16 THE ANATOMY OF SCIENCE 



in the random order of their arrival. No longer 

 does he check off the oldest boy with "eeny" and 

 the next oldest with "meeny," but he notices 

 that the last boy enters at the word "nigger." 

 The next day the boys come in another order, 

 but again the last one enters at the word "nig- 

 ger," and this proves always to be the case if 

 the boys are all there. The lame boy says to 

 himself, "If it had been a larger class the last 

 word might always have been 'toe.' " 



The boy has now made an important obser- 

 vation, and if he tries the same method with 

 other sets of objects he discovers an empirical 

 law, perhaps the most important scientific law 

 that has ever been discovered. He finds that for 

 any such set, regardless of the order in which 

 the individuals occur, there is a constant some- 

 thing which indeed can be represented by an 

 order-name, but this order-name now answers 

 the question "How many?" 



I do not mean to imply that historically the 

 ordinal number came before the cardinal, nor 

 can we know how, in course of time, the law that 

 every set has a cardinal number was abstracted 

 from particular sets of objects, events and 

 ideas ; nor how this law itself underwent further 

 refinement until it now seems almost to be a 



