Book 11
3
Again, how can the infinite exist independently unless number and magnitude, of which infinity is an attribute, also exist independently?Aristotle has argued that they do not in Aristot. Met. 1.9.16-25. And further, if the infinite is accidental, it cannot, qua infinite, be an element of things; just as the invisible is not an element of speech, although sound is invisible. It is clear also that the infinite cannot exist actually.
4
Otherwise any part of it which we might take would be infinite; for infinity and the infinite are the same, if the infinite is substance and is not predicated of a subject. Therefore it is either indivisible, or if it is partible, the parts into which it is divisible are infinite. But the same thing cannot be many infinites; for just as a part of air is air, so a part of the infinite will be infinite, if the infinite is a substance and principle.
5
Therefore it is impartible and indivisible. But this is impossible of the actually infinite, because it must be some quantity. Therefore infinity is an accidental attribute. But if so, as we have said, it cannot be it that is a principle, but that of which it is an accident: airAccording to Anaximenes; cf. Theophrastus, Phys. Opin. Fr. 2 (Ritter and Preller 26). or the even. According to the Pythagoreans. Cf. Aristot. Met. 1.5.5. n
5
The foregoing inquiry is general; but what follows will show that the infinite does not exist in sensible things.
6
If the definition of a body is that which is bounded by surfaces, then no body, whether sensible or intelligible, can be infinite nor can there be any separate and infinite number, since number or that which involves number is numerable. This is clearly shown by the following concrete argument. The infinite can neither be composite nor simple. For (a) it cannot be a composite body if the elements are limited in numberThis is proved in Aristot. Physics 1.6.;
