Gödel and Turing: we cannot use classical mathematics to build an interpreter that runs classical mathematics
Church and Turing: we can use constructive mathematics to run constructive mathematics
Minsky and Turing: we can use constructive mathematics to run classical mathematics
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This seems important and interesting but I think I need an essay length explanation. Is there one?
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no, I only just realized it, and I have ADHS so may not write the essay
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basic train of thoughts: Gödel's incompleteness theorem (and Turing's subsequent adaptation to computational machinery) shows that mathematics itself is incomplete. that was a shock: mathematics is the domain of all formal languages, but mathematics cannot be generated using them
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