Abstract
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.
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Bibliography
Kurt Gödel, Collected Works, Volume I (Publications 1929–1936), Volume II (Publications 1938–1974), Volume III (Unpublished essays and lectures), ed. Solomon Feferman, Dawson, et al., Oxford University Press Inc., New York, 1995.
A. M. Turing, On computable numbers, with an application to the Entscheidungsproblem, Proceedings of the London Mathematical Society, ser. 2, vol. 42 (1936–7), pp. 230–265; reprinted on pages 116–151 of The Undecidable, edited by Martin Davis, Raven Press, Hewlett, New York 1965.
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Hodges, W. (1998). Turing’s Philosophical Error?. In: Landau, L.J., Taylor, J.G. (eds) Concepts for Neural Networks. Perspectives in Neural Computing. Springer, London. https://doi.org/10.1007/978-1-4471-3427-5_6
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DOI: https://doi.org/10.1007/978-1-4471-3427-5_6
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Print ISBN: 978-3-540-76163-1
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