Commentary Aristotle Physics
Lecture 8. The relation of “being moved” and “has been moved”
Now, everything that changes changes in time, and that in two senses: the time in which a thing is said to change may be the primary time, or on the other hand, it may be by reason of something else (such as 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 “first,” in which the word is said to express just this. It may also, however, be made evident by the following argument.
Let XR 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 K. Now, in the time XK, it either is in motion or is not in motion, and the same is likewise true of the time KR.
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, XR cannot be the primary time in which it is in motion, for its motion will have reference to a time other than XR. It must, then, have been in motion in any part of XR.
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 KL in the primary time XR, then a thing that is in motion with equal velocity and began its motion at the same time will have traversed half the distance in half the time.
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. 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 terminates 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 XR (or, in fact, in any period of it), 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, 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 does not perish or cease to be moved 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, 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.
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 that what 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 as we saw, 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.
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, therefore, must previously have been changing.
For the same proof also holds good of change with respect to what is not continuous, namely, changes between contraries and between contradictories.
In such cases, we have only to take the time in which a thing has changed and again apply the same reasoning.
So, what has changed must have been changing and what 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.
The reason for 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 such that one part is continually increasing and the other continually decreasing.
So it is evident also how what has become must previously have been in process of becoming, and that which is in process of becoming must previously have become—that is, everything 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, such as the foundation stone of a house.
So, too, in the cases of that which is corruption 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.
Thus, a thing cannot be in process of becoming without having become, or have become without having been in process of becoming. So, too, in the case of corruption and having perished: corruption must be preceded by having perished, and having perished must be preceded by corruption.
It is evident, then, that what has been made was previously being made, and what is being made must necessarily have been made, provided that divisible and continuous things are involved, for all magnitudes and all periods of time are infinitely divisible.
Consequently, no absolutely first stage of change can be represented by any particular part of space or time that the changing thing may occupy.
826. After explaining how a first is to be taken in motion and how not, the Philosopher now explains the order of precedence among the things present in motion.
First, he sets out things needed for explaining the proposition;
second, he explains the proposition, at “and, now that this” (236b32; [828]).
827. He therefore says first (236b19) that whatever is being changed is being changed in time, as we have explained.
But something is being changed in a time in two ways:
in one way, first and per se;
in another way, by reason of something else, that is, by reason of a part, as when something is said to be changed in a year because it is being changed in a day.
With this distinction in mind, he states what he intends to prove: if something is being first moved in a time, it is necessarily being moved in some part of that time.
This he proves in two ways.
First, he proves it from the definition of first, for here, something is said to be in a thing first if it belongs to it by reason of each and every part, as was said in the beginning of book 5.
Second, he proves the same thing with an argument. Let XR be the time in which something is being first moved, and since time is divisible, let XR be divided at K. Then, of necessity, in the part XK of the time, the object is either being moved or not, and likewise for the part KR. Now, if it be said that it is being moved in neither of those parts, it follows that it is not being moved in the whole time, but is at rest throughout that time, for it is impossible for a thing to be in motion in a time without being in motion in some part of it. But, if it be supposed that it is being moved in just one part of the time, it will follow that it is not being first moved in the time called XR, because that would require motion in respect to both parts and not in respect to just one. Therefore, of necessity, it must be in motion in each part of the time XR. And that is what we want to demonstrate: if something is being first moved in a time, it is being moved in every part of it.
828. Then, at “and, now that this” (236b32), he sets about proving the main proposition.
And about this, he does two things:
first, he introduces the proofs of the proposition;
second, he argues for the truth, at “so, what has” (237b3; [838]).
About the first, he does two things:
first, he shows that, before each state of being moved, there was a state of completed motion;
second, he shows that, conversely, there was a state of being moved before each state of completed motion, at “and not only must” (237a17; [832]).
829. He proves the first with three arguments.