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 B. A. W. RUSSELL, Essay on the Foundations of Geometry. 401 mere sense -perception indeed he has already repeatedly done so. But in that case his whole argument vanishes ; since it can at best only prove that a perception of different existents must precede, as psychological condition, any other kind of cog- nition. Mr. Russell fails therefore to prove even that one form of externality, time, is necessary to the diversity implied in judg- ment ; for he does not prove, what indeed he cannot prove, since he presupposes it, that there would be no diversity, unless we perceived diverse existents, but only that we could not come to know of it. But it is necessary for him to go farther, and to maintain that time alone is not sufficient. And here it seems possible to join issue with him on a mere question of fact. For he assumes that the complexity of an object presented in time alone must be purely adjectival, i.e. presumably containing a diversity of content only, not of existents. But, in fact, nothing seems more certain than that my mental state at any moment must be regarded as containing a diversity of existents, which are certainly not in space. The pleasure I have simultaneously with the cognition of a certain object is not merely diverse in content from that cognition ; for this would be equally true of it when the cognition was repeated without the pleasure. There is therefore some other diversity between a cognition that is present and a pleasure that is present than the mere diversity between pleasure and cognition. And it seems impossible to distinguish this additional diversity from that diversity of existence which distinguishes different things in space, or which distinguishes my pleasure at one moment from my pleasure at another. It seems then certain that diverse mental things can both exist and be known to exist simultaneously, although they are not in space, and hence the argument that space is necessary for the experience of diversity is reduced to the psychological argument that a cognition of things in space is necessary either as cause or as simultaneous condition for the cognition of our own mental states. There is one other point in Mr. Russell's philosophical conclu- sions about space which seems to rest on the same confusion about the relation of logical presupposition. This is his treatment of the antinomies. Mr. Russell thinks that these can all be avoided if ' space is regarded, so far as it is valid, as only spatial order ' (p. 196) or ' as relations between unextended material atoms ' (p. 198). ' Empty space, which arises by an inevitable illusion out of the spatial element in sense-perception, may be regarded, if we wish to retain it, as the bare principle of relativity, the bare logical possibility of relations between diverse things ' (ib.). I think we might retort on Mr. Russell the dictum which he quotes from Lotze that ' contradictions in a necessary subjective intuition form as great a difficulty as in anything else ' (p. 196) ; for it seems impossible to distinguish a ' necessary 26