Why we shouldn’t fault Lucas and Penrose for continuing to believe in the Gödelian argument against computationalism - II
نویسنده
چکیده
One reason why Lucas and Penrose should not be faulted for continuing to believe in their well-known Gödelian arguments against computationalism lies in the lack of an adequate consensus on the term ‘computation’. For instance, Boolos, Burgess and Jeffrey (2003: Computability and Logic, 4th ed. CUP, p37) define a diagonal function, d, any value of which can be computed effectively, although there is no single algorithm that can effectively compute d. Now, the straightforward way of expressing this phenomenon should be to say that there are well-defined real numbers that are instantiationally computable, but not algorithmically computable. Yet, following Church and Turing, such functions are labeled as effectively uncomputable!
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