266. There is in every judgment perception of identity or non-identity, accordingly as it is affirmative or negative. The verb _is_ does not express the union, but the identity of the predicate with the subject; and when accompanied with the negation _not_, it simply expresses non-identity, abstracting union or separation. This is so true and so exact, that in things really united an affirmative judgment is impossible, because they have no identity. We must, then, in such cases, if we would be enabled to make an affirmation, express the predicate in the concrete, that is, in some sense involving the idea of the subject itself in it; for the same property affirmed in the concrete cannot be in the abstract, but must rather be denied. Thus we may say, man is rational; but not, man is rationality: a body is extended; but not, a body is extension: paper is white; but not, paper is whiteness. Why is this? Is it that rationality is not in man, extension is not united to body, nor whiteness to paper? Certainly not; but if rationality be in man, extension in body, and whiteness in paper, we have only not to perceive identity between the predicates and subjects, to render affirmation impossible; on the contrary, despite the union, we have negation: thus we may say, man is not rationality; a body is not extension; paper is not whiteness. We have said that, in order to save the expression of identity, we used the concrete instead of the abstract term, and involved in the former the idea of the subject. It cannot be said that paper is whiteness, but it may be said that paper is white; for this last proposition means that paper is a white thing; that is, we make the general idea of a _thing_, or the idea of a modifiable subject, enter into the predicate while in the concrete; and this subject is identical with the paper modified by whiteness. 267. Thus it is easy to see, that the expression, _union of the predicate with the subject_, is, at the best, inexact. Every affirmative proposition expresses the identity of the predicate with the subject. Use authorizes these modes of speaking, which still produce some confusion when we endeavor perfectly to understand these matters. And it must be observed, that ordinary language here, as often elsewhere, is admirably exact and appropriate. Nobody says, paper is whiteness, but, paper is white. It is only when we would greatly heighten the degree, to which a subject possesses a quality, that we express it in the abstract, and then we join with it the pronoun _itself_. Thus, speaking hyperbolically, we say a thing is beauty itself, whiteness itself, goodness itself. 268. Even what in mathematics is called equality, also means identity. Thus in this class of judgments, besides what we have observed of general in them all, to wit: the identity saved by expressing the predicate in the concrete, the very relation of equality denotes identity. This needs explanation.