THE INDIRECT METHOD OF INFERENCE. 103 



the premises are plainly of the form 



A - B, (i) 



= 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 riot-element ; 

 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. (J) 



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

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

 self -contradictory combinations. Our second premise 



