This perception of the intellectual superiority of objects which are constituted at the conclusion of thinking over those which formed its data may fairly be termed the empirical factor in the idealistic logic. The essence of the realistic reaction, on its logical side, is exceedingly simple. It starts from those objects with which science, approved science, ends. Since they are the objects which are _known_, which are true, they are the real objects. That they are also objects for intervening thinking is an interesting enough historical and psychological fact, but one quite irrelevant to their natures, which are precisely what knowledge finds them to be. In the biography of human beings it may hold good that apprehension of objects is arrived at only through certain wanderings, endeavors, exercises, experiments; possibly acts called sensation, memory, reflection may be needed by men in reaching a grasp of the objects. But such things denote facts about the history of the knower, not about the nature of the known object. Analysis will show, moreover, that any intelligible account of this history, any verified statement of the psychology of knowing assumes objects which are unaffected by the knowing--otherwise the pretended history is merely pretense and not to be trusted. The history of the process of knowing, moreover, implies also the terms and propositions--truths--of logic. That logic must therefore be assumed as a science of objects real and true, quite apart from any process of thinking them. In short, the requirement is that we shall think things as they are themselves, not make them into objects constructed by thinking. This revival of realism coincided also with an important movement in mathematics and logic: the attempt to treat logical distinctions by mathematical methods; while at the same time mathematical subject-matter had become so generalized that it was a theory of types and orders of terms and propositions--in short, a logic. Certain minds have always found mathematics the type of knowledge, because of its definiteness, order, and comprehensiveness. The wonderful accomplishments of modern mathematics, including its development into a type of highly generalized logic, was not calculated to lessen the tendency. And while prior philosophers have generally played their admiration of mathematics into the hands of idealism (regarding mathematical subject-matter as the embodiment or manifestation of pure thought), the new philosophy insisted that the terms and types of order constituting mathematical and logical subject-matter were real in their own right, and (at most) merely led up to and discovered by thinking--an operation, moreover, itself subjected (as has been pointed out) to the entities and relationships set forth by logic.