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
Very nice. However the final statement "we can use constructive mathematics to run classical mathematics" has a different use of the word "run' from the first statement. Run in the former is 'specify' and in the latter it is 'execute'.
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Replying to @IntuitMachine @Plinz
If I'm a computer and I can both specify and execute mathematics would this be equivalent to a demonstration of the final statement?
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Replying to @philip_baldock @IntuitMachine
Very informally put, Gödel demonstrates that there is mathematics that can be specified but not executed. Constructivism brackets these parts of mathematics as non-existent.
2:45 PM - 23 Sep 2018
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