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

Mate Szabo
Oxford University
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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Reprint years 2017, 2018
DOI 10.1080/01445340.2017.1396520
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Elements of Intuitionism.Michael Dummett - 1977 - Oxford University Press.
An Unsolvable Problem of Elementary Number Theory.Alonzo Church - 1936 - Journal of Symbolic Logic 1 (2):73-74.
Elements of Intuitionism.Nicolas D. Goodman - 1979 - Journal of Symbolic Logic 44 (2):276-277.
Finite Combinatory Processes—Formulation.Emil L. Post - 1936 - Journal of Symbolic Logic 1 (3):103-105.

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