218 REASONING. 



Some A is B : No A is B, therefore Some A is not B. 

 This, too, is not to conclude one proposition from 

 another, but to repeat a second time something which 

 had been asserted at first; with the difference, that 

 we do not here repeat the whole of the previous asser- 

 tion,, but only an indefinite part of it. 



A third case is, where, the antecedent having 

 affirmed a predicate of a given subject, the conse- 

 quent affirms of the same subject something already 

 connoted by the former predicate : as, Socrates is a 

 man, therefore Socrates is a living creature ; where 

 all that is connoted by living creature was affirmed of 

 Socrates when he was asserted to be a man. If the 

 propositions are negative, we must invert their order, 

 thus : Socrates is not a living creature, therefore he 

 is not a man ; for if we deny the less, the greater, 

 which includes it, is already denied by implication. 

 These, therefore, are not really cases of inference ; 

 and yet the trivial examples by which, in manuals of 

 Logic, the rules of the syllogism are illustrated, are 

 often of this ill-chosen kind ; demonstrations in form, 

 of conclusions to which whoever understands the 

 terms used in the statement of the data, has already, 

 and consciously, assented. 



The most complex case of this sort of apparent 

 inference is what is called the Conversion of Proposi- 

 tions ; which consists in making the predicate become 

 a subject, and the subject become a predicate, and 

 framing out of the same terms, thus reversed, another 

 proposition, which must be true if the former is true. 

 Thus, from the particular affirmative proposition, Some 

 A is B, we may infer that Some B is A. From the 

 universal negative, No A is B, we may conclude that 

 No B is A. From the universal affirmative proposi- 

 tion, All A is B, it cannot be inferred that All B is A ; 



