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Qiaochu_Yuan comments on Second-Order Logic: The Controversy - Less Wrong
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No, Solvent is making the same point as in my answer: in order to write down large enough numbers to guarantee that Turing machines don't halt, you need to write down a function larger than the busy beaver function, and any such function fails to be computable because you can use it to solve the halting problem.
Ah, I see now, thanks!