VI.] 



THE INDIRECT METHOD OF INFERENCE. 



105 



a thin slip of wood one inch broad and about one-eighth 

 inch thick. Short steel pins are then driven in an inclined 

 position into the wood. When a letter is a large capital 

 representing a positive term, the pin is fixed in the upper 

 part of its space ; when the letter is a small italic repre- 

 senting 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 

 my one letter say A, so that all the combinations marked 

 A "can be lifted out and placed upon a separate ledge. 

 Thus we ha,ve 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's, obtaining the AB's ; and in like 

 manner we may select any other classes such as the aB's, 

 the ab's, or the abc's. 



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 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 &'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 Ab's which are incapable of existing consist- 

 ently with premise (i), and the combinations 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 EC's. 

 We now find our combinations arranged as below. 



The lower line contains all the combinations which are 

 inconsistent with either premise ; we have carried out in a 



