On the irremovability of mathematical subject
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May 24, 2010
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Abstract
In the paper the author attempts to show that the Mathematical Subject is irremovable from the Philosophy of Mathematics. In doing so he wants to argue, first, that Church's Thesis should be seen as a statement about the Mathematical Subject. Second, he wants to show that philosophical relations between some problems such as Koenig's lemma vs Fan theorem, or Goedel's theorem on incompleteness vs. Halting problem, could be better grasped within the framework of the Mathematical Subject.
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Olszewski, A. (2010). On the irremovability of mathematical subject. Philosophical Problems in Science (Zagadnienia Filozoficzne W Nauce), (46), 100–117. Retrieved from https://zfn.edu.pl/index.php/zfn/article/view/170
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References
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Troelstra A.S., van Dalen D., Constructivism in Mathematics, North–Holland, Amsterdam, New York 1988.
Dummett Michael, Elements of Intuitionism, Clarendon Press, Oxford 1977.
Chang C.C., Keisler H. Jerome, Model Theory, North-Holland, Amsterdam 1973.
Field Hartry, Saving Truth from Paradox, Oxford University Press 2008.
Grzegorczyk A., Zarys arytmetyki teoretycznej, PWN,Warszawa 1971.
Heijenoort van J., From Frege to G¨odel, Harvard University Press, Cambridge 1967.
Hilbert D., Cohn-Vossen S., Geometria poglądowa, PWN,Warszawa 1956.
Hodges Wilfrid, A Shorter Model Theory, Cambridge University Press, Cambridge 1997.
Olszewski Adam, Teza Churcha. Kontekst historyczno-filozoficzny, Universitas, Kraków 2009.
Quinon P., Zdanowski K., The Intended Model of Arithmetic. An Argument from Tennenbaum’s Theorem, [w:] Computation and Logic in the Real World, CiE 2007, Local Proceedings, (ed.) S.B.
Cooper, B. Loewe i A. Sorbi, 2007.
Sipser Michael, Introduction to the Theory of Computation, PWS Publishing Company 1997.
Smullyan Raymond M., Diagonalization and Self-Reference, Oxford Logic Guides, Oxford 1994.
Smullyan Raymond M., First-Order Logic, Dover Publications, New York 1995.
Troelstra A.S., van Dalen D., Constructivism in Mathematics, North–Holland, Amsterdam, New York 1988.