Page:Mind (New Series) Volume 6.djvu/352

336 B. RUSSELL: view that quantity is an independent category. Both in ex- tensive and in intensive quantity, this view leads to hopeless contradictious. It remains to adopt the other view, that quantity is an immediate sense-datum, irreducible, like colour or sound, to conceptual terms. To this view too, I fear, we shall find fatal objections. What, to begin with, does quantity mean on our present hypothesis ? We have a series of distinguishable psychical states, all having a certain aspect which we call by a certain name. But among the instances of this aspect, comparison discovers differences differences which, though they exist between the instances of one conception, cannot be used, like the differences between species of the same genus, for the formation of fresh and more specialised conceptions. We are brought back, in fact, to immediate sensible appre- hension : just as the difference between red and green remains for ever indescribable in conceptual terms, so the difference between two quantities of the same kind seems irreducible and ultimate. We seem at last to have reached quantity pure and simple, which was not attainable as the limit of arithmetical development, nor yet as an intrinsic conceptual property of quantitative things. Nothing can be said of quantity, in our present sense, except that we have series of sensations, feelings and emotions, which, while they are so similar that we apply the same name to all, can yet, by means of this one irreducible aspect of intensity, be arranged in a graduated scale of greater and less. But with the definite, measurable, objective quantities of mathematics, this purely psychical, non-measurable, indivisible intensity has nothing whatever to do. For mathematics, therefore, such a result is utterly barren. But there are other reasons for not resting content with this result. M. Poincare, in a very able article on the mathematical continuum, 1 has satisfactorily proved, I think, that quantity must be conceptual. Quantities may un- doubtedly be given in sense, but not quantity. The reason is this. If quantity be sensational, two quantities which give indistinguishable sensations must be equal. Now the smallest perceptible differences of sensation are finite, so that no ground can exist, if quantity be sensational, for the creation of the continuum. Nevertheless there is ground for the continuum. Suppose we have three sensations 1 Revue de M&. et de Morale, January, 1893. I take this opportunity of calling attention to the splendid work which this review, and the school it represents, have done on our present question and on the kindred question of Zeno's arguments against motion.