Book 14
2
He is wrong; for even in the natural world the principles from which these things are derived are perfect and complete—for it is man that begets man; the seed does not come first.Cf. Aristot. Met. 9.8.5. It is absurd also to generate space simultaneously with the mathematical solids (for space is peculiar to particular things, which is why they are separable in space, whereas the objects of mathematics have no position) and to say that they must be somewhere, and yet not explain what their spatial position is.
3
Those who assert that reality is derived from elements, and that numbers are the primary realities, ought to have first distinguished the senses in which one thing is derived from another, and then explained in what way number is derived from the first principles. Is it by mixture? But (a) not everything admits of mixturee.g. to admit of mixture a thing must first have a separate existence, and the Great-and-Small, which is an affection or quality of number (Aristot. Met. 14.1.14) cannot exist separately.; (b) the result of mixture is something different; and unity will not be separable,sc. when it has once been mixed. Cf. Aristot. De Gen. et Corr. 327b 21-26. nor will it be a distinct entity, as they intend it to be.
4
Is it by composition, as we hold of the syllable? But (a) this necessarily implies position; (b) in thinking of unity and plurality we shall think of them separately. This, then, is what number will be—a unit plus plurality, or unity plus the Unequal.
4
And since a thing is derived from elements either as inherent or as not inherent in it, in which way is number so derived? Derivation from inherent elements is only possible for things which admit of generation.And numbers are supposed to be eternal. Cf. Aristot. Met. 14.2.1-3. Is it derived as from seed?
