If you could build a machine that was able to generate every relevant scientific fact from first principles, do you think it would be done at some point, or that it would never stop?
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By classical notion of truth did people think that all truths would be provable inside the system? Because I see how they disproved that.
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Classical mathematics was "timeless", i.e. a statement could be considered true regardless of the cost of computing it. Gödel and Turing could show that this breaks the semantics of mathematics if a proof is not effectively computable (i.e. the cost to compute it is not finite).
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