364 THE SCIENCE OF LOGIC 



JUNCTIVE SYLLOGISM. The mood in which, by denying portion 

 of the alternatives, we posit the remainder, is called the Modus 

 Tollendo Ponens. From the nature of the alternative proposition 

 it is evident that this mood is always valid. It will be noted that 

 we need only contradict one alternative in order to posit the re 

 mainder : the contrary of any alternative is not only sufficient but 

 superfluous. For example, from the premisses &quot; Either all A s 

 are B or all Cs are D ; but some A s are not B &quot; we can infer the 

 same conclusion as if the minor were &quot; No A s are B&quot; viz. the 

 conclusion that &quot; Therefore all Cs are D &quot;. As in the case of 

 mixed hypothetical, we may distinguish four forms of the present 

 mood according to the affirmative or negative character (a) of the 

 alternative sublated in the minor, and (b) of the alternative posited 

 in the conclusion. They are : 



(1) Either X or Y, but not X, therefore Y ; 



(2) Either X or not Y, but not X, therefore not Y ; 



(3) Either not X or Y, but X y therefore Y ; 



(4) Either not X or not Y, but X, therefore not Y. 



These four forms will be seen to be equivalent to the four cor 

 responding forms of the Modus Ponens of the mixed hypothetical 

 syllogism (176) when the denial of the first alternative is taken 

 as the antecedent of the hypothetical premiss, and to the four 

 corresponding forms of the Modus Tollens when the denial of the 

 second alternative is so taken. Thus, the first form &quot; Either X 

 or Y, but not X, therefore Y&quot; will yield (\yifnotX then Y, but 

 not X, therefore Y&quot; which is the Modus Tollendo Ponens of the 

 Modus Ponens ; and (2) &quot; If not Y then X y but not X, therefore 

 Y,&quot; which is the Modus Tollendo Ponens of the Modus Tollens. 



The only other possible &quot; mood &quot; of the mixed disjunctive 

 syllogism is that in which, by positing in the minor a portion of 

 the alternative major, we sublate the remainder of the latter in the 

 conclusion. This is called the Modus Ponendo Tollens ; and it may 

 be expressed thus : &quot; Either X or Y, but X, therefore not Y&quot; 

 This mood informally invalid, because the correct formal interpre 

 tation of the alternative proposition is the non-exclusive interpreta 

 tion : &quot; Either X or Y or possibly both &quot; : which does not give us 

 any right to sublate either alternative by positing the other (145). 

 The fallacy corresponds to that referred to in the case of mixed 

 hypothetical (177). 



Of course, if we know from the subject-matter in question 



