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The incompleteness theorem is plausibly applicable to human reasoning. How do you prove "this sentence is false"?
by GoblinSlayer 2y ago
The incompleteness theorem is plausibly applicable to human reasoning. How do you prove "this sentence is false"?
- bubblyworld 2y agoThat's not quite the incompleteness theorem, which is about sentences that are unprovable but nevertheless have a truth value. I think the liar's paradox is of a different kind. It's a sentence that looks well-formed but arguably has no truth value. If you were to formalise human reasoning as a logical system, such sentences would not be definable in it. Either way, for Penrose's argument to work you actually need the proof of Gödel's theorem to hold, not just the result.