ORDER, NUMBER, QUANTITY 263 



as such words as "organization," "pattern," "structure," 

 "complexity," "disorganization," and the like. 



But it is important to determine the empirical foundation 

 not merely for the general fact of number but also for specific 

 numbers. Though all complexes possess number, they do not 

 all possess the same number. When do two complexes possess 

 the same number? Presumably, when they possess some- 

 thing in common. But this feature which they possess 

 jointly is nothing very obvious. As Russell says, "it must 

 have required many ages to discover that a brace of pheas- 

 ants and a couple of days were both instances of the num- 

 ber 2: the degree of abstraction involved is far from easy." x 

 Clearly, not just any sort of resemblance will suffice; a pair of 

 shoes and a trio of crows may both be black, but they will not 

 thereby possess the same number. The similarity must re- 

 side, rather, in the holistic properties. Yet how may this 

 similarity be determined? The method which first suggests 

 itself is to count the respective groups and determine the 

 number of each. But this will not do, for counting itself 

 presupposes that individual numbers have been recognized 

 and arranged into a series. What is required is an activity by 

 means of which the individual members may be selected 

 from the respective groups and correlated with one another. 

 This is called the activity of setting up a one-to-one correla- 

 tion, and two aggregates which can be thus correlated are 

 said to be similar to one another. Two classes may be said 

 to be similar when for every member of the first class there is 

 one and only one member of the second, and for every mem- 

 ber of the second there is one and only one member of the 

 first. 2 By means of this technique it is possible to ascertain 

 that two groups have the same number without knowing 

 what number either group possesses. For example, in a room 

 in which every seat is occupied and there is no one standing, 

 the number of individuals is the same as the number of seats ; 

 the relation 'occupying' 1 constitutes the correlating rela- 



1 Introduction to Mathematical Philosophy, p. 3. 



2 If the occurrence of the word "one" in this definition is considered objection- 

 able, it may be avoided by a different phrasing. See Russell, op. cit., p. 15. 



