Finally, with the word—the substitute for the abstract intuition—the mental dissociation approximates to a real dissociation: the abstract character, incarnated in the word, seems, as happens only too often, to exist by itself. The process of abstraction, with its fitting instrument, is completely constituted. During these successive phases, and afterwards, throughout the course of the historical development of human intelligence, the progress of abstraction and of generalisation, depends upon two principal causes: one general, i. e., utility; the other accidental and sporadic, the advent of inventors. I. In his book on _Darwinism_ (Ch. XV.) Wallace, in contesting the theory that applies the law of conservation of variations, useful in the struggle for existence, to the mental faculties, insists at length upon the mathematical faculty; he maintains that it is an inexplicable exception, a case that cannot be reduced to law. The inaptitude of inferior races for even the simplest calculations is well known; how—from such a rudimentary origin—could it develop into the genius of a Newton, a Laplace, or a Gauss? What motive power accounts for this development? The author establishes by a host of sufficiently useless historical details, that mathematical superiority played no part in the struggle of tribe with tribe, and later on of people with people (Greeks against Persians), and that the victory resulted from other causes, moral and social. For this there is abundant evidence. But since mathematical aptitude is only a particular instance of abstraction, albeit one of the most perfect, the question ought to be proposed under a more general form. Had the aptitude for abstraction, _ab initio_, any practical value? Yes, “the motive power that caused its development, that Wallace claims without specifying it, is utility.” To avoid possibility of equivocation, let us remark that the development of the attitude for abstracting and generalising may be explained in a two-fold manner: by acknowledging the influence of heredity, and by omitting it. In the former case, it is supposed that this aptitude appears as a “spontaneous variation” in the individual or race, that it fixes itself, is reciprocal, grows by slow accumulation in the course of generations. This theory postulates the heredity of acquired characters, which is accepted by some, rejected by others, more especially since the advent of Weismann. I refrain from invoking it, by reason of its hypothetical and disputed nature. The probability of any transmission would moreover be far harder to establish here than in other psychical directions, such as imagination, or feeling.