FIGURES AND MOODS OF THE SYLLOGISM 331 



which is next to A in scientific importance, is also next in diffi 

 culty to prove, having four ways. Then comes the I proposition, 

 which gives us indefinite though positive knowledge, with six ways 

 for proof. And least important of all is the O proposition, with 

 its indefinite and negative information, and its eight ways of 

 proof. 



165. THE VALID MOODS AND THE EXISTENTIAL IMPORT OF 

 PROPOSITIONS. In the chapter on the Existential Import of Judg 

 ments and Propositions, we examined the bearing of the various con 

 ceivable hypotheses, there suggested, on the doctrine of opposition 

 and immediate inference (127). How do those suppositions 

 affect the validity of syllogistic reasoning ? 



(1) If propositions be interpreted as implying the existence 

 of their subjects, their predicates, and the contradictories of these, 

 then all the moods given already as valid remain valid. 



(2) If propositions be taken to imply the existence of their 

 subjects only, then, since the negative proposition will not guar 

 antee the existence of its predicate, any mood will be invalid in 

 which the minor term, S, occurs as the predicate of a negative 

 minor premiss. This cannot happen in the first (direct), second, 

 or third figures. It does happen, however, in Camenes, and its 

 subaltern mood of the fourth figure, (or Celantes with its subaltern, 

 the corresponding indirect moods of the first; cf. 173): these 

 moods are, therefore, invalid, if their conclusions be stated cate 

 gorically, i.e. without the proviso, &quot; If 5 exist&quot;. 



It will be found, further, that on the present supposition the 

 reduction of these moods (to Celarent of the first figure) is impos 

 sible (168). They involve the conversion of the new conclusion 

 P e S, the existence of whose predicate, S, was not given in the 

 original premisses, where 5 was predicate of an E proposition. 

 In all other cases of reduction that involve the conversion of E 

 (or the contraposition of A, as in Faksoko), the term whose 

 existence is not guaranteed in these processes has its existence 

 guaranteed in the other premiss. Hence the reduction of all the 

 other moods is legitimate on the present supposition. 



(3) On &quot; the supposition that no proposition implies the ex 

 istence either of its subject or of its predicate, all the ordinarily 

 recognized moods of figures I and 2 are valid, but none of those 

 of figures 3 and 4 excepting Camenes and the weakened form of 

 Camenes&quot;. 1 



1 KKYNES, op. cit., p. 393. 



