290 THE SCIENCE OF LOGIC 



Opposition of Alternative Judgments. Before considering the 

 opposition of these judgments we must decide whether they are 

 to be interpreted modally or assertorically . Both interpretations 

 are possible, but the assertoric seems to keep more closely 

 to common usage. This will be seen by asking how a person 

 would contradict the ordinary alternative forms &quot;Every S is 

 either P or Q&quot; and &quot;Either X or Y&quot;. Interpreted modally, 

 their contradictories would be &quot;An S need not be either P or Q,&quot; 

 and &quot;Possibly (Perhaps] neither X nor Y&quot; respectively. In 

 terpreted assertorically, they would be &quot; Some S s are neither P 

 nor &amp;lt;2&quot; and &quot;Neither X nor Y&quot; respectively. The latter forms 

 would in all probability be regarded as necessary for denial of 

 the original propositions, thus showing that the assertoric inter 

 pretation is the more usual one. 



The typical modal forms would be : 



A Either X or Y \ 

 ^-Neither X nor y } Necessa ^ 

 I_ Perhaps Either X or Y \ 

 ^-Perhaps Neither X nor Y j 

 The typical assertoric forms would be 



A All S s are either P or Q\ . 



T- AT- (-&amp;gt; / n /7 f Universal. 



E No Ss are either P or Q ) 



ISome S s are either P or Q \ Part i cu lar. 

 O Some Ss are neither P nor Q } 



It will be observed that in both cases the negative forms are 

 not alternative but remotive propositions, and are equivalent to 

 the copulative or conjunctive categoricals : Both X and Y ; Per 

 haps both X and Y ; All Ss are both P and Q ; Some S s are 

 both P and Q. 1 



Eductions from Alternative Judgments. In order to secure 

 eductions analogous to those from categorical propositions, we 



1 For a fuller treatment of inferences from complex and compound (alternative 

 and conjunctive) propositions, see Keynes, op. cit., Appendix C, chap, ii., pp. 478 

 sqq. When dealing with propositions that have simple predicates, we cannot dis 

 tinguish between merely incompatible and contrary propositions. We can, however, 

 when the predicate is a complex term. Thus the propositions, &quot; He is both sober 

 and industrious &quot; and &quot; He is either not sober or not industrious&quot; (or &quot; He is not 

 both sober and industrious&quot;), are contradictories. The propositions, &quot; He is both 

 sober and industrious&quot; and &quot;He is neither sober nor industrious,&quot; are contraries. 

 The propositions &quot; He is both sober and industrious &quot; and &quot; He is not sober &quot; (or 

 &quot; He is not industrious &quot;) are incompatible or repugnant, simply. 



