354 THE SCIENCE OF LOGIC 



does so, for the A proposition cannot be regarded as the expression of a pro 

 position which would more naturally be /. The really important syllogisms 

 in the two moods in question are not those like the above &quot; where the pre 

 misses are palpably in an unnatural form,&quot; but &quot; those in which the position 

 of the middle term, as predicate of the major premiss and subject of the 

 minor, is the natural position &quot;. And &quot; here conversion to the first figure pro 

 duces a result as unnatural as there conversion to the fourth figure produced 

 in the premisses of an argument naturally belonging to the first &quot;- 1 An ex 

 ample of such a syllogism (Fesapo, or Fapesmo] would be &quot; No mineral 

 waters are alcoholic, and All alcohol is taxed, therefore, Some things 

 taxed are not mineral waters &quot;. Is there, then, any more natural way of 

 showing the validity of Fesapo or Fresison than by converting both premisses, 

 and arguing in Ferio ? Two other ways at least are possible. We may 

 show, as in the second figure, that the falsity of the conclusion would be in 

 compatible with what is granted in the premisses, by the reductio ad impos- 

 sibile, thus : &quot; If all things taxed were minerals, alcohol would be a 

 mineral; but it cannot be, for no mineral is. alcoholic&quot;. Or, we may con 

 vert the first premiss to &quot; No alcohol is a mineral water,&quot; and proceed by 

 fudeo-ts or exposition, as in the third figure, to point to an instance of 

 alcohol as a proof that a thing may be taxed and yet not be a mineral. 

 Which of these two processes reveals the line of thought really followed in 

 Fesapo and Fresison ? The cogency of the inference is so concealed in the 

 actual form of the premisses that it is not easy to detect or lay bare the real 

 line of thought. But it will help us if we ask : How could we most naturally 

 prove this conclusion, that &quot; Some things taxed are not mineral waters &quot; 

 by using the same middle term (alcohol) ? Obviously, by asking ourselves ; 

 Is alcohol taxed ? and is it a mineral water ? In other words, we validate an 

 argument in Fesapo or Fresison most naturally by having recourse to ex 

 position by reducing it to the third figure, rather than by the reductio ad 

 impossibile, or by reducing it to Ferio in the first. 



We cannot better conclude the foregoing analysis, which is based on that 

 of Mr. Joseph, than by quoting the latter s excellent summary of the results of 

 his inquiry: 2 &quot; There are three figures, each with a distinctive character, and 

 the imperfect figures are misrepresented by reduction to the first. The 

 first is the chief, because the demonstrative, but not because the only figure. 

 Arguments in it need not be demonstrative, but when they are, our thought is 

 moving on a higher level of intelligence, though not of cogency, than in the 

 other figures. In realizing the validity of the second figure, the inconsistency 

 involved in denying the conclusion is a more prominent moment in our 

 thought than the &amp;gt; necessity of admitting it. The third figure appeals not to 

 relations of concepts, but to experience of the conjunction of attributes (or their 

 disjunction) in the same subject, and from that argues the general possibility, 

 under conditions unspecified, of what is exhibited in a given case. There is no 

 fourth figure ; but in the first three moods of the first figure we may also argue 

 to the converse of their conclusions ; and two moods may be added, with an 

 universal negative minor premiss, in which, while the major term cannot be 

 denied of the minor without fallacy, the minor can be denied of the major ; 

 though such a conclusion is only particular, and realized by the help of exposi- 



1 JOSEPH, op. /., p. 305. a o/&amp;gt;. cit., pp. 306-7. 



