Kurt Gödel

"Gödel" beralih ke halaman ini. Untuk the programming language, lihat Gödel (programming language). Untuk other uses, lihat Godel (disambiguation).

Kurt Friedrich Gödel (/ˈkɜːrt ɡɜːrdəl/; Jerman: [ˈkʊʁt ˈɡøːdəl] ^ⓘ; 28 April 1906 – 14 Januari 1978) adalah seorang ahli matematika, logika dan filsuf asal Austria, yang kemudian beralih menjadi warganegara Amerika Serikat. Bersama dengan Aristoteles dan Gottlob Frege, ia dianggap sebagai tokoh logika paling penting dalam sejarah, di mana Gödel memberikan dampak luar biasa pada pemikiran ilmiah dan filsafat pada abad ke-20, ketika tokoh lain seperti Bertrand Russell, A. N. Whitehead, dan David Hilbert mempelopori penggunaan logika dan teori himpunan untuk memahami dasar-dasar matematika.

Kurt Gödel
Lahir	Kurt Friedrich Gödel (1906-04-28)28 April 1906 Brünn, Austria-Hungary (sekarang Brno, Czech Republic)
Meninggal	14 Januari 1978(1978-01-14) (umur 71) Princeton, New Jersey, Amerika Serikat
Tempat tinggal	Amerika Serikat
Kewarganegaraan	Austria, Amerika Serikat
Almamater	University of Vienna
Dikenal atas	Teorema ketaklengkapan Gödel, Teorema kelengkapan Gödel, konsistensi hipotesis continuum dengan ZFC, Gödel metric, Gödel's ontological proof
Penghargaan	Albert Einstein Award (1951); National Medal of Science (USA) in Mathematical, Statistical, and Computational Sciences (1974) Fellow of the British Academy
Karier ilmiah
Bidang	Matematika, Logika matematika
Institusi	Institute for Advanced Study
Disertasi	Über die Vollständigkeit des Logikkalküls
Pembimbing doktoral	Hans Hahn
Tanda tangan

Riwayat hidup

Masa kecil

Gödel lahir pada tanggal 28 April 1906, di Brünn, Austria-Hungary (sekarang Brno, Czech Republic) dalam keluarga etnis Jerman dengan ayah bernama Rudolf Gödel, manajer sebuah pabrik tekstil, dan ibu, Marianne Gödel (nama keluarga gadisnya, Handschuh). }}. From p. 80, which quotes Rudolf Gödel, Kurt's brother and a medical doctor. The words "a severe nervous crisis", and the judgement that the Schlick assassination was its trigger, are from the Rudolf Gödel quote. Rudolf knew Kurt well in those years.</ref> He developed paranoid symptoms, including a fear of being poisoned, and spent several months in a sanitarium for nervous diseases.

In 1933, Gödel first traveled to the U.S., where he met Albert Einstein, who became a good friend. He delivered an address to the annual meeting of the American Mathematical Society. During this year, Gödel also developed the ideas of computability and recursive functions to the point where he was able to present a lecture on general recursive functions and the concept of truth. This work was developed in number theory, using Gödel numbering.

In 1934 Gödel gave a series of lectures at the Institute for Advanced Study (IAS) in Princeton, New Jersey, entitled On undecidable propositions of formal mathematical systems. Stephen Kleene, who had just completed his PhD at Princeton, took notes of these lectures that have been subsequently published.

Gödel would visit the IAS again in the autumn of 1935. The traveling and the hard work had exhausted him, and the next year he took a break to recover from a depressive episode. He returned to teaching in 1937. During this time, he worked on the proof of consistency of the axiom of choice and of the continuum hypothesis; he would go on to show that these hypotheses cannot be disproved from the common system of axioms of set theory.

He married Adele Nimbursky (née Porkert, 1899–1981), whom he had known for over 10 years, on September 20, 1938. Their relationship had been opposed by his parents on the grounds that she was a divorced dancer, six years older than he was.

Subsequently, he left for another visit to the USA, spending the autumn of 1938 at the IAS and the spring of 1939 at the University of Notre Dame.

Relocation to Princeton, Einstein and US citizenship

After the Anschluss in 1938, Austria had become a part of Nazi Germany. Germany abolished the title of Privatdozent, so Gödel had to apply for a different position under the new order. His former association with Jewish members of the Vienna Circle, especially with Hahn, weighed against him. The University of Vienna turned his application down.

His predicament intensified when the German army found him fit for conscription. World War II started in September 1939. Before the year was up, Gödel and his wife left Vienna for Princeton. To avoid the difficulty of an Atlantic crossing, the Gödels took the trans-Siberian railway to the Pacific, sailed from Japan to San Francisco (which they reached on March 4, 1940), then crossed the U.S. by train to Princeton, where Gödel would accept a position at the Institute for Advanced Study (IAS).

Gödel very quickly resumed his mathematical work. In 1940, he published his work Consistency of the axiom of choice and of the generalized continuum-hypothesis with the axioms of set theory, which is a classic of modern mathematics. In that work he introduced the constructible universe, a model of set theory in which the only sets that exist are those that can be constructed from simpler sets. Gödel showed that both the axiom of choice (AC) and the generalized continuum hypothesis (GCH) are true in the constructible universe, and therefore must be consistent with the Zermelo–Fraenkel axioms for set theory (ZF). This result has had considerable consequences for working mathematicians, as it means that they can assume the axiom of choice when proving the Hahn-Banach theorem. Paul Cohen later constructed a model of ZF in which AC and GCH are false; together these proofs mean that AC and GCH are independent of the ZF axioms for set theory.

Albert Einstein was also living at Princeton during this time. Gödel and Einstein developed a strong friendship, and were known to take long walks together to and from the Institute for Advanced Study. The nature of their conversations was a mystery to the other Institute members. Economist Oskar Morgenstern recounts that toward the end of his life Einstein confided that his "own work no longer meant much, that he came to the Institute merely ... to have the privilege of walking home with Gödel".

Gödel and his wife Adele spent the summer of 1942 in Blue Hill, Maine, at the Blue Hill Inn at the top of the bay. Gödel was not merely vacationing but had a very productive summer of work. Using Heft 15 [volume 15] of Gödel's still-unpublished Arbeitshefte [working notebooks], John W. Dawson, Jr. conjectures that Gödel discovered a proof for the independence of the axiom of choice from finite type theory, a weakened form of set theory, while in Blue Hill in 1942. Gödel's close friend Hao Wang supports this conjecture, noting that Gödel's Blue Hill notebooks contain his most extensive treatment of the problem.

On December 5, 1947, Einstein and Morgenstern accompanied Gödel to his U.S. citizenship exam, where they acted as witnesses. Gödel had confided in them that he had discovered an inconsistency in the U.S. Constitution that would allow the U.S. to become a dictatorship. Einstein and Morgenstern were concerned that their friend's unpredictable behavior might jeopardize his application. Fortunately, the judge turned out to be Phillip Forman, who knew Einstein and had administered the oath at Einstein's own citizenship hearing. Everything went smoothly until Forman happened to ask Gödel if he thought a dictatorship like the Nazi regime could happen in the U.S. Gödel then started to explain his discovery to Forman. Forman understood what was going on, cut Gödel off, and moved the hearing on to other questions and a routine conclusion. -->

Akhir hayat

Gödel menjadi anggota tetap "Institute for Advanced Study" di Princeton pada tahun 1946. Sekitar waktu ini ia berhenti mempublikasikan karyanya, meskipun terus bekerja. Ia menjadi profesor penuh pada institut itu pada tahun 1953 dan pensiun sebagai profesor emeritus pada tahun 1976.

Gravestone of Kurt and Adele Gödel in the Princeton, N.J., cemetery

Pada akhir hidupnya, Gödel mengalami beberapa kali gangguan mental dan penyakit. Ia menderita ketakutan besar akan diracuni; ia hanya mau makan makanan yang disiapkan oleh istrinya, Adele. Pada akhir tahun 1977, istrinya masuk rumah sakit selama 6 bulan dan tidak mampu menyiapkan makanan untuk suaminya. Akibatnya, Gödel tidak mau makan, sehingga akhirnya meninggal karena kelaparan. Beratnya hanya 65 pound (sekitar 30 kg) ketika meninggal. Pada akta kematian tertulis bahwa ia meninggal akibat "kekurangan gizi dan inanition karena gangguan kepribadian" pada Princeton Hospital tanggal 14 Januari 1978. Adele's death followed in 1981.

Pandangan agama

Gödel adalah seorang penganut teguh aliran teisme. Ia memegang keyakinan bahwa Allah adalah sosok pribadi, yang berbeda dengan pandangan sahabatnya, Albert Einstein.

Warisan

Sebuah yayasan bernama Kurt Gödel Society didirikan pada tahun 1987 untuk menghormatinya. Merupakan suatu organisasi internasional yang mempromosikan riset dalam bidang logika, filsafat dan sejarah matematika. University of Vienna membuka "Kurt Gödel Research Center for Mathematical Logic". Association for Symbolic Logic telah mengundang pembicara khusus tahunan sebagai "Kurt Gödel lecturer" sejah tahun 1990.

Publikasi penting

Dalam bahasa Jerman:

• 1930, "Die Vollständigkeit der Axiome des logischen Funktionenkalküls." Monatshefte für Mathematik und Physik 37: 349–60.
• 1931, "Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme, I." Monatshefte für Mathematik und Physik 38: 173–98.
• 1932, "Zum intuitionistischen Aussagenkalkül", Anzeiger Akademie der Wissenschaften Wien 69: 65–66.

Dalam bahasa Inggris:

• 1940. The Consistency of the Axiom of Choice and of the Generalized Continuum Hypothesis with the Axioms of Set Theory. Princeton University Press.
• 1947. "What is Cantor's continuum problem?" The American Mathematical Monthly 54: 515–25. Revised version in Paul Benacerraf and Hilary Putnam, eds., 1984 (1964). Philosophy of Mathematics: Selected Readings. Cambridge Univ. Press: 470–85.
• 1950, "Rotating Universes in General Relativity Theory." Proceedings of the international Congress of Mathematicians in Cambridge, 1: 175–81

Dalam terjemahan bahasa Inggris:

• 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.
• Kurt Godel, 2000. 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.
  • 1930. "The completeness of the axioms of the functional calculus of logic," 582–91.
  • 1930. "Some metamathematical results on completeness and consistency," 595–96. Abstract to (1931).
  • 1931. "On formally undecidable propositions of Principia Mathematica and related systems," 596–616.
  • 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 978-0-19-503964-1 / Paperback:ISBN 978-0-19-514720-9,
  • Volume II: Publications 1938–1974 ISBN 978-0-19-503972-6 / Paperback:ISBN 978-0-19-514721-6,
  • Volume III: Unpublished Essays and Lectures ISBN 978-0-19-507255-6 / Paperback:ISBN 978-0-19-514722-3,
  • Volume IV: Correspondence, A–G ISBN 978-0-19-850073-5,
  • Volume V: Correspondence, H–Z ISBN 978-0-19-850075-9.

Lihat pula

• Gödel machine
• Gödel Prize
• Gödel's speed-up theorem
• Teorema ketaklengkapan Gödel
• Original proof of Gödel's completeness theorem
• Slingshot argument

Pustaka

• Dawson, John W., 1997. Logical dilemmas: The life and work of Kurt Gödel. Wellesley MA: A K Peters.
• 1911 Encyclopædia Britannica/Brünn. (September 19, 2007). In Wikisource, The Free Library. Retrieved 10 pm EST March 13, 2008.
• Rebecca Goldstein, 2005. Incompleteness: The Proof and Paradox of Kurt Gödel. W. W. Norton & Company, New York. ISBN 0-393-32760-4 pbk.

Pustaka tambahan

• John L. Casti and Werner DePauli, 2000. Gödel: A Life of Logic, Basic Books (Perseus Books Group), Cambridge, MA. ISBN 0-7382-0518-4.
• John W. Dawson, Jr. Logical Dilemmas: The Life and Work of Kurt Gödel. AK Peters, Ltd., 1996.
• John W. Dawson, Jr, 1999. "Gödel and the Limits of Logic", Scientific American, vol. 280 num. 6, pp. 76–81
• Torkel Franzén, 2005. Gödel's Theorem: An Incomplete Guide to Its Use and Abuse. Wellesley, MA: A K Peters.
• Ivor Grattan-Guinness, 2000. The Search for Mathematical Roots 1870–1940. Princeton Univ. Press.
• Jaakko Hintikka, 2000. On Gödel. Wadsworth.
• Douglas Hofstadter, 1980. Gödel, Escher, Bach. Vintage.
• Stephen Kleene, 1967. Mathematical Logic. Dover paperback reprint ca. 2001.
• Stephen Kleene, 1980. Introduction to Metamathematics. North Holland ISBN 0-7204-2103-9 (Ishi Press paperback. 2009. ISBN 978-0-923891-57-2)
• J.R. Lucas, 1970. The Freedom of the Will. Clarendon Press, Oxford.
• Ernest Nagel and Newman, James R., 1958. Gödel's Proof. New York Univ. Press.
• Procházka, Jiří, 2006, 2006, 2008, 2008, 2010. 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. Volume V,Brno,Princeton 2010, ISBN 80-903476-9-X. In Germ., Engl.
• Procházka, Jiří, 2012. "Kurt Gödel: 1906–1978: Historie". ITEM,Brno, Wien, Princeton. Volume I. ISBN 978-80-903476-2-5. In Ger., Engl.
• Ed Regis, 1987. Who Got Einstein's Office? Addison-Wesley Publishing Company, Inc.
• Raymond Smullyan, 1992. Godel's Incompleteness Theorems. Oxford University Press.
• Olga Taussky-Todd, 1983. Remembrances of Kurt Gödel. Engineering & Science, Winter 1988.
• Hao Wang, 1987. Reflections on Kurt Gödel. MIT Press.
• Hao Wang, 1996. A Logical Journey: From Godel to Philosophy. MIT Press.
• Yourgrau, Palle, 1999. Gödel Meets Einstein: Time Travel in the Gödel Universe. Chicago: Open Court.
• Yourgrau, Palle, 2004. A World Without Time: The Forgotten Legacy of Gödel and Einstein. Basic Books. Book review by John Stachel in the Notices of the American Mathematical Society (54 (7), pp. 861–868):

Pranala luar

• Kurt Gödel di Mathematics Genealogy Project
• Weisstein, Eric Wolfgang (ed.). "Gödel, Kurt (1906–1978)". ScienceWorld. 
• Kennedy, Juliette. "Kurt Gödel." In Stanford Encyclopedia of Philosophy.
• Time Bandits: an article about the relationship between Gödel and Einstein by Jim Holt
• "Gödel and the limits of logic" by John W Dawson Jr. (June 2006)
• Notices of the AMS, April 2006, Volume 53, Number 4 Kurt Gödel Centenary Issue
• Paul Davies and Freeman Dyson discuss Kurt Godel
• "Gödel and the Nature of Mathematical Truth" Edge: A Talk with Rebecca Goldstein on Kurt Gödel.
• It's Not All In The Numbers: Gregory Chaitin Explains Gödel's Mathematical Complexities.
• Gödel photo g.
• (Inggris) Kurt Gödel di Find a Grave
• National Academy of Sciences Biographical Memoir
• John J. O'Connor and Edmund F. Robertson. Kurt Gödel di MacTutor archive.