HYPOTHETICAL AND DISJUNCTIVE SYLLOGISMS 361 



but not vice versa. In other words, the hypothetical proposition 

 is not reciprocal in virtue of its form. Of course, if we know from 

 our acquaintance with the particular subject-matter of a given 

 hypothetical proposition that it is de facto reciprocal, that A gives 

 not merely a sufficient, but the indispensable, or only possible, reason 

 for C, and that, therefore, C involves A just as A involves C, then 

 we can infer from the presence or truth of C to the presence or 

 truth of A, and from the absence or falsity of A to the absence or 

 falsity of C : but our inference here is material, not forma!. 



The formal fallacy of inferring the falsity of C from the falsity 

 of A is analogous to illicit major in the categorical syllogism ; 

 that of inferring the truth of A from the truth of C is analogous 

 to undistributed middle in the categorical syllogism. This will 

 be evident if we reduce the mixed hypothetical syllogism to the 

 categorical (182). 



178. THE REASONING IN THE MIXED HYPOTHETICAL SYL 

 LOGISM is MEDIATE REASONING. Some logicians have, for 

 various reasons, held that the reasoning in mixed hypothetical 

 syllogisms is immediate, not mediate. 1 Of course, there is no 

 middle term proper : it is not a term but a proposition which 

 serves as a &quot;middle&quot; or &quot;mediate&quot; element, by means of which 

 we reach the conclusion, and which is itself dropped out in the 

 process. There is, therefore, in the process, a real link or bond 

 which enables us to connect two elements of thought, and which 

 serves that purpose alone. This we regard as sufficient and 

 essential to constitute an inference &quot; mediate,&quot; as distinct from 

 &quot; immediate&quot;. 



Moreover, in the mixed hypothetical syllogism we infer from 

 two propositions, neither of which is inferable from the other, and 

 both of which are necessary to reach the conclusion. From the 

 proposition &quot; If A is B, C is D &quot; we can infer immediately &quot; If C is 

 not D, A is not B &quot; ; but we cannot infer categorically that A is 

 not B&quot; ui.less we are also given, as in the mixed hypothetical 

 syllogism, the premiss that &quot; C is not D&quot;. 



Furthermore, the mixed hypothetical is reducible to the 

 categorical syllogism (182); and the latter is, admittedly, a 

 mediate inference. 



There seems, therefore, to be no valid reason why we should 

 not regard the mixed hypothetical syllogism as**a process of 

 mediate inference. Of course, whenever the conjunction &quot;If&quot; is 

 1 KEYNES, op. cit., pp. 354, 357 , JOSEPH, op. cit., p. 316, n. 



