Oh! My Godel's Lost Letter Proof Needs Revision

 

Based on the Reddit page comment by JoshuaZ1, whom I believe to be Dr. Joshua Zelinsky, I think that my GLL proof might be wrong too.  The same logic applies:


ZFC is consistent --> ZFC_PROOFS cannot be proved to be outside of P


But we could also write:


PA is consistent --> PA_PROOFS cannot be proved to be outside of P


Wait!  That's the issue.  The GLL proof stands...but not with P != NP.  We can only prove that Proofs cannot be proved to be outside of P in ZFC.  The reason why this doesn't lead to a contradiction is, we are proving that PA_PROOFS cannot be proved to be outside of P, and we *cannot* do this for ZFC proofs.  The mistake is, don't replace "PROOFS cannot be proved to be outside of P" with P != NP.


I think that's right!  I'm glad to be done with P vs. NP, I tend to have a limitless ability to confuse myself about proofs like this.

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