356 INTRODUCTION TO PHILOSOPHY OF SCIENCE 



recognition of empirical necessity by more or less precise 

 statements of necessity and probability. Each of these will 

 be examined in greater detail. 



(1) Although, as will be shown in the next section, the 

 question as to whether all scientific laws are quantitative 

 rather than qualitative in character is debatable, never- 

 theless from the point of view of operational techniques 

 measurement is the most important method by which pre- 

 cision is introduced into science. If one agrees, for the 

 moment, that most scientific laws are expressible in terms 

 of measured values, the meaning of the notion of scientific 

 law must depend on an analysis of the operational techniques 

 employed in procuring measured values. This implies that 

 the meaning of scientific law is tied up with measurement 

 and all of the assumptions on which it is based. It implies, 

 further, that from this point of view a scientific law states 

 not a correlation between events in the strict sense of the 

 term but rather a correlation between numbers on measuring 

 instruments and recording devices. For example, the law of 

 falling bodies replaces spaces by numbers on meter sticks, 

 and times by readings of clocks; what it states is that the 

 numbers obtained from one recording device vary in a cer- 

 tain way as compared with the numbers obtained from 

 another device. And in a deeper sense the meaning of the 

 law is a function not only of the methods of obtaining the 

 numbers, but also of the methods of constructing and cali- 

 brating the instruments. This dependence of law upon the 

 techniques by which it is derived is in complete harmony 

 with the dependence of scientific concepts in general upon 

 the methods by which they are measured. Repeated refer- 

 ence to this feature of scientific concepts has been made 

 in the preceding chapters. 



(2) The operational techniques which are involved in the 

 transformation of empirical correlations into precise func- 

 tional relations are highly complex in character. They may 

 be discussed briefly as (a) generalization, (b) interpolation, 

 and (c) approximation, (a) Generalization, or abstraction, 



