LECTURE 2 (242 a 16-243 a 2)

MOBILE OBJECTS AND MOTIONS CANNOT PROCEED TO INFINITY. THERE MUST BE AN IMMOBILE FIRST MOVER

             891. After the Philosopher has shown that whatever is moved is moved by another, here he proceeds to prove the principle proposition; namely, that there is a first motion and a first mover.

             Concerning this he makes two points. First he states his intention. Secondly, where he says, 'For let us suppose . . .' (242 a 21), he proves his position.

             He says, therefore, first that since it has been shown universally that whatever is moved is moved by another, then this must also be true of local motion. Hence, whatever is moved in place is moved by another. He applies what was demonstrated universally above to local motion because local motion is the first of motions, as will be shown in Book VIII. And so with respect to this motion he proceeds here to the proof of a first mover.

             Let there be something which is moved with respect to place. This is moved by another. This other is either moved or is not moved. If it is not moved, the proposition is established, namely, that there is a mover which is immobile. This immobility is a property of the first mover. If, however, the mover is itself moved, then it must be moved by another mover; and again, this mover, if it is also moved, is moved by another. Now this cannot continue to infinity, but must stop with something. There will be, therefore, some first mover which will be the first cause of motion, such that it is not moved itself but moves others.

             892. Next where he says, 'For let us suppose . . .' (242 a 21), he proves what he has supposed.

             Concerning this he makes three points. First he states the proof. Secondly, where he says, 'It might be thought . . .' (242 b 19), he shows that this proof is not sufficient. Thirdly, where he says, 'But if (as we see . . .' (242 b 24), he adds a certain thing which strengthens the argument.

             He says, therefore, first that if it is not granted that there is some first cause of motion because whatever is moved is moved by another, then it follows that movers and motions proceed to infinity. And he shows that this is impossible. Let A be something which is moved in respect to place by B. And B is moved by C; C is moved by D; and this continues by ascending to infinity. It is clear that when a thing moves because it is moved, the mover and the mobile object are moved simultaneously. For example, if the hand by its own motion moves a staff, the hand and the staff are moved simultaneously. Hence B is moved simultaneously when A is moved; and for the same reason when B is moved, C is moved simultaneously; and when C is moved, D is moved simultaneously. Therefore the motions of A and of all the others are simultaneous and in the same time. And the motion of each one of these infinites can be considered separately. Now each one of these mobile objects is moved by each one of the movers, but not in such a way that one of them is moved by all. Rather, individual objects are moved by individual movers. Nevertheless, although the movers and mobile objects are infinite, the motion of each mobile object is one in number. And although all the motions are infinite in number, they are not infinite in the extremes, that is, they are not infinite by a privation of extremes. Rather the motion of each one is finite, having a determinate extreme.

             He proves as follows that the motion of each of the infinite mobile objects is finite and one in number. Since everything which is moved is moved between two termini, i.e., from something to something, then in respect to the different modes of identity of the termini the motion itself must be one in different ways, that is, either in number, or in species, or in genus.

             Motion is one in number when it is from the numerically same terminus from which and to the numerically same terminus to which. Moreover the motion must occur in numerically the same time and the mobile object must be numerically the same. In order to explain what he has said, he adds that a motion is one in number when it is from the same thing and to the same thing, for example, from 'this white', which indicates a thing which is one in number, to 'this black', which also indicates something which is one in number. And the motion must occur with respect to 'this time', which also is one in number. For if the motion occurs with respect to another time, although it be equal, the motion would not be one in number but only in species.

             A motion is one in genus when it is in the same category, either substance or any other genus. For example, every generation of substance is the same in genus, and likewise every alteration is the same in genus.

             And motion is one in species when it is from the same thing with respect to species and to the same thing with respect to species. For example, every blackening, which is from white to black, is the same in species. And likewise every perversion from good to evil is the same in species. These points were discussed in Book V.

             Let us grant these two suppositions; namely, the mover and the moved are moved simultaneously, and the motion of any mobile object can be taken as finite and one. Let E be the motion of the mobile object A. Let F be the motion of B. And let G H be the motion of C D and of all the following mobile objects. Let the time in which A is moved be J. Since the motion of A is determinate and finite, then the time J of this motion is also determinate and not infinite. For it was shown in Book VI that the finite and the infinite are found together in time and in motion. From what has been said it is clear that in the same time in which A is moved, B also is moved, and so are all the others. Therefore, the motion of all, which is E F G H, is in a finite time. But this motion is infinite because it is the motion of infinite things. Therefore, it follows that there is an infinite motion in a finite time, which is impossible. This follows because in the time in which A is moved all of the others, which are infinite in number, are moved. And as far as this proposition is concerned it makes no difference whether the motion of every mobile object is of equal velocity or whether the inferior mobile objects are moved more slowly and in a longer time. For it follows absolutely that there is an infinite motion in a finite time because each one of the mobile objects necessarily has a velocity and a finite slowness. But there cannot be an infinite motion in a finite time. Therefore, mobile objects and movers cannot proceed to infinity.

             893. Next where he says, 'It might be thought . . .' (242 b 19), he shows that the preceding argument does not come to a proper conclusion. He says that in the above discussion there seems to be a demonstration of the principal proposition, namely, that movers and mobile objects do not proceed to infinity. However, it is not adequately demonstrated that no inconsistency follows from the premises. For it is possible and it happens that there is infinite motion in a finite time. However, this is not one and the same motion, but different motions insofar as the things which are moved are infinite. For nothing prevents infinite things from moving simultaneously in a finite time. And this was the conclusion of the foregoing argument. For there were infinite, diverse mobile objects, and so their motions were diverse. But the unity of motion requires not only a unity of time and of termini, but also a unity of the mobile object, as was said in Book V.

             894. Next where he says, 'But if (as we see . . .' (242 b 24), he shows how the above argument can be made effective.

             First he shows how it can be effective after a supposition has been made. Secondly, where he says, 'Whether this unity . . .' (242 b 27), he shows how it is effective simply.

             He says, therefore, first that what is primarily moved locally and bodily and immediately by some moving mobile object must be touched by it, as a staff is touched by a hand, or it must be continuous with it, as one part of air is continuous with another, and as one part of an animal is continuous with another part. In all cases it seems to happen that the mover is always joined to the mobile object in one of these ways.

             Let one of these ways be assumed, namely, that from all the infinite mobile objects and movers there is effected a unity, namely, the whole universe, through a certain continuation. Since this actually occurs, let it be granted. And let that whole, which is a certain magnitude and continuum, be called A B C D, and let its motion be called E F G H. Now someone might say that E F G H is the motion of finite mobile objects, and thus it cannot be the motion of the whole infinite. Hence he adds that it makes no difference to the proposition whether the magnitude which is moved is assumed to be finite or infinite. For as when A is moved in the finite time J, all of the finite mobile objects, which are infinite in number, are simultaneously moved. And thus in the same time the whole infinite magnitude is moved simultaneously. Hence an impossibility follows, whichever of these is assumed. It makes no difference whether there is a finite magnitude consisting of magnitudes infinite in number, or whether there is an infinite magnitude whose motion takes place in finite time. For it was shown above that an infinite mobile object cannot be moved in a finite time. Therefore, that which follows, namely, that movers and mobile objects proceed to infinity, is impossible. It is clear, therefore, that one thing being moved by another does not proceed to infinity. Rather this will come to an end somewhere, and there will be some first mobile object which is moved by another immobile thing.

             895. The foregoing proof proceeds from a certain supposition, namely, that all the infinite movers and mobile objects are mutually continuous and constitute one magnitude. And so it might seem to someone that this argument does not conclude without qualifications. Therefore he adds that it makes no difference that this proof has proceeded from a certain supposition. For an impossibility cannot follow from a contingent supposition, even if it is false. Since, therefore, the foregoing argument leads to an impossibility, this impossibility does not follow from the contingent supposition. Rather, it follows from something else which must be impossible, because an impossibility follows from it. And so it is clear that in demonstrations which lead to an impossibility, it makes no difference whether a false or a true contingency is joined to the impossible. For when a false contingency is added, that from which an impossibility follows is shown to be impossible, just as when a true contingency is added. For just as the impossible cannot follow from the true, neither can it follow from the contingent.

             896. But someone might say that it is not contingent that all mobile objects are continuous. Rather it is impossible for the elements to be continuous with each other and with the celestial bodies. But it must be said that the contingent and the impossible are taken in different ways when something is demonstrated of a genus and when something is demonstrated of a species. For when a species is treated, that must be taken as impossible which is repugnant to either the genus or the specific difference from which the nature [ratio] of the species is constituted. But when a genus is treated, everything which is not repugnant to the nature [ratio] of the genus is taken as contingent, even though it may be repugnant to the differentia which constitutes the species. For example, if I am speaking of animal, I can say that every animal being winged is contingent. But if I descend to the consideration of man, it would be impossible for this animal to be winged. Now Aristotle is speaking here about movers and mobile objects in general and is not yet applying his remarks to determinate mobile objects. To be contiguous or continuous is indifferently related to the nature [ratio] of the mover and the mobile object. Therefore, he states as a contingency that all mobile objects are continuous with each other. This, however, is impossible if mobile objects are considered according to their determinate natures.