[88] Dugas. Du Psittacisme et de la pensée symbolique, pp. 121 et seq.
[89] Paulhan. Revue philosophique. July, 1889, pp. 77 et seq.
[90] Höffding. Psychologie. Eng. tr., p. 168.
[91] Maclellan & Dewey (Psychology of Number and Its Application to Methods of Teaching Arithmetic, New York, 1895) made pedagogical deductions from this fact. They ask, for beginners, that the examples should be borrowed from continuous quantity, and that number be considered as a particular species of measure.—In his book Our Notions of Number and Space (Boston, 1894) Nichols, taking a theory of James about judgments of number as the basis of his experiments, tries to show that the simultaneous sensation of two points applied to the skin originates in the successive sensation of a distinct contact upon two separate tactile circles.
[92] I do not insist on any such rash thesis. A discussion of it will be found in the Report of the Int. Congress of Exp. Psychol. in London (cit., pp. 35-41).
[93] Psychology, II., p. 653.
[94] Liard, La science positive et la métaphysique, p. 226. It should be remarked that the process by subtraction is met with even among uncivilised people, though very rarely. The plan of making numerals by subtraction, says Tylor (op. cit., I., p. 264), is known in North America, and is well shown in the Aino language of Yesso, where the words for 8 and 9 obviously mean “two from ten,” “one from ten.”
[95] “The childish and savage practice of counting on the fingers and toes lies at the foundation of our arithmetical science. Ten seems the most convenient arithmetical basis offered by systems founded on hand-counting, but twelve would have been better, and duodecimal arithmetic is in fact a protest against the less convenient decimal arithmetic in ordinary use. The case is the not uncommon one of high civilisation bearing evident traces of the rudeness of its origin in ancient barbaric life.” (Tylor, loc. cit., I. p. 272)
[96] For the most recent view of this discussion, with the arguments on either side, see Couturat: De l’Infini mathématique (1896). 2nd part. Bk. III.
[97] Cournot, op. cit., I., p. 331 et seq. Renouvier, Logique, I., pp. 377-394. Poinsot, Théorie nouvelle de la rotation des corps, p. 78.