Page:Mind (New Series) Volume 8.djvu/268

254 CRITICAL NOTICES: vening length in the author's sense. As, however, the subsequent discussion is confined to the dissimilarity of measurable quantities of the same kind, the above limitation does not impair the validity of the argument. The dissimilarity of two quantities is evidently capable, at most, of a substitutive measurement. Where the quantities themselves are measurable, the dissimilarity must be measured, if measurable at all, by some function of the two quantities. This function is not the mathematical difference, for the dissimilarity is infinite when one of the quantities is zero and the other finite. Moreover, the mathematical difference is a radically distinct idea, dependent wholly on divisibility. Thus the difference of two lengths is a length, but their dissimilarity is a relation. The dissimilarity between 1 and 2 is greater than that between 6 and 7, though the difference is the same. Also the mathematical differences may differ when the dissimilarities are the same. This distinction is certainly of great importance. It is one, moreover, which mathematics and preoccupation with spatio- temporal quantities tend to obscure. In finding a function for measuring dissimilarity, certain requirements are laid down. (1) The dissimilarity must vanish when the quantities are equal ; (I It must be infinite when one quantity is finite and the other is zero infinite ; (3) The dissimilarity between A and B plus that betweer B and C must be equal to that between A and C. These conditior are essentially similar to those which, in non-Euclidean Geometrj regulate the expression of distance in terms of co-ordinates, anc Herr Meinong might have simplified a needlessly complicated piece of mathematics by reference to this analogous case. The conclusion is, that the function required is the logarithm of the ratio, just as, in non-Euclidean Geometry, it is the logarithm of the Anharmonic Eatio. 1 To this conclusion, if we remember the meaning of substitutive measurement, there seems no valid obj( tion. It must be remembered that, in such measurement, the er to be attained is mainly practical theoretically, the quantitie in question are not measured at all. But there is a propositioi essential to Herr Meinong' s formula, which has great theoretic importance. If the dissimilarity of A and B is equal to that of and D, then A, B, C, D are proportionals a theorem which, correct, throws a new light on Weber's Law. The fifth section deals with psychical measurement and the terpretation of Weber's Law. This section is somewhat marrec I think, by a division of psychical quantities into extensive and intensive. The author does not accept the view that psychical quantities must be intensive. He urges, in agreement with Mr. Bradley, 2 that psychical quantities may be extensive, since the pr 1 Cf., e.g., Whitehead, Universal Algebra, book vi., chap. i. 2 " What Do We Mean by the Intensity of Psychical States ? " Mi 1895.