Suppose that Turing is wrong. Then Turing gave an algorithm which should defeat Rice's Theorem. Therefore, I may simply ask, to Hewitt: Could you please write u

Suppose that Turing is wrong. Then Turing gave an algorithm which should defeat Rice's Theorem. Therefore, I may simply ask, to Hewitt: Could you please write up a short program in a popular Turing-complete programming language which proves or disproves Goldbach's Conjecture? It should be trivial! Of course, on actual computers, Turing's result applies, Rice's Theorem manifests, and such a program will likely run indefinitely, until we get bored and give up. The point that Hewitt has made in another thread is typical misdirection. See, it doesn't matter which order of logic we're talking about; in general, we have results for higher order logic, all the way up to Lawvere's fixed-point theorem for any Cartesian closed category. To fight this, Hewitt has to disclaim the entirety of 20th-century mathematics. (At least he's internally consistent -- he does deny modern maths!) Sad fact is that, ever since 1976 (http://www.laputan.org/pub/papers/aim-353.pdf http://www.laputan.org/pub/papers/aim-353.pdf) folks have recognized that Hewitt's claims about the foundations of computation are not just wrong, but flamebait. But he never had the humility to learn from his mistakes.