Gödelian sentences and semantic arguments
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Опубликован:
06.08.2020
Ключевые слова:
Gödelian sentences, Gödel’s incompleteness theorem, semantical argument, truth theory, arithmetic, proof, provability
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Аннотация
This paper contains some philosophical reflections on Gödelian (undecidable) sentences and the recognition of their truth using semantic arguments. These reflections are not new, similar matters have been extensively addressed in the philosophical literature. The matter is rather one of emphasis.
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Article Details
Как цитировать
Sandu G. Gödelian sentences and semantic arguments // Логические исследования / Logical Investigations. 2020. Т. 26. № 1. C. 60-77.
Раздел
Философия и логика
Copyright (c) 2020 Gabriel Sandu
Это произведение доступно по лицензии Creative Commons «Attribution-NonCommercial» («Атрибуция — Некоммерческое использование») 4.0 Всемирная.
Литература
Dummett, 1963 – Dummett, M. “The Philosophical Significance of Go ̈del’s Theorem”, Ratio, Vol. 5, pp. 140–155. Reprinted in: Dummett, M. Truth and Other Enigmas, London, Duckworth, 1979, pp. 186–201.
Feferman, 1962 – Feferman, S. “Transfinite recursive progressions of axiomatic theor- ies”, The Journal of Symbolic Logic, 1962, Vol. 27, pp. 259–316.
Feferman, 1991 – Feferman, S. “Reflections on incompleteness”, Journal of Symbolic Logic, 1991, Vol. 56, pp. 1–49.
Feferman, 2005 – Feferman, S. “Predicativity”, in: The Oxford handbook of philosophy of mathematics and logic, ed. by S. Shapiro, Oxford: Oxford University Press, 2005, pp. 590–624.
Go ̈del, 1947 – Go ̈del, K. “What is Cantor’s continuum problem?”, The American Mathematical Monthly, 1947, Vol. 54, pp. 515–525.
Horsten, 2011 – Horsten, L. The Tarskian Turn. Deflationism and Axiomatic Truth, MIT Press, 2011.
Hyttinen, Sandu, 2004 – Hyttinen, T., Sandu, G. “Deflationism and Arithmetical Truth”, Dialectica, 2004, Vol. 58, pp. 413–426.
Isaacson, 1991 – Isaacson, D. “Some considerations on arithmetical truth and the omega-rule”, in: Proof, logic, and formalization, ed. by M. Detlefsen, Routledge, 1991, pp. 49–138.
Isaacson, 1996 – Isaacson, D. “Arithmetical truth and hidden higher-order concepts”, in: Logic Colloquium ’85, Amsterdam: North-Holland, 1987, pp. 147–169. Re- printed in: The philosophy of mathematics, ed. by W.D. Hart, Oxford University Press, 1996, pp. 203–224.
Ketland, 1999 – Ketland, J. “Tarski’s Paradise and Deflationist Truth”, Mind, 1999, Vol. 108, pp. 69–94.
Koellner, 2006 – Koellner, P. “On the question of absolute undecidability”, Philosophia Mathematica, 2006, Vol. 14, pp. 153–188. Revised and reprinted in: Kurt G ̈odel: Essays for his Centennial, S. Feferman, C. Parsons, S.G. Simpson (eds.), Lecture Notes in Logic, Vol. 33. Association of Symbolic Logic, 2009.
Myhill, 1960 – Myhill, J. “Some Remarks om the notion of proof”, Journal of Philo- sophy, 1960, Vol. 57, pp. 461–471.
Shapiro, 1998 – Shapiro, S. “Truth and Proof: Through Thick and Thin”, Journal of Philosophy, 1998, Vol. 95, pp. 493–521.
Tarski, 1956 – Tarski, A. “The Concept of Truth in Formalized Languages”, in: Logic, Semantics, Metamathematics, ed. by A. Tarski, 2d edition, Oxford University Press, 1956, pp. 152–278.
Tennant, 2002 – Tennant, N. “Deflationism and the Go ̈del Phenomena”, Mind, 2002, Vol. 111, pp. 551–582.
Feferman, 1962 – Feferman, S. “Transfinite recursive progressions of axiomatic theor- ies”, The Journal of Symbolic Logic, 1962, Vol. 27, pp. 259–316.
Feferman, 1991 – Feferman, S. “Reflections on incompleteness”, Journal of Symbolic Logic, 1991, Vol. 56, pp. 1–49.
Feferman, 2005 – Feferman, S. “Predicativity”, in: The Oxford handbook of philosophy of mathematics and logic, ed. by S. Shapiro, Oxford: Oxford University Press, 2005, pp. 590–624.
Go ̈del, 1947 – Go ̈del, K. “What is Cantor’s continuum problem?”, The American Mathematical Monthly, 1947, Vol. 54, pp. 515–525.
Horsten, 2011 – Horsten, L. The Tarskian Turn. Deflationism and Axiomatic Truth, MIT Press, 2011.
Hyttinen, Sandu, 2004 – Hyttinen, T., Sandu, G. “Deflationism and Arithmetical Truth”, Dialectica, 2004, Vol. 58, pp. 413–426.
Isaacson, 1991 – Isaacson, D. “Some considerations on arithmetical truth and the omega-rule”, in: Proof, logic, and formalization, ed. by M. Detlefsen, Routledge, 1991, pp. 49–138.
Isaacson, 1996 – Isaacson, D. “Arithmetical truth and hidden higher-order concepts”, in: Logic Colloquium ’85, Amsterdam: North-Holland, 1987, pp. 147–169. Re- printed in: The philosophy of mathematics, ed. by W.D. Hart, Oxford University Press, 1996, pp. 203–224.
Ketland, 1999 – Ketland, J. “Tarski’s Paradise and Deflationist Truth”, Mind, 1999, Vol. 108, pp. 69–94.
Koellner, 2006 – Koellner, P. “On the question of absolute undecidability”, Philosophia Mathematica, 2006, Vol. 14, pp. 153–188. Revised and reprinted in: Kurt G ̈odel: Essays for his Centennial, S. Feferman, C. Parsons, S.G. Simpson (eds.), Lecture Notes in Logic, Vol. 33. Association of Symbolic Logic, 2009.
Myhill, 1960 – Myhill, J. “Some Remarks om the notion of proof”, Journal of Philo- sophy, 1960, Vol. 57, pp. 461–471.
Shapiro, 1998 – Shapiro, S. “Truth and Proof: Through Thick and Thin”, Journal of Philosophy, 1998, Vol. 95, pp. 493–521.
Tarski, 1956 – Tarski, A. “The Concept of Truth in Formalized Languages”, in: Logic, Semantics, Metamathematics, ed. by A. Tarski, 2d edition, Oxford University Press, 1956, pp. 152–278.
Tennant, 2002 – Tennant, N. “Deflationism and the Go ̈del Phenomena”, Mind, 2002, Vol. 111, pp. 551–582.