Kalmár's Argument Against the Plausibility of Church's Thesis

History and Philosophy of Logic 39 (2):140-157 (2018)
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Abstract

In his famous paper, An Unsolvable Problem of Elementary Number Theory, Alonzo Church identified the intuitive notion of effective calculability with the mathematically precise notion of recursiveness. This proposal, known as Church's Thesis, has been widely accepted. Only a few papers have been written against it. One of these is László Kalmár's An Argument Against the Plausibility of Church's Thesis from 1959. The aim of this paper is to present Kalmár's argument and to fill in missing details based on his general philosophical thoughts on mathematics.

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10.1080/01445340.2017.1396520

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An Argument against the Plausibility of Church's Thesis.László Kalmár - 1959 - In A. Heyting (ed.), Constructivity in mathematics: Proceedings of the colloquium held at Amsterdam 1957. Amsterdam: North-Holland. pp. 72-80.
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Mate Szabo
University of Oxford

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References found in this work

Elements of Intuitionism.Michael Dummett - 1977 - New York: Oxford University Press. Edited by Roberto Minio.
Elements of Intuitionism.Michael Dummett - 1980 - British Journal for the Philosophy of Science 31 (3):299-301.
An Unsolvable Problem of Elementary Number Theory.Alonzo Church - 1936 - Journal of Symbolic Logic 1 (2):73-74.
Finite combinatory processes—formulation.Emil L. Post - 1936 - Journal of Symbolic Logic 1 (3):103-105.

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