Can You Deny The PNC? (_Metaphysics_ Γ.3, 1005b11-34)

In Metaphysics Γ.3, Aristotle argues that it is impossible to deny the PNC. However, as several commentators—including Code, Barnes, Priest, Kirwan, and Dancy—have objected, Aristotle’s argument appears to rely on the invalid inference from 1 to 2 as follows: 1. For all p, it is impossible to believe that p and not-p. 2. Therefore, it is impossible to believe that it is possible that there is a p such that p and not-p. We argue that this objection turns on a misunderstanding of Aristotle’s text, and that Aristotle's argument is valid and quite strong.