Commentary Aristotle Physics
Lecture 18. Reflected motion is not continuous
If we look at the question reasonably, the same result would also appear to be indicated by the following arguments.
Everything whose motion is continuous must, on arriving at any point in the course of its locomotion, have been previously also in process of locomotion to that point, if it is not forced out of its path by anything.
For instance, on arriving at B, a thing must also have been in process of locomotion to B, and that not merely when it was near to B, but from the moment of its starting on its course.
For there can be no reason for its being so at any particular stage rather than at an earlier one. So, too, in the case of the other kinds of motion.
Now, we are to suppose that a thing proceeds in locomotion from A to C and that, at the moment of its arrival at C, the continuity of its motion is unbroken and will remain so until it has arrived back at A.
Then, when it is undergoing locomotion from A to C, it is at the same time undergoing also its locomotion from C to A.
Consequently, it is simultaneously undergoing two contrary motions, since the two motions that follow the same straight line are contrary to each other.
With this consequence, there also follows another. We have a thing that is in process of change from a position in which it has not yet been; thus, inasmuch as this is impossible, the thing must come to rest at C.
Therefore, the motion is not a single motion, since motion that is interrupted by stationariness is not single.
Further, the following argument will serve better to make this point clear universally in respect of every kind of motion.
If (1) the motion undergone by what is in motion is always one of those already enumerated and the state of rest that it undergoes is one of those that are the opposites of the motions (for we found that there could be no other besides these), and moreover, (2) what is undergoing a particular motion, but not always (by this I mean one of the specifically distinct motions, not some part of the whole motion) must have been previously undergoing the state of rest that is the opposite of the motion—the state of rest being privation of motion—then, inasmuch as the two motions that follow the same straight line are contrary motions and it is impossible for a thing to undergo simultaneously two contrary motions, what is undergoing locomotion from A to C cannot also simultaneously be undergoing locomotion from C to A.
And, since the latter locomotion is not simultaneous with the former but is still to be undergone, before it is undergone, there must occur a state of rest at C, for this, as we found, is the state of rest that is the opposite of the motion from C. The foregoing argument, then, makes it plain that the motion in question is not continuous.
Our next argument has a more special bearing than the foregoing on the point at issue.
We will suppose that there has simultaneously occurred in something a corruption of not-white and a becoming of white.
Then, if the alteration to white and from white is a continuous process and the white does not remain any time, there must have occurred simultaneously a corruption of not-white, a becoming of white, and a becoming of not-white. For the time of the three will be the same.
Again, from the continuity of the time in which the motion takes place, we cannot infer continuity in the motion, but only successiveness. In fact, how could contraries (such as whiteness and blackness) meet in the same extreme point?
1123. After proving with proper reasons that reflected motion is not continuous, the Philosopher now proves the same with common and logical reasons.
About this, he does two things:
first, he expresses his intention;
second, he proves his proposition, at “everything whose motion” (264a9; [1124]).
He says first that, if someone wishes to prove the proposition in question reasonably, that is, logically, it will be seen from the reasons to be given that the same thing follows, namely, that reflected motion is not continuous.
1124. Then, at everything whose motion (264a9), he proves the proposition:
first, for reflected local motion only;
second, in common for all motions, at “further, the following” (264a21; [1126]).
The first argument is this. Everything in continuous motion has been, from the very beginning of its motion, in the process of being carried (as toward an end) to that at which it arrives according to change of place, unless there is some obstacle (because an obstacle could deflect it in another direction). He exemplifies this by saying that, if something in local motion has arrived at B, it was being moved toward B not only when it was near B, but as soon as it began to be moved. For there is no reason that it should be tending more toward B now than before. And the same is true in other motions.
But, if a reflected motion should be continuous, it will be true to say that what is in motion from A to C and is then reflected back to A is in a continuous motion. Therefore, in the very first part of the motion from A to C, it was being moved to its final terminus in the part A; in this way, while it is being moved from A, it is being moved toward A.
It follows, therefore, that it is being simultaneously moved with contrary motions, because, in the sphere of rectilinear motions, to be moved from a thing and to be moved toward the same are contrary. But, in circular motions, this is not contrary. Now, it is impossible for something to be moved simultaneously with contrary motions. Therefore, it is impossible for a reflected motion to be continuous.
1125. Then, at “with this consequence” (264a18), from the same middle, he leads to another impossibility. For if something, while it is being moved from A, is being moved toward A, it cannot be moved toward A except from a counter-point C, in which the mobile was not yet present when it began to be moved from A. It follows, then, that something is being moved from a terminus at which it is not present, which is impossible. For it cannot leave a place in which it is not. Thus, it is impossible for a reflected motion to be continuous. And, if this is impossible, then it is necessary that the mobile be at rest at the point of reflection, C. From this, it is plain that it is not one motion, because a motion interrupted by rest is not one.
1126. Then, at “further, the following” (264a21), he proves the same thing in a more universal way for every genus of motion, with three arguments.
The first of them is this. Whatever is in motion is being moved with respect to one of the species of motion listed previously. In like manner, whatever is at rest is so with respect to a rest that is opposite to one of the given species of motion. For it was shown above in book 5 that no motions other than the ones listed are possible.
Let us, therefore, take a motion that is distinct from other motions in the sense of being specifically distinct from others, as whitening is distinct from blackening—but not distinct in the way that one part of a motion is distinct from other parts of the same motion, as one part of the motion of whitening is distinct from other parts of the same whitening.
Taking, therefore, one motion in the way described, it is true to say that whatever is not forever being moved with this motion was before, of necessity, at rest with an opposite rest, as whatever is not being forever whitened was at some time at rest with a rest opposite to whitening.
But this proposition would not be true if some definite part of the motion should be taken, for it is not necessary that what was not forever being moved in this part of the whitening was previously at rest with an opposite rest, because, before, the thing was becoming white in some other part of the whitening. And, because of this, he states significantly, not some particular part of the whole motion.
This proposition he now proves. When one of two things that are in privative opposition is not in its recipient, the other must be. But rest is opposed to motion privatively. Therefore, if a mobile was existing at a time when motion was not in it, it follows of necessity that rest would then have been in it.
Accordingly, since this proposition has been proved, he takes the minor premise from the argument already presented above and says that, if rectilinear motions from A to C and from C to A are contrary, and contrary motions cannot coexist, it is plain that, when something was being moved from A to C, it was not at the same time being moved from C to A. Consequently, it was not forever being moved with respect to the motion from C to A.
Hence, according to the previous proposition, it is necessary that the mobile first rest with an opposite rest. For it has been shown in book 5 that rest in C is opposed to a motion from C. Therefore, it was at rest in C. Therefore, the reflected motion was not one and continuous, since it was interrupted by the interposition of rest.
1127. He presents the second argument at “our next argument” (264b1). Non-white ceases to be at the same time that white comes to be; similarly, white ceases to be at the same time that non-white comes to be. But, if reflected motion in every genus is continuous, it will follow that an alteration is terminated at whiteness and begins to depart from whiteness in such a way as to form a continuous motion, and that it does not rest there for any time; for if rest should intervene, the alteration would not be continuous. But, as has been said, when the white comes to be, the non-white ceases to be, and when departure from white occurs, non-white comes to be.
Therefore, it will follow that non-white is ceasing to be and coming to be at the same time, for these three things are present at the same time: the coming to be of white, the ceasing to be of non-white, and the coming to be of non-white—that is, if the reflected motion is continuous without any interval of rest.
This, however, is plainly impossible, namely, that non-white should be coming to be and ceasing to be at the same time. Therefore, a reflected motion cannot be continuous.
Now, this argument is seen to refer to generation and ceasing to be. For this reason, he says that this argument is more proper than the previous ones, because it is more apparent in contradictories that they cannot be true at the same time. And, yet, what is said in generation and ceasing to be applies to all motions, since, in every motion, there is a kind of generation and ceasing to be. For just as, in the case of alteration, white is generated, and non-white ceases to be, so too in every other motion.
1128. He gives the third argument at “again, from the continuity” (264b6). As was had in book 5, it is not necessary that, if the time is continuous, a motion be continuous on that account. For motions of diverse kinds, even though they succeed one another in continuous time, are not on that account continuous, but are rather consequent upon one another, for continua must have one common terminus. But there cannot be one common terminus in things that are contrary and specifically different, such as whiteness and blackness. Since, therefore, a motion from A to C is contrary to one from C to A in any genus of motion, as was shown in book 5, it is impossible that those two motions be continuous to one another—even though the time be continuous—with no intervening rest. It remains, therefore, that a reflected motion can in no way be continuous.
It should be noted that the foregoing arguments are called logical because they proceed from certain common things, namely, from the property of contraries.