INFERENCE IN GENERAL. 221 



In a manual for young students, it would be 

 proper to dwell at greater length upon the conversion 

 and sequipollency of propositions. For, although that 

 cannot be called reasoning or inference which is a 

 mere reassertion in different words of what had been 

 asserted before, there is no more important intellectual 

 habit, nor any the cultivation of which falls more 

 strictly within the province of the art of logic, than 

 that of discerning rapidly and surely the identity of 

 an assertion when disguised under diversity of lan- 

 guage. That important chapter in logical treatises 

 which relates to the Opposition of Propositions, and 

 the excellent technical language which logic provides 

 for distinguishing the different kinds or modes of 

 opposition, are of use chiefly for this purpose. Such 

 considerations as these, that contrary propositions 

 may both be false, but cannot both be true ; that 

 sub-contrary propositions may both be true, but 

 cannot both be false ; that of two contradictory pro- 

 positions one must be true and the other false ; that 

 of two subalternate propositions the truth of the 

 universal proves the truth of the particular, and the 

 falsity of the particular proves the falsity of the 

 universal, but not vice versa*; are apt to appear, at 

 first sight, very technical and mysterious, but when 



*A11 AisB} 

 No AisBf contranes - 



Some A is B \ 



a A A r> fsubcontranes. 



Some A is not B } 



All A is B } 



Some A is not B Contradictories. 



No AisB) , 



SomeAisBf alsocontradlctones - 

 All AisB) No AisB ) 

 Some A is Bf and Some A is not B } pectively subalternate. 



