160 DOGMATISM AND EVOLUTION 



lying concept of number itself, and below it the concepts of 

 implication and inclusion, are absolutely final. This we see no 

 sufficient reason to believe. On the contrary, the utterly un- 

 expected development which the concept of number has recently 

 undergone through researches in the theory of infinite numbers 

 is an index of the possibilities which may yet be in store. Nothing 

 could ever have seemed more necessary than that if 2X X, 

 X = o; and yet we know today that there is a distinct class of 

 other roots. The old number-theory, which was thought to be 

 absolutely true, is seen to be true only within a certain limitation, 

 namely, that the numbers considered be finite. It has been 

 aufgehoben refuted as absolute, and taken up and preserved as 

 part of an ampler whole. For all that we know, the theory of 

 today may be similarly aufgehoben tomorrow. 



The classification of contemporary human races presents in tem- 

 poral cross-section a picture of the evolution of humanity. The 

 classification of the sciences presents in a like cross-section a pic- 

 ture of the evolution of human judgment. Of this evolution, we re- 

 peat, the pragmatist theory of truth has taken insufficient account. 



Nothing is more dangerously misleading than an indiscriminate 

 induction from the various stages of a given development. That 

 most, if not all, laws are approximate, that their validity is 

 relative to the satisfaction of the particular wants of individual 

 men, and hence that validity is determined by maximal individual 

 satisfaction, is true enough to be exceedingly false. It is like 

 Hume's theory founded upon a similar sweeping induction 

 that justice is whatever custom makes it. Whereas, for example, 

 Locke had claimed that taxation without representation is un- 

 just, Hume observes: "What authority any moral reasoning can 

 have, which leads into opinions so wide of the general practice 

 of mankind in every place but this single kingdom, it is easy to 

 determine." 1 Hume's induction was correct. He might even 

 have added that in Great Britain the suffrage was strangely 

 limited. And yet Locke was more than half right, because the 

 norm which he described lay athwart the course of social evolu- 



^Essay XXXIV. 



