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Khoth comments on We won't be able to recognise the human Gödel sentence - Less Wrong Discussion
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I think it's perfectly reasonable to encounter your Gödel sentence and say you don't know it's true. You just have to think "this is only true if the logic I use is consistent. I'd like to think it is, but I don't actually have an ironclad proof of that (Luckily for me - if I did have such a proof, I'd know I was inconsistent). So I can't actually prove this statement"
That would only work if you also say "there must be an error somewhere in Gödel's proof".
Gödel's proof assumes the consistency of the theory that G is being created for. It's not an error in the proof, but it's not an assumption you're allowed to make when talking about your own logical system.