Page:Mind (New Series) Volume 6.djvu/354

338 B. RUSSELL : By this solution, quantity becomes essentially measure using this word to mean any sort of quantitative comparison. We may now sum up the preceding argument, and give it a positive form. Seeing that number, as used in measure- ment, could not exhaust the nature of quantities, we inferred that this nature was to be found by analysis of the unit. But when we analysed the unit, we found that any attempt to give it quantitative attributes led to a contradiction. We now see that this must be so, for the unit, taken in isolation, is not quantitative at all. What is quantitative is only the relation of the unit to a content which differs from it in a certain manner, and only the possibility of such a relation, which is external to the unit, leads us to speak of the unit as a quantity. The truth of quantity, therefore to use a Hegelian phrase is measure. We no longer have the contradiction that quantity both is, and is not, a mere rela- tion, for our refusal to regard it as a mere relation was based wholly on the view that it must be an intrinsic property of quantities. We can now see the reason why extensive quantities are more amenable to measurement than intensive quantities. For the definition of extensive quantities is, that a change is homogeneous with the quantity changed. Now extensive quantities i.e. spaces and times are themselves relations, and may therefore be homogeneous with that re- lation of difference in which, as we now see, quantity really consists. 1 The terms, being already relations, may be homo- geneous with their difference, which is itself a relatioa. There is also, I think, another reason why the quantitative treatment is felt to be more fundamental in the case of spaces and times. The essential prerequisite for quantity, -as we now see, is the existence of a continuum of qualitatively similar objects, for it is this which renders quantitative com- parison possible. Now in extensive quantities, the con- tinuum is actually given not indeed as a definite whole, but as an extent with vanishing boundaries. The continuum is primarily undivided, and remains indifferent to its divi- sions, which thus appear as bits of it. The assemblage of .all possible temperatures or degrees of pleasure is obviously a, construction of thought ; space and time, on the contrary, seem like " infinite given wholes," of which particular spaces and times are limitations. The continuum required for quantitative treatment is thus more prominent in the case of extensive than in that of intensive quantities it is given, instead of being a mere construction of thought. 1 Of. James, Psychology, vol. ii., pp. 148-51.