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.
At the outset, counting was, as we found, merely the perception of a plurality; abstraction being practically at zero. Later on a rudiment of numeration appeared, under a practical concrete form: we have perception plus the word—a poor auxiliary, whose part is so insignificant as to be mostly negligible. We noted the different stages of this concrete abstract period, marked by the increasing importance of the word. Finally we arrived at the point at which it is the prime and almost the only factor. Number under its abstract form, as it results, from a long elaboration, consists in a collection of unities that are, or are reputed, similar. We have therefore first to examine how the idea of unity is formed. Next by what mental operation the sequence of numbers is constituted, lastly what is the part played by the sign.
I. To common sense nothing appears more easy than to explain how the idea of unity is formed. I see a man, a tree, a house; I hear a sound; I touch an object; I smell an odor, and so on: and I distinguish this single state from a plurality of sensations. John Stuart Mill seems to admit that number (at least in its simplest forms) is a quality of things that we perceive, as white, black, roundness, hardness: there is a distinct and special state of consciousness corresponding to one, two, three, etc.
Even if we admit this very doubtful thesis, we should arrive at last only at perceived numbers, with which consistent and extended numeration is impossible. It can only be carried on with homogeneous terms, i. e., such as are given by abstraction.