LAW, CAUSE 357 



is the method by which the difference between laws of co- 

 existence and laws of succession is lost in science. Empirical 

 necessity becomes generalized into logical or mathematical 

 necessity. Empirical laws state the dependence of the oc- 

 currence of one event upon that of another; scientific laws 

 state the dependence of one measured value upon another. 

 In the case of causal laws one may say that science generalizes 

 the notion of cause and effect into the notion of reason and 

 consequence — an operation which involves loss of the tem- 

 poral features of the empirical correlation. The outcome of 

 this operation, and its justification, will be discussed further 

 in connection with scientific law. (b) Interpolation is the 

 serial operation by which the discontinuity of measured 

 values is replaced by a continuous function. The presump- 

 tion is that the measured values obtained are an adequate 

 indication of the general type of serial order involved, and 

 hence that interpolation of probable values between any 

 two actual values is justified. In the case of a ball rolling 

 down an inclined plane, for example, the discrete values 

 representing the positions of the ball at successive moments 

 may be replaced by a variable which changes continuously, 

 since the reasonable assumption is that the ball behaves in 

 between any measured points in essentially the same way 

 as it does at the measured points, (c) Approximation is 

 the method of idealization by which a simple mathematical 

 function is substituted for a table giving parallel columns 

 of measured values. Such a complex table is, of course, a 

 scientific law in the most general sense of the term. But 

 simplicity of correlation is much to be desired in the inter- 

 ests of intelligibility ; consequently simple rather than com- 

 plex relations are sought in every case. Approximation is 

 the method by which discrete values are replaced by points 

 plotted on a coordinate system. Due to the inaccuracies of 

 measurement the points seldom lie on a smooth curve. But 

 by increasing the number of points one can obtain a general 

 notion of the path of the curve, and the line may be drawn 

 even though it does not pass through all of the points. If 



