CATEGORICAL JUDGMENTS AND PROPOSITIONS 233 



Every proposition reached by the transposition of the terms 

 of another may be called in a wide sense the converse of the 

 latter. Thus &quot; All P s are S s &quot; would be, in this wider sense, the 

 converse of &quot; All S s are P s&quot;. This is also called tiut geomet 

 rical converse : because the propositions of geometry are, as a 

 rule, thus reciprocal. But, taken in this wider sense, the converse 

 of a true proposition need not be itself true : or, if true, its truth 

 must be known independently of the convertend. It is only 

 when the process of conversion is so conducted that the converse 

 is necessarily involved in the convertend, that we have illative 

 conversion, or logical conversion in the technical sense. And for 

 the legitimacy of this process the two following rules must be 

 observed : 



RULE OF QUALITY : The quality of the proposition must re 

 main unchanged ; 



RULE OF QUANTITY : No term may be distributed in the con 

 verse which was not distributed in the convertend. 



Applying these rules to the four traditional predicative forms, 

 A, E, I, O, we obtain the following results : 



All S is P converts to Some P is S. 

 Some S is P ,, ,, Some P is S. 

 No S is P No P is S. 

 Some S is not P has no converse. 



In other words A converts to I ; I converts to I ; E converts to 

 E ; O does not convert at all. 



About the Rule of Quality there can be no difficulty ; for, since 

 the same two terms are compared in convertend and in converse, 

 it is clear that in order that the latter be true it must affirm or 

 deny the connexion according as this was affirmed or denied in 

 the convertend. 



The reason for the Rule of Quantity is no less obvious. 

 While unfolding what was implicit in the original proposition,, 

 we are obviously not at liberty to connect, in the converse, any 

 more of the denotation of either term, any greater portion of either 

 term, with the other, than was connected with this latter in the 

 convertend. This is exactly what the Rule of Quantity lays 

 down. If we bear in mind that &quot;Universals distribute their sub 

 jects and particulars do not ; while negatives distribute their 

 predicates and affirmatives do not&quot; (91), we shall have no 

 difficulty in working out the results set down above. 



