Page:Mind (New Series) Volume 6.djvu/351

ON THE RELATIONS OF NUMBER AND QUANTITY. 335 type for our discussion. Pleasure is unrelated with any extensive quantity unless it were the coinage it is wholly subjective, and it is commonly regarded as a quantity. It has, therefore, every characteristic required for a type of intensive quantity. A measure of pleasures, as Hedonists have to acknowledge, is unattainable. A sum of pleasures, as their opponents have urged, is not itself a pleasure. Similarly a difference of pleasures is not a pleasure, and a "balance of pleasures over pains " is unmeaning. All these are properties of intensive quantities generally, and reveal the fundamental impossi- bility of a Calculus of intensive quantities. For a strict Hedonist, the problem of weighing two small pleasures against one big one ought to be meaningless, since an aggregate of two pleasures does not form a single quantity of pleasure. But, further, if we take quantity as a category, applicable to single quantities, there is, if I am not mistaken, a con- tradiction in the idea of intensive quantity. Intensive quantity, while it must be regarded as belonging, in different measures, to the separate terms of a quantitative comparison, must also be a mere relation between those terms, and thus in its essence ratio, or, in the looser sense, measure. The measurement of intensive quantities is only possible as to the more or less, and is effected, not by any objective or scientific test, but by immediate subjective comparison. The kind of comparison involved can only be indicated, not described, and the possibility of exhausting the differences of two quantities by this kind of comparison is what constitutes them quantities of the same kind. Now two intensive quantities of the same kind, in all the conceptual pro- perties which can be assigned to either alone, are completely identical ; the difference of quantity, therefore, is a difference in a property which appears not to exist before comparison. To return to our former example : suppose we have two pleasures which, so far as they are quantitative, are both abstract or mere pleasure. Then qud mere pleasure, the two are conceptually identical ; the quantity of either is not a thing describable per se, but is simply and solely that which makes one pleasure greater than the other. This would seem to reduce intensive quantity to a relation between two terms, and yet, in asserting that one term is greater than another, we definitely assert so we agreed at the beginning of this discussion that each separately has a quantity. It is impossible, therefore, if quantity be an intrinsic pro- perty of quantitative things, to content ourselves with the