THE INDIRECT METHOD OF INFERENCE. 101 



C = some 



D = heavenly bodies, 

 we have the premises 



A - AB, (i) 



CD = bCV. (2) 



Now from (i) we can draw the Contrapositive 



b = ab, 

 and substituting this expression for b in (2) we obtain 



CD = a&CD, 



which expresses the conclusion of the argument that 

 * some heavenly bodies are not fixed stars. 



Contrapositive of a Simple Identity. 



The reader should carefully note that when we apply 

 the process of Indirect Inference to a simple identity 

 of the form 



A = B, 



we may obtain further results. If we wish to know 

 what is the term not-B, we have as before, by the Law of 

 Duality, 



b = A6 -I- ab, 

 and substituting for A we obtain 



b = B6 | ab = ab. 

 But we may now also draw a second Contrapositive ; for 



we have 



a = aB -|- ab, 

 and substituting for B its equivalent A we have 



a = aA. [ ab = ab. 



Hence from the single identity A = B we can draw 

 the two propositions 



a = ab 

 b = ab, 



and observing that these propositions have a common 

 term we can make a new substitution, getting 



a = b. 



