GÖDEL'S THEOREM IS A RED HERRING

Lucas (1961), in an interesting and provoking article, has stimulated much discussion amongst logicians, but I still do not believe that his conclusions are correct. I have argued (Good, 1967) that the assertion that human logic can do some things that a Turing machine cannot do cannot be proved by means of Godel's theorem. Lucas (1967) misrepresents me when he says that I 'deny that there could be any peculiarly mental powers, since if there were, they could be described, and if they could be described, a computer could be programmed to simulate them'. What I maintained was merely that 'mentalism' does not follow from Gddel's theorem. I argued further that the essence of the matter is contained in transfinite counting and I think it is misleading to put the emphasis on Godel's theorem. It is also necessary to point out that the human cannot know that the G6delian formula is true: he can at best believe it by believing that the formal system he starts with is co-consistent. (A system is said to be to-consistent if there is no sequence of propositions P(i), Pfe), • • •, each of which is