88 ROYCE— PRINCIPLES OF THEORETICAL SCIENCE. 



[April 19, 



study of the first principles of theoretical science as a branch of 

 what is called logic, it was until recently the fashion to say that since 

 Aristotle logic has made no progress ; that that marvellous thinker 

 had already seen nearly all of what the human mind can see regard- 

 ing the structure of our thinking processes, and regarding the way 

 in which we can use principles provisionally assumed, for the pur- 

 pose of drawing conclusions from them. The principal addition 

 that was supposed to have been made to logic since Aristotle was 

 confined, according to this view, to a study of that inductive logic 

 which is concerned rather with the application of our thinking pro- 

 cesses to the discovery, the collection and the arrangement of facts, 

 than with the structure of our thinking process itself. I wish 

 to call attention on this occasion to the fact that this familiar asser- 

 tion concerning logic and concerning its stagnation since Aristotle, 

 in no longer true. We are today in the midst of a very vigorous and 

 many-sided movement which interests the students of several differ- 

 ent sciences, and which involves a rapid advance towards an answer 

 to those very questions which I have just enumerated. We are to- 

 day in a way to grow very rapidly in our comprehension of the 

 range, of the varieties, and of the logical nature, of the funda- 

 mental conceptions upon which all theoretical science depends. We 

 are no longer confined to the commonplace observations just cited 

 regarding the peculiarly advantageous character of quantitative con- 

 cepts and theories. We begin to know zt'hy the concept of quantity 

 has the logical usefulness that it possesses. And as we come to 

 know this, we see that the concept of quantity is one only amongst 

 the exact and definable fundamental concepts upon which scientific 

 theory depends. We discover that even the quantities get their log- 

 ical usefulness for purposes of scientific theory from certain charac- 

 ters which they share with a very large number of other concepts, 

 namely from their character of being capable of serial arrangements, 

 and from their further character of constituting what is now called 

 a group, with reference to certain specific operations. The series 

 concept and the group concept thus obtain a logical place amongst 

 fundamental concepts which permits us at once to view the quantita- 

 tive theories as a special instance only amongst an infinite, but again 

 perfectly determinate range of possible theories, some of which have 



