 Turing’s own view of the status of his thesis is very different from that expressed by Kripke, Sieg, and Dershowitz and Gurevich. According to Turing, his thesis is not susceptible to mathematical proof. He did not consider either argument I or argument II to be a mathematical demonstration of his thesis: he asserted that I and II, and indeed “[a]ll arguments which can be given” for the thesis, are