EXPLANATORY SCIENCE 209 



symbol has important relations to any other symbol; any 

 symbol might be removed from the scheme or modified with- 

 out affecting the other symbols in any significant way. The 

 integration of a descriptive science is achieved by introduc- 

 ing hypotheses which serve to relate apparently discon- 

 nected propositions by showing that they are jointly im- 

 plied by the hypotheses. Hence an explanatory science 

 which is precisely the expanded descriptive science, exhibits 

 relations of super-, and sub-, and coordination of proposi- 

 tions. Every proposition is either an underived proposition 

 (axiom, postulate, hypothesis) or a derived proposition 

 (theorem, corollary, descriptive law); and every derived 

 proposition takes its place subordinate to the hypothesis 

 from which it can be derived, and coordinate with all other 

 derived propositions deducible from the same hypothesis. 

 The ideal of explanatory science is the construction of a 

 single system of postulates from which all other propositions 

 in the system may be derived. The special and general 

 theories of relativity approach the ideal of such a postulate 

 scheme in the field of physics. 



The increased compactness of an explanatory science is 

 accomplished by the introduction of highly integrating 

 propositions. Such a science is distinguished from a descrip- 

 tive science by the presence of universal laws in place of 

 statements of occasional correlations, and by the presence 

 of mathematical functional relations in the place of qualita- 

 tive correlations. Since explanatory science is not tied down 

 to what is clearly given it may ^assert universal laws, even 

 though they may be hypothetical in character. Hence one 

 may generalize in explanatory science from what happens 

 in a few cases to what happens universally and without 

 exception. This becomes an important instrument of in- 

 tegration, for every future case is derivable from such a 

 law. Furthermore, mathematical techniques of measure- 

 ment and correlation may be introduced. Relations of mere 

 presence and absence are replaced by relations of degree of 

 quantitative manifestation. For example, the colors become 



