Aristotle, Metaphysics

[1086b] [1] They considered that the particulars in the sensible world are in a state of flux, and that none of them persists, but that the universal exists besides them and is something distinct from them.This theory, as we have said in an earlier passage,¹ was initiated by Socrates as a result of his definitions, but he did not separate universals from particulars; and he was right in not separating them. This is evident from the facts; for without the universal we cannot acquire knowledge, and the separation of the universal is the cause of the difficulties which we find in the Ideal theory.Others,² regarding it as necessary, if there are to be any substances besides those which are sensible and transitory, that they should be separable, and having no other substances, assigned separate existence to those which are universally predicated; thus it followed that universals and particulars are practically the same kind of thing. This in itself would be one difficulty in the view which we have just described.³

Let us now mention a point which presents some difficulty both to those who hold the Ideal theory and to those who do not. It has been stated already, at the beginning of our treatise, among the problems.⁴ If we do not suppose substances to be separate, that is in the way in which particular things are said to be separate, we shall do away with substance in the sense in which we wish to maintain it; but if we suppose substances to be separable, [20] how are we to regard their elements and principles?If they are particular and not universal, there will be as many real things as there are elements, and the elements will not be knowable. For let us suppose that the syllables in speech are substances, and that their letters are the elements of substances. Then there must be only one BA, and only one of each of the other syllables; that is, if they are not universal and identical in form, but each is numerically one and an individual, and not a member of a class bearing a common name.(Moreover, the Platonists assume that each Ideal entity is unique.) Now if this is true of the syllables, it is also true of their letters. Hence there will not be more than one A, nor more than one of any of the other letters,⁵ on the same argument by which in the case of the syllable there cannot be more than one instance of the same syllable. But if this is so, there will be no other things besides the letters, but only the letters.

Nor again will the elements be knowable; for they will not be universal, and knowledge is of the universal. This can be seen by reference to proofs and definitions; for there is no logical conclusion that a given triangle has its angles equal to two right angles unless every triangle has its angles equal to two right angles, or that a given man is an animal unless every man is an animal.