PhilGoetz comments on Reason as memetic immune disorder - Less Wrong
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Could be correct or wildly incorrect, depending on exactly what he meant by it. Of course you have to delete "the only", but I'd be pretty doubtful of any humans trying to do recursive self-modification in a way that didn't involve logical proof of correctness to start with.
One of the big problems is that he was trying to talk about the logical correctness of human-level symbolic statements about the world. Even if the logic is correct, there is no correct, consistent mapping from the analog world, to symbolic descriptions, and back. A mapping that's close enough to work 99.99% of the time isn't good enough when you're talking about proof.