106 THE PRINCIPLES OF SCIENCE. 



problem it is best to form, in the first place, a complete 

 series of all the combinations of terms involved in it. 

 If there be two terms A and B, the utmost variety of 

 combinations in which they can appear are 



AB 



A.b 



aB 



ab. 



The term A appears in the first and second ; B in the 

 first and third ; a in the third and fourth ; and b in the 

 second and fourth. Now if we have any premise, say 



A = B, 



we must ascertain which of these combinations would be 

 rendered self-contradictory by substitution ; the second 

 and third would have to be struck out, and there would 



remain 



AB 



ab. 

 Hence we draw the following inferences 



A = AB, B = AB, a = ab, b = ab. 

 Exactly the same method must be followed where a 

 question involves a greater number of terms. Thus by 

 the Law of Duality the three terms A, B, 0, give rise to 

 eight conceivable combinations, namely 



ABC (a) 



ABc (ft) 



AbC (7) 



Abe (8) 



aBC (e) 



abC (?) 



ale. (0) 



The development of the term A is formed by the first four 

 of these ; for B we must select (a), (ft), (e), () ; C consists 

 of (a), (7), W ; b of (7), (J), (,), (0), and so on. 



