How Not To Use the Church-Turing Thesis Against Platonism

Philosophia Mathematica 19 (1):74-89 (2011)

Abstract
Olszewski claims that the Church-Turing thesis can be used in an argument against platonism in philosophy of mathematics. The key step of his argument employs an example of a supposedly effectively computable but not Turing-computable function. I argue that the process he describes is not an effective computation, and that the argument relies on the illegitimate conflation of effective computability with there being a way to find out . ‘Ah, but,’ you say, ‘what’s the use of its being right twice a day, if I can’t tell when the time comes?’ Why, suppose the clock points to eight o’clock, don’t you see that the clock is right at eight o’clock? Consequently, when eight o’clock comes round your clock is right. Lewis Carroll
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DOI 10.1093/philmat/nkr001
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On Computable Numbers, with an Application to the Entscheidungsproblem.Alan Turing - 1936 - Proceedings of the London Mathematical Society 42 (1):230-265.
Philosophy of Mathematics: Structure and Ontology.Stewart Shapiro - 2002 - Philosophy and Phenomenological Research 65 (2):467-475.
An Introduction to Gödel's Theorems.Peter Smith - 2007 - Cambridge University Press.
An Introduction to Gödel's Theorems.Peter Smith - 2009 - Bulletin of Symbolic Logic 15 (2):218-222.

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