Physics · Book VIII

Aristotle · a new plain-English translation from the original language

1| Is it, then, the same way with alteration and with growth? For there is something that causes growth and something that grows, and in some quantity of time a certain quantity causes growth and a certain quantity grows. And likewise with what causes alteration and what is altered — some definite thing has been altered by some definite amount, in respect of more and less, and in some definite time: in double the time, double the alteration, and double the alteration in double the time; half in half the time (or half of the half), or double in an equal time. But if what causes alteration or growth causes so much growth or alteration in so much time, it does not follow that half of it will cause half the growth in half the time, or half in half; rather, it may well cause no alteration or growth at all, just as with weight. Book Eight.

2| Did motion ever come to be, when it did not exist before, and does it in turn pass away again in such a way that nothing is in motion, or did it neither come to be nor does it pass away, but always was and always will be — belonging to the things that are as something deathless and unceasing, a kind of life, as it were, present in everything that is constituted by nature? All those who say anything about nature agree that motion exists, because they construct an ordered world, and their whole inquiry concerns coming-to-be and passing-away, which cannot occur without motion existing. But those who say there are infinitely many worlds, and that some of these worlds come to be while others pass away, say that motion always exists (for the comings-to-be and passings-away of the worlds must occur together with motion); whereas those who hold there is one world, whether it always exists or not, make their assumptions about motion accordingly. If, then, it is possible for nothing to be in motion at some time, this must happen in one of two ways: either as Anaxagoras says (for he says that when all things were together and at rest for infinite time, intellect introduced motion and separated them out), or as Empedocles says, that things are in motion for a period and again at rest — in motion whenever Love makes the one out of the many, or Strife makes many out of the one, and at rest in the times between — speaking as follows: "insofar as the one has learned to grow out of the many,"

3| "and again, when the one grows apart, they come out as more — in this respect they come to be, and their existence is not everlasting; but insofar as these things never cease continually exchanging places, in this respect they are forever unmoved, going around in a circle." We must suppose that by "insofar as these things exchange places" he means from this state to that. We must, then, examine how matters stand concerning these things; for it is worth the effort — not only for the study of nature — to see the truth, but also for the method concerning the first principle.

4| Let us begin, first, from the distinctions we made earlier in our works on nature. We say that motion is the actuality of what is potentially movable, insofar as it is potentially movable. It is necessary, then, that the things capable of being moved exist, for each kind of motion. And even apart from the definition of motion, everyone would agree that it is necessary for what is capable of being moved, with respect to each kind of motion, actually to be moved — for example, that what is alterable is what undergoes alteration, and what is changeable in place is what undergoes locomotion; so that a thing must be combustible before it burns, and capable of burning before it burns anything. Must not these things, too, then, either have come to be at some time when they did not exist, or be eternal? If, then, each of the movable things came to be, it is necessary that, prior to the change in question, another change and motion occurred, by which the thing capable of being moved or of moving came to be. But if they existed always, with motion not existing, this appears unreasonable straightaway to anyone who considers it, and yet, as we press the point further, it turns out to be all the more a necessary consequence. For if, among the things that are movable and the things that are able to move others, at one time there will be some first mover and some thing moved, and at another time there will be nothing, but it is at rest, then this state must have changed beforehand; for there was some cause of the rest — for rest is a privation of motion.

5| So there will be a change prior to the first change. For some things cause motion in only one way, while others cause even contrary motions — for example, fire heats but does not cool, whereas knowledge seems to be one and the same capacity for contraries. Yet even there something of the same kind appears to hold: for what is cold, in a way, heats when it turns about and departs, just as the man who has knowledge errs deliberately, when he applies his knowledge in the opposite way. But in any case, whatever things are capable of acting and being acted on, or of causing motion and being moved, are not capable of this in every circumstance, but only when they are in a certain condition and near one another. So that whenever they come near, the one causes motion and the other is moved, once it comes to be the case, as it was before, that the one is the mover and the other the moved. If, then, a thing was not always in motion, it is clear that they were not previously in the condition in which the one was capable of moving and the other of being moved, but one of the two of them had to change; for this necessarily happens in the case of relative terms — for example, if something that was not double is now double, one of the two, if not both, must have changed. There will, therefore, be some change prior to the first change. And besides this, the earlier—

6| And how, later on, will there be time once time is not? Or how could there be time when there is no motion? If then time is a number of motion, or a kind of motion, then, since time always exists, motion too must necessarily be eternal. But indeed, on the subject of time, everyone appears to be of one mind except for one man: they say it is ungenerated. And it is by this very argument that Democritus shows that it is impossible for everything to have come to be: for time, he says, is ungenerated. Plato alone generates it: for he says it comes to be together with the heaven, and that the heaven has come to be. If, then, it is impossible either for time to exist or to be conceived without the now, and the now is a kind of middle point, holding both a beginning and an end at once — a beginning of the time that is to be, an end of the time that has passed — then time must always exist. For the outer limit of whatever time is taken as the last will fall within one of the nows (for nothing is to be found in time besides the now), so that, since the now is both a beginning and an end, time must always exist on both sides of it. But indeed, if there is time, it is clear that motion too must exist, if time is some affection of motion.

7| The same argument applies also to motion's being indestructible. For just as, in the case of motion's coming to be, it turned out that there must be some change prior to the first, so here too there must be a later change after the last. For a thing does not stop being in motion and being movable at the same time — for example, being burned and being combustible (for it is possible to be combustible without being burned) — nor does it stop being able to move something and actually moving it at the same time. And the destructive thing too will need to be destroyed when it destroys, and what destroys that in turn will need to be destroyed later — for destruction too is a kind of change. If, then, these things are impossible, it is clear that motion is eternal, and not a case of existing at one time and not at another; for indeed to say so seems rather more like a fabrication.

8| Likewise too with saying that this is simply how things are by nature, and that this must be taken to be a principle — which is presumably what Empedocles would say, that Love and Strife prevailing and setting things in motion by turns belongs to things of necessity, while for the time in between they are at rest. And perhaps those too who posit a single principle, as Anaxagoras does, would say something of this sort. But surely nothing among the things that are by nature, and in accordance with nature, is disorderly; for nature is the cause of order for all things. Now the unlimited stands in no ratio to the unlimited; but every order is a ratio. But for a thing to be at rest for an unlimited time and then at some point be set in motion, with no difference in this — that it happens now rather than earlier — and again for it to have no order at all, is no longer the work of nature. For what is by nature either holds simply, and not in one way at one time and another way at another — for example, fire by nature is carried upward, and not at one time and not at another — or else, where it is not simple, there is some ratio governing it. That is why it is better to say, as Empedocles does — and as anyone else who has said things are so — that the whole is at rest in turn and again in motion; for something of this sort already has some order to it. But even this the one who asserts it must not merely state, but must also give its cause, and must not posit anything, nor claim any unreasoned postulate, but must bring forward either an induction or a demonstration.

9| For the things posited are not themselves causes, nor was this what it is to be Love or Strife; rather, the one has as its being the bringing together, the other the separating out. But if the 'in turn' is further specified, one must state the cases in which this holds, as, for example, that there is something that brings human beings together — friendship — and that enemies flee from one another; for this is posited as holding in the whole as well, since it evidently holds so in some particular cases. But that it happens through equal periods of time as well needs some account. And in general, to suppose that it is a sufficient principle that something always either is or comes to be in a certain way is not a correct assumption to make — which is the point to which Democritus reduces the causes concerning nature, saying that the earlier too came about in just this way, while he does not think one should seek a principle for the 'always,' speaking correctly about some cases, but not correctly when he applies it to all cases. For the triangle too always has its angles equal to two right angles, but nevertheless there is some other cause of this eternity; whereas of principles there is no other cause, since they are eternal. Let this much, then, be said to show that there was no time, nor will there be, when there was no motion, or when there will be none.

10| The opposite arguments to these are not hard to resolve. On considering the following points, it might seem, above all, possible for motion at some time not to exist at all — first, because no change is eternal; for change is, by its nature, always from something into something, so that every change must necessarily have as its limit the opposites between which it occurs, and nothing moves into the unlimited. Again, we see that it is possible for a thing to be set in motion without either being in motion or having any motion in itself — as in the case of inanimate things, none of whose parts, nor the whole, is in motion, but which, while at rest, are at some point set in motion; and it would be fitting for it either to be always in motion or never, if — not existing — it does not come to be. This sort of thing is by far most evident in the case of ensouled things; for though no motion is present in us at some times, still, though at rest, we are nevertheless at some point set in motion, and a principle of motion arises in us out of ourselves, even if nothing moves us from outside. For we do not see this happen in the same way with inanimate things; rather, something else external always moves them; but the animal, we say, moves itself. So that if it is ever completely at rest, motion would come to be in something unmoved, out of itself and not from outside. And if this can happen in an animal, what prevents the same thing from happening also in the case of the whole? For if it happens in the small world, it happens too in the great one; and if in the world, then also in the unlimited, if indeed it is possible for the unlimited to be in motion and, as a whole, at rest.

11| Of these points, then, the first one stated — that the motion into opposites is not always one and the same in number — is correctly said. For this is perhaps necessary, if it is not always possible for the motion of one and the same thing to be one and the same; I mean, for example, whether the note of a single string is one and the same, or always different, though the string is in the same condition and moved in the same way. But nevertheless, however this may be, nothing prevents some motion from being the same by virtue of being continuous and eternal; this will become clearer from what follows later. As for a thing's being set in motion without previously being in motion, there is nothing strange in that, if what will move it is at one time present from outside and at another time not. How this could be, however, must be investigated — I mean how the same thing, by the same thing capable of moving it, is at one time moved and at another time not; for the one who raises this difficulty is puzzled by nothing other than why it is not the case that, among the things that are, some are always at rest and others always in motion. But the third point would seem most of all to present a difficulty — that motion, not present before, comes to be, as happens in the case of ensouled things; for a thing at rest before afterward walks, nothing external having moved it, as it seems.

12| But this is false. For we see that something among the connate parts is always in motion within the animal; and of this motion the animal itself is not the cause, but rather, perhaps, its surroundings. And we say that the animal moves itself not with respect to every motion, but with respect to motion in place. Nothing, then, prevents — indeed it is perhaps necessary — that many motions arise in the body owing to its surroundings, and that some of these move the thought or the desire, and that this in turn now moves the whole animal, as happens in the case of sleep; for although no motion connected with perception is present, some motion nevertheless is present, and animals wake up again. But this too will become clear about these matters from what follows.

13| The starting point of the inquiry is the same as for the puzzle already stated: why is it that some existing things are at one time in motion, at another at rest again? Necessarily, either all things are always at rest, or all are always in motion, or some are in motion and others at rest; and again, of these, either the things in motion are always in motion and the things at rest are always at rest, or all are by nature equally capable of both motion and rest, or there is a remaining third possibility besides these. For it is possible that some existing things are always unmoved, others always in motion, and others share in both — and this is what we must state. For this view provides a solution to all the puzzles that have been raised, and it is the end toward which this whole inquiry of ours is directed. Now to say that all things are at rest, and to seek an argument for this while disregarding perception, is a kind of weakness of mind, and a dispute about a whole rather than a part; nor is it a dispute only with the student of nature, but with all the sciences, so to speak, and all opinions, since all of them make use of motion. Further, objections concerning starting points, just as in arguments about mathematics they are nothing to the mathematician — and likewise in the other sciences — so too the objection just raised is nothing to the student of nature; for it is a hypothesis that nature is a principle of motion.

14| And roughly speaking, to say that all things are in motion is also false, though a lesser departure from correct method than the other view. For nature was posited as a principle within things natural, a principle of rest just as much as of motion; motion, all the same, belongs to nature. And some say that of existing things, it is not that some are in motion and others not, but that all are in motion always, only this escapes our perception. Against these people, even though they do not specify what kind of motion they mean, or whether they mean every kind, it is not difficult to reply. For a thing cannot continuously be growing or diminishing — there is also the intermediate stage. The argument is like the one about the drop wearing away the stone, and about plants splitting rocks as they grow: it does not follow that, because the drop pushed out or removed so much, half that amount was removed in half the time before; rather, just as with the hauling of a ship, the drops of such-and-such a number move so much, but a fraction of them does not move that much in any period of time at all. So what is removed is divided into many parts, but none of them was moved separately — they were all moved together. It is clear, then, that it is not necessary that something is always departing just because the wasting-away is divisible into infinitely many parts; rather the whole sometimes departs all at once. And it is the same with any kind of qualitative change: it does not follow that, because the thing altering is divisible into infinitely many parts, the alteration itself is so divided; rather it often happens all at once, as with freezing.

15| Further, when something falls sick, there must be a period of time in which it will be restored to health — the change does not happen at the limit-point of a time. And the change must be into health, and into nothing else. So to say that alteration is continuous is to fly in the face of the plain evidence in an extreme way. For alteration is toward the contrary state; but a stone becomes neither harder nor softer. And as for locomotion, it would be astonishing if it had escaped our notice that a stone is moving downward, or is at rest on the ground. Further, the earth and each of the other elements necessarily remain in their own proper places, and are moved out of them only by force; so if some of them are in fact in their own proper places, it is necessary that not all things are in motion with respect to place. That it is impos-

16| -sible that either all things are always in motion or all things are always at rest, one might be convinced from these considerations and other such ones. But neither, in fact, is it possible that some things are always at rest and others always in motion, with nothing ever at rest at one time and in motion at another. We must say that this is impossible, just as with the views stated earlier, and for the same reasons — we see the changes we described happening in the very same things — and besides this, that whoever disputes it is fighting the plain evidence. For there will be neither growth nor forced motion, unless something previously at rest is moved contrary to nature. So this account does away with coming-to-be and passing-away altogether. And indeed motion is generally thought by everyone to be a coming-to-be and a passing-away of something: for the thing changes into what it comes to be, or comes to be in it, and it passes away out of what it changes from, or passes away there. So it is clear that some things are in motion, and others are at rest, at different times. But to claim that all things are at one time at rest and at another in motion —

17| this must now be joined to the arguments made long ago. We must again make our starting point the same one from which we set out before, taking up what has just been distinguished. For either all things are at rest, or all are in motion, or, of existing things, some are at rest and others in motion. And if some are at rest and others in motion, then necessarily either all things are at one time at rest and at another in motion, or some are always at rest and others always in motion, or of these same things some are always at rest and others always in motion while others still are at one time at rest and at another in motion. That it is not possible for all things to be at rest has already been stated, but let us state it again now. For even if, in point of truth, the case is as some say — that what is is infinite and unmoved — still that is not at all how it appears to perception; many existing things are seen to be in motion. So if there is such a thing as false opinion, or opinion at all, then motion also exists, and equally if there is such a thing as imagination, and equally if a thing sometimes appears one way and sometimes another; for imagination and opinion are themselves generally held to be a kind of motion. But to investigate this question, and to look for an argument for things we are better placed to know than to need an argument for, is to judge badly between what is better and what is worse, between what deserves credence and what does not, and between a starting point and what is not a starting point. Likewise it is impossible for all things to be in motion, or for some to be always in motion and others always at rest. Against all these views a single piece of evidence suffices: we see some things at one time in motion and at another at rest. So it is plain that it is equally impossible for all things to be at rest, or for all to be continuously in motion, as it is for some to be always in motion and others always at rest. It remains, then, to examine whether all things are of such a kind as to be capable of both motion and rest, or whether some are of that kind while others are always at rest and others always in motion; for this is what we must demonstrate.

19| Of things that move and are moved, some move or are moved accidentally, others in their own right. Accidentally, for instance, whatever belongs to things that move or are moved, and also things that move or are moved as a part of something else; in their own right, whatever does not move or is moved through belonging to the mover or the moved thing, nor through some part of it moving or being moved. Of the things that move or are moved in their own right, some do so by themselves and others by something else, and some by nature, others by force and contrary to nature. For a thing that is moved by itself is moved by nature — each of the animals, for example (for the animal is moved by itself); and whatever things have within themselves the principle of their motion, these we say are moved by nature. Hence the animal as a whole moves itself by nature, though its body may be moved either by nature or contrary to nature — for it makes a difference what kind of motion it happens to be moved with, and out of what element it is composed. And of the things moved by something else, some are moved by nature and others contrary to nature: contrary to nature, for instance, earthy things moving upward and fire moving downward; and further, the parts of animals are often moved contrary to nature, contrary to the positions and manners proper to their motion. And it is especially in things moved contrary to nature that the fact that the moved thing is moved by something is plain, because it is evident that it is moved by something else. After the things moved contrary to nature, among things moved according to nature, come those moved by themselves — the animals, for instance; for here it is not unclear that the thing is moved by something, but rather how we should distinguish within it the mover from the moved. For it seems that, just as in ships and other things not naturally constituted, so too in animals the mover and the moved are divided from each other, and it is in this way that the whole thing moves itself.

20| But the remaining part of the division just stated raises the greatest difficulty. For among the things moved by something else, we set down some as moving contrary to nature, and it remains to set against these the ones we say move by nature. These are the ones that would present the difficulty of what moves them — for example light things and heavy things. For these move by force toward the places opposite their own, but toward their own places — the light thing up, the heavy thing down — by nature; but what moves them is no longer clear, as it is when they move contrary to nature. For to say that they move themselves is impossible; for this is characteristic of living things and proper to things that have soul, and they would then be able to stop themselves as well (I mean, for instance, if something is the cause in it of walking, it is also the cause of not walking), so that if moving upward is up to fire itself, clearly moving downward is also up to it. And it is unreasonable, too, that they should be moved by themselves in only one kind of motion, if indeed they move themselves. Further, how can something continuous and naturally unified move itself? For insofar as a thing is one and continuous and not by mere contact, it is unaffected; but insofar as it is divided, in that respect one part is naturally suited to act and the other to be acted on. None of these things, then, moves itself (for they are naturally continuous).

21| Nor does any other continuous thing move itself, but in every case the mover must be divided from the thing moved, as we see with soulless things when one of them moves something that has soul. But it turns out that these too are always moved by something; this would become clear if we divided up the causes. And what has been said can also be grasped in the case of the things that move: for some are movers of a thing contrary to its nature, as a lever is not by nature a mover of the weight, while others are movers by nature, as what is actually hot is a mover of what is potentially hot. And likewise in the other such cases. And in the same way, what is potentially qualified or quantified or somewhere is by nature movable, whenever it has such a principle within itself, and not accidentally (for the same thing could be both qualified and quantified, but the one is accidental to the other and does not belong to it in its own right). Fire and earth, then, are moved by something — by force whenever contrary to nature, but by nature whenever, being potentially so, they move toward their own actualities.

22| But since 'potentially' is said in several ways, this is the reason why it is not clear what moves such things — for instance fire upward and earth downward. For someone learning is potentially knowledgeable in one way, and someone who already has the knowledge but is not exercising it is potentially knowledgeable in another way. And always, whenever the acting factor and the acted-upon factor are together, the potential becomes actual — for instance the learner, from being potential in one way, becomes potential in another (for the one who has the knowledge but is not contemplating it is in a way potentially knowledgeable, but not in the way he was before learning); and when it is in this state, if nothing prevents it, it is active and contemplates, or else it will be in a state of contradiction and ignorance. And the same holds for natural things too: the cold is potentially hot, and when it changes it is now fire, and it burns, unless something prevents and impedes it. And it holds likewise for the heavy and the light: the light comes to be from the heavy, as air comes from water (for this is potential in the first sense), and it is now light, and it will act as such at once, unless something prevents it. And the actuality of the light thing is being somewhere, namely up, and it is prevented when it is in the opposite place. And this holds in the same way for quantity and for quality.

23| And yet this is exactly what is asked: why on earth light things and heavy things move to their own place. The cause is that each is naturally suited to be somewhere, and this is what being light and being heavy consist in, the one determined by the up, the other by the down. And a thing is potentially light or heavy in several ways, as has been said: for when it is water, it is potentially light in one way, and when it is air, it is still potentially light in a sense (for it is possible for it, being impeded, not to be up); but if the impediment is removed, it acts as such and comes to be ever higher. And likewise a quality changes into being so in actuality: for the man of knowledge contemplates at once, unless something prevents it; and a quantity extends itself, unless something prevents it. Now the one who moves what stands underneath and impedes a thing does move it in one sense, but in another sense does not — for example, the one who pulls out the pillar, or the one who removes the stone from the wineskin in the water; for he moves it accidentally, just as the ball that rebounds was not moved by the wall but by the one who threw it. It is clear, then, that none of these things moves itself; but it has a principle of motion — not of moving or of acting, but of being acted on. If, then, everything that is moved is moved either by nature or contrary to nature and by force, and all the things moved by force and contrary to nature are moved by something, and by something other than themselves, and again, of the things moved by nature, both those moved by themselves are moved by something, and also those not moved by themselves, such as light things and heavy things (for they are moved either by what generated them and made them light or heavy, or by what released the things impeding and preventing them) — then everything that is moved would be moved by something.

24| And this in two ways: either the mover does not move through itself, but through another which moves the mover, or it moves through itself, and this either as the first thing next after the last, or through several intermediaries — for example a stick moves a stone and is itself moved by the hand, which is moved by the man, who is no longer moved by being moved by something else. We say, then, that both move — both the last of the movers and the first — but the first more so; for that moves the last, but the last does not move the first, and without the first the last will not move, whereas the first will move without the last — for example the stick will not move unless the man moves it. If, then, it is necessary that everything that is moved be moved by something, and either by something that is itself moved by another or not, and if by another, then there must be some mover which is not itself moved by another as a first mover, but if the first is of this sort, the other alternative is not necessary (for it is impossible for the mover, being itself moved by another, to go on to infinity, since among infinite things there is no first one) — if, then, everything that is moved is moved by something, and the first mover is moved but not by another, it must be moved by itself.

25| Further, this same argument can also be approached in the following way. For everything that moves, moves with something and by means of something. For the mover moves either by itself or by another, for instance a man moves either by himself or by means of a stick, and the wind knocked something down either by itself or by means of the stone it pushed. But it is impossible to move by means of that with which it moves, without the thing itself moving by itself; but if it moves by itself, there is no need for there to be another thing by means of which it moves, whereas if that by means of which it moves is something else, there is something that will move, not by means of something, but by itself, or else it will go on to infinity. If, then, a moved thing moves something, it must come to a stop and not go on to infinity; for if the stick moves by being moved by the hand, the hand moves the stick; and if something else moves this too by means of something, then something else again is what moves this. Whenever, then, one thing always moves another by means of something, there must be, prior to it, something that moves by itself. If, then, this thing is moved, but nothing else moves it, it must move itself; so that by this argument too, either the thing moved is moved directly by what moves itself, or it eventually arrives at such a thing.

26| And in addition to what has been said, for those who look at the matter in this way too, the same things...

27| These results will follow. For if everything that is moved is moved by something that is itself moved, then either this belongs to things accidentally, so that what is moved does move something, but not because of its own being moved, or else it does not belong accidentally but in its own right. First, then, if it is accidental, the mover need not itself be moved. And if this is so, it is clear that it is possible that at some time nothing among the things that are should be in motion; for what is accidental is not necessary but admits of not being the case. If, then, we posit this as possible, nothing impossible will follow from it, though it will perhaps be false. But that there should be no motion is impossible; for it has been shown earlier that motion must always exist. And it is reasonable that this should be so. For there must be three things: the thing moved, the mover, and that by which it moves. Now the thing moved must be moved, but need not move anything; while that by which the mover moves both moves and is moved (for this changes together with, and in the same respect as, the thing moved; this is clear in the case of things that move something in respect of place, for they must touch one another up to a point); but the mover, in the sense in which it is not identical with that by which it moves, is unmoved. Since we observe the last term, which is capable of being moved but has no source of motion in itself, and also that which is moved, not by another, but by itself, it is reasonable, not to say necessary, that there should also be a third thing, that which moves while being itself unmoved. That is why Anaxagoras is right when he says that intellect is unaffected and unmixed, since he makes it the source of motion; for only in this way could it move things while being itself unmoved, and only so could it govern them while being unmixed.

28| But suppose, then, that the mover is moved not accidentally but of necessity, and that if it were not itself moved it would not move anything; then the mover, in being moved, must be moved either in the same species of motion as the motion it produces, or in a different one. I mean, for instance, either that what heats is itself being heated, and what restores to health is itself being restored to health, and what carries is itself being carried, or else that what restores to health is being carried, while what carries is being increased. But it is plain that this is impossible. For one must, pressing the division down to the ultimate kinds, say, for example, that if something teaches geometry, this very thing is being taught that same geometry, or if it throws, it is being thrown in the same manner of throwing; or, if not in that way, then one thing is moved from a different genus of motion, for instance, what carries is being increased, and what increases this is being altered by something else, and what alters this is undergoing yet some other motion. But it must come to a stop; for motions are finite in kind. And to turn back again and say that what alters is being carried is to do the same thing as if one had said outright that what carries is being carried and what teaches is being taught (for it is clear that everything that is moved is moved also by the mover further up the chain, and more so by the earlier of the movers. But this, at any rate, is impossible; for it turns out that what teaches is learning, though of these it is necessary that the one not have the knowledge and the other have it.

29| There is a further absurdity, even worse than these: it follows that everything capable of moving something is itself movable, if indeed everything that is moved is moved by something that is itself moved. For it will be movable, just as if one were to say that everything capable of restoring health must itself be restorable to health, and everything capable of building must itself be buildable, either immediately or through a series of intermediate terms. I mean, for instance, suppose everything capable of moving something is movable by something else, but not movable with the very motion which it produces in the thing next to it, but with a different one, for instance, what is capable of restoring health is capable of learning; still, mounting upward, this will at some point arrive at the same species of motion, as we said before. Now one of these alternatives is impossible, the other is fanciful; for it is absurd that what is capable of altering should of necessity be capable of increasing. It is not, then, necessary that what is moved always be moved by something else which is itself also being moved; there will therefore be a stop. So either the first thing moved will be moved by something at rest, or it will move itself. But indeed, if one had to consider which is the cause and principle of motion, the thing that moves itself, or the thing that is moved by another, everyone would posit the former; for what is a cause in its own right is always prior, as a cause, to what is a cause only in virtue of something else, when that other thing is itself a cause too. So this must be examined, taking a fresh starting point: if something moves itself, how does it move itself, and in what way?

30| Now everything that is moved must be divisible into parts that are always further divisible; for this has been demonstrated earlier, in our general account of nature, that everything moved in its own right is continuous. It is impossible, then, for the thing that moves itself to move itself as a whole in every respect; for if it did, the whole would be carried and would produce the same locomotion, being one and undivided in species, and it would be altered and would produce alteration, so that it would be teaching and learning at the same time, and would be restoring to health and being restored to the same health. Further, it has been determined that what is movable is being moved potentially, not in actuality; and what is potential proceeds toward actuality, and motion is the incomplete actuality of what is movable. But the mover already exists in actuality, for instance, what is hot heats, and in general whatever has the form generates it in another. So the same thing, in the same respect, will be at once hot and not hot. And likewise for each of the other cases in which the mover must bear the same name as what it produces. Therefore, of the thing that moves itself, one part moves and another is moved.

31| That there cannot be a self-mover of such a kind that each of the two parts is moved by the other is clear from the following. For in that case there would be no first mover at all, if indeed each is going to move the other in turn (for what is prior is more responsible for the motion of what comes after it, and will move it more; for to move was said in two ways, one where a thing is itself moved by another, the other where it moves through itself; and what is further from the thing moved is nearer to the starting principle than what is in between). Further, the mover need not be moved unless by itself; so it would be only accidentally that the other member moves it in turn. Let it be granted, then, that it is possible for it not to move the other; then one part will be moved, and the other, the mover, will be unmoved. Further, the mover need not be moved in turn; rather, it is necessary either that something unmoved move something, or that a thing be moved by itself, if indeed motion must always exist. Further, it would be moved by the very motion which it produces, so that what heats would itself be heated.

32| But indeed, not even in the case of the thing that primarily moves itself will either a single part, or several parts, move each other. For if the whole is moved by itself, it will be moved either by some part of itself, or as a whole by the whole. Now if it is by some part of it being moved by itself, this would be the primary self-mover (for once separated, this part will move itself, while the whole no longer will); but if the whole is moved by the whole, these would be moving themselves only accidentally. So, since this is not necessary, let it be assumed that they are not moved by themselves in this way. Of the whole, then, one part will move while being itself unmoved, and the other part will be moved; for only in this way is it possible for something to be self-moved. Further, if indeed the whole moves itself, one part of it will move, and another will be moved. The line AB, then, will be moved both by itself and by the part A. And since what moves is, in one case, moved by another, and in another case unmoved

33| ...being, and one part moves while the other moves nothing, what moves itself must consist of an unmoved mover and, further, of something moved that does not itself move anything — and this of necessity, not merely as it happens to be. For let A be a mover, but itself unmoved; let B be both moved by A and also move that which is C; and let C be moved by B but move nothing at all — for even if the motion should in fact reach C through several intermediate terms, let it be through one only. Then the whole, ABC, moves itself. But if I take away C, AB will still move itself, A being the mover and B being moved, while C will not move itself, nor will it be moved at all. But neither again will BC move itself without A; for B moves by being moved by another, not by being moved by some part of itself. Therefore AB alone moves itself. It is necessary, then, that what moves itself contain a part that moves but is itself unmoved, and a part that is moved but of necessity moves nothing — the two either both touching one another, or one touching the other. Now if the mover is continuous (for what is moved must be continuous), each part will touch the other. It is clear, then, that the whole moves itself not because some part of it is of such a kind as to move itself, but the whole moves itself as a whole, being both moved and mover, because part of it is the mover and part the moved. For it does not move as a whole, nor is it moved as a whole, but A moves, and B alone is moved.

34| There is a difficulty, however, if one takes away a part of A — supposing the mover, though unmoved, to be continuous — or a part of B, the thing moved: will what remains of A still move, or will what remains of B be moved? For if so, AB would not be the primary thing that is moved by itself. For once something has been taken away from AB, what remains of AB will still move it. Or rather: nothing prevents either part — or at least the moved part — from being divisible in potentiality, though undivided in actuality; and if it is divided, it no longer has the same nature; so that nothing prevents it from being present primarily, potentially, in things that are divisible. It is clear, then, from this that the primary mover is unmoved. For whether the moved thing comes immediately to a stop at something moved by something else, tracing back to a first unmoved thing, or whether it comes to a stop at something moved, which moves and stops itself, in either case it follows that what is primarily the mover of all moved things is unmoved.

35| Since motion must always exist and must never fail, there must be something eternal, one or several, that is the first mover; and the first mover is unmoved. Now whether each of the unmoved-but-moving things is itself eternal is not relevant to the present argument; but that there must be something unmoved in its own right, altogether outside change — both without qualification and accidentally — yet capable of moving something else, is clear if we consider it as follows. Let it be granted, if one wishes, that in the case of some things it is possible for them at one time to exist and at another not to exist without coming to be or perishing (for it is perhaps necessary, if something without parts at one time exists and at another does not, that everything of this kind should exist at one time and not at another without undergoing change). And let it also be granted that some of the principles which are themselves unmoved but capable of moving something exist at one time and not at another. But it is not possible that all should be of this kind; for it is clear that there is something that is the cause, for the things that move themselves, of their existing at one time and not existing at another. For everything that moves itself must have magnitude, if nothing without parts is moved; but from what has been said there is no necessity that the mover have magnitude.

36| Now nothing among the unmoved things that do not always exist is the cause of some things coming to be and others perishing, this happening continuously; nor again is any one of them the cause of these particular things, and another of those. For neither each of them singly nor all of them together are the cause of what is eternal and continuous; for that things should hold in this way is itself eternal and necessary, whereas these things are all unlimited in number, and do not all exist together. It is clear, then, that even if, ten thousand times over, some of the things that are unmoved but move something — and many of the things that move themselves — perish, while others come to be in their place, and this unmoved thing moves that thing, and something else moves some other thing, nonetheless there is something that encompasses them all, over and above each one, which is the cause of some things existing and others not, and of the continuous change; and this is a cause of motion for these, and these in turn are causes of motion for the others. If, then, motion is eternal, the first mover too will be eternal, if it is one; and if there are several, there will be several eternal movers. But we must suppose it to be one rather than many, and finite rather than infinite; for when the same consequences follow on either supposition, the finite is to be preferred, since among things that exist by nature, the finite and the better must hold, where possible, rather than the alternative. And one is enough — one which, being first among unmoved things and eternal, will be a principle of motion for the rest.

37| It is clear also from the following that the first mover must be one and eternal. For it has been shown that motion must always exist. And if it always exists, it must be continuous; for what is always is continuous, whereas what is merely successive is not continuous. But surely if it is continuous, it is one. And a motion is one if it comes from one mover and one moved thing; for if different things move it one after another, the motion as a whole is not continuous, but successive.

38| From these considerations, then, one might be persuaded that there is something first that is unmoved — and again by looking back at the starting points. That there are some things among existing things which at one time are in motion and at another are at rest is evident. And through this it has become clear that neither do all things move, nor do all things rest, nor are some always at rest while others are always in motion; for the things that go both ways, having the capacity both to be moved and to be at rest, show this concerning them. Since, then, these facts are evident to everyone, and we wish also to display the nature of each of the two classes — namely that some things are always unmoved and others always in motion — proceeding toward this point and having laid down that everything moved is moved by something, and that this something is either unmoved or moved, and if moved, is moved either by itself or, in every case, by something else — we have gone on to grasp that among moved things the principle is what moves itself, but of all things without qualification it is the unmoved. And we see plainly that there are things of this kind which move themselves, such as the class of ensouled things and of animals; and these gave rise to the opinion that motion might perhaps come to be that did not exist at all before, because we observe this happening in their case (for though at one time unmoved, they move again, as it seems). But this we must grasp: that they produce in themselves a single motion, and that they do not do so in the strict sense —

39| for the cause is not from the animal itself; rather, there are present in animals other natural motions which they do not undergo through themselves — such as growth, decay, and respiration — which each of the animals undergoes while it is at rest, not being in motion with respect to the motion that comes from itself. The cause of this is the surrounding environment and much of what enters the body, as, in some cases, food; for while it is being digested, they sleep, and while it is being separated out, they wake and move themselves, the first principle being from outside — which is why they are not always continuously moved by themselves; for what moves them is something else, itself moved and changing in relation to each of the things that move themselves. In all these cases the primary mover is itself moved, and what is the cause of the animal's moving itself is itself moved by something, though only accidentally; for the body changes place, so that what is in the body, by leverage, also moves itself. From these considerations one may be persuaded that if...

40| belongs to the class of things that are themselves unmoved but move other things while also being moved accidentally, it is impossible for it to cause continuous motion. So if motion must be continuous, there must be some first mover that is unmoved even accidentally, if there is to be, as we said, an unceasing and undying motion among the things that are, and if what is is to remain in itself and in the same condition. For if the principle remains, the whole must also remain, since it is continuous with the principle. But being moved accidentally by itself and being moved accidentally by another are not the same thing: being moved accidentally by another belongs also to some of the principles in the heaven — those that are carried in more than one motion — while the other belongs only to perishable things. But indeed, if there is always something of this sort, moving something while itself unmoved and eternal, then the first thing moved by it must also be eternal. This is clear also from the fact that there could not otherwise be coming-to-be, perishing, and change for other things, unless something itself in motion should set them in motion by its motion. For the unmoved will always move in the same way and produce a single motion, since it itself undergoes no change in its relation to what is moved.

41| But that which is moved by what is itself moved, though ultimately by what is unmoved, will not be the cause of the same motion, because it stands in different relations to things at different times; rather, because it is in opposite places or forms, it will each time present each of the other things as being moved in the opposite way — now at rest, now in motion. So it has become clear from what has been said, including the puzzle we raised at the start: why on earth it is not the case that all things either move or are at rest, or that some are always in motion and others always at rest, but instead some things are in motion at one time and not at another. For the cause of this is now clear: some things are moved by something unmoved and eternal, and are therefore always in motion, while others are moved by something that is itself moved and changing, so that they too must change. But the unmoved, as has been said, since it remains simply, in the same way, and in the same condition, will produce one and simple motion.

42| Nonetheless, if we take up another starting point, this will become clearer still. For we must examine whether it is possible for some motion to be continuous or not, and if it is possible, which motion this is, and which is the first of the motions. For it is clear that if motion must always exist, and this particular motion is first and continuous, it is because the first mover produces this motion, which must be one and the same, continuous, and first. Since there are three kinds of motion — motion in respect of magnitude, motion in respect of affection, and motion in respect of place, which we call locomotion — this last must be the first. For growth cannot occur without alteration having occurred first: what grows, in one sense grows by what is like it, but in another sense by what is unlike it, for nourishment is said to be the contrary added to the contrary. But whatever is added, once assimilated, is added as like to like. So the change into contraries must be alteration. But indeed, if a thing is altered, there must be something that alters it and makes what is potentially hot actually hot. It is clear, then, that the mover does not stand in the same relation throughout, but is now nearer, now farther, from what is being altered. And this cannot occur without locomotion. If, then, motion must always exist, locomotion too must always exist as the first of the motions, and, if of locomotion itself one kind is prior and another posterior, it is the prior kind.

43| Further, condensation and rarefaction are the principle of all the affections. For heavy and light, soft and hard, hot and cold, are all thought to be certain forms of density and rarity. Condensation and rarefaction are combination and separation, in respect of which the coming-to-be and perishing of substances are said to occur. And things that are being combined or separated must change in respect of place. And indeed, in the case of what grows and what diminishes, the magnitude also changes in respect of place. Further, looking at it from this angle too, it will be clear that locomotion is first. For "first," as in other cases, so too in the case of motion, may be said in several senses. A thing is called prior in one sense when, if it does not exist, the others will not exist, while it can exist without the others; and a thing is called prior in time, and a thing is called prior in substance. So then, since motion must exist continuously, and it could exist continuously either by being itself continuous or by being in succession — but rather it exists as continuous, and it is better for it to be continuous than to be in succession, and we always suppose that the better exists in nature, if it is possible, and it is possible for it to be continuous (this will be shown later; for now let this be assumed) — and since this continuous motion cannot be anything other than locomotion, locomotion must be first. For there is no necessity for what is carried in locomotion either to grow or to be altered, nor indeed to come to be or to perish; but none of these other motions is possible unless the continuous motion exists, which the first mover produces.

44| Further, it is first in time; for only eternal things can be moved with this motion. But in the case of any one thing that has coming-to-be, locomotion must be the last of the motions. For after coming-to-be, alteration and growth come first, and locomotion is a motion belonging only to things already completed. But there must be some other thing, prior, moving in locomotion, which will be the cause of coming-to-be for the things that come to be, itself not coming to be — as, for example, what begets is prior to what is begotten. Since coming-to-be might indeed seem to be the first of the motions for this reason, that the thing must come to be first. Now this is indeed how it stands for any one of the things that come to be, but something else must be in motion prior to the things that come to be, itself being and not coming to be, and prior to this again another. But since it is impossible for coming-to-be to be first (for then all things in motion would be perishable), it is clear that none of the motions in the following series is prior either. By "in the following series" I mean growth, then alteration, diminution, and perishing; for all of these are posterior to coming-to-be, so that if coming-to-be is not prior to locomotion, then none of the other changes is prior to it either. And in general, what is coming to be appears incomplete and moving toward a starting point, so that what is later in coming-to-be is prior in nature. And locomotion belongs last of all to everything that is subject to coming-to-be.

45| That is why some living things are wholly unmoved because of a deficiency — for example, plants and many kinds of animals — while it belongs to those that reach completion. So that, if locomotion belongs more to things that have more fully attained their nature, this motion would also be first among the others in respect of substance, both for these reasons and because, of all the motions, it is in being carried in locomotion that what is moved departs least from its substance. For this is the only motion in respect of which nothing changes of what a thing is, just as in alteration the quality changes, and in growth and diminution the quantity. And it is especially clear that what moves itself moves, most properly and in the strictest sense, with this motion — the motion in respect of place. And yet we say that this — what moves itself — is the principle among things moved and moving, and first for the things that are moved. That locomotion, then, is the first of the motions, is clear from these considerations. Which locomotion is first must now be shown. And at the same time, what was assumed both just now and earlier — that it is possible for some motion to be continuous and eternal — will become clear by the same method. That, then, none of the other motions can be continuous is clear from the following. For all motions and changes are from opposites to opposites: for coming-to-be and perishing, being and not-being are the limits; for alteration, the contrary affections; and for growth and diminution, either largeness and smallness, or completeness of magnitude and incompleteness.

46| Motions are contrary when they go to contrary things. And whatever is not always undergoing this particular motion, but existed before it, must have been at rest before it. It is clear, then, that what is changing will be at rest in the contrary state. The same holds for changes generally: for perishing and coming-to-be are opposed, both without qualification and each particular perishing to the corresponding particular coming-to-be. So if it is impossible to undergo opposite changes at the same time, the change will not be continuous, but there will be a time between them. For it makes no difference whether the changes that stand in contradiction are contrary or not, so long as it is impossible for both to belong to the same thing at once (this point is of no use to the argument); nor does it matter whether it is not necessary to rest at the point of contradiction, nor whether change is the contrary of rest (for presumably what does not exist does not rest, and perishing is a change into what does not exist) — the only thing that matters is whether a time comes to be between them; for in that case the change is not continuous. For even in the earlier arguments it was not the contrariety that did the work, but the fact that they cannot belong at the same time.

47| There is no need to be troubled by the fact that the same thing will turn out to be contrary to more than one thing — for instance, motion is contrary both to rest and to motion in the opposite direction — but one should grasp only this: that the contrary motion is opposed in some way both to motion and to rest, just as the equal and the moderate are opposed both to what exceeds and to what is exceeded, and that it is impossible for opposite motions or changes to belong to a thing at the same time. Further, in the case of coming-to-be and perishing, it would seem altogether absurd if what has come to be must at once perish and persist for no time at all. So from these considerations conviction may be gained for the other cases as well; for it is natural that the same should hold alike in all of them.

48| Let us now say that it is possible for there to be a motion that is infinite, one, and continuous, and that this is circular motion. For everything that is carried moves either in a circle, or in a straight line, or in a combination of the two; so that if neither of the first two is continuous, the motion composed of both cannot be continuous either. That what is carried along a finite straight line does not move continuously is clear: for it turns back, and what turns back along the straight line undergoes contrary motions; for up is contrary to down in respect of place, and forward to backward, and left to right — these are the contrarieties of place. What the one and continuous motion is has been determined earlier: it is the motion of one thing, in one time, and undifferentiated in species (for there were three things: the thing moved, for instance a man or a god; and the when, for instance a time; and third, the in-which — and this is place or affection or form or magnitude). But contraries differ in species, and are not one; and the differentiae just named belong to place. A sign that the motion from A to B is contrary to the motion from B to A is that they stop and check each other, if they occur at the same time. And likewise on a circle: the motion from A to B is contrary to the motion from A to C (for they stop each other, even if they are continuous and no turning back occurs, because contraries destroy and impede one another); but the motion to the side is not contrary to the motion upward.

49| It is most of all clear that motion on a straight line cannot be continuous, from the fact that what turns back must come to rest — not only on a straight line, but even if it is being carried in a circle. For being carried in a circle and being carried on a circle are not the same thing: sometimes the moving thing keeps going on continuously, and sometimes, having arrived back at the same point from which it set out, it turns back again. That it must come to rest is confirmed not only by perception but also by argument. Here is the starting point. There being three things — a beginning, a middle, and an end — the middle stands in relation to each of the other two, and is one in number but two in account. Further, the potential and the actual are different things, so that any point whatever among those within the extremities of the straight line is potentially a middle, but is not actually a middle, unless the thing moving divides the line at that point and, having come to a stop, begins to move again; in this way the middle becomes both a beginning and an end — a beginning of the later motion, and an end of the earlier one (I mean, for instance, if the thing A, being carried along, comes to rest at B and is again carried on to C). But when it is carried continuously, A can neither have come to be nor have ceased to be at the point B, but can only be there at the now, and in no time at all, except the time of which the now is the dividing point, within the whole time.

50| (But if someone posits that it has come to be and has ceased to be there, then A, being carried, will always come to a stop; for it is impossible for A both to have come to be at B and to have ceased to be there at the same time — they must therefore occur at different points of time. There will accordingly be a time in between; so A will be at rest at B. And the same holds for the other points as well, for the argument is the same for all of them. So whenever the thing carried, A, treats the point B as a middle that is both an end and a beginning, it must come to a stop, because it makes it two, just as it would if one actually thought of it that way.) But it has ceased to be at the point A, the starting point, and it has come to be at C, when it finishes and comes to rest.

51| So this same point must be made in answer to the puzzle as well; for the puzzle runs as follows. Suppose the line E is equal to the line Z, and A is carried continuously from the extremity toward Γ, and at the same time A is at the point B; and suppose D is carried from the extremity of Z toward H uniformly and at the same speed as A — then D will arrive at H before A arrives at Γ; for what set out earlier and departed earlier must arrive earlier. For A has not come to be at B and departed from it at the same time, and that is why it lags behind. For if it were at the same time, it would not lag behind, but would instead have to come to rest. One must not, then, posit that, at the moment A came to be at B, D was at the same time moving from the extremity (for if A will have come to be at B, then it will also have ceased to be there, and not at the same time — rather, this occurred at a division of time, and not in a time). So here, in the case of continuous motion, it is impossible to speak this way; but in the case of a thing that turns back, one must speak in just this way. For if the thing at H is carried toward D and, having turned back again, is carried downward, it has used the extremity at which D is as both an end and a beginning, treating the one point as two — and that is why it must come to rest;

52| and it has not come to be at D and departed from D at the same time; for in that case it would at once be and not be there at the same now. But then again, the old solution must not be given either; for it is not possible to say that the thing at H is at the point D at a mere division, and has neither come to be there nor ceased to be there. For what is actual, not what is merely potential, must reach an end. Now the points in between exist only potentially, but this point exists actually, and it is an end from below and a beginning from above; and the same accordingly holds for the motions. It is necessary, then, that what turns back on the straight line come to rest. It is not possible, then, for continuous motion on a straight line to be everlasting. And one must answer in the same way those who pose Zeno's argument, that one must always traverse the half, and these halves are infinite, and it is impossible to get through what is infinite — or as some pose this same argument differently, demanding that, along with the motion, one count the half as it comes to be each time, one by one, so that it turns out that the one who has traversed the whole has counted an infinite number; but this is admittedly impossible. Now in the first arguments about motion

53| We used to solve this by saying that time itself contains infinite parts within it; for there is nothing strange in someone's traversing infinite parts in infinite time. And the infinite belongs alike to length and to time. But this solution is adequate against the questioner, since the question asked was whether it is possible to traverse or count infinite things in a finite time; but it is not adequate with respect to the fact and the truth. For if someone, leaving aside length and the question whether it is possible to traverse infinite things in a finite time, raises the same question about time itself, since time too has infinite divisions, this solution will no longer suffice, but we must state the truth, which we stated in the arguments just given. For if someone divides a continuous thing into two halves, he uses the one point as two, since he makes it both a beginning and an end. This is what both the one who counts and the one who divides into halves do. But if it is divided in this way, neither the line nor the motion will remain continuous; for continuous motion is motion of something continuous, and in the continuous there are infinite halves, but not in actuality, only in potentiality.

54| If someone makes them actual, he will not preserve continuity but will bring the thing to a halt, which is plainly what happens in the case of the man counting the halves. For he must count the one point as two, since it will be the end of one half and the beginning of the other, if he does not count the continuous line as one but as two halves. So we must say to the questioner, if it is asked whether it is possible to traverse infinite things either in time or in length, that it is possible in one way and not possible in another. For if they exist actually, it is not possible, but if potentially, it is possible; for the thing moving continuously has traversed infinite things accidentally, but not without qualification; for it is accidental to the line to have infinite halves, but its substance and its being are something different. And it is clear too, unless someone treats the point that divides the earlier and the later of time as always belonging to the later part with respect to the thing itself,

55| that the same thing will at once both exist and not exist, and will not exist at the very moment it has come to be. The point, then, is common to both, to the earlier and the later, and it is the same and one in number, though not the same in account, since of the one part it is the end and of the other the beginning; but with respect to the thing, it always belongs to the affection of the later part. Let time be represented by AΓB, and the thing by D. This thing, during time A, is white, and during B, not white. Then during Γ it is white and not white. For at any point whatever within A it is true to say it is white, if it was white throughout that entire time, and during B, not white; but Γ belongs to both. We must not, then, grant this for every point, but only excepting the final now, that at Γ; and this now already belongs to the later part. And if it was becoming not-white and the white was perishing throughout the whole of A, then it has come to be, or has perished, at Γ. So it is at that point that it is first true to say white or not white; otherwise, it will not be at the moment it has come to be, and it will be at the moment it has perished, or else it will necessarily be at once both white and not white, and, in general, both being and not being.

56| But if whatever previously did not exist must come to be existent, and if at the moment it is coming to be it does not yet exist, then time cannot be divided into indivisible times. For if in time A the thing D was coming to be white, and it has come to be, and exists, in another indivisible time adjacent to it, in B — since if it was coming to be in A, it was not yet white, but in B it is — then there must be some coming-to-be between the two, and therefore also a time in which it was coming to be. For the same account will not hold for those who do not speak of indivisibles as it does for us: rather, in the very time in which it was coming to be, it has come to be and exists at the final point of that time, a point which has nothing next to it and nothing following it in succession; but the indivisible times themselves are in succession to one another. And it is clear that if it was coming to be throughout the whole of time A, there is no more time in which it has come to be and was coming to be than the time in which it was merely coming to be, throughout. These, then, are roughly the arguments one might trust as proper to the subject; but examining the matter dialectically, one might think the same conclusion follows from the considerations below as well. For everything that moves continuously, if it is deflected by nothing, was already moving, before it arrived, toward the very point it arrived at in its locomotion — for instance, if it arrived at B, it was moving toward B from the start, and not only when it was near, but from the very moment it began to move.

57| For why should it be moving toward it more now than earlier? And the same holds in the other cases too. So the thing moving from A, when it arrives at Γ, will again move back toward A, moving continuously. Then, at the very time it is moving from A to Γ, it is at that same time also moving toward A with the motion coming from Γ, so that it will be undergoing the contrary motions at once; for motions along a straight line are contrary to one another. And at the same moment it changes from the one motion into the other, in which there is no interval. If, then, this is impossible, it must come to rest at Γ. The motion, therefore, is not one; for a motion broken by rest is not one motion. Further, this is also clear, and more generally so, from the following considerations about motion as a whole. If everything that moves is moved with one of the kinds of motion mentioned and is at rest with one of the opposed kinds of rest, since there was no other rest besides these, and if that which is not always moving with this particular motion — I mean motions that differ in kind, not merely a part of the same whole motion — must previously have been at rest with the opposed rest, since rest is the privation of motion, then, if motions along a straight line are contrary to one another, and it is not possible to be moved with contrary motions at the same time, the thing moving from A toward Γ could not also be moving at the same time from Γ toward A. But since it is not moving both at once, and yet it is going to be moved with this latter motion, it must first have come to rest at Γ;

58| for this was the rest opposed to the motion from Γ. It is clear, then, from what has been said, that the motion will not be continuous. Further, this argument too is even more proper to the subject than those already given. For the not-white has perished and the white has come to be at the same moment. If, then, the alteration to white and from white is continuous and does not remain in one state for any length of time, then the not-white has perished and the white has come to be, and the not-white has come to be, all at the same moment; for the time will be the same for all three. Further, it is not the case that if time is continuous, motion is continuous too, but only that it is successive. And how could the extreme point be the same for contraries, for instance for whiteness and blackness? But the motion along a circle's circumference will be one and continuous; for nothing

59| impossible follows from it. For the thing moving from A will at the same time be moving toward A, in accordance with the same forward course, since it will arrive there, and it is moving toward that very point; but it will not be moving the contrary or the opposite motions at the same time. For not every motion toward a point is contrary or opposite to the motion away from that point; rather, contrariety belongs to motion along a straight line, since on that line there is a contrary in respect of place, as with things diametrically opposite, for they are the furthest apart from one another, whereas motion over the same stretch of length is the opposite kind of motion. So nothing prevents the thing from moving continuously and leaving no time in between; for circular motion goes from itself back to itself, while motion along a straight line goes from itself to something else, and circular motion is never in the same places twice, whereas motion along a straight line is often in the same places. So a motion that is always coming to be in one place and then another admits of being continuous, but one that is often in the same places does not; for it would have to be moving the opposite motions at the same time. So it is not possible to move continuously either around a semicircle or around any other arc; for necessarily the same path must often be traversed, and the contrary changes must be undergone, since the beginning does not join up with the end. But the beginning and end of the circle do join up, and the circle alone is a complete motion.

60| It is clear from this division that the other kinds of motion also cannot be continuous; for in all of them the same things happen to move repeatedly — for instance, in alteration, the intermediate qualities, and in quantitative change, the magnitudes in between, and likewise in coming-to-be and perishing. For it makes no difference whether one posits few or many things in which the change occurs, nor whether one inserts something in between or removes it; either way the result is that the same things move repeatedly. It is clear from this, then, that the natural philosophers who say that all perceptible things are always in motion are not speaking correctly. For they must be moving with one of these kinds of motion — and above all, on their view, undergoing alteration; for they say that things are always flowing and perishing, and moreover they call coming-to-be and perishing alteration. But our account has now stated, universally, concerning every motion, that with no kind of motion is it possible to move continuously except circular motion — so that this holds neither for alteration nor for increase. Let this much, then, be said by us: that no change is either infinite or continuous except circular locomotion.

61| That among locomotions circular locomotion is primary is clear. For every locomotion, as we said earlier, is either circular or in a straight line or mixed. And these latter must be posterior to the circular, for they are composed out of it and the straight. And circular is prior to straight, for it is simpler and more complete. For it is not possible to move on an infinite straight line — there is no such infinite thing, and even if there were, nothing would be moved on it, since the impossible does not happen, and to traverse the infinite is impossible. And motion on a finite straight line, if it turns back, is composite and is two motions; if it does not turn back, it is incomplete and perishable. And prior, both in nature and in account and in time, is the complete to the incomplete, and the imperishable to the perishable. Further, that motion which admits of being eternal is prior to that which does not: circular motion admits of being eternal, but none of the others does, neither locomotion of another kind nor any other kind of motion at all; for there must come to be a standstill, and if there is a standstill, the motion has perished.

62| It is reasonable that it should turn out that circular motion is one and continuous, and not motion in a straight line. For straight motion has a determinate beginning, end, and middle, and has all of these within itself, so that there is a point from which the moving thing will start and a point at which it will finish (for everything comes to rest at its limits, either the point it moves from or the point it moves to); but of circular motion these are undetermined. For why should any one point on the line be its limit any more than any other? For each point alike is beginning and middle and end, so that the moving thing is always both at a beginning and at an end, and never so. That is why the sphere both moves and is in a way at rest, for it occupies the same place. The cause is that all these belong to the center: it is beginning and middle and end of the magnitude, so that, because this point lies outside the circumference, there is nowhere the moving thing will come to rest as having completed its course (for it is always moving about the middle, not toward an extremity); and because this point stays fixed always, the whole is in a way always at rest and moves continuously. And it works the other way round too: because circular motion is the measure of motions, it must be the first (for all things are measured by the first, and it is because it is first that it is the measure of the others).

63| Further, only circular motion can be uniform. For things moving in a straight line move unevenly from the starting point to the end, since everything, the further it gets from the point of rest, moves faster; but of circular motion alone neither beginning nor end is present in it by nature, but lies outside it. That locomotion is the primary kind of motion is testified to by all who have made mention of motion, for they assign the principles of it to whatever produces this kind of motion. For separation and combination are motions in respect of place, and it is in this way that Love and Strife produce motion: the one separates, the other combines. And Anaxagoras too says that Intellect, the first mover, separates. Likewise also all those who name no such cause but say that motion occurs because of the void — for they too say that nature moves by locomotion (for motion because of the void is locomotion, and is, as it were, motion in place), and hold that none of the other kinds of motion belongs to the primary things but only to what is composed of them; for they say that increase and decrease and alteration occur as the indivisible bodies combine and separate. And in the same way also all those who construct coming-to-be and perishing by means of density and rarity —

64| for they too order these things by combination and separation. And besides these, there are those who make soul the cause of motion; for they say that the thing that moves itself is a principle among moving things, and that the animal, and everything ensouled, moves itself with locomotion. And indeed we say that only what moves in respect of place is moved in the strict sense; for if a thing is at rest in the same place but is increasing or decreasing, or happens to be altering, we say it is moving in a certain respect, but we do not say it is moving without qualification. That there always was and always will be motion for all time, then, and what the principle of eternal motion is, and further what the first motion is, and what motion alone can be eternal, and that the first mover is unmoved — this has now been stated.

65| That this mover must be without parts and have no magnitude, let us now state, first marking out the points prior to it. One of these is that nothing finite can cause motion for an infinite time. For there are three things: the mover, the moved, and the third, time. These are either all infinite, or all finite, or some are, for instance two of them, or one. Let A be the mover, B the moved, and let the time, infinite, be C. Now let D move some part of B, namely the part on which E stands; this will not take a time equal to C, for the greater thing takes more time. So the time, call it Z, will not be infinite. So then, by continuing to add to D, I shall use up A, and by adding to E, I shall use up B; but I shall not use up the time by always subtracting an equal amount from it, for it is infinite. So the whole of A will move the whole of B in a finite time, that of C. It is not possible, then, for anything infinite to be moved, in respect of motion, by anything finite. That it is not possible, then, for

66| the finite to produce motion for an infinite time is clear; and that it is altogether impossible for there to be an infinite power in a finite magnitude is clear from the following. Let it be granted that a power is always greater which produces an equal effect in a shorter time — for example in heating or sweetening or throwing, and in general in causing motion. It is necessary, then, that what is acted upon should be affected in some way by what is finite but has infinite power, and be affected more than by anything else; for the infinite power is the greater. But indeed there cannot be any time in which this happens. For if A is the time in which the infinite power heated or pushed, and in AB a finite power did so, then, always taking a greater finite power in proportion to this one, I shall at some point arrive at having produced the same motion in the time A; for by always adding to a finite quantity I shall exceed any determinate amount, and likewise by subtracting I shall fall short of it. So the finite power will produce motion in a time equal to that of the infinite power. But this is impossible. Therefore nothing finite can have infinite power. Nor, therefore, can anything infinite have finite power.

67| And yet it is possible for there to be more power in a smaller magnitude; but still more so, more power in a greater one. Let AB, then, be infinite. Now BC has a certain power, which in a certain time moved D, in the time EZ. If, then, I take double of BC, it will move D in half the time of EZ (for let this be the ratio), so that it will move it in the time ZH. Now taking a portion in this way, I will never exhaust AB, but I will always take a smaller portion of the given time. The power will therefore be infinite; for it exceeds every finite power, if indeed for every finite power the time it takes to move something must also be finite (for if such-and-such a power moves something in a certain time, a greater power will move it in a shorter but still determinate time, in inverse proportion); and every power that exceeds every determinate power is infinite, just as a multitude or magnitude that exceeds every determinate one is infinite. This can also be shown in the following way: we shall take some power the same in kind as the power in the infinite magnitude, but existing in a finite magnitude, which will measure out the finite power that is in the infinite magnitude.

68| That it is not possible, then, for an infinite power to exist in a finite magnitude, nor a finite power in an infinite magnitude, is clear from these considerations. But concerning things that are carried along in motion, it is well to raise a certain puzzle first. For if everything that is moved is moved by something — as many things, that is, as do not move themselves — how is it that some things are moved continuously when what moved them is no longer in contact with them, for example things that are thrown? But if what moved it also moves something else at the same time — for example the air, which, being moved, moves the projectile in turn — it is equally impossible for the thing to continue being moved once the first mover is not in contact with it and not moving it; rather, all things must be moved together and must have stopped together the moment the first mover stops, even if, like the lodestone, it makes what it moved capable in turn of moving something else. It is necessary, then, to say this: that the first mover makes the air, or the water, or some other such thing that is by nature capable of both moving and being moved, capable of moving something. But it does not cease being a mover and being moved at the same time; rather, the thing stops being moved at the same moment that what was moving it stops moving it, while it is still, for the time being, itself a mover. That is why it in turn moves something else next to it; and the same account applies to this in turn. But it stops when the power of moving that comes to belong to what is next in the series keeps growing continually smaller.

69| And it finally stops when the earlier mover no longer makes it a mover, but leaves it only something moved. And these — the mover and the thing moved — must stop together, and the whole motion with them. This kind of motion, then, occurs among things that admit of being at one time in motion and at another at rest, and it is not continuous, but only appears to be; for it belongs to things that are either successive or in contact, since the mover is not one thing, but a series of things each next to another. That is why motion of this sort occurs in air and water, which some call mutual replacement. It is impossible to resolve the puzzles raised in any other way than the one stated. For mutual replacement makes all the things involved be moved and move at the same time, so that they also stop at the same time; but as it is, some single thing plainly appears to be moved continuously. By what, then, is it moved? For it is not by the same thing throughout.

70| Since among the things that are there must be some continuous motion, and this motion is one, and the one motion must belong to some magnitude (for what has no magnitude is not moved) and must belong to one thing and be caused by one thing (for otherwise it will not be continuous, but one motion will simply be next to another, and divided from it) — if, then, the mover is one, it moves either while itself being moved or while being unmoved. Now if it is moved, it will have to keep pace with and change along with the moved thing, while at the same time being moved by something else; so that the series will come to a stop and arrive at last at something moved by what is unmoved. For this unmoved mover need not change along with anything, but will be able to move the other thing forever (since moving in this way involves no exertion), and this motion is uniform, either alone or most of all; for the mover undergoes no change whatsoever. And the thing moved, too, must undergo no change in its relation to that mover, so that the motion may remain uniform. It must, then, be situated either at the center or on the circumference, for these are the only governing points. But the things nearest the mover are moved fastest. And such is the motion of the circle; the mover, therefore, is there, at the circumference. But there is a puzzle here: whether it is possible for something that is itself moved to move something else continuously, rather than only as what pushes does, again and again, seeming continuous merely because its actions are successive.

71| For either the mover itself must be constantly pushing or pulling, or both, or else one thing must keep taking over from another in succession, as was said earlier concerning things thrown, on the supposition that the air, being divisible, moves the object because one part of it is always being moved by another. But on either account it is not possible for the motion to be one, but only a series of motions each next to the last. The only continuous motion, then, is the one that the unmoved mover produces; for since it is always in the same state, it will stand in the same relation to the thing moved, and continuously so. Now that these points have been settled, it is clear that it is impossible for the first mover, being unmoved, to have any magnitude. For if it has magnitude, it must be either finite or infinite. That there cannot be an infinite magnitude has been shown earlier, in the Physics; and that a finite magnitude cannot have infinite power, and that it is impossible for anything to be moved by a finite magnitude for an infinite time, has now been shown. But the first mover produces a motion that is eternal, and does so for infinite time. It is clear, then, that it is indivisible, has no parts, and has no magnitude at all.

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