Lecture 21 — Preliminaries for proving that the first mover must be without parts and without magnitude

We have now to assert that the first mover must be without parts and without magnitude, beginning with the establishment of the premises on which this conclusion depends.

One of these premises is that nothing finite can cause motion during an infinite time. We have three things: the mover, the moved, and, third, that in which the motion takes place, namely the time.

These are either all infinite or all finite or partly—that is to say two of them or one of them —finite and partly infinite.

Let A be the motion, B the moved, and C the infinite time.

Now, let us suppose that D moves E, a part of B. Then the time occupied by this motion cannot be equal to C, for the greater the amount moved, the longer the time occupied.

It follows that the time Z is not infinite. Now we see that, by continuing to add to D, I shall use up A, and by continuing to add to E, I shall use up B, but I shall not use up the time by continually subtracting a corresponding amount from it, because it is infinite.

Consequently, the duration of the part of C that is occupied by all A in moving the whole of B will be finite.

Therefore, a finite thing cannot impart to anything an infinite motion. It is clear, then, that it is impossible for the finite to cause motion during an infinite time.

It has now to be shown that, in no case, is it possible for an infinite force to reside in a finite magnitude. This can be shown as follows.

We take it for granted that the greater force is always that which in less time than another does an equal amount of work when engaged in any activity, such as in heating or sweetening or throwing—in fact, in causing any kind of motion.

Then, that on which the forces act must be affected to some extent by our supposed finite magnitude possessing an infinite force as well as by anything else, in fact, to a greater extent than by anything else, since the infinite force is greater than any other.

But, then, there cannot be any time in which its action could take place. Suppose that A is the time occupied by the infinite power in the performance of an act of heating or pushing, and that AB is the time occupied by a finite power in the performance of the same act.

Then, by adding to the latter another finite power and continually increasing the magnitude of the power so added, I shall at some time or other reach a point at which the finite power has completed the motive act in the time A.

For by continual addition to a finite magnitude, I must arrive at a magnitude that exceeds any assigned limit, and in the same way, by continual subtraction, I must arrive at one that falls short of any assigned limit.

So, we get the result that the finite force will occupy the same amount of time in performing the motive act as does the infinite force. But this is impossible.

Therefore, nothing finite can possess an infinite force. So, it is also impossible for a finite force to reside in an infinite magnitude.

It is true that a greater force can reside in a lesser magnitude, but the superiority of any such greater force can be still greater if the magnitude in which it resides is greater.

Now let AB be an infinite magnitude. Then BC possesses a certain force that occupies a certain time, let us say the time EZ, in moving D. Now, if I take a magnitude twice as great at BC, the time occupied by this magnitude in moving D will be half of EZ (assuming this to be the proportion); so, we may call this time ZT.

That being so, by continually taking a greater magnitude in this way, I shall never arrive at the full AB, but I shall always be getting a lesser fraction of the time given. Therefore, the force must be infinite, since it exceeds any finite force. Moreover, the time occupied by the action of any finite force must also be finite, for if a given force moves something in a certain time, a greater force will do so in a lesser time, but still a definite time, in inverse proportion. But a force must always be infinite—just as a number or a magnitude is—if it exceeds all definite limits.

This point may also be proved in another way—by taking a finite magnitude in which there resides a force the same in kind as that which resides in the infinite magnitude, such that this force will be a measure of the finite force residing in the infinite magnitude.

It is plain, then, from the foregoing arguments, that it is impossible for an infinite force to reside in a finite magnitude or for a finite force to reside in an infinite magnitude.

1141. After showing of what sort the first motion is, the Philosopher here shows of what sort is the first mover.

And it is divided into two parts:

first, he mentions his intention;

second, he carries out his proposal, at one of these premises (266a12; [1142]).

He says first (266a10), then, that, since it was said above that the first mover is immobile, now we must assert that the first mover is indivisible and has no magnitude, as being wholly incorporeal. But, before we show this, certain things necessary for this proof must be settled in advance.

1142. Then, at one of these premises (266a12), he carries out his proposal:

first, he sets out things required for proving the main proposition;

second, he proves the main proposition, at now that these points (267b17; [1172]).

About the first, he does three things:

first, he shows that an infinite motion supposes an infinite power;

second, he shows that an infinite power cannot exist in a magnitude, at it has now to be shown (266a24; [1146]);

third, he shows that the first mover must be one that causes a continuous and undying motion, at but, before proceeding (266b27; [1160]).

He says first (266a12) that, among the things to be established before the main proposition, one is that it is impossible for anything of finite power to cause motion for an infinite time. This he now proves. There are three things in every motion: one of which is what is moved, another of which is the mover, and the third of which is the time in which the motion occurs. But all three must be infinite, or all three finite, or some finite and some infinite, that is, either two only or one only. Suppose, therefore, that A is the mover, B the mobile, and C the infinite time. Then let D, a part of A, move E, a part of B. Under these conditions, it could be concluded that D moves E in a time not equal to time C (in which A moved B), but in less time.

For it has been proved in book 6 (Lect. 7, n. 824.) that the entire mobile requires more time to pass a certain point than it takes for a part of it. Therefore, since the time C is infinite, it follows that the time in which D moves E will not be infinite, but finite. So, let that time be Z, such that, just as A moves B in the infinite time C, D moves E in the finite time Z. But, since D is part of A, then, if we add to D by subtracting from A, A will eventually be entirely taken away or used up, since it is finite, and every finite is used up by subtraction, if the same quantity is continually taken away, as said in book 3. (Lect. 10, n. 378.) And likewise, B will be used up, if continual subtractions are made from it and added to E, because B is also finite. But no matter how much is taken from the time C—even if the same amount is continually taken away—all of C will not be used up, because it is infinite.

From this, he concludes that the entire A moves the entire B in a finite time, which is part of C. And this does indeed follow from the premises, because additions are made to the time of the motion in the same ratio as they are made to the mobile and to the mover. Since, therefore, by subtracting from the entire mobile and mover and by adding to their parts, the whole mobile and the whole mover are at length used up, such that all that was in the whole is added to the part, it will follow that, by proportional additions being made to the time, there will result a finite time in which the whole mover will move the whole mobile. Thus, if the mover is finite and the mobile also finite, the time too must be finite.

According to this, therefore, it is not possible that anything be moved by a finite mover with an infinite motion according to an infinite time. And, so, what was first proposed is now plain: it does not happen that a finite mover should cause motion for an infinite time.

1143. But Avicenna raises a difficulty about this demonstration of Aristotle. For it seems not to be universal, since there exists a finite mover and mobile from which nothing can be subtracted or taken away, such as a heavenly body, which nevertheless was not excluded from Aristotle’s proof. Hence. it seems that the proof is either particular or it proceeds from a false assumption.

To this objection, Averroes answers in his commentary that although nothing can be subtracted from the heavenly body, yet the conditional is true that, if a part be taken away from the body, that part will move or be moved in less time than the whole body.

For there is nothing to prevent a conditional from being true, even if its antecedent be impossible, as is patent from this conditional: “If a man flies, he has wings.” But whatever takes away the truth of a true conditional is false, even though the antecedent of the conditional be false. Now, the truth of the above conditional cannot stand with the statement that the finite moves for an infinite time, as is evident through Aristotle’s deduction. Thus, from the truth of the foregoing conditional, Aristotle concludes that it is impossible for a finite thing to cause motion for an infinite time.

However, it may be said more briefly that, when Aristotle speaks in his demonstrations of removing or subtracting, it does not always have to be understood in the sense of destroying a thing’s continuity, which is impossible in a heavenly body; rather, subtraction can be understood in the sense of designating. For example, I can, without disturbing the continuity of a piece of wood, designate by touch or thought a certain point as though dividing the whole, and in this way, I can remove a part from the whole and say that there is less whiteness in that part than in the whole. In like manner, it can be said that there is less power to move in a part of a heavenly body—a part removed by designating it—than in the whole.

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 (Lect. 8–9.) and will be proved in De caelo 1. (Aristotle, De caelo 1.5ff.; cf. St. Thomas, Commentary on De Caelo, bk. 1, lect. 9ff.) 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. (Lect. 9, n. 1049.) 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. (Lect. 6, n. 197.)

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. (Lect. 11, n. 384.)

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, (Lect. 5, n. 794.) 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. (Lect. 17.) 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.

Again, the conclusion seems to be false. For the greater the power of a body, the longer it can endure. If, therefore, the power of no body were infinite, no body could endure to infinity. Now, this is plainly false, both according to his own opinion and according to the tenets of the Christian faith, which posits that the substance of the world will endure to infinity.

It could also be objected that the division and addition that he uses have no correspondence in reality, but since this was sufficiently discussed previously, it can be passed over at the present time.

1148. Thus, answering these doubts in order, it must be said with respect to the first one that the Philosopher in this place does not intend an ostensive demonstration, but one that leads to an impossibility—that is, one in which, since an impossibility follows from something given, that which was given is concluded to be impossible. For it is not true that the first supposition can possibly coexist with the conclusion. Thus, the supposition that there was some power that could remove the genus from a species would allow us to conclude that this power could make man not be animal; but, because this is impossible, the supposition too is impossible. From this, then, it cannot be concluded that it is possible for a power to exist that could make man not be animal. So, too, from the fact that an infinite power exists in a magnitude, it follows of necessity that motion exists in non-time; but since this is impossible, it is impossible for an infinite power to exist in a magnitude; nor can it be concluded from this that it is possible for an infinite power to move in non-time.

1149. To the second doubt, Averroes responds in his commentary at this place that the argument of Aristotle here proceeds from power under the account of its infinity. But finite and infinite belong to quantity, as was proved in book 1. (Lect. 3, n. 21.) Hence, finite and infinite do not properly belong to a power that is not in a magnitude.

But this answer is contrary both to the intention of Aristotle and to the truth. It is contrary to Aristotle’s intention because, in the preceding demonstration, Aristotle proved that a power that causes motion for an infinite time is infinite, and from this, he later concludes that the power moving the heavens is not a power existing in a magnitude. (Lect. 23, n. 1172.)

It is also against the truth. For since every active power is according to some form, magnitude—and consequently its finiteness and infinity—belong to a power in the way it belongs to form. But magnitude belongs to form both per se and per accidens: it belongs per se according to the perfection of the form, as a whiteness is called “great” even in a small amount of snow, according to the perfection of its proper account; it belongs per accidens according to the extension that a form has in a subject, as a whiteness can be called “great” on account of the size of its surface.

Now, this second magnitude cannot belong to a power not in a magnitude, but the first magnitude certainly can, because the less non-material powers are restricted through union with matter, the more perfect and more universal they are.

But swiftness of motion does not follow upon a magnitude of power that is per accidens by extension with the magnitude of the subject; rather, it follows one that is per se, according to its proper perfection, for the more perfect a thing is in act, the more vehemently is it active. Hence, it cannot be said that a power that does not exist in a magnitude, because it is not infinite with the infinity of magnitude that depends on the magnitude of the subject, therefore cannot cause an increase of swiftness to infinity, that is, move in non-time.

Hence, the same Commentator solves this same difficulty in another way in Metaphysics 11, where he says that a heavenly body is moved by a twofold mover—that is, by a conjoined mover, which is the soul of the heavens, and by a separated mover, which is not moved either per se or per accidens. And, because that separated mover has infinite power, the motion of the heaven acquires from it a perpetual duration; but because the conjoined mover has finite power, the motion of the heaven acquires from it a determinate swiftness.

But even this answer is not sufficient. For since both seem to follow upon an infinite power—namely, that it act for an infinite time (as the preceding demonstration concluded) and that it act in non-time (as this demonstration seems to conclude)—the doubt still remains as to why the soul of the heaven, which acts in virtue of an infinite separated mover, obtains from it the ability to act for an infinite time rather than the ability to act with infinite swiftness, that is, in non-time.

1150. In answer to this doubt, it must be said that every power not in a magnitude acts through intellect, for so the Philosopher proves in Metaphysics 11 that the heaven is moved by its mover. (Aristotle, Metaphysics, Λ.7; cf. St. Thomas, Commentary on Metaphysics, bk. 12, lect. 7.) But no power in a magnitude acts as though through intellect, for it was proved in De anima 3 (Aristotle, De anima, ch. 4; cf. St. Thomas, Commentary on De anima, bk. 3, lect. 1.) that the intellect is not a power of any body.

Now, this is the difference between an agent that acts through intellect and a material agent: the action of the material agent is proportioned to the nature of the agent, for heating proceeds in proportion to the heat, but the action of an intellectual agent is not proportioned to its nature, but to the form apprehended, for a builder does not build as much as he can, but as much as the account of the conceived form requires.

Consequently, if an infinite power existed in a magnitude, it would follow that the motion produced by it would be in proportion to it, as the present demonstration shows. But, if an infinite power is not in a magnitude, a motion does not proceed from that power in proportion to its power, but according to the account of the thing apprehended, that is, according as it fits the end and nature of the subject.

Another point that should be noted is that, as was proved in book 7, (Lect. 5, n. 922.) only things having magnitude are moved; hence the swiftness of motion is an effect received from the mover into something having magnitude. But it is plain that nothing having magnitude can receive an effect equal proportionately to the power that is not in a magnitude, because every corporeal nature is related to the incorporeal as a certain particular to what is absolute and universal. Hence, if there is an infinite power that is not in a magnitude, it cannot be concluded that, from it, there results an infinite swiftness in a body that is the effect proportionate to such a power, as has been said.

But there is nothing to prevent a magnitude from receiving the effect of a power existing in a magnitude, because the cause is proportioned to the effect. Hence, if it were supposed that an infinite power existed in a magnitude, it would follow that a corresponding effect would exist in a magnitude, namely, an infinite swiftness. But this is impossible; therefore, the first too is impossible.

1151. From this, the resolution of the third doubt is clear. For to be moved for an infinite time is not repugnant to the account of a moved magnitude, for it befits a circular magnitude, as was shown above. (Lect. 20.) But to be moved with an infinite speed—that is, in non-time—is contrary to the account of a magnitude, as was proved in book 6. (Lect. 5, n. 794.) Hence, the first mover, possessing infinite power, is, according to Aristotle, the cause of a motion that lasts an infinite time, but not one that has infinite speed.

1152. The fourth doubt is, according to Averroes in his commentary, answered by Alexander’s saying that a heavenly body acquires eternity from a separated mover having infinite power, as well as perpetuity of motion. Hence, just as it is not from the infinity of a heavenly body that it is perpetually moved, so, too, it is not from the infinity of the heavenly body that it endures forever. Both are from the infinity of the separated mover.

Now, Averroes tries to refute this answer, both in his commentary on this passage and in Metaphysics 11, and says that it is impossible for something to acquire perpetuity of existence from another, because it would follow that something perishable in itself could be eternal. Yet something can acquire perpetuity of motion from another, for motion is an act existing in a mobile but caused by a mover. He thus says that, in a heavenly body considered in itself, there is no potency to non-existence, because its substance has no contrary, but there is a potency to rest, because rest is contrary to its motion. And that is why it does not have to acquire perpetuity of existence from another, but must acquire perpetuity of motion from another.

That a heavenly body has no potency to non-existence happens, he says, because a heavenly body is not composed of matter and form as though of potency and act. Rather, says he, such a body is matter existing in act, while its form is its soul, in such a way that it is not constituted in being through the form, but only in motion. Consequently, says he, there is present in it not a potency to existence, but solely a potency to place, as the Philosopher says in Metaphysics 11. (Aristotle, Metaphysics, Λ.2; cf. St. Thomas, Commentary on Metaphysics, bk. 12, lect. 2.)

1153. But this solution conforms neither to the truth nor to the intention of Aristotle.

It is not in conformity with truth on a number of counts:

first, because he says that a heavenly body is not composed of matter and form—which is utterly impossible. For it is plain that a heavenly body is something actual, otherwise it would not be in motion—something that is in potency only is not a subject of motion, as was proved in book 6. But whatever is actual is either a subsisting form, as are the separated substances, or has form in something else, which is related to the form as matter and as potency to act. Now, it cannot be said that a heavenly body is a subsistent form, because then it would be understood in act, and neither sensible nor existing under quantity. Therefore, it must be a composite of matter and form, and of potency and act. Consequently, in some sense, it has a potency to non-existence.

But, even if a heavenly body were not a composite of matter and form, it would still be necessary to place in it, in some sense, a potency in respect of existence. For every simple self-subsisting substance necessarily either is its own existence or shares in existence. But a simple substance that is self-subsistent existence itself cannot be but one, just as whiteness, if whiteness were a subsistent being, could be but one. Consequently, every substance after the first simple substance participates in existence. But every participant is composed of the participant and what it participates in, and the participant is in potency to what it participates in. Therefore, in every substance, however simple, other than the first simple substance, there is a potency to existence.

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. (Aristotle, De interpretatione, 1.13.)

His position is also contrary to the intention of Aristotle, who, in a certain demonstration in De caelo 1.12, (Cf. St. Thomas, Commentary on De Caelo, bk. 1, lect. 27.) 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 (Aristotle, Metaphysics Δ.5; cf. St. Thomas, Commentary on Metaphysics, bk. 5, lect. 6.) and in the beginning of this book 8 of the Physics, (Lect. 3, n. 995.) 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. (Lect. 9, n. 957.) 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.