532 PSYCHOLOGY. 



of the mind. Tliis acute author rejects in particular the 

 notion which wouki make our judgment of the distance 

 between two sensations depend upon our mentally travers- 

 ing the intermediary steps. We may of course do so, and 

 may often tind it useful to do so, as in musical intervals, or 

 figured lines- But we need not do so ; and nothing more 

 is really required for a comparative judgment of the amount 

 of a 'distance' than three or four impressions belonging to 

 a common kind. 



The vanishing of all perceptible difference between two 

 numerically distinct things makes them quaJitntively the 

 sa7ne or equal. Equality, or qualitative (as distinguished 

 from numerical) identity, is thus nothing but the extreme 

 degree of likeness.^ 



We saw above (p. 492) that some persons consider that 

 the ditference between two objects is constituted of two 

 things, viz., their absolute identity in certain respects, plus 

 their absolute non-identity in others. We saw that this theory 

 would not apply to all cases (p. 493). So here any theory 

 which would base likeness on identity, and not rather iden- 

 tity on likeness, must fail. It is supposed perhaps, by most 

 people, that two resembling things owe their resemblance 

 to their absolute identity in respect of some attribute or 

 attributes, combined with the absolute non-identity of the 

 rest of their being. This, which may be true of compound 

 things, breaks down when we come to simple impressions. 



" When we compare a deep, a middle, and a high note, e.g. C, /sharp, 

 a'", we remark immediately that the first is less like the third than the- 

 second is. The same would be true of c d e in the same region of the 

 scale. Our very calling one of the notes a ' middle ' note is the expres- 

 sion of a judgment of this sort. But where here is the identical and 

 where the non-identical part ? We cannot think of the overtones ; for 

 the first-named three notes have none in common, at least not on musi- 

 cal instruments. Moreover, we might take simple tones, and still our 

 judgment would be unhesitatingly the same, provided the tones were 

 not chosen too close together. . . . Xeither can it be said that the 

 identity consists in their all being sounds, and not a sound, a smell, and 

 a color, respectively. For this identical attribute comes to each of them- 

 in equal measure, whereas the first, being less like the third than the 

 second is, ought, on the terms of the theory we are criticising, to have 



* Stumpf, pp. lll-l-,'l. 



