CONDITIONAL JUDGMENTS AND PROPOSITIONS 271 



are &quot;Sometimes if an S is M it is not P&quot; and &quot; Sometimes if A is 

 y Cis D &quot;. We may take, as a material example, the following : 



A If any country is well governed its people are happy. 



E If any country is well governed its people are not happy. 



I Sometimes if a country is well governed its people are happy. 



O Sometimes if a country is well governed its people are not 

 happy. 



Here A means that happiness always de facto 1 accompanies 

 good government ; E that whenever we have good government 

 we have never de facto happiness accompanying it ; I that good 

 government is sometimes accompanied, O that it sometimes is 

 not accompanied, by happiness. 



If we interpret the conditional modally&amp;gt; we have only to sub 

 stitute for the signs of quantity the modal signs &quot; must&quot; &quot; cannot&quot; 

 &quot; may&quot; and &quot; need not &quot;. Remembering, then, that the force of 

 the problematic is to deny the necessary connexion asserted by 

 the apodeictic, we might write, in the example just given : 



A If a country be well governed its people must be happy. 



E If a country be well governed its people cannot be happy. 



I Though a country be well governed nevertheless its people 

 may be happy. 



O Though a country be well governed nevertheless its people 

 need not be happy. 



In the latter pair of propositions the conjunctions &quot; though &quot; 

 and &quot; nevertheless&quot; (&quot; yet,&quot; &quot; still &quot;) make their appearance for the 

 first time. Their force is to connect or conjoin two statements 

 whose mutual compatibility excludes some (suggested) neces 

 sary combination of judgments. Propositions of this kind are 

 commonly called adversative or discretive propositions. 



The modal statement of the conditional brings out its inferential element 

 better than the assertoric form. The latter, too, is open to ambiguity. 

 Take the proposition, &quot; If any parents gamble some children will be ill- 

 treated^. Is this an A or an I proposition? It will be A if it be inter 

 preted to mean that the ill-treatment of some children always follows the 

 gambling of parents ; it will be I if it be taken to mean that the ill-treatment 

 of some children results, at least sometimes, from the gambling of parents. 

 In the example given the latter is probably meant, for it alone is true. The 

 proposition, &quot; If a man plays recklessly he sometimes loses&quot; is interpreted 

 by Professor Welton 2 as an A proposition, on the ground that it means &quot; If 

 any man plays recklessly // always follows that he has some losses &quot;. This 

 latter, however, would scarcely be admitted as universally true, and hence 



1 i.e. interpreting the forms assertorically. z op. cit. t i., p. 273. 



