THE INDIRECT METHOD OF INFERENCE. 103 



the premises are plainly of the form 



A = B, (i) 



C = 60. (2) 



Now by the Indirect method we obtain from (i) the 

 Contrapositive 



b = a, 

 and inserting in (2) the equivalent for b we have 



C = aO, (3) 



or the letter w is not a vowel/ 



Miscellaneous Examples of the Method. 



We can apply the Indirect Method of Inference how 

 ever many may be the terms involved or the premises 

 containing those terms. As the working of the method 

 is best learnt from examples, I will take a case of two 

 premises forming the syllogism Barbara : thus 



Iron is a metal (i) 



Metal is element. (2) 



If we want to ascertain what inference is possible con 

 cerning the term Iron, we develop the term by the Law 

 of Duality. Iron must be either metal or not-metal ; iron 

 which is metal must be either element or not-elemerit ; 

 and similarly iron which is not-metal must be either 

 element or not-element. There are then altogether four 

 alternatives among which the description of iron must be 

 contained ; thus 



Iron, metal, element, (a) 



Iron, metal, not-element, (/3) 



Iron, not-metal, element, (7) 



Iron, not-metal, not-element. () 



Our first premise informs us that iron is a metal, and if 

 we substitute this description in (7) and (3) we shall have 

 self -contradictory combinations. Our second premise 



