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[1067a] [1] nor fire nor any other element.Apart from the question of how any of them could be infinite, the All, even if it is finite, cannot be or become any one of the elements, as Heraclitus says1 all things at certain times become fire. The same argument applies as to the One which the physicists posit besides the elements; for all change proceeds from the contrary, e.g. from hot to cold.2

Again, a sensible body is in some region, and the region of the whole and of the part (e.g. of the earth) is the same.3 Therefore if the infinite body is homogeneous, it will be immovable or will always be in motion4; but this is impossible, for why should there be rest or motion below rather than above or in any other region? E.g., if there were a clod, in what region would it move or be at rest?The region proper to the body which is homogeneous with the clod is infinite. Then will the clod occupy the whole of that region? How can it? Then what of its rest or motion? It will either rest everywhere—in which case it cannot move—or move everywhere; in which case it cannot rest.5 And if the whole is not alike throughout, the regions proper to its parts are unlike also; and (a) the body of the whole is not one, except in virtue of contact; (b) the parts will be either finite or infinite in kind.Finite they cannot be, for then those of one kind would be infinite6 and those of another would not (if the whole is infinite); e.g., fire or water would be infinite. [20] But such a condition would involve the destruction of the contraries. But if the parts are infinite7 and simple, the regions proper to them are infinite and the elements will be infinite. And since this is impossible,8 the regions are finite9 and the whole must be finite.

In general, there cannot be an infinite body and a place for bodies if every body which is sensible has either weight or lightness; for it will have to move either towards the center or upwards, and the infinite—either the whole or the half—cannot do either; for how can you divide it? How can the infinite be part up and part down, or part extreme and part center?Further, every sensible body is in some place, and of place there are six kinds,10 but these cannot exist in an infinite body. In general, if an infinite place is impossible, so is an infinite body; because that which is in a place is somewhere, and this means either up or down or one of the other kinds of place, and each of these is a limit.

The infinite is not the same in the sense that it is one nature whether it applies to magnitude or to motion or to time; the posterior is derived from the prior sense, e.g. motion is called infinite in virtue of the magnitude involved when a thing is moved or changed or increased, and time is so called on account of motion.11

1 Cf. Hereclitus Fr. 20-22 (Bywater).

2 The argument seems to be: Since all change is from contrary to contrary, and it is impossible that either (a) one of the elements should be contrary to the rest, or (b) one material principle should be contrary to all four elements, it follows that no one element, and similarly that no one material principle apart from the elements, can be the ultimate material principle of the universe.

3 i.e., the region of the universe which is proper to a given element is proper also to any part of that element. The proper region of earth is the center, of fire the circumference of the universe. Cf. Aristot. De Caelo 1.2.

4 Ross is evidently right in taking this to refer to the rest or motion of the parts. An infinite body cannot move as a whole, because there is no space outside it.

5 If earth is an infinite body, its region must be infinite. But the infinite has no center (cf. sect. 13). Therefore a clod, which cannot occupy the whole region proper to earth, will have no region proper to itself to which it can move or in which it can rest.

6 sc. in quantity. If the universe is infinite in quantity, and the elements are limited in kind, some of the elements (or at least one) must be infinite in quantity. But this is impossible, just as it is impossible that all the elements should be infinite in quantity. Cf. sect. 7 above

7 sc. in kind or number.

8 Cf. sect. 6 n.

9 Cf. sect. 14 n.

10 i.e., above and below, before and behind, right and left (Aristot. Phys. 205b 31).

11 Cf. Aristot. Met. 5.13.5.

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