124 EEASONTNG. 



great general. When we say that all quadrupeds are warm-blooded, we 

 assert, not only that the attributes connoted by " quadruped " and those 

 connoted by " warm-blooded " sometimes co-exist, but that the former nev- 

 er exist without the latter: now the proposition. Some warm-blooded crea- 

 tures are quadrupeds, expresses the first half of this meaning, dropping the 

 latter half ; and therefore has been already affirmed in the antecedent prop- 

 osition. All quadrupeds are warm-blooded. But that all warm-blooded 

 creatures are quadrupeds, or, in other words, that the attributes connoted 

 by " warm-blooded " never exist without those connoted by " quadruped," 

 has not been asserted, and can not be inferred. In order to re-assert, in an 

 inverted form, the whole of what was affirmed in the proposition. All quad- 

 rupeds are warm-blooded, we must convert it by contraposition, thus. Noth- 

 ing which is not warm-blooded is a quadruped. This proposition, and the 

 one from which it is derived, are exactly equivalent, and either of them may 

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

 ruped are present, those of a warm-blooded creature are present, 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 equipollency of propositions. For though 

 that can not be called reasoning or inference which is a mere re-assertion in 

 different words of what had been asserted before, there is no more impor- 

 tant 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 Op- 

 position 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 can not both be true ; that subcontrary 

 propositions may both be true, but can not 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 universal proves the truth of the 

 particular, and the falsity of the particular proves the falsity of the univer- 

 sal, but not vich versa ^'"^ are apt to appear, at first sight, very technical and 

 mysterious, but when explained, seem almost too obvious to require so form- 

 al a statement, since the same amount of explanation which is necessary 

 to make the principles intelligible, would enable the truths which they con- 

 vey to be apprehended in any particular case which can occur. In this 

 respect, however, these axioms of logic are on a level with those of mathe- 

 matics. That things which are equal to the same thing are equal to one 

 another, is as obvious in any particular case as it is in the general state- 

 ment : and if no such general maxim had ever been laid down, the demon- 

 strations in Euclid would never have halted for any difficulty in stepping 

 across the gap which this axiom at present serves to bridge over. Yet no 



All AisB) , . 

 No AisBl^^"*™"^^- 

 Some A is B "> , . . 

 SomeAisnotBi-^"^^«"t''^"«^- 

 All A is B ) . T , • 

 SoineAisnotBP«"''^^^^'«™«- 

 No A is B) 1 . V ^ • 



Some A is Bf ^^'° contradictories. 



Some A is b} ""^ Some A is not b} respectively subalternate. 



