Book 11
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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
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The foregoing inquiry is general; but what follows will show that the infinite does not exist in sensible things.
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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.;
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for the contraries must be equal, and no one of them must be infinite; for if the potency of one of the two corporeal elements is in any way inferior, the finite element will be destroyed by the infinite. And every element cannot be infinite, because body is that which has extension in all directions, and the infinite is that which is extended without limit; so that if the infinite is corporeal it will be infinite in all directions.sc. and so no other body can exist beside it.
