206 INTRODUCTION TO PHILOSOPHY OF SCIENCE 



sense arose, and in terms of which it is to be accounted for. 

 Whatever else the explanatory propositions may do, they 

 must at least explain the descriptive propositions. Otherwise 

 they become purely arbitrary, subject to no criterion except 

 that of internal consistency. 



What is maintained here may be clarified by pointing out 

 the thesis with which it is contrasted. It is usually asserted 

 that sciences are capable of being divided into two mutually 

 exclusive classes — the empirical, inductive, existential, real, 

 or a posteriori, and the rational, deductive, non-existential, 

 ideal, or a priori. The former, illustrated by experimental 

 physics, biology, and sociology, are derived from the realm 

 of events, and therefore refer to this realm; the latter, 

 illustrated by logic, geometry, and rational mechanics, are 

 not derived from the realm of events, and therefore do not 

 refer to this realm. Hence the former may be called real 

 sciences, while the latter must be called ideal. But since 

 the latter exhibit an important logical structure they may 

 be called deductive or necessary, while the former must be 

 called inductive or probable. A proposition which belongs 

 to one type of science cannot also at the same time belong to 

 another. Hence no proposition can be both logically neces- 

 sary and empirically true. Einstein has formulated this 

 thesis clearly in a statement which is frequently quoted: 

 "As far as the laws of mathematics refer to reality, they are 

 not certain; and as far as they are certain, they do not refer 

 to reality." 1 



The unfortunate consequence of this dichotomy is that it 

 leaves inexplicable the problem of how the rational sciences 

 contribute to the understanding of the empirical sciences. 

 There is not only pure mathematics, but applied mathe- 

 matics; not only rational mechanics, but empirical mechan- 

 ics. If rational sciences have not been derived from and do 

 not talk about events, how can they have any application to 

 such events? The goal of science is neither propositions 

 having a maximum of necessity and a minimum of truth, 



1 A. Einstein, Sidelights on Relativity (London: Methuen, 1922), p. 28. 



