THE INDIRECT METHOD OF INFERENCE. 113 



And as the second member of this is identical with the 

 second member of ( i ) we may substitute, obtaining 



A = AB. 



This process of reducing useless alternatives, may be 

 applied again and again ; for it is plain that 



A = AB (CD | Cd -I- cD ! cd) 



communicates no more information than that A is B. 

 This abstraction of indifferent terms is in fact the con 

 verse process to that of development described in p. 104 ; 

 and it is one of the most important operations in the 

 whole sphere of reasoning. 



The reader should observe that in the proposition 



we cannot abstract C and infer 



A = B; 

 but from 



AC | Ac = BC I Be 



we may abstract all reference to the term C. 



Illustrations of the Indirect Method. 



An infinite variety of arguments and logical problems 

 might be introduced here to show the comprehensive 

 character and powers of the Indirect Method. We can 

 treat either a single premise or a series of premises. 



Take in the first place a simple definition, such as a 

 triangle is a three-sided rectilinear figure. Let 

 A = triangle 

 B three-sided 

 C = rectilinear figure, 

 then the definition is of the form 



A- BC. 



If we take the series of eight combinations of three 

 letters (see p. 106) and strike out those which are 



I 



