INFERENCE IN GENERAL. 123 



ly cases of inference ; and yet the trivial examples by which, in manuals of 

 Logic, the rules of the syllogism are illustrated, are often of this ill-chosen 

 kind ; formal demonstrations ol conclusions to which whoever understands 

 the terms used in the statement of the data, has already, and consciously, 

 assented.* 



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

 the Conversion of propositions; which consists in turning the predicate 

 into a subject, and the subject into a predicate, and framing out of the same 

 terms thus reversed, another proposition, which must be true if the former 

 is true. Thus, from 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 proposi- 

 tion, All A is B, it can not 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 convert- 

 ible into Some B is A. This process, Avhich converts a universal propo- 

 sition into a particular, is termed conversion joer accidens. From the prop- 

 osition, Some A is not B, we can not even infer that some B is not A; 

 though some men are not-Englishmen, it does not follow that some English- 

 men are not men. The only mode usually recognized of converting a pai'- 

 ticular 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 contra- 

 position. In this case, however, the predicate and subject are not merely 

 reversed, but one of them is changed. Instead of [A] and [B],the terms 

 of the new proposition are [a thing which is not B], and [A]. The origi- 

 nal proposition. Some A is not B, is first changed into a proposition equi- 

 pollent with it, Some A is " a thing which is not B ;" and the proposition, 

 being now no longer a particular negative, but a particular affirmative, ad- 

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



In all these cases there is not really any inference; there is in the con- 

 clusion no new truth, nothing but what was already asserted in the prem- 

 ises, 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 proposition. This follows from our previous analysis of the Ira- 

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

 ereigns are tyrants, what is the meaning of the assertion ? That the attri- 

 butes connoted by the term " lawful sovereign," and the attributes connoted 

 by the term " tyrant," sometimes co-exist 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 col- 

 lection 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 co-exist in the same subject; which is also the 

 exact meaning which would be expressed by saying, that no rash man is a 



* The different cases of Equipollency, or "Equivalent Propositional Forms," are set forth 

 with some fullness in Professor Bain's Logic. One of the commonest of these changes of 

 expression, that from affirming a proposition to denying its negative, or vice versa, Mr. Bain 

 designates, very happily, by the name Obversion. 



t As Sir William Hamilton has pointed out, "Some A is not B " may also be converted in 

 the following form : " No B is some A." Some men are not negroes ; therefore. No negroes 

 are some men (e. g., Europeans). 



