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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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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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