114 THE PRINCIPLES OF SCIENCE. 



inconsistent mth the definition, we have the following 



result : 



ABC -*%&- 



Bc. 



Abe a&c. 



For the description of the class C we have 



C - ABC -I- a&C, 



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

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

 For the class & we have 



I = a&C I a&c. 



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 



a& = a&C I a&c ; 



and as we have two propositions identical in the second 

 side of each we may substitute, getting 



& = a&, 



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

 rectilinear or not). 



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 form 



A = A&, (i) 



B = C. (2) 



No immediate substitution can be made ; but if we take 

 the contrapositive of (2), namely 



& = c, (3) 



