ON THE EELATIONS OF NUMBEE AND QUANTITY. 337 A, B, C, of which A is indistinguishable from B, and B from C, but not A from C. Then on a purely sensational basis we have necessarily A = B, B = C, A^C. To avoid this contradiction, we have to assume that B is not equal to A and C, and with this assumption w r e have abandoned the purely sensational nature of quantity. Im- mediate comparison remains the ultimate arbiter as to differences of quantity, but it may force thought to assume differences where it cannot discover them itself. The idea of continuous quantity, of the ordered series proceeding by infinitesimal gradations, is thus a product of thought. Quantities may be given in sense, but they become quantity only by an act of thought. Quantity, then, is conceptual, but is not an intrinsic property of quantitative things. What, under these cir- cumstances, must quantity be ? There remains one possible view, and this I think is the truest. We held that quantity must be intrinsic, because we supposed it to be a common property of quantities. Just as mass is a common property of masses, discoverable by abstraction from their individual peculiarities, so, we held, quantity must be a common property of quantities. This seemed obvious, but I believe it was the source of all our difficulties. Quantity is not a common property of quanti- tative things, any more than similarity is a common property of similar things. Quantity is a conception of relation, of comparison ; it expresses the possibility of a certain kind of comparison with other things. Whether this comparison is possible or not, depends, primarily at any rate, not on the nature of the quantitative thing, but on the possible ex- istence of other things sufficiently similar for quantitative comparison. With this, our previous difficulties cease. A quantity is any content whatever, so soon as this content is capable of a certain kind of comparison with other con- tents. 1 In a quantity, taken in isolation, we cannot dis- cover, therefore, any of the properties of quantity. A quantity is really as improper an expression, for things which can be quantitatively compared, as " a likeness " for a photograph. To search for the nature of quantity in malysis of particular quantities, therefore, is as absurd as to search for the nature of likeness in a study of photography. 1 Cf. Bosanquet's Logic, vol. i., p. 124. 22
