ARISTOTLE'S PRIOR AND POSTERIOR ANALYTICS

THE PURE OR ASSERTORIC SYLLOGISM 39very strong, and for my own part I think they cannot stand upagainst criticism. I It seems probable that Aristotle's theory ofsyllogism will not founder in a sea of discredit, but will always beregarded as the indispensable foundation of fonnallogic.Aristotle nowhere defends the syllogism against the charge ofpetitio principii, which we first find in Sextus Empiricus;1 but hewould have had his own defence. He would have had to admitthat the form of the major premiss, 'All B is A' or 'A belongs toall B', is compatible with its being either an empirical generalizationor a nominal definition of B, and that when it is either ofthese, the syllogism is a petitio principii. But he would havepointed out that in dealing with a certain type of subject-matter(e.g. in mathematics) a universal truth may be ascertained bythe consideration of even a single instance-that the genericuniversal is different from the enumerative. You may know by auniversal proof that all triangles have their angles equal to tworight angles, without having examined every triangle in theworld,J and even without having examined the various species oftriangle. Again, to the objection that we have no right to saythat all C is B unless we know it to have all the attributes ofB, including A, he would have replied by his distinction of propertyfrom essence. Among the attributes necessarily involvedin being B he distinguishes a certain set of fundamental attributeswhich is necessary and sufficient to distinguish B from everythingelse; and he regards its other necessary attributes as flowing fromand demonstrable from these. To know that C is B it is enoughto know that it has the essential nature of B-the genus and thedifferentiae; it is not necessary to know that it has the propertiesof B. Thus each premiss may be known independently of theconclusion, and neither premiss need commit a petitio principii.The objector might then say that the premisses taken togethercommit a petitio principii, that we cannot know both withoutalready knowing the conclusion. To this Aristotle would havereplied by a distinction between potential and actual knowledge.In knowing the premisses we potentially know the conclusion;but to know anything potentially is not to know it, but to bein such a state that given one further condition we shall passimmediately to knowing it. The further condition that is neededI Such, for instance, as is brought against them by Dr. Ewing in Proc. ofArist. Sac. xl (1939-40), 207-44.1 Pyrrh. Hypot. 195-203. l An. Pr. 67"B-21.