NATURE AND CHARACTERISTICS OF INFERENCE 405 



scribe as analytic, or in materia necessaria ; they are common 

 in mathematics ; and they do not involve the reasonings dependent 

 on them in any petitio principii. They give us absolute or meta 

 physical certitude about their conclusions. (U) &quot; The major pre 

 miss may be an imperfect (i.e. scientific) induction, based on 

 evidence that does not include the conclusion &quot; 1 The general 

 laws or truths which we reach by scientific induction (wrongly 

 called &quot; imperfect&quot; cf. 207) can become major premisses of 

 syllogisms which apply these truths to explain particular facts 

 brought under them. There is here no petitio principii : the 

 minor and conclusion disclose these facts for the first time to the 

 mind : hence they could not have been the basis of our knowledge 

 of the major. Such syllogisms give us not metaphysical or 

 absolute, but physical certitude, conditional on the stability and 

 uniformity of the natural phenomena with which they deal, (c] 

 &quot; The major premiss may be based on authority, or may be ac 

 cepted on testimony ; or it may be the expression of a civil law, 

 or of a command, or of a rule of conduct ; and in none of these 

 cases can it be in any degree grounded on the conclusion.&quot; 2 In 

 the wide domains of the social, political, and economic sciences, 

 of history and jurisprudence, of religion, natural and supernatural, 

 the reasoning employed is, for the most part, syllogistic inference 

 from general principles, maxims, laws, etc., which are either de 

 liverances of authority, or generalizations of moral universality 

 and necessity from the observed course of human conduct. 

 These are not collective, but abstract, universals. Having to do 

 with phenomena within the domain of free will, they are, of course, 

 less stable and more liable to exception than in the preceding 

 cases : and since it is on their stability that the conclusions de 

 rived from them are based, we can have only moral certitude 

 about the latter. 



Were we to understand by an analytic proposition one in which the pre 

 dicate gives us the whole or part of the definition or connotation of the subject- 

 term (85), we might inquire whether a syllogism containing such a proposition 

 as major premiss is necessarily a petitio principii. Dr. Keynes says it is : 

 &quot; For if M by definition includes P amongst its properties, I am not justified 

 in saying of S that it is M unless I have already satisfied myself that it is P. The 

 following is an example : All triangles have three sides ; the figure ABC is 

 a triangle ; therefore it has three sides &quot;. 3 Here there is apparently no escape 

 from the petitio princ ipii : I cannot know that ABC is a triangle unless by 



l op. cit., p. 427. *ibid., p. 428. Cf. MERCIER, Logique, pp. 196-200. 



3 ibid., p. 426. 



