THE LOGICAL ABACUS. 



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italic representing a negative term, the pin is fixed in 

 the lower part of the space. Now, if one of the series of 

 combinations be ranged upon a ledge of the black-board, 

 the sharp edge of a flat rule can be inserted beneath the 

 pins belonging to any one letter say A, so that all the 

 combinations marked A can be lifted out and placed upon 

 a separate ledge. Thus we have represented the act of 

 thought which separates the class A from what is not- A. 

 The operation can be repeated ; out of the A s we can in 

 like manner select those which are B, obtaining the AB s ; 

 and in like manner we might select any other class such 

 as the aB s, the ab s or the abcs. 



If now we take the series of eight combinations of the 

 letters A, B, C, a, b, c, and wish to analyse the argument 

 anciently called Barbara, having the premises 



A = AB (i) 



B = BC, (2) 



we proceed as follows : Firstly we raise the combinations 

 marked a, leaving the A s behind ; out of these A s we 

 move to a lower ledge such as are not-B s, and to the 

 remaining AB s we join the a s which have been raised. 

 The result is that we have divided all the combinations 

 into two classes, namely, the A& s which are incapable of 

 existing consistently with premise (i), and the combina 

 tions which are consistent with the premise. Turning 

 now to the second premise, we raise out of those which 

 agree with (i) the b s, then we lower the Bc s ; lastly we 

 join the b s to the BC s. We should now find our com 

 binations arranged as below. 



