Commentary Aristotle Physics
Lecture 2. There must be an immobile first mover
Since everything that is in motion must be moved by something, let us take the case in which a thing is in locomotion and is moved by something that is itself in motion, and that again is moved by something else that is in motion, and that by something else, and so on continually. Then the series cannot go on to infinity, but there must be some first mover.
For let us suppose that this is not so and take the series to be infinite. Let A then be moved by B, B by C, C by D, and so on, each member of the series being moved by that which comes next to it.
Then, since it was hypothesized that the mover, while causing motion, is also itself in motion, and the motion of the moved and the motion of the mover must proceed simultaneously (for the mover is causing motion and the moved is being moved simultaneously) it is evident that the respective motions of A, B, C, and each of the other moved movers are simultaneous.
For though they are all moved severally one by another, yet we may still take the motion of each as numerically one, since every motion is from something to something and is not infinite in a privative sense.
For a motion may be the same generically, specifically, or numerically. By “a motion that is numerically one,” I mean a motion that proceeds from the same into the same in the same period of time; as for example, from this white, which is one in number, into this black, in this time, which is numerically one; for if the motion occurs in another time, it will not be numerically one, but specifically one. It is generically the same motion if it belongs to the same category (for instance, substance).
It is specifically the same motion if it proceeds from something specifically the same to something specifically the same (for instance, from white to black or from good to bad).
But we have dealt with this question above.
Let us take the motion of each separately, and let E be the motion of A, Z of B, and H and O, respectively, the motions of C and D;
now, let us further take the time in which A has completed its motion, and let it be represented by K. Then, since the motion of A is determined, the time will also be determined, and K will not be infinite.
But the motions of A and B and each of the others occur in the same time. It happens, therefore, that the motion composed of all the individual motions, EZHO, when it is infinite, occurs in a finite time, which is K.
For the movers and the things moved are infinite. For either the motions of A, B, and the others are equal or their motions are greater; but this makes no difference, for in both cases, the whole motion is infinite.
And consequently (since the whole motion must occupy the same time as the motion of A, which is finite), the motion will be infinite in a finite time, which is impossible.
It might be thought that what we set out to prove has thus been shown, but our argument so far does not prove it, because it does not yet prove that anything impossible results from the contrary supposition;
for in a finite time, there may be an infinite motion, though not of one thing, but of many. In the case that we are considering, this is so: each thing accomplishes its own motion, and there is no impossibility in many things being in motion simultaneously.
But if (as we see to be universally the case) that which primarily is moved locally and corporeally must be either in contact with or continuous with that which moves it, the things moved and the movers must be continuous or in contact with one another, such that they all together form a single unity.
For we shall take as actual that which is theoretically possible. If, then, A, B, C, D form an infinite magnitude that passes through the motion EZHO in the finite time K, this involves the conclusion that an infinite motion is passed through in a finite time; and whether the magnitude in question is finite or infinite, this is impossible in either case.
Therefore, the series must come to an end, and there must be a first mover and a first moved.
For the fact that this impossibility results only from the assumption of a particular case is immaterial, since the case assumed is theoretically possible, and the assumption of a theoretically possible case ought not to give rise to any impossible result.
891. After showing that whatever is moved is moved by some other, the Philosopher now turns to the proof of his main proposition, namely, that there exists a first motion and a first mover.
About this, he does two things: first, he proposes what he intends; second, he proves his proposition, at “for let us suppose” (242a20; [892]).
He says first (242a15) that, since it has been proved for all cases that whatever is moved is moved by some other, it must be true even in regard to local motion that whatever is being moved with respect to place is being moved by something else. Now, he applies to local motion in particular the very proposition that he proved universally true, because local motion is the first of the motions, as will be proved in book 8. Therefore, it is according to this motion that he now proceeds to demonstrate a first mover.
Therefore, let us take something that is being moved in regard to place. This thing is being moved by something else. Now, that something else is in turn being moved by something else or it is not. If it is not, we have the proposition clinched: there exists a mover that is immovable, which is a property of the first mover.
But, if that something else is also being moved by something other, this other is being moved by still another, which is itself being moved by yet another mover. This, however, cannot go on to infinity, but a halt must be made at some mover. Therefore, there will be a first mover that will be the first cause of the motion; it will be of such a nature that it is itself not being moved, but moves the others.
892. Then, at “for let us suppose” (242a20), he proves a statement not yet proved. About this, he does three things: first, he gives the proof; second, he shows that the proof he gives is insufficient, at “it might be thought” (242b20; [893]); third, he supplies what was lacking in the insufficient proof, at “but if” (242b24; [894]).
He says first (242a20) that, if it is not granted that there is a first cause of the motion, then, since whatever is being moved is moved by some other, it follows that an infinite series of movers and moved is involved. And he shows that such a situation is impossible.
Let A, then, be something that is being moved in respect of place and let it be moved by B; let B be moved by C, and C by D, and so on to infinity in ascending order. Now, it is evident that, when something moves by virtue of the fact that it is itself being moved by another, then both the mover and the mobile are being moved simultaneously, just as, when the hand by its motion moves a stick, the hand and the stick are moved at one and the same time. Therefore, B is being moved simultaneously with A, and C with B, and D with C.
Therefore, the motion of A and that of all the others exist together and at the same time. And we could have considered one by one each of these infinite motions. Likewise, although each one of these mobiles is being moved by some mover—not in the sense that one is being moved by all, but one by another—nevertheless, even though there be an infinitude of movers and mobiles, yet the motion of each of the mobiles is numerically one motion. And, although all the motions are infinite in number, they are not infinite in a privative sense, that is, as though lacking a boundary, but the motion of each mobile is finite and has its own definite boundaries.
He proves that the motion of each one of the infinite mobiles is numerically one and finite by the fact that, since whatever is moved is moved between two termini—that is, from something to something—then, necessarily, according to the diverse ways in which the termini are identical, the motion itself will be one in diverse ways: numerically, specifically, or generically.
Motions are numerically the same when they are from the same terminus from which into the same numerical terminus to which, provided that it takes place in the same numerical time and that the numerically same mobile is involved. To explain what he means, he adds that a motion that is numerically one is from the same into the same—for example, from this white (the same numerical white) into this black (the same numerical black), and in this same numerical time. For if all the conditions but time were numerically the same, the motion would be one not numerically, but specifically.
But a motion is generically one when it is in the same predicament, that is, of substance or some other genus; for example, all generations of substance are generically the same, and all alterations likewise.
But a motion is specifically one when it is from the same specific terminus to the same specific terminus; for example, every case of blackening, which is from white to black, is specifically the same, and every case of becoming depraved, which is from good to bad, is specifically the same. All this was explained in book 5.
Keeping in mind, therefore, these two facts—that the mover and the moved are being moved together, and that the motion of each of the mobiles can be taken as one and finite—let us take the motion of mobile A and call it motion E, and the motion of B and call it Z, and let the motion of C be called I, and of all the others following be called T. Also, let the time in which A is being moved be K.
Now, since the motion of A is determined, that is, finite, then the time K of that motion is definite and not infinite, because we showed in book 6 that a finite time corresponds to a finite motion and that an infinite time corresponds to an infinite motion.
From what we have said, however, it is clear that, in the very same time that A is being moved, B is being moved, and so for all the others; hence, the motion of all, the motion EZIT, occurs in finite time. But this motion is infinite, since it is the motion of an infinite number.
Therefore, it will follow that an infinite motion occurs in finite time, which is impossible. Now, why does our conclusion follow? Because, in the very same time that A is being moved, all the others are being moved, and they are infinite in number.
It makes no difference, so far as our proposition is concerned, whether the motion of all the mobiles had equal velocity or not, or whether the lower mobiles move more slowly and in a greater time, for in any case, it will follow that an infinite motion occurs in finite time—since each of the mobiles must have a finite rapidity and a finite slowness. However, it is impossible for an infinite motion to occur in finite time. Therefore, it is also impossible that we go to infinity in the series of mobiles and movers.
893. Then, at “it might be thought” (242b20), he shows that the foregoing argument is not conclusive. And he says that, in the above way, we seemed to have demonstrated the main proposition, that one does not go to infinity in the series of movers and mobiles. Yet it is not an efficacious proof, because no impossibility flows from these premises. For it is possible that there be an infinite motion in finite time so long as the motion is not one and the same, but different—that is, insofar as an infinite number of things are being moved. For there is nothing to prevent an infinite number of things from being moved at once in finite time. And it was this that our argument concluded. For the infinite mobiles were diverse, and so their motions were diverse, because, for a motion to be one, it is required not only that the time be one and that the termini be identical but also that the mobile be one, as was proved in book 5.
894. Then, at “but if” (242b24), he shows how to make the argument efficacious: first, how it can be made efficacious by making another assumption; second, how it is efficacious all by itself, at “for the fact that” (242b34).
He thus says first that what is locally and corporeally being moved first and immediately by a mobile mover must be touched by it, as a stick is touched by the hand, or must be continuous with it, as one part of the air is continuous with the next part or as one part of an animal is continuous with another. And this seems to occur in everything, namely, that the mover is always in contact with the mobile in one of these ways.
Let us therefore take one of these ways, namely, that from all the infinite mobiles and movers there is formed one thing—namely, the whole universe—through some kind of continuity. Since this is something contingent, let us take it for granted and let that whole unit—which is a continuous magnitude—be called ABCD and its motion EZIT. And, because someone could say that EZIT was the motion of finite mobiles, and so not the motion of an infinite whole, he adds that, so far as our proposition is concerned, it makes no difference whether the magnitude is finite or infinite. For just as, when A was being moved in a finite time K, each of the finite mobiles that are infinite in number were being moved at the same time, so also, in the same time, the entire infinite magnitude will be moved all at once. Therefore, an impossibility follows whichever one is taken: either a finite magnitude composed of magnitudes infinite in number, or an infinite magnitude whose motion occurs in finite time. For it has been proved above that an infinite mobile cannot be moved in finite time. Therefore, the premise from which this impossibility followed is itself impossible, that is, that we go to infinity in the series of movers and things moved. It is clear, therefore, that the process of one thing being moved by another does not go on to infinity, but a halt must be made and there will exist a first mobile that is being moved by a mover that is immovable.
895. Since our proof depended on an assumption—namely, that all the infinite movers and moved form a continuum and constitute one magnitude—it might seem to someone that the conclusion is not absolute. Consequently, he adds that it makes no difference to the validity of this conclusion that it should have proceeded from this assumption. For an impossibility cannot follow from an assumption that is contingent, even if the assumption be false.
Therefore, since the proof led to an impossibility, that impossibility did not follow from our contingent premise, but from some other cause that must be impossible, since an impossibility followed from it.
So it is clear that, in demonstrations that lead to an impossibility, it makes no difference whether a false contingent assumption or something true be joined to what is impossible.
For that is shown to be impossible that, by the addition of some false contingent statement, gives rise to an impossibility, just as if something impossible should follow from it by the addition of a true proposition. For just as an impossibility cannot follow from a true premise, so neither can it from a contingent one.
896. But someone could say that for all mobiles to form one continuum is not contingent, but impossible, for the elements cannot form a continuum with one another and with the heavenly bodies.
But it must be answered that “contingent” and “impossible” are taken in one sense when something is demonstrated about a genus and in another sense when something is demonstrated about a species. When a discussion is about the species, whatever is repugnant either to the genus or the specific difference, which forms the account of the species, must be regarded as impossible.
But when the discussion is about the genus, we can take as contingent anything to which the genus is not repugnant, even though the difference that constitutes a species of that genus is repugnant to it. For example, if I am speaking of animal, I can suppose as a contingent proposition that all animals are winged; but if I go a step further and consider man, it is impossible for this animal to have wings.
Now, since Aristotle is here speaking about mobiles and movers in a general way without making applications to particular mobiles, and to be in contact or to be continuous is a matter of indifference if you consider the general account of mover and mobile, he therefore takes it as contingent that all mobiles mutually form a continuum, even though this is impossible if you consider the mobiles in their specific natures.