Commentary Aristotle Physics
Lecture 9. There is no actually infinite sensible body
The preceding consideration of the various cases serves to show us whether it is or is not possible that there should be an infinite sensible body. The following arguments give a general demonstration that it is not possible.
It is the nature of every kind of sensible body to be somewhere, and there is a place appropriate to each, the same for the part and for the whole, such as for the whole earth and for a single clod, and for fire and for a spark.
Suppose that the infinite sensible body is homogeneous. Then each part will be either immovable or always being carried along. Yet neither is possible. For why downward rather than upward or in any other direction? For instance, if you take a clod, where will it be moved or where will it be at rest? For it is supposed the place of the body related to it is infinite.
Will it occupy the whole place, then? And how? What, then, will be the nature of its rest and of its motion, or where will they be?
It will either be at home everywhere, and then it will not be moved; or it will be moved everywhere, and then it will not come to rest.
But if the all [whole] has dissimilar parts, the proper places of the parts will be dissimilar also, and the body of the all will have no unity except that of contact. Then, further, the parts will be either finite or infinite in variety of kind.
Finite they cannot be, for if the all is to be infinite, some of them would have to be infinite while the others were not—for instance, fire or water will be infinite. But, as we have seen before, such an element would destroy what is contrary to it.
(This indeed is the reason that none of the physicists made fire or earth the one infinite body, but either water or air or what is intermediate between them, because the abode of each of the two was plainly determinate, while the others have an ambiguous place between up and down.)
But, if the parts are infinite in number and simple, their proper places too will be infinite in number, and the same will be true of the elements themselves. If that is impossible, and the places are finite, the whole too must be finite; for the place and the body cannot but fit each other. Neither is the whole place larger than what can be filled by the body (and then the body would no longer be infinite). Nor is the body larger than the place, for there would be either an empty space or a body whose nature it is to be nowhere.
Anaxagoras gives an absurd account of why the infinite is at rest. He says that the infinite bears itself up. This is because it is in itself, since nothing else contains it, if we assume that wherever anything is, it is there by its own nature. But this is not true: a thing could be somewhere by compulsion and not where it is its nature to be. Even if it is true as true can be that the whole is not moved (for what is fixed by itself and is in itself must be immovable), yet we must explain why it is not its nature to be moved. It is not enough just to make this statement and then decamp.
Anything else might be in a state of rest, but there is no reason why it should not be its nature to be moved. The earth is not carried along, and would not be carried along if it were infinite, provided it is held together by the center.
But it would not be because there was no other region in which it could be carried along that it would remain at the center, but because this is its nature.
Yet in this case also we may say that it fixes itself. If, then, in the case of the earth, supposed to be infinite, it is at rest not because it is infinite but because it has weight, and what is heavy rests at the center and the earth is at the center, similarly the infinite also would rest in itself not because it is infinite and fixes itself, but owing to some other cause.
Another difficulty emerges at the same time. Any part of the infinite body ought to remain at rest. Just as the infinite remains at rest in itself because it fixes itself, so too any part of it you may take will remain in itself.
The appropriate places of the whole and of the part are alike: for instance, of the whole earth and of a clod the appropriate place is the lower region; of fire as a whole and of a spark, the upper region.
If, therefore, to be in itself is the place of the infinite, that also will be appropriate to the part. Therefore, it will remain in itself.
In general, the view that there is an infinite body is plainly incompatible with the doctrine that there is necessarily a proper place for each kind of body, if every sensible body has either weight or lightness, and if a body has a natural locomotion toward the center if it is heavy, and upward if it is light. This would need to be true of the infinite also.
But neither character can belong to it: it cannot be either as a whole, nor can it be half the one and half the other. For how should you divide it? Or how can the infinite have the one part up and the other down, or an extremity and a center?
Further, every sensible body is in place, and the kinds or differences of place are up–down, before–behind, right–left; and these distinctions hold not only in relation to us and by arbitrary agreement, but also in the whole itself. But in the infinite body they cannot exist.
In general, if it is impossible that there should be an infinite place, and if every body is in some place, there cannot be an infinite body. Surely, what is in a special place is in place, and what is in place is in a special place. Thus, just as the infinite cannot be quantity—that would imply that it has a particular quantity, like two or three cubits, for quantity just means these—so a thing’s being in place means that it is somewhere, and that is either up or down or in some other of the six differences of position, but each of these is a limit.
358. After showing that there is no infinite sensible body on the assumption that the elements are finite, the Philosopher here shows the same absolutely, without assumptions of any kind.
First, he declares his intention;
second, he carries out his proposal, at “it is the nature” (205a10; [359]).
He says first (205a7) that, in what follows, it is necessary to consider every body universally, without any suppositions, and ask whether any natural body can be infinite. And, from the following reasons, it will be clear that none can.
Then, at it is the nature (205a10; [359]), he proves his proposition with four reasons.
The second reason begins at “in general, the view” (205b24; [367]);
the third at “further, every sensible body” (205b31; [368]);
the fourth at “in general, if it is impossible” (205b35; [369]).
In regard to the first reason, he does three things:
first, he lays down certain facts presupposed by his reasoning;
second, he gives the reasoning itself, at “suppose that the infinite” (205a12; [360]);
third, he excludes a false opinion, at “Anaxagoras gives” (205b1; [364]).
359. Therefore (205a9), he lays down three presuppositions:
First, that every sensible body has a natural aptitude to be in some definite place.
Second, that every natural body has, among available places, some place that befits it.
Third, that the natural place of the whole and that of the part are the same, such as of all earth and each clod or of all fire and each spark. A sign of this is that a part of some body is at rest in any part of the whole in which it is placed.
360. Then, at “suppose that the infinite” (205a12), he gives the reason, which is this. If an infinite body be supposed, it must have parts either of the same species, as water or air, or of varying species, as a man or a plant has.
If all its parts are of the same species, it follows according to our presuppositions that either it is entirely immobile and is never moved or it is always being moved. But both of these are impossible: in the second case, rest is excluded from natural things; and in the other, motion. Thus, in both cases, the account of nature is denied, for nature is a principle of motion and of rest.