INFERENCE IN GENERAL. 



105 



connoted by living creature was aflBrm- 

 ed of Socrates when he was asserted 

 to be a man. If the propositions are 

 negative, we must invert their order, 

 thus : Socrates is not a living creature, 

 therefore he is not a man ; for if we 

 deny the less, the greater, which in- 

 cludes it, is already denied by impli- 

 cation. These, therefore, are not 

 really 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 of con- 

 clusions 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 pre- 

 dicate, and framing out of the same 

 terms thus reversed another proposi- 

 tion, 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 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 convertible 

 into Some B is A. This process, 

 which converts an universal proposi- 

 tion into a particular, is termed con- 

 version per accidens. From the pro- 

 position, Some A is not B, we cannot 

 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 



* The diiferent cases of ^quipollency, 

 or " Equivalent Prepositional Forms," are 

 set forth with some fulness in Professor 

 Bain's Logic. One of the commonest of 

 these changes of expression, that from 

 aflSrming a proposition to denying its nega- 

 tive, or vice vend, Mr. Bain designates, 

 very happily, by the name Obversion. 



usually recognised of converting 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 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 BJ, and [A]. The original pro- 

 position, Some A is not B, is first 

 changed into a proposition aequipollent 

 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, admits of 

 conversion in the first mode, or, as it 

 is called, simple conversion.* 



In all these cases there is not really 

 any inference ; there is in the conclu- 

 sion no new truth, nothing but what 

 was already asserted in the premises, 

 and obvious to whoever apprehends 

 them. The fact asserted in the con- 

 clusion is either the very same fact, or 

 part of the fact, asserted in the original 

 proposition. This follows from our 

 previous analysis of the Import of 

 Propositions. "When we say, for ex- 

 ample, that some lawful sovereigns are 

 tyrants, what is the meaning of the 

 assertion ? That the attributes con- 

 noted 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 sove- 

 reigns ; 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 conse- 

 quences 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 



* As Sir William Hamilton has pointed 

 out, " Some A is not B" may also be con- 

 verted in the following form : " No B is 

 tome A." Some men are not negroes ; 

 therefore. No negroes are tome men (e.g. 

 Europeans). 



