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  alteration: what corresponds in the category of quality to equality in

  the category of quantity is 'likeness'. However, let us say that there

  is equal velocity where the same change is accomplished in an equal

  time. Are we, then, to find the commensurability in the subject of the

  affection or in the affection itself? In the case that we have just

  been considering it is the fact that health is one and the same that

  enables us to arrive at the conclusion that the one alteration is

  neither more nor less than the other, but that both are alike. If on

  the other hand the affection is different in the two cases, e.g.

  when the alterations take the form of becoming white and becoming

  healthy respectively, here there is no sameness or equality or

  likeness inasmuch as the difference in the affections at once makes

  the alterations specifically different, and there is no unity of

  alteration any more than there would be unity of locomotion under like

  conditions. So we must find out how many species there are of

  alteration and of locomotion respectively. Now if the things that

  are in motion-that is to say, the things to which the motions belong

  essentially and not accidentally-differ specifically, then their

  respective motions will also differ specifically: if on the other hand

  they differ generically or numerically, the motions also will differ

  generically or numerically as the case may be. But there still remains

  the question whether, supposing that two alterations are of equal

  velocity, we ought to look for this equality in the sameness (or

  likeness) of the affections, or in the things altered, to see e.g.

  whether a certain quantity of each has become white. Or ought we not

  rather to look for it in both? That is to say, the alterations are the

  same or different according as the affections are the same or

  different, while they are equal or unequal according as the things

  altered are equal or unequal.

  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 velocity if in an equal time there are produced

  two things that are the same and specifically inseparable, e.g. two

  men (not merely generically inseparable as e.g. two animals).

  Similarly one is quicker than the other if in an equal time the

  product is different in the two cases. I state it thus because we have

  no pair of terms that will convey this 'difference' in the way in

  which unlikeness is conveyed. If we adopt the theory that it is number

  that constitutes being, we may indeed speak of 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 an affection by 'more', of a

  quantity by 'greater.'

  5

  Now since wherever there is a movent, its motion always acts upon

  something, is always in something, and always extends to something (by

  'is always in something' I mean that it occupies a time: and by

  'extends to something' I mean that it involves the traversing of 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). then, A the movement

  have moved B a distance G in a time D, then in the same time the

  same force A will move 1/2B twice the distance G, and in 1/2D it

  will move 1/2B the whole distance for G: thus the rules of

  proportion will be observed. Again if a given force move a given

  weight a certain distance in a certain time and half the distance in

  half the time, half the motive power will move half the weight the

  same distance in the same time. Let E represent half the motive

  power A and Z half the weight B: then the ratio between the motive

  power and the weight in the one case is similar and proportionate to

  the ratio in the other, so that each force will cause the same

  distance to be traversed in the same time. But if E move Z a

  distance G in a time D, it does not necessarily follow that E can move

  twice Z half the distance G in the same time. If, then, A move B a

  distance G 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 G the ratio between which and the whole of G is proportionate to

  that between A and E (whatever fraction of AE may be): in fact it

  might well be 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 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.

  If on the other hand we have two forces 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 in any given case we have a definite thing that

  cause increase and a definite thing that suffers increase, and the one

  causes and the other suffers a certain amount of increase in a certain

  amount of time. Similarly we have a definite thing that causes

  alteration and a definite thing that undergoes alteration, and a

  certain amount, or rather degree, of alteration is completed in a

  certain amount of time: thus in twice as much time twice as much

  alteration will be completed and conversely twice as much alteration

  will occupy twice as much time: and the alteration of half of its

  object will occupy half as much time and in half as much time half

  of the object will be altered: or again, in the same amount of time it

  will be altered twice as much.

  On the other hand if that which causes alteration or increase causes

  a certain amount of increase or alteration respectively in a certain

  amount of time, it does not necessarily follow that half the force

  will occupy twice the time in altering or increasing the object, or

  that in twice the time the alteration or increase will be completed by

  it: 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

  IT remains to consider the following question. 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?

  Now the existence of motion is asserted by all who have anything

  to say about nature, because they all 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 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 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,

  And One disjoined makes manifold arise,

  Thus they Become, nor stable is their life:

  But since their motion must alternate be,

  Thus have they ever Rest upon their round':

  for we must suppose that he means by this that they alternate from the

  one motion to the other. We must consider, then, how this matter

  stands, for the 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 fulfilment of the movable in

  so far as it is movable. Each kind of motion, therefore, necessarily

  involves the presence of the things that 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, 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 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 movent and a first moved, and another time

  when there is no such thing but only something that is at rest, then

  this thing that is at rest must previously have been in 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 heating but not cooling, whereas it would seem that

  knowledge may be directed to two contrary ends while remaining 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 respectively of

  affecting 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

  rendered the one motive and the other movable. So if the motion was

  not always in process, it is clear that they must have been in a

  condition not such as to render them capable respectively of being

  moved and of causing motion, and one or other of them must have been

  in process of 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 been in process

  of change. It follows then, that there will be a process of change

  previous to the 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 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

  had a becoming together with the universe, the universe according to

  him having had a becoming. Now since time cannot exist and is

  unthinkable apart from the moment, and the moment 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 moment, since time contains

  no point of contact for us except the moment. Therefore, since the

  moment 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 as a becoming of motion would in
volve, as we saw, the

  existence of a process of change previous to the first, in the same

  way a perishing of motion would involve the existence of a process

  of 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 the process 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 in process of being

  burned-nor, when a thing ceases to be movent, does it therefore at the

  same time cease to a be motive. Again, the destructive agent will have

  to be destroyed, after what it destroys has been destroyed, and then

  that which has the capacity of destroying it will have to be destroyed

  afterwards, (so that there will be a process of change subsequent to

  the last,) for being destroyed also is a kind of change. If, then,

  view which we are criticizing involves these impossible

  consequences, it is clear that motion is eternal and cannot have

  existed at one time and not at another: in fact such a view can hardly

  be described as anythling else than fantastic.

  And much the same may be said of the view that such is the ordinance

  of nature 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 like

  Anaxagoras, assert a single principle (of motion) would hold this

  view. But that which is produced or directed by nature 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 involves no order,