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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Replying to @Plinz
This seems important and interesting but I think I need an essay length explanation. Is there one?
1 reply 0 retweets 5 likes -
Replying to @vgr
no, I only just realized it, and I have ADHS so may not write the essay
1 reply 0 retweets 8 likes -
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
2 replies 0 retweets 12 likes -
there is a small branch of mathematics that only accepts statements as true that have actually been constructed. constructive mathematics turns out to be identical to computation. Church and Turing demonstrated that computation contains itself, i.e. we can compute all computers
3 replies 0 retweets 11 likes
Is this like Brouwer intuitionist math? They reject law of excluded middle and proof by reductio ad absurdum so they only accept proof by construction and reject standard continuum math.
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