INFERENCE IN GENERAL. 109 



man, therefore Socrates is a living creature ; where all tliat is connoted 

 by living creature was aflirmcd of Socrates when he was asserted to 

 be a man. If the propositions are negative, we must invcit their 

 order, thus : Socrates is not a living creature, therefore he is not a 

 man ; for if we deny tlie less, the greater, which includes it, is already 

 denied by implication. These, therefore, are not really cases of infer- 

 ence ; and yet the trivial examples by which, in manuals of Logic, the 

 rules of the syllogism are illustrated, arc often of this ill-choscu kind ; 

 demonstrations in form, of conclusions to which whoever understands 

 the terms used in the statement of the data, has already, and con- 

 sciously, assented. 



The most complex case of this sort of apparent inference is what is 

 called the Conversion of Propositions ; which consists in making the 

 predicate become a subject, and the subject become a predicate, and 

 framing out of the same terms, thus reversed, another j^roposition, 

 which must be true if the former is true. Thus, fi-om the particular 

 affirmative proposition, Some A is B, we may infer that Some B is A.' 

 From the universal negative. No A is B, we may conclude that No 

 B is A. From the universal affirmative proposition, All A is B, it 

 cannot be inferred that All B is A ; though all water is liquid, it is not 

 implied that all liquid is water ; but it is implied that some liquid is 

 so ; and hence the proposition. All A is B, is legitimately conveitible 

 into Some B is A. This process, which converts an universal propo- 

 sition into a particular, is termed conversion per accidens. From the 

 proposition. Some A is not B, \ye cannot even infer that Some B is 

 not A : though some men are not Englishmen, it does not follow that 

 some Englishmen are not men. The only legitimate conversion, if 

 such it can be called, of a particular negative proposition, is in the 

 form. Some A is not B, therefore, something which is not B is A ; and 

 this is termed conversion by contraposition. In this case, however, 

 the predicate and subject are not merely reversed, but one of them is 

 altered. Instead of [A] and [B], the terms of the new proposition 

 are [a thing which is not B], and [A]. The original proposition, 

 Some A is not B, is first changed into a proposition asquipollent with 

 it. Some A is " a thing which is not B ;" and the proposition, being 

 now no longer a paiticular negative, but a particular affirmative, admits 

 of conversion in the first mode, or, as it is called, simple conversion. 



In all these cases there is not really any infei'ence ; there is m the 

 conclusion no new truth, nothing but what was already asserted in the 

 premisses, and obvious to whoever apprehends them. The fact as- 

 serted in the conclusion is either the very same fact, or part of the fact, 

 asserted in the original proposition. This follows fi'om our previous 

 analysis of the Import of Propositions. When we say, for example, 

 that some la\vful sovereigns arc tyrants, what is the meaning of the 

 assertion ? That the attributes connoted by the temi " lawful sover- 

 eign," 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 fool, we 

 mean that the attributes connoted by " great general," and those con- 



