Commentary Aristotle Physics
Now he was deceived by the equivocation in “potency.” For “potency” sometimes refers to what is open to opposites. In this sense, potency is excluded from a heavenly body and from separated simple substances, because, in Aristotle’s opinion, they have no potency to non-existence, for simple substances are forms only, and it belongs per se to a form that it exist, while the matter of a heavenly body is not in potency to another form. For just as a heavenly body is related to its figure (of which it is the subject) as potency to act and yet cannot not have such a figure, so the matter of the heavenly body is related to its form as potency to act, and yet it is not in potency to being deprived of this form or to non-being. For not every potency is open to opposites; otherwise, possibility would not follow upon necessity, as is said in Peri hermeneias 2.
His position is also contrary to the intention of Aristotle, who, in a certain demonstration in De caelo 1.12, uses the fact that a heavenly body has the potency or the power to exist always. Therefore, he cannot avoid the problem by saying that, in a heavenly body, there is no potency to existing, for this is evidently false and contrary to the intention of Aristotle.
1154. Therefore, let us see whether he adequately refuted the solution of Alexander, who says that a heavenly body acquires its perpetuity from something else. His refutation would indeed be good if Alexander had posited that a heavenly body had of itself a potency to existence and non-existence, and that it acquired its perpetual existence from another.
This I say while keeping in mind his intention, and not excluding the omnipotence of God, by which this corruptible can put on incorruptibility (1 Cor 15:53)—to discuss which now does not pertain to the present question.
Still Averroes, even supposing his intention, cannot come to a conclusion against Alexander, who did not posit that the heavenly body acquires its perpetuity from something else as though it had a potency to existence and non-existence, but as though not having its existence from itself.
For whatever is not its own existence participates in existence from the first cause that is its own existence. Hence, he himself professes in his book De substantia orbis that God is the cause of the heavens not only with respect to its motion, but with respect to its substance as well, which would not be true unless it has its existence from something else. But the only existence it has from another is a perpetual one; consequently, its perpetuity is from another.
And this is in agreement with the teachings of Aristotle, who, in Metaphysics 5 and in the beginning of this book 8 of the Physics, says that there are some necessary things that have a cause of their necessity. In the light of this, the solution according to the intention of Alexander is plain: just as a heavenly body derives its motion from elsewhere, so too its existence. Hence, just as a perpetual motion demonstrates the infinite power of the mover but not of the mobile, so too its perpetual duration demonstrates the infinite power of the cause from which it derives its existence.
1155. But the potency of a heavenly body to existence is not exactly the same as its potency to perpetual motion. However, the difference is not the one he assigns—namely, that, in a heavenly body, there is a potency to opposites with respect to motion, these being rest and motion—rather, it is to opposites which are different places.
But they differ in respect of something else. For motion in itself falls under time, whereas existence in itself does not fall under time, but only according as it is subject to motion. Therefore, if there is an existence not subject to motion, it in no way falls under time. Hence, the potency to be moved for an infinite time regards the infinity of time directly and per se.
But a potency to exist for an infinite time, if that existence is changeable, regards a quantity of time, and therefore, a greater power is required for something to endure in changeable existence for a longer time. But a potency in respect to unchangeable existence has no relationship to a quantity of time. Hence, the magnitude or infinity of time has nothing to do with the magnitude or infinity of the power in respect to such existence. Therefore, granting the impossible assumption that a heavenly body did not derive its existence from elsewhere, its perpetuity would not be grounds for concluding that an infinite power exists in it.
1156. Then, at, therefore, nothing finite (266b5), he proves that, in an infinite magnitude, there cannot exist a finite power.
And this he does with two arguments, with respect to the first of which he does three things:
First, he mentions the conclusion intended: just as there cannot be an infinite power in a finite magnitude, so neither can there be a finite power in an infinite quantity taken as a whole (for if a finite part of the infinite be taken, it will have a finite power). He mentions this conclusion not as though it were needed for proving his principal conclusion, but as cohering with and akin to the conclusion previously demonstrated.
1157. Second, at “it is true that a greater” (266b7), he mentions something that could lead someone to suppose that there is a finite power in an infinite magnitude. For we see some lesser magnitude that has greater energy than a larger magnitude, as a small amount of fire has more active power than a large amount of air. But that does not permit us to conclude that an infinite quantity has a finite power, for if a still greater magnitude is taken, it will have greater power; for example, even though a greater quantity of air has less power than a small fire, yet, if the quantity of air be much increased, it will have more power than the small fire.
1158. Third, at “now let AB” (266b8), he presents his intended demonstration. Let AB be an infinite quantity, and BC a finite magnitude of another kind having a finite power; let D be a mobile that is being moved by the magnitude BC in time EZ. But, because BC is a finite magnitude, it is possible to take a larger magnitude; let us therefore take one that is in double proportion.
Now, the greater the power of a moving cause, the more it moves in less time, as was proved in book 7. Therefore, the double of BC will move the same mobile D in one half the time—namely, ZT—such that the time EZ is bisected by the point T. By continually adding to BC, the time of the motion will be decreased, yet no matter how much is added to BC, it can never traverse AB, which exceeds BC beyond any proportion, as the infinite exceeds the finite. And, since AB has finite power, it moves D in a finite time. Consequently, by continually lessening the time BC consumes in moving, we shall reach a time less than the time consumed by AB in its action of moving, because every finite is surpassed by dividing. It will follow, therefore, that the lesser power will move in less time, and this is impossible. What remains, therefore, is that there was an infinite power in the infinite magnitude, for the power of the infinite magnitude exceeded every finite power.
This has been proved by subtracting time, because every finite power must have some determinate time in which it causes motion. This is clear from the following consideration. If so much power acts in so much time, a greater power will move in a time smaller but yet definite—that is, finite—according to an inverse proportion such that, by as much as is added to the power, by so much is the time decreased. Consequently, no matter how much is added to a finite power, so long as the power remains finite so will the time always remain finite, for a time will be reached that will be as much less than a previously given time as the power growing by addition is greater than a power previously given.
But, in causing motion, an infinite power surpasses every determinate time, just as happens in all other cases involving the infinite—for every infinite, such as that of number and magnitude, exceeds everything determinate in its genus. Thus, it is plain that an infinite power exceeds every finite power, because the excess of power over power corresponds to the decrease of time from time, as has been said. Hence, it is evident that the above-stated conclusion—namely, that the power of an infinite magnitude is infinite—follows of necessity from the premises.
1159. Then, at “this point may also” (266b20), he cites another proof for the same proposition, which differs from the first merely in this: the first proceeds on the assumption of a finite power existing in a finite magnitude of another kind, but this second proof proceeds on the assumption of a certain other finite power in another finite magnitude of the same genus as the infinite magnitude. For example, if air is the infinite magnitude having a finite power, we will assume a finite power existing in some finite magnitude of another specimen of air. On these grounds, it is clear that the finite power of the finite magnitude will, if sufficiently multiplied, measure the finite power in the infinite magnitude, because a finite thing is measured or even exceeded by a smaller finite thing taken a certain number of times. Since, therefore, in a magnitude of the same kind, the greater magnitude must have more power (as a greater amount of air has more power than a smaller amount), that finite magnitude that has the same proportion to the previously taken finite magnitude as the finite power of the infinite magnitude has to the power of the previously taken finite magnitude, must have equal power to the power of the infinite magnitude. For example, if the finite power of an infinite magnitude were to be one hundred times the finite power of a given finite magnitude, then the magnitude one hundred times the size of that finite magnitude has a power equal to the power of the infinite magnitude, for in a thing of the same genus, the magnitude and the power increase in proportion.
However, the conclusion we have reached is impossible, because either the finite magnitude would have to be equal to an infinite one or a smaller magnitude of the same genus would have a power equal to a larger magnitude of the same genus. Therefore, the assumption from which this conclusion followed is also impossible, namely, that an infinite magnitude may have a finite power.
In summary, therefore, he argues for two demonstrated conclusions:
that, in a finite magnitude, there cannot be infinite power;
and that, in an infinite magnitude, there cannot be finite power.