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 W 



ale. (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 ale. 



For B we have two alternatives thus stated, 



B = ABC I aBC ; 

 and for I we have 



I abC [ ale. 



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 Alecedarium. It holds in logical science a posi 

 tion of importance which cannot be exaggerated. As we 

 proceed from logical to mathematical considerations it will 



