VI.] . THE INDIRECT METHOD OF INFERENCE. 87 



a = nh 

 h = ab, 



and observing that these propositions have a common term 

 lib we can make a new substitution, gettinff 



a — h. 

 Tliis result is in strict accordance \vith 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 

 beai's 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 ever}^ 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 



j\Iercury = 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 versa. 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 usintj 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 tf 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 tlie 

 thing from the class defined. 

 Taking the terms 

 A = vowel, 



B = letter which, can be sounded alone, 

 C = letter 10, 

 tiie promises are plainly of the forms 



A = H, (I) 



C = bO. (2) 



