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Mechanism and Gödel's Theorems

that some interesting difficulties arise. In Section IV of his paper Benacerraf constructs what he considers to be a Lucas-type argument, apparently in an attempt to see what, if anything, follows from Gddel's theorems for the mechanism issue. And indeed he does produce an interesting and relevant result-roughly, that if men are Turing machines then there are certain limitations on what they can prove about their own deductive abilities. But in the Appendix that immediately follows Section IV Benacerraf seems to take back this result by giving an argument that undercuts the original argument of Section IV. Furthermore, the argument of the Appendix is paradoxical in that it appears to force us to conclude either that a seemingly analytic assumption is false or that a seemingly valid rule of inference is invalid. Hence we are left with the impression that one can remove the implications of Gddel's theorems for mechanism only at the price of accepting a paradox. In Section 3 of this paper I show how to avoid the purported implications of G6del's theorems for mechanism without accepting the paradoxical argument of the Appendix to Benacerraf's paper. This will be preceded (Section I) by a brief summary of the argument given in Benacerraf's Section IV, and (Section z) by a summary, criticism, and reconstruction of the argument given in the Appendix to Benacerraf's paper.2