180 REASONING. 



for the other; for, to say that when the attributes of a quad- 

 ruped are present, those of a warm-blooded creature are pre- 

 sent, is to say that when the latter are absent the former are 

 absent. 



In a manual for young students, it would be proper to 

 dwell at greater length on the conversion and sequipollency of 

 propositions. For, though 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 language. 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 con- 

 siderations as these, that contrary propositions may both be 

 false, but cannot both be true ; that subcontrary propositions 

 may both be true, but cannot both be false ; that of two con- 

 tradictory propositions one must be true and the other false ; 

 that of two subalternate propositions the truth of the uni- 

 versal 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 explained, seem almost too obvious 

 to require so formal a statement, since the same amount 

 of explanation which is necessary to make the principles intel- 

 ligible, would enable the truths which they convey to be 



*A11 Ai 8 B lcontrari ^ 



No A is B 



Some A is B j sub contraries. 

 Some A is not B ) 



A11 A is B 1 contradictories. 

 Some A is not B ) 



No A is B ) , 



[ also contradictories. 

 Some A is B ) 



A11 A is B \ and No A is B J tivel 8uba i terna te. 



Some A is B> Some A is not B ) 



