6 UNIVERSITY OF MISSOURI BULLETIN 



transformation of certain fundamental parts of logic, and 

 thus the establishment of philosophy for the first time upon a 

 secure footing. "There is," he writes, "every reason to hope 

 that the near future will be as great an epoch in pure philos- 

 ophy as the immediate past has been in the principles of math- 

 ematics. Great triumphs inspire great hopes; and pure 

 thought may achieve, within our generation, such results as 

 will place our age, in this respect, on a level with the greatest 

 age of Greece." The most learned of contemporary Amer- 

 ican philosophers has repeated this estimate of the importance 

 for philosophy of the recent developments in mathematics : 

 because of them, writes Professor Royce, "we are to-day, for 

 the first time, in sight of what is still, as I freely admit, a 

 rather distant goal, namely, the relatively complete rational 

 analysis of the fundamental categories of human thought." 

 I cite these utterances to show how those most at home in 

 these studies now feel about them; I ought to add that I do 

 not myself take quite so enthusiastic a view of the value of 

 certain new tendencies in mathematics or of their serviceable- 

 ness to philosophy. But the men from whom I quote are 

 themselves mathematicians ; and where it is merely a question 

 of dogmatic expressions of opinion, without argument, their 

 judgment has a degree of authority to which mine cannot 

 pretend. 



In the mathematical conceptions fundamental to the 

 science of physics, again, in other words, in the domain 

 where, above all, Newton won his immortality there has 

 taken place within the past five years a revolution which sober 

 mathematicians do not hesitate to compare to that initiated by 

 Newton one which some, indeed, seem to regard as more 

 momentous than his ; though the name of Einstein as yet 

 scarcely falls upon the general ear with so impressive a sound 

 as the name of the author of the Principia. I refer, of course, 

 to the introduction of the principle of the relativity of time. 

 Let me quote the words of an eminent German mathematician 

 concerning this: "This new way of apprehending the notion 



