CONTRIBUTION TO THE THEORY OF SCIENCE 237 



If after this cursory survey we review the ground we have covered, 

 we shall recognize the following general relations: In each case the 

 development of a science consists in correlating concepts formed from 

 definite abstractions derived from experience; and by this means we 

 achieve in our minds a mastery over certain parts of our experiences. 

 Such correlations are termed according to the degree of their univer- 

 sality and reliability, rules or laws. A law is the more important, the 

 more definite its statement concerning the greatest possible number of 

 things; and the more accurately it consequently permits of predicting 

 the future. Every law is based upon incomplete induction and is 

 therefore liable to modification by experience. Hence the development 

 of science is of necessity twofold. 



In the first place actual relations are examined to see whether or 

 not new relations other than those already known may not be dis- 

 covered, i. e., constant relations between individual peculiarities. This 

 is the inductive method. And because the possibilities of experience 

 are unlimited it must ever be an incomplete method. 



In the second place, relations discovered by induction are applied 

 to cases which have not yet been investigated. Cases resulting from 

 the combination of several inductive laws are particularly liable to be 

 studied. If the combination is correctly made and if the inductive 

 laws are absolutely certain, the result has a claim to unconditional 

 validity. This is the limiting case which all sciences strive to ap- 

 proach. It is almost attained by the simplest sciences, mathematics 

 and certain parts of mechanics. This is termed the deductive method. 



In the actual practise of every science both methods of investigation 

 constantly alternate. The best method to discover new and significant 

 inductions is to make a deduction even though its basis be insuffi- 

 cient, requiring subsequent proof from experience. Sometimes the in- 

 vestigator is not conscious of the separate steps of his deduction. In 

 such cases scientific instinct is spoken of. On the other hand, great 

 mathematicians have informed us that they used to find their general 

 laws by induction, by trying and considering individual cases, and that 

 their deductive derivation from other known laws is an independent 

 operation which at times did not follow until much later. Even to- 

 day there are a number of mathematical propositions which have not 

 reached the second stage and which are therefore at present of a purely 

 inductive and empirical character. The part that such laws play in 

 the sciences rapidly increases as we pass up the series. 



Another peculiarity which may be mentioned here is that in the 

 series all preceding sciences assume the characteristics of applied 

 sciences in respect to succeeding ones because they are essential to 

 the course of the last without being themselves increased. They are 

 merely helps to the latter. 



