And now we must consider the same question in the case of becoming and perishing: how is one becoming of equal velocity with another? They are of equal [20] velocity if in an equal time there are produced two things that are the same and specifically inseparable, e.g. two men (not two animals). Similarly one is quicker than the other if in an equal time the product is different in the two cases. (For we have no pair of terms that will convey this difference in the way in which dissimilarity functions for qualities.) If substances were numbers, there would be a greater number and a lesser number within the same species; but there is no common term that will include both relations, nor are there terms to express each of them separately in the same way as we indicate a higher degree or preponderance of [25] an affection by ‘more’, of a quantity by ‘greater’.
5 · Now since a mover always moves something and is in something, and extends to something (by ‘is in something’ I mean that it occupies a time; and by ‘extends to something’ I mean that it involves a certain amount of distance—for at any moment when a thing is causing motion, it also has caused motion, so that there must always be a certain amount of distance that has been traversed and a certain amount of time that has been occupied). If, then, A is the mover, B the moved, C the distance moved, and D the time, then in the same time the same force A will move [250a1] ½B twice the distance C, and in ½D it will move ½B the whole distance C; for thus the rules of proportion will be observed. Again if a given force moves a given object a certain distance in a certain time and half the distance in half the time, half the [5] motive power will move half the object the same distance in the same time. Let E represent half the motive power A and F half B: then they are similarly related, and the motive power is proportioned to the weight, so that each force will cause the same distance to be traversed in the same time.
But if E moves F a distance C in a time D, it does not necessarily follow that E [10] can move twice F half the distance C in the same time. If, then, A moves B a distance C in a time D, it does not follow that E, being half of A, will in the time D or in any fraction of it cause B to traverse a part of C the ratio between which and the whole of C is proportionate to that between A and E—in fact it might well be [15] that it will cause no motion at all; for it does not follow that, if a given motive power causes a certain amount of motion, half that power will cause motion either of any particular amount or in any length of time: otherwise one man might move a ship, since both the motive power of the ship-haulers and the distance that they all cause the ship to traverse are divisible into as many parts as there are men. Hence Zeno’s reasoning is false when he argues that there is no part of the millet that does not [20] make a sound; for there is no reason why any such part should not in any length of time fail to move the air that the whole bushel moves in falling. In fact it does not of itself move even such a quantity of the air as it would move if this part were by itself; for no part even exists otherwise than potentially in the whole.
[25] If there are two movers each of which separately moves one of two weights a given distance in a given time, then the forces in combination will move the combined weights an equal distance in an equal time; for in this case the rules of proportion apply.
Then does this hold good of alteration and of increase also? Surely it does; for there is something that causes increase and something that suffers increase, and the [30] one causes and the other suffers a certain amount of increase in a certain amount of time. Similarly with what alters and what is altered—something is altered a certain [250b1] amount, or rather degree, in a certain amount of time: thus in twice as much time twice as much alteration will be completed and twice as much alteration will occupy twice as much time; and half in half the time, and in half half, or again, in the same amount of time it will be altered twice as much.
One the other hand if that which causes alteration or increase causes a certain [5] amount of increase or alteration in a certain amount of time, it does not necessarily follow that it will do half in half the time or in half the time half: it may happen that there will be no alteration or increase at all, the case being the same as with the weight.
BOOK VIII
1 · Was there ever a becoming of motion before which it had no being, and is it perishing again so as to leave nothing in motion? Or are we to say that it never had any becoming and is not perishing, but always was and always will be? Is it in fact an immortal never-failing property of things that are, a sort of life as it were to all naturally constituted things?
[15] Now the existence of motion is asserted by all who have anything to say about nature, because they all48 concern themselves with the construction of the world and study the question of becoming and perishing, which processes could not come about without the existence of motion. But those who say that there is an infinite number of worlds, some of which are in process of becoming while others are in [20] process of perishing, assert that there is always motion (for these processes of becoming and perishing of the worlds necessarily involve motion), whereas those who hold that there is only one world, whether everlasting or not, make corresponding assumptions in regard to motion. If then it is possible that at any time nothing should be in motion, this must come about in one of two ways: either in the manner [25] described by Anaxagoras, who says that all things were together and at rest for an infinite period of time, and that then Mind introduced motion and separated them; or in the manner described by Empedocles, according to whom the universe is alternately in motion and at rest—in motion, when Love is making the one out of many, or Strife is making many out of one, and at rest in the intermediate periods of time—his account being as follows:
Since One hath learned to spring from Manifold, [30]
And One disjoined makes Manifold arise,
Thus they Become, nor stable is their life: [251a1]
But since their motion must alternate be,
Thus have they ever Rest upon their round:49
for we must suppose that he means by ‘alternate’ that they change from the one motion to the other. We must consider, then, how this matter stands; for the [5] discovery of the truth about it is of importance, not only for the study of nature, but also for the investigation of the First Principle.
Let us take our start from what we have already laid down in our course on Physics. Motion, we say, is the actuality of the movable in so far as it is movable. Each kind of motion, therefore, necessarily involves the presence of the things that [10] are capable of that motion. In fact, even apart from the definition of motion, every one would admit that in each kind of motion it is that which is capable of that motion that is in motion: thus it is that which is capable of alteration that is altered, and that which is capable of local change that is in locomotion; and so there must be something capable of being burned before there can be a process of being burned, [15] and something capable of burning before there can be a process of burning. Moreover, these things also must either have a beginning before which they had no being, or they must be eternal. Now if there was a becoming of every movable thing, it follows that before the motion in question another change or motion must have taken place in which that which was capable of being moved or of causing motion [20] had its becoming. To suppose, on the other hand, that these things were in being throughout all previous time without there being any motion appears unreasonable on a moment’s thought, and still more unreasonable, we shall find, on further consideration. For if we are to say that, while there are on the one hand things that are movable, and on the other hand things that are motive, there is a time when there is a first mover and a first moved, and another time when there is no such thing but only something that is at rest, then this thing must previously have been in [25] process of change; for there must have been some cause of its rest, rest being the privation of motion. Therefore, before this first change there will be a previous change. For some things cause motion in only one way, while others can produce either of two contrary motions: thus fire causes hea
ting but not cooling, whereas it would seem that knowledge may be directed to two contrary ends while remaining [30] one and the same. Even in the former class, however, there seems to be something similar; for a cold thing in a sense causes heating by turning away and retiring, just as one possessed of knowledge voluntarily makes an error when he uses his knowledge in the reverse way. But at any rate all things that are capable of affecting [251b1] and being affected, or of causing motion and being moved, are capable of it not under all conditions, but only when they are in a particular condition and approach one another: so it is on the approach of one thing to another that the one causes motion and the other is moved, and when they are present under such conditions as [5] rendered the one motive and the other movable. So if the motion was not always in process, it is clear that they cannot have been in a condition such as to render them capable respectively of being moved and of causing motion, but one or other of them needed change; for in what is relative this is a necessary consequence: e.g. if one thing is double another when before it was not so, one or other of them, if not both, must have changed. It follows, then, that there will be a change previous to the [10] first.
(Further, how can there be any before and after without the existence of time? Or how can there be any time without the existence of motion? If, then, time is the number of motion or itself a kind of motion, it follows that, if there is always time, motion must also be eternal. But so far as time is concerned we see that all with one [15] exception are in agreement in saying that it is uncreated: in fact, it is just this that enables Democritus to show that all things cannot have had a becoming; for time, he says, is uncreated. Plato alone asserts the creation of time, saying that it is simultaneous with the world, and that the world came into being. Now since time [20] cannot exist and is unthinkable apart from the now, and the now is a kind of middle-point, uniting as it does in itself both a beginning and an end, a beginning of future time and an end of past time, it follows that there must always be time; for the extremity of the last period of time that we take must be found in some now, [25] since in time we can take nothing but nows. Therefore, since the now is both a beginning and an end, there must always be time on both sides of it. But if this is true of time, it is evident that it must also be true of motion, time being a kind of affection of motion.)
The same reasoning will also serve to show the imperishability of motion: just [30] as a becoming of motion would involve, as we saw, a change previous to the first, in the same way a perishing of motion would involve a change subsequent to the last: for when a thing ceases to be moved, it does not therefore at the same time cease to be movable—e.g. the cessation of being burned does not involve the cessation of the capacity of being burned, since a thing may be capable of being burned without being burned—nor, when a thing ceases to be a mover, does it therefore at the same [252a1] time cease to be motive. Again, the destructive agent will have to be destroyed when it has destroyed, and then that which has the capacity of destroying it will have to be destroyed afterwards; for being destroyed is a kind of change. If, then, this is impossible, it is clear that motion is eternal and cannot have existed at one time and [5] not at another: in fact, such a view can hardly be described as anything else than fantastic.
And much the same may be said of the view that such is how things naturally are and that this must be regarded as a principle, as would seem to be the view of Empedocles when he says that the constitution of the world is of necessity such that Love and Strife alternately predominate and cause motion, while in the intermediate period of time there is a state of rest. Probably also those who, like Anaxagoras, assert a single principle would hold this view. But that which holds by [10] nature and is natural can never be anything disorderly; for nature is everywhere the cause of order. Moreover, there is no ratio in the relation of the infinite to the infinite, whereas order always means ratio. But if we say that there is first a state of rest for an infinite time, and then motion is started at some moment, and that the fact that it is this rather than a previous moment is of no importance, and that it [15] involves no order, then we can no longer say that it is nature’s work; for if anything is of a certain character naturally, it either is so invariably and is not sometimes of this and sometimes of another character (e.g. fire, which travels upwards naturally, does not sometimes do so and sometimes not) or there is a ratio in the variation. It would be better, therefore, to say with Empedocles and anyone else who may have [20] maintained such a theory as his that the universe is alternately at rest and in motion; for in a system of this kind we have at once a certain order. But even here the holder of the theory ought not only to assert the fact: he ought also to explain the cause of it; i.e. he should not make any mere assumption or lay down any unreasoned axiom, but should employ either inductive or demonstrative reasoning. The Love and Strife [25] postulated are not in themselves causes, nor is it of the essence of either that it should be so, the essential function of the former being to unite, of the latter to separate. If he is to go on to explain this alternate predominance, he should adduce cases where such a state of things exists, as he points to the fact that among mankind we have something that unites men, namely Love, while on the other hand enemies avoid one another: thus from the observed fact that this occurs in certain cases comes the assumption that it occurs also in the universe. Then, again, some [30] argument is needed to explain why the predominance of each lasts for an equal period of time. But it is a wrong assumption to suppose universally that we have an adequate first principle in virtue of the fact that something always is so or always happens so. Thus Democritus reduces the causes that explain nature to the fact that things happened in the past in the same way as they happen now; but he does not think fit to seek for a principle to explain this ‘always’: so, while his theory is right in [252b1] so far as it is applied to certain individual cases, he is wrong in making it of universal application. Thus, a triangle always has its angles equal to two right angles, but there is nevertheless an ulterior cause of the eternity, whereas principles are external and have no ulterior cause. Let this conclude what we have to say in [5] support of our contention that there never was a time when there was not motion, and never will be a time when there will not be motion.
2 · The arguments that may be advanced against this position are not difficult to dispose of. The chief considerations that might be thought to indicate that motion may exist though at one time it had not existed at all are the following:
First, it may be said that no change is eternal; for the nature of all change is [10] such that it proceeds from something to something, so that every change must be bounded by the contraries that mark its course, and no motion can go on to infinity.
Again, we see that a thing that neither is in motion nor contains any motion within itself can be set in motion; e.g. inanimate things that are (whether the whole [15] or some part is in question) not in motion but at rest, are at some moment set in motion; whereas, if motion cannot have a becoming before which it had no being, these things ought to be either always or never in motion.
The fact is evident above all in the case of animate beings; for it sometimes happens that there is no motion in us and we are quite still, and that nevertheless we are then at some moment set in motion, that is to say it sometimes happens that we [20] produce a beginning of motion in ourselves from within ourselves, without anything having set us in motion from without. We see nothing like this in the case of inanimate things, which are always set in motion by something else from without: the animal, on the other hand, we say, moves itself; therefore, if an animal is ever in a state of absolute rest, we have a motionless thing in which motion can be produced [25] from the thing itself, and not from without. Now if this can occur in an animal, why should not the same be true also of the universe as a whole? If it can occur in a small world it could also occur in a great one; and if it can occur in the world, it could also occur in the infinite; that is, if the infinite could as a whole possibly be in m
otion or at rest.
Of these objections, then, the first-mentioned—that motion to opposites is not [30] always the same and numerically one—is a correct statement; in fact, this may be said to be necessary, provided that it is possible for the motion of that which is one and the same to be not always one and the same. (I mean that e.g. we may question whether the note given by a single string is one and the same, or is different, although the string is in the same condition and is moved in the same way.) But still, however this may be, there is nothing to prevent there being a motion that is the [253a1] same in virtue of being continuous and eternal: we shall have something to say later that will make this point clearer.
The Complete Works of Aristotle Page 74
