IN TROD UCTION. 2 1 



General Formula of Logical Inference. 



The one supreme rule of inference consists, as I have 

 said, in the direction to affirm of anything whatever is 

 known of its like, equal or equivalent. The Substitution 

 of Similars is a phrase which seems aptly to express the 

 power of mutual replacement existing between any two 

 objects which are to a sufficient degree like or. equivalent. 

 It is a matter for further investigation to point out when 

 and for what purposes a degree of similarity less than 

 complete identity is sufficient to warrant substitution. 

 For the present we think only of the exact sameness 

 expressed in the form 



A = B. 



Now if we take the letter C to denote any third con- 

 ceivable object, and use the sign &> in its stated meaning 

 of indefinite relation, then the general formula of all 

 inference may be thus exhibited : 



From A = B C 



we may infer A C 



or, in words In whatever relation a thing stands to a 

 second thing, in the same relation it stands to the like or 

 equivalent of that second thing. The identity between A 

 and B allows us indifferently to place A where B was or 

 B where A was, and there is no limit to the variety of 

 special meanings which we can bestow upon the signs 

 used in this formula consistently with its truth. Thus if 

 we first specify only the meaning of the sign o, we may 

 say that if C is the weight of B, then C is also the weight 

 of A. Similarly 



If C is the father of B, C is the father of A ; 



If C is a fragment of B, C is a fragment of A ; 



If C is a quality of B, C is a quality of A ; 



If C is a species of B, C is a species of A ; 



If C is the equal of B, C is the equal of A ; 

 and so on ad infinitum. 



