VI.] THE INDIRECT METHOD OF INFERENCE. 99 



For the description of the class C we have 

 C = ABC -I- ahC, 

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

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

 For the class h we have 



h = cibQ -I- ahc. 

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

 simplification hy abstraction described in the last section ; 

 ibr by the Law of Duality 



ah — ahC -I- ahc ; 

 and as we have two propositions identical in the second 

 side of each we may substitute, getting 



h = ah, 

 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 = Ah, (I) 



B = C. (2) 



No immediate substitution can be made ; but if we take 

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



h = 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, I>, C, of the Logical Alphabet ; it will 

 ne found that only three combinations, namely, 



Ahc 



aliC 



ahc, 



are consistent with the premises, whence it results that 



A = Ahc, 



\i 2 



