Kurt Gödel

Kurt Friedrich Gödel (Brno, 28 april 1906 — Princeton (New Jersey), 14 jannewaris 1978) wie in Eastenryksk-Amerikaansk wiskundige, logikus en filosoof. Hy wurdt sjoen as ien fan de belangrykste logisy fan alle tiden.

Libben

Gödel hat in tige grutte ynfloed hân op it wittenskiplike en filosofyske tinken fan de 20e iuw, meidat hy it eardere wurk fan Bertrand Russell, A.N. Whitehead en David Hilbert om de wiskunde op in formele basis fan in slutend oerkoepeljend aksiomatysk systeem te basearjen, tige ûndergroef.^[1]

Yn 1931 bewiisde Gödel nammentlik dat binnen elk selskonsistint rekursyf aksiomatysk systeem, dat krêftich genôch is om de rekkenkunde fan de natuerlike getallen te beskriuwen (Peano-rekkenkunde), der tenminste ien wiere stelling oer de natuerlike getallen bestiet, dy't net bewiisd wurde kin op basis fan de aksiomata fan dit systeem. By de bewiisfiering fan dizze stelling ûntwikkele Gödel in technyk dy't tsjintwurdich bekend stiet as de Gödel-nûmering, dy't oan eltse formele útspraak in natuerlik getal takent. Dizze stelling stiet bekend as de earste ûnfolsleinheidsstelling fan Gödel. Dat resultaat betsjutte de ein fan it logysk positivisme fan de Wiener Kreis.

Yn syn twadde ûnfolsleinheidsstelling toande Gödel letter oan dat de kontinuümhypoteze net werlein wurde kin binnen de konsistinte aksioma’s fan de samlingenlear. Kurt Gödel levere fierder belangrike bydragen oan de bewiisteory troch de ferbannen te ferdúdlikjen tusken de klassike logika, de yntuïsjonistyske logika, en de modale logika.

De Kurt Gödel Society, oprjochte yn 1987, waard nei him ferneamd. It is in ynternasjonale organisaasje foar it stypjen fan ûndersyk op it mêd fan de logika, filosofy en de skiednis fan de wiskunde.

De freonskip tusken Albert Einstein en Gödel wie legindarysk, wat ek blykte út de wannelingen dy't se tegearre ûndernommen fan en nei it IAS. De aard fan harren petearen wie foar de oare leden fan it ynstitút in geheim. De ekonoom Oskar Morgenstern ferhellet dat Einstein him oan de ein fan syn libben yn betrouwen sei dat syn “eigen wurk net folle mear betsjutte, mar dat hy allinnich noch mar nei it ynstitút gie om it foarrjocht te hawwen tegearre mei Gödel op hûs oan rinne te kinnen.

Boarnen, noaten en referinsjes

Boarnen, noaten en/as referinsjes:

(dú) 1931, Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme, Monatshefte für Mathematik und Physik 38: 173-98.
(dú) 1932, Zum intuitionistischen Aussagenkalkül, Anzeiger Akademie der Wissenschaften Wien 69: 65–66.
(in) 1940. The Consistency of the Axiom of Choice and of the Generalized Continuum Hypothesis with the Axioms of Set Theory. Princeton University Press.
(in) 1947. What is Cantor's continuum problem? - The American Mathematical Monthly 54: 515-25. Revised version in Paul Benacerraf and Hilary Putnam, eds., 1984
(in) 1964. Philosophy of Mathematics: Selected Readings. Cambridge Univ. Press: 470-85.
Kurt Godel - 1992. On Formally Undecidable Propositions Of Principia Mathematica And Related Systems, tr. B. Meltzer, with a comprehensive introduction by Richard Braithwaite. Dover reprint of the 1962 Basic Books edition.
[1] On Formally Undecidable Propositions Of Principia Mathematica And Related Systems, tr. Martin Hirzel
Jean van Heijenoort - 1967. A Source Book in Mathematical Logic, 1879-1931. Harvard Univ. Press.
- Jean van Heijenoort "The completeness of the axioms of the functional calculus of logic," 582-91.
- Jean van Heijenoort 1930 - "Some metamathematical results on completeness and consistency," 595-96. Abstract to (1931).
- Jean van Heijenoort 1931.- "On formally undecidable propositions of Principia Mathematica and related systems," 596-616.
- Jean van Heijenoort 1931a. - "On completeness and consistency," 616-17.
My philosophical viewpoint, c. 1960, unpublished.
The modern development of the foundations of mathematics in the light of philosophy, 1961, unpublished.
Collected Works: Oxford University Press: New York. Editor-in-chief: Solomon Feferman.
- Volume I: Publications 1929-1936 ISBN 0-19-503964-5,
- Volume II: Publications 1938-1974 ISBN 0-19-503972-6,
- Volume III: Unpublished Essays and Lectures ISBN 0-19-507255-3,
- Volume IV: Correspondence, A-G ISBN 0-19-850073-4.
- Volume V: Correspondence, H-Z ISBN 0-19-850075-0
(in) John L. Casti and Werner DePauli, 2000. Gödel: A Life of Logic, Basic Books (Perseus Books Group), Cambridge, MA. ISBN 0-7382-0518-4.
(in) John W. Dawson, Jr. Logical Dilemmas: The Life and Work of Kurt Gödel. AK Peters, Ltd., 1996.
(in) John W. Dawson, Jr, 1999. "Gödel and the Limits of Logic", Scientific American, vol. 280 num. 6, pp. 76–81
(in) Torkel Franzén, 2005. Gödel's Theorem: An Incomplete Guide to Its Use and Abuse. Wellesley, MA: A K Peters.
(in) Rebecca Goldstein, 2005. Incompleteness: The Proof and Paradox of Kurt Gödel. W. W. Norton & Company, New York. ISBN 0-393-32760-4 pbk.
(in) Ivor Grattan-Guinness, 2000. The Search for Mathematical Roots 1870–1940. Princeton Univ. Press.
(in) Jaakko Hintikka, 2000. On Gödel. Wadsworth.
(in) Douglas Hofstadter, 1980. Gödel, Escher, Bach. Vintage.
(in) Stephen Kleene, 1967. Mathematical Logic. Dover paperback reprint ca. 2001.
(in) J.R. Lucas, 1970. The Freedom of the Will. Clarendon Press, Oxford.
(in) Ernst Nagel and Newman, James R., 1958. Gödel's Proof. New York Univ. Press. Oersetting drs. J.M. Debrot De stelling van Gödel Aula 540 Het Spectrum ISBN 90-274-5286-5
(in) Procházka, Jiří, 2006, 2006, 2008, 2008. Kurt Gödel: 1906–1978: Genealogie. ITEM, Brno. Volume I. Brno 2006, ISBN 80-902297-9-4. In Ger., Engl. Volume II. Brno 2006, ISBN 80-903476-0-6. In Germ., Engl. Volume III. Brno 2008, ISBN 80-903476-4-9. In Germ., Engl. Volume IV. Brno, Princeton 2008, ISBN 978-80-903476-5-6. In Germ., Engl.
(in) Ed Regis, 1987. Who Got Einstein's Office? Addison-Wesley Publishing Company, Inc.
(in) Raymond Smullyan, 1992. Godel's Incompleteness Theorems. Oxford University Press.
(in) Hao Wang, 1987. Reflections on Kurt Gödel. MIT Press.
(in) Wang, Hao. 1996. A Logical Journey: From Godel to Philosophy. MIT Press.
(in) Yourgrau, Palle, 1999. Gödel Meets Einstein: Time Travel in the Gödel Universe. Chicago: Open Court.
(in) Yourgrau, Palle, 2004. A World Without Time: The Forgotten Legacy of Gödel and Einstein. Basic Books.
(in) Hao Wang. Skolem and Gödel pdf
(ned) Igor Kramer. Gödel. Eindexamenproject Nederlandse Film en Telefyzje Akademy 2007
(in) Hector Rosario Kurt Gödel’s Mathematical and Scientific Perspective of the Divine
(in) O'Connor, John J.; Robertson, Edmund F., "Kurt Gödel", MacTutor History of Mathematics archive
(in) Kurt Gödel by it Mathematics Genealogy Project
(in) Weisstein, Eric W., Gödel, Kurt (1906-1978) by ScienceWorld.
(in) Kennedy, Juliette. "Kurt Gödel." In Stanford Encyclopedia of Philosophy.
(in) Time Bandits – een artikel over de relatie tussen Gödel en Einstein troch Jim Holt
(in) Gödels Theorem and Information – Skreaun troch Gregory Chaitin
(in) "Gödel and the limits of logic" troch John W Dawson Jr. (juny 2006)
(in) Notices of the AMS, April 2006, Volume 53, Number 4 Kurt Gödel Centenary Issue
(in) Paul Davies and Freeman Dyson discuss Kurt Godel
(in) "Gödel and the Nature of Mathematical Truth" Edge: In petear mei Rebecca Goldstein oer Kurt Gödel.

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