THE SCIENCES OF THE IDEAL 159 



light the unity of truth, either, as in mathematics, by developing 

 systems of truth which are significant by virtue of their actual rela- 

 tions to this unity, or, as in philosophy, by explicitly seeking the 

 central idea about which all the many ideas cluster. 



Now, an ancient and fundamental problem for the philosophers 

 is that which has been called the problem of the categories. This 

 problem of the categories is simply the more formal aspect of the 

 whole philosophical problem just defined. The philosopher aims to 

 comprehend the unity of the system of human ideas and ideals. Well, 

 then, what are the primal ideas? Upon what group of concepts do 

 the other concepts of human science logically depend? About what 

 central interests is the system of human ideals clustered? In ancient 

 thought Aristotle already approached this problem in one way. 

 Kant, in the eighteenth century, dealt with it in another. We stu- 

 dents of philosophy are accustomed to regret what we call the ex- 

 cessive formalism of Kant, to lament that Kant was so much the 

 slave of his own relatively superficial and accidental table of catego- 

 ries, and that he made the treatment of every sort of philosophical 

 problem turn upon his own schematism. Yet we cannot doubt that 

 Kant was right in maintaining that philosophy needs, for the suc- 

 cessful development of every one of its departments, a well-devised 

 and substantially complete system of categories. Our objection to 

 Kant's over-confidence in the virtues of his own schematism is due 

 to the fact that we do not now accept his table of categories as an 

 adequate view of the fundamental concepts. The efforts of philo- 

 sophers since Kant have been repeatedly devoted to the task of 

 replacing his scheme of categories by a more adequate one. I am 

 far from regarding these purely philosophical efforts made since 

 Kant as fruitless, but they have remained, so far, very incomplete, 

 and they have been held back from their due fullness of success by 

 the lack of a sufficiently careful survey and analysis of the processes 

 of thought as these have come to be embodied in the living sciences. 

 Such concepts as number, quantity, space, time, cause, continuity, 

 have been dealt with by the pure philosophers far too summarily 

 and superficially. A more thoroughgoing analysis has been needed. 

 But now, in comparatively recent times, there has developed a re- 

 gion of inquiry which one may call by the general name of modern 

 logic. To the constitution of this new region of inquiry men have 

 principally contributed who began as mathematicians, but who, in 

 the course of their work, have been led to become more and more 

 philosophers. Of late, however, various philosophers, who were 

 originally in no sense mathematicians, becoming aware of the im- 

 portance of the new type of research, are in their turn attempting 

 both to assimilate and to supplement the undertakings which were 

 begun from the mathematical side. As a result, the logical problem 



