220 REASONING. 



individual. Now this is also precisely what we mean, 

 when we say that some tyrants are lawful sovereigns ; 

 which, therefore, is not a second proposition inferred 

 from the first, any more than the English translation 

 of Euclid's Elements is a collection of theorems 

 different from, and consequences of, those contained 

 in the Greek original. Again, if we assert that no 

 great general is a fool, we mean that the attributes 

 connoted by " great general," and those connoted 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. 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 

 coexist, but that the former never exist without the 

 latter : now the proposition, Some warm-blooded 

 creatures are quadrupeds, expresses the first half of 

 this meaning, dropping the latter half; and, therefore, 

 has been already affirmed in the antecedent proposi- 

 tion, 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 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 contraposi- 

 tion, thus, Nothing 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 quadruped are present, those 

 of a warm-blooded creature are present, is to say, that 

 when the latter are absent the former are absent. 



