[69] De l’intelligence, I., Bk. IV., Chap. I., p. 254, first ed.
[70] Mental Evolution in Man, pp. 74 and 75.
[71] As Paulhan remarks, “L’abstraction et les idées abstraites” (Revue Philosophique, Jan., 1889, p. 26 et seq.), these two processes are initially linked one with the other, so that we find analytical syntheses, and synthetical analyses.
[72] Op. cit., VIII., 158-165.
[73] We have touched on this subject incidentally in La psychologie des sentiments (Part II, IX, § 2, pp. 305 et seq.). Many tribes do not get beyond polydemonism, peopling the universe with innumerable genii; this is the reign of the concrete. A certain progress is marked by subordinating the genius of each tree to the god of the forest, the different genii of a river to the god of the river, etc. At a degree higher, the intellect constitutes a single god for water, one for fire, one for the earth, etc. Thus there come to be genii of individual, specific, and generic origin.
[74] Tylor, Primitive Culture, I., gives abundant data on this question. Chap. VII. is entirely devoted to it.
[75] In the account of his travels among the Damaras (in his Tropical South Africa, p. 133) Galton says: “In practice, whatever they may possess in their language, they certainly use no numeral greater than three. When they wish to express four, they take to their fingers, which are to them as formidable instruments of calculation as a sliding-rule is to our English schoolboy. They puzzle very much after five, because no spare hand remains to grasp and secure the fingers that are required for ‘units,’—yet they seldom lose oxen: the way in which they discover the loss of one, is not by the number of the herd being diminished, but by the absence of a face they know.” [This tallies with what we said above, [Chap. I.], as to so-called numeration in animals and children.] “When bartering is going on, each sheep must be paid for separately. Thus suppose two sticks of tobacco to be the rate of exchange for one sheep, it would sorely puzzle a Damara to take two sheep and give him four sticks. I have done so and seen a man first put two of the sticks apart and take a sight over them at one of the sheep he was about to sell. Having satisfied himself that one was honestly paid for, and finding to his surprise that exactly two sticks remained in hand to settle the account for the other sheep, he would be afflicted with doubts; the transaction seemed to come out too pat to be correct, and he would refer back to the first couple of sticks, and then his mind got hazy and confused, and wandered from one sheep to the other, and he broke off the transaction until two sticks were put into his hand and one sheep driven away, and then the other two sticks given him and the second sheep driven away.” Galton relates many other similar facts which he had himself witnessed.
[76] And the barley-corn of English measure.—Tr.
[77] Wundt (Logik, I., pp. 113 et seq.) gives what he regards as a complete classification of concepts, but it does not correspond with our design. It may be summarised as follows. Four classes: I. Identical or equivalent concepts; Aristotle = Alexander’s tutor. II. Subordinate or superordinate concepts; mammals and vertebrates, etc. III. Co-ordinated concepts, comprising five species: i. Disjunctive concepts; sound and noise, French and German, etc. They are subordinate to a larger concept. ii. Correlative concepts, with reciprocal relations; men and women, mountain and valley. iii. Contrary concepts; high and low, good and bad. iv. Contingent concepts; such, i. e., as touch, with very minute, perceptible differences; this highly important category comprises numbers. v. Interferent concepts, which coincide or partially cross; negro and slave, rectangle and parallelogram. IV. Concepts which are interdependent; etc., space and movement, crime and punishment, demand and supply, labor and wages. This table may suit the logician but not the psychologist, because it presents the concepts under what may be termed the static order, i. e., ready formed: we, on the other hand, are considering them as dynamic, i. e., in their becoming and order of genesis.
[78] For details, with quotations in point, consult Agassiz: De l’espèce, Chap. III., and E. Perrier, La Philosophie zoologique avant Darwin, Chap. II.