34. IDENTITY.—Considering the order in which we acquire our ideas we are easily convinced that the notion of finite being is antecedent to that of infinite being. Moreover, it is from reflection on finite beings that we arrive at the most abstract notion of being in general. We make the object of this latter notion definite only by dividing it off mentally from nothingness, conceived _per modum entis_, or as an _ens rationis_. Thus the natural way of making our concepts definite is by _limiting_ them; it is only when we come to reflect on the necessary implications of our concept of “infinite being” that we realize the possibility of conceiving a being which is _definite_ without being really _limited_, which is definite by the very fact of its infinity, by its possession of unlimited perfection; and even then our imperfect human mode of conceiving “infinite being” is helped by distinguishing or dividing it off from all finite being and contrasting it with the latter. All this goes to prove the truth of the teaching of St. Thomas, that the mental function of _dividing_ or _distinguishing_ precedes our concepts of unity and multitude. Now the concepts of _identity_ and _distinction_ are closely allied with those of unity and multitude; but they add something to these latter. When we think of a being as one we must analyse it further, look at it under different aspects, and _compare it with itself_, before we can regard it as _the same_ or _identical_ with itself. Or, at least, we must think of it twice and compare it with itself in the affirmative judgment “This is itself,” “A is A,” thus formulating the logical _Principle of Identity_, in order to come into possession of the concept of _identity_.(151) Every affirmative categorical judgment asserts _identity_ of the predicate with the subject (“_S is P_”): asserts, in other words, that what we apprehend under the notion of the predicate (_P_) is _really identical_ with what we have apprehended under the _distinct_ notion of the subject (_S_). The synthetic function of the affirmative categorical judgment _identifies_ in the real order what the analytic function of mental abstraction had _separated_ in the logical order. By saying that the affirmative categorical judgment asserts identity we mean that by asserting that “this is that,” “man is rational” we identify “this” with “that,” “man” with “rational,” thus _denying_ that they are _two_, that they are _distinct_, that they _differ_. Identity is one of those elementary concepts which cannot be defined; but perhaps we may describe it as _the logical relation through which the mind asserts the objects of two or more of its thoughts to be really one_.