102 THE PRINCIPLES OF SCIENCE. 



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 negative 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 w 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 



