92 THE PRINCIPLES OF SCIENCE. [chap. 



we inust ascertain which of these combinations will be 

 rendered self-contradictory by substitution; the second 

 and third will have to be struck out, and tliere wall remain 

 only AB 



ha. 

 Hence we draw the followincr inferences 



A = AB, B = AB, a ^ ah, h = ah. 

 Exactly the same method must be followed when 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 (e) 



ABc 1/3) aBc {^ 



AbG (7) abC (v) 



Abe (S) abc. {$) 



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 (a), (7), (e), {rj) ; b of (7), (S), (7;), {0), and so on. 



Now if we want to investigate completely the meaning 



of the premises A = AB (i) 



B = BC (2) 



we examine each of the eight combinations as regards each 

 premise; (7) and (S) are contradicted by (i), and (/3) and 

 Vs) by (2), so that there remain only 



ABC (a) 



aBC (e) 



abG (v) 



abc. • (6) 



To describe any term under the conditions of the premises 

 (i) and (2), we have simply to draw out the proper com- 

 binations from this list ; thus, A is represented only by 

 ABC, that is to say 



A = ABC, 

 similarly c = ahc. 



For B we have two alternatives thus stated, 



B = ABC -I- aBC ; 

 and for h we have 



h = abC -I- abc. 

 When we have a problem involving four distinct terms 

 we need to double the number of combinations, and as 

 we add each new term the combinations become twice 

 as numerous. Thus 



