646 PSYCHOLOGY 



worse tlian bad is worse than good, east of east is east of 

 west ; etc., etc., ad libitum.'^ Symbolically, we might write 

 itasa<5<c<c?.... and say that any number of 

 intermediaries may be expunged without obliging us to 

 alter anything in what remains written. 



The principle of mediate comparison is only one form 

 of a law which holds in many series of homogeneously 

 related terms, the law that skipping intermediary terms- 

 leaves relations the same. This axiom of skipped intermedi- 

 aries or of TRANSFERRED RELATIONS occurs, as we soon shall 

 see, in logic as the fundamental principle of inference, in 

 arithmetic as the fundamental property of the number- 

 series, in geometry as that of the straight line, the plane 

 and the parallel. It seems to be on the whole the broadest and 

 deepest laio of mans thought. 



In certain lists of terms the result of comparison may 

 be to find no-difference, or equality in place of difference. 

 Here also intermediaries may be skipped, and mediate com- 

 parison be carried on with the general result expressed by 

 the axiom of mediate equality, "equals of equals are equal," 

 which is the great principle of the mathematical sciences. 

 This too as a result of the mind's mere acuteness, and in 

 utter independence of the order in which experiences come 

 associated together. Symbolically, again : « = & = c = f? . . , 

 with the same consequence as regards expunging terms 

 which we saw before. 



CLASSIFICATORY SERIES. 



Thus we haye a rather intricate system of necessary and 

 immutable ideal truths of comparison, a system applicable to 

 terms experienced in any order of sequence or frequency, or 

 even to terms never experienced or to be experienced, such 

 as the mind's imaginary constructions would be. These 

 truths of comparison result in Classifications. It is, for some 

 unknown reason, a great aesthetic delight for the mind to 

 break the order of experience, and class its materials in serial 

 orders, proceeding from step to step of difference, and to 

 contemplate untiringly the crossings and inosculations of the 



*Cf. Bradley, Logic, p. 326. 



