In 1936 Alan Turing described a "universal machine" which he argued could compute the same things as any human "computer". Kurt Gödel praised Turing's work but spent much of his career looking for gaps in Turing's argument. In 1972 Gödel wrote a short note consisting of three Remarks. The third Remark was headed A philosophical error in Turing's work. He suggested that human beings might be able to compute by "mental procedures' some things which can"t be computed by "mechanical procedures". The background to this question is developed and a discussion is given as to what Gödel may have meant by his note.