404 INTRODUCTION TO PHILOSOPHY OF SCIENCE 



between these two types of relations is, of course, not easy 

 to make; hence an element of arbitrariness always enters. 

 But, granting that it has been correctly made, the neglect 

 of the unessential is presumed not to introduce any impor- 

 tant element of artificiality into the tabular representation. 

 The point which is here emphasized may be well illustrated 

 with reference to mathematics. This science has relations 

 to almost all of the other sciences, but the relations are so 

 various in character that no conceptual scheme could ade- 

 quately represent them. By virtue of its deductive structure 

 and its concern with highly abstract notions, mathematics 

 is closely affiliated with logic; by virtue of its application as a 

 technique of measurement, it is connected with physics; 

 by virtue of its non-experimental character, it tends to be 

 grouped with the sociological sciences; and by virtue of the 

 "mental" and idealized character of its subject matter, it 

 becomes closely associated with the psychological sciences. 

 The problem in this connection has to do not merely with 

 representing the fact of the various relations, which could be 

 easily indicated merely by the drawing of lines, but with 

 representing the fact that each of these relations is different 

 in kind from the others and would therefore require a dif- 

 ferent type of connecting link. As soon as the classificatory 

 scheme adapts itself to these highly complicated and in- 

 volved elements, its diagrammatic character is destroyed. 

 Hence it seems preferable to neglect all but one of these 

 relationships, even at the risk of introducing artificiality 

 into the representation. A classificatory scheme must 

 reveal nature in the same way that a well-fitting garment 

 suggests the underlying figure, not by portraying clearly all 

 details of its form but by neglecting or hiding some of its 

 features, and emphasizing and exhibiting others. A table of 

 the sciences represents a compromise between an ideal form 

 and the gross complexities of nature. 



As a consequence, one must be continually on his guard 

 against constructing a scheme which is in accord with an 

 a priori philosophical point of view rather than with the 



