Commentary Aristotle Physics
He proves that this body would be either entirely mobile or entirely at rest by the fact that no reason can be given for its being moved either up or down or in any direction whatsoever. He makes this clear by an example. Let us suppose that the entire infinite body that is similar throughout is earth. Then it will be impossible to say where any clod of earth should move or be at rest, because each part of infinite place would be occupied by some body related to it, that is, of the same species. Can it be said that one clod of earth would be moved so as to occupy successively all the infinite places, as the sun is moved so as to be in each part of the zodiacal circle? And how could one clod of earth pass through all the parts of infinite place? Now, nothing is moved toward the impossible: if, therefore, it is impossible for a clod of earth to be moved so as to occupy all the infinite places, in which place will it rest and in which will it be in motion? It will either always be at rest, and thus never in motion, or it will always be in motion and thus never at rest.
361. If we suppose the other possibility, that the infinite body has parts that are unlike in species, it will then follow that there would be unlike places for the unlike parts, for the natural place of water is one thing and that of earth is another. But, on this supposition, it follows at once that the body of this infinite whole would not be one body simply, but one through contact, and thus there will not be one infinite body as our supposition granted.
362. Because someone might not consider this impossible, he adds another reason against this, saying that, if the infinite whole is composed of unlike parts, these parts will be either of a finite number of species or of an infinite number.
It will not be the first, because it then follows that, if the whole is infinite, then some of the parts will be finite and some infinite; otherwise, we would be able to get an infinite composed all of finites. On this assumption, it follows that those that are infinite will corrupt the others, on account of contrariety, as was said in previous reasoning. For this reason, no one of the early philosophers who posited one infinite principle posited it to be fire or earth, which are extremes. Rather, they posited water or air or some mean between them, because the places of the former were clear and determinate—namely, above and below. But it is not the same with the others, for earth is below with respect to them and fire above.
363. But, if someone admits the other alternative—namely, that the parts of the body are infinite in species—it follows that their places also are infinite in species, and that the elements are infinite. But, if it is impossible that the elements be infinite, as was already proved in book 1, and that places be infinite, since it is not possible to find infinite species of place, it is necessary to admit that the whole body is finite. And because he had concluded that there is an infinity of places from the infinite of bodies, he adds that it is impossible not to equate body with place, for no place is greater than the body it contains, nor can a body be infinite if its place is not infinite, nor can a body in any way be greater than its place. This is so because, if the place is greater than the body, there will be some empty place; if the body is greater than its place, then some part of the body is in no place.
364. Then, at “Anaxagoras gives” (205b1) he excludes an error.
First, he states the error and says that Anaxagoras claimed that the infinite is at rest but gave an invalid reason for its rest. For he said that the infinite bears itself up—that is, sustains itself—since it exists in itself and not in something else, for nothing contains it. And thus it could not be moved outside itself.
365. Second, at “if we assume” (205b4), he disproves this statement with two reasons.
The first of these is that Anaxagoras so assigned his reason for the rest of the infinite as to suppose that, wherever a thing is, that is its natural place. For the only reason he gave for saying that the infinite is at rest is that it exists in itself. But it is not true that, where a thing is, there it is always naturally disposed to be, because some things are somewhere by force and not by nature.
Now, although it is true that an infinite whole is not moved, because it is sustained and remains in itself and for that reason is immobile, yet a reason should be given why it is not naturally disposed to be moved. One cannot evade this simply by saying that the infinite is not moved, for by the same reasoning, there is nothing to prevent any other body from not being moved while it might be naturally disposed to be moved. For even if earth were infinite, just as now it will not be carried further when it is in the center, so even then no part in the center would move further, but this would not be because it had no other natural place except the center where it could be sustained, but because it does not have a natural aptitude to be moved from the center.
If, therefore, this is the case with earth, that the reason it rests at the center is not that it is infinite but that it has weight that accounts for its remaining in the center, then similarly, in the case of any other infinite, the reason it rests should be given, and this is not simply because it is infinite or that it supports itself.
366. He gives another argument at “another difficulty” (205b18). Thus, he states that, if the whole infinite is in repose because it remains within itself, it follows that any part of it is necessarily at rest, since it remains within itself.
For the place of the whole and that of the part are the same, as was said: for instance, that of fire and a spark upward, that of earth and a clod of earth downward.
If, therefore, the place of the whole infinite is itself, it follows that any part of the infinite will remain at rest within itself as in its proper place.
367. He gives a second reason against Anaxagoras at “in general, the view” (205b24), saying that it is clearly impossible to say both that there is an actually infinite body and that there is some place for each body, if every sensible body is either heavy or light, as the ancients said who posited the infinite. For if the body is heavy, it will be naturally carried to the center; if it is light, it will be carried upward. If, therefore, there be an infinite sensible body, it is also necessary that there be in it an up and a center. But it is impossible that the infinite body should sustain in itself either of these, either an up or a center, or even that it sustain both according to different centers. For how could the infinite be divided so that one part would be “up” and another “down,” or how can there be in the infinite a boundary or a center? Therefore, there is no infinite sensible body.
368. He gives the third reason, at “further, every sensible body” (205b31), saying that every sensible body is in place. But the differences of place are six: above and below, before and behind, and to the right and to the left. These are determined not only in relation to us but even in the whole universe itself. For such positions are determined in themselves in those things in which there are determinate principles and terms of motion. Hence, in living things: “up” and “down” are determined according to the motion of food; “front” and “rear” according to the motion of sense; “right” and “left” according to forward motion, which begins from the right. But in inanimate things, in which there are no determinate principles of such motions, “right” and “left” are said with respect to us, for a column is said to be “at the right” that is to the right of a man, and “at the left” that is at his left of a man. But, in the whole universe, “up” and “down” are determined according to the motion of heavy and light things, while according to the motion of the heavens, the rising sun determines “right” and the setting sun, “left”; “front” is determined by the upper hemisphere and “rear” by the lower hemisphere; “above” by the south and “below” by the north. Now, such things cannot be determined in an infinite body. It is therefore impossible for the whole universe to be infinite.
369. He gives the fourth reason at “in general, if it is impossible” (205b35), saying that, if it is impossible that there be an infinite place because every body is in a place, it follows that there can be no infinite body. That an infinite place is impossible he proves thus. To be in place and to be in some place are convertible, just as to be man and to be some man, or to be quantity and to be some quantity. Therefore, just as it is impossible that there be infinite quantity, because then it would follow that some quantity is infinite (such as two cubits or three cubits), which is impossible, likewise infinite place is impossible, because it would follow that some place is infinite (either up or down or some other place), which is impossible, since each of these implies a definite term, as was said. Therefore, no sensible body is infinite.