110 REASONING. 



noted by "fool," never coexist in the same subject; which is also the 

 exact meaning which we express when we say, that no fool is a great 

 general. Wlien we say that all quadrupeds are wann-blooded, we as- 

 sert, not only that the atti'ibutes connoted by "quadruped" and those 

 connoted by " warm-blooded" sometimes coexist, but that the former 

 never exist without the latter : now the proposition. Some wann- 

 blooded creatures are quadrupeds, expresses the first half of this mean- 

 ing, dropping the latter half; and, therefore, has been already affirmed 

 in the antecedent proposition, All quadrupeds are wann-blooded. But 

 that all wann-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 cannot be 

 infened. In order to reassert, in an inverted form, the whole of what 

 was affii-med in the proposition, All quadrupeds are warm-blooded, we 

 must convert it by contraposition, thus. Nothing which is not wann- 

 blooded is a quadruped. This proposition, and the one from which it 

 is derived, are exactly equivalent, and either of them may be substitu- 

 ted for the other ; for, to say that when the attributes of a quadruped 

 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 

 gi-eater length upon the conversion and Eequipollency 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 pi'ovince of the ait 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 distinguisliing 

 the different kinds or modes of opposition, are of use chiefly for this 

 purpose. Such considerations as these, that conti-ary propositions may 

 both be false, but cannot both be tnie ; that sub-contrary propositions 

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

 propositions one must be true and the other false ; that of two subal- 

 ternate 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 versci;* 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 intelligible, would enable 

 the truths which they convey to be apprehended in any pai'ticulai- case 

 which can occur. In this respect, however, these axioms of logic are 

 on a level with those of mathematics. That things which are equal to 

 the same thing are equal to one another, is as obvious in any pai'ticular 



'fo iSlho-traries. 



«JL^ ^ ^-^ Lf -a \ contradictories, 

 some A is not B J 



Some A is B 5 ^^^° contradictories. 



tielis ^ S -'^ilelSnot b | -spectxvely subaltemate. 



