332 THE SCIENCE OF LOGIC 



(4) If particulars be interpreted as implying, and universals 

 as not implying, the existence of their subjects, then (a] all the 

 moods with universal conclusions will be valid : (ti) all the moods 

 in which one premiss is particular will also be found to be valid ; 

 while (c] all the moods in which from two universals we infer a 

 particular will be invalid. Therefore, all the subaltern moods and 

 all the strengthened syllogisms are, on this hypothesis, invalid ; 

 while the fifteen named fundamental moods are valid. 1 



1 66. THE SYLLOGISM AND THE QUANTIFICATION OF THE 

 PREDICATE. If Hamilton s doctrine of quantifying the predicate 

 were strictly adhered to (108, 109), it would remove all distinction 

 between subject and predicate, and, consequently, all distinction 

 of figures in the syllogism. For this &quot; unfigured syllogism &quot; 

 Hamilton gives the axiom of identity and diversity (.151): &quot; In 

 so far as two notions either both agree, or one agreeing the other 

 does not, with a common third notion, in so far these notions 

 do or do not agree with each other &quot;. 



But, apart altogether from the intrinsic unsoundness of the 

 whole quantification doctrine, every attempt to carry its applica 

 tion into the theory of the syllogism leads to results which, as 

 Dr. Keynes remarks, 2 are &quot;the reverse of simplification &quot;. 



A &quot; table of valid moods resulting from the recognition of Y [Only S is 

 P] and [its contradictory (108)] ^ \Not S alone is /&amp;gt;], in addition to A, E, I, 

 and O &quot; is made out by Dr. Keynes himself. As each of these six propositions 

 has some other form among the six to express its simple converse, it follows 

 that &quot; a valid mood in any figure is reducible to any other figure by the simple 

 conversion of one or both of the premisses. Hence, if the valid moods in any 

 one figure are determined, those of the remaining figures may be immediately 

 deduced therefrom.&quot; 



&quot; It will be found that in each figure there are twelve valid moods, which 

 are neither strengthened nor weakened.&quot; 3 



167. FINDING MIDDLE TERMS AND CONSTRUCTING FORM 

 ALLY VALID SYLLOGISMS. Scholastic logicians have been ac 

 customed to incorporate, in their treatment of the syllogism, 

 rules and directions for discovering middle terms which would 

 serve to &quot; prove&quot; judgments put forward as theses. 4 This &quot; dis 

 covery of a middle term &quot; Inventio Medii, as the process was 

 called is analogous to ftvt formation of an hypothesis in inductive 

 inquiry, and, like the latter, is a work of original endeavour 



1 KEYNES, op. cit., p. 393. 2 op. cit., 378. z ibid., p. 381. 



4 Cf. ZIGLIARA, Summa Philosophica, i. (35), xi. HICKEY, Summula Philos. 

 Schol., i. ; p. 102. 



