Abstract
This paper explores Church's Thesis and related claims madeby Turing. Church's Thesis concerns computable numerical functions, whileTuring's claims concern both procedures for manipulating uninterpreted marksand machines that generate the results that these procedures would yield. Itis argued that Turing's claims are true, and that they support (the truth of)Church's Thesis. It is further argued that the truth of Turing's and Church'sTheses has no interesting consequences for human cognition or cognitiveabilities. The Theses don't even mean that computers can do as much as peoplecan when it comes to carrying out effective procedures. For carrying out aprocedure is a purposive, intentional activity. No actual machine does, orcan do, as much.
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Church, Alonzo (1936), ‘An Unsolvable Problem of Elementary Number Theory,’ American Journal of Mathematics 58, pp. 345–363. Reprinted in Davis 1965.
Curry, Haskell B. and Robert Feys (1958), Combinatory Logic, vol 1. Amsterdam: North-Holland Publishing Company.
Davis, Martin (1965), The Undecidable. Hewlett, New York: Raven Press.
Gandy, Robin (1980), ‘Church's Thesis and Principles for Mechanisms,’ The Kleene Symposium, edited by Jon Barwise, H. Jerome Keisler, Kenneth Kunen. Amsterdam: North-Holland Publishing Company, 123–148.
Kearns, John T. (1969), ‘Combinatory Logic with Discriminators,’ The Journal of Symbolic Logic 34, pp. 561–575.
Kearns, John T. (1996), Reconceiving Experience, A Solution to a Problem Inherited from Descartes. Albany, N.Y.: State University of New York Press.
Kleene, Stephen C. (1987), ‘Reflection on Church's Thesis,’ Notre Dame Journal of Formal Logic 28, pp. 490–498.
Kreisel, Georg (1987), ‘Church's Thesis and the Ideal of Informal Rigor,’ Notre Dame Journal of Formal Logic 28 pp. 499–519.
Nelson, R. J. (1987), ‘Church's Thesis and Cognitive Science,’ Notre Dame Journal of Formal Logic 28, pp. 581–614.
Shanker, S. G. (1987), ‘Wittgenstein versus Turing on the Nature of Church's Thesis,’ Notre Dame Journal of Formal Logic 28, pp. 615–649.
Shapiro, Stewart (1980), ‘On the Notion of Effectiveness,’ History and Philosophy of Logic I, pp. 209–230.
Shapiro, Stewart (1981), ‘Understanding Church's Thesis,’ Journal of Philosophical Logic 10, pp. 353–365.
Turing, Alan (1937), ‘On Computable Numbers,’ with an Application to the Entscheidungsproblem,’ Proceedings of the London Mathematical Society s. 2, vol 42, 230–265. Reprinted in Davis (1965), 115–154.
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Kearns, J.T. Thinking Machines: Some Fundamental Confusions. Minds and Machines 7, 269–287 (1997). https://doi.org/10.1023/A:1008202117814
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DOI: https://doi.org/10.1023/A:1008202117814