Lecture 23 — The first mover cannot have magnitude

We proceed from the positions

(1) that there must be continuous motion in the world of things;

(2) that this is a single motion;

(3) that a single motion must be a motion of a magnitude (for that which is without magnitude cannot be in motion);

(4) that the magnitude must be a single magnitude moved by a single mover (for otherwise, there will not be continuous motion, but a consecutive series of separate motions);

and (5) that, if the motion is a single thing, it is either itself in motion or itself unmoved.

If, then, it is in motion, it will have to be subject to the same conditions as that which it moves: it will itself be in process of change and, in being so, will also have to be moved by something.

Thus, we have a series that must come to an end, and a point will be reached at which motion is imparted by something that is unmoved.

Thus, we have a mover that has no need to change along with that which it moves, but will be able to cause motion always

(for the causing of motion under these conditions involves no effort).

And this motion alone is regular, or at least it is so in a higher degree than any other, since the mover is never subject to any change. So, too, in order that the motion may continue to be of the same character, the moved must not be subject to change in respect of its relation to the mover.

Moreover, the mover must occupy either the center or the circumference, since these are the first principles from which a sphere is derived.

But the things nearest the mover are those whose motion is quickest, and in this case, it is the motion of the circumference that is the quickest: therefore, the mover occupies the circumference.

There is a further difficulty in supposing it to be possible for anything that is in motion to cause motion continuously and not merely in the way in which it is caused by something repeatedly pushing (in which case the continuity amounts to no more than successiveness).

Either such a mover must itself continue to push or pull or perform both these actions or else the action must be taken up by something else and be passed on from one mover to another (the process that we described before as occurring in the case of things thrown,

since the air or the water, being divisible, is a mover only in virtue of the fact that different parts of the air are moved one after another).

And, in either case, the motion cannot be a single motion, but only a consecutive series of motions.

The only continuous motion, then, is that which is caused by the unmoved mover, and this motion is continuous, because the mover remains always invariable such that its relation to that which it moves remains also invariable and continuous.

Now that these points are settled, it is clear that the first unmoved mover cannot have any magnitude. For if it has magnitude, this must be either a finite or an infinite magnitude. Now, we have already proved in our course on physics that there cannot be an infinite magnitude, and we have now proved that it is impossible for a finite magnitude to have an infinite force, and also that it is impossible for a thing to be moved by a finite magnitude during an infinite time. But the first mover causes a motion that is eternal and does cause it during an infinite time. It is clear, therefore, that the first mover is indivisible, without parts, and without magnitude.

1164. Having resolved the doubt he raised about the motion of projectiles, from the solution of which he concluded that a motion involving a number of movers is not one continuous motion, the Philosopher now turns to his main task, namely, to prove that the first mover is one.

About this, he does two things:

first, he states his proposition;

second, he raises a doubt and solves it, at there is a further difficulty (267b9; [1170]).

About the first, he does three things:

first, he proves the unity of the first mover through the continuity of motion;

second, he shows how a continuous motion comes from one mover, at if, then, it is in motion (267a25; [1166]);

third, he shows where the principle of a continuous motion is, at moreover, the mover (267b6; [1168]).

1165. That there must be one mover he proves (267a21) through the continuity of motion, taking what he had previously proved, (Cf. Lect. 14, n. 1086.) namely, that some continuous motion must always exist. But a continuous motion is one, as was said in book 5. (Lect. 7, n. 703.) Therefore, there must always be some one motion. But, for a motion to be one, it must be of one moved magnitude (because something not able to be divided into parts cannot be moved, as was proved in book 6) (Lect. 12. Cf. lect. 5, n. 796.) and it must be moved by one mover. For if the mobiles are diverse or the movers are diverse, a motion will not be one, and consequently, not continuous. Rather, it will be one motion divided from another—on account of the division of the mobile or mover—and will have consecutive motions. It is necessary, therefore, that the mover be one and that it be either a moved mover or a mover that is immovable.

1166. Then, at if, then, it is in motion (267a25), he shows how, from one mover, there can be a continuous motion.

About this, he does two things:

first, he shows how, from one mover, there can be a motion ever continuous;

second, he shows how it is regular, at and this motion alone (267b3; [1167]).

He says, therefore (267a25), that one motion from one mover is, as has been said, either from a moved mover or a unmoved mover. If it is the former, it follows that it is moved by something, as was proved above. (Lect. 7ff.) But this cannot go on to infinity, as was proved above. (Lect. 9.) Therefore, the series of movers and mobiles must stop, and a first mobile moved by an immobile mover be reached, which mover does not move of necessity, because it is not moved by another. For whatever is moved by another moves of necessity, to the extent that necessity is imposed upon it by its mover. And, because it is changed from its disposition, it cannot cause motion that is always uniform, for its disposition varies.

But nothing other imposes necessity on a unmoved mover, nor does its disposition vary. Hence, it does not act of necessity, but it can move always, because to move thus—namely, without change of self—is unwearying. For fatigue occurs to some movers in moving because they are also simultaneously moved themselves, and from fatigue, it occurs that they cannot always act as movers. Hence, it remains that a unmoved mover can move with a perpetual continuous motion.

1167. And, because perfect continuity and unity of motion require that a motion be regular and uniform, as was had in book 5, (Lect. 7, n. 708.) therefore, at and this motion alone (267b3), he shows that a motion from an immobile mover is regular.

And he says that either solely the motion from an immobile mover is regular or, if any others are regular also, the former is the most regular. Now, he uses this disjunction because the disposition of a moved mover sometimes remains the same for some time without variation (at least as far as any sensible perception is concerned), and accordingly, such a mover seems for a time to cause a uniform motion. But that which is always such moves above all with a uniform motion, since such a mover is subject to no change whatsoever. He says this in order to show that there are some movers that are not moved with the same kind of motion as they cause, as a heavenly body is not moved by the motion of alteration, but by some other, namely, local motion. But the first mover, being utterly immobile, is moved by no change.

In order that a motion be regular and uniform, it is required that the mover be wholly immobile; besides that, in order that the motion be similar, that is, uniform, it is required that what is moved not undergo any change other than that which the immobile mover causes in it, as a heavenly body is moved with local motion by an immobile mover and, beyond that, has no other change. For if it were altered, its disposition to the motion would not remain constant and, consequently, the motion would not be uniform.

1168. Then, at moreover, the mover (267b6), he shows where the beginning of the first continuous motion is. And, because it was proved that the first motion is circular and belongs to a circular magnitude, (Lect. 19–20.) the first beginning of this motion must be either in the middle (that is, the center) or on the circle, because both are principles of a circular magnitude. For in a circular magnitude, lines are extended from the center to the circumference. Hence, one of these must be taken as principle, and the other as terminus.

Then he shows by the following argument that the principle of the first motion is on the circle. Every motion, the closer it is to the moving principle, the swifter it is, because it receives a stronger impression from the mover. But we perceive in the motion of the whole firmament, which motion proceeds from the first immobile mover, that the closer some mobile approaches the outermost circumference, so much the swifter is its motion. Therefore, the mover is on the circle and not in the center.

The major premise of this argument is plain. But, in order to make the minor plain, it must be considered that a twofold motion is found in heavenly bodies:

one is the motion of the entire firmament in its daily revolution from east to west, and this is the first motion;

the other is the motion by which the stars are moved contrariwise from west to east.

Now, in this second motion, the closer a heavenly body is to the center, the swifter its motion, as is evident from the calculations of astronomers, who assign one month for the motion of the Moon, one year for the motions of the Sun, Mercury, and Venus, two years to Mars, twelve years to Jupiter, thirty to Saturn, and thirty-six thousand years to the fixed stars. (That is, the precession of the equinoxes, a cycle that actually occurs over approximately twenty-six thousand years.)

But, with respect to the motion of the entire firmament, it is the opposite. For the farther a heavenly body is from the earth, the swifter is its motion, because it traverses a larger magnitude in the same time. For the circumferences of circles are greater the farther they are from the center, and yet all the heavenly bodies are revolved with the motion of the whole in the same period of time. Consequently, the outermost bodies are swifter. Hence, what remains is that the principle of the first motion is not in the center but on the circumference.

1169. But now a difficulty arises about this conclusion. For the first mover, as he will conclude below, is indivisible and has no magnitude, and its power does not exist in a magnitude. But whatever is such does not seem to have a definite position in a body. Hence, it does not befit the first mover to be in one part of the first mobile more than in another.

But it should be stated that the first mover is said to be in some part of its mobile not through any determination of its substance, but through its efficient causality of motion, because it begins to move at some part of the object it acts upon. And it is for that reason that the first mover is said to be in the heavens rather than in the earth, and rather in the east, where the motion begins.

And this is not to be understood as though the mover fixes itself to some definite part of the mobile, since there is no definite part of the mobile always in the east, but the part now in the east is later in the west. Thus, it is clear that the power of the mover is said to be in the east by virtue of the inflow of motion, and not through any determination of its substance.

It should also be noted, with respect to the motion of a sphere, that, simultaneously with its motion, it has a kind of immobility:

for the parts are moved as to change of place both as to subject and as to account, but the whole is moved as to change of place in account but not as to subject, as was shown in book 6. (Lect. 11, n. 871.)

And he mentions here that these two things are attributed to the two principles of the spherical magnitude,

for the principle of the motion has its seat on the circumference, while the principle of immobility derives from the fixity of the center.

1170. Then, at there is a further difficulty (267b9), he raises a doubt about the foregoing.

First, he raises it;

second, he solves it, at either such a mover must (267b11; [1171]).

For he had said previously that an immobile mover can cause continuous motion, and so here (267b9) he subsequently asks whether a moved mover can cause a continuous motion in such a way, namely, that it be truly continuous without any interruption, such as the interruption that occurs when someone pushes a body and then pushes it again. For it is clear that this motion, which is in this way continuous from the standpoint of the mobile, is not truly continuous, because the motions are not continuous, but one follows the other; for the one pushing does not continually push, but at intervals, in such a way that one push is consecutive to another.

1171. Then, at either such a mover must (267b11), he resolves this difficulty and shows that no moved mover can cause a continuous motion. For it is necessary to say that a mobile that is seemingly being moved continuously is being moved either immediately through the whole motion by a moved mover, or else through many intermediates, one in contact with the other, as was said with respect to projection. (Lect. 22, nn. 1162–63.) And this division is valid whether the moved mover acts by pushing or pulling or both (as in twirling), as was explained in book 7. (Lect. 3, n. 906.) Nor does it happen that a thing is moved locally by a moved mover in more than one way per se and not per accidens (for something being carried is being moved per accidens).

And because he had said that, in things that are projected, the mover is constantly different, and this seems to be false because the projected body seems to be continually moved by an air that remains one, he therefore adds, in order to refute this, that it is because air or water are easy to divide that now one and now another (so to speak) mover acts, but yet it acts as if being continually moved, so long as the motion of the projectile lasts; and, although the air seems one, nevertheless it is different through division.

And, in either case—that is, whether the moved mover acts by pushing or by pulling—the motion cannot be one, but must be consecutive for the reason given above, (Lect. 22, n. 1163.) when the motion of projection was discussed, namely, on account of the diversity of movers. What remains, therefore, is that only the motion from an immobile mover can be forever continuous, because this mover remains always similar, according to the same disposition in itself. For that reason, it can maintain itself always and continuously in a similar way with respect to the mobile, namely, so as to move it uniformly.

But it should be noted that the Philosopher here attributes eternity of continuous motion to the immobility of the mover, whereas above he attributed it to its infinite power. (Lect. 21, n. 1142.) For eternity of continuous motion, if regarded with respect to the motion’s repetition, looks to the immobility of the mover, since, if it always remains constant with itself, it can always repeat the same motion. But the infinite power of the mover regards the motion’s whole perpetuity or infinity per se, as was said above. (Lect. 21, nn. 1144–45.)

It should be noted, too, that, because no moved mover can cause a perpetual, continuous motion, he therefore intends to prove in Metaphysics 11 (Aristotle, Metaphysics, Λ.8; cf. St. Thomas, Commentary on Metaphysics, bk. 12, lect. 9.) a number of immobile movers according to the number of the heavenly motions, as though that consideration followed upon this.

1172. Then, at now that these points (267b17), from the premises already demonstrated, (Lect. 21ff.) he argues for the main conclusion. And he says that, from the foregoing, it is plainly impossible for the first immobile mover to have any magnitude or to be a body or to be a power residing in a body. For if it had any magnitude, it would be either finite or infinite. But it was proved in book 3, when nature in common was discussed, that an infinite magnitude is not possible. (Lect. 8, 9.) What remains, therefore, is that, if it does have magnitude, it will have a finite magnitude. But that such is not so he proves on the ground that it is impossible for a finite magnitude to possess infinite power, such as the first immobile mover must necessarily have. Therefore, it cannot have a finite magnitude.

But that the first immobile mover must have infinite power he proves from something previously demonstrated: (Lect. 21, n. 1142.) it is impossible for something to be moved for an infinite time by a finite power. Now, the first mover causes a motion that is perpetual and continuous and is one and the same for infinite time, for otherwise, this motion would not be continuous. Therefore, it has infinite power. Thus, it does not have a finite magnitude, and an infinite magnitude is impossible.

It is plain, therefore, that the first mover is indivisible, both as having no part (as even a point is indivisible) and as wholly without magnitude, as though existing outside the genus of magnitude.

And thus does the Philosopher, in his general consideration of natural things, terminate at the first principle of the whole of nature, who is the one above all things, the ever-blessed God. Amen.