O UNIVERSITY OF MISSOURI BULLETIN 



transformation of certain fundamental parts of logic, jnd 

 thus the establishment of philosophy for the first time upcp. a 

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

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

 ophy as the immediate past has been in the principles of r^ath- 

 ematics. Great triumphs inspire great hopes ; and pure 

 thought may achieve, within our generation, such resufs as 

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

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

 ican philosophers has repeated this estimate of the impdtance 

 for philosophy of the recent developments in mathetlatics : 

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

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

 rather distant goal, namely, the relatively complete litional 

 analysis of the fundamental categories of human thjught." 

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

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

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

 certain new tendencies in mathematics or of their senceable- 

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

 themselves mathematicians; and where it is merely a|uestion 

 of dogmatic expressions of opinion, without argumflt, their 

 judgment has a degree of authority to which miri cannot 

 pretend. I 



In the mathematical conceptions fundamental to the 

 science of physics, again, — in other words, in tW domain 

 where, above all, Newton won his immortality — fiere has 

 taken place within the past five years a revolution w^ch sober 

 mathematicians do not hesitate to compare to that ijtiated by 

 Newton — one which some, indeed, seem to regarj as more 

 momentous than his ; though the name of Einstjn as yet 

 scarcely falls upon the general ear with so impress^ a sound 

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

 to the introduction of the principle of the relativr of time. 

 Let me quote the words of an eminent German maematician 

 concerning this: "This new way of apprehendinshe notion 



