190 INTRODUCTION TO PHILOSOPHY OF SCIENCE 



not so apparent as they are in the case of description. To 

 speak of a piece of gold as a deformation in space- time is to 

 say something more abstruse about it than to say that it is 

 yellow and hard, though both are cases of classification; to 

 characterize time as an instance of the mathematical con- 

 tinuum is to speak in more abstract terms than to say that 

 it is a succession of events, though both are cases of ordering; 

 to say that the space covered by a falling body is a function 

 of the time of fall is to correlate events in nature, though in a 

 less obvious way than to say that every falling body occupies 

 space and endures through time. 



Classification and ordering, when employed as techniques 

 of elaboration, are usually characterized as abstractive. The 

 foundation for this use lies in the fact that the properties 

 specified, whether non-serial or serial, are highly general, 

 and such as apply to a wide range of events. Hence any 

 characterization of events by means of mathematical or 

 logical properties constitutes an abstract representation of 

 them. One of the best examples of abstractive techniques is 

 to be found in measurement. 1 This is an operation which 

 involves recognition of the quantitative features of events 

 and the possibility of ordering them on the basis of certain 

 types of relationships. The operation is called measurement, 

 and the number so obtained is called the measured value; 

 through the operation it becomes applied to the event as an 

 abstract feature of it. The use of mathematics as a tool in 

 science is based upon its abstract character. Similar applica- 

 tions of abstractive techniques may be seen in the "reduc- 

 tion' 1 of consciousness to physiological processes, and of 

 physiological processes to physico-chemical processes. 



Correlation and associational techniques may be called, 

 by contrast, concretive. They are concerned not with sim- 

 plification through neglect of specific differences, but with 

 complication through the association of events into more 

 inclusive wholes. As was seen in Chapter VI, any association 

 of events determines a more complex event of which the 



1 See Chapter VI, pp. 112-115. 



