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I never said it is a paradox. I never said that PA or Q is inconsistent. I said that they cannot prove their own consistency by Gödels theorem. Hence we don't k
by erichahn 5y ago
I never said it is a paradox. I never said that PA or Q is inconsistent. I said that they cannot prove their own consistency by Gödels theorem. Hence we don't know if Gödels theorem was formalized in an inconsistent system.
Honestly it would be weird if the incompleteness theorems don't apply to themselves.
- ProfHewitt 5y agoThe logical contradiction is that allowing the [Gödel 1931] proposition I'mUnprovable into foundations makes the foundations inconsistent.