INFERENCE IN GENERAL. 179 



In all these cases there is not really any inference ; there is 

 in the conclusion no new truth, nothing hut what was^ already 

 asserted in the premises, and obvious to whoever apprehends 

 them. The fact asserted in the conclusion is either the very 

 same fact, or part of the fact, asserted in the original proposi- 

 tion. This follows from our previous analysis of the Import 

 of Propositions. When we say, for example, that some lawful 

 sovereigns are tyrants, what is the meaning of the assertion ? 

 That the attributes connoted by the term " lawful sovereign," 

 and the attributes connoted by the term " tyrant," sometimes 

 coexist in the same 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 rash man, 

 we mean that the attributes connoted by " great general," 

 and those connoted by " rash," never coexist in the same sub- 

 ject; which is also the exact meaning which would be ex- 

 pressed 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 " 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 quad- 

 rupeds are warm-blooded, we must convert it by contra- 

 position, thus, Nothing which is not warm-blooded is a quad- 

 ruped. This proposition, and the one from which it is derived, 

 are exactly equivalent, and either of them may be substituted 



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