The Basic Works of Aristotle (Modern Library Classics) (57 page)

5
     Since everything that changes changes from something to something, that which has changed must at the moment when it has first changed be in that to which it has changed. For that which changes retires from or leaves that from which it changes: and leaving, if not identical with changing, is at any rate a consequence of it.
(10)
And if leaving is a consequence of changing, having left is a consequence of having changed: for there is a like relation between the two in each case.

One kind of change, then, being change in a relation of contradiction, where a thing has changed from not-being to being it has left not-being.
(15)
Therefore it will be in being: for everything must either be
or not be. It is evident, then, that in contradictory change that which has changed must be in that to which it has changed. And if this is true in this kind of change, it will be true in all other kinds as well: for in this matter what holds good in the case of one will hold good likewise in the case of the rest.

Moreover, if we take each kind of change separately, the truth of our conclusion will be equally evident, on the ground that that which has changed must be somewhere or in something.
(20)
For, since it has left that from which it has changed and must be somewhere, it must be either in that to which it has changed or in something else. If, then, that which has changed to B is in something other than B, say C, it must again be changing from C to B: for it cannot be assumed that there is no interval between C and B,
(25)
since change is continuous. Thus we have the result that the thing that has changed, at the moment when it has changed, is changing to that to which it has changed, which is impossible: that which has changed, therefore, must be in that to which it has changed. So it is evident likewise that that which has come to be, at the moment when it has come to be, will
be,
and that which has ceased to be will
not-be:
for what we have said applies universally to every kind of change, and its truth is most obvious in the case of contradictory change.
(30)
It is clear, then, that that which has changed, at the moment when it has first changed, is in that to which it has changed.

We will now show that the ‘primary when’ in which that which has changed effected the completion of its change must be indivisible, where by ‘primary’ I mean possessing the characteristics in question of itself and not in virtue of the possession of them by something else belonging to it. For let AC be divisible, and let it be divided at B.
(35)
If then the completion of change has been effected in AB or again in BC, AC cannot be the primary thing in which the completion of change has been effected. If, on the other hand, it has been changing in both AB and BC (for it must either have changed or be changing in each of them), it must have been changing in the whole AC: but our assumption was that AC contains only the
completion
of the change.
[236a]
It is equally impossible to suppose that one part of AC contains the process and the other the completion of the change: for then we shall have something prior to what is primary.
¹⁴
So that in which the completion of change has been effected must be indivisible.
(5)
It is also evident, therefore, that that in which that which
has ceased to be has ceased to be and that in which that which has come to be has come to be are indivisible.

But there are two senses of the expression ‘the primary when in which something has changed’. On the one hand it may mean the primary when containing the
completion
of the process of change—the moment when it is correct to say ‘it has changed’: on the other hand it may mean the primary when containing the
beginning
of the process of change. Now the primary when that has reference to the
end
of the change is something really existent: for a change may really be completed,
(10)
and there is such a thing as an end of change, which we have in fact shown to be indivisible because it is a limit. But that which has reference to the beginning is not existent at all: for there is no such thing as a beginning of a process of change, and the time occupied by the change does not contain any primary when in which the change began.
(15)
For suppose that AD is such a primary when. Then it cannot be indivisible: for, if it were, the moment immediately preceding the change and the moment in which the change begins would be consecutive (and moments cannot be consecutive). Again, if the changing thing is at rest in the whole preceding time CA (for we may suppose that it is at rest), it is at rest in A also: so if AD is without parts, it will simultaneously be at rest and have changed: for it is at rest in A and has changed in D.
(20)
Since then AD is not without parts, it must be divisible, and the changing thing must have changed in every part of it (for if it has changed in neither of the two parts into which AD is divided, it has not changed in the whole either: if, on the other hand, it is in process of change in both parts, it is likewise in process of change in the whole: and if, again, it has changed in one of the two parts, the whole is not the primary when in which it has changed: it must therefore have changed in every part).
(25)
It is evident, then, that with reference to the beginning of change there is no primary when in which change has been effected: for the divisions are infinite.

So, too, of that which has changed there is no primary part that has changed. For suppose that of DE the primary part that has changed is DF (everything that changes having been shown
¹⁵
to be divisible): and let HI be the time in which DF has changed.
(30)
If, then, in the whole time DF has changed, in half the time there will be a part that has changed, less than and therefore prior to DF: and again there will be another part prior to this, and yet another, and so on to infinity. Thus of that which changes there cannot be any primary part that has changed. It is evident, then, from what has
been said,
(35)
that neither of that which changes nor of the time in which it changes is there any primary part.
[236b]

With regard, however, to the actual subject of change—that is to say that in respect of which a thing changes—there is a difference to be observed. For in a process of change we may distinguish three terms—that which changes, that in which it changes, and the actual subject of change, e. g. the man, the time, and the fair complexion.
(5)
Of these the man and the time are divisible: but with the fair complexion it is otherwise (though they are all divisible accidentally, for that in which the fair complexion or any other quality is an accident is divisible). For of actual subjects of change it will be seen that those which are classed as essentially, not accidentally,
(10)
divisible have no primary part. Take the case of magnitudes: let AB be a magnitude, and suppose that it has moved from B to a primary ‘where’ C. Then if BC is taken to be indivisible, two things without parts will have to be contiguous (which is impossible): if on the other hand it is taken to be divisible, there will be something prior to C to which the magnitude has changed, and something else again prior to that, and so on to infinity, because the process of division may be continued without end.
(15)
Thus there can be no primary ‘where’ to which a thing has changed. And if we take the case of quantitative change, we shall get a like result, for here too the change is in something continuous. It is evident, then, that only in qualitative motion can there be anything essentially indivisible.

6
      Now everything that changes changes in time,
(20)
and that in two senses: for the time in which a thing is said to change may be the primary time, or on the other hand it may have an extended reference, as e. g. when we say that a thing changes in a particular year because it changes in a particular day. That being so, that which changes must be changing in any part of the primary time in which it changes. This is clear from our definition of ‘primary’,
¹⁶
in which the word is said to express just this: it may also, however,
(25)
be made evident by the following argument. Let VQ be the primary time in which that which is in motion is in motion: and (as all time is divisible) let it be divided at J. Now in the time VJ it either is in motion or is not in motion, and the same is likewise true of the time JQ. Then if it is in motion in neither of the two parts, it will be at rest in the whole: for it is impossible that it should be in motion in
a time in no part of which it is in motion. If on the other hand it is in motion in only one of the two parts of the time,
(30)
VQ cannot be the primary time in which it is in motion: for its motion will have reference to a time other than VQ. It must, then, have been in motion in any part of VQ.

And now that this has been proved, it is evident that everything that is in motion must have been in motion before. For if that which is in motion has traversed the distance JK in the primary time VQ,
(35)
in half the time a thing that is in motion with equal velocity and began its motion at the same time will have traversed half the distance. But if this second thing whose velocity is equal has traversed a certain distance in a certain time, the original thing that is in motion must have traversed the same distance in the same time.
[237a]
Hence that which is in motion must have been in motion before.

Again, if by taking the extreme moment of the time—for it is the moment that defines the time, and time is that which is intermediate between moments—we are enabled to say that motion has taken place in the whole time VQ or in fact in any period of it,
(5)
motion may likewise be said to have taken place in every other such period. But half the time finds an extreme in the point of division. Therefore motion will have taken place in half the time and in fact in any part of it: for as soon as any division is made there is always a time defined by moments. If, then, all time is divisible,
(10)
and that which is intermediate between moments is time, everything that is changing must have completed an infinite number of changes.

Again, since a thing that changes continuously and has not perished or ceased from its change must either be changing or have changed in any part of the time of its change, and since it cannot be changing in a moment, it follows that it must have changed at every moment in the time: consequently, since the moments are infinite in number,
(15)
everything that is changing must have completed an infinite number of changes.

And not only must that which is changing have changed, but that which has changed must also previously have been changing, since everything that has changed from something to something has changed in a period of time. For suppose that a thing has changed from A to B in a moment.
(20)
Now the moment in which it has changed cannot be the same as that in which it is at A (since in that case it would be in A and B at once): for we have shown above
¹⁷
that that which has changed, when it has changed, is not in that from which it has changed. If, on the other hand, it is a different moment, there
will be a period of time intermediate between the two: for,
(25)
as we saw,
¹⁸
moments are not consecutive. Since, then, it has changed in a period of time, and all time is divisible, in half the time it will have completed another change, in a quarter another, and so on to infinity: consequently when it has changed, it must have previously been changing.

Moreover, the truth of what has been said is more evident in the case of magnitude, because the magnitude over which what is changing changes is continuous.
(30)
For suppose that a thing has changed from C to D. Then if CD is indivisible, two things without parts will be consecutive. But since this is impossible, that which is intermediate between them must be a magnitude and divisible into an infinite number of segments: consequently, before the change is completed, the thing changes to those segments. Everything that has changed,
(35)
therefore, must previously have been changing: for the same proof also holds good of change with respect to what is not continuous, changes, that is to say, between contraries and between contradictories.
[237b]
In such cases we have only to take the time in which a thing has changed and again apply the same reasoning. So that which has changed must have been changing and that which is changing must have changed, and a process of change is preceded by a completion of change and a completion by a process: and we can never take any stage and say that it is absolutely the first.
(5)
The reason of this is that no two things without parts can be contiguous, and therefore in change the process of division is infinite, just as lines may be infinitely divided so that one part is continually increasing and the other continually decreasing.
¹⁹

So it is evident also that that which has become must previously have been in process of becoming,
(10)
and that which is in process of becoming must previously have become, everything (that is) that is divisible and continuous: though it is not always the actual thing that is in process of becoming of which this is true: sometimes it is something else, that is to say, some part of the thing in question, e. g. the foundation-stone of a house. So, too, in the case of that which is perishing and that which has perished: for that which becomes and that which perishes must contain an element of infiniteness as an immediate consequence of the fact that they are continuous things: and so a thing cannot be in process of becoming without
having become or have become without having been in process of becoming.
(15)
So, too, in the case of perishing and having perished: perishing must be preceded by having perished, and having perished must be preceded by perishing. It is evident, then, that that which has become must previously have been in process of becoming, and that which is in process of becoming must previously have become: for all magnitudes and all periods of time are infinitely divisible.
(20)

Consequently no absolutely first stage of change can be represented by any particular part of space or time which the changing thing may occupy.