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by Tainnor
583 days ago
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It's "obvious" in the sense that it's a trivial corollary of the completeness theorem (so it wouldn't be true for second order logic, for example). Hilbert's program failed in no contradiction to what GP wrote because the language of FOL theorems is only recursively enumerable and not decidable. It's obvious that something is true if you've found a proof, but if you haven't found a proof yet, is the theorem wrong or do you simply have to wait a little longer? |
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