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How not to use the church-turing thesis against platonism

Rafal Urbaniak (UGent)
(2011) PHILOSOPHIA MATHEMATICA. 19(1). p.74-89
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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.
Keywords
nominalism, Church-Turing thesis, platonism, computability

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Citation

Please use this url to cite or link to this publication:

MLA
Urbaniak, Rafal. “How Not to Use the Church-turing Thesis Against Platonism.” PHILOSOPHIA MATHEMATICA 19.1 (2011): 74–89. Print.
APA
Urbaniak, R. (2011). How not to use the church-turing thesis against platonism. PHILOSOPHIA MATHEMATICA, 19(1), 74–89.
Chicago author-date
Urbaniak, Rafal. 2011. “How Not to Use the Church-turing Thesis Against Platonism.” Philosophia Mathematica 19 (1): 74–89.
Chicago author-date (all authors)
Urbaniak, Rafal. 2011. “How Not to Use the Church-turing Thesis Against Platonism.” Philosophia Mathematica 19 (1): 74–89.
Vancouver
1.
Urbaniak R. How not to use the church-turing thesis against platonism. PHILOSOPHIA MATHEMATICA. 2011;19(1):74–89.
IEEE
[1]
R. Urbaniak, “How not to use the church-turing thesis against platonism,” PHILOSOPHIA MATHEMATICA, vol. 19, no. 1, pp. 74–89, 2011.
@article{3148473,
  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.},
  author       = {Urbaniak, Rafal},
  issn         = {0031-8019},
  journal      = {PHILOSOPHIA MATHEMATICA},
  keywords     = {nominalism,Church-Turing thesis,platonism,computability},
  language     = {eng},
  number       = {1},
  pages        = {74--89},
  title        = {How not to use the church-turing thesis against platonism},
  url          = {http://dx.doi.org/10.1093/philmat/nkr001},
  volume       = {19},
  year         = {2011},
}

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