Aristotle (384-322 BC)

Physics

Translated by R. P. Hardie and R. K. Gaye

Book VI

Chapter 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. 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. 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. 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 Β is in something other than Β, say Γ, it must again be changing from Γ to Β: for it cannot be assumed that there is no interval between Γ and Β, 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. 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 ΑΓ be divisible, and let it be divided at Β. If then the completion of change has been effected in ΑΒ or again in ΒΓ, ΑΓ 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 ΑΒ and ΒΓ (for it must either have changed or be changing in each of them), it must have been changing in the whole ΑΓ: but our assumption was that ΑΓ contains only the completion of the change. It is equally impossible to suppose that one part of ΑΓ contains the process and the other the completion of the change: for then we shall have something prior to what is primary. So that in which the completion of change has been effected must be indivisible. It is also evident, therefore, that 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, 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. For suppose that ΑΔ 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 ΓΑ (for we may suppose that it is at rest), it is at rest in Α also: so if ΑΔ is without parts, it will simultaneously be at rest and have changed: for it is at rest in Α and has changed in Δ. Since then ΑΔ 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 ΑΔ 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). 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 ΑΕ the primary part that has changed is ΔΖ (everything that changes having been shown to be divisible): and let ΘΙ be the time in which ΔΖ has changed. If, then, in the whole time ΔΖ has changed, in half the time there will be a part that has changed, less than and therefore prior to ΔΖ: 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, that neither of that which changes nor of the time in which it changes is there any primary part.

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. 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, divisible have no primary part. Take the case of magnitudes: let ΑΒ be a magnitude, and suppose that it has moved from Β to a primary ‘where’ Γ. Then if ΒΓ 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 Γ 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. 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.

Book VI Chapter 4

Book VI Chapter 6