Why Gödel's theorem cannot refute computationalism

摘要

Gödel's theorem is consistent with the computationalist hypothesis. Roger Penrose, however, claims to prove that Gödel's theorem implies that human thought cannot be mechanized. We review his arguments and show how they are flawed. Penrose's arguments depend crucially on ambiguities between precise and imprecise senses of key terms. We show that these ambiguities cause the Gödel/Turing diagonalization argument to lead from apparently intuitive claims about human abilities to paradoxical or highly idiosyncratic conclusions, and conclude that any similar argument will also fail in the same ways.