656 



SCIENCE. 



[N. S. Vol. XXIII. No. 591. 



Carlyle's ' Gospel of Work ' into close prox- 

 imity witli a disquisition on ' The Theory of 

 Invariants of Quadratic Differential Quan- 

 tics.' Moreover, the scheme, with its uniform 

 recurrence of ' divisions,' ' departments ' and 

 ' sections,' has an undue a priori rigidity, and 

 does not properly take account of the actual 

 contemporary interlacings of the problems of 

 different sciences. The congress would prob- 

 ably have been more fruitful if the metaphor 

 chosen to express its purpose had been, not 

 the unification, but the cross-fertilization, of 

 the sciences. In that casfe, perhaps, a greater 

 proportion of the participants would have been 

 at pains to make themselves intelligible and 

 directly serviceable to men in other though 

 not alien specialties; and we might have had 

 a useful series of indications of just the light 

 that workers in each field most need to have 

 thrown upon their problems by workers in 

 other fields. As it is, the ' unity of knowl- 

 edge ' sometimes shows only in a pretty ab- 

 stract sense ; and now and then the ' unifica- 

 tion of the sciences ' seems to owe more to the 

 bookbinder than to the philosopher. 



Concerning the propriety of grouping phi- 

 losophy and mathematics together as ' norma- 

 tive sciences ' much might be said ; but the 

 arrangement at all events serves to bring into 

 clearer relief one of the real tendencies of the 

 moment: the disposition to merge logic, meta- 

 physics and mathematics together in a more 

 fundamental science, a morphology of the pri- 

 mary formal concepts, which shall yield a new 

 logic of relations. To-day — in the opinion of 

 an influential group of thinkers, both philos- 

 ophers and mathematicians — as at the begin- 

 ning of the seventeenth century, philosophy is 

 to be revivified by a transfusion of blood with 

 mathematics; and mathematics is to be made 

 more simple, more clear and more fruitful 

 than ever before. As the subject is a favorite 

 one with Professor Royce, he naturally im- 

 proved the occasion, in his general address on 

 the field of the whole ' division,' to insist upon 

 the epoch-making significance of this new 

 mathematical logic, and especially of the work 

 of Kempe (which later is again set forth by 

 Bocher). It is an evidence of the strength 



of this tendency that the names of certain 

 protagonists of the movement, Dedekind, 

 Weierstrass, Cantor, Peirce, Peano, recur 

 throughout the volume with greater apparent 

 frequency than the name of Kant. It is of 

 interest also to note that, partly because of 

 this and partly because of other tendencies of 

 contemporary thought, Leibniz, ' the first and 

 greatest of German philosophers ' — as he is 

 called in Professor A. E. Taylor's very inter- 

 esting paper — is enjoying a notable revival, 

 much at Kant's expense. The signs of this 

 appear alike in the papers of Eoyce, Taylor 

 and Howison. This inclination to go ' back 

 of Kant' — whose reputation has long been 

 chiefly an obstruction to the progress of logic 

 and metaphysics — is, so far as it goes, an en- 

 couraging symptom. There are those, how- 

 ever — and the present reviewer is among them 

 — who find in much of the new mathematics 

 only a straining of the concepts of ordinal 

 arrangement and of correspondence into log- 

 ical functions for which they are not fitted; 

 who do not make out how, after all, the con- 

 cepts of quantity and number can be reduced 

 to anything else; who suspect the antinomies 

 to be one of Kant's really sound contributions 

 to logic; and who, in any case, can not share 

 Royce's confidence in the direct serviceable- 

 ness of the new logic of relations in the more 

 concrete branches of philosophy. These, 

 however, are too large matters to be argued 

 out here. In emphasizing the tendency in 

 question, the present volume at any rate gives 

 a true picture of one striking feature of the 

 contemporary situation. But another not less 

 conspicuous tendency of the period — that 

 known as pragmatism — is hardly so well rep- 

 resented. But for two or three brief refer- 

 ences by writers unfriendly to the doctrine, 

 no reader of this collection of papers would 

 guess that pragmatism is the theme which, 

 above all, fills our philosophical journals with 

 controversy. 



Of the two general papers in philosophy. 

 Professor Howison's, on ' Fundamental Con- 

 cepts and Methods ' is only a torso. The com- 

 prehensive survey promised in the introduc- 

 tion does not appear; the part printed consists 



