Did Aristotle Endorse Aristotle?s Thesis? A Case Study in Aristotle?s Metalogic

Since McCall (1966), the heterodox principle of propositional logic that it is impossible for a proposition to be entailed by its own negation-in sym-bols, -(-v-> v)-has gone by the name of Aristotle's thesis, since Aristotle apparently endorses it in Prior Analytics 2.4, 57b3-14. Scholars have contested whether Aristotle did endorse his eponymous thesis, whether he could do so consistently, and for what purpose he endorsed it if he did. In this article, I reconstruct Aristotle's argument from this passage and show that he accepts this thesis. Further, I show that the argument he gives is, making plausible assump-tions, a correct proof in a consistent fragmentary nonclassical metalogic for a metatheorem he previously states concerning his assertoric syllogistic. In this way, Aristotle's argument emerges as a fascinating case study in the use of a nonclassical metalogic to prove a result about a nonclassical object system.