Gödel and Turing's thesis This paper concerns Gödel's remarks on Turing's thesis. Of fundamental importance to this analysis are unpublished notes kept among Gödel's papers. The first section concerns Gödel's position on the possibility of a definition of computability before 1937. The second and main section presents different notes on Turing's famous paper of 1937. Before 1937, Gödel qualified as mechanical procedures defined by rules that ignore the meaning of symbols and only consider their exterior form. Several notes then show that Gödel interpreted Turing's thesis as the claim that mechanical procedures in that sense can be represented by Turing machines. But Turing himself intended to define finite procedures. This shift enabled Gödel after 1964 to criticize Turing's paper. The third and last section deals with Gödel's argument against Turing, in which Gödel aimed to establish the existence of finite but non-mechanical procedures. Keywords : Turing, Gödel, machines, computability, incompleteness
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