Logic deals with the true significance of the principle of identity (also with that of contradiction; the exact relation of these two, and the various modes of stating it are controversial matters outside the present subject). The proposition A = A is axiomatic and self-evident. It is the primitive measure of truth for all other propositions; however much we may think over it we must return to this fundamental proposition. It is the principle of the distinction between truth and error; and he who regards it as meaningless tautology, as was the case with Hegel and many of the later empiricists (this being not the only surprising point of contact between two schools apparently so different) is right in a fashion, but has misunderstood the nature of the proposition. A = A, the principle of all truth, cannot itself be a special truth. He who finds the proposition of identity or that of non-identity meaningless does so by his own fault. He must have expected to find in these propositions special ideas, a source of positive knowledge. But they are not in themselves knowledge, separate acts of thought, but the common standard for all acts of thought. And so they cannot be compared with other acts of thought. The rule of the process of thought must be outside thought. The proposition of identity does not add to our knowledge; it does not increase but rather founds a kingdom. The proposition of identity is either meaningless or means everything. Upon what do the propositions of identity and of non-identity depend? The common view is that they are judgments. Sigwart, for instance, who has recently discussed the matter, puts it as follows: The two judgments A is B and A is not B cannot be true at the same time because the judgment “An unlearned man is learned” would involve a contradiction because the predicate “learned” is affirmed of a subject of which the judgment has been made implicitly that he is unlearned, so that in reality two judgments are made, X is learned and X is unlearned. The “psychologismus” of this method of argument is plain. It has recourse to a temporary judgment preceding the formation of the conception “unlearned man.” The proposition, however, A is not A claims validity quite apart from the past, present, or future existence of other judgments. It depends on the conception “unlearned man.” It makes the conception more certain by excluding contradictory instances. This, then, gives us the true function of the principles of identity and non-identity. They are materials for conceptions.