LECTURE 9 (205 a 7-206 a 7)

HE PROVES WITHOUT SUPPOSITIONS THAT THERE IS NO ACTUALLY INFINITE SENSIBLE BODY

             358. After the Philosopher has shown, upon the supposition that the elements are finite, that there is no infinite sensible body, he here shows the same thing without qualification and without any supposition.

             First he states his intention. Secondly, he develops his position, where he says, 'It is the nature . . .' (205 a 10).

             He says, therefore, first that in the things which follow it is necessary to consider universally with reference to every body, without any presuppositions, whether any natural body happens to be infinite. From the arguments which follow it should become clear that there is no such thing.

             Next where he says, 'It is the nature . . .' (205 a 10), he proves his position with four arguments. The second argument begins where he says, 'In general, the view . . .' (205 b 24). The third begins where he says, 'Further every sensible body . . .' (205 b 32). The fourth begins where he says, 'In general, if it is impossible . . .' (205 b 36).

             With reference to the first argument he makes three points. First, he assumes certain things which are necessary for the argument. Secondly, he sets forth the argument, where he says, 'Suppose (a) that the infinite . . .' (205 a 13). Thirdly, he refutes a certain false opinion, where he says, 'Anaxagoras gives . . .' (205 b 1).

             359. Therefore, he assumes three things. The first is that every sensible body has a natural aptitude to be in some place.

             The second is that some place, among all the places that are, belongs to each natural body.

             The third is that the same natural place belongs to both the whole and the part, e.g., to the whole earth and to one clod, to the whole of fire and to one spark. A sign of this is that when a part of a body is put in any part of the place of the whole, it rests there.

             360. Next where he says, 'Suppose (a) that the infinite . . .' (205 a 13), he sets forth the argument, which is as follows. If a body is given as infinite, then it is necessary either that the whole be of one species with its parts, such as water or air, or that it have parts of different species, such as a man or a plant.

             If all the parts are of one species, it follows from what has been said either that it is altogether immobile and never would be moved, or that it is always moved. Each of these is impossible. For rest is excluded from natural things by one of these alternatives, and motion is excluded by the other. And in either case the intelligibility [ratio] of nature is destroyed, for nature is a principle of motion and rest.

             He proves that it would follow that [this body] would be totally mobile or totally at rest by the fact that we could not assign a reason why it would be moved upward rather than downward or in any direction.

             He clarifies this with an example. Let us assume that this whole infinite body with like parts is earth. We will not be able to state where some clod of earth would be moved or where it would be at rest, because some body akin to it, i.e., of the same species, will occupy every part of the infinite place. Therefore, can it ever be said that one clod is moved so that it would contain, i.e., would occupy, successively the whole infinite place, as the sun is moved such that it is in every part of the zodiac circle? And how could one clod of earth pass through all the parts of an infinite place? Moreover nothing is moved in an impossible way. If, therefore, it is impossible for a clod to be moved to occupy a whole infinite place, where will its rest be, and where will its motion be? For it is necessary either that it always be at rest, and so never be moved, or that it always be moved, and so never rest.

             361. If, however, the other part of the division is granted, i.e., that the infinite body has parts different in species, it follows that there are different places for the different parts. For the natural place of water is different than the natural place of earth. But from this position it follows first that the body of the infinite whole is not one simply, but accidentally, i.e., by contact. And so there will not be one infinite body, as was supposed.

             362. But since someone might not think that this is inconsistent, he adds another argument against this. He says that if the infinite whole is composed of dissimilar parts, then it is necessary for such parts, which are dissimilar in species, to be of species which are either finite in number or infinite in number.

             But these parts cannot be of finite species. For if the whole is infinite, then certain parts must be finite in quantity and others infinite. Otherwise the infinite could be composed of things which are finite in number. Granting this, it follows that the parts which are infinite would corrupt the others because of contrariety, as was said above in the preceding argument.

             And so none of the ancient natural philosophers who posited one infinite principle said that it was fire or earth, which are extremes. Rather they said that it was water or air or some intermediate between these, because the places of fire and earth are clear and determined, i.e., above and below. However this is not true of water and air. Rather earth is below them and fire above them.

             363. And if one should take the other part of the division, i.e., that these partial bodies are infinite in respect to species, it also follows that places are infinite in respect to species, and that the elements are infinite. If, however, it is impossible for the elements to be infinite, as was proved in Book I, and if it is impossible for places to be infinite, since it is impossible to find infinite species of places, then the whole body must be finite.

             Since he has argued to the infinity of places from the infinity of bodies, he adds that one must equate body and place. For place cannot be greater than the quantity which body happens to have. Nor can there be an infinite body if place is not infinite. Nor can body be greater than place in any way. For if place is greater than body, it follows that there is a void somewhere. And if body is greater than place, it follows that a part of the body is not in any place.

             364. Next where he says, 'Anaxagoras gives . . .' (205 b 1), he refutes a certain error. First he sets forth the error. He says that Anaxagoras maintained that the infinite is at rest. But Anaxagoras did not suitably assign the reason for its rest. For he said that the infinite supports; i.e., sustains, itself, because it is in itself and not in another, since nothing contains it. And so it cannot be moved outside itself.

             365. Secondly, where he says, '. . . on the assumption . . .' (205 b 4), he refutes this position with two arguments. The first of these is that Anaxagoras has assigned the reason for the rest of the infinite as if it is natural for a thing to be where it is. For he says that the infinite is at rest only because it is in itself. But it is not true that a thing is always where it is naturally disposed to be. For some things are where they are by violence and not by nature.

             Therefore, although it is most true that the infinite is not moved since it is sustained by and remains in itself, and thus is immobile, we must still explain why it is not naturally disposed to be moved. For one cannot evade the issue by saying that the infinite is not moved. For there is nothing to prevent us from applying the same argument to anything else which is not moved even though it is naturally disposed to be moved. For if the earth were infinite, then just as it is not moved now when it is at the centre, so also it would not be moved then in respect to that part which would be at the centre. But this is not because there is no place except the centre where it would be sustained. Rather it is because it does not have a natural aptitude to be moved at the centre. If, therefore, it is true in respect to the earth that its infinity is not the reason why it is at rest at the centre (rather the reason is its heaviness by which it is naturally disposed to remain at the centre), so in respect to any other infinite thing there must be a reason to explain why it is at rest. And this reason is not that it is infinite or that it sustains itself.

             366. He sets forth the other argument where he says, 'Another difficulty emerges . . .' (205 b 18). He says that if the infinite whole is at rest because it remains in itself, then it follows of necessity that every part is at rest because it remains in itself. For the place of the whole and the place of the part are the same, as was said above, e.g., above for fire and the spark, and below for earth and the clod. If, therefore, the place of the infinite whole is the whole itself, then it follows that every part of the infinite remains in itself as in its proper place.

             367. He sets forth the second argument where he says, 'In general, the view . . .' (205 b 24).

             He says that it is completely clear that it is impossible to say that there is an infinite body in act and that there is some place for each body, assuming that every sensible body has either heaviness or lightness, as the ancients who posited an infinite said. For if a body is heavy, it must naturally be carried to the centre; if it is light, it must be borne upward. If, therefore, there is an infinite sensible body, then in that infinite body there must be an above and a centre. But it is impossible for an infinite whole to sustain either of these in itself, i.e., either an above or a centre, or even that it sustain each of them in respect to different halves. For how could the infinite be divided so that one part of it is above and the other below? And in the infinite what is the end or the centre? Therefore, there is no infinite sensible body.

             368. He sets forth the third argument where he says, 'Further, every sensible body . . .' (205 b 32). He says that every sensible body is in place. However, there are six different places: above and below, before and behind, to the right and to the left. And these are determined not only with reference to us, but also in the whole universe itself.

             For positions of this sort, in which the beginnings and ends of motion are determined, are determined themselves. Hence in animated things above and below are determined with reference to the motion of growth, before and behind with reference to the motion of sense, to the right and to the left with reference to progressive motion whose starting point is from the right.

             However, in inanimate things in which there are no determinate principles of motions, right and left are named in relation to us. For that column is said to be 'on the right' which is to the right of a man, and that is said to be 'on the left' which is to the left of a man.

             But in the whole universe up and down are determined by the motion of heavy and light things; right is determined by the rising motion of the heavens and left by the falling motion of the heavens; before is the higher hemisphere and behind is the lower hemisphere; up is the meridian and down is the northern region. These, however, cannot be determined in an infinite body. Therefore, it is impossible for the whole universe to be infinite.

             369. He sets forth the fourth argument where he says, 'In general, it is impossible . . .' (205 b 36). He says that if it is impossible for there to be an infinite place, since every body is in place, then it follows that it is impossible for there to be an infinite body.

             He proves as follows that it is impossible for there to be an infinite place. To be in place and to be in some place are convertible, just as to be man and to be some man, and to be a quantity and to be some quantity, are convertible. Therefore, just as it is impossible for quantity to be infinite because it would then follow that some quantity is infinite, e.g., two cubits or three cubits (which is impossible), so also it is impossible for place to be infinite because it would follow that some place is infinite, either above or below or the like. And this is impossible because each of these signifies some limit, as was said above. Therefore, no sensible body is infinite.