462 



SCIENCE. 



[N. S. Vol. XX. No. 510. 



the ordinal number of series and the philo- 

 sophical concept of the formal structure of 

 an ideally completed self. I have main- 

 tained that this formal identity throws 

 light upon problems which have as genuine 

 an interest for the student of the philos- 

 ophy of religion as for the logician of 

 arithmetic. In the same connection it may 

 be remarked that, as Couturat and Russell, 

 amongst other wrriters, have very clearly 

 and beautifully shown, the argument of 

 the Kantian mathematical antinomies needs 

 to be explicitly and totally revised in the 

 light of Cantor's modern theory of infinite 

 collections. To pass at once to another, 

 and a very different instance : The modern 

 mathematical conceptions of what is called 

 group theory have already received very 

 wide and significant applications, and 

 promise to bring into unity regions of re- 

 search which, until recently, appeared to 

 have little or nothing to do with one an- 

 other. Quite lately, however, there are 

 signs that group theory will soon prove to 

 be of importance for the definition of some 

 of the fundamental concepts of that most 

 refractory branch of philosophical inquiry, 

 esthetics. Dr. Emch, in an important 

 paper in the Monist, called attention, some 

 time since, to the symmetry groups to 

 which certain esthetically pleasing forms 

 belong, and endeavored to point out the 

 empirical relations between these groups 

 and the esthetic effects in question. The 

 grounds for such a connection between the 

 groups in question and the observed 

 esthetic 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 (al- 

 though the author has approached the sub- 

 ject without being in the least consciously 

 influenced, as I understand, by the con- 

 ceptions of the mathematical gToup 

 theory), still actually lead, if I correctly 



grasp the writer's meaning, to the doctrine 

 that the esthetic object, viewed as a psy- 

 chological 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 esthetic concepts, and speak sub- 

 ject to correction. But the unexpected, 

 and in case of Miss Puffer's research, quite 

 unintended, appearance of group theory in 

 recent esthetic analysis is to me an impress- 

 ive instance of the use of relatively new 

 mathematical conceptions in philosophical 

 regions which seem, at first sight, very re- 

 mote from mathematics. 



That both the group concept and the 

 concept of the self just suggested 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 funda- 

 mental 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 sjTn- 

 pathy. In a word: Our common problem 

 is the theory of the categories. That prob- 

 lem can be solved only by the cooperation 

 of the mathematicians and of the philos- 

 ophers. JOSIAH ROTCE. 



Haevard Univeksitt. 



SCIENTIFIC BOOKS. 

 The Harriman Alasha Expedition. Vol. X. 

 Crustaceans. By Mary J. Eathbun, Har- 

 riet Richardson, S. J. Holmes and Leon 

 J. Cole. New York, Doubleday, Page and 

 Co. 1904. Pp. x-f-33Y. 8vo; with xxvi 

 plates and 128 figures in the text. 

 In working out the shrimps of the Harri- 

 man expedition Miss Eathbun was obliged to 

 review the entire material of that group from 

 northwest America which had accumulated in 

 the ISTational Museum and, in addition to the 



