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Tyrrell_McAllister comments on No coinductive datatype of integers - Less Wrong Discussion
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If I understand you, yes. By the "original Turing machine", I meant the machine T that putatively can interpret an input string as an integer or, alternatively, reject the input string as not corresponding to any integer.
So, can we actually construct such a machine that is provably immune to the "attack" in your proof, in the sense that no Turing machine could implement the attack? Or are you saying that Rice's theorem (with which I will have to acquaint myself) says that pretty much any Turing machine T that maps strings to integers will fit the bill? (Though, the one in cousin_it's OP doesn't . . .)
Hmm. So T is an acceptor, A is an attacker. A(T) is an infinite sequence of symbols produced after examining T's source code, and T(A(T)) = ⊥ means T never rejects the sequence. Then what I was asserting is ¬∃A:∀T:T(A(T)) = ⊥. What you're asking now is whether ∀T:∃A:T(A(T)) = ⊥ and I can't immediately work out the answer.