CONDITIONAL JUDGMENTS AND PROPOSITIONS 277 



of quantity in the pure hypothetical ; for its antecedent is not an 

 event, nor a group of attributes occurring in time or space (133), 

 but an abstract judgment which is either true or false once and 

 for ever (84). Quantity is here replaced by modality. But, 

 turning to modality, we encounter another obstacle to the for 

 mation of a square of opposition : for our conception of the 

 hypothetical judgment as one that asserts a necessary conse 

 quence is applicable only to the apodeictic forms, If A then C 

 and If A then not C, and not to the problematic forms, If A then 

 perhaps C, and If A then perhaps not C} 



It would be desirable, if possible, to overcome these two diffi 

 culties, in quality and modality, and to construct for hypothetical 

 a square of opposition analogous to the modal square for con 

 ditionals and categoricals. The distinctions of quality can be 

 preserved, as in the case of conditionals, by regarding the form 

 which leads up to a negative consequent If A then not C as 

 negative. The distinction between apodeictic and problematic can 

 be introduced only by so widening our definition of the hypo 

 thetical as to admit of the latter forms (If A then perhaps C ; If A 

 then perhaps not C). There is no reason why we should not do 

 this. The four forms, A, E, I, and O, will be hypothetical, if, 

 with Dr. Keynes, 2 we &quot; define a hypothetical as a proposition 

 which, starting from the hypothesis of the truth (or falsity] of a 

 given proposition^ affirms (or denies] that the truth (or falsity) of 

 another proposition is a necessary consequence thereof &quot;. We then 

 have the following four forms : 



A If A (or not A] then (necessarily) C. 

 E If A (or not A) then (necessarily] not C. 

 I If A (or not A] then possibly (perhaps) C. 

 O If A (or not A) then possibly (perhaps) not C. 



What corresponds to actual existence in the universe of discourse, in regard 

 to the existential import of assertoric categoricals, is possible truth m regard 

 to these modal hypotheticals. Thus, if we start with the independent assump 

 tion of the possible truth of A, the doctrine of opposition holds good here, 

 just as it did in the analogous assumption in the case of categoricals (124). 

 Without this assumption, however, A and O, E and I, will not be really con 

 tradictories unless A and E be interpreted differently from I and O in regard 

 to implying the possible truth of their antecedents. There is no need to 



1 In these problematic forms, as in conditionals, it will be observed that 

 &quot; Though 1 may with advantage be substituted for &quot;//&quot;. 

 p. 266. 



