332 INTRODUCTION TO PHILOSOPHY OF SCIENCE 



they are attached are touched by observers, and, conse- 

 quently, that the study of force is a matter for physiology 

 rather than for physics. The scientific definition of force 

 must, therefore, satisfy two criteria: It must enable one to 

 measure force and to differentiate between the various kinds 

 of "forces"; but it must enable one to locate and to measure 

 forces in situations not involving the immediate contact of 

 the observer. 



The essential operational act, therefore, by which the 

 scientific notion of force is derived from its empirical founda- 

 tion is measurement. This, as has been seen, is a type of 

 abstraction. But it differs from other types of abstraction 

 in that it attempts to devise a physical correlate for itself. 

 Measuring instruments are physical events, and they are 

 related to the events which they measure by physical con- 

 nections. Hence the "mental'' operation of generalizing a 

 qualitative event so as to retain only its quantitative features 

 has a parallel in the "physical' operation of inventing, 

 setting-up, and reading recording instruments. Both proc- 

 esses begin with qualitative events and end with numbers. 

 But whereas the former has no recognized principles or rules 

 for its guidance (it is usually described simply as the "neg- 

 lect" of individual features with the "retention" of common 

 features), the latter is capable of accurate formulation in 

 terms of certain recognized techniques determined by the 

 character of the event to be measured, the nature of the 

 recording device and its calibration, and its application in a 

 specific situation. There are rules for measuring, and the 

 meaning of any physical concept must not be separated from 

 its techniques of measurement. ' In general, we mean by any 

 concept nothing more than a set of operations; the concept is 

 synonymous with the corresponding set of operations. If the 

 concept is physical, as of length, the operations are actual 

 physical operations, namely, those by which length is meas- 

 ured; or if the concept is mental, as of mathematical con- 

 tinuity, the operations are mental operations, namely those 

 by which we determine whether a given aggregate of magni- 



