358 INTRODUCTION TO PHILOSOPHY OF SCIENCE 



this line can be expressed in a simple functional formula, 

 the desired approximation has been achieved. Examples 

 of this process can be found in almost any elementary 

 textbook of science. 



(3) Since scientific laws state repeated associations of 

 events, an analysis of this important notion is required. 

 Whether a law is asserted as true without exception, or 

 merely as true in general, is a question of its derivation or 

 justification, i.e., a question of the logical techniques by 

 means of which it was obtained, or by means of which it 

 must be verified. A problem of this kind is usually called 

 inductive according to one of the many meanings of this 

 ambiguous word. A few remarks may be made on the in- 

 ductive problem. 



The character of the problem is not hard to discern. 

 Empirical correlations are, as was seen, of various kinds — 

 single, occasional, frequent, and universal. Such correlations 

 exhibit increasing degrees of empirical necessity, and hence 

 increasing degrees of relevance in the problem of under- 

 standing the structure of nature. It seems clear that science 

 is more interested in correlations possessing a high degree of 

 necessity than in those possessing a low degree. Hence it is 

 one of the important aims of science to express scientific laws 

 with as wide a scope of generality as the evidence permits. 

 The occurrence of a given correlation creates a finite proba- 

 bility that it will repeat, and the common assumption of 

 science is that, as the number of situations in which the 

 correlation occurs increases, the probability that it will be 

 found in still further situations also increases. There is 

 always a tendency, therefore, for the scientific formulation of 

 laws to run ahead of the evidence, i.e., for laws to be asserted 

 with wider generality than the actual situations justify. This 

 determines the inductive problem, which may be formulated 

 approximately as follows: On the basis of an association known 

 to hold in a finite number of cases, what may be asserted either 

 as to other cases not examined or as to all possible cases? 



Though the problem has had a long and venerable history, 



