 According to some authors, Gödel’s incompleteness theorems show that human mathematical capacities outstrip the capacities of any Turing machine (Nagel and Newman 1958). J.R. Lucas (1961) develops this position into a famous critique of CCTM. Roger Penrose pursues the critique in The Emperor’s New Mind (1989) and subsequent writings. Various philosophers and logicians have answered the critique, arguing that existing formulations suffer from fallacies, question-begging assumptions, and even outright mathematical errors (Bowie 1982; Chalmers 1996b; Feferman 1996; Lewis 1969, 1979; Putnam 1975: 365–366, 1994; Shapiro 2003). There is a wide consensus that this criticism of CCTM lacks any force. It may turn out that certain human mental capacities outstrip Turing-computability, but Gödel’s incompleteness theorems provide no reason to anticipate that outcome.