Thanks Sam. I thought about this some more and realized where I went wrong - I was applying the deduction theorem incorrectly (as other comments in this thread have pointed out).

By the way, when you say that PA proves its own inconsistency, do you mean that $P A ⊢ □ (\neg C o n (P A))$ or that $P A ⊢ \neg C o n (P A)$ ? From your reasoning I agree that if we assume $\neg □ C \to C$ then we can arrive at $P A ⊢ □ C$ and $P A ⊢ □ (\neg C)$ , from which we can conclude that $P A ⊢ □ (\neg C o n (P A))$ . If you meant that $P A ⊢ \neg C o n (P A)$ though, could you explain how you arrived at that?