i64 SCIENCE AND METHOD. 



aereed ; but what Mr. Russell claims, and what appears 

 to me doubtful, is that after these appeals to intuition 

 we shall have finished : we shall have no more to make, 

 and tve shall be able to construct the whole of mathe- 

 matics without bringing in a single new element. 



IV. 



M. Couturat Is fond of repeating that this new logic 

 is quite independent of the idea of number. I will 

 not amuse myself by counting how many instances 

 his statement contains of adjectives of number, 

 cardinal as well as ordinal, or of indefinite adjectives 

 such as several. However, I will quote a few 

 examples : — 



"The logical product of two or of several propo- 

 sitions is " 



" All propositions are susceptible of two values only, 

 truth or falsehood." 



" The relative product of two relations is a relation." 

 " A relation is established between two terms." 

 Sometimes this difficulty would not be impossible 

 to avoid, but sometimes it is essential. A relation is 

 incomprehensible without two terms. It is impossible 

 to have the intuition of a relation, without having 

 at the same time the intuition of its two terms, and 

 without remarking that they are two, since, for a 

 relation to be conceivable, they must be two and 

 two only. 



V. 



Arithmetic. 



I come now to what M. Couturat calls the ordinal 

 theory, which is the groundwork of arithmetic properly 



