Commentary Aristotle Physics
1144. But there is another and greater difficulty. For it does not seem to be against the prerogatives of a finite mover to cause motion for an infinite time, for if that finite thing is imperishable or impassible in its nature and never loses its nature, it will maintain itself always in the same way with respect to causing motion. For the same thing, remaining in the same state, will always do the same. Hence, there would be no reason for its not being able to move later as it did before. This is evident to sense, for we observe that the sun can move lower bodies in an infinite time.
To settle this difficulty, we must investigate the sequence of demonstration set forth by Aristotle. For it should be certain that the conclusion is to be interpreted in the sense in which it follows from the premises.
We should consider, therefore, that the time of a motion may be taken in two senses, especially in local motion:
in one sense, according to the parts of the mobile;
in another sense, according to the parts of the magnitude along which the motion passes.
For it is plain that one part of the mobile passes a designated point of the magnitude before the whole does, and that the whole traverses part of the magnitude before it traverses all of it. Now, it is plainly clear from the procedure of Aristotle’s demonstration that he is speaking of the time of motion according to the parts of the mobile and not according to the parts of the magnitude. For in his demonstrations, he assumes that part of the mover moves part of the mobile in less time than the whole moves the whole. But this could not be true if we took time of motion according to the parts of the magnitude traversed by the motion, since the ratio of the part of the mover to the part of the mobile is the same as that of the whole mover to the whole mobile. Hence, a part will always move part with the same velocity as the whole moves the whole. Thus, in an equal time, part of the mobile moved by part of the mover will traverse some magnitude and the whole mobile moved by the whole mover will also.
Or perhaps the whole will be moved in less time than the part, because a united force is greater than a divided force, and the greater the force of the mover, the swifter the motion and the less the time.
Therefore, this must be understood in the sense that the time of motion is taken according to parts of the mobile, because one part of the mobile will pass a definite point in less time than the whole will. In this sense, it is impossible for anything but an infinite mobile to be moved for an infinite time. But an infinite mobile cannot be moved by a finite mover, since the power of the mover is always greater than the power of the mobile. Hence, an infinite mobile must be moved by an infinite power. Consequently, just as an impossibility follows from the assumption that a finite mover moves a finite mobile with an infinite motion according to the parts of the mobile, so, once this problem is removed, one must further conclude that an infinite motion belongs to an infinite mobile from an infinite mover.
1145. But, against this, someone could object that Aristotle did not prove above that motion is infinite according to the parts of the mobile in the way that the motion of an infinite body is said to be infinite, for the entire corporeal universe is finite, as was proved in book 3 and will be proved in De caelo 1. Hence, the demonstration of Aristotle does not seem to be verified as concluding to his proposition, namely, that the first mover, which causes an infinite motion, is infinite.
But it should be said that what is the first cause of an infinite motion must be the per se cause of the infinity of the motion, because the cause that is per se is always prior to that which is so by virtue of something else, as has been said above. Now, the power of a per se cause is determined to a per se effect, and not to a per accidens effect, for that is the way Aristotle taught causes are to be compared to their effects in book 2.
But, because motion can be infinite in two ways, as has been said, according to the parts of the mobile and according to the parts of the length along which the motion takes place, the motion is infinite per se from the parts of the mobile, but per accidens according to the parts of the length. For the quantity of motion based on the parts of the mobile belongs to it by reason of its proper subject, and so is present in it per se, whereas the quantity of motion based on the parts of the length is based on constant repetition of the mobile’s motion, in the sense that a whole mobile, having completed its entire motion upon one part of the length, now successively traverses another. Thus, the first cause of the infinity of motion has power over the infinity of motion that is per se, in such a way as to enable it to move an infinite mobile if there should be such. Hence, it must be infinite. And, even though the first mobile be finite, it has, nevertheless, a certain likeness to the infinite, as was said in book 3.
But, in order that something be the cause of a motion that is infinite through repetition (which is per accidens), infinite power is not required, but an immobile finite power is enough, because, so long as the power remains the same, it will be able to repeat the same effect, as the sun has a finite energy yet can move the lower elements over an infinite time, should motion be eternal, as Aristotle posits. For it is not the first cause of the infinity of motion, but is something as though moved by another to move in an infinite time, according to the position stated above.
1146. Then, at “it has now to be shown” (266a24), he shows that the power in a magnitude must be proportional to the magnitude in which it exists.
First, he shows that, in a finite magnitude there cannot be an infinite power, which is what he chiefly intends;
second, he shows that, on the other hand, in an infinite magnitude, there cannot be a finite power, at “therefore, nothing finite” (266b5; [1156]).
That an infinite power cannot exist in a finite magnitude he proves (266a23), first setting out two assumptions.
The first is that a greater power produces an equal effect in less time than a lesser power, as a greater heating force raises a thing on which it acts to an equal temperature in less time, and the same is true of a sweetener, or a hurler, or any cause of motion.
And, from this assumption, he concludes that, since an infinite power is greater than a finite power, then, necessarily, if there is a finite magnitude possessing an infinite power, one or a number of things will in the same time undergo a greater change from such an agent than from another having finite power, or, conversely, that which undergoes an equal change will do so from it in less time. Either interpretation suits what Aristotle says here—to a greater extent than by anything else.
The second assumption is that, since whatever is being moved is being moved in time, as was proved in book 6, it cannot be that something undergoing change is changed in no time by an agent of infinite power. Therefore, it is changed in time.
From this, he proceeds in the following manner. Let A be the time in which an infinite power causes change by heating or throwing, and let the time in which a finite power is causing change be AB, which is longer than A. Now, no matter how big a finite power is, a still greater may be taken. So, if we take another finite power greater than the first that caused change in time AB, it will act in a shorter time. Again, a third and greater power will cause the change in still less time. And, thus, by always taking a finite power, I will at length come to a finite power that will produce the change in time A, for when an addition is continually made to a finite power, any predetermined ratio will be exceeded. But, as the power is increased, the time is decreased, because a greater power can cause a change in less time.
In this way, therefore, it will follow that a finite power will produce a change in a time equal to that used by the infinite power, which was assumed as acting in time A. But this is impossible. Therefore, no finite magnitude has an infinite power.
1147. Now, there are many doubts about this argument.
First, it does not seem conclusive in any way. For what belongs per se to a thing cannot be taken from it by any power however great, for it is not due to any lack of power, nor does it conflict with infinity of power, if it be said that it is impossible for man not to be an animal. But to exist in time belongs per se to motion, for motion is found in the definition of time, as was had above in book 4. Therefore, if an infinite moving power is conceded to exist, it does not follow that motion exists in non-time, as Aristotle here concludes.
Likewise, if the sequence of the argument of the Philosopher is considered, it will be seen that his conclusion that motion exists in non-time is inferred from the fact that the moving power is infinite; but an infinite moving power can also not be in a body. Therefore, for the same reason, it follows that such a power, if it is infinite, will move in non-time. Hence, from the impossibility of being moved in non-time, it cannot be inferred that no infinite power exists in a magnitude, but absolutely that no moving power at all is infinite.
Again, two things seem to pertain to the magnitude of a power: the swiftness of motion and its duration. And any superabundance in the power causes a corresponding superabundance in each of these two things. But, with respect to the superabundance of an infinite power, he showed above that a perpetual motion depends on an infinite power, but not that an infinite power does not exist in a magnitude. Therefore, here too, with respect to excess of swiftness, he ought not to conclude that no infinite power exists in a magnitude, but that the power that moves in an infinite time would, on account of its infinity, also move in non-time.