15. Copulative being may be applied without the substantive; thus when we say that the ellipse is curvilinear, we abstract both the existence and non-existence of any one ellipse; and the proposition would be true although no ellipse at all were to exist. The reason is that the verb _to be_, when copulative, expresses the relation of two ideas. 16. This relation is of identity, but in such a way that more than the union of the two is needed before a predicate can be affirmed of a subject. The head is united to the man, but it cannot, therefore, be said, "man is his head;" the sensibility is united to the reason in the same man, but we cannot say, "sensibility is reason;" whiteness is in union with the wall, but we cannot say "the wall is whiteness." The affirmation, then, of a predicate expresses the relation of identity, and this is why, when this identity does not exist with respect to the predicate in the abstract, it is expressed in the concrete, in order that something involving identity may enter into it. The wall is whiteness: this proposition is false, because it affirms an identity which does not exist; the wall is white: this proposition is true, because white means something which has whiteness, and the wall is really something which has whiteness; here, then, is the identity which the proposition affirms.[18] [18] See Bk. I., Chs. XXXVI., XXVII., and XVIII. 17. The predicate is, then, in every affirmative proposition, identified with the subject. When we perceive, therefore, we affirm the identity. Judgment, then, is the perception of the identity. We do not, however, deny that in what we call assent there is often something more than the simple perception of identity; but we do not understand how we need any thing more than to see it evidently in order to assent to it. What we call assent, adhesion of the understanding, seems to be a kind of metaphor, as if the understanding would adhere, would yield itself to the truth, if it were presented; but in reality we very much doubt if, with respect to what is evident, there be any thing but perception of the identity. 18. Hence it follows, that if the same ideas were to correspond in the very same manner to the same words, the opposition and diversity of judgments in different understandings would be impossible. When, then, this diversity or opposition does exist, there is always a discrepancy in the ideas.