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 



Ab 



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, C, give rise to 

 eight conceivable combinations, namely 



ABC . () 



ABc (0) 



AbC (7) 



Abe (S) 



aBC (e) 



aBc (0 



abC W 



abc. (0) 



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

 of these ; for B we must select (a), (/3), (e), () ; C consists 

 of (), (?), W M ; b of (7), (S), (,), (&amp;lt;9), and so on. 



