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.¹ 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, 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,² 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. 1087aOn the other hand, if the first principles are universal, either the substances composed of them will be universal too, or there will be a non-substance prior to substance; because the universal is not substance, and the element or first principle is universal; and the element or first principle is prior to that of which it is an element or first principle. All this naturally follows when they compose the Ideas of elements and assert that besides the substances which have the same form there are also Ideas each of which is a separate entity. But if, as in the case of the phonetic elements, there is no reason why there should not be many A’s and B’s, and no “A itself” or “B itself” apart from these many, then on this basis there may be any number of similar syllables. The doctrine that all knowledge is of the universal, and hence that the principles of existing things must also be universal and not separate substances, presents the greatest difficulty of all that we have discussed; there is, however, a sense in which this statement is true, although there is another in which it is not true. Knowledge, like the verb “to know,” has two senses, of which one is potential and the other actual. The potentiality being, as matter, universal and indefinite, has a universal and indefinite object; but the actuality is definite and has a definite object, because it is particular and deals with the particular. It is only accidentally that sight sees universal color, because the particular color which it sees is color; and the particular A which the grammarian studies is an A. For if the first principles must be universal, that which is derived from them must also be universal, as in the case of logical proofs³; and if this is so there will be nothing which has a separate existence; i.e. no substance. But it is clear that although in one sense knowledge is universal, in another it is not.