178 REASONING. 



illustrated, are often of this ill- chosen kind; formal demon- 

 strations of 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 proposi- 

 tion, 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 pro- 

 position, All A is B, is legitimately convertible 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, we 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 mode usually recognised of converting a particular nega- 

 tive proposition, is in the form, Some A is not B, therefore, 

 something which is not B is A; and this is termed conver- 

 sion by contraposition. 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 

 original proposition, Some A is not B, is first changed into 

 a proposition sequipollent 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 con- 

 version.* 



* 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). 



