168 NORMATIVE SCIENCE 



The grounds for such a connection between the groups in question 

 and the observed aesthetic effects, seemed, in the paper of Dr. Emch 

 to be left largely in the dark. But certain papers recently published 

 in the country by Miss Ethel Puffer, bearing upon the psychology 

 of the beautiful (although the author has approached the subject 

 without being in the least consciously influenced, as I understand, 

 by the conceptions of the mathematical group theory), still actually 

 lead, if I correctly grasp the writer's meaning, to the doctrine that 

 the aesthetic object, viewed as a psychological whole, must possess 

 a structure closely, if not precisely, equivalent to the ideal structure 

 of what the mathematician calls a group. I myself have no authority 

 regarding aesthetic concepts, and speak subject to correction. But 

 the unexpected, and in case of Miss Puffer's research, quite unin- 

 tended, appearance of group theory in recent aesthetic analysis is to 

 me an impressive instance of the use of relatively new mathematical 

 conceptions in philosophical regions which seem, at first sight, very 

 remote from mathematics. 



That both the group concept and the concept of the self just sug- 

 gested are sure to have also a wide application in the ethics of the 

 future, I am myself well convinced. In fact, no branch of philosophy is 

 without close relations to all such studies of fundamental categories. 



These are but hints and examples. They suffice, I hope, to show 

 that the workers in this division have deep common interests, and 

 will do well, in future, to study the arts of cooperation, and to regard 

 one another's progress with a watchful and cordial sympathy. In a 

 word: Our common problem is the theory of the categories. That 

 problem can be solved only by the cooperation of the mathema- 

 ticians and of the philosophers. 



