HYPOTHETICAL AND DISJUNCTIVE SYLLOGISMS 357 



quality of the &quot; If&quot; proposition just as in the case of categoricals 

 the quantity of the predicate depends on the quality of the proposi 

 tion. Thus, the consequent of the proposition &quot; If any S is M that 

 S is always P &quot; is undistributed, because the proposition, being 

 affirmative, refers indefinitely to &quot;some&quot; cases of 5 being P y and 

 does not by any means tell us that the cases of 5 being M are all 

 the cases of 5 being P : S may be P on other grounds and for 

 other reasons also. Whereas, in the negative proposition &quot; Some 

 times if an S is M that S is not P&quot; the consequent viz. S being 

 P 1 is distributed ; for, the some instances referred to of S being 

 M are not any instances of 5 being P ; they are excluded from the 

 whole class of cases in which S is P. 



Both premisses and conclusion may, however, be expressed 

 in the modal, as well as in the quantified form : &quot; If B is true C 

 is true ; If A is true B is true ; therefore, If A is true C is true &quot; ; 

 or&quot; If any S is M that S is always P ; If any S is R that S is 

 always M ; therefore, If any S is R that S is always P&quot;. But 

 even though they be expressed in the modal or abstract form, the 

 syllogistic rules of quantity, as well as of quality, apply to them : 

 the consequent of the affirmative hypothetical is undistributed. 

 Hence in these syllogisms we may have fallacies analogous to un 

 distributed middle and illicit process. If Q then R ; if P then not 

 Q ; therefore, if P then not R &quot; is an example of illicit major. 



The two syllogisms given above are examples of the mood 

 Barbara of the first figure. Professor Welton gives the following 

 material example: 2 &quot;If any person is selfish, he is unhappy; if 

 any child is spoilt, that child is selfish ; therefore if any child is 

 spoilt, he is unhappy &quot;. By recognizing the ordinary distinctions 

 of quality, and of quantity [or modality (139)], in &quot;If&quot; proposi 

 tions, we may express pure hypothetical reasonings in the same 

 number of valid moods as we have for categorical syllogisms. 

 Since, however, &quot;If&quot; propositions which are particular or prob 

 lematic give us comparatively little information, it is only the 

 moods whose premisses and conclusions are universal that are of 

 any importance. 



An example of Cesare in the second figure would be : &quot; If any 

 act is done from a sense of duty, it is never formally wrong ; if 



1 In this rule that the consequent of a negative hypothetical is distributed the 

 consequent itself must be taken affirmatively ; the negative copula being understood 

 to determine the relation of consequent to antecedent. 



2 Logic, i, p. 349. 



