Page:Mind (New Series) Volume 6.djvu/349

 ON THE RELATIONS OF NUMBER AND QUANTITY. 333 is homogeneous. Since all extensive quantities may be re- garded as parts of larger extensive quantities, this means that the whole collection may be regarded as parts of an infinite whole out of which they are divided. It is to be observed that all these properties belong to space and time. I have now to prove that extensive quantity contains a contradiction which is precisely the same as that contained in space and time, the contradiction, namely, of being at once a relation or adjective and more than a mere relation or adjective. A change of extensive quantity, we said, is itself an ex- tensive quantity. But a change is an adjective of the thing changed, which must be supposed to preserve its identity throughout the change. Hence, either the original quantity was not a mere adjective, but to some extent a thing, capable of varying determinations without loss of identity ; to this alternative there are tw opbjections first, the change of ex- tensive quantity is a mere adjective of the original quantity, with which it is thus not homogeneous, and second, the original quantity, though merely a quantity, is capable of preserving its identity while becoming merely another quantity, which is absurd. Or the original and subse- quent quantities, and the change of quantity, are all adjectives of something distinct from them ; but in this case, it becomes absurd to speak of dividing quantities parts of an adjective are meaningless. Thus extensive quantity is an adjective, because it is homogeneous with a change, which is necessarily adjectival ; but it is not a mere adjective, because it can be divided and has parts. Precisely the same antinomy may be derived, as is more commonly done, from infinite divisibility. For since any extensive quantity is divisible, it is possessed of some thiughood ; since it has parts, it is a complex thing ; now any complex thing must be composed of simple things ; but this composi- tion out of simple things is precisely what infinite divisibility denies. An extensive quantity must, therefore, it would seem, be a hypostatised adjective or relation. When we cease to hypostatise it, it becomes intensive its divisibility ceases, and a change of quantity is no longer homogeneous with the quantity changed. This brings us to the consideration of the second kind of quantity, the intensive. At this point, it will be well to consider briefly the funda- mental similarity and difference between the ideas of number and quantity. Both depend, to begin with, upon the appli- cation of the same conception to different contents. In