Tag: ENTSCHEIDUNGSPROBLEM
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A hard theorem becomes easy over time.
The basic result of the incompleteness proofs is pretty simple. The proofs are complicated because the idea was literally unthinkable until programming was invented. The heroic efforts of Gödel, Skolem, Post, and Church to create a mathematics in which doing mathematics could be represented as some sort of calculation were an incredible feat of imagination. But…
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Gödel’s Lost Letter
Gödel’s perspective in this letter is a refutation of the simplistic take on Turing’s proof seen so often in the computer science literature. In particular: After all, one would simply have to choose the natural number n so large that when the machine does not deliver a result, it makes no sense to think more…