200 INTRODUCTION TO PHILOSOPHY OF SCIENCE 



latter may be said to be explained by it. Hence one may say 

 that propositions about molecules explain propositions about 

 heat, and propositions about heat describe facts in which 

 heat occurs. A descriptive science is constituted by proposi- 

 tions of the kind X. An explanatory science would pre- 

 sumably be constituted by propositions of the kind Y; 

 however, for reasons to be disclosed later, it seems better to 

 characterize an explanatory science as including a descrip- 

 tive science, and, hence, as any science constituted by 

 propositions of the kind Y and the kind X in the relation 

 Y implies X. Though the Y propositions would not ordi- 

 narily be called descriptive, they may easily become so by 

 any techniques which permit y to appear in the more clearly 

 given; for example, in the Brownian movement one may be 

 said in effect to be observing molecules; hence through such 

 activities the propositions about molecules may be con- 

 sidered as approximating to descriptive propositions. 



The essence of the explanatory relation, then, lies in the 

 relation of implication. Whenever there is a logical structure 

 consisting of premises and conclusion, the premises may be 

 said to explain the conclusion. The premises give the reasons 

 for the conclusion, the conditions which — if satisfied — will 

 determine the truth of the conclusion. Hence the relation of 

 explanation holds between any group of underived proposi- 

 tions (postulates, axioms, definitions, principles) and the cor- 

 responding group of derived propositions (theorems, corol- 

 laries, laws). The underived propositions need not be 

 ultimately underivable, but are simply, at the moment, 

 considered as underived. The theorems and corollaries of a 

 system of geometry may be said to be explained by the 

 corresponding postulate system, and the laws of empirical 

 science may be said to be explained by the proper set of 

 principles and theories. 



However, although the implicative relation seems to ex- 

 press the essence of explanation, it does not exhaust that 

 relation. Implication is necessary for explanation, but is it 

 sufficient? According to Campbell, "Explanation in general 



