Don’t they immediately imply that any project to formalise mathematics is doomed to fail? An overview of Gödel incompleteness Gödel’s incompleteness theorems are often regarded as placing strict limits on the power of logic. General logic incompleteness David Hilbert Kurt Gödel Torkel Franzén, Gödel’s Theorem: An Incomplete Guide to its Use and Abuse, A K Peters 2005.Do Gödel's incompleteness theorems matter? Machine Logic At the junction of computation, logic and mathematics Do Gödel's incompleteness theorems matter? Smullyan, Gödel’s Incompleteness Theorems, Oxford University Press, New York, Oxford 1992.ġ0. Hofstadter, Gödel, Escher, Bach, an Eternal Golden Braid, Basic Books, NY 1979.ĩ. Kurt Gödel: Collected Works, Volume I: Publications 1929-1936, Oxford University Press, New York, Oxford 1986 Volume III, Oxford University Press, 1995.Ĩ.ĝouglas R. Peter Smith, An Introduction to Gödel’s Theorems, Cambridge University Press 2007.ħ. Stewart Shapiro, The limits of logic: higher-order logic and the Loewenheim-Skolem theorem, Darmouth Publishing Company, Aldershot 1996.Ħ. Computable Functions, Logic, and the Foundations of Mathematics, Wadsworth & Brooks, Pacific Grove 1989ĥ. (Cienie umysłu, Zysk i S-ka, Poznań 2000.)Ĥ.Ğpstein, Richard L. Roger Penrose, Shadows of the mind, Oxford: Oxford University Press 1994. (Twierdzenie Gödla, PWN, Warszawa 1966.)ģ.
Stanisław Krajewski Twierdzenie Gödla i jego konsekwencje filozoficzne: od mechanicyzmu do postmodernizmu, IFiSPAN Warszawa 2003.Ģ.Ğrnest Nagel, James R. Inspirations: limitations of classical paradigm ? Type of courseġ. Philosophical applications of Gödel’s theorems Models, Loewenheim-Skolem therem, Solem’s paradoxĬonsequences of metalogical theorems for Mechanism The background of Gödel’s and Tarski’s theoremsįormalized theories, arithmetization, representability, recursive functions
More specifically the following topic will be covered: Krajewski Gödel’s Theorem and its Philosophical Consequences, IFiSPAN, Warsaw 2003. Much of the course will follow the book (in Polish) by S. Also abuses and misapplications of the theorems will be discussed, especially those committed by the philosophers who seem to think that Gödel’s theorem is just a metaphor that can be freely applied. The consequences of the theorem will be studied – for the philosophy of mathematics, and more widely, those indicating limitations of formal methods, of our descriptions of the world, as well as corollaries affecting the philosophy of mind. Their background, principal mathematical techniques, and sketches proofs will be presented. Course of lectures “Limitative Theorems in logic and their philosophical consequences” will focus on the most important metalogical theorems, namely on the famous Gödel’s incompleteness theorems as well as Tarski’s theorem and Loewenheim-Skolem theorem.
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