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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I don't know what these claims mean, esp. the "Minsky-Turing" one. What did Minsky prove?
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Replying to @johncarlosbaez @XiXiDu
I don’t think that Minsky and Turing have proven that minds are computers, but I think each of them made a very good case, which lead to a whole academic field.
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None of what you just wrote is about "we can use constructive mathematics to run classical mathematics". I guess your argument is that computers are based on constructive math and can be intelligent and thus think about classical mathematics. Okay, but...
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... there are purely mathematical ways to study the extent to which constructive math can "run" classical math. These avoid a detour through more speculative territory and let one prove a bunch of theorems, both positive and negative, about this question.
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You seem to inhabit a universe in which your brain allows you to think mathematically instead of constructively. The implication of AI is that we are not in this universe, and you are just constructing the constructive parts of a nonconstructive language.
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