THE INDIRECT METHOD OF INFERENCE. 107 



Now if we want to investigate completely the meaning 



of the premises 



A = AB (i) 



B = EC, , (2) 



we examine each of the eight combinations as regards 



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



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



ABC (a) 



aBC (e) 



abC fa) 



abc. (0) 



To describe any term under the conditions of the premises 

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

 binations from this list ; thus A is represented only by 



ABC or 



A = ABC, 



similarly c = abc. 



For B we have two alternatives thus stated, 



B = ABC -I- aBC ; 

 and for b we have 



b = abC | 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 



A, B produce four combinations 



A, B, C, eight 



A, B, C, D sixteen 



A, B, C, D, E thirty-two 



A, B, C, D, E, F sixty-four 

 and so on. 



I propose to call any such series of combinations the 

 Logical Abecedarium. It holds in logical science a posi- 

 tion of importance which cannot be exaggerated. As we 

 proceed from logical to mathematical considerations it will 



