ARISTOTLE'S PRIOR AND POSTERIOR ANALYTICS

THE PURE OR ASSERTORIC SYLLOGISM 29combinations; for instead of appealing to their form as the sourceof their invalidity, he appeals to our supposed knowledge ofcertain particular propositions in each case. Whereas in dealingwith the valid moods he works consistently with ABr for thefirst figure, MN8 for the second, lIP}; for the third, and, bytaking propositional functions denoted by pairs of letters, notactual propositions about particular things, makes it plain thatvalidity depends on form, and thus becomes the originator offormal logic, he discovers the invalidity of the invalid moodssimply by trial and error. The insufficiency of the proof is veiledfrom his sight by the fact that he takes it to be not a mere matterof fallible experience, but self-evident, that all horses are animalsand no stones are animals-relying on the correctness of a systemof classification in which certain inclusions and exclusions aresupposed to be already known. He would have done better topoint to the obvious fact that the propositions 'All B is A andNo C is B' have no tendency to show either that all or some or noC is A or that some C is not A.I t is only syllogisms in the first figure that are directly validatedby the dictum de omni et nullo. For the validation of syllogisms inthe other two figures Aristotle relies on three other methods-conversion,reductio ad impossibile, and £KOEu,S"-about each of whichsomething must be said.(I) All the moods of the second and third figures but four l arevalidated by means of the simple conversion of premisses in E orI, with or without change of the order of the premisses and acorresponding conversion of the conclusion. Cesare, for instance,is validated by simple conversion of the major premiss; No P isM, All 5 is M becomes No M is P, All 5 is M, from which itfollows directly that no 5 is P. Camestres is validated by conversionof the minor premiss, alteration of the order of thepremisses, and conversion of the resultant conclusion; All P is M,No 5 is M becomes No M is 5, All P is M, from which it followsthat no P is 5, and therefore that no 5 is P. To such validationno objection can be taken. But in the discussion of conversionwhich Aristotle prefixes to his discussion of syllogism he saysZthat All B is A entails that some A is B; and he uses this form ofconversion in validating syllogisms in Darapti and Felapton. 3 Inthis he comes into conflict with a principle which plays a largeI Viz. Cesare, Carnestres, Festino, Disarnis, Datisi, Ferison.Z 25"7-10. 3 28"17-22,26--9.