ORDER, NUMBER, QUANTITY 271 



operations play a somewhat larger part in the determination 

 of the meanings of its basic concepts. 



QUANTITY : EMPIRICAL FOUNDATION 



The greatest difficulty in connection with the concept of 

 quantity is a terminological one. Authorities disagree es- 

 sentially in the way in which "magnitude" and "quantity' 

 are to be used, and in the way in which these two notions 

 are to be connected with "number' 1 ' and "measurement." 1 

 In the face of this confusion almost any use of terms is 

 justifiable. In what follows, the term "magnitude" will be 

 avoided, and the term "quantity" will be considered to be 

 empirically definable as a certain feature of groups, and 

 scientifically definable as the number which is attached 

 through the technique of measurement to such empirical 

 groups. 



The fact that one speaks commonly of quantity of time, 

 quantity of space, quantity of light, quantity of pleasure, 

 and the like, suggests that there are events which exhibit 

 certain properties which may be defined as quantitative. 

 The problem is to locate such events and then endeavor to 

 select that property in terms of which they are identified. 



The most obvious feature of quantities is that they are 

 always quantities of something — length, duration, motion, 

 weight, sensitivity, pain, wealth, etc. This is simply to say 

 that quantities are always qualities, i.e., events which exhibit 

 quantitative differences or resemblances also exhibit quali- 

 tative similarities. Thus if three lines differ quantitatively 

 they resemble one another qualitatively in the fact of one- 

 dimensional extension, and if three pleasures differ quanti- 

 tatively they resemble one another in being pleasures of the 

 same kind — say, of taste, or of musical appreciation. 



The second feature of quantity is its relativity; an event 

 is called a quantity only by virtue of the existence of at 

 least two other events which exhibit varying degrees of the 



1 See Bertrand Russell, Principles of Mathematics, Part III; W. E. Johnson, Logic 

 (Cambridge: Cambridge University, Vol. II, 1922), Chap. VII; A. Spaier, La pensSe 

 et la quantite (Paris: Alcan, 1927). 



