Israel, D. Reflections on Godel’s and Gandy’s Reflections on Turing’s Thesis. Minds and Machines, vol. 12, no. 2, pp. 181-201, May 2002.
We sketch the historical and conceptual context of Turing’s analysis of algorithmic or mechanical computation. We then discuss two responses to that analysis, by Gödel and by Gandy, both of which raise, though in very different ways. The possibility of computation procedures that cannot be reduced to the basic procedures into which Turing decomposed computation. Along the way, we touch on some of Cleland’s views.