Aristotle, Physics. Book III, Chapter 13


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It now remains that we enumerate the reasons through which the infinite appears not only to subsist in capacity, but as that which is definite: for some of these reasons are not necessary; and against others certain other true objections may be urged: for neither is it necessary that there should be an infinite sensible body in energy, in order that generation may not fail; since it is possible that the corruption of one thing may be the generation of another, since the universe is finite. Further still; to touch and to be finite differ from each other: for the former is a relative, and pertains to a certain thing, (since whatever touches, touches something) and is an accident to something finite. But that which is finite is not a relative; nor can anything whatever touch anything whatever. To believe, likewise, in the existence of infinite magnitude because it can be conceived, is absurd: for excess and defect are not in the thing, but in the conception of it: for anyone may conceive each of us to be manifold daily greater than he is, by increasing him infinitely; yet a man will not on this account surpass a city in dimensions, or be of such a magnitude as we possess, because someone has conceived him to be so, but because he does possess such a magnitude. This however, is accidental. But time, motion and intellection, are infinite, that which is assumed not remaining. But magnitude is neither infinite by diminution, nor by intellective increase. And thus concerning the infinite we have shown in what manner it is, and in what manner it is not, and what it is.


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