April 24, 1896.] 



SCIENCE. 



633 



this way it will not be the first, for the rocks are 

 filled with the remains of races which have 

 been destroyed because their internal adjust- 

 ments failed, at last, to correspond to the order 

 of nature, after a long period of more or less 

 perfect agreement. 



There is no direct evidence that the concep- 

 tions in question are innate. The indirect 

 evidence from the inconceivability of their 

 negation is worthless, because of the imperfec- 

 tion of our minds. The statement that thought 

 is impossible without them is no assurance that 

 our race may not, like many races which 

 have gone before, some time find itself where 

 the old order changes. Finally the modern stu- 

 dent finds still a fourth reason for questioning 

 the necessity of these ideas ; the fact that evidence 

 is adequate to account for them, and that the 

 assumption that they are innate is unnecessary. 



" It is impossible to prove that the cogency of 

 mathematical first principles is due to anything 

 more than these circumstances ; that the experi- 

 ences with which they are concerned are among 

 the first which arise in the mind ; that they are 

 so incessantly repeated as' to justify us, accord- 

 ing to the ordinary laws of ideation, in expect- 

 ing that the associations which they form will 

 be of extreme tenacity ; while the fact that 

 the expectations based upon them are always 

 verified finishes the process of welding them to- 

 gether. Thus, if the axioms of mathematics 

 are innate, nature would seem to have taken 

 unnecessary trouble, since the ordinary process 

 of association appears to be amply sufiicient to 

 confer upon them all the universality and ne- 

 cessity which they actually possess." 



Your correspondent M. M. complains that my 

 assertion, that the only test of truth is evidence, 

 gives him 'a slight feeling of dizziness,' as if it 

 were something radical and revolutionary. He 

 may be interested to know that about 2500 

 years ago Heraclitus warned his fellowmen of 

 the danger of seeking truth in their own little 

 worlds instead of the great and common world, 

 while Bacon gives more energetic expression to 

 the same conviction in the following words: 



" This is a rotten and pernicious idea or esti- 

 mation that the majesty of man's mind suffers 

 diminution, if it be long and deeply conversant 

 with experiences. * '■^ And this opinion or state 



of mind received much strength from another 

 wild and unfounded opinion, which held that 

 truth is innate in the mind of man and not intro- 

 duced from without, and that the senses rather 

 excite than inform the understanding. ' ' 



Most students of the principles of science ad- 

 mit that the mind of man has not yet attained 

 to knowledge of causes, but that it has, so far, 

 discovered nothing except a little of the order of 

 nature. Xhe reason why events, either mental 

 or physical, occur in one order rather than an- 

 other is a mystery which is absolutely unsolved. 

 We can say no more of them than that "they 

 appear together, but we do not know why." 



If this is true it is clear that we are in no 

 position to say of any event that it cannot be 

 true in the absence of any other event. ' ' The 

 distinction between the necessary and the suifi- 

 cient condition for the truth of a statement," 

 which M. M. seeks to establish, has therefore no 

 warrant in our knowledge of nature ; for while 

 we may seek to ' govern nature in opinion we 

 are thrall' unto her in necessity.' 



Whether there be such a thing as formal logic, 

 distinct from the empirical logic of events, or 

 not, I believe my associates are pretty well 

 agreed that all attempts to make practical ap- 

 plication of formal logic have ended in failure. 

 " The two ways of contemplation are not unlike 

 the two ways of action commonly spoken of by 

 the ancients ; the one pleasant and smooth in 

 the beginning and in the end impassable, the 

 other rough and troublesome in the entrance 

 but after a while fair and even. So it is in 

 contemplation ; if a man will begin with cer- 

 tainties, he shall end in doubts, but if he will 

 be content to begin with doubts he shall end 

 in certainties. 



" Once on a time there were two brothers. 

 One was called Prometheus, because he always 

 looked before him and boasted that he was wise 

 beforehand. 



"The other was called Epimetheus, because 

 he always looked behind him and did not boast 

 at all, but said humbly, like the Irishman, that 

 he would sooner prophesy after the event. 



"Well, Prometheus was a very clever fellow, 

 of course, and invented all sorts of wonderful 

 things, but, unfortunately, when they were set 

 to work, to work was just what they would not 



