Page:Mind (New Series) Volume 8.djvu/266

 252 CBITICAL NOTICES: The first section of the book consists of a discussion of the nature and range of quantity. It is pointed out that quantities need not be divisible, since relations may be quantities. Distance in space, for example, is unquestionably both a quantity and a relation : to suppose distance divisible, can only arise from a con- fusion between distance and length (Strecke). In like manner, the author continues, similarity and dissimilarity are quantities : two things may be more or less similar, but the similarity is certainly indivisible. In this sweeping assertion that similarity and dissimilarity are always quantities, the author ignores an important controversy. Had he applied his doctrine to the relations of other pairs of terms than quantities of the same kind, it would, I think, have led him into serious errors. If the relations in question are reducible to identity and diversity of content, they cease to be properly quantities. Moreover this reduction is certainly valid in some cases. Herr Meinong asserts, for example, that between a colour and a tone there is more difference than between two colours (p. 44). It would be truer to say that there are more differences. Wherever the relations in question are reducible to complete identity in some points, and complete diversity in others, there quantity seems not properly applicable. Diversity of content appears to be incapable of quantity : we cannot say that diversity in respect of one content is equal or unequal to diversity in respect of another. But there are other cases and it is to these, fortu- nately, that the author applies his doctrine where a difference exists which is not reducible to mere diversity of content. Such cases are, among others, differences of position and of magnitude ; and differences of magnitude, naturally, have the chief importance in discussing Weber's Law. The second section deals with comparison, especially as to mag- nitude. Apart from the possible objection that magnitude is a notion essentially dependent upon comparison, and that the present section ought, therefore, to have been the first, the account of quanti- tative comparison is excellent. Likeness and unlikeness are notions not demanding a definition ; but they are not the only results of quantitative comparison, which is unique in yielding, not mere difference of magnitude, but the relations of greater and less. Whatever appears different, on immediate comparison, is different; but what is different only appears so down to a certain limit. Below this limit, a difference is imperceptible. Differences should not be described by their perceptibility, where such a description can be avoided ; for our knowledge of the difference perceived is prior to our knowledge of the perception of difference, and a direct treatment of differences, where possible, is preferable to the indirect treatment by means of their perceptibility. Two just perceptible differences need not be equal ; but we have a well-grounded pre sumption, in favour of their equality, where there is equal suscej tibility to differences.