THE DOCTRINE OF REDUCTION 353 



permit either of these latter terms to be predicated of the other, a separate 

 mood is explicitly recognized for each alternative : Cesare and Camestres in 

 the second figure ; Disamis and Datisi in the third. Darapti combines in 

 itself both alternatives : since the premisses agree both in quality and in 

 quantity, their transposition does not give even the external semblance of a 

 new mood. It is true that &quot; in many and probably in most cases of syllo 

 gism in these figures it would be difficult to say which of the two terms was 

 naturally major and which naturally minor, for they are not generally terms 

 belonging to one series in a classification.&quot; l Whenever the extremes are 

 so related that one is naturally minor and the other naturally major, and, 

 nevertheless, it is the former that is predicated of the latter in the conclusion 

 the mood may be regarded as an indirect mood. For example, this syllo 

 gism in Festino might be regarded as indirect ; &quot; No clergymen are members 

 of Parliament ; Some professional men are members of Parliament ; there 

 fore, Some professional men are not clergymen &quot;. 



The conclusions of the fourth figure, or of the indirect moods of the 

 first, are indeed valid ; but their connexion with their premisses, or, in other 

 words, the cogency of the sequence, is not easily apparent. By what sort of 

 reflection or consideration do we persuade ourselves of its validity ? From 

 the premisses (of Bramantip or Baralipton] : All nitrogenous foods are flesh- 

 forming ; and All grains are nitrogenous : how do we justify the inference 

 that Some flesh-forming foods are grains f Apparently, by reflecting &quot; either 

 that from the given premisses it follows that All grains are flesh-forming^ 

 and our other conclusion follows by conversion from that : or else that if no 

 flesh-forming foods were grains, no nitrogenous foods would be grains ; and 

 that in that case grains could not all, or any, of them be nitrogenous &quot; 2 i.e. 

 either by the typical reasoning of the first figure, or by the reductio ad im- 

 possibile which is characteristic of the second. The same is true of Camenes 

 \Celantes} and Dimaris [Dabitis]. By the reduction of these three moods to 

 the first figure, we &quot; recognize in outward form as major and minor terms what 

 we must acknowledge to be so in our thought &quot;. 3 Since, therefore, the simplest 

 way of realizing their validity is by reasoning in the corresponding direct moods 

 of the first figure and converting the conclusion, there is no ground for erecting 

 those moods into an independent f gure. 



But Fesapo (or Fapesmo) and Fresison (Frisesomorum) have no corre 

 sponding direct moods of the first figure, by arguing in which we might see 

 the validity of the former. Aristotle exhibited their validity by converting 

 both premisses, and so reducing these moods to Ferio. This process does 

 indeed reveal the natural movement of our thought whenever the premisses 

 in these moods are merely less natural expressions of those we obtain from 

 them by conversion. &quot; What tarnishes is not gold; and Some things of 

 gold are ancient ornaments ; therefore Some ancient ornaments do not 

 tarnish &quot; . in this syllogism (in Fresison^ or Frisesomorum) we are really 

 arguing in the first figure, in Ferio : we validate our inference by reverting 

 in thought to the more natural premisses : &quot; Gold does not tarnish; and 

 Some ancient ornaments are of gold&quot;. But such cases are rare. More 

 frequently, the reduction of Fresison (or Frisesomorum&quot;) to Ferio gives un 

 natural premisses. And the reduction of Fesapo (Fapesmo} to Ferio always 



JOSEPH, op. cit., p. 259. *ibid., p. 301. 3 ibid., pt 304. 



VOL. I. 23 



