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Gödel’s Incompleteness Theorems: An Interdisciplinary Review
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In the following article, authors offer a modern proof of Gödel’s incompleteness theorems. Authors then briefly recount what its immediate reception in the scientific community was like, and finally appraise the ultimate impact it has had, and issues it has raised, in a wide variety of fields - ranging from mathematics to philosophy of mind.
Keywords
Incompleteness, Consistency, Philosophy of Mathematics, Turing Machine, Anti-Mechanism.
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- J W Dawson Jr, The Reception of Gödel’s Incompleteness Theorems, in PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association, Philosophy of Science Association, Vol 2, page 253–271, 1984.
- S C Kleene, N De Bruijn, J de Gischolar_main, and A C Zaanen, Introduction to Metamathematics, van Nostrand, New York, Vol 483, 1952.
- S C Kleene, The work of Kurt Gödel, Journal of Symbolic Logic, Vol 41, No 4, page 761–778, 1976.
- K Gödel, Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I, Monatshefte fúr mathematik und physik, Vol 38, No 1, page 173–198, 1931.
- J W Dawson Jr, Discussion on the Foundation of Mathematics, History and Philosophy of Logic, Vol 5, No 1, page 111–129, 1984.
- I Grattan-Guinness, In memoriam Kurt Gödel: His 1931 correspondence with zermelo on his incompletability theorem, Historia mathematica, Vol 6, No 3, page 294–304, 1979.
- M Davis, The undecidable: Basic papers on undecidable propositions, unsolvable problems and computable functions, Courier Corporation, 2004.
- P Finsler, Formale beweise und die entscheidbarkeit, Mathematische Zeitschrift, Vol 25, No 1, page 676–682, 1926.
- D Hilbert, Die Grundlagen der Mathematik II, Springer, 1939.
- P Mancosu, Between Vienna and Berlin: The Immediate Reception of Gödel’s Incompleteness Theorems, History and Philosophy of Logic, Vol 20, No 1, page 33–45, 1999.
- L Wittgenstein, Remarks on the Foundations of Mathematics, 1956.
- L Wittgenstein, Tractatus logico-philosophicus (trans Pears and McGuinness), 1961.
- L Wittgenstein, Philosophical Grammar, University of California Press, 2005.
- L Wittgenstein, Philosophical Remarks, University of Chicago Press, 1980.
- J Floyd, H Putnam, A Note on Wittgenstein’s Notorious Paragraph about the Gödel Theorem, The Journal of Philosophy, Vol 97, No 11, page 624–632, 2000.
- G Priest, M Kolbeland, B Weiss (eds), Wittgenstein’s Remarks on Gödel’s Theorem, in Wittgenstein’s Lasting Significance, Routledge, Taylor Francis, London, chapter 8, page 207–227, 2004.
- M Steiner, Wittgenstein as his Own Worst Enemy: The Case of Gödel’s Theorem, Philosophia Mathematica, Vol 9, No 3, page 257–279, 2001.
- V Rodych, Misunderstanding Gödel: New Arguments about Wittgenstein and New Remarks by Wittgenstein, Dialectica, Vol 57, No 3, page 279–313, 2003.
- D Hilbert, Mathematical Problems, Bull Amer Math Soc, Vol 8, page 437–479, 1901-1902.
- G Gentzen, Die widerspruchsfreiheit der reinen zahlentheorie, Mathematische annalen, Vol 112, No 1, page 493–565, 1936.
- M Davis, Hilbert’s tenth problem is unsolvable, The American Mathematical Monthly, Vol 80, No 3, page 233–269, 1973.
- A Weir, Formalism in the Philosophy of Mathematics, in The Stanford Encyclopedia of Philosophy, E N Zalta (ed), Metaphysics Research Lab, Stanford University, 2020.
- F A Rodriguez-Consuegra, Some basic theorems on the foundations of mathematics and their philosophical implications, in Kurt Gödel: Unpublished Philosophical Essays, F A Rodriguez-Consuegra (ed), Basel: Birkhäuser Basel, page 129–170, 1995.
- M Detlefsen, Hilbert’s formalism, Revue Internationale de Philosophie, Vol 47, No 186, page 285–304, 1993.
- L Horsten, Philosophy of Mathematics, in The Stanford Encyclopedia of Philosophy, E N Zalta (ed), Metaphysics Research Lab, Stanford University, 2019.
- P Simons, Formalism, in Philosophy of Mathematics, A D Irvine (ed), Amsterdam, North Holland, page 291–310, 2009.
- G Hellman, How to Gödel a Frege-Russell: Gödel’s Incompleteness Theorems and Logicism, Nous, Vol 15, No 4, page 451–468, 1981.
- M van Atten, Essays on Gödel’s Reception of Leibniz, Husserl, and Brouwer, ser. Logic, Epistemology, and the Unity of Science, Springer International Publishing, 2014.
- R Tieszen, Dirk van Dalen. Mystic, Geometer, and Intuitionist: The life of L E J Brouwer. Vol 2: Hope and Disillusion, Oxford: Clarendon Press, 2005. pp x+ 441–946. ISBN 0-19-851620-7 (hardcover), Philosophia Mathematica, Vol 15, No 1, page 111–116, 2007.
- K Gödel, S Feferman, Kurt Gödel: Collected Works: Volume III: Unpublished Essays and Lectures, Oxford University Press on Demand, Vol 3, 1986.
- H Putnam, What is Mathematical Truth?, Historia Mathematica, Vol 2, No 4, page 529–533, 1975.
- B J Copeland, The Church-Turing Thesis, in The Stanford Encyclopedia of Philosophy, E N Zalta (ed), Metaphysics Research Lab, Stanford University, 2020.
- A M Turing, On Computable Numbers, with an Application to the Entscheidungsproblem, Proceedings of the London Mathematical Society, Vol s2-42, No 1, page 230–265, 1937.
- H Putnam, After Gödel, Logic Journal of the IGPL, Vol 14, No 5, page 745–754, 2006.
- J R Lucas, Minds, Machines and Gödel, Philosophy, Vol 36, No 137, page 112–127, 1961.
- E Nagel, J Newman, Gödel’s Proof, ser Routledge Classics, Routledge, 2005.
- P Benacerraf, God, the Devil, and Gödel, Etica E Politica, University of Trieste, Department of Philosophy, Vol 5, No 1, page 1–15, 2003.
- R Penrose, M Gardner, The Emperor’s New Mind: Concerning Computers, Minds, and the Laws of Physics, ser Popular Science Series, OUP Oxford, 1999.
- H Putnam, Minds and machines, in Dimensions of Minds, S Hook (ed), New York University Press, New York, USA, page 138–164, 1960.
- D Hofstadter, Gödel, Escher, Bach: An Eternal Golden Braid, ser Pulitzer Prize in letters: General non-fiction, Basic Books, 1999.
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