In conclusion, have we general ideas, or merely general terms? It must first be remarked that the expressions, “general ideas or notions,” “concepts,” are equivocal or rather multivocal. We have seen that concepts differ widely in their psychological nature according to their degree, having but one characteristic in common—that of being extracts. It is therefore chimerical to attempt to include them all under a single definition. To take the highest only, as most frequently debated, some say, “There are no general ideas but only general terms.” To others the general idea is only an indefinite series of particular ideas, or “a particular idea that the mind proposes as the first stake in a forward march.”[88] To others it is a system of tendencies accompanied or not by the possibility of images.[89] For my own part I prefer the formula of Höffding[90]: “General ideas exist therefore in the sense that we are able to concentrate the attention on certain elements of the individual idea, so that a weaker light falls on the other elements.” This is the sole mode of existence that can be legitimately conceded to them. In regard to the higher concepts we have endeavored to show that they have their distinctive psychological nature: on the one hand a clear and conscious element which is always the word, and sometimes in addition the fragmentary image; on the other an obscure and unconscious factor,—without which, nevertheless, symbolic thought is only a mechanism turning in the air, and producing naught but phantoms. CHAPTER V. EVOLUTION OF THE PRINCIPAL CONCEPTS. After this general study of the nature of the most elevated forms of abstraction, we must take the principal concepts one by one, and retrace their evolution in outline. Let us once more note that we are concerned with pure psychology, and are to eliminate all that depends on the theory of knowledge and other transcendental speculations. As regards the _first_ origin of our notions of time, space, cause, etc., each may adopt the opinion that pleases him. Whether we admit the hypothesis of _à priori_ forms of the mind (Kant), or that of an innate sense acquired by repetition of experience in the species, and fixed by heredity in the course of centuries (Herbert Spencer), or any other whatsoever—it is clear that the appearance of these concepts, and the data of their evolution, depend on experimental conditions, and consequently fall within our province. Accordingly it is with their empirical genesis, and development through experience, that we are concerned—and with that alone. SECTION I. CONCEPT OF NUMBER. The lower phases of this concept are already known to us. We have traversed them in considering numeration, in brutes, children, and aborigines. And here we return to it finally under its higher aspects.