NECESSARY TRUTHS— EFFECTS OF EXPERIENCE. 645 



if the result be not the same, then the objects are not those 

 originally meant. 



This last princijjle, which we may call the axiom of con- 

 stant result, holds good throughout all our mental opera- 

 tions, not only when we compare, but when we add, divide, 

 class, or infer a given matter in any conceivable way. 

 Its most general expression would be "^Ae Same operated 

 on in the same luay gives the Same" In mathematics it 

 takes the form of " equals added to, or subtracted from, 

 equals give equals," and the like. We shall meet with it 

 again. 



The next thing which we observe is that the operation 

 of comparing may he repeated on its own results ; in other 

 words, that we can think of the various resemblances and 

 differences which we find and compare them with each 

 other, making differences and resemblances of a higher 

 order. The mind thus becomes aicare of sets of similar differ- 

 em^es, and forms series of terms with the same kind and amount 

 of difference between them, terms ivhich, as they succeed each 

 other, maintain a constant direction of serial increase. This 

 sense of constant direction in a series of operations we saw 

 in Chapter XIII (p. 490) to be a cardinal mental fact. 

 "A differs from B differs from C differs from D, etc.," 

 makes a series only when the differences are in the same 

 direction. In any such difference-series all terms differ 

 in just the same way from their predecessors. The num- 

 bers 1, 2, 3, 4, 5, . . . the notes of the chromatic scale in 

 music, are familiar examples. As soon as the mind grasps 

 such a series as a whole, it perceives that tioo terms taken 

 far apart differ more than tiuo terms taken near together, 

 and that any one term differs more from a remote than 

 from a near successor, and this no matter what the terms 

 may be, or what the sort of difference may be, provided it 

 is always the same sort. 



This PRINCIPLE OF MEDIATE COMPARISON might be briefly 

 (though obscurely) expressed by the formula "more than 

 the more is more than the less " — the words more and less 

 standing simply for degrees of increase along a constant 

 direction of differences. Such a formula would cover all 

 possible cases, as, earlier than early is earlier than late,, 



