V!.] THE INDIRECT METHOD OF INFERENCE. 87 



a = ab 

 b = ab, 



and observing that these propositions have a common term 

 ab we can make a new substitution, getting 



a = b. 



This result is in strict accordance with the fundamental 

 principles of inference, and it may be a question whether 

 it is not a self-evident result, independent of the steps of 

 deduction by which we have reached it. For where two 

 classes are coincident like A and B, whatever is true of 

 the one is true of the other ; what is excluded from the one 

 must be excluded from the other similarly. Now as a 

 bears to A exactly the same relation that b bears to B, the 

 identity of either pair follows from the identity of the 

 other pair. In every identity, equality, or similarity, we 

 may argue from the negative of the one side to the nega- 

 tive of the other. Thus at ordinary temperatures 



Mercury = liquid-metal, 

 hence obviously 



Not-mercury = not liquid-metal ; 

 or since 



Sirius = brightest fixed star, 



it follows that whatever star is not the brightest is not 

 Sirius, and vice versd. Every correct definition is of the 

 form A = B, and may often require to be applied in the 

 equivalent negative form. 



Let us take as an illustration of the mode of using this 

 result the argument following : 



Vowels are letters which can be sounded alone, (i) 

 The letter w cannot be sounded alone ; (2) 



Therefore the letter iv is not a vowel. (3) 



Here we have a definition (i), and a comparison of a 

 thing with that definition (2), leading to exclusion of the 

 thing from the class defined. 

 Taking the terms 

 A == vowel, 



B = letter which can be sounded alone, 

 C = letter w, 

 the premises are plainly of the forms 



A = B, (I) 



C = 60. (2) 



