CATEGORICAL JUDGMENTS AND PROPOSITIONS 24 1 



&quot; No woman is now hanged for theft in England &quot; converts to &quot; No one 

 now hanged for theft in England is a woman &quot;. 



These last two examples are peculiar : they suggest questions about the 

 sphere of reference of the judgment, and about the existence of the things 

 spoken of, in that sphere. These questions will recur later on (Chap. VII.). 



Exclusive and exceptive propositions, such as &quot; None but the brave 

 deserve the fair,&quot; when resolved into their constituents, yield (i) an I proposi 

 tion, &quot; Some brave deserve the fair,&quot; which may be converted simply ; and (2) 

 an E proposition, &quot; No non-brave deserve the fair,&quot; which also converts simply 

 to &quot; None who deserve the fair are non-brave &quot;. This latter obverts to &quot; All 

 who deserve the fair are brave,&quot; which gives (i) as its converse, and which is 

 itself the simple predicative form that represents most fully the force of the 

 original exponible. 



1 1 9. CONTRAPOSITION is that process of immediate inference 

 by which from a given proposition we infer another having for its 

 subject the contradictory of the original predicate. This definition 

 leaves it an open question whether the predicate of the inferred 

 proposition will be the original subject or its contradictory. It 

 may be either : for each of these forms [(P S) and (P 5)] is 

 the obverse of the other. 



We arrive at both forms indirectly by a successive application 

 of obversion and conversion. Each form makes an assertion about 

 the contradictory of the original predicate. This contradictory 

 term can be reached only by obverting the original proposition ; 

 and it can be transposed into the place of the subject if this 

 obverse proposition can be converted. Thus SaP obverts to 

 SeP : and this latter converts to PeS which is the first con- 

 trapositive form given above. By obverting this again we get 

 PaS, the second form given above. 



Some logicians call the former of these two the contrapositive, 

 seeing that it is reached first ; and the latter the obverted contra- 

 positive. Others, however, looking upon contraposition as a 

 species of conversion calling it conversion by contraposition, or 

 conversion by negation and seeing that ordinary conversion does 

 not change the quality of the original proposition, fix upon the 

 second and more symmetrical form (P S) as the contrapositive. 

 Modifying somewhat a suggestion of Dr. Keynes, 1 we will call 

 the former (P 5) the partial or simple contrapositive, and the 

 latter (P S) the/// or obverted contrapositive. 



Hence the following rule : 



^op.cit., p. 135. 

 VOL. I. 1 6 



