October 7, 1904.] 



SCIENCE. 



453 



another— these are never, for us men, phe- 

 nomenally present data. Hence the philos- 

 opher, however much he ought, as indeed 

 he ought, to take account of phenomena, 

 and of the results of the special physical 

 sciences, is quite as deeply interested in his 

 own way, as the mathematician is inter- 

 ested in his way, in the consideration of an 

 ideal realm. Only, unlike the mathema- 

 tician, the philosopher does not first ab- 

 stract from the empirical suggestions upon 

 which his exact ideas are actually based, 

 and then content himself merely with de- 

 veloping the logical consequences of these 

 ideas. On the contrary, his main interest 

 is not in any idea or fact in so far as it is 

 viewed by itself, but rather in the inter- 

 relations, in the common significance, in 

 the unity, of all fundamental ideas, and in 

 their relations both to the phenomenal facts 

 and to life ! On the whole, he, therefore, 

 neither consents, like the student of a 

 special science of experience, to seek his 

 freedom solely through conformity to the 

 phenomena which are to be described; nor 

 is he content, like the pure mathematician, 

 to win his truth solely through the exact 

 definition of the formal consequences of his 

 freely defined hypotheses. He is making 

 an effort to discover the sense and the unity 

 of the business of his own life. 



It is no part of my purpose to attempt 

 to show here how this general philosophical 

 interest differentiates into the various in- 

 terests of metaphysics, of the philosophy of 

 religion, of ethics, of esthetics, of logic. 

 Enough — I have tried to illustrate how, 

 while, both the philosopher and the mathe- 

 matician have an interest in the meaning 

 of ideas rather than in the description of 

 external facts, still there is a contrast which 

 does, indeed, keep their work in large meas- 

 ure asunder, viz., the contrast due to the 

 fact that the mathematician is directly con- 

 cerned with developing the consequences of 

 certain freely assumed systems of postu- 



lates or hypotheses; while the philosopher 

 is interested in the significance, in the 

 unity and in the relation to life, of all the 

 fundamental ideals and postulates of the 

 human mind. 



Yet not even thus do we sufficiently state 

 how closely related the two tasks are. For 

 this very contrast, as we have also sug- 

 gested, is, even within its own limits, no 

 final or perfectly sharp contrast. There 

 is a. deep analogy between the two tasks. 

 Par the mathematician, as we have just 

 seen, is not evenly interested in developing 

 the consequences of any and every system 

 of freely assumed postulates. He is no 

 mere solver of arbitrary ideal puzzles in 

 general. His systems of postulates are so 

 chosen as to be not trivial, but significant. 

 They are, therefore, in fact, but abstractly 

 defined aspects of the very system of 

 eternal truth whose expression is the uni- 

 verse. In this sense the mathematician is 

 as genuinely interested as is the philosopher 

 in the significant use of his scientific .free- 

 dom. On the other hand, the philosopher, 

 in reflecting upon the significance and the 

 unity of fundamental ideas, can only do 

 so with success in ease he makes due in- 

 quiry into the logical consequences of gix'on 

 ideas. And this he can aecomplisk only 

 if, upon occasion, he employs the exact 

 methods of the mathematician, and de- 

 velops his systems of ideal truth with the 

 precision of which only mathematical re- 

 search is capable. As a fact, then, the 

 mathematician and the philosopher deal 

 with ideal truth in ways which are not only 

 contrasted, but profoundly interconnected. 

 The mathematician, in so far as he con- 

 sciously distinguishes significant from 

 trivial problems, and ideal systems, is a 

 philosopher. The philosopher, in so far 

 as he seeks exactness of logical method, in 

 his reflection, must meanwhile aim to be, 

 within his own limits, a mathematician. 

 He, indeed, will not in future, like Spinoza, 



