HYPOTHETICAL AND DISJUNCTIVE SYLLOGISMS 359 



a particular case, of a general rule is made more explicit ; but, 

 on the other hand, it is the abstract, hypothetical form that em 

 phasizes the necessary character of the universal premiss involved : 

 and it is on the necessary truth of this universal premiss that the 

 cogency of the syllogism depends. The major premiss If S is 

 M it is P lays down the general principle, the abstract, neces 

 sary law ; the minor This, these, some, all S s are M brings a 

 case or class of cases under it ; the conclusion explicitly applies 

 the law to those cases This, these, some, all S s are P. 



176. &quot; MOODS&quot; OF THE MIXED HYPOTHETICAL SYLLOGISM. 

 The major of the mixed hypothetical syllogism states that the 

 antecedent is a &quot; sufficient reason &quot; for the consequent : that it 

 expresses a truth with which the falsity of the consequent is in 

 compatible (138). Therefore the assertion, in the minor premiss, 

 of the truth of the antecedent, warrants the assertion, in the conclu 

 sion, of the truth of the consequent ; and, vice versa, the assertion, in 

 the minor premiss, of the falsity of the consequent, warrants the 

 assertion, in the conclusion, of the falsity of the antecedent (140). 

 We have thus two &quot; moods&quot; of the mixed hypothetical syllogism : 

 one, called the Modus Ponens or constructive syllogism in which 

 the minor premiss posits, or asserts the truth of, the antecedent of 

 the major premiss ; the other, called the Modus Tollens or destruc 

 tive syllogism in which the minor premiss sublates, or asserts the 

 falsity of, the consequent of the major premiss. 



Of each of these moods there are four possible forms, accord 

 ing as the antecedent and the consequent of the major premiss are 

 both affirmative, both negative, or one affirmative and the other 

 negative. Thus, we have in the Modus Ponens : 



(1) The Modus Ponendo Ponens : If A then C ; But A ; There 



fore C ; 



(2) The Modus Ponendo Tollens : If A then not C ; But A ; There 



fore not C ; 



(3) The Modus Tollendo Ponens: If not A then C ; But not A ; 



Therefore C ; 



(4) The Modus Tollendo Tollens: If not A then not C ; But not A ; 



Therefore not C. 



Similarly, in the Modus Tollens we have : 



(i) The Modus Tollendo Tollens : If A then C ; But not C ; 



Therefore not A ; 



