Note 13 — Chapter V · ANALYTICA PRIORA I.

Ibid. p. 25, a. 15: εἰ οὖν μηδενὶ τῶν Β τὸ Ἀ ὑπάρχει, οὐδὲ τῶν Ἀ οὐδενὶ ὑπάρξει τὸ Β. εἰ γὰρ τινι, οἷον τῷ Γ, οὐκ ἀληθὲς ἔσται τὸ μηδενὶ τῶν Β τὸ Ἀ ὑπάρχειν· τὸ γὰρ Γ τῶν Β τί ἐστιν.

Julius Pacius (p. 129) proves the Universal Negative to be convertible simpliciter, by a Reductio ad Absurdum cast into a syllogism in the First figure. But it is surely unphilosophical to employ the rules of Syllogism as a means of proving the legitimacy of Conversion, seeing that we are forced to assume conversion in our process for distinguishing valid from invalid syllogisms. Moreover the Reductio ad Absurdum assumes the two fundamental Maxims of Contradiction and Excluded Middle, though these are less obvious, and stand more in need of proof than the simple conversion of the Universal Negative, the point that they are brought to establish.