Commentary Aristotle Physics
But if it is taken in the second sense—according to the beginning of the change (that is, according to the first part of the motion)—then there is no first in which something has been changed. For no beginning of a change can be definitely pointed out—that is, no part that is not preceded by some other part. In like manner, it is not possible to isolate a first time in which something is first being moved.
823. Then, at “for suppose that AD” (236a17), he proves that, if one looks at the beginning of a motion, it is not possible to assign a first in which something has been changed.
He proves this first with an argument from time;
second, with an argument from the mobile, at “so, too, of that which” (236a27; [824]);
third, with an argument from that in which the motion occurs, at “however, with regard” (236a35; [825]).
As to the first, he gives this reason. Let AD be an element of time in which something has been first changed. Now, AD must be either divisible or indivisible. If it is the latter, two difficulties ensue.
The first is that the nows in time are consecutive. This difficulty follows from the fact that time is divided just like motion, as was shown above. But, if any part of the motion was present in AD, then AD must have been a part of time and, consequently, time will be composed of indivisibles. However, the indivisibles of time are the nows. It will follow, therefore, that the nows are consecutive in time.
And there is a second difficulty. Let us suppose that, in the time CA, which preceded AD, the same mobile that was being moved in time AD was entirely at rest. If, therefore, it was at rest in the entire time CA, it was at rest in A, which is an element of the time CA. If, therefore, AD is indivisible, as we supposed, it will follow that a thing is at rest and in motion at the same time; for we have already concluded that it was at rest in A and assumed that it was in motion in AD. But, if AD is indivisible, then A is the same as AD. It will follow, therefore, that a thing is at rest and in motion in the same time.
It should be noted, however, that, if a thing was at rest throughout an entire time, it does not follow that it was at rest in the last indivisible of that time; for we have already shown that, in the now, things are neither at rest nor in motion. But Aristotle concludes this here by arguing from what his adversary has proposed: that the element of time in which the object was first being moved is an indivisible. And if it can be in motion in an indivisible of time, there is no reason why it could not also be at rest.
Therefore, having rejected the indivisibility of time AD, we are left with the fact that it is divisible. And, since it is in AD that the object is said to be first moved, then it is being moved in any part of AD.
This he now proves. Let AD be divided into two parts; then the object is being moved either in neither part or in both parts or in one part only. If in neither part, then it is not being moved in the whole time. If in both parts, then it could be granted that it is being moved in the whole time. But, if in one part only, it will follow that it is being moved in the whole time but not first, but by reason of the part. Therefore, since it is agreed to be moving in the whole time, it has been in motion in each part of the whole time. But time is divided infinitely, just like any continuum; consequently, it is possible always to consider a part smaller than a previous one (such as a day before a month and an hour before a day). Therefore, it is evident that it is impossible to find a time in which it is first being moved such that a previous could not be found. For if you were to assume that it is in a day that the object is first moved, that assumption would not be true, because it would have been first moved in the first part of the day before it was moved in the whole day.
824. Then, at “so, too, of that which” (236a27), he establishes the same point by considering the mobile, and he concludes from the foregoing that in that which is being changed it is not possible to take something that is first changed. Now, this is to be understood in the sense that some definite point is to be crossed through the motion of the whole or of the part: it is evident that the first part of the mobile will first pass a given point, and a second part will pass it after that, and so on.
Otherwise, if it were understood in the sense of the absolute nature of motion, what we have to say would not be to the point, for it is clear that the whole is being moved at the same time as all the parts, but the whole does not pass a certain point all at once, but part before part continuously. Hence, just as it is impossible to find a first part of the mobile than which there is not a previous smaller part, so also is it impossible to isolate a part of the mobile that would be first moved.
And because time and mobile are correspondingly divided, as we have shown above, he now concludes about the mobile what was concluded about time. Here is his proof. Let DE be a mobile, and (because every mobile can be divided, as was proved above) let DZ be the part that is first being moved. And let DZ be moved such that it passes a definite point in the time TI. If, therefore, DZ has been changed in this whole time, it follows that what has been changed in half the time is both less than DZ and moved prior to DZ. And, for the same reason, there will be something prior to that, and so on forever, because time can be divided infinitely. It is evident, therefore, that one cannot find something in the mobile that has been first changed. Hence, it is clear that a first cannot be found in motion, whether we consider the time or the mobile.
825. Then, at “however, with regard” (236a35), he proves the same thing by considering that in which the motion occurs.
But first he mentions that the situation with respect to that in respect of which a thing changes is not exactly the same as it was with respect to time and the mobile. For since there are three things to be considered in change—the mobile that is being changed (e.g., a man), that in which it is being changed (the time), and that into which it is being changed (e.g., white)—two of these, the time and the mobile, are always divisible. But with white it is another story, because a white thing is not divisible per se, but it and things like it are divisible per accidens, inasmuch as the subject of whiteness or of any other quality is divisible.
Now, the per accidens division of white can take place in two ways.
In one way, the white can be divided per accidens according to the quantitative parts, as when a white surface is split into two parts.
In another way, it can be according to greater or less intensity, for the fact that one and the same part is whiter or less white is not due to the account of whiteness (because, if it existed in isolation, whiteness would be constant and never subject to more and less, any more than a substance is susceptible to more and less), but to the varying degrees in which a divisible subject participates in whiteness.
Therefore, neglecting what is divided per accidens in motion and considering only what is divided per se, it is impossible to find a first.
And he proves this first of all in magnitudes in which there is local motion. Let the magnitude AC be divided at B, and suppose that C is that into which something is first moved from B. Now, BC is either divisible or indivisible. If it is the latter, it follows that an indivisible will be touching an indivisible, for there is no reason that the second part of the motion will not be into an indivisible, since we can divide a magnitude just as the motion was divided, and as time was.
But, if BC is divisible, it is possible to take a stage prior to B than to C, and so the thing will be changed from B into that stage before it is changed into C, and into a stage prior to that one, and so on, because there is no limit to the division of a magnitude. It is therefore evident that it is impossible to find a first stage into which a thing has been changed in local motion.
The same is true in change of quantity, that is, growing and decreasing. For even these changes are in terms of a continuum—that is, in terms of added quantity or subtracted quantity—in which no first is to be found, since there can be division to infinity.
And so it is clear that it is only in qualitative change that something is per se indivisible. But, inasmuch as divisibility is found in this per accidens, likewise no first is discernible in such change. This is true whether the succession consists in part being altered after part (for it is evident that no first part of white can be found any more than a first part of magnitude can) or the succession is based on one and the same thing becoming more and more white or less and less white, for a subject can be modified in an infinite number of ways with regard to degrees of whiteness. Thus, the motion involved in alteration can be continuous and not possess a first.