PROPOSITIONS. 55 



deduction, with simple, partial, or limited identities be- 

 tween negative terms, in the forms 



a = b, a = ab, aC = bC. 



It would be equally possible to represent affirmative 

 propositions in the negative form. Thus ' Iron is solid/ 

 might be expressed as * Iron is not not-solid/ or ' Iron is not 

 fluid'; or, taking A and b for the terms 'iron,' and * not -solid/ 

 the form would be 



A-J; 



But there are very strong reasons why we should em- 

 ploy all propositions in their affirmative form. All infer- 

 ence proceeds by the substitution of equivalents, and a 

 proposition expressed in the form of an identity is ready 

 to yield all its consequences in the most direct manner. 

 As will be more fully shown, we can infer in a negative 

 proposition, but not by it. Difference is incapable of 

 becoming the ground of inference ; it is only the implied 

 agreement with other differing objects, which admits of 

 deduction ; and it will always be found advantageous to 

 employ propositions in the form which exhibits clearly all 

 the implied agreements. 



Conversion of Propositions. 



The old books of logic contain many rules concerning 

 the conversion of propositions, that is, the transposition 

 of the subject and predicate in such a way as to obtain 

 a new proposition which will be equally true with the 

 original. The reduction of every proposition to the 

 form of an identity renders all such rules and processes 

 needless. Identity is essentially reciprocal. If the colour 

 of the Atlantic Ocean is the same as that of the Pacific 

 Ocean, that of the Pacific must be the same as that of 

 the Atlantic. Sodium chloride being identical with 

 common salt, common salt must be identical with sodium 



