DISCRIMINATION AND COMPARISON. 533 



less of the identical quality. . . . It thus appears impracticable to define 

 all possible cases of likeness as partial identity pZw^ partial disparity; 

 and it is vain to seek in all cases for identical elements."* 



And as all compound resemblances are based on Simple 

 ones like these, it follows that likeness ilberhaupt must not 

 be conceived as a special complication of identity, but 

 rather that identity must be conceived as a special degree 

 of likeness, according to the proposition expressed at the 

 outset of the paragraph that precedes. Likeness and dif- 

 ference are ultimate relations perceived. As a matter of 

 fact, no two sensations, no two objects of all those we know, 

 are in scientific rigor identical. We call those of them 

 identical whose difference is unperceived. Over and above 

 this we have a conception of absolute sameness, it is true, 

 but this, like so many of our conceptions (cf. p. 508), is an 

 ideal construction got by following a certain direction of 

 serial increase to its maximum supposable extreme. It 

 plays an important part, among other permanent meanings 

 possessed by us, in our ideal intellectual constructions. 

 But it plays no part whatever in explaining psychologically 

 how we perceive likenesses between simple things. 



THE MEASURE OF DISCEIMINATIVE SENSIBILITY. 



In 1860, Professor G. T. Feclmer of Leipzig, a man of 

 great learning and subtlety of mind, jDublished two volumes 

 entitled ' Psychophysik,' devoted to establishing and ex- 

 plaining a law called by him the psychophysic law, which 



* Stuinpf, pp. 116-7. I have omitted, so as not to make my text too intri- 

 cate, an extremely acute and conclusive paragraph, which I reproduce here : 

 " We may generalize : Wherever a number of sensible impressions are 

 apprehended as a series, there in the last instance must perceptions of sim- 

 ple likeness be found. Proof: Assume that all the terms of a series, e.g. 

 the qualities of tone, c d efg, have .something in common, — no matter what 

 it is, call it X; then I say that the diiiering parts of each of these terms 

 must not only be differently constituted in each, but must themselves form 

 a series, whose existence is the ground for our apprehending the original 

 terms in serial form. We thus get instead of the original series a b c d ef 

 . . . the equivalent series Xa, X/3, Xy, . . . etc. What is gained ? The 

 question immediately arises : How {?, a (S y known as a series? According 

 to the theory, these elements must themselves be made up of a part common 

 to all, and of parts differing in each, which latter parts form a new series, 

 and so on ad infinitum, which is absurd." 



