The modal argument for hypercomputing minds

Abstract

We now know both that hypercomputation (or super-recursive computation) is mathematically well-understood, and that it provides a theory that according to some accounts for some real-life computation (e.g., operating systems that, unlike Turing machines, never simply output an answer and halt) better than the standard theory of computation at and below the “Turing Limit.” But one of the things we do not know is whether the human mind hypercomputes, or merely computes—this despite informal arguments from Gödel, Lucas, Penrose and others for the view that, in light of incompleteness theorems, the human mind has powers exceeding those of TMs and their equivalents. All these arguments fail; their fatal flaws have been repeatedly exposed in the literature. However, we give herein a novel, formal modal argument showing that since it's mathematically possible that human minds are hypercomputers, such minds are in fact hypercomputers. We take considerable pains to anticipate and rebut objections to this argument.