156 NORMATIVE SCIENCE 



way, in the consideration of an ideal realm. Only, unlike the mathe- 

 matician, the philosopher does not first abstract from the empirical 

 suggestions upon which his exact ideas are actually based, and then 

 content himself merely with developing 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 interrelations, 

 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 gen- 

 eral philosophical interest differentiates into the various interests of 

 metaphysics, of the philosophy of religion, of ethics, of aesthetics, 

 of logic. Enough I have tried to illustrate how, while both the 

 philosopher and the mathematician 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 measure 

 asunder, namely, the contrast due to the fact that the mathematician 

 is directly concerned with developing the consequences of certain 

 freely assumed systems of postulates or hypotheses; while the philo- 

 sopher is interested in the significance, in the unity, and in the re- 

 lation 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 suggested, 

 is, even within its own limits, no final or perfectly sharp contrast. 

 There is a deep analogy between the two tasks. For the mathema- 

 tician, as we have just seen, is not evenly interested in developing 

 the consequences of any and every system of freely assumed pos- 

 tulates. He is no mere solver of arbitrary ideal puzzles in general. 

 His systems of postulates are so chosen as to be not trivial, but sig- 

 nificant. They are, therefore, in fact, but abstractly defined aspects 

 of the very system of eternal truth whose expression is the universe. 

 In this sense the mathematician is as genuinely interested as is the 

 philosopher in the significant use of his scientific freedom. On the 

 other hand, the philosopher, in reflecting upon the significance and 

 the unity of fundamental ideas, can only do so with success in case 

 he makes due inquiry into the logical consequences of given ideas. 

 And this he can accomplish only if, upon occasion, he employs the 

 exact methods of the mathematician, and develops his systems of 



