v-i.] THE INDIRECT METHOD OF INFERENCE. 



For the description of the class C we have 



C - ABC -I- abC, 



that is, " a rectilinear figure is either a triangle and three- 

 sided, or not a triangle and not three-sided." 

 For the class b we have 



I = abC ( abc. 



To the second side of this we may apply the process of 

 simplification by abstraction described in the last section ; 

 for by the Law of Duality 



ab = abC -\- abc ; 



and as we have two propositions identical in the second 

 side of each we may substitute, getting 



6 = ab, 



or what is not three-sided is not a triangle (whether it be 

 rectilinear or not). 



Second Example. 



Let us treat by this method the following argument : 

 " Blende is not an elementary substance ; elementary 

 substances are those which are undecomposable ; 

 blende, therefore, is decomposable." 

 Taking our letters thus 



A = blende, 



B = elementary substance, 

 C = undecomposable, 

 the premises are of the forms 



A = AJ, (i) 



B = C. (2) 



No immediate substitution can be made ; but if we take 

 the contrapositive of (2) (see p. 86), namely 



& = c, (3) 



we can substitute in (i) obtaining the conclusion 



A = Ac. 



But the same result may be obtained by taking the eight 



combinations of A, B, C, of the Logical Alphabet ; it will 



be found that only three combinations, namely, 



Abc 



aBG 



abc, 



are consistent with the premises, whence it results that 

 A = Abc, 



H 2 



