50 Wisconsin Academy of Sciences, Arts, and Letters. 



(2)." In this expression it is plain that book (2) must be in relation 

 with some other element of my thought or else out of relation with each, 

 that is, irrelevant. If it be irrelevant, it has nothing to do with my 

 thought and requires no consideration. If it be related, it must be 

 with book (1) and in the relation of identity; otherwise there is no 

 repetition. Letting this relation be roughly expressed by "is," and 

 expressing thought in Tull, I obtain "I have the book (1) is the 

 book (2)". But this sentence itself is the expression of two thoughts 

 with a common factor, namely "I have the book (1)" and "Book (1) is 

 book (2)." That is, the present expression is precisely analogous to 

 "I have a book will please you", itself divisible into "I have a book" 

 and "Book will please you." The same result would be reached by a 

 double conception of book with "will please 5''0U." I may as well then 

 dismiss these cases and center attention at once on "I have a book 

 will please you." 



In this sentence suppose then that "book" is thought of once with 

 "I have" and again with "will please you." Tabulating the total I obtain 

 "I have the book (1) book (2) will please you." In this total it is more 

 necessary even than in the preceding ease to find a relation between 

 some term of one thought and a term of the other. For, if none such 

 be found, it is plain that one thought has nothing to do with the other, 

 a status which absolutely violates my conscious purpose. Also there 

 is no relation except between book (1) and book (2) ; and their re- 

 lation must again be that of identity. Otherwise the two thoughts 

 are after all concerned with different books; that is, on the one hand 

 the thoughts have still nothing to do with each other and on the other 

 hand there is no repetition. 



If there be then repetition, there must be an identity of book (1) 

 and book (2). The thought total may therefore be represented, with 

 the aid again of "is", as follows: "I have a book (1) is a book (2) 

 will please you." 



If, however, I adopt the policy of repetition, consistency requires me 

 to go further. Book (1) should be thought of once in "I have a 

 book (1)" and again in "Book (1) is a book (2)". Also book (2) 

 should be thought once in "Book (1) is a book (2)" and again in 

 "Book (2) will please you." Relations being supplied as before, my 

 thought in full would be "I have a book (1) is a book (1) is a book (2) 

 is a book f^) will please you." This, hovv^ever, is the merest begin- 

 ning. Each idea named by the word "book" is still a common factor, 

 inviting double thinking as before, with still further expansions as its 

 corollary. V/ere I to respond to all such invitations, my thought would 

 take the form "I have a book (1) is a book (2) is a book (3) is a 

 book (n)." That is, my imaginary library would overwhelm me; my 

 thought would never be completed. It seems accordingly rational to as- 

 sume that, in some cases at least the common factor of two thoughts is 



