DEDUCTIVE REASONING. 61 



other case the rule will be found capable of verification by 

 the principle of inference. The process when performed as 

 here described will be found free from the liability to 

 error which I have shown a to exist in Immediate Inference 

 by added Determinants, as described by Dr. Thomson b . 



Inference with Tivo Simple Identities. 



One of the most common forms of inference, and one to 

 which I shall especially direct attention, is practised with 

 two simple identities. From the two statements that 

 London is the capital of England and London is the 

 most populous city in the world/ we instantaneously draw 

 the conclusion that The capital of England is the most 

 populous city in the world/ Similarly, from the identities 

 Hydrogen = Substance of least density 

 Hydrogen = Substance of least atomic weight, 

 we infer 



Substance of least density = Substance of least atomic 



weight. 



The general form of the argument is exhibited in the 

 symbols 



B = A (i) 



B=C (2) 



hence A = C. (3) 



We may describe the result by saying that terms 

 identical with the same term are identical with each 

 other ; and it is impossible to overlook the analogy to the 

 first axiom of Euclid that things equal to the same thing 

 are equal to each other. It has been very commonly sup 

 posed that this was a fundamental principle of thought 

 incapable of reduction to anything simpler. But I enter 

 tain no doubt that this form of reasoning is only one case 



a Elementary Lessons in Logic, p. 86. 

 b &amp;lt; Outline of the Laws of Thought, 87. 



