se either; so all that is left is that it does so through something else. For by measuring movement measures rest too. Time, he says, not only measures movement and rest, but it also measures incidentally the moving and resting objects themselves: I mean the substances themselves. For because it measures their movement and rest, it may be said to measure them too incidentally, since it is incidental to the moving object that it is man or heaven or anything else. And if time is measure of movement and rest, all entities that neither move nor are at rest are not measured by time: for example the centres and poles,142 and also souls and angels and suchlike. For these are exempt from movement and rest; nor, then, will they be measured by time. Consequently, they will not be in time either, anyway if the things said to be in time are those measured by time in respect of their being in movement or at rest. such as are not measured by time, since they are neither moving nor at rest. It follows that they are not in time either. Having said which beings are in time, and which are not in time, he proceeds to show for non-beings, too, which of them would be in time, and which would not. He says, then, that all non-beings that are found in the domain of the impossible, along with their contradictories, are said not to be in time; instead, they are everlasting beings or non-beings. E.g., that the diagonal of the square is commensurate with the side is one of the impossibles. Consequently, that is said to be not in time, since one cannot assign a time greater than its non-obtaining. Since, then, the non-being of that is

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not in time, the being that is contradictory to it – I mean, the diameter’s being incommensurate with the side – would also not be in time; for one cannot assign a time greater than its obtaining. For it is always the case. So, among non-beings, the impossible is not in time, for its contradictory – I mean, of course, the necessary – is also not in time; instead, the obtaining of the one is everlasting as is the non-obtaining of the other. But, among non-beings, all the ones that can sometimes be and sometimes not-be: those are your ones that are in time. Of these there is a triple distinction: of things that contingently are not, some have already come to be and are not, such as Homer; others are going to be and are not yet, such as the future occurrence of an eclipse or some other thing that is going to be; and some things have already come to be and will be again, as e.g. the sunrise has both come to be and will be again.143 So everything that is-not in those ways is in time, since one can assign a time greater than their non-being in virtue of (kata)144 the time during which (kata) they were. I say then in general, for both beings and non-beings, that whatever is necessary or impossible is not in time (for the former always are, and the latter always are not); whereas whatever beings and non-beings are contingently so, are, or are-not, in time: the beings because there is a certain time that exceeds their being during which they are not, and the non-beings because there is a certain time that exceeds their non-being during which they are.145 Since time is measure of movement, it is measure of rest too incidentally [221b7-8]: note that many texts do not have incidentally, and Alexander does not mention it either. 221b9 For whereas what is in movement necessarily moves, this is not so for what is in time. For time is not movement Since someone might have raised the question how time is measure of rest (for if time is number of movement, and not only movement is in time but also rest, it would seem that rest too is in movement, given that rest is in time and time is in movement), he says that whereas what is in movement necessarily moves, there is not a

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parallel necessity for what is in time to be moving. If time were the same as movement, it would be necessary that what is in time moves as an immediate consequence. But as things are, it is not necessary that what is present in X is thereby also in that to which X is incidental. For it is not the case that what is present in the sweet must also be present in the honey (since the sweet is incidental to the honey), nor that what is present in white must also be in white-lead pigment. Similarly, it is also not the case that what is in time must also be in movement because time is incidental to movement. At all events, that which is in a day need not also be in the circling of the heaven because is measure of the revolution of the heaven. For it is possible to be at rest in a day, and presumably what is at rest is not in movement. In this way, then, it is neither absurd nor impossible that rest as well as movement is in time. 221b12 Not everything that is at rest,146 but that which lacks movement and is of a nature to move

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He stated that ‘that which is at rest too’ has the possibility of being in number of movement [221b11-12]. , to block someone from saying: ‘Since the centre and the poles of the universe are at rest, are they too therefore in time?’ he says that he did not state that if something is immobile it can be in time. What rests is not the immobile, but that which is of a nature to move but is not moving. Although the poles and the centres are immovable they are not at rest, for they are not of a nature to move; hence they are not in time either. For what is at rest is in time the immovable is not, and what is at rest is what is of a nature to move but is not moving. 221b14 To be in number means that there is a certain number of the thing Since he said ‘what is at rest, too, has the possibility of being in number of movement’, he states again in what sense some things are said to be in number. It is that there is a certain number of them; in other words, they have been numbered: either according to the plurality of the substrates, as when we say that the ten horses are in

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number, or their having their being itself numbered, as when we say that the Trojan war went by in a certain number of time (for it occupied ten years). So since this is to be in number, and time is a sort of number, for a thing to be in time would be for it to have a certain time that numbers its being. E.g. we speak of the Trojan war as having come about in a certain time, and likewise of Homer, because there has come about147 a certain part of time in which they existed. So in this way rest too is said to be in time, through there being a certain time in which rest has being.

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221b16 But time will measure what moves and what is at rest, the one qua moving, the other qua at rest because time also measures things such as men or horses and in general everything, not as such. For it is not as man that the man is measured by time, but insofar as he has a certain continuance in respect of his being. So measures things’ movement or rest as such; and incidentally it measures things’ existences148 themselves as well, through the fact that the moving or resting object is a man or white or whatever else.149 221b20 Thus none of the things that neither move nor are at rest are in time; for to be in time is to be measured in respect of time, while time is measure of movement and rest. That what is neither moving nor at rest is not in time he establishes by employing the following sort of syllogism in the second figure:150 to be in time is to be measured by time;151 things that are not moving nor at rest are not measured by time; therefore things that are neither moving nor at rest are not in time (Q.E.D.) Aristotle propounds first the conclusion of this syllogism, by saying Thus none of the things that neither move nor are at rest is in time. Of the two premisses, he propounded the major and affirmative one that says that what is in time is measured by time; but the minor and negative one that speaks of what is neither moving nor at rest – he did not propound itself; however, he has propounded the one that makes it true and from which it is deduced.

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This is and time is measure of movement and rest, which we must understand as supplemented by ‘only’. That time is measure of movement and rest he showed earlier. But if time is measure only of movement and rest, it is true that none of the things that neither move nor are at rest is measured by time. For this is deduced through conversion by negation according to the second of hypothetical :152 if things measured by time either move or are at rest, then whatever neither moves nor is at rest is not measured by time. is the second and negative premiss of the syllogism from which it was deduced that what is neither moving nor at rest is not in time. 221b23 Plainly, then, neither will all of what is-not be in time.

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Having said which beings are in time, i.e. all that move and are at rest, and which are not, i.e. the things to which the contradictory to these , he now wants to prove this very result for non-beings too, i.e. that whichever non-beings are impossible are not in time, and whichever are-not contingently are in time. 221b25 For in general, if time is measure of movement in itself

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That impossibles are not in time he also shows by the following : if time is measure of movement per se and of other things incidentally, i.e. of the objects which are substrates of the movement or the rest, and to be in time is to be measured by time, it follows that whatever neither moves nor is at rest is not measured by time: but impossibles fit that description, because they are immovably in the non-being; therefore they are not measured by time. Consequently, they are not even incidentally in time. For the substances that are measured incidentally by time are all those that either move or are at rest. Consequently, all those that possess neither movement nor rest would not be measured by time even incidentally. Nor, therefore, would they be incidentally in time. 221b31 Of the non-beings that time contains, some were, e,g. Homer once upon a time, some will be, e.g. something in the

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future, the direction in which it contains them; and if it contains them in both directions, they both were and will be. that of all non-beings that are in time – ones which are also contained by time, i.e.153 ones such that there is a time greater than their non-being – some were and are no longer, some will be and are not yet, and some both were and will be again. With things that are past, time contains their non-being in accordance with the past time during which they existed, whereas with things that are future what contains is the future time during which they will be.154 Thus time greater than of their non-being: in the case of things which have already occurred, the past during which they existed is greater than ever-occurring time in which they are not;155 and in the case of future things, the future time in which they will be is greater than the time in which they are not; while in the case of things that have occurred and will be again, a time greater of their non-being would contain them156 in either direction – the ones which have already happened 157 in virtue of the past during which they were, and the ones that will be in virtue of the future time during which they will be. if in both directions, both: i.e. if time contains their non-being both ways, both towards the past and towards the future, then both, i.e. they both were before and will be again.

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222a2 Whichever it does not contain at all,158 neither were nor are nor will be.

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I.e., the non-beings whose non-being time in no way contains, neither in virtue of the past nor in virtue of the future, neither were before nor are now nor will be hereafter. Which these are he signified by saying those whose contradictories always are, such as the diagonal’s being incommensurate with the side. In other words,159 given that this is always the case and is so of necessity, its contradictory, i.e. the diagonal’s being commensurate with the side, never is and it is impossible for it to be. So just as the diagonal’s being incommensurate with the side is not in time because it is not con-

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tained by time in either direction but is the case through the whole of time, so its opposite, which never obtains, does not have its non-being in time because its non-obtaining stretches out along with all time. 222a10 The now is what makes time continuous, as has been said.

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He now sets out to give separate consideration to the temporal terms, what each signifies: for example, what is now, what is some time,160 what is just-now, what is recently, what is long ago, what is suddenly? He first discusses now, and says that now is in two senses, instantaneous and broad. He first discusses the instantaneous now, and says what he also said before: that the now, being one and the same, is cause of both continuity and division of time. For when it is taken as common boundary of both times, the past and the future, it makes continuous by means of itself the different parts of time. For he himself says in Book V, when defining the continuous, that is continuous if its parts are in contact at a common boundary [227a10-17]. So if the now is the common boundary of the parts of time, it would be what makes time continuous. So: whenever it is taken as one both in substrate and in description – I mean, as one common boundary – then it becomes what makes time continuous; whereas when it is taken as one in substrate but not one in description, as the end of one and beginning of the other, then it becomes a division of time. It is just as with lines and their points. When in thought I take some point on the line, if I take it simply as boundary of both the lines (so also the centre of the circle is a common boundary of all the straight lines drawn from it to the circumference), then the point is what makes the line continuous; but when the point in question becomes subject of two descriptions, e.g. if we think of the line as being cut, and the point is end of one and beginning of the other, then it divides the line. So it is with the now too: if it is taken as having one description, that of ‘common boundary’, it becomes what makes time continuous, whereas when it is taken as having two descriptions it becomes what divides time. But the now differs from the point in that the point can

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also be taken in actuality,161 whereas the now cannot. For the now does not stay, but is always in flux. Now in the broad sense is the vicinity of the instantaneous now. E.g. ‘When did he come?’ ‘Now’, we say, because the time is close to the instantaneous now; and similarly for the future we say ‘He’ll come now’ because he will come today. But of what happened long ago or will be in the distant future we do not say that it happened or is going to be now. E.g. we do not say that the events at Troy happened now, because much time has intervened; nor do we say that what is going to be after much time is going to be now. Some-time signifies a determinate time connected with the present instantaneous now.162 It is said in respect of the past and in respect of the future, and in both cases involves the present now as one boundary. E.g. ‘When did the Trojan war happen?’ – we might say ‘A thousand years ago’;163 and ‘When will the eclipse happen?’ – we say (for some number n) ‘After n months’. So some-time (to pote) is a particular determinate time connected with the present now, and when (hote) the thing happened. If that is what some-time is (a particular determinate time, either past or future, connected with the present instantaneous now), and there is no time that we actually specify that is not some-time (whether we specify it on the side of the past or on the side of the future), reason suggests that every time is bounded. He therefore164 says: ‘Will time give out or not?’, and he says that it will not give out [222a29-30; cf. 222b6-7]. For if some-time is in each case given determination165 by two nows, and every now is both beginning and end, time will never give out and it will always be possible to specify some-time. Hence time will never give out.166 However, someone who does not regard time as everlasting would not concede that every now is subject to the two descriptions ‘beginning’ and ‘end’, but that there will be a now that will be an end and not also a beginning.167 So establishes that time will not give out on the basis of movement.168 If there is always movement, he says, necessarily there is always time [222a29-30]. That there is always movement he tries to show in the eighth book of this treatise; but he shows anything but this, as we have demonstrated in our lectures on that book.169

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Just-now (êdê), he says, is what is close to the present instantaneous now, being either part of past time or of future , since it is said of both directions. E.g. when people ask ‘When is your walk?’ I reply using ‘just-now’ because is not far removed from the present now. In the case of the past we say “I’ve just-now walked’, but no one says ‘just-now’ with reference to distant times; e.g. one would not say that Troy has just-now been taken, nor that things which are going to happen a long time ahead are just-now about to happen. So what is the difference between just-now and now in the broad sense? Well, I say that either the identical meaning is expressed by both words, or, if what is expressed is not identical and the difference is of any importance, they will differ in respect of quantity, in that the broad now is closer to the instantaneous now than just-now is. Recently, too, is close to now, but part of the past only, not of the future. ‘When did he come?’ “Recently’ we say, because the time is close to the present now. By contrast, no Greek applies ‘recently’ to the future – no one says ‘I shall recently wash myself’; ‘I shall recently walk’ – but only to the past. Long ago, he says, is what is far from the present. ‘The Trojan war happened long ago’, , because it is at a great temporal distance from the present. Suddenly, he says, is said of what changes in a time too small to perceive; e.g. we say that a storm has arisen suddenly when the environment changes in a short time, and because of the shortness we are not aware of the change. ‘He has died suddenly’ because the critical moment was so brief that we were not aware of the changeover from being to non-being; it was as if we saw from being to non-being immediately. 222a13 but not as obvious as it is with the point which stays put The now is not as obvious both dividing time and making it continuous as the point is making continuous and dividing the line. The reason is that the point can stay put, i.e. it can be taken in actuality, whereas the now, far from stopping, is in flux.

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222a14 But it divides potentially He says potentially in place of in thought. Hence the division of time is in thought. For the now does not divide time potentially either, since it would also divide it in actuality. As things are, time is one and continuous, being divisible only in thought.

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222a14 and in so far as this is true of it, the now is always different I.e. in so far as it divides. For insofar as it divides it is subject of two descriptions, that of ‘end’ and that of ‘beginning’ (since its being end of the past is one thing, and its being beginning of the future another), whereas insofar as it makes the past and the future continuous it is one and the same not only in substrate but also in description, for it is regarded as common boundary of both. Bring to mind, if you will, two ants that have travelled from the two ends of the line and both terminate their movement at one and the same point: the point at which the movements have been terminated is a sort of common boundary and terminus of both movements. This illustrates the way in which the now, if we do not take it in simple terms as having two descriptions170 but as having a single one, that of ‘boundary ’, is what makes time continuous. 222a15 just as with mathematical lines, in so far as what is always the same point is, if we divide in thought, always different and different, whereas in so far as it is one it is the same in every way171 I.e., just as in mathematics: suppose that in thought we take a certain point on the line, this being always a single one (it is single through being taken in thought and not in actuality) – when we take it as dividing the line, we take it as different and different in description, whereas when as not dividing it but as having one and the same description in relation to both parts of the line, it becomes one not only in substrate but also in description. Just

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so, then, when we take the now in thought: if we regard it as having two descriptions it becomes a division of time, but if as having one description what makes for continuity. (In some there is also this wording: insofar as it is one, to that extent the point is always the same,172 i.e. so far as the point is one not only in substrate but also in description, the point being one in that way becomes what makes for continuity of the line: whereas if we divide in thought it is always different and different: i.e. we make this one point different and different in description when we divide the line in thought.) whereas in so far as it is one, it is the same in every way [222a17]. This recapitulates what was said before: that when we take it as one in every way, it has the same description and makes the line continuous. For the division and the synthesis173 are the same thing and in virtue of the same thing [222a19-20]. For with the point taken in thought, the division and the synthesis are the same in substrate. For it is the same thing that, according to a different and different conception, is thought either as divided or as united. and in virtue of the same: i.e. in virtue of one and the same point, since it is this [sc. the point] that through itself either unifies or divides the line, being taken differently and differently. 222a21 another when the time is near the former.

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I.e., the broad now is a certain time near the instantaneous now, both in the direction of past time and in that of future time; but neither what happened long ago, e.g. the events at Troy, nor what will be in the distant future, e.g. a cataclysm (if there is going to be one), is said to have happened or to happen now (even though the time to them is continuous), because they are not close to the instantaneous now.174 222a24 Some-time is time determined in relation to the former now Some-time, he says, is a time determined by two nows, the present

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one and the one in which the thing has happened or will be. E.g. ‘When was Troy taken?’ ‘A thousand years ago’, we say, determining this time at both ends by the long ago now when Troy was taken and by the present one. Similarly, we say that there will be an eclipse after a given amount of time, again determining the time at both ends by the present now and by the future one at which the eclipse will be. In saying determined in relation to the former now he prompts us to supply ‘and in relation to the later one’, since the former now is prior to a posterior one; but prior and posterior vary in how they are understood: with the some-time of the past, the now at which the thing happened is prior whereas the present is posterior, but with the future it is the reverse: the present now is prior whereas the future one at which the thing will be is posterior.175

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222a27 So there will be a particular quantity of time from this176 to that For if some-time must be characterized by limitation in relation to the now (I mean the present one), it follows that there belongs to this time177 a particular determinate quantity measured from the present to that . So it was correctly said that some time is a determinate time [cf. 222a24-5]. 222a28 But if there is no time that is not a some-time, every time would be bounded.178 For if ‘some-time’ is said about every time (for every time is in the past and the future, and some-time is in these), and some-time is characterized by limitation, then every time, too, is characterized by limitation. On this basis he also raises the difficulty: if every time is characterized by limitation, will time fail or not? For the fact that every is bounded will make it seem that too gives out. On the contrary: although every specified time is bounded, still if movement (time being its number) is everlasting, too must be everlasting. So is it (he says) numerically one and the same time or one only in kind? And he says that as it is with movement, so it is with time. If is numerically one and the same, so is

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time, and if it is one only in kind, time too is one only in kind. He brings out the answer as if it depends on a supposition, but the truth is obvious: time is one only in kind, not numerically, because the same is true also of movement.179 222a33 Since the now is end and beginning of time

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If the now is end of the past and beginning of the future, it would be in the same situation as the circle is in relation to convex and concave. Its line in respect of one and the same substrate is both convex and concave according to different aspects. So if the now is like this, and one and the same is both beginning and end – beginning of one thing and end of another – time will never fail, since any given limit of time will be the beginning of another time. (For it is impossible that one and the same now be beginning and end of the same time, since in that case opposites would obtain together and in the same respect.) So if this is how it is with the now,180 time will always be at a beginning; hence it will not give out. 222b7 Just-now the part of future time that is near the present indivisible now [and to the part of past time which is near the present now] that just-now a part of either past or future time that is near the instantaneous now. Of something that is distant from it, one does not say ‘just-now’.

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222b12 Recently too a certain part of past time181 We have already said how these differ from each other: the broad now, and just-now, and recently. Long ago too part of past time, but that which is far from the instantaneous now, not what is near it. 222b14 Suddenly what has departed from its former condition in a time imperceptible because of its smallness.

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For when (a) a change occurs from something to something and (b) because the time is so short we are not aware of its , we say that such a thing changed suddenly: e.g. a spark smouldering away imperceptibly among the dry sticks makes the whole forest go up in a blaze. Because we do not notice the change far within, we say that the forest has caught fire suddenly. 222b16 but it is the nature of all change to shift things from their former condition

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Since he said [222b15] ‘shifted from its former condition’ when he should have said ‘changed from’, he therefore adds here ‘I said “shifted from its former condition” because every change shifts things from their former condition’. 222b16 It is in time that all things come into being and pass away Having already said it earlier [221a30-b2], he now states more articulately how it is that everything is said to pass away because of time. He reports that while some among the ancients used to call time the wisest of all things, the Pythagorean Paron ( says) shed a truer [222b19] light on it when he said that time is the stupidest because time tends to generate forgetfulness. For if time is a sort of change or at any rate an attribute of change, and every change by nature shifts things from their former condition, it makes sense that time should be cause of shifting-from rather than of coming to be. True as it is that shifting from a given form is accompanied by coming to be of another form, this is so incidentally. For change qua change simply shifts away from something; the shift from a given form is incidentally accompanied by another form because of the efficient cause that uses the change as its instrument, but the change considered in itself brings about nothing but a shift from the pre-existing form.182 In itself, then, change is cause of perishing, and incidentally of coming to be. 222b22 A sufficient indication of this is that nothing comes into

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Translation being without itself somehow undergoing movement and doing something [but a thing perishes even without undergoing movement at all].

It is, he says, sufficient evidence that time is in itself cause rather of perishing and of coming into being incidentally, that for every coming into being there is a determinate efficient cause, e.g. human of human, house-builder of house, and so on. The point is: it is impossible for anything to come into being without its undergoing movement and changing, and everything that undergoes movement is moved by some motive cause; hence whatever comes into being comes into being through the agency of some cause – I mean through the agency of that which induces movement and change. (And because what is coming into being undergoes movement, and every movement is measured in respect of time, time is said incidentally to be cause of coming into being.) Consequently, in every case of coming into being one can see the cause since that which comes to be necessarily always undergoes movement, whereas in some cases of perishing one cannot see any efficient cause other than time alone. For a house might fall apart through dilapidation due solely to time, and so too a cloak and things of that sort will perish even though, far from there occurring any apparent movement in their vicinity, they are under fixed and stable conditions; so that we have no other apparent cause apart from time to which to assign the causation of their perishing. It is in response to ordinary parlance and to there not being any obvious cause to which to assign the causation of the perishing, that Aristotle says the above, since he himself has immediately added that time is not primarily cause of any perishing, in the words: still, even this change is not the product of time; instead, this change too occurs in time incidentally [222b25-7]. So what is the efficient cause of the perishing? We say that it is not the nature of matter to sustain the forms forever; and it is not its nature to sustain them forever because it has the potentialities of all of them, and it must be actual in respect of every potentiality in it if it is not going to have its potentialities in vain. So that is why it is such as not to be able to support one and the same form forever: so that it may be actual in respect of the other potentialities too. This, then, in the first place, is what causes perishing; and, besides, there

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is that things that come into being have limited potentiality.183 For just as there is a determinate measure of growth such that the nature stops on reaching it, so too each entity has its determinate measure of existence such that things perish when they reach it. Thus the efficient cause of things’ perishing is that none of them has infinite potentiality.

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222b30 These distinctions having been drawn, it is evident that, necessarily, every change is and everything that undergoes movement undergoes movement in time.184 Having discussed the temporal terms, he now sets out some difficulties that belong to the discussion of time – except that first he now proves what he has just stated, i.e. that all movement is in time. He proves it by this sort of syllogism (A): all movement has the prior and the posterior [the minor premiss]; the prior and the posterior are in time [the major premiss]; therefore all movement is in time. Or he also in the third figure185 as follows (B): the prior and the posterior are in time; the prior and the posterior are in movement; therefore movement is in time. He proves each of the premisses, the minor [of A] as follows: all movement has faster and slower; the faster and the slower have the prior and the posterior (for, we say, the faster is prior in arriving at the end-point, the slower is posterior); therefore every movement has the prior and the posterior. (When we say that all movement has the faster and the slower we are not talking about movement case by particular case, but about the kind movement in itself.) I mean that the faster and the slower are in the totality of locomotion as a totality, and within locomotion they are in the totality of circular locomotion as a totality. For some circular locomotions are of swift velocity, others of slow velocity; and it is the same with the other .186 That, then, is how he proves the minor premiss [of A]. He proves the major premiss [of A] too, as follows: the prior and the posterior are judged in terms of their degree of remove from the now (for it is by being closer to the now or further from it that one item is said to be prior and another posterior); but degree of remove from the now, he says, is in time – since if the now is in time, degree of remove from the now will also be in time: for what

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is it to be at a remove from the now if not to be at a distance from it in respect of time? So: if the prior and posterior are judged in terms of remove from the now, and degree of remove from the now is in time, it follows that the prior and posterior are in time too.187 The prior and the posterior, he says, are said in opposite ways with respect to past and future time. In the case of past time we apply ‘prior’ to what is further removed from the now, and ‘posterior’ to what is closer to the now (e.g. we say that the Trojan war was prior to the Peloponnesian war), whereas in the case of the future it is the other way round: we apply ‘prior’ to what is closer to the now and ‘posterior’ to what is further from it. E.g. we say that the digestive process that occurs in the stomach is prior to that which occurs in the liver. Having said this much he next lays out two difficulties that belong to the discussion of time. (1) In what way is time related to soul? Is it the case that if soul were not, time would not be either, or is it possible for time to be even if soul were removed? And (2) How is it that time is everywhere, on the earth, in the sea, and in the heaven? He solves the second difficulty first, by saying: because time is measure of movement, and these things – heaven, earth, and sea – are all subject to movement. Since, then, these are subject to movement and time is number of movement, obviously these are measured by time. Thus it makes sense that time is said to be in all these, since whether they are moving or at rest, no matter what, both their movement and their rest are measured by time. So just as I say that the day is everywhere188 – not because the day is a concomitant of the movement or the rest of these things, but because the day is the measure of the movement and the rest of all things – in the same way we say that time too is everywhere. For the day is a given time. Time has its definition and its being from the first of the movements, as has been stated at several points. As for the second difficulty, the question of how time is related to soul – if there is no soul that numbers, is there time or not? – he meets it as follows. If time is number of movement (number that is numbered, not that numbers), and it is absolutely necessary that if that which numbers were not, then the numbered would not be either (for these are correlatives, I mean what numbers and what is numbered),

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and that if what is numbered were not, the number would not be either: it follows of absolute necessity that if soul were not, there would not be number either. For what does the numbering is nothing other than soul: not all soul, but rational soul. So if soul were removed, that which numbers would be removed too; and if that which numbers were removed, the numerable would be removed too; and if the numerable were removed, the number would be removed too; and if the number were removed, time would be removed too. So if the soul were removed, time would be too. But in response to this someone will say: if saying ‘numerable’ and ‘number’ were the same, it would indeed be absolutely necessary that if the soul were removed, the numerable would be removed, and that if the latter were removed, time too ; but as things are, saying ‘number’ and ‘numerable’ are not the same. So what rules it out that although time as numerable is removed if soul is removed, still as number is not removed? For the decad of the stones as something numerable is removed if soul is removed, but as number it is not. For the decad of the stones has being, even if soul does not. However (he says) if it is a general truth that with all soul being removed all movement too would be removed [cf. 223a27], and with all movement being removed, time too would be removed – at least if time is an attribute of movement – it follows by absolute necessity that with soul being universally removed, time too would be removed. For with soul removed, not only are the movements that come about through the agency of soul removed along with it, but so too are the physical ones such as those of heavy objects and those of light ones.189 For the cosmos would be no cosmos if the circular movement is removed, and that is removed if soul is removed. It was therefore rightly said that if soul is removed, time too is removed. Moreover, this holds not only of all soul without distinction, but of rational soul too, since if rational soul is not, the non-rational soul too is not – at any rate if the rational is naturally prior to the non-rational. Besides, if it has been shown to be an absolute necessity that before other-moved beings, i.e. bodies,190 there are self-moving ones, and that before beings that move in time191 there are evermoving ones, and that before all moving things without distinction there are the immovable causes, i.e. souls: then it is clearly an

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absolute necessity that if these are removed all movement is removed.192 222b31 for the faster and the slower apply to all change 5

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I have said in what way he means that the faster and the slower apply to all change: i.e. not to each one by one, numerically speaking, but to every change generically speaking, e.g. to locomotion, and within this to circular movement. However, with things that come into being and pass away, one can also see faster and slower in their individual changes. 222b33 In the phrase ‘moving faster’ I refer to that which changes before another into the condition in question, when it moves over the same interval and with regular movement

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By condition in question he means the end-point towards which the movement tends. So what arrives at the end-point prior to , moving with uniform movement, is what moves faster, provided that the interval is the same. He was right to add when it moves with uniform movement, for if it moves non-uniformly, moving now quicker now slower, it would not be possible to make the distinction. 223a2 e.g. in the case of locomotion, if both things move along the circumference of a circle, or both along a straight line193 The interval must be the same not only in quantity but also in quality. For if one object moves along a straight line and the other along a circumference of equal magnitude, the one moving along the circumference may, although really faster-moving, arrive at the endpoint later. For what moves along the circumference is impeded by the bend. This is shown by horses racing, for they can be seen moving more slowly on the bend.194 and similarly in all other cases: e.g. movement along a helix. In terms of speed, a thing does not move in the same way along the helix as it does along the straight line.

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222b30-1 it is evident that, necessarily, every change is and everything that undergoes movement undergoes movement in time Having stated the conclusion he wishes to prove, he does not first state the premisses by which it is deduced: instead, he first proves each of them, and then, having proved them, assembles the whole syllogism [S1]. First he proves its minor premiss, i.e. the one that says ‘the prior and the posterior are in all change’. He proves it by the following syllogism [S2]: in every movement there is the faster and the slower; the faster and the slower are prior and posterior;195 therefore the prior and the posterior are in every movement. the faster and the slower apply to all change is the minor premiss [of S2]. I mean that which changes before another into the condition in question when it moves over the same interval and with uniform movement: this is the major [of S2]. If the faster is what changes before, obviously the slower is what changes after. 223a4 But what is prior is in time

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the major premiss of the whole syllogism [S1] by which it is proved that every movement is in time. That prior and posterior are in time he proves next. 223a5 for we say ‘prior’ and ‘posterior’ with reference to the remove from the now That the prior and the posterior are in time he proves by means of the following: 223a6 the now is the boundary of the past and the future If the now is the boundary of the parts of time, it follows that the now is in time.

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Translation 223a8 for in that in which the now is, the degree of remove from the now will also be

Given that the now is in time, he shows how the prior and the posterior are in time too, as follows. Since (he says) in that in which the now is, the distancing from the now would also be (for what is at a distance from the now is at a distance from it in respect of time), it follows that if the prior and posterior are judged by reference to the degree of remove from the now, and the degree of remove from the now is in time because so is the now, therefore the prior and the posterior too will be in time. 223a8 ‘prior’ is used contrariwise with reference to past and to future time

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He said that the prior and the posterior are judged by the degree of remove from the now; but this was indeterminate. For nor can one speak in an unqualified way of what is at a nearer or further remove from the now, as this gives different results for past and for future time. For this reason he makes precisely that distinction [at 223a8-13].

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223a13 So that since the prior is in time, and every movement involves a prior He now concisely brings together the most important premisses of the syllogism [S1]. In every movement, he says, there is prior and posterior; prior and posterior are in time; therefore every movement is in time.

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223a17 It is also worth considering how time can be related to the soul Here he starts to lay out the difficulties mentioned above. 223a17 and why time is thought to be in everything

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This is the second difficulty. 223a18 It is because it is an attribute, or state, of movement the solution of the second difficulty. If, he says, time is a sort of state or attribute of movement, since it is number of it, and all these are subject to movement – I mean heaven, earth, sea, and the rest – it makes sense that time is in them all.

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223a19 all these things are subject to movement (for they are all in place) That all these things are subject to movement, I mean heaven, earth, sea, and the rest, is clear, he says, from the fact that they are in place – as if from things’ being in place it immediately follows, with no restriction, that they are subject to movement too. Of course, he says, the way in which being in place applies to each of them determines the way in which being subject to movement applies. For what is potentially in place is potentially subject to movement too, and what is in place in actuality is subject to movement in actuality.196 Similarly:197 what is in place in terms of its whole self is also subject to movement in terms of its whole self, and what is in place by parts is also subject to movement by parts. But this is completely false even on the basis of the very views held by Aristotle. For certainly the spheres within the sphere of the fixed stars are in place in terms of their whole selves, but even so they do not move in terms of their whole selves;198 and the earth is in place in terms of its whole self, but even so does not move in terms of its whole self. For it alters part by part, even if an incidental result is that at some point it is all altered. A parallel: although all its parts undergo coming into being and perishing, it is not said itself to be perishing in terms of its whole self, but part by part; just so, although they all undergo alteration, it would not be said to alter as a whole, but part by part. Well, when Aristotle said that place and movement are together, both in respect of potentiality and in respect of actuality, i.e. if place is potentially, movement too is potentially, and if in actuality, movement too is in actuality, he did not add ‘and if the place as a

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whole or by parts, so also the movement’, but his interpreters say that he did, given that being in place is either as a whole or by parts. Thus if the way things are in place determines the way they are subject to movement, given that they are in place as wholes or part by part they would be subject to movement in those ways. That is what I say on that point; but the general statement that what is in place is immediately therefore subject to movement should not be understood in a way that renders place the unrestricted cause of movement, but as being subject to movement unrestrictedly follows from being in place.199 Next he sets out the second difficulty and solves it.200 223a24 number is either what has been, or what can be, numbered

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Number, he says, is nothing other than what is numbered, potentially or in actuality. For it has been said that number is in two senses: that numbers201 and that is numbered; and it is obvious that each of them is either potentially or in actuality. So here he says of numbered number that it is potentially or in actuality. Thus if what can be numbered were removed, number too would be removed; and what can be numbered is removed if that which numbers, i.e. the soul, is removed. 223a26 but only that by being which time is, i.e. if movement can exist without soul If soul is removed (he says), time is removed along with it. For it is not possible for time to be without soul, unless the substrate of time, i.e. movement. But in saying if movement can exist without time he indicates that movement too is removed if soul is removed.

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223a28 the prior and posterior occur in movement, and time is these in so far as they are numerable Since he said ‘it is impossible for there to be time unless there is soul,

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but only that by being which time is’, i.e. the substrate of time (for just this is signified by ‘by being which’), and movement is the substrate of time, he did not want to argue for precisely this point again here, namely that movement is substrate to time. For the prior and posterior, he says, occur in movement, and time is nothing other than the prior and posterior that occur in movement in so far as they are numerable. Thus if time is the prior and the posterior in movement, with the prior and posterior being in movement as in a substrate, time too in this way would be in movement. 223a29 One might also raise the question what sort of movement is time the number of. To the aforesaid questions about time he adds some further ones. First: if time is number of movement, and there are many kinds of movement – growth, diminution, alteration, coming into being and perishing – what sort of movement is time number of? He says that it is number of every movement in so far as they are movements. For it is not in so far as growth is growth that time has the role of its measure, nor in so far as alteration is alteration; instead, it is in so far as each of these is movement that it is measured by time. So time functions as measure of every movement. It measures each of them simply as a distancing. Thus they are measured by time in virtue of what is common in them, not of what is peculiar. To this question he next adds another one, as follows [223b1-2]: since it is possible for two movements to occur together (for while one object is moving in respect of place, another in the same time may be undergoing alteration, or one may be moving in a circle, another in a straight line), are there two times, each movement being measured by its own time, or does one and the same time function as measure of several movements? Well, he says that one and the same time functions as measure of the movements that take place together. And there is nothing strange about this. Just as the number in the soul, which is one and the same, e.g. ten (hê dekas), measures the external tens (dekades) such as of horses and of human beings and of stones, etc., and just as the pint which is one and the same measures wine and water and all liquids – the reason being that it is

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not qua being of such and such a character that each of them is measured in this way, but qua being of some quantity or other – so too time, which is one and the same, functions as measure of several movements that are equal and occur together. For if the movements are not equal, but one is greater, another lesser, then in virtue of the fact that one of the times is greater, it is not equal to the other. And if they are equal but not together, for this reason too they are not numerically the same. However, even times that are not together are the same in kind: e.g. today is the same as tomorrow in kind.202 He now asks [cf. 223b12ff.]: if time is measure of the circular movement, and things that are measured are each measured by a measure homogeneous with it (for the ten horses are measured by the single horse and the ten humans by the single human, and similarly the ten cubit-piece of wood by the cubit-long part of itself), time too, being numerable, must be numbered by means of a time. So what is this time whereby all time is numbered? He first makes a start on the solution to this with what he already said earlier [220b14-16]: that time not only measures movement but movement also measures time; and that some movements are non-uniform (such as those that occur in the realm of coming into being and perishing), while others are uniform (such as the of the spheres), and of the latter some are faster, some slower. For while one of them has a period from the same to the same in thirty years, another in twelve, and another in a year, and others in other intervals, one is faster and more easily cognized than all the others, namely the movement of the sphere of the fixed stars, which has its period to the same in twenty-four hours (I mean the day-night span). So: since the measure is what is both smallest and most easily cognized, it makes sense that the time defined by this movement, I mean one day (i.e. the day-night span), should be the homogeneous measure whereby all time is numbered. For we say that a month is 30 revolutions of the sphere of the fixed stars, and a year is 365, and in general every time arises through some pluralization203 of the day. First, then, movement defines the smallest measure of time,204 and then by means of this all time gets numbered. And just as we have measured the cubit into digits,205 different people doing it in different ways – some into 22, some into 24, yet others into 28 – so we have split the day-night

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period into many parts; e.g. in the case of us into 24, which we have called ‘hours’. Although one can divide these too indefinitely, we do so with reference to these, just as the half digit or a third or tenth of a digit is determined by reference to the digit. In the same way, then, the half-hour time-length and the other fractions are determined by reference to the hour. However, among movement in general, the one that is shortest and easy to cognize is the revolution of the sphere of the fixed stars. The measure that consists in this is the day, and then by means of this various times are measured: week, month, year, and the other divisions of time. Because of this, he says [223b21-3], some of the ancients thought that the circular motion of the heaven is time, i.e. because time is determined by means of this. For the time-measure is marked off by means of this, and every other movement is measured by this , since it measures206 and defines the time that is the measuring-unit for all movement. So the basis for defining time is what believed to be time. He next shows that the things commonly and customarily said about time fit the theory of time that he has stated [223b23-33]. People say that human affairs are a circle because it is by time that they are measured and determined as having their beginning and end: e.g. periods of health and illness, of prosperity and misfortune, war and peace. These all come round again after each other and take over from each other as if in a sort of circle. So: since these events are picked out in terms of time, and time seems to be a sort of circle, people therefore say that the events themselves are a circle; and they say that time itself is a circle because it is measure of the circular movement and is measured by the circular movement. Thus, he says, saying that human affairs form a circle is nothing other than saying that time is a sort of circle; and saying that time is a sort of circle is nothing other than saying that time is measured by circular motion. Next: earlier on, when stating that one and the same time has the function of measuring different movements, he supported the point by the consideration that also in the case of numbers one and the same number, e.g. ten (hê dekas), may function as measure of different numerables, e.g. ten (deka) horses and ten human beings [223b4-7]. Now, therefore, he wants to show how one and the same

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number measures differences of substance; and at the same time he provides a criterial rule enabling us to tell when things which have something predicated commonly of them do share with each other in just what it is that is predicated and are without difference in that respect, and when they are not without difference in respect of what is predicated commonly of them.207 Accordingly, he says [224a2ff.] that when things which have one thing predicated of them differ from each other in the differentiating respect that what is predicated has within itself,208 then what is predicated commonly of them is not one and the same; whereas when the things which have something common predicated of them do not differ from each other in the differentiating respect that belongs to what is predicated, what is commonly predicated of them is one and the same. E.g. (he says) figure is predicated of triangle and circle; but since triangle and circle differ from each other in the differentiating respect whereby what is predicated is divided – for the differentiae of figure are bounded by straight lines and bounded by a curved line, and in this way triangle differs from circle – for this reason what is predicated commonly of them is not the same. I.e.: if it is said that the triangle is (a)209 figure, and so is the circle: still, figure is one and another in the two cases. For bounded by a curved line is added to figure predicated of the circle, and bounded by rectilinear lines to of the triangle, thereby making one of them (a) figure bounded by straight lines, and the other (a) bounded by a curved line; and these are different from each other. If, however, I take two triangles, the equilateral and the scalene, figure which is commonly predicated of them is one and the same for both, because they do not differ from each other in the differentiating respect that belongs to what is predicated. For the differentiae of figure qua figure are bounded by straight lines and bounded by a curved line, and the equilateral and the scalene do not differ from each other in this way, since both are bounded by straight lines. So, as I said, one and the same figure is predicated of both; however, it is not also the case that one and the same triangle is predicated of both, for they differ from each other in the differentiating respect that belongs to what is predicated. Isosceles and scalene are differentiae of triangle, and by these differentiae the two trian-

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gles differ from each other. So it is not the case that one and the same triangle is predicated of both. That is the rule.210 In response to the rule one might see a difficulty in what Aristotle himself everywhere tells us.211 How, , are genera synonymously predicated of the species, even though the species differ from each other by the differentiating respect belonging to what is predicated? E.g. animal has rational and non-rational, yet even so animal is predicated synonymously of man and of horse; thus one and the same animal is predicated of both. Yet according to what we have just been saying, if the same animal is not predicated of man and of horse for the reason that they differ from each other in the differentiating respect belonging to what is predicated, it would not be predicated of them synonymously. So here perhaps he did not treat the predicated as genera, nor simply as more212 universal and remote in definition from each particular subject213 (which is how it is with things that by a common term are said to belong in all the and to have their being in many). instead the things that have a common essence yet belong to each in a way peculiar , and have their real existence in the particulars 214 about animal in me and in this horse. These are not really the same; however, things that are said to be predicated as genera do not have an existential grounding peculiar to them: instead, it is our conception that focuses on something in common in all and considers it as a single something when really and in itself it is not so at all, as he himself has said. The universal, he says, is either nothing or it is posterior [DA I, 402b5-8]. Our thought separated (so to speak) this common feature from the co-existing attributes (e.g. animal from rational and non-rational, from mortal and immortal), and in conception focused on it itself by itself (not that it exists by itself), and gave it a universal name and focused on it as a sort of single nature. In this way it does predicate it synonymously of all the others. If, however, you focus on the animal that is present in each and exists in reality, since this is either rational or non-rational, the in the horse would not be the same in essence as the one in me, whereas the human species that is in Socrates is the same in essence as in Plato,

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because neither of them215 is combined with a differentia that separates it from the other. Here, then, on the the common essence that has real existence, and has its existence as a whole in each of the particular cases, he says that those subjects that differ from one another by some difference that belongs to what is predicated commonly of them – a difference that belongs to the genus itself – are not the same in terms of what is predicated; whereas with those that do not differ from each other by this difference, what is predicated is one and the same in essence.216 So, then, too with the ten horses and ten asses and stones: since they do not differ from each other in the differentiating respect that belongs to what is predicated (i.e. the in the horses is not a different form of ten from the in the men), therefore what belongs to them in common and measures them, the ten (hê dekas), is one and the same, and they do not differ at all from each other in terms of the form of ten. Consequently, even if they are measured by the ten, and this is one and the same in them all, it follows that the different – I mean the ten (deka) horses and the ten men and the ten stones, etc. – are measured by what is one and the same. For the form of ten (hê dekas), which has its being primarily in soul: which is why it is regarded as one in respect of the number of its substrate (i.e. the soul), this being always one and the same.217 223a30 of any kind The solution to the first question [cf. 223a20-30] that time is number of movement without qualification: not of this or that , but without qualification of every movement in so far as it is movement. 223a33 And so it is simply number of continuous movement, not of any particular kind of it.

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plural, e.g. alteration and growth and locomotion, or a multiplicity of locomotions, time is not suitable for measuring their plurality; rather, the numerical unit is. For as the unit, and not time, measures the ten horses and the ten stones, time does not measure the many movements as many. Number, that is to say the unit, does that. However, time does measure each movement in itself, single as each is and continuous, by measuring the prior and the posterior in it.

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223b1 But something else as well may have been moved now From this point on the second difficulty [cf. 223b1-4], that while one thing moves something else may also move in the same time; hence time is number of each movement. So, he says, is the time different for each movement, and for the two movements will there also be two equal times together, or not? His answer is that time that would measure movements that are equal and occur together, is one.

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223b4 for if there were dogs and horses, and seven of each, it would be the same number This is an illustration of how the same measure can measure several objects together, given that they are equal. So just as the seven horses and the seven dogs have one and the same number to measure them, the seven (hê heptas), so one and the same time can measure the equal movements.

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223b7 yet one may in fact be fast and the other not, and one may be locomotion and the other alteration Just as in the example the measured objects were not the same, one lot being horses, the other dogs, while that which measures is one and the same, so too in the case of time the movements measured by the same time different both in the very species of movement and in the fact that one of them is faster, the other slower. Suppose in the same time, in the course of one day, a horse and a sheep move at their fastest: the time that measures these move-

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ments, unequal in speed as they are, is one and the same – the one day. 782,1

223b10 and for this reason, while the movements are different and separate, the time is everywhere the same, because the number of things that are equal and together is the same

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Another difficulty: if each thing is measured by some measure homogeneous , what is the homogeneous measure whereby time is measured? The sequence of the argument is as follows. Since there is such a thing as locomotion, and in locomotion there is included circular movement, and each thing is measured by some one, minimal, homogeneous entity, e.g. ten horses by the one horse, a one-hundred cubit piece of wood by the cubit-length piece, the time that is measure of movement must likewise be measured by something homogeneous and minimal. Since, then, the circular movement is a minimal measure of movement, and not only is movement measured by time but also time by movement, it is clear that the time that is measured by the smallest movement218 will be the homogeneous measure of the whole of time. And this is the day-night period. By this are measured week, month, year, and every time. and each thing is measured by some one thing homogeneous with it. For even if each is primarily measured by heterogeneous, all the same it is also measured by homogeneous, that which is primarily measured by what is heterogeneous.219

Translation

93

223b16 this is so [i.e. time is measured by movement as well as movement by time [223b15-16]] because by the time of the defined movement is measured the quantity both of movement and of time220 He states in what way movement and time measure reciprocally. It is, he says, because the movement primarily defined by time221 is measure both of all movement and of time. For the time defined by this is measure of every time. So if the movement defined by time is measure both of movement and of time, it is clear that time and movement measure reciprocally.

783,1

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223b18 if, then, what is first is the measure of everything homogeneous with it, regular circular movement is measure above all else If, he says, what is first in each domain is measure of what is homogeneous with it, given that the absolutely first movement is the uniform circular movement, this would be time’s measure par excellence. For by this is defined the primary time that is measure of every time.

10

223b19 because the number of this is the most cognizable There are, he says, two grounds on which the revolution of the sphere of the fixed stars is shown to be measure of all other movements. The movement must be both minimal and most easily cognized, and both hold of the circular locomotion of the sphere of the fixed stars. For of all 222 it is far and away both smallest and most cognizable. revolution is the night-day, which is most easily cognized by everyone. It is uniform but not uniquely so, since is distinctive of every revolution, whereas being minimal and most easily cognized belongs above all to that one. 223b21 This is also why time is thought to be the movement of the sphere

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94

Translation

Because, he says, all the other movements are measured by the revolution of the sphere of the fixed stars in the way that has been explained, the ancients therefore thought that time is just this: the revolution of the sphere. Because time is measured by this, they surmised that time is just this. 25

784,1

223b23 This also explains the common saying that human affairs are a circle I.e., shared human custom confirms this : that the circular locomotion is measure both of time and of every movement. For that is why people say that human affairs form a circle: it is because they are measured by time; and that time is a circle because it is measure of circular movement. 223b25 and that in all other things that have natural movement [and coming into being and passing away]

5

I.e., with everything else too that comes into being and perishes – plants, animals, metals, and the rest – people say that there is a circle. 223b26 This is because all these things are discriminated by time

10

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People say (he says) that human affairs form a circle because everything is discriminated by time: i.e. comes to be in time and is measured by time, being given its beginning and end by time. Time, he says, is thought to be a circle; so if human affairs are in time and time is a sort of circle, it follows that human affairs too would be a sort of circle. But time is thought to be a circle because it is measure of a certain circle and revolution, and is itself measured by the latter. So since what measures time is a sort of circle, time too is believed to be a sort of circle. 223b33 for apart from that which measures223 nothing else is observed in what is measured; the whole is just a plurality of measures

Translation

95

That it makes sense to think of time as a circle (given that the circular locomotion is measure of time) he proves as follows. What is measured, he says, looks to be nothing but the identical measure multiplied. E.g. the hundred-cubit piece of wood is nothing but the cubit multiplied, and ten is nothing but one multiplied, with unit as measure of number. So if the circular locomotion is measure of time, time likewise would be nothing but many circular locomotions; and if so, it is an apt saying that time is a circle. 224a2 It is said rightly, too, that the number of the sheep and of the dogs is the same number if the two numbers are equal, but not the same ten (dekas) or the same tens (deka ta auta) In the course of showing that time that is together is everywhere one and the same functions as measure of every movement, he used an example taken from numbers: one and the same number, e.g. seven, measures the seven horses and the seven dogs and in general all things contained by the equivalent number [cf. 223b4]. Consequently, he now wants to show that this holds good; and at the same time he gives the rule which I have already mentioned when what is predicated commonly of certain things is one and the same for all of them, and when it is not one . So, he says, it is true to say that the number of the sheep and horses ( that measures them) is one and the same if the objects measured (i.e. the horses and the sheep)224 are equal, even though (he says) the ten (hê deka) is not the same, meaning now by ‘ten’ (dekas) the number that is with the substrate. Hence to make the point clearer, he added not  the same tens, i.e. animals or unspecified corporeal objects.

20

25

785,1

5

10

224a4 just as the equilateral and the scalene are not the same triangles For they do not admit of the same specification of triangle. Similarly, then, the ten horses are not the same as the ten sheep.

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96

Translation 224a5 yet they are the same figure, because they are both triangles

Shape is on the one hand bounded by straight lines, and on the other hand curved,225 since both are bounded by straight lines, i.e. both triangles admit of the same definition consisting in shape bounded by straight lines. 20

25

786,1

5

224a6 For things are called the same if they do not differ by a differentia of X, but not if they do He ascends to universal language in giving the rule which things they are that are the same in terms of what is predicated commonly of them, and which are not the same. They are said to be the same, then, when they do not differ from each other by some differentia of what is predicated. E.g. isosceles and scalene differ by a differentia of triangle, which is why they are not the same triangles; while as figure they do not differ by a differentia of what is predicated, for both are bounded by straight lines. This, then, is why as figures they are both the same, the equilateral and the scalene, but as triangles they are not the same: they differ by the differentia of triangle. 224a9 but are in one and the same division of it I.e. they under the same section of the division. For of figures, one is bounded by straight lines, the other is curved. Both the triangles, then, under bounded by straight lines; and again: of figures bounded by straight lines, one is triangle, the other is something else. So as figures the isosceles and the scalene are no different from each other, since both under the same section of the division, bounded by straight lines; and as bounded by straight lines they are the same, since they under the same section of the division of bounded by straight lines, i.e. under triangle. However, as triangles they are not the same, since they do not fall under the same section of the division of

Translation

97

triangle; instead, one falls under one , the other under another.

10

224a12 the number226 too is the same, for the number of them does not differ by a differentia of number; but it is not the same seven (heptas);227 for the things of which is asserted differ Having confirmed the universal rule by reference to the case of the figures, he now brings it to bear on the issue at hand. So: of the seven (hepta) dogs and seven horses the number commonly predicated is one and the same, for they do not differ from each other by a differentia of number; e.g. both are odd-numbered. Hence the number that is commonly theirs and available to measure them is one and the same for both. However, insofar as each is a seven (heptas) it is not the same seven . For a seven (heptas) is already thought along with the substrates;228 so if the substrates differ from each other, the sevens (heptades) too will differ from each other. This, then, is how it stands with time in its function of measuring movements. There is no ground for denying that time in its function of measuring movements is one and the same although the things measured are different.

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Notes 1. Natural philosophy studies changeable things, and change implies time; cf. Aristotle, Phys. III, 200b20-1. 2. i.e. the same as he had used in approaching the previous topic, namely the void (Phys. IV, 213a12ff.). 3. i.e. he proceeds to show this for the now, having shown it for time. 4. In the Gregorian calendar this date is 5 April, 517 AD, when Philoponus was about 27 years old. I owe the calculation to Adrian Gratwick. Pachon was a month in the Alexandrian calendar. 5. Aristotle does not say ‘from eternity’, and the present argument does not depend on it; thus it would work equally well against the view such as we find in the Timaeus (taken at face value) that time had a beginning. This was Philoponus’ own view as a Christian. Again, the notion of the now as ‘flowing’ is not in Aristotle’s text. The notion is based in part on the general association between time and the flux of physical things: see 735,24-5 and e.g. Damascius ap. Simplicium, in Phys. 798,5-26 (Sorabji (2004), vol. 2, 210). A more precise notion of the flowing now is based on 220a1ff., where Aristotle presents the relation of the now to time (khronos, i.e. extended time) as analogous to the relation of an object in locomotion to its locomotion. Philoponus expounds the passage with an explicit analogy between the flowing point that generates the line (an idea associated with Xenocrates; cf. Aristotle, DA I 409a3-5), and the flowing now that generates time (727,10-26). Simplicius, in Phys. 722.30-4 (Sorabji ibid.) uses the same analogy. 6. We should understand (c1) as reached by division plus elimination of the other alternative: ‘either (c1) it is destroyed in something or (c2) it is destroyed in nothing’. We thus get the five divisions mentioned at line 29. 7. i.e. (a2). 8. The argument comes at Phys. VI, 231a21-b10, esp. b6-10. Philoponus places it in ‘the last books’ because in the preface to his entire commentary on the Physics, after listing the subjects to be dealt with as matter, form, place, time, and movement, he says that the first four are covered ‘in the first four books’ while movement is covered ‘in the last four books’ (in Phys. I, 2.13-17). Thus books VI and V belong with ‘the last books’. 9. Phys. V, 226b18-227b2, esp. 226b34-227a5. Philoponus’ wording here

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Notes to pages 6-13

seems to ignore Aristotle’s insistence that if B is ephexes to A, then B is (in some way) posterior to A, so that ‘– is ephexes to – ’ is an asymmetric relation. 10. Presumably this follows because if the now N1 perishes in a later now N2 the two nows are together at some point, implying two coincident time-intervals (one bounded by one and one by the other). 11. i.e. Philoponus’ commentary on the Categories, 35b41ff. 12. Bekker has ‘The now which is not etc.’. 13. Philoponus is alluding to Aristotle’s doctrine that points (nows being point-like; cf. Phys. VI, 233b33-234a24) are-and-are-not without perishing or coming to be; Phys. VIII, 217b16-20; Metaph. XI, 1060b17-19. 14. See n. 8. 15. i.e. (a2) at 703,25. 16. i.e. the entire spherical cosmos; cf. Cael. I, 278b19-21. 17. Aristotle simply declares that there would be one time even if (per impossibile) there were many revolving cosmoi (218b3-5). (Thus he implies that time is not the revolution of any particular cosmos.) Perhaps this makes sense at this stage, given that the countability and measurability of time have not yet entered Aristotle’s discussion (see 219b1ff.). Philoponus, on the other hand, risks incoherence by bringing in measurement here. He is in no position to assume that if there were multiple cosmoi there would even so be a single time in terms of which to compare the speeds of their revolutions; for although it is intelligence (nous) that counts temporal units (cf. 223a16-29), the counting is based on perceptible repetitions. Percipients are animals operating within a given cosmos, and they cannot perceive the revolutions of any other. 18. In the second figure both premisses have the middle term as predicate. The middle term in the present example is ‘contains all things’. 19. i.e. the statement that A is in B can be correct in virtue of a sense of being in that is not in play (and may even be excluded) when we correctly state that A is in time. 20. In the third figure both premisses have the middle term as subject. 21. kinêsis haplôs: the contrast is with the view that time is something belonging to movement, 716,4-8. 22. kinêsis haplôs, again. Here the contrast is between movement tout court, and A’s movement, B’s movement. 23. I have taken hoti at 711,1 as governing all the subsequent clauses within Vitelli’s parenthesis (710,32-711,4). I have kept the parenthesis but within it have punctuated differently from Vitelli. Between them, the examples show (a) that ‘Faster and slower belong to movement’ holds for both superlunary and sublunary domains, and (b) that it is obvious to anyone, not only to students of astronomy. 24. khronôi, which occurs in Aristotle: ‘by’ here is instrumental. Unlike Aristotle (although see 221a9), Philoponus also frequently speaks of movement as ‘measured (or: determined) by time’, e.g. at 745,6.28; 746,4.18.27.

Notes to pages 14-23

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For this Philoponus says hupo khronou, a locution suggesting agency. He probably uses this simply as the passive of ‘time measures (or: determines) movement’, a locution which does occur in Aristotle, e.g. 220b17 and 221a1-2. In the context of temporal measurement, hupo khronou might also be translated ‘under the heading of time’, i.e. ‘in terms of time’. (It is worth noting that at 767,21, where Philoponus is discussing efficient causes and using hupo + genitive for that purpose, he refrains from also using it to speak of things being measured by time, and opts for the dative khronôi; 767,28.) 25. Vitelli prints this as a quotation but not as a lemma. 26. Vitelli prints this as a quotation but not as a lemma. 27. i.e. against identifying time with the celestial revolution. 28. i.e. of the spheres in this cosmos. 29. See n. 18. 30. i.e. are not properties of time. 31. The reference is to Phys. V, 225a1-225b9. Philoponus speaks of the ‘next books’ because he divides the books of the Physics into a first group and a last group, and V is the first of the last group (see n. 8). 32. apiontas; the sense is not clear, and Vitelli suspects corruption. 33. Reading periêlthen at 715,20. 34. The meaning may vary between ‘pluralize’ and ‘count’. 35. Presumably this means that time is not immediately related to alteration and growth: we specify the time taken by one of those processes in terms of celestial locomotions. Relatedly, we do not specify the time of any process in temporal units based on stages of growth etc. (‘the war lasted for three seedling-to-sapling stages’), because even for organisms of the same species such stages differ in temporal length. 36. i.e. ‘All movement is measured (or measurable) in temporal units’. 37. ‘Pint’ and ‘bushel’ originally referred to physical containers of these volumes. 38. Here, Philoponus uses ‘number’ and ‘measure’ interchangeably. Aristotle’s actual question is whether time is the number counted or the number with which we count (219b5-9). He does not explicitly introduce time-measurement until 220b14. 39. i.e. the movement whose regular repetition determines the basic unit of time. 40. At 219a15 Aristotle said entautha men dê têi thesei, thus creating the expectation that the next clause, connected by de, would include something contrary to en têi thesei. 41. At 719,16 Vitelli, following the codices, prints têi kinêsei; but if Philoponus wrote this, it was a slip of the pen for tôi megethei: see Aristotle, 219a16-18. 42. Bekker has ‘the prior and the posterior of them in movement’. 43. Aristotle’s wording at 219a19 is ho  pote on kinêsis esti. Philoponus in his comment abridges this to to ho pote on and explains it as meaning ‘in

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Notes to pages 23-29

respect of substrate’; cf. 729,10-11 and 775,17-18. See also 726,15-18, with n. 61 below. There are other interpretations of Aristotle’s formula: see Brague (1982), 97-144 and Coope (2005), 173-7. 44. For the translation cf. Phys. VI, 232a9 and 241a2-4. 45. Reading hekateron instead of heteron at 722,21. 46. The continuance or stretch of a movement is not quite the same as the time it takes. This is because when Aristotle’s account is fully developed we see that the time taken by a particular movement is an interval in which other things are happening too, everywhere in the cosmos. The continuance of a given movement is an intrinsic aspect of it analogous to the spatial extendedness of a given body. 47. The ROT has ‘Time is not movement, but only movement in so far as it admits of enumeration’. 48. By switching from the present ‘is numbered’ to the perfect ‘has been numbered’ Philoponus perhaps makes the thought more precise: the number is a definite total. However, what follows is confused: the meaning surely is ‘ not insofar as it [sc. movement] is movement, but insofar as it is prior and posterior’. 49. See n. 20. 50. i.e. number with which we number (count). 51. Philoponus’ solution to the problem at 723,25ff. emphasized that time is number that is numbered, not number that numbers (i.e. the number with which we number). Because Philoponus uses ‘numbers’ and ‘measures’ almost interchangeably in much of his discussion, he now has the problem of 724,10ff.: how to reconcile the first solution with the fact that Aristotle speaks of time as measuring movement. 52. The meaning of the ‘whereas’ clause is not entirely clear. Presumably ‘all other things’ refers to all properties apart from movement. ‘Always the same’ must mean ‘always the same as long as they exist’. 53. The ROT has: ‘[E]very simultaneous time is the same; for the now is the same in substratum – though its being is different’. Philoponus does not use the notion of substratum in his present comments on this passage, but see n. 61 on 726,27-8 below. 54. See n. 35. 55. Philoponus may be saying that the division was incomplete because the option now to be considered was a diairetic section which it should have included; but it seems more likely that he means that the process of division (demanding ‘Yes’/‘No’ answers at each stage) could not have captured this option, so that the process (as applied to the present inquiry) was bound to be incomplete. 56. The first alternative is what Philoponus finds below in Aristotle, not the one that is ‘closer to the truth’ (I owe this point to a referee). 57. On the reference to ‘books’ in the plural, see n. 8. 58. i.e. without a temporally divisible process of coming to be and passing away: see n. 13.

Notes to pages 30-39

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59. The ROT translates: ‘which is just what its being now was supposed to mean’. 60. i.e. ‘one cannot say that it is in this together with saying that it is in this’. Philoponus is talking about successive speech-acts, with ‘this’ referring to something different in each. 61. The quoted phrase which Philoponus here explains as ‘it is the same in substrate’ is ho de pote on esti, to auto. He may be misquoting 219b10-11, where Aristotle’s wording was to nun to auto ho pot’ ên (translated here as ‘the now is the same whatever it was’), or (a smaller misquotation) 219b26, where the wording is ho men pote on nun esti, to auto. 62. Translating Philoponus’ homoiôs de kai. Bekker has kai homoiôs dê. 63. In Aristotelian physics this is true of unforced movements. 64. Signs of the zodiac. 65. i.e. as well as caused. 66. i.e. that which stands to the now as substrate. 67. Reading kata ta diapheronta at 729,22-3. 68. i.e. in the context of a given movement, every particular now can be said to be ‘prior and posterior in movement’ (as opposed to ‘in place’). But the referent of the phrase is guaranteed to be always other and other, since the empirical cash-value of ‘now’ depends on what occurs now, which is never the same. 69. In Bekker, aei, ‘always’, ‘in each case’, occurs here. 70. i.e. exist or not-exist. 71. Suppose that the motion is that of a stone: the thought here is not that the now measures the stone, but that it measures the stone-in-motion, i.e. what we might describe as ‘the stone-at-P1-now-and-at-P2-now’, where P1 and P2 are positions along the track, and each ‘now’ has a different referent. Between them the nows determine a measurable temporal interval. The interval’s actual temporal measure (say, 10 seconds) belongs, of course, to the movement from P1 to P2; but it equally belongs to the stone-in-motionfrom-P1-to-P2. In this sense, the now (i.e. the prior now and the posterior now) measures (i.e. makes possible the temporal measurement of) the stone-in-motion. 72. i.e. the taking. 73. i.e. at which. 74. This is by analogy with the two movements’ having something between them that is not movement, i.e. rest, the privation of movement. Between the two times would be privation of time. 75. i.e. the locomotion is divisible in thought at any point where theobject-in-motion happens to be. 76. The unity of the movement from P1 to P2 is ensured not by the unity of the substrate of movement, e.g. a stone, but by the fact that the stone in that motion is describable throughout as ‘moving from P1 to P2’. 77. So that this is its one description.

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Notes to pages 39-40

78. diorizei; Bekker has horizei. 79. anankê histanai, i.e. the point must be stationary. ROT has a pause is necessary; but this is more appropriate for interruption of movement, whereas Aristotle here is concerned merely with lines and points. The thought as I understand it is: for a point on a line to be taken as end of one section and beginning of the next (‘taken twice’), it must be stationary in relation to the line (or no determinate sections are demarcated). 80. i.e. pluralizes. 81. This phrase is puzzling. 735,22-3 suggests that taking a point twice takes time and involves distinct pointings or acts of reference. Does taking X twice together mean referring to X twice but simultaneously? If so, taking X twice together is a logical impossibility whatever X may be; in this respect there is no difference between the now and the point. 82. Philoponus recognizes the following possibilities: (1) Dividing a line in actuality, i.e. separating the results so that the locus of division becomes two points each terminating a distinct line (and analogously for dividing planes and solids). (2) Physically interrupting a movement or turning the moving object in a different direction (implying an intervening period of rest). (3) Dividing something continuous, solely in thought. Remarks: (a) (2) applies only to sublunary objects and movements. (b) Only (3) applies to movements while they are going on. (c) Only (3) applies to celestial movements (cf. 732,28-30). (d) Only (3) applies to time. We also have: (4) Taking the same item twice, i.e. referring to it and re-referring to it in the same way (e.g. as ‘this’ each time); cf. 735,7-8. (5) Referring to an item once and applying to it two descriptions such as ‘ends X’ and ‘begins Y’. (Cf. 735,7-9. Confusingly, however, at 735,19-21 Philoponus glosses (4) in terms of ‘two descriptions’; cf. 734,6-8.) Remarks: (e) (1) is incompatible with (4), since the operation in (1) yields two items to refer to. (f) (4) (and no doubt also (5)) can be done with points on lines (and with lines on planes, etc.). (g) At 735,7 Philoponus says that (4) cannot be done with the object-in-locomotion. Here he is thinking of the object-in-locomotion as a series of instantaneous stages each analogous to a now. Let ‘O’ stand for the stone, and ‘LA-B(O)’ for the stone in locomotion from A to B. Then if I refer twice to LA-B(O) using that very expression, I necessarily refer to different items each time. Philoponus needs this to prove that (4) cannot be done with the now. (h) Thus only (5) can be done with the object-in-locomotion understood as

Notes to pages 41-43

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in (g): the same instantaneous stage can be described as marking the end of one section of the movement and the start of the next (cf. (b) above). (i) Only (5) can be done with the now. 83. Reading kai hôs arkhês legô kai hôs teleutês at 736,4-5. 84. oude morion ho khronos tês kinêseôs (see also 737,4) = 220a19. Bekker reads: oude morion to nun tou khronou : ‘neither is the now part of time’, which is close in meaning to what Philoponus says Aristotle ought to have said there (737,3-4). 85. Thus the lines are not continuous with each other: cf. Phys. V, 227a10-13; VI, 231a22. 86. If nows pluralize time by being parts of it, so that one succeeds another as afternoon succeeds forenoon, whatever divides them will be something we have to take twice, thus destroying the continuity of time. How is this supposed to follow? Perhaps the thought is that the divider is not a now (since ex hypothesi a now is a part of time, whereas the divider is a mere boundary); hence it cannot do what only a now can do, namely ensure temporal continuity (cf. 220a5; 222a10-11); and without continuity the two parts are merely contiguous: portions of time laid end to end. What was meant to be the boundary between them is in fact two things: the point that belongs to one as its end, and the point that belongs to the other as its beginning. 87. Reading amerê tou meristou at 737,1. 88. Emending tou megethous at 737,10 to to megethos. The phrase then refers to the temporally measurable aspect of physical movements. Philoponus implies a contrast with ‘the flow of the now from which time derives’. The latter makes temporal measure possible, hence has no temporal measure itself. 89. So Philoponus says that Aristotle should have said ‘p’ rather than the ‘q’ that occurs in the text used by Philoponus; then argues, using the examples of decad and bushel, that ‘q’ is literally true; then reinterprets the terms in ‘q’ so that it becomes synonymous with ‘p’. He may well be right about what Aristotle ‘should have said’ (cf. n. 84), and also in not being satisfied with the literal meaning of ‘q’ since the argument whereby this yields a truth is forced; but his reinterpretation of q is even more forced. 90. hêi de arithmei. Bekker has hêi d’ arithmei, arithmos, i.e. ‘but insofar as it numbers, it is number’. 91. ho de arithmos tônde; Bekker reads ho de arithmos ho tônde. 92. i.e. presupposed by. 93. 220a21-2, and Philoponus’ initial comments ad loc. are obscure because we are not told what it is of which the now is only incidentally limit. But it then becomes apparent that the limited item is a given movement or phase of movement. This might have seemed more obvious in Philoponus’ text with its mention of movement at 220a19. Philoponus may think that Aristotle is refuting a pair of views about the relation of the now to movement: (a) nows are parts of movement, and (b) the now is the limit of a movement.

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Notes to pages 43-48

94. i.e. not the same collection of ten. 95. i.e. the same prior-posterior pair. 96. Alexander Aphrodisiensis ap. Simplicium, in Phys. 729,8-13, from Alexander’s lost commentary on this part of the Physics. 97. At 219b6-9 Aristotle contrasted number with which we number (count) with number numbered (counted), and said that time was the latter. Alexander, followed by Philoponus (cf. 723,28 and 744,14-16), calls the first member of this pair ‘number that numbers’ (see also Alexander’s On Time, 93,39 [Thêry] in Sharples, 1982). This is confusing because it generates the thought that when Aristotle says ‘the now numbers’ (220a22), he may mean ‘The now is a number with which we number’ (in which case there could only be one now, just as there is one ten in the number series) instead of the innocuous proposition ‘The now is the basis of temporal countability’. Alexander considers emending but then argues (followed here laboriously by Philoponus) that the innocuous sense is intended. 98. haplôs men: Bekker has ho men haplôs. 99. Philoponus needs the converse, that everything continuous is a magnitude. 100. Philoponus is paraphrasing 220b5-8, where Aristotle explains that ‘the same time is everywhere together’ whereas prior and posterior times are not the same. Aristotle’s wording implies that the same stretch of time is everywhere together (i.e. simultaneous movements do not occupy each its own time); thus this stretch of time is present (or ‘now’) only in the broad sense of containing the current punctiform now; cf. 222a20-2. 101. i.e. the number with which we number; 219a6-8. 102. Philoponus uses the noun dekas to refer both to the unique abstract number ten, and to any group of ten, which of course can be one of many groups of ten. When, as here, he speaks of the dekas ‘in’ the horses and the different dekas ‘in’ the human beings as substrates, is he simply referring to the groups of ten, or to some third ontological category? See also 785,9-10, where he speaks of the dekas of e.g. horses as ‘the number with the substrate’. 103. i.e. long. 104. Philoponus has just discussed the option of applying the complex formulae ‘measures principally’ and ‘measures secondarily’ vel sim. to distinguish, respectively, the container C set up as a standard measure, and some pre-measured quantity of grain etc. placed in C to test its correctness as the measure it is supposed to be. (The thought there is that an unmeasured measure is more truly a measure than something that functions as a measure only because it has been – and is known to have been – measured.) Philoponus is now suggesting that the simple terms ‘measures’, and ‘determines’ be used (respectively) instead of ‘measures principally’ and ‘measures secondarily’. It is not clear what ‘the first proposal’ (tên prôtên thesin, 7) refers to.

Notes to pages 48-53

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105. 220a27-8, but with some words omitted. Philoponus gives the lemma in full at 739,25-6. 106. Bekker has hoi duo. 107. Stephen Menn informs me that the first few lines of Nicomachus’ Theologumena arithmeticae state that three is the first number-in-actuality, but without giving the reason given here by Philoponus. 108. Presumably Philoponus is referring to whatever the repeated movement is on which all time-measurement is based. If the sweep of the minute-hand on Big Ben is this movement, then by definition this minutehand cannot take more or less than an hour to complete a circuit. Thus to say that this movement does not admit of fast nor slow is to say that it is necessarily invariant. It is still true, of course, that the minute-hand on Big Ben moves faster or slower (covers more or less distance in an hour) than other moving objects. 109. Philoponus has dê; Bekker reads de. 110. Philoponus has proteros  husteros; Bekker reads proteron  husteron. 111. Vitelli gives the lemma as it appears in Bekker, reading tôi heni hippôi (cf. 220b22). Philoponus comments as if he read tôi en hippôi, i.e. ‘by means of the number in horse’, and converted this to the more coherent ‘by means of the number in the horses’. However, he refers to ‘the one horse’ at 746,1 in a similar context. 112. êpeidê here, epei in Bekker. 113. tôi kinoumenôi; but the argument requires tôi metroumenôi, ‘the object that is measured’. 114. As Vitelli suspects, there is surely a lacuna at 746,5. 115. i.e. it is no part of the object measured. 116. i.e. a standard measure. 117. It is not clear whether the pint in the soul and the external pint are, respectively, the original stipulation of what size of container is to be the standard pint measure, and the standard container (the pint pot); or whether they are, respectively, the thought-content ‘standard pint’ that governs every use of a standard container to measure wine etc., and the pint of wine measured. Ideally, there is a unique physical standard pint. The temporal analogue of the pint set apart or the pint in the soul is, presumably, an abstract unit of time measurement, as when we say ‘It is a three day journey’ without reference to any particular days. 118. i.e. ‘What part of movement [or: the movement] is it whose temporal length is defined as the primary unit of temporal measure for all the movement (pasês tês kinêseôs)?’ The expression ‘all the movement’ at 19, 20, and 22 (cf. 30) is ambiguous between ‘all movement in the universe’ and ‘all of that movement of which the primary unit of temporal measure is a part’, which refers to a celestial motion. However, ‘given that all the movement is single and continuous’ (21-2) can only refer to the celestial motion.

108

Notes to pages 53-59

119. Lacuna; the missing word may be ‘which’, referring to movement. If ‘which’ is inserted, and ‘measure’ here taken as synonymous with ‘determine’, Philoponus is asking, with typical verbosity: ‘Which part of all the movement is the standard of temporal measurement for any part that is not the standard of temporal measurement?’ 120. Accepting Vitelli’s conjecture of muriostêmorion at 23. A schoinos was a large unit of land-measurement used in Egypt. 121. It is not clear whether he means that different societies measure e.g. the same day-long period in terms of different sub-units, or that they deal in days of different lengths. There were different understandings of the absolute length of a schoinos. 122. That there is movement is an everlasting fact, and some individual movements are everlasting. 123. Actually, Aristotle starts by saying that it is one of two things, and then argues to exclude the first. 124. This formulation runs into the difficulty that, standardly in Aristotle, parts of time are themselves extended times, hence not nows (see also 750,18-26). But this can be met by pointing out the naturalness of saying that the unit is part of number (number begins at two to the Greek way of thinking) without itself being a number or divisible into numbers; the force of the analogy then supports viewing the now (pro tem.) as a part of time that is not a time. 125. There is a lacuna at 747,35; I have followed Vitelli’s conjecture on the missing words. 126. Sophocles, Ajax 646-7. 127. Menander, Georgus fr. 3 of lines 157-67, Koerte (97 Kock). 128. Actually, at 192a21-2 Aristotle says that if A and B are contraries they make each other perish, whereas Philoponus needs ‘If A makes B perish, they are contraries’. 129. dêlon de, as in Bekker. 130. i.e., according to these interpreters, the apodosis is ‘it is measure of rest too’. 131. Thus according to Philoponus the structure is: since p, q & r; and if p, s. 132. Philoponus understands ‘its being’ as ‘its essence’, ‘what it is to be movement’. 133. See Metaph. VII, chs 6 and 10-11. 134. This makes sense only if it means, in effect: the primary time-unit is defined by reference to the rotation of that sphere uniquely (cf. 770,2-3). For Philoponus, this unit-defining relationship between that movement and time is the primary meaning of ‘time measures movement’. For this relationship is what makes possible temporal measurement of all other movements. Here, Philoponus writes as if the primary meaning of ‘Time measures movement’ is the only one. 135. A referee suggested that at 6 ei should be supplied in the text after palin.

Notes to pages 59-63

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136. i.e. of ‘whatever is in X co-exists with X’ to ‘whatever co-exists with X is in X’. 137. i.e. can be substituted for it. 138. This is from Bekker’s text; the lemma in Vitelli is garbled. 139. Bekker’s text has ‘will be’ instead of ‘is’. 140. i.e. its duration. 141. If B is incidental to A then (as the term indicates) B must co-occur with A. From the supposition that time per se measures a movement, while incidentally it measures some object’s rest, Philoponus believes he can extract the absurdity that the rest would be incidental to movement (in the same object). 142. Of the celestial spheres. 143. (a) Evidently Philoponus excludes things which always are although they might not be, or might not have been, and things which never are although they might be or might have been (where ‘might’ is understood as ontological contingency, not as epistemic). In the Aristotelian context the first exclusion is reasonable, since in that context the only explanation of something’s being always would be that it necessarily exists or obtains. The second is less reasonable: he overlooks the case of my cloak’s being cut up: this event is neither necessary nor impossible: but it may never occur, because the cloak may wear out first (cf. Int. 19a12-16; also Metaph. VI, 1027b8-11, where it is said to be necessary that a given person will die, but not that he will die through violence or through disease). (b) In this passage Philoponus counts as contingent all things that are at one time and are not at another. However, the Aristotelian cosmology recognizes as necessary some transient events such as particular eclipses and sunrises (their occurrence is inevitable given the necessary movements of the spheres responsible for the changes of moon and sun; cf. GC 337b10-338b5). However, these points do not affect Philoponus’ present argument. 144. I read kata before ton khronon in 754,35. Cf. 759,23-4 and 759,30760,1. Assigning a greater time than that of their non-being consists in adding to it the time in which they are. This is ambiguous between two possibilities, and Philoponus’ text here does not make it clear which is meant. (1) We measure a non-being’s time of non-being from the present to when it ceased to exist if it is-not through being wholly in the past, and from the present to when it will begin to exist if it is-not though being wholly in the future, and then add the period of its being to obtain a period longer than that of its non-being. If the non-being is something that has occurred and will recur, we add two periods of being, past and future, to the intervening period of non-being (which spans the present). Alternative (2) is that we add the period or periods of X’s being to the entire time in which X is not (i.e. if it is past, including the time before it existed, and mutatis mutandis if it is future), thereby arriving at a greater time overall than the time of non-being. (It is assumed that items in the third category have short individual occur-

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Notes to pages 63-67

rences by comparison with the intervals between occurrences.) Alternative (2) commits anyone who accepts the Aristotelian everlastingness of the world in both directions (but not Philoponus, who held that the world was created and will come to an end) to the discomfort of recognizing infinities of different magnitudes, since the entities in question are non-existent for infinite periods. (For Philoponus’ rejection of infinities of different magnitudes, see Philoponus contra Aristotelem ap. Simplicium, in Phys. 1179,15-26; Sorabji (2004), vol. 2, 176). I suspect, however, that alternative (2) in any case fails to fit the terms of the theory. For Aristotle, the field of things whose non-being is contained by time is the field of things whose being is wholly in the past, or wholly in the future, or both (221b31-222a2). Thus for a nonbeing whose non-being consists in being wholly past we cannot include in the calculation the time, infinite or not, before it came to exist or started to happen, because that was not time when it was past, i.e. had the non-being of past things; and correspondingly for something that is-not because it is has not yet begun. With entities of the third class we are likewise only entitled, for any pair of instances past and future, to consider the finite interval during which it is true that a wholly past one is past and a wholly future one future. Furthermore, Philoponus evidently sees the way the non-being of contingents is in time as analogous to the way in which a team of horses is in number, so that the former is temporally countable. 145. The full formula is kata ton khronon kath’ hon ouk eisi/eisi (cf. 759,23-4.30-760,1, and see the previous note). 146. Bekker reads: ou gar pan to akinêton êremei. Vitelli has Ou gar pan to êremoun. 147. The perfects gegonenai and gegenêsthai at 19 suggest ‘past and over’. 148. i.e. durations of existence. 149. Whiteness and the whiteness of a particular substance cannot be temporally measured as such. 150. See n. 18. 151. Aristotle has khronôi, Philoponus has hupo khronou. 152. This classification goes back to Chrysippus. 153. Reading toutesti at 759,21. 154. i.e. the future time in which they will be makes it the case that their non-being is temporally contained, i.e. temporally exceeded. 155. i.e. if added in it makes a greater time, and so with the future entities mentioned at 759,26-8. In the case of the past entities the time of their non-being is singled out as ‘ever-occurring’, perhaps because the interval between the present and a past entity is always growing. 156. ‘them’ refers to these non-beings as such. 157. i.e. contained in respect of their non-being. 158. Since the lemma in Vitelli is garbled I have translated here from Bekker. Philoponus comments as if he understands what he is reading as tantamount to this.

Notes to pages 67-73

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159. The text is slightly uncertain but not so as to affect the philosophical meaning. 160. The indefinite pote, an adverb like the other terms listed here. The usual translation would be ‘at some time’, but this will prove awkward below. 161. i.e. by physical division. 162. As the examples just below show, here and at 28-31 Philoponus means in effect that some-time refers to a time made determinate by its connection to (i.e. by its finite distance from) the present instant. Pote is a variable whose values are given by a complex expression such as ‘ten years ago’, ‘ten years on [sc. from now]’: one part of the expression specifies a length of time, and the other part links this directionally to the present. 163. Philoponus is speaking from Aristotle’s point of view; from his own, the answer would make the Trojan war almost contemporary with Plato and Aristotle! 164. The boundedness of every time motivates the question whether time comes to an end. 165. peratoutai. This would normally be translated ‘is limited’, but that suggests that instances of some time are temporal intervals between the present and the now of some past or future event; whereas in fact they are temporal locations identified by the lengths plus directions of such intervals. 166. As at Aristotle 222b6, the future tense only has inferential force; i.e. the ‘not giving out’ applies in both temporal directions. 167. Philoponus himself argues for this elsewhere: see the Arabic paraphrase of his comments on Physics VIII 251b10-28 in Lettinck, Philoponus on Aristotle Physics 5-8, London, 1994, 135. 168. Here, Philoponus seems to write as if (1) ‘Every now is both beginning and end’ and (2) ‘There is always movement’ are independent Aristotelian grounds for (3) ‘Time will never give out’. However, in Physics VIII Aristotle uses (3) as a ground for (2), and (1) as the ground for (3) (251b10-28). 169. See Philoponus contra Aristotelem ap. Simplicium, in Phys.1178,7-35 (Sorabji [2004], vol. 2, 179-80), and 1179,15-26 (Sorabji ibid., 176). 170. i.e. the descriptions ‘end of X’ and ‘beginning of Y’ are simple by comparison with the description ‘common boundary of X and Y’. 171. Both here and in the other reading which Philoponus mentions below, the wording differs considerably from the Bekker text, but the meaning is the same. 172. The alternative reading is instead of what has been translated as ‘in so far as what is always the same point’. 173. Instead of sunthesis Bekker has henôsis (‘unification’). However, Philoponus speaks of unification at 764,19-20. 174. i.e. the present one. 175. In fact, when Aristotle refers to ‘the former now’ at 222a25, he evidently means the instantaneous present (the ‘broad’ present being the latter now).

112

Notes to pages 73-80

176. i.e. the present now, mentioned in the same line. 177. i.e. to a given some-time. E.g. the determinate temporal quantity of having been a thousand years ago from the present belongs to the ‘when’ of the Trojan war. 178. This appears as a quotation but not as a lemma in Vitelli. 179. Philoponus is referring to ‘specified time’, i.e. a determinate period such as a year. Time in this sense is obviously one only in kind, not in number. 180. Philoponus leaves this as a supposition; see n. 167. 181. To de arti morion ti kai auto tou parelêluthotos khronou. Bekker reads kai to arti to engus tou parontos nun, to morion tou parelthontos. 182. It may seem that Philoponus (and Aristotle in the original text) overlooks the way in which Aristotle’s own analysis of movement and change (‘the actuality of what is potentially F qua potentially F’) foregrounds the positive terminus ad quem of the subject’s transition (Physics III, 201a9-b15). However, the same analysis also features the agent of the change: that which introduces F into the subject (201a19-25; 202a3-12; 202a13-21). (In natural philosophy one would be studying agents whose nature it is to affect patients in various ways.) From the point of view, so to speak, of the naturally F-bearing agent, the only interesting or distinctive thing about the particular change that is instrumental for producing F in a given subject lies in its being a shift from some incompatible condition G. Hence if we (a) assume the specific contribution of the agent and then (b) concentrate on the change by itself, we see the latter as nothing but a shift from the terminus a quo. 183. Unlike the just mentioned cause of perishing, this explanation links perishing with having come into being. 184. There is an insignificant divergence from Bekker. 185. See n. 20. 186. Like Aristotle (cf. 222b31-223a4), Philoponus is anxious to avoid suggesting that every individual movement varies in speed. 187. Philoponus does not offer separate proofs of the premisses of B, because B has the same major premiss as A, and its minor can be reached by legitimate conversion from the minor of A. 188. The example is famous from Plato’s Parmenides, 131b3-5. 189. For this contrast of ‘physical’ (phusikos, ‘natural’) versus psychological movements cf. 195,24-7; 197,2-5 and 13-22; 378,22-3. See Sorabji (2004), vol. 2, 44-54. 190. The basis for the doctrine that bodies are always ‘other-moved’ is in Aristotle, Physics VIII, 255b13-256a3. 191. i.e. whose movements have a temporal beginning and end. 192. Even if Philoponus assumes that only human souls have it in their nature to measure movements by counting out the temporal units, his argument seems to allow for the situation in which, although there were no human souls (whether or not this is a possibility) and therefore no countable

Notes to pages 80-84

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temporal numbers, there would still be the temporal numbers themselves, i.e. things would still have their actual temporal durations and relations of prior and posterior. Thus the temporal numbers, hence time, are as ‘objective’ as the decad of stones mentioned at 770,20-3. But, by the argument Philoponus has just given, if there were no soul whatsoever, there would no more be stones, or any decad of stones, than there would be time. 193. Printed by Vitelli as a quotation but not as a lemma. 194. Since the comparands are each assumed to be moving at constant speed, Philoponus somehow regards the horses as moving at the same speed throughout even though they are slowed down by the bend in the track. Somehow he identifies their actual speed with what their speed would have been if, ceteris paribus, they had been running on a completely rectilinear track. Possibly he takes it that the only real variations in a thing’s speed are those due to its going faster or slower from within itself (‘its own speed’); certainly this is how we compare the speeds of different jockey-horse combinations in the same race, where external conditions are supposedly the same for all. The vagueness of ‘does not move in the same way in terms of speed’, (771,27) used of the object moving along a helix, may betray uncertainty about what to say. Perhaps Philoponus on the one hand wants to stop short of saying that its speed (= its own speed?) is less in that situation than it would have been if, with the same expenditure of effort etc., it had been moving along a straight line, but on the other hand is not about to abandon the definition of ‘slower’ in terms of actually taking more time to cover the same distance. 195. i.e. are defined by reference to prior and posterior. 196. Philoponus here refers to lines 223a20-1, but he used a text with topos (‘place’) at 20, where Bekker has khronos (‘time’). At 774,25-6 Philoponus mentions others who also read topos, but who interpreted the lines in a way that contradicts Aristotelian doctrine. Their interpretation rested on the mistaken assumption that if property A (e.g. being subject to movement) is based on property B (e.g. being in place) ‘immediately and with no restriction’, and B comes in various forms, then B’s being present in some particular form determines that A is present in precisely the same form (cf. 774,2-5). 197. The next sentence shows that Philoponus does not accept the statement introduced by ‘Similarly’. His point must be that this statement bears a likeness to the previous one, which he does accept. 198. i.e. each always rotates in the same place. 199. Here Philoponus implies that the opponents are guilty of a fallacious shift from ‘Immediately and unrestrictedly being F implies being G’ to ‘The precise way in which x is F unrestrictedly determines that x is G in that same way’. It is like arguing that since being a non-transparent surface implies being coloured, being a non-transparent three-sided surface entails being coloured in three ways.

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Notes to pages 84-92

200. In Aristotle’s exposition (223a16-18) and in Philoponus’ earlier discussion (769,25-30), this was listed as the first of two difficulties, although in each case it was dealt with second. 201. See n. 97. 202. ‘times’ here is the variable for multiples of a given period, i.e. days, years, etc. 203. poluplasiasmos: this is the technical word for multiplication, but Philoponus is also thinking of divisions of the day. 204. i.e. the smallest natural unit. At 777,25 and 27 Philoponus uses the first person plural and aorist tense to indicate that these are man-made units. 205. The digit was a length of about 2 cm. 206. i.e. establishes as a measure. 207. The criterion is for distinguishing cases where, for generic terms A, B, and C, ‘A is C and B is C’ entails ‘A and B are the same (kind of) C’ from cases where the entailment fails. 208. pros heauto: literally, ‘in relation to itself’. The differentiating respect corresponds to a diairetic question. E.g., given that X is a figure, ‘Is X bounded by straight lines or by a curve?’ The correct answer gives the differentia of X qua figure. 209. There is no indefinite article in the Greek. 210. The rule solves the paradox: since each of isosceles triangle and scalene triangle is the same figure, namely a triangle, the isosceles and the scalene ought to be the same triangle; but that is absurd. The rule explains why being the same thing, namely a triangle, does not entail being the same triangle. 211. Cat. 1a6-12; Top. II, 109b6-7; IV, 127b6-7. 212. ‘more’ only qualifies ‘universal’. 213. The ultimate subjects are particulars. 214. Vitelli, surely correctly, posits a lacuna here (778,31). I think there may also be something missing after alla in line 29. 215. The reference is probably to the human species in Socrates and the human species in Plato. 216. Today we might say: although ‘animal’ means the same in (1) ‘Socrates is (an) animal’ as it does in (2) ‘Puss is (an) animal’, the animalityelement in the truth-maker for (1) differs in essence from that in the truth-maker for (2): it consists in humanity for (1), whereas it consists in felinity for (2). By contrast, the animality-element in the truth-makers for (1) and for (3) ‘Plato is (an) animal’ is the same in essence for both. 217. This does not imply that there is only one soul possessed of the form of ten. The point is that the substrate of this ten is always the one kind of thing, soul, whereas the tens that it ‘measures’ have as their substrates things of different kinds: horses, stones, etc. 218. i.e. the smallest repeating natural movement.

Notes to pages 92-97

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219. The time-lengths week, month, year, etc. are primarily measured not by a unit of time but by the rotation of the sphere of the fixed stars. However, a single rotation of this sphere defines (‘primarily measures’) the temporal unit in terms of which the other time-lengths are measured. I have translated hekaston, ‘each’, at 782,24 as if it refers only to the week, the month, the year, etc., i.e. to continuously recurring periods of time. Thus Philoponus is not stating here that the point also applies to the time-length of every particular ‘ordinary’ movement such as Coriscus’ walk through Athens on a particular occasion. 220. Bekker has hupo after hoti at 223b16. hupo is absent from the lemma in Vitelli, but Philoponus comments as if it were present (783,2-3). With hupo the translation is: ‘ because by the movement that is defined in respect of time is measured the quantity both of movement and of time’. The philosophical content is the same either way. 221. Or: ‘in terms of time’, i.e., in effect, ‘for the purpose of measuring time’; see n. 24. 222. i.e. everlastingly recurring movements. 223. to metroun; Bekker reads to metron, ‘the measure’. 224. ‘the objects measured’ refers to the group of horses and the group of sheep. 225. At 785,17 a lacuna follows peripheres (‘curved’): the missing material would have been more or less identical with 779,10-11, ou diapherousi  to skalênon (or: skalênes, as in codex K; a referee suggested that homoioteleuton with peripheres could account for the lacuna). 226. de; Bekker has dê. 227. heptas. Bekker has dekas, ‘ten’. 228. i.e. along with each group of substrates.

Bibliography Aristotle, ed. I. Bekker, Berlin 1834. Aristotle, ed. W.D. Ross, Oxford Classical Text, Oxford, 1950, reprinted with corrections 1956-1982. Aristotle, Revised Oxford Translation, ed. J. Barnes, Princeton, 1984. Brague, R., Du temps chez Platon et Aristote, Paris, 1982. Coope, U., Time for Aristotle, Physics IV.10-14, Oxford, 2005. Lettinck, P., Philoponus on Aristotle Physics 5-8, London, 1994. Sharples, R.W., ‘Alexander of Aphrodisias, on Time’, Phronesis, vol. 27, no. 1 (1982), pp. 58-81. Sorabji, R.R.K., The Philosophy of the Commentators 200-600 AD, vol. 2, London, 2004.

English-Greek Glossary a fortiori: pollôi mallon, pollôi proteron academic audiences, for: akrôamatikos accompany: parakolouthein acknowledge beforehand: prohomologein admit of: epidekhesthai analogy: analogia ant: murmêx apprehend along with: sunepinoein arbitrary, random: apoklêrôtikos argue, argue against: epikheirein arrive: epigignesthai articulate: diêrthrômenos aspect: skhesis assumption: lêmma attribute to: anagein epi attribute: pathos awareness: sunaisthêsis, ennoia be present: enistanai be there, exist, be real: huparkhein, huphistanai before: proteron belong to, hold of, be attribute of, be data about: huparkhein bend: kampsis bound, limit (v.): perainein, peratoun, perazein break off, intermit, interrupt: dialeipein, dialambanein broad: platikos bushel: medimnos classify along with: sunkatatattein clear away: anakathairesthai

co-exist with: suneinai, sunhuparkhein cognition: gnôsis cognizable: gnôrimos cognize: gnôrizein coincide: epharmozein come round again: anastrephesthai common feature: koinonia conception, thought: epinoia conclude, deduce: sunagein conclusion, bring to: sumperainesthai conjunction: sundesmos consider, focus on, observe, see: theôrein continuance, stretch (temporal): paratasis continuate, stretch, along with: sumparateinesthai continuity, source of continuity: sunekheia contrast: antidiastolê convention, by: thesei corporeal mass: sômatôtês correspond with, follow, be determined by: akolouthein, hepesthai count up: episôreuein criterial: diakritikos day-night span: hêmeronuktion definitive: horistikos denial, by way of: arnêtikôs description: logos determine at both ends: perihorizein difficulty: aporia direct: epiblêtikos

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English-Greek Glossary

discrete: dihôrizmenos discriminate: krinein distancing: diastasis distinctive: kharaktêristikos dot apart: diastizein duration: hôra essence: ousia establish, prove: kataskeuazein exempt: exairein existence, existential grounding, reality: huparxis, hupostasis extend, stretch, along with: sunekteinesthai, sumparekteinesthai extended: diastatos fail: epileipein fixed stars, sphere of the: aplanês flow, be in flux: rhuiskesthai flowing, passage: rhusis follow as consequence: parakolouthein form: eidos former: proteron formulate (an argument): gumnazein general (adj.): genikos genus: genos give out, fail: hupoleipein grasp, able to: antilêptikos halting (n.): stasis imaginative: phantastikos immediately in sequence: ekhomenos imperceptible: anepaisthêtos (to be) implemented: sunestêkenai infinite potentiality, having: apeirodunamos instantaneous: akariaios interval: diastasis interval: diastêma introduce along with: suneisagein just-now: êdê

juxtaposition: parathesis kind: eidos know: ginôskein language: lexis, logos later: husteron lectures: skholai lie alongside: parakeisthai limit, end (n.): peras lose (sc. awareness): paraireisthai meaning: nous measure out: katametrein, parametrein measure reciprocally: antimetrein millet-seed: kenkhros non-beings: ta mê onta non-obtaining: anuparxia non-rational: alogos notice, register: ephistanai notice: sêmaioun notion: hupolêpsis object (i.e. purpose): skopos obtain, occur: huparkhein obtaining: huparxis pint: xestês pluralization: poluplasiasmos point: sêmeion, stigmê posterior: husteron prior: proteron rational: logikos real (i.e. genuine): gnêsios reality: ousia, huparxis recapitulation: analêpsis reference: anaphora regular: tetagmenos remove (degree of): apostasis rule: kanôn segment: tmêma select: ekkrinein self-evidence: enargeia sequence (of thought, argument): akolouthia, sunekheia

English-Greek Glossary set apart: exairein signifying: dêlôtikos simple-minded: euêthês smoulder: huposmukhein solid (i.e. three-dimensional) object: sôma solution: lusis solve: epiluesthai some-time: pote species: eidos stage-by-stage arrivals: kinêmata state: hexis stay for, stay: diamenein stay on: epidiamenein subordinate clause: suntaxis subsist: huphistanai subsist with: sunhuphistanai substance: ousia substrate, subject: hupokeimenon support, confirm: pistousthai surmise: huponoein sustain: stegein

take away, destroy: anairein take note (of): noein, ennoein take on, be subject of: anadekhesthai take over from: diadekhesthai taking note (act of): ennoia taking: lêpsis temporal: khronikos term: prosrhêma terminate: apoperatoun text: graphê thought (of): ennoia thought: dianoia together: hama total mass: holotêtês transparently weak: euphorêtos treatise: pragmateia

tacitly add something: proshupakouein take away along with: sunanairein

without break: adiakopôs wording: lexis

unclarity: adêlia unfamiliar: asunêthês unify: henoun unit: monas

119

Greek-English Index adêlia: unclarity, 712,11ff. adiakopôs: without break, 732,22 adiaphoros: without difference, 778,24 adiastatos: unextended, dimensionless, 703,9; 732,16ff. adunata: impossibles, 758,27 aei: continually, 732,1 aeikinêtos: ever-moving, 771,1 agnôristos: uncognizable, 727,16 agnôstos: uncognizable, 730,3ff. aïdios: everlasting, 747,1ff.; 748,35; 754,3ff.; 755,28; 762,3; 765,21ff. aiôn: eternity, 703,24; 704,10 aitia: cause, causality, 748,27; 783,13 aitiasthai: to assign causation, 748,32ff.; 768,4-6 aition: cause, 734,18; 748,7.22ff.; 760,24; 767,17ff.; 768,5ff.15; 771,2; 775,4; (see also poiêtikon aition) aitios [sc. khronos]: time as cause, 753,24; 767,11; 768,7 akariaios: instantaneous, 760,22; 761,17; 761,25ff.; 762,10; 764,23.27; 766,13.19 akhronos: non-temporal, 726,13 akinêtizein: to be immobile, 757,4 akinêtos: immovable, 757,5ff.; 759,10; 771,2 akolouthein: to correspond to, 717,28; 726,32; 728,17ff.; 729,2; 739,27; 745,7.12 akolouthia: sequence (of thought, argument) 707,3 akolouthos: fitting with, 778,6

akrôamatikos: for academic audiences, 705,20 alogos: non-rational, 770,32ff. amerês: partless, 704,23; 722,2; 726,21; 737,1 amesos: immediate, 762,33 anabainein: to ascend, 785,22 anadekhesthai: to take on, be subject of, 722,18; 735,9; 736,5; 761,10; 762,4; 763,12 anagein epi: to attribute to, 748,24 anairein: to take away, destroy, 720,12ff.; 731,2; 770,12ff.; 775,11ff. anakathairesthai: to clear away, 709,2 analêpsis: recapitulation, 764,14 analogia: analogy, 732,9 anankazein: to necessitate, 752,21 anaphora: reference, 777,28ff. anastrephesthai: to come round again, 778,10 anepaisthêtos: imperceptible, 766,25 angelos: angel, 747,27; 750,5ff.; 755,10 anisotakhês: of unequal velocity, 709,22; 781,25 anômalos: non-uniform (of speed), 771,17; 777,11 anomogenês: heterogeneous, 782,4 antapodidonai: to state the antithesis, 719,15 antidiastolê: contrast, 705,20 antikeimenos: contradictory, 755,18ff.; 758,26ff.; 760,12.16 antilêptikos: able to grasp, 754,10 antimetrein: to measure

Greek-English Index reciprocally, 741,22; 742,10; 745,6; 782,28; 783,5 antistrephein: to convert, 752,10.16.26.31 antistrophê: conversion, 752,15.17.22; 758,19 antithesis: negation, 758,19 anuparxia: non-obtaining, 755,21.28; 760,17 aoristos: indeterminate, 742,2; 773,11 apeikazein: to liken, 750,20 apeirodunamos: having infinite potentiality, 768,20 aphestanai: to be removed, 762,14; 769,15; 773,11 aphorizein: to identify, mark off, specify, 738,7; 745,29; 746,23ff.; 778,2 aplanês: of the fixed stars, 709,24; 718,8; 751,8ff.; 774,15; 777,16.21.32; 783,13 apodidonai: to give the apodosis, 749,19ff. apoklêrôtikos: random, arbitrary, 704,27 apoperatoun: to terminate, 763,19ff. apophasis: negation, 754,13.15 apophatikos: negative, 754,17; 758,12.22 aporia, aporein: difficulty, to raise a difficulty, 723,25; 725,17.27; 726,17; 740,2.8; 742,30.31; 745,32; 765,18; 769,29; 770,4; 773,24; 775,5; 779,18; 781,7; 782,12 apostasis: degree of remove, 769,14ff.; 773,6ff. arnêtikos: in denial mode, 754,16 asômatos: incorporeal, 747,26 asullogistos: invalid, 709,32; 713,9 asunêthês: unfamiliar, 724,4 atelês: incomplete, 725,22 atopos: absurd, 724,18; 725,18; 733,12; 752,18; 756,26; 776,22 autokinêtos: self-moved, 771,1

121

axiôma: axiom, 703,14.22; 706,19; 707,3 bradukinêtos: of slow velocity, 769,9; 777,13 dekas: the number ten, a collection of ten objects, 737,7; 738,1.22; 741,8; 746,1; 776,23; 778,19; 780,16ff.; 785,9 dêlôtikos: signifying, 733,28 diadekhesthai: to take over from, 778,10 diairein: to divide, 724,7; 732,13ff.; 735,27; 736,20ff.; 761,5ff.; 763,2ff.; 764,2ff.; 786,2 diairesis: division, 703,22.30; 706,16; 708,2; 725,23; 732,7ff.; 736,27; 738,28; 739,19; 764,8ff. diairetos: divisible, 708,4-10; 742,34; 745,12 diakritikos: criterial, 778,22 dialambanein peri: to examine, 702,12.13 dialambanein: to interrupt, 732,24; 733,2; 735,29 dialeipein: to break off, intermit, interrupt, 733,29; 734,1; 739,21ff. diamenein: to stay for, stay, 735,5ff. dianoia: thought, 743,22; 779,36 diaphora: difference, distinction, differentiating respect, differentia, 755,30; 766,17; 778,26ff.; 785,24ff. diastasis: distancing, interval, 773,4; 776,14 diastatos: extended, having dimension, 702,24; 703,2; 705,5.7; 732,16 diastêma: interval, 722,12; 731,24; 771,16ff.; 771,20 diastizein: to dot apart, 704,15ff. diêrthrômenos: articulate, 767,5 diestêkenai: to be at a distance from, 762,27; 769,16; 773,4

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dihôrizmenos: discrete, 723,26ff.; 724,16 diorizein: to make a distinction, mark off, 735,4; 773,14 duas hê: the number two, 743,1.9ff. eidos: form, kind, species, 725,5.6; 738,8; 741,14ff.; 744,21; 749,12; 750,4; 754,10; 765,23ff.; 767,12; 768,11ff.; 777,6.31ff.; 779,19; 780,16; 781,23 ekhomenos: immediately in sequence, 707,15 ekkrinein: to select, 750,11 ekstasis: shifting-from, 767,3 enantios: contrary, 740,3; 743,1; 748,15ff.; 766,8; 769,19 enargeia: self-evidence, 708,26 endekhomenôs: contingently, 755,30; 756,3; 759,1 endoxa: received opinions, 705,21; 708,24 enhuparkhein: to be present in, 742,22; 780,4 enistanai: to be present, 703,1ff.; 740,35ff.; 761,25ff.; 762,13.23ff.; 744,9; 762,23ff. ennoein: to take note of, 711,16.17 ennoia: awareness, thought, taking note, 711,15ff.; 712,19; 714,4ff.; 716,26; 717,21ff.; 722,21ff.; 749,10 epharmozein: to coincide, 704,16 ephexês: next, 703,27; 704,8-25; 707,11 ephistanai: to notice, register, 711,23; 715,20; 716,27 epiblêtikos: direct, 754,16 epidekhesthai: to admit of, 785,14.19 epidiamenein: to stay on, 703,26.27.34; 704,1.4.30 epigignesthai: to arrive, 725,20 epikheirein: to argue, argue against, 702,15.16; 706,3; 707,15; 708,23 epikheirêma: argument, 712,28 epileipein: to fail, 765,19

epiluesthai: to solve, 708,26; 725,27; 726,17; 740,8; 769,29; 775,5 epinoein: to think, 761,10 epinoia: conception, thought, 733,1ff.; 734,24; 761,6; 763,7ff.; 764,1ff.; 779,33; 780,1 episôreuein: to count up, 731,32 êremein: to be at rest, 755,4ff.; 756,12ff.; 769,33ff. êremia: rest, 733,2ff.; 735,29; 745,30; 754,9ff.; 749,25.32; 756,12ff.; 768,4; 769,33ff. eschatos: extreme, 736,1ff. euêthês: simple-minded, 709,31; 713,11 euphorêtos: transparently weak, 710,12 exairein: to exempt, set apart, 746,11ff.; 755,10; 779,27 existanai: to shift away, 753,14.23 exôterikoi logoi: exoteric arguments, 705,20 genesis kai phthora: coming into being and perishing, 732,25; 748,7ff.; 753,23.4; 767,17.21ff.; 777,11ff.; cf. 726,12 genikos: general, 730,15 genos: genus, 771,8; 779,19.27; 780,12 gêraskein: to get old, 754,5 ginôskein: to know, 754,11ff. gnêsios: real (i.e. genuine), 705,23 gnôrimos: cognizable, 730,2; 777,16.32; 783,5ff. gnôrizein: to cognize, 727,16ff.; 728,32; 730,6ff.; 744,2.28 gnôsis: cognition, 754,10 graphê: text, 738,26 gumnazein: to formulate (an argument), 702,32; 703,32; 714,23; 717,9 hama: together, 703,15; 704,1.2; 706,4; 724,33ff.; 725,14; 726,5.24; 731,9ff.; 735,8;

Greek-English Index 738,8ff.; 747,17.25ff.; 750,12ff.; 752,2; 776,22.28; 777,1 haplôs: simply, straightforwardly, without distinction or qualification, speaking generally, 710,26; 725,24ff.; 742,6; 750,4.6; 761,7; 767,13; 771,2; 780,26ff. hêlix: helix, 771,27ff. hêmeronuktion: day-night span, 711,12; 777,17ff.; 782,21; 783,17 henoun: to unify, 764,20 hepesthai: to correspond with, follow, be determined by, 720,21; 729,3; 730,4; 733,20; 735,5; 743,22; 775,4 heterogenês: heterogeneous, 738,1 heterokinêtos: other-moved, 770,34 hexis: state, 774,2 holotêtês: total mass, 751,25 homalos: uniform (of movement), 740,33; 771,15; 777,12; 783,9 homoeidês: same in kind, 746,11 homogenês: homogeneous, 745,33; 746,2ff.; 737,33 homokhronos: contemporaneous, synchronous, 708,15; 725,19 hôra: duration, hour, 711,16; 777,16.31 horismos: definition, specification, 720,28; 785,14 horistikos: definitive, 752,19; 778,4 horizein: to determine, mark off, define, 714,7.13ff.; 721,22ff.; 722,17.28; 727,19; 732,28; 734,23; 735,31; 739,3; 741,29; 742 ,7; 743, 28ff.; 746,6.21ff.; 748,21; 760,28; 761,24; 765,14; 768,17ff.; 770,2; 777,23; 778,1ff. ; 783,1ff.,10 horizôn: horizon, 727,19 horos: boundary, 760,29; 772,24 hote: when, 747,30ff.; 751,32ff. hulê: matter 768, 11 *huparkhein: to be there, be real, exist, obtain, occur, belong to,

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hold of, be attribute of, be data about, 703,7; 705,26; 712,1; 719,27; 720,15ff.; 742,23ff.; 743,2; 750,12; 756,18ff.; 757,20; 759,24ff.; 760,16; 766,8.13; 771,23; 780,2.12; 786,18 huparxis: existence, obtaining, existential grounding, 705,27; 730,2; 755,25ff.; 768,18; 779,33 huphistanai: to subsist, be there, 703,2.12; 706,4ff.; 710,19; 712,16; 730,9ff.; 735,22; 739,20; 750,24; 751,15; 780,10 hupokeimenon: substrate, subject, 704,30; 717,30; 720,27; 721,2; 722,22; 727,33ff.; 729,13ff.; 730,23; 733,27; 736,9; 738,5; 740,15; 741,10; 743,4; 744,1ff.; 751,1ff.,21; 757,13; 761,2ff.; 763,16; 764,6ff.; 766,2; 775,17.23; 779,28; 780,10.23; 786,19ff.; cf. 726,7.9; 775,24ff. hupoleipein: to give out, fail, 761,35; 762,2ff.; 765,20; 766,6 hupolêpsis: notion, 712,14 huponoein: to surmise, 783,24 huposmukhein: to smoulder, 766,25 hupostasis: reality, existence, 703,14; 779,30; 780,9 hupothesis: supposition, 765,26 hupothêtikos: hypothetical, 758,20 husteron: later, posterior, 703,24.26.32.33.34; 704,4; 717,27; 720,23.26; 722,8.29; 723,5; 725,18.20.24.28.29; 726,10.27; 727,29; 728,31; 729,1.21; 730,27.28; 731,26.27.29; 732,2.4; 735,5.18; 736,11.24; 737,24.26; 738,17.34; 739,7.12; 744,6.9; 746,28; 747,16.18; 750,26.27; 751,3; 765,6.7.9; 768,27.28; 769,11.13.16.18.21.23; 771,23; 772,17.19.21; 773,2.5.7.10.19; 776,1

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idios: peculiar, 776,15.19; 779,29.33 isotakhês: of equal velocity, 709,20 kampsis: bend, 771,24ff. kanôn: rule, 754,13; 778,22; 779,17; 785,22; 786,14 kat’allo: through something else, 754,20.24ff. katagêraskein: to grow old, 748,4; 753,19 katametrein: to measure out, 746,5 kataphatikos: affirmative, 709,32; 713,9; 752,16; 754,16; 758,11; kataskeuazein: to establish, prove, 703,21.22; 707,3; 723,9; 725,9; 758,4; 762,5; 768,25.30; 769,10; 772,2ff.,16; 784,18 katêgorein: to predicate, 724,7ff.; 778,23ff.; 785,23ff. kath’auto: through itself, 754,24; 755,1 katholikos: universal (adj.), 779,27; 785,22 katholou: universal, 752,16.26; 779,35; 780,2 kekhôrismenos: remote, 704,25ff. kenkhros: millet-seed, 747,30ff.; 752,12ff. kentron: centre, 755,10; 757,1; 761,8 kharaktêristikos: distinctive, 752,8.29 khôrizein: to separate, 779,36; 780,8; 782,7 khronikos: temporal, 768,23; 760,19 kinêmata (pl.): stage-by-stage arrivals, 721,11.21; 722,2 koinônein: to share, 778,23 koinonia: common feature, 779,35 koinos: common, 712,14; 713,1; 732,11; 734,9; 737,30; 760,25ff.; 763,16ff.; 776,14; 778,5; 778,23ff.; 779,28ff.; 783,27; 786,15ff.

krinein: to discriminate, 718,22ff.; 723,10ff. ; 754,14ff.; 778,11 kurios: principal, strict, 741,33; 742,4; 747,22.34; 748,3; 750,10ff.; 754,20 lêgein: to cease, 741,5 lêmma: assumption, 717, 6 lêpsis: taking, 731,26 lexis: wording, language, text, 707,4; 731,13; 764, 9 logikos: rational, 770,12.32ff. logos: description, 725,11; 728,3ff.; 729,23; 730,3; 733,28ff.; 741,15; 743,6; 761,2ff.; 762,3; 763,12ff.; 764,5ff. lusis: solution, 777,8; 780,26 mê onta, ta: non-beings, 755,15ff.; 758,27; 759,20ff. menein: to stay, 725,20 meristos: divisible into parts, 702,24; 706,1; 737,1 metabainein: to make a transition, 721,3 metabasis: passage, transitional stage, 728,21; 730,10 metekhein: to participate in, 740,17 monas: unit, one, 731,15ff.,30ff.; 743,7ff.; 745,33; 749,15; 750,22.28; 781,1ff. murmêx: ant, 763,17 noein: to take note, 722,10 nous: meaning, 742,32 organon: instrument, 767,15 ouranos: heaven, 709,15-24; 737,10; 752,12ff.,25 ousia: essence, substance, reality, 705,27; 712,7; 725,27; 726,9; 727,33; 730,8ff.; 739,20; 755,5; 759,12; 778,22; 779,29; 780,6ff. oxukinêtos: of swift velocity, 769,9; 771,23 pantôs: universally, in all cases,

Greek-English Index unrestrictedly, 747,33; 750,14.27; 775,3 paradromein: to pass (of time), 715,21 paraireisthai: to lose (sc. awareness), 711,20ff. parakeisthai: to lie alongside, side by side, 724,19; 727,27 parakolouthein: to accompany, be a consequence of, 702,13; 728,24; 753,8; 767,12; 769,36 paralogismos: paralogism, 725,22.26 paralogizesthai: to commit a fallacy, 713,7 parametrein: to measure out, 709,29 paratasis: continuance, stretch (temporal), 722,25; 724,29; 744,8ff.; 749,11f.; 754,18.25ff.; 757,26 parathesis: juxtaposition, 727,24 paratrekhein: to run past, 753,20 parerkhesthai: to pass away, 753,20 paskhein hupo: to be affected by, 749,2ff.; 753,19 pathos: attribute, 716,10; 721,9; 747,7ff.; 750,18ff.; 751,1ff.; 767,10; 770,25; 774,3 perainein: to limit, 765,17ff. peras: end, limit, 705,4; 722,14ff.; 734,9; 735,20ff.; 736,5; 737,19ff.; 738,5ff.; 739,1; 744,10; 761,10ff.; 763,17ff.; 766,6 peratoun: to bound, limit, 732,13; 736,2; 761,35 perazein: to bound, 736,1ff.; 747,2; 751,18; 761, 33; 768,16 peretteuein: to be superfluous, 749,16.23 periekhein: to contain, 703,15-18; 704,3; 706,17-20; 707,29ff.; 739,3; 741,6; 747,34; 750,16; 759,21ff. periektikos: capable of containing, 707,29

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perihorizein: to determine at both ends, 765,1 phantastikon, to: the imaginative (part of the soul), 716,19ff. phtheiresthai: to perish, 703,27; 706,23; 725,21; 748,14ff.; 767,6; 774,2.19ff. phthora: perishing, 706,23; 768,15ff.; see also genesis kai phthora phusikos: physical (contr. with psychological), 770,28; natural philosopher, 702,12 pistousthai: to support, confirm, 778,18; 783,27; 786,14 platikos: broad, in a broad sense, 741,1; 761,17; 760,22; 762,16ff.; 764,23 poiêtikon aition: productive cause, 727,21; 767,15.23; 768,1ff. pollôi mallon, pollôi proteron: a fortiori, 726,11; 746,13 pôlos: pole, 755,10; 757,2 poluplasiasmos: pluralization, 777,22 pote: some-time, 761,24ff.; 765,12ff. pragmateia: treatise, 762,7 prohomologein: to acknowledge beforehand, 742,31 pros ti, ta: relatives, 742,11.15 proshupakouein: to tacitly add something to, 758,15; 765,5 prosrhêma: term, 760,19; 768, 23 protasis: premiss, 724,14; 758,10.22; 768,30; 769,10; 772,3ff.,16ff.; 773,17 proteron: before, former, prior, 703,24.26.32.33.34; 704,3.4; 717,27; 720,23.26; 722,8.29; 723,5; 725,18.20.24.27.29; 726,9.26; 727,28; 728,31; 729,1.21; 730,27.28; 731,26.29; 732,2.3; 735,5.17; 736,10.24; 737,24.26; 738,17.34; 739,7.12; 744,6.9; 746,28; 747,16.18; 750,26.27; 751,3; 760,4.9; 764,8; 765,5.6.8.9; 768,26.28;

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769,11.13.16.18.20.21.23; 772,11.13.17.19.21; 773,2.5.7.10.18; 776,1 psukhê: soul, 716,20; 740,10ff.,26; 741,8; 743,22.29ff.; 744,14; 747,24; 750,5; 769,26ff.; 770,5ff.; 771,3; 775,16ff.; 776,23; 780,23ff. rhuiskesthai: to flow, be in flux, 703,25; 722,20; 727,11 rhusis: flowing, passage, 719,20; 727,22ff.; 735,25; 737,11; 761,17; 763,5 sêmainein: to signify, 749,12; 750,11.24; 760,10; 761,24; 775,24 sêmaioun: to notice, 750,24; 751,32 sêmeion: point, 704,9ff.; 727,11.22ff.; 731,3; 734,4; 735,2.21; 737,1; 761,5ff.; 763,4ff.,18ff.; 764,10 skhêma: figure (syllogistic), 709,33; 713,10; 722,9; 758,5; 768,28; geometric shape, 778,3ff.; 785,26ff. skhesis: aspect, content, meaning, 717,31; 725,28; 720,29; 726,9; 730,23; 741,15; 766,3 skholai: lectures, 762,9 skopos: object (sc. purpose), 745,19.27ff. sôma: solid (i.e. three-dimensional object), 708,13 sômatôtês: corporeal mass, 709,5; 713,6 stasis: halting, 732,24; 733,8 stegein: to sustain, 768,11ff. sterêsis: privation, 754,11 stigmê: point, 727,10; 728,28; 733,19; 735,1.19; 736,17; 27; 763,3.26; 764,11ff. sullogismos: syllogism, 718,21; 758,5ff.,22; 768,25; 777,2.16 sumbebêkenai: to be incidental, 716,10; 737,20ff.; 754,29; kata sumbebêkos: 728,5ff.; 753,6; 754,19ff.; 757,28; 759,11ff.; 767,13.22ff.

sumparateinesthai: to continuate, stretch along with, 724,22; 754,19; 760,17 sumparekteinesthai: to extend along with, 739,20 sumperainesthai: to bring to conclusion, 739,8 sumperasma: conclusion, 730,21ff.; 758,9; 772,2 sumplekein: to combine, 709,33; 780,8 sumplokê: combination, 710,1 sunagein: to conclude, deduce, 710,5; 712,18; 729,10; 730,29; 752,18.23; 758,14ff. sunanairein: to take away along with, 711,29; 731,2ff.; 775,16 sunaisthanesthai: to be aware of, 716,27; 766,24ff. sunaisthêsis: awareness, 711,20 sundesmos: conjunction, 749,16.24 suneinai: to co-exist with, 752,31; 753,7 suneisagein: to introduce along with, 731,3 sunekheia: continuity, source of continuity, 727,3; 732,7.21; 739,21; 76024ff.; 764,8; sequence of argument, 749,27ff.; 782,13 sunekhein: to make continuous, 760,26; 763,2ff.; sunekhês: continuous, 717,12ff.; 723,25ff.; 724,17; 727,2; 732,23; 739,18ff.; 742,32ff.; 744,1ff.; 745,12; 746,21; 760,28; 763,9; 780,30ff. sunekteinesthai: to extend alongside, 728,24 sunepinoein: to apprehend along with, 711,18; 716,12.20; 718,31; 742,10 sunêtheia: custom, 783,27 sunêthês: customary, 778,5 sungenês: homogeneous with, 777,4.20; 782,12ff.; 783,8 sunhaptein: to be in contact, connect, 760,29; 761,24ff.

Greek-English Index sunhuparkhein: to co-exist with, 747,4; 750,50; 752,15; 753,5ff.; 779,36 sunhuphistanai: to subsist with, 750,26ff. sunistanai: to be implemented, 702,24 sunkatatattein: to classify along with, 746,11ff. sunônumos: synonymous, 779, 19ff.; 780,3 suntaxis: subordinate clause, 749,17 sunthesis: synthesis, 764,18 sunthetos: composite, 750,2ff.

127

takhukinêtos: of swift velocity, 777,13 tetagmenos: regular, 718,16ff. theios: divine, 747,24 theôrein: to consider, focus on, see, observe, 739,5; 754,24; 755,18; 767,16; 778,6; 779,33; 780,2ff. theos: God, 747,27 thesei: by convention, 723,8; 746,24 thesis: position, 719,14.15.18; 735,21ff. tmêma: cut, division-segment, 703,29.32; 708,2; 740,21

Subject Index References are to the nearest preceding page and line number, which appear in the margins of the translation, and to the notes to the translation. Alexander of Aphrodisias: 738,25; 745,15; 756,5; n.97 ancients, views of the: 708,20-711,10; 712,5-20; 777,35; 783,20 angels: 747,25; 750,5; 755,10 Brague, L.: n.43 Chrysippus: n.152 contrariety: 748,15 Coope, U.: n.43 date of this commentary: 703,15 exoteric arguments: 705,15-20 God: 747,25 Homer: 755,30; 757,15; 759,15 horse-racing: 771,25 hypothetical argument: 758,20 imaginative part (of the soul): 716,20 Menander: n.127 Menn, S.: n.107 Nicomachus of Gerasa: n.107 number smallest: 739,25; 743,5-15 two senses of: 718,20-5; 722,25; 723,20; 724,1; 731,20; 739,5; 741,10; 744,10-15; 775,5

Paron: 767,5 Philoponus Christianity of: n.5 commentary on the Categories: 705,20 lectures on Physics VIII: 762,5 on infinities: n.144 Plato: n.188 poles and centre (of the universe): 757,1-5 Sardinia, sleepers in: 715,15-20; 722,20 Saturn (the planet): 710,30 schoinos (unit of land measurement): 746,20 Sharples, R.W.: n.97 sophistic argument: 725,25-30; 728,1 Sophocles: n.126 soul, rational and non-rational: 770,30 syllogism, figures of: 709,30; 5; 713,10; 723,5; 758,5; 768,25 Timaeus: n.5 Trojan war: 705,10, 708,15; 750,15; 757,15; 761,20.25; 762,15.25; 764,25; 765,1 Xenocrates: n.5 zodiac, signs of: 727,10-15; 731,25; 732,1