CHAPTER XV 



MOTION, FORCE, MATTER 



As one approaches the concepts at this level, measurement 

 techniques become increasingly important. The view that 

 qualitative events are not properly a part of the subject 

 matter of science unless they can be replaced by quantities, 

 i.e., by measured values, has already been presented. 1 Such 

 a view would entitle one to examine the present concepts 

 at their highest level of abstraction and to say that by them 

 one means simply numbers obtained by reading measuring 

 devices; e.g., by force is meant simply the number obtained 

 by reading a spring balance. Since numbers are properly 

 the subject matter of mathematics, this view involves the 

 reduction of physics without remainder to mathematics. 

 The danger in this position has already been pointed out. 

 If qualitatively different events in science are reduced ex- 

 haustively to numbers, all possibility of differentiation dis- 

 appears for there is no mathematical difference between the 

 number 2 which represents a force and the number 2 which 

 represents a motion. Numbers which are measured values 

 are always measured values of something, and they function 

 in the equations of science not as mere numbers but as 

 5, /, v, etc., i.e., as qualitatively distinct entities. The view 

 of science which reduces quality to quantity neglects the 

 fact that measuring instruments must be devised in the first 

 place, must be calibrated by reference to judgments of per- 

 ception, and must be manipulated in any given situation. 



Hence the attempt will be made in the present chapter to 

 avoid that extreme abstraction which reduces motion, force, 

 and matter to pure numbers. This is not to deny that they 

 are quantitative. But it is to recognize that the process of 

 attaching numbers to them involves specific instruments 



1 Chapter XII. 



312 



