io6 



EEASONING. 



by " rash," never coexist in the same 

 subject ; which is also the exact mean- 

 ing which would be expressed by saying, 

 that no rash man is a great general. 

 When we say that all quadrupeds are 

 warm-blooded, we assert, not only that 

 the attributes connoted by "quad- 

 ruped " and those connoted by " warm- 

 blooded " sometimes coexist, but that 

 the former never exist without the 

 latter : now the proposition. Some 

 warm-blooded creatures are quadru- 

 peds, expresses the first half of this 

 meaning, dropping the latter half ; 

 andthereforehas been alreadyaflBrmed 

 in the antecedent proposition, All 

 quadrupeds are warm-blooded. But 

 that aU 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 cannot be inferred. 

 In order to reassert, in an inverted 

 form, the whole of what was affirmed 

 in the proposition. All quadrupeds are 

 warm-blooded, we must convert it by 

 contraposition, thus. Nothing which 

 is not warm-blooded is a quadruped. 

 This proposition, and the one from 

 which it is derived, are exactly equi- 

 valent, 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 aequi- 

 poUency 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 im- 

 portant 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 im portant 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 con- 

 trary 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 propositions one 

 must be true and the other false ; that 

 of two subaltemate 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 versd ; * 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 neces- 

 sary to makethe principles intelligible, 

 would enable the truths which they 

 convey to be apprehended in any par- 

 ticular 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 statement ; 

 and if no such general maxim had ever 

 been laid down, the demonstrations 

 in Euclid would never have halted for 

 any difficulty in stepping across the 



lom:iSnotB}-^--*rarie8. 

 simeiSnotB}--tradictories. 



also contradictories. 



„„, No AisB 

 ^^°- Some A is not B 



Borne A is B 



J- respectively subaltemate. 



