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Yes, but can Turing machines do enough mathematics? The second order Peano Axioms are categorical and the first order axioms are not. The Incompleteness Theor
by yequalsx 10y ago
Yes, but can Turing machines do enough mathematics? The second order Peano Axioms are categorical and the first order axioms are not. The Incompleteness Theorem tells us that there are statements that are true in the standard model of N that are not provable by a Turing Machine.