HYPOTHETICAL AND DISJUNCTIVE SYLLOGISMS 363 



1 80. THE MIXED DISJUNCTIVE (OR MIXED ALTERNATIVE) 

 SYLLOGISM. This form of syllogism is one in which an inference 

 is drawn from the alternative character of the major premiss by 

 means of a categorical minor which denies one (v\ some, but not alf) 

 of the alternatives. The disjunctive major Either X is true or Y 

 is true ; S is either P or Q ; Either A is B, or C is D, or E is F 

 states that either of a number of alternatives is true [and that 

 possibly all are true (145)]. The negative categorical minor sub- 

 lates or denies one or more not all of the alternatives given 

 in the major : thus giving us the right to affirm the remaining 

 alternatives in the conclusion categorically if one only be left, 

 alternately if more than one be left For, given the alternative 

 judgment &quot; Either X is true or Y is true &quot; we know that &quot; If X is 

 not true, Y is true&quot; and that &quot; If Y is not true, X is true &quot; (146). 

 Consequently, if in addition to the major we are also given that 

 &quot; X is not true&quot; we can infer categorically that &quot; Y is true &quot; ; or 

 if with the major we are also given that &quot; Y is not true] we can 

 infer that &quot; X is true &quot;. 



When the alternatives are negative either not-X or not- Y 

 they are more usually expressed in the strictly disjunctive form 

 Not both X and F(i4i). Hence, if either of the negative alter 

 natives is asserted to be false, e.g. if we sublate not-X, which by 

 the principle of the excluded middle posits X the other negative 

 alternative, not-Y, is inferred to be true, i.e. not-Y is posited ; or, 

 which is the same, Y is sublated. Hence, from the premisses 

 &quot; No man can serve God and mammon ; Saints serve God&quot; we can 

 infer that &quot; Saints do not serve mammon &quot;. But, if for minor we 

 took the proposition &quot; Spendthrifts do not serve God&quot; we could 

 infer nothing as to whether they served mammon or not : for the 

 original proposition states that a man must either not serve God 

 or not serve mammon or that he may possibly not serve either. 

 &quot;Either not-X or not-Y&quot; has been interpreted to mean &quot;Either 

 not-X or not- Y, or possibly both not-X and not- Y&quot; (145). 



Not every syllogism which contains a disjunctive (alternative) 

 premiss is a mixed disjunctive syllogism. We have the latter 

 only when the inference is based on, &ci& proceeds from, the dis 

 junction or alternation in the major. Such syllogisms, therefore, as 

 &quot; M is either P or Q ; S is M ; therefore, S is either P or Q&quot; are 

 categorical syllogisms in which one of the extremes happens to be 

 an alternative term. They may occur in any figure. 



181. VALID AND INVALID &quot; MOODS&quot; OF THE MIXED Dis- 



