360 THE SCIENCE OF LOGIC 



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



Therefore not A ; 



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



Therefore A ; 



(4) The Modus Ponendo Ponens : If not A then not C ; But C ; 



Therefore A. 



It will be noticed that each subordinate form of the Modus 

 Ponens is practically identical with a corresponding subordinate 

 form of the Modus Tollens, and vice versa. Each&quot; can be got from 

 the other by contraposing or converting the major (140). Thus, 

 contraposing the major of the first form of the Modus Ponens 

 we obtain &quot; If not C then not A ; But A ; Therefore C &quot; which 

 is the same as the fourth form of the Modus Tollens, except that 

 the antecedent and consequent are transposed. Similarly, by con 

 verting the major of the second form of the Modus Tollens we 

 obtain &quot; If C then not A ; But C ; Therefore not A &quot; which is 

 the second form of the Modus Ponens, with a similar transposition 

 of antecedent and consequent. 



In reasonings in the Modus Tollens care must be taken to 

 infer only the contradictory, not the contrary, of the original ante 

 cedent. Whether in the minor we sublate the consequent by 

 asserting its contradictory, or its contrary, we are warranted in 

 inferring from this merely that the antecedent is not true ; i.e. in 

 inferring its contradictory. For instance, from the premisses : &quot; If 

 there were no insane people, all lunatic asylums would be superfluous ; 

 but no lunatic asylums are superfluous &quot; : we cannot infer that 

 therefore &quot; all are insane&quot; (!) but only that therefore &quot; some are 

 insane &quot;. 



177. FALLACIES IN THE MIXED HYPOTHETICAL SYLLOGISM. 

 We have already seen (138) why we cannot pass from the 

 affirmation of the consequent to the affirmation of the antecedent, 

 or from the denial of the antecedent to the denial of the conse 

 quent, of the hypothetical proposition ; why, in other words, we 

 can infer nothing from the premisses : &quot; If A then C ; but C&quot; ; or 

 from the premisses : &quot; If A then C ; but not A &quot;. It may be well 

 to recall the reason here. It is because the form of the hypotheti 

 cal proposition does not guarantee, or imply in any way, that the 

 antecedent (A] is the indispensable or only possible ground for the 

 consequent (C], or that the latter could not be verified on other 

 grounds and in other circumstances : it merely states that A is a 

 sufficient reason for C, that A implies C, that .wherever A is, C is, 



