Let's limit the scope of the discussion in, say properties of number,


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送交者: steven 于 2008-01-09, 18:16:30:

回答: how do you prove they are equivelant? 由 xinku 于 2008-01-09, 17:57:17:

i.e, the theory of number. Your first assumption is that human mind can always correct its own mistake, that means human mind can at least tell if a well-formed statement of the properties of number is either true or false. That means the human mind is capable to decide, for an arbitrary well-formed statement, whether this statement is a member of the theory of number. That means human mind is capable to solve membership problem which is equivalent to halting problem. So your first assumption is that human mind can solve halting problem. There is no need to go on, because, Turing machine cannot solve halting problem.



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