Page:Mind (New Series) Volume 8.djvu/416

402 CRITICAL NOTICES subjective intuition ' from his own ' unavoidable psychological illusion ' : the only possible distinction lies in the word ' illusion,' which, however, is not a psychological term, but is distinguished from 'intuition,' only as implying that its object is false the very thing which the ' intuition ' presupposed and was invented to explain. But we can not only say that such an explanation fails to avoid the difficulty ; it seems that the reason why it does fail is that it involves a definite logical error. For it is only, if our intuition of space be true, that we have any reason to believe in these relations between unextended atoms ; in other words, empty space and spatial order are equally presupposed in experience, and if we reject the one, we have no longer any reason for accepting the other. The same result seems to follow from a consideration of the other phrase by which Mr. Eussell tries to explain away empty space. ' A mere name for the logical possibility of spatial relations ' (p. 197) can surely mean nothing but ' that which renders spatial relations possible ' ; and hence if there be no empty space, it would seem to follow that there can be no spatial relations. This point seems to be closely connected with another philo- sophical error which constantly appears throughout Mr. Eussell's mathematical discussions an error which seems to arise from a certain ambiguity in the use of the term 'relativity'. Thus Mr. Eussell states on page 160 ' Position is not an intrinsic, but a purely relative, property of things in space. If there could be such a thing as absolute position, in short, metrical Geometry would be impossible.' This statement Mr. Eussell seems to regard as equivalent to the statement that all points are qualitatively similar ; and he seems to base it upon the fact that ' so long as we leav matter out of account, one position is perfectly indistinguish- able from another ' (p. 77). A similar argument is used with regard to the relativity of magnitude. ' Magnitude ' he says ' is nothing apart from comparison ' (p. 87) ; and again ' To speak of differences of magnitude in a case where comparison cannot reveal them, is absurd ' (p. 154). But it would seem that this is a purely psychological argument : it assumes that nothing is distinct unless it has some property which will enable the mind to distinguish it. Mr. Eussell himself seems sufficiently to expose the fallacy of this assumption in a note on page 165, where he says ' although measurement and the judgment of quantity express the result of comparison, yet the terms compared must exist before the comparison'. The principle implied here seems directly to contradict such a statement as we find only two pages earlier : ' Positions exist only by virtue of other positions ' (p. 163). The true view seems rather to be, that though positions have that qualitative similarity which is necessary for the axiom of free mobility, yet this in no way prevents them from having also a qualitative and intrinsic difference, though this perhaps we could not have discovered apart from the qualitative differences of