Commentary Aristotle Physics
815. Then, at “the same reasoning” (235a34), he shows the same for that in which the motion takes place. And he says that, in the same way, it can be demonstrated that the length in which something is moved locally can be divided according to the division of time and of motion and of being moved. And what we say of the length in local motion is to be understood of everything in which there is motion, except that, in some, the division is per accidens, as in the case of qualities in the motion of alteration, as was said. And hence it is that all those things are divided, because the subject of change can be divided, as was explained above. Consequently, if one is divided, all the others must be.
816. Then, at “so, too, in the matter” (235a37), he says that, just as the above-mentioned things follow upon one another in divisibility, so also in being finite or infinite, such that, if one of them is finite, all the others are, and if one is infinite, so are all the others.
817. Then, at “and we now see” (235b1), he shows in which of the five above-mentioned things divisibility and finite and infinite are first found. He says that the subject of change is the first root from which the divisibility and finiteness and infinity of the others flow, because what is naturally first in motion is the mobile, which of its very nature has the properties called divisibility, finiteness, and infinity. Hence, from it, divisibility and finiteness flow to the others.
But how the mobile is divisible and how the others are divided through it we have already shown. How the mobile is infinite will be explained later in this book 6.
Lecture 7
How there can be a first motion
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 what 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, since both are related to both in a similar way. Since one kind of change is change in a relation of contradiction, a thing that has changed from non-being to being has left non-being. Therefore, it will be in being, for everything must either be or not be.
Thus, it is evident that, in contradictory change, what 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 what 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 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, 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, and thus that which has changed must be in that to which it has changed. So it is evident likewise that what has come to be, at the moment when it has come to be, will be, and what 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, as soon as it is changed, is in that to which it has changed.
The “primary when” in which that which has changed effected the completion of its change must be atomic, and by “primary,” I mean having the characteristics in question not because of something else belonging to it, but because of itself.
For let AC be divisible, and let it be divided at B. 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.
It is equally impossible to suppose that one part of AC contains the process of the change and the other its completion, 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 in which what has ceased to be has so ceased is atomic, as is that in which what has come to be has come to be.
But there are two senses of the expression “in which something has been first changed.”
On the one hand, it may mean the first time 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 first time containing the beginning of the process of change.
Now, the first time that has reference to the completion is something really existent, since a change may really be completed, and there is such a thing as the 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 the beginning of a change, and the time occupied by the change does not contain any first time in which the change began.
For suppose that AD is such a first time. 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, and 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).
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; but if 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 first time in which it has changed, and it must therefore have changed in every part.
It is evident, then, that, with reference to the beginning of change, there is no first time in which change has been effected, since 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 DZ (everything that changes having been shown to be divisible), and let OI be the time in which DZ has changed.
If DZ has changed in the whole time, then there will be a part that has changed in half the time, a part less than, and therefore prior to, DZ.
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.
However, with regard 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 (for instance, 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 that are classed as essentially divisible, not accidentally, 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.
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.