LAW, CAUSE 355 



as will be seen later, the refinement in the recording of the 

 number of associations, the ascertainment of the degree of 

 similarity holding between them, the noting of exceptions, 

 if any, and consequently an assignment of the degree of 

 probability to the scientific law. Degree of probability and 

 necessity constitutes the scientific refinement of variations 

 in empirical necessity. The further complications in this 

 problem will be discussed in the proper place. Here all 

 that is required for emphasis is that a single correlation 

 involves a finite degree of empirical necessity. Whether 

 this is to be reduced, as in the case of Hume, to a subjective 

 factor such as expectation, or whether it is to be considered 

 as existing in the association itself as an objective property 

 capable of additive increase through multiplication of cases — 

 these are questions which are perhaps not important for a 

 philosophy of science. 



In summary, an empirical law is a repeated association of 

 events. The events so associated are usually qualitative 

 rather than quantitative in character, and the association 

 itself is either of coexistence or of succession. Causal laws 

 are the most important type of law of succession, and may 

 designate either mere sequences which occur repeatedly, or 

 connections which exhibit causal efficacy. Every empirical 

 law possesses a greater or lesser degree of empirical necessity, 

 depending upon the frequency with which the association 

 occurs. 



law: operational derivation 



An empirical law becomes a scientific law through three 

 significant operations: (1) measurement, which replaces qual- 

 itative events by quantitative ones, (2) a highly complex 

 operation involving generalization, interpolation, and ap- 

 proximation, which replaces special types of empirical cor- 

 relation by timeless logical interrelationships, discontinuous 

 values by continuous variables, and highly complex 

 correlations by simple functions, and (3) ascertainment of 

 frequencies and degrees of analogy, which replaces vague 



