Why Gödel's Theorem Cannot Refute Computationalism

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. 1. INTRODUCTION How do we think? This is one of the oldest questions, and only recently has any progress been made towards answering it. While nobody has a fully plausible account, one apparently useful methodology can be summed up as the computationalist hypothesis --- roughly, the hypothesis that the human brain can be understood as a kind of biological computer, and mental activity as a kind ..