Comment by dwohnitmok

> PA proves that if it can prove everything that it proves that it can prove, then PA must have a proof of one of the two previous statements.

I don't believe this is true. I don't know what result you're using here, but I think you're mixing up "provable" and "true".

In particular your line of reasoning violates Lob's Theorem, which is a corollary of the second incompleteness theorem.