ORDER, NUMBER, QUANTITY 261 



sense it applies only to simple events, and not to complexes 

 except as they themselves are distinguishable from other 

 complexes. The two notions are obviously interrelated, yet 

 they are not identical; for example, if a group has number 

 the members of the group must be numerically distinguish- 

 able, and if an event is numerically distinguishable (from 

 another event) there must be a group (of at least two) which 

 possesses number; but it is clear that the property which is 

 possessed by the individual members is not the same as the 

 property which is possessed by the group. Before one can 

 talk about empirical foundations, therefore, one must decide 

 which of these two notions is the proper meaning to be 

 given to the concept. Jevons, for example, defines number 

 as "the empty form of difference"; 1 but Russell defines it as 

 a property of similar classes. 2 



But, in the second place, contingent upon this fact a new 

 problem arises. Which of the two notions is psychologically 

 more primitive? In other words, is all recognition of num- 

 bered groups a synthetic act involving a very rapid counting 

 of individuals, or is all recognition of individuals an analytic 

 act involving selection from totalities? Expressing the 

 same idea crudely, does one build up the idea of "many" 

 by combining "ones," or does one build up the idea of "one" 

 by breaking up a "many "? It is not likely that this question 

 can be answered with any finality. The conclusions of the 

 recent Gestalt psychology suggest that there is such a thing 

 as an immediate recognition of wholes and patterns; this 

 would seem to argue for the fact that, in certain situations 

 at least, plurality is psychologically more primitive than 

 distinguishability. Yet the notion of number is so intimately 

 associated in one's mind with the notion of counting, and 

 the ascertainment of number in very large groups is so cer- 

 tainly a matter of counting, that plurality seems to occupy a 

 secondary place in the order of experiential derivation. 



Since the issue is not important one may adopt, as in the 

 case of the concept of order, an arbitrary point of view. 



1 Principles of Science, p. 158. 2 Introduction to Mathematical Philosophy, p. 18. 



