404 THE SCIENCE OF LOGIC 



But the objection is not unanswerable. The simple answer to 

 it is that we can &quot; be assured of the mortality of all men &quot; without 

 being &quot;already certain of the mortality of every individual man &quot; 

 including Socrates. And if we can, the objection evidently 

 falls to the ground. The proposition &quot;All men are mortal&quot; does 

 not express a mere collective judgment : it is the denotative or 

 extensive expression of the strictly abstract judgment, &quot;Man, as 

 such, is mortal &quot;. This judgment embodies a necessary truth : that 

 the nature of man, being composite, is subject to dissolution of its 

 component parts, i.e subject to death, mortal (87). And we attain 

 to certitude about this abstract truth, not by any inference/tt?w the 

 particular instances, but by an analytic examination of the nature 

 of man : for which, of course, the study of some instances is 

 necessary. Then, having reached the abstract truth that &quot; Man 

 as such, is, of his nature, mortal,&quot; we immediately universalize it 

 into &quot; All men [actual and possible, past, present, and future] are 

 mortal&quot; ; and we do so quite independently of any information 

 about unexamined individuals. 



196. SOME CLASSES OF SYLLOGISMS EXAMINED. A syllogism 

 may, of course, commit the fallacy of Petitio Principii in many 

 other ways than by having a collective major : rarely, however, 

 so openly as in this example given by Dr. Keynes : * All M is P 

 (for all S is P and all M is 5) ; and all S is M ; therefore all S 

 is P. But in the same context the author states that we have 

 the fallacy of petitio principii whenever &quot;the major premiss is an 

 analytic proposition &quot;. If the &quot;analytic proposition&quot; be under 

 stood in the sense in which we have accepted it (85-88), i.e. as a 

 proposition in mater ia necessaria, this statement is not true : on 

 the contrary, it is only in so far as the universal premiss is abstract 

 and necessary, and in proportion to the degree of that necessity 

 (metaphysical, physical, or moral), that the syllogism will conclude 

 cogently, and be exempt from danger of invalidity through the 

 possible occurrence of an exception to the general rule in the 

 case or cases to which the syllogism seeks to apply the rule. 

 And, similarly, our certitude about the conclusion will never be 

 higher than our certitude about the universal premiss. We may 

 distinguish three classes of cases, (a) &quot; The major premiss may 

 itself be accepted as axiomatic, or it may be deducible (without 

 the aid of the conclusion) from more ultimate principles that 

 are accepted as axiomatic.&quot; 2 These premisses we would de- 

 1 op. cit., p. 426. 2 ibid., p. 427. 



