vi.] THE INDIRECT METHOD OF INFERENCE. Ill 



or class so far as furnished by that proposition in accordance 

 with the Laws of Thought. The machine is thus the em- 

 bodiment of a true logical system. The combinations are 

 classified, selected or rejected, just as they should be by a 

 reasoning mind, so that at each step in a problem, the 

 Logical Alphabet represents the proper condition of a mind 

 exempt from mistake. It cannot be asserted indeed that 

 the machine entirely supersedes the agency of conscious 

 thought; mental labour is required in interpreting the 

 meaning of grammatical expressions, and in correctly im- 

 pressing that meaning on the machine ; it is further required 

 in gathering the conclusion from the remaining combina- 

 tions. Nevertheless the true process of logical inference 

 is really accomplished in a purely mechanical manner. 



It is worthy of remark that the machine can detect any 

 self-contradiction existing between the premises presented 

 to it; should the premises be self-contradictory it will be 

 found that one or more of the letter-terms disappears 

 entirely from the Logical Alphabet. Thus if we work the 

 two propositions, A is B, and A is not-B, and then inquire 

 for a description of A, the machine will refuse to give it 

 by exhibiting no combination at all containing A. This 

 result is in agreement with the law, which I have ex- 

 plained, that every term must have its negative (p. 74). 

 Accordingly, whenever any one of the letters A, B, C, D, a, 

 b, c, d, wholly disappears from the alphabet, it may be 

 safely inferred that some act of self-contradiction has been 

 committed. 



It ought to be carefully observed that the logical 

 machine cannot receive a simple identity of the form 

 A = B except in the double form of A = B and B = A. 

 To work the proposition A = B, it is therefore necessary to 

 press the keys 



A (left), copula, B (right), full stop ; 

 B (left), copula, A (right), full stop. 



The same double operation will be necessary whenever the 

 proposition is not of the kind called a partial identity 

 (p. 40). Thus AB = CD, AB = AC, A = B -|- C, A -I- B 

 = C -i- D, all require to be read from both ends separately. 



The proper rule for using the machine may in fact be 

 given in the following way : (i) Head each proposition as 

 it stands, and play the corresponding keys : (2) Convert the 



