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{{Redirect|Gödel|the[[bahasa programming languagepemrograman]]|Gödel (programming language)|otherkegunaan useslain|Godel (disambiguationdisambiguasi)}}
{{Infobox scientist
| name = Kurt Gödel
| image = <!--Kurt1925 kurt gödel (cropped).jpg-->png
| image_size =
| caption = Kurt Gödel (1925)
|birth_name=Kurt Friedrich Gödel
| birth_date = {{birth date|1906|4|28}}
| birth_place = Brünn, [[Austria-Hungary]] (sekarang [[Brno]], [[Czech Republic]])
| death_date = {{death date and age|1978|1|14|1906|4|28}}
| death_place = [[Princeton, New Jersey|Princeton]], [[New Jersey]], [[Amerika Serikat]]
| residence = [[Amerika Serikat]]
| citizenship = Austria, [[Amerika Serikat]]
| field = [[Matematika]], [[Logika matematika]]
| work_institutions = [[:en:Institute for Advanced Study|Institute for Advanced Study]]
| alma_mater = [[:en:University of Vienna|University of Vienna]]
| thesis_title = Über die Vollständigkeit des Logikkalküls
| doctoral_advisor = [[:en:Hans Hahn (mathematician)|Hans Hahn]]
| doctoral_students =
| influences =
| influenced =
| known_for = [[Teorema ketaklengkapan Gödel]], [[:en:Gödel's completeness theorem|Teorema kelengkapan Gödel]], konsistensi [[:en:Continuum hypothesis|hipotesis continuum]] dengan [[:en:ZFC|ZFC]], [[:En:Gödel metric|metrik Gödel]], [[:en:Gödel's ontological proof|bukti ontologi Gödel]]
| prizes = [[Albert Einstein Award]] (1951); [[National Medal of Science]] (USA) in Mathematical, Statistical, and Computational Sciences (1974)<br/>[[Fellow of the British Academy]]
| religion = [[TheistTeisme]]<ref>{{cite book|title=A to Z of Mathematicians|year=2005|publisher=Infobase Publishing|isbn=9780816053384|author=Tucker McElroy|page=118|quote=Gödel had a happy childhood, and was called "Mr. Why" by his family, due to his numerous questions. He was baptized as a Lutheran, and re- mained a theist (a believer in a personal God) throughout his life.}}</ref>
| signature = Kurt Gödel signature.svg
| footnotes =
}}
'''Kurt Friedrich Gödel''' ({{IPAc-en|ˈ|k|ɜr|t|_|g|ɜr|d|əl}}; {{IPA-de|ˈkʊʁt ˈɡøːdəl|lang|Kurt gödel.ogg}}; {{lahirmati|[[Austria]] |28|4|1906|[[Princeton, New Jersey]], [[Amerika Serikat]]|14|1|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]],<ref name="Stanford&Son">For instance, in their ''[http://plato.stanford.edu/entries/principia-mathematica/ Principia Mathematica'']'' (''Stanford Encyclopedia of Philosophy'' edition).</ref> [[A. N. Whitehead]],<ref name="Stanford&Son"/> dan [[David Hilbert]] mempelopori penggunaan logika dan [[teori himpunan]] untuk memahami [[:en:foundations of mathematics|dasar-dasar matematika]].
 
Gödel mempublikasikan [[teorema ketaklengkapan Gödel|kedua teorema ketidaklengkapan hasil pemikirannya]] pada tahun 1931 ketika ia berusia 25 tahun, setahun setelah meraih gelar doktor pada [[:en:University of Vienna|University of Vienna]].<!-- The first incompleteness theorem states that for any self-consistent [[recursive set|recursive]] [[axiomatic system]] powerful enough to describe the arithmetic of the [[natural number]]s (for example [[Peano arithmetic]]), there are true propositions about the naturals that cannot be proved from the [[axioms]]. To prove this theorem, Gödel developed a technique now known as [[Gödel numbering]], which codes formal expressions as natural numbers.
Baris 43:
Gödel attended the ''Evangelische Volksschule'', a Lutheran school in Brünn from 1912 to 1916, and was enrolled in the ''Deutsches Staats-Realgymnasium'' from 1916 to 1924, excelling with honors in all his subjects, particularly in mathematics, languages and religion. Although Kurt had first excelled in languages, he later became more interested in history and mathematics. His interest in mathematics increased when in 1920 his older brother Rudolf (born 1902) left for [[Vienna]] to go to medical school at the [[University of Vienna]]. During his teens, Kurt studied [[Gabelsberger shorthand]], [[Johann Wolfgang von Goethe|Goethe]]'s ''[[Theory of Colours (book)|Theory of Colours]]'' and criticisms of [[Isaac Newton]], and the writings of [[Immanuel Kant]].
-->
=== Belajar di Vienna ===
Pada usia 18, Gödel mengikuti abangnya di [[Wina]] (''Vienna'') dan kuliah di University of Vienna. Saat itu ia sudah menguasai matematika setingkat universitas.<ref>Dawson 1997, p. 24.</ref> Meskipun awalnya berniat untuk belajar [[:en:theoretical physics|fisika teoretis]], ia juga mengikuti kuliah matematika dan filsafat. Pada masa ini, ia menganut ide [[:En:mathematical realism|realisme matematika]]. Ia membaca karya [[Immanuel Kant]], ''[[:en:Metaphysical Foundations of Natural Science|Metaphysische Anfangsgründe der Naturwissenschaft]]'', dan berpartisipasi dalam [[Vienna Circle]] bersama [[Moritz Schlick]], [[Hans Hahn (mathematician)|Hans Hahn]], dan [[Rudolf Carnap]]. Gödel kemudian belajar [[:en:number theory|teori bilangan]]<!--, buttetapi whenketika heia tookikut partsuatu inseminar ayang seminar rundiorganisir byoleh [[Moritz Schlick]] whichyang studiedmempelajari buku karya [[Bertrand Russell]]'s book ''Introduction to Mathematical Philosophy'', heia becamemenjadi interestedtertarik inpada [[mathematicallogika logicmatematika]]. According toMenurut Gödel, mathematicallogika logicmatematika wasadalah "asuatu scienceilmu priorpengetahuan tosebelum allsemua othersyang lain, whichyang containsmemuat theide-ide ideasdan andprinsip-prinsip principlesmelandasi underlyingsemua allilmu sciencespengetahuan."<ref>Gleick, J. (2011) ''[[The Information: A History, a Theory, a Flood]],'' London, Fourth Estate, p181.</ref>
 
AttendingKetika amenghadiri lecturekuliah byyang diberikan oleh [[David Hilbert]] indi [[Bologna]] onmengenai completenesskelengkapan anddan consistencykonsistensi ofsistem mathematicalmatematika, systemsjalan may have sethidup Gödel's lifemenjadi courseterfokus. InPada tahun 1928, Hilbert anddan [[Wilhelm Ackermann]] publishedmenerbitkan ''Grundzüge der theoretischen Logik'' (''[[:en:Principles of Mathematical Logic|Prinsip-prinsip logika matematika]]''), ansuatu introductionpendahuluan tokepada [[:en:first-order logic|logika tingkat pertama]] indi which the problem ofmana completenesssoal waskelengkapan poseddiungkapkan: ''AreApakah theaksioma-aksioma axioms of asistem formal systemmemadai sufficientuntuk tomenurunkan derivesetiap everypernyataan statementyang thatbenar isdalam truesemua in all models ofmodel thesistem systemitu?''
 
ThisIni becamemenjadi thetopik topicyang thatdipilih oleh Gödel choseuntuk forkarya his doctoral workdoktoralnya. InPada tahun 1929, atpada theusia age23 of 23tahun, he completed hisia doctoralmenyelesaikan [[dissertationdisertasi]] underdoktoralnya di bawah bimbingan Hans Hahn's supervision. InDi itdalamnya, heia establishedmenyatakan thekelengkapan completeness of thedari [[:en:first-order predicate calculus|kalkulus predikat tingkat pertama]] ([[:en:Gödel's completeness theorem|Teorema kelengkapan Gödel]]). HeIa wasmeraih awardedgelar hisdoktor doctoratepada intahun 1930. His thesisTesisnya, alongbersama withdengan somesejumlah additionalkarya worktambahan, was published bydipublikasikan theoleh Vienna Academy of Science.
 
=== Teorema Ketidaklengkapan ===
{|class="toccolours" style="float: right; margin-left: 0.5em; margin-right: 0.5em; font-size: 84%; background:#white; color:black; width:30em; max-width: 30%;" cellspacing="5"
|style="text-align: left;"| "Kurt Gödel's achievement in modern logic is singular and monumental – indeed it is more than a monument, it is a landmark which will remain visible far in space and time. ... The subject of logic has certainly completely changed its nature and possibilities with Gödel's achievement." —[[John von Neumann]]<ref>Halmos, P.R. "The Legend of von Neumann", The American Mathematical Monthly, Vol. 80, No. 4. (April 1973), pp. 382–394</ref>
|}
 
InPada tahun 1931, andketika whilemasih still indi Vienna, Gödel published hismenerbitkan [[Gödel'sTeorema incompletenessketaklengkapan theoremsGödel|incompletenessteorema theoremsketaklengkapan]] indalam ''Über formal unentscheidbare Sätze der "Principia Mathematica" und verwandter Systeme'' (calleddalam bahasa inInggris Englishdisebut "[[:en:On Formally Undecidable Propositions of Principia Mathematica and Related Systems|On Formally Undecidable Propositions of "''Principia Mathematica''" and Related Systems]]").<!-- In that article, he proved for any [[Recursion theory|computable]] [[axiomatic system]] that is powerful enough to describe the arithmetic of the [[natural numbers]] (e.g. the [[Peano axioms]] or [[ZFC|Zermelo–Fraenkel set theory with the axiom of choice]]), that:
# If the [[formal system|system]] is [[consistency proof|consistent]], it cannot be [[Completeness (logic)|complete]].
# The consistency of the [[axiom]]s cannot be proven within the [[Axiomatic system|system]].
These theorems ended a half-century of attempts, beginning with the work of [[Frege]] and culminating in ''[[Principia Mathematica]]'' and [[philosophy of mathematics#Formalism|Hilbert's formalism]], to find a set of axioms sufficient for all mathematics.-->
<!--
In hindsight, the basic idea at the heart of the incompleteness theorem is rather simple. Gödel essentially constructed a formula that claims that it is unprovable in a given formal system. If it were provable, it would be false, which contradicts the idea that in a consistent system, provable statements are always true.
Baris 67:
In his two-page paper ''Zum intuitionistischen Aussagenkalkül'' (1932) Gödel refuted the finite-valuedness of [[intuitionistic logic]]. In the proof he implicitly used what has later become known as [[intermediate logic|Gödel–Dummett intermediate logic]] (or [[t-norm fuzzy logic|Gödel fuzzy logic]]).
-->
=== Tahun 1930-an: pekerjaan selanjutnya dan kunjungan ke Amerika Serikat ===
 
Gödel menyelesaikan [[:en:habilitation|habilitasinya]] di Vienna pada tahun 1932, dan pada tahun 1933 ia menjadi seorang ''[[:en:Privatdozent|Privatdozent]]'' (dosen tanpa bayaran) di sana. Pada tahun 1933 [[Adolf Hitler]] mulai berkuasa di Jerman, dan pada tahun-tahun berikutnya, Nazi mulai naik pengaruhnya di Austria, dan di kalangan ahli matematika Vienna.
Dalam bulan 1936, [[:en:Moritz Schlick|Moritz Schlick]], yang seminarnya membangkitkan ketertarikan Gödel pada logika, dibunuh oleh seorang mahasiswa pro-Nazi. Ini menimbulkan "suatu krisis syarafsaraf berat" dalam diri Gödel.<ref name=Casti2001>{{Cite book
| last1 = Casti | first1 = John L.
| last2 = Depauli | first2 = Werner
| year = 2001
| title = Gödel : a life of logic
| doi = 10.1287/moor.1050.0169
| isbn = 0-7382-0518-4
| location = Cambridge, Mass.
| publisher=Basic Books
| journal=Mathematics of Operations Research
| volume = 31
| page = 147
| last3 = Koppe
| first3 = Matthias
| last4 = Weismantel
| first4 = Robert
| postscript = <!--None-->
}}. Dari halaman 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>
Ia mulai mengalami gejala-gejala paranoid, termasuk ketakutan akan diracuni, dan melewatkan beberapa bulan di sebuah [[sanitarium]] untuk penyakit syarat.<ref>Dawson 1997, pp. 110–112</ref>
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Kemudian, ia pergi lagi ke Amerika Serikat, tinggal selama musim gugur 1938 di IAS dan musim semi 1939 di [[University of Notre Dame]].
 
=== Relokasi ke Princeton, Einstein dan kewarganegaraan Amerika Serikat ===
Setelah [[Anschluss]] pada tahun 1938, Austria menjadi bagian dari [[Nazi]] [[Jerman]].
Jerman menghapuskan gelar jabatan ''[[:en:Privatdozent|Privatdozent]]'', sehingga Gödel harus melamar pekerjaan pada posisi lain di bawah aturan baru. Hubungannya dulu dengan orang-orang Yahudi yang menjadi anggota Vienna Circle, terutama dengan Hahn, menjadi faktor yang merugikannya. University of Vienna menolak lamaran pekerjaannya.
 
Keadaannya menjadi lebih sulit ketika tentara Jerman memutuskan ia harus masuk wajib militer. [[Perang Dunia II]] dimulai pada bulan September [[1939]].
Sebelum setahun, Gödel dan istrinya meninggalkan Vienna dan pergi ke [[Princeton, New Jersey|Princeton]]. Untuk menghindari kesulitan menyeberangi [[samudra Atlantik]], pasangan Gödels naik [[:en:trans-Siberian railway|kereta api trans-Siberia]] ke [[samudra Pasifik]], berlayar dari [[Jepang]] ke [[San Francisco]] (tiba tanggal 4 Maret 1940), kemudian melintasi Amerika Serikat naik kereta api ke Princeton, di mana Gödel menerima posisi pada [[:en:Institute for Advanced Study|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.{{Citation needed|date=August 2013}} 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 (mathematician)|Paul Cohen]] later constructed a [[structure (mathematical logic)|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]] juga tinggal di Princeton pada waktu itu. Gödel dan Einstein menjadi sahabat karib, dan dikenal sering berjalan jauh bersama dari dan ke Institute for Advanced Study. Isi percakapan mereka merupakan misteri bagi anggota institut yang lain. Ahli ekonomi [[:en:Oskar Morgenstern|Oskar Morgenstern]] mengenang bahwa di akhir hidupnya Einstein mengakui "pekerjaannya sendiri tidak lagi berarti banyak, dan ia datang ke institut hanya ... untuk mendapatkan kesempatan berjalan pulang bersama Gödel".<ref>Goldstein (2005), p.&nbsp;33.</ref>
 
Gödel dan istrinya, Adele, melewatkan musim panas tahun 1942 di [[:en:Blue Hill, Maine|Blue Hill, Maine]], yaitu di Blue Hill Inn pada puncak di teluk itu. Gödel tidak hanya berlibur, tetapi juga sangat produktif dalam bekerja. Menggunakan ''Heft'' 15 [volume 15] dari karya Gödel ''Arbeitshefte'' [buku catatan kerja] yang belum diterbitkan, [[:en:John W. Dawson, Jr.|John W. Dawson, Jr.]] menyimpulkan bahwa Gödel menemukan suatu bukti ketidak-tergantungan aksioma pilihan dari teori jenis finit, suatu bentuk [[teori himpunan]] yang diperlemah, ketika tinggal di Blue Hill pada tahun 1942. Teman dekat Gödel, Hao Wang, mendukung konjektur ini, mengamati bahwa buku catatan Gödel ketika di Blue Hill memuat penjabaran yang paling luas mengenai soal ini.
 
Pada tanggal 5 Desember 5, 1947, Einstein dan Morgenstern menemani Gödel ke tempat ujian kewarganegaraan Amerika Serikat, di mana mereka menjadi saksi-saksi. Gödel telah mengatakan kepada mereka bahwa ia menemukan suatu inkonsistensi dalam [[:en:U.S. Constitution|Konstitusi Amerika Serikat]] yang dapat menjadi Amerika Serikat suatu negara diktator. Einstein dan Morgenstern kuatir tingkah laku teman mereka yang tidak dapat diramalkan itu akan menyebabkan aplikasi warganegara itu gagal. Untungnya, hakim penguji ternyata adalah [[:en:Phillip Forman|Phillip Forman]], yang mengenal Einstein, bahkan memimpin penyumpahan warganegara Einstein sendiri. Semua berjalan lancar sampai Forman kebetulan bertanya kepada Gödel apakah ia berpikir suatu diktatorial seperti [[Nazi]] dapat terjadi di Amerika Serikat. Gödel kemudian mulai menjelaskan penemuannya kepada Forman. Forman mengerti apa yang terjadi, memotong perkataan Gödel, meneruskan dengan pertanyaan lain dan kesimpulan rutin.<ref>Dawson 1997, pp. 179–180. The story of Gödel's citizenship hearing is repeated in many versions. Dawson's account is the most carefully researched, but was written before the rediscovery of Morgenstern's written account. Most other accounts appear to be based on Dawson, hearsay or speculation.</ref><ref>{{cite web |url = http://robert.accettura.com/wp-content/uploads/2010/10/Morgenstern_onGoedelcitizenship.pdf|title = History of the Naturalization of Kurt Gödel|author = Oskar Morgenstern|date = September 13, 1971|format = PDF|accessdate=June 20, 2012}}</ref>
 
=== Akhir hayat ===
Baris 125:
He studied and admired the works of [[Gottfried Leibniz]], but came to believe that a hostile conspiracy had caused some of Leibniz's works to be suppressed.<ref>John W. Dawson, Jr. [http://books.google.com/books?id=gA8SucCU1AYC&pg=PA166&dq=godel+leibniz&lr= Logical Dilemmas: The Life and Work of Kurt Gödel.] A K Peters, Ltd., 2005. P. 166.</ref> To a lesser extent he studied [[Immanuel Kant]] and [[Edmund Husserl]]. In the early 1970s, Gödel circulated among his friends an elaboration of Leibniz's version of [[Anselm of Canterbury]]'s [[ontological argument|ontological proof]] of God's existence. This is now known as [[Gödel's ontological proof]]. Gödel was awarded (with [[Julian Schwinger]]) the first [[Albert Einstein Award]] in 1951, and was also awarded the [[National Medal of Science]], in 1974.{{citation needed|date = January 2014}}
-->
[[FileBerkas:Kurt godel tomb 2004.jpg|rightka|thumbjmpl|200px|GravestoneBatu ofnisan Kurt anddan Adele Gödel indi thepekuburan Princeton, N.J., cemetery]]
Pada akhir hidupnya, Gödel mengalami beberapa kali [[gangguan mental]] dan penyakit. Ia menderita [[:en:persecutory delusions|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.<ref>{{cite web|url=http://www.nature.com/nature/journal/v435/n7038/full/435019a.html|title=Gödel's universe|author=Davis, Martin|work=Nature|date=May 4, 2005}}</ref> Beratnya hanya 65 pound (sekitar 30&nbsp;kg) ketika meninggal. Pada akta kematian tertulis bahwa ia meninggal akibat "kekurangan gizi dan kelaparan karena gangguan kepribadian" pada [[:en:Princeton Hospital|Princeton Hospital]] tanggal 14 Januari 1978.<ref>{{cite book
| last = Toates
| first = Frederick
|author2=Olga Coschug Toates
| title = Obsessive Compulsive Disorder: Practical Tried-and-Tested Strategies to Overcome OCD
|url = https://archive.org/details/obsessivecompuls00fred
| publisher=Class Publishing
| year = 2002
| pageyear = 2212002
|page = [https://archive.org/details/obsessivecompuls00fred/page/n235 221]
| isbn = 978-1-85959-069-0}}</ref> Adele meninggal tiga tahun kemudian pada tahun 1981.
 
== Pandangan agama ==
Gödel adalah seorang penganut teguh aliran [[teisme]].<ref>{{cite book|title=A to Z of Mathematicians|year=2005|publisher=Infobase Publishing|isbn=9780816053384|author=Tucker McElroy|page=118|quote=Gödel had a happy childhood, and was called "Mr. Why" by his family, due to his numerous questions. He was baptized as a Lutheran, and re-mained a theist (a believer in a personal God) throughout his life.}}</ref> Ia memegang keyakinan bahwa Allah adalah sosok pribadi, yang berbeda dengan pandangan sahabatnya, [[Albert Einstein]].
<!--
He believed firmly in an afterlife, stating: "Of course this supposes that there are many relationships which today's science and received wisdom haven't any inkling of. But I am convinced of this [the afterlife], independently of any theology." It is "possible today to perceive, by pure reasoning" that it "is entirely consistent with known facts." "If the world is rationally constructed and has meaning, then there must be such a thing [as an afterlife]."<ref>Hao Wang, "A Logical Journey: From Gödel to Philosophy", 1996, pp. 104–105.</ref>
 
In an unmailed answer to a questionnaire, Gödel described his religion as "baptized Lutheran (but not member of any religious congregation). My belief is ''[[Theism|theistic]]'', not [[Pantheism|pantheistic]], following [[Gottfried Wilhelm Leibniz|Leibniz]] rather than [[Spinoza]]."<ref>Gödel's answer to a special questionnaire sent him by the sociologist Burke Grandjean. This answer is quoted directly in Wang 1987, p.&nbsp;18, and indirectly in Wang 1996, p.&nbsp;112. It's also quoted directly in Dawson 1997, p.&nbsp;6,who cites Wang 1987. The Grandjean questionnaire is perhaps the most extended autobiographical item in Gödel's papers. Gödel filled it out in pencil and wrote a cover letter, but he never returned it. "Theistic" is italicized in both Wang 1987 and Wang 1996. It is possible that this italicization is Wang's and not Gödel's. The quote follows Wang 1987, with two corrections taken from Wang 1996. Wang 1987 reads "Baptist Lutheran" where Wang 1996 has "baptized Lutheran". Wang 1987 has "rel. cong.", which in Wang 1996 is expanded to "religious congregation".</ref> Describing religion(s) in general, Gödel said: "Religions are, for the most part, bad—but religion is not".<ref>Wang 1996 p. 316</ref> About Islam he said: "I like Islam, it is a consistent [or consequential] idea of religion and open-minded."<ref> Wang 1996, p. 148 , 4.4.3. It is one of Gödel's observations, made between
November 16 and December 7, 1975, which Wang found hard to classify under the main topics considered elsewhere in the book. </ref>
-->
Baris 153 ⟶ 154:
[[Douglas Hofstadter]] wrote a popular book in 1979 called ''[[Gödel, Escher, Bach]]'' to celebrate the work and ideas of Gödel, along with those of artist [[M. C. Escher]] and composer [[Johann Sebastian Bach]]. The book partly explores the ramifications of the fact that Gödel's incompleteness theorem can be applied to any [[Turing-complete]] computational system, which may include the [[human brain]].
-->
== 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 ''[[:en:Principia Mathematica|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 [[:en:Paul Benacerraf|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 [[:en:R. B. Braithwaite|Richard Braithwaite]]. Dover reprint of the 1962 [[Basic Books]] edition.
* Kurt Godel, 2000.<ref>{{cite journal|doi=10.1007/BF01700692|author=Kurt Godel |year=1931|url=http://www.research.ibm.com/people/h/hirzel/papers/canon00-goedel.pdf|title=Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme, I|trans_title=On formally undecidable propositions of Principia Mathematica and related systems I|journal=Monatshefte für Mathematik und Physik|volume= 38|pages= 173–198|access-date=2014-12-26|archive-date=2004-09-16|archive-url=https://web.archive.org/web/20040916041216/http://www.research.ibm.com/people/h/hirzel/papers/canon00-goedel.pdf|dead-url=yes}}</ref> ''On Formally Undecidable Propositions Of Principia Mathematica And Related Systems'', tr. Martin Hirzel
* [[:En:Jean van Heijenoort|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.
* [http://www.geocities.ws/kandathil/godel_phil_view.html "My philosophical viewpoint"] {{Webarchive|url=https://web.archive.org/web/20140407062159/http://www.geocities.ws/kandathil/godel_phil_view.html |date=2014-04-07 }}, c. 1960, tidak dipublikasikan.
* [http://www.geocities.ws/kandathil/godel_fom.html "The modern development of the foundations of mathematics in the light of philosophy"] {{Webarchive|url=https://web.archive.org/web/20140422105228/http://www.geocities.ws/kandathil/godel_fom.html |date=2014-04-22 }}, 1961, tidak dipublikasikan.
* ''Collected Works'': Oxford University Press: New York. Editor-in-chief: [[:en:Solomon Feferman|Solomon Feferman]].▼
 
** Volume I: Publications 1929–1936 ISBN 978-0-19-503964-1 / Paperback:ISBN 978-0-19-514720-9,
▲*''Collected Works'': Oxford University Press: New York. Editor-in-chief: [[:en:Solomon Feferman|Solomon Feferman]].
** Volume III: Publications 1929–19361938–1974 ISBN 978-0-19-503964503972-16 / Paperback:ISBN 978-0-19-514720514721-96,
** Volume IIIII: PublicationsUnpublished 1938–1974Essays and Lectures ISBN 978-0-19-503972507255-6 / Paperback:ISBN 978-0-19-514721514722-63,
** Volume IIIIV: UnpublishedCorrespondence, EssaysA–G and Lectures ISBN 978-0-19-507255-6 / Paperback:ISBN 978-0-19-514722850073-35,
** Volume IVV: Correspondence, A–GH–Z ISBN 978-0-19-850073850075-5,9.
**Volume V: Correspondence, H–Z ISBN 978-0-19-850075-9.
 
== Lihat pula ==
{{Portal|Biography|Logic}}
* [[Gödel machine]]
* [[Gödel Prize]]
* [[Gödel's speed-up theorem]]
* [[Teorema ketaklengkapan Gödel]]
* [[Original proof of Gödel's completeness theorem]]
* [[Slingshot argument]]
 
== Referensi ==
 
{{Reflist|30em}}
 
== Pustaka ==
 
* Dawson, John W., 1997. ''Logical dilemmas: The life and work of Kurt Gödel''. Wellesley MA: A K Peters.
* [http://en.wikisource.org/w/index.php?title=1911_Encyclop%C3%A6dia_Britannica/Br%C3%BCnn&oldid=447734 1911 Encyclopædia Britannica/Brünn]. (September 19, 2007). In Wikisource, The Free Library. Retrieved 10&nbsp;pm EST March 13, 2008.
Baris 200 ⟶ 202:
 
== 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.
* [[:en:John W. Dawson, Jr|John W. Dawson, Jr]]. ''Logical Dilemmas: The Life and Work of Kurt Gödel''. AK Peters, Ltd., 1996.
Baris 206 ⟶ 209:
* [[:en:Ivor Grattan-Guinness|Ivor Grattan-Guinness]], 2000. ''The Search for Mathematical Roots 1870–1940''. Princeton Univ. Press.
* [[:en:Jaakko Hintikka|Jaakko Hintikka]], 2000. ''On Gödel''. Wadsworth.
* [[:en:Douglas Hofstadter|Douglas Hofstadter]], 1980. ''[[:en:Gödel, Escher, Bach|Gödel, Escher, Bach]]''. Vintage.
* [[:en:Stephen Kleene|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)
Baris 216 ⟶ 219:
* [[:en:Raymond Smullyan|Raymond Smullyan]], 1992. ''Godel's Incompleteness Theorems''. Oxford University Press.
* [[:en:Olga Taussky-Todd|Olga Taussky-Todd]], 1983. [http://calteches.library.caltech.edu/605/02/Todd.pdf Remembrances of Kurt Gödel]. Engineering & Science, Winter 1988.
* [[:en:Hao Wang (academic)|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.&nbsp;861–868): <!-- Comment<ref>http://www.ams.org/notices/200707/tx070700861p.pdf</ref>-->
 
== Pranala luar ==
{{Commons category|Kurt Gödel}}
{{Wikiquote}}
* {{MathGenealogy|id=19539}}
* {{ScienceWorldBiography | urlname=Goedel | title=Gödel, Kurt (1906–1978)}}
* Kennedy, Juliette. [http://plato.stanford.edu/entries/goedel "Kurt Gödel."] In Stanford Encyclopedia of Philosophy.
* [http://www.newyorker.com/archive/2005/02/28/050228crat_atlarge Time Bandits]: an article about the relationship between Gödel and Einstein by Jim Holt
* [http://plus.maths.org/issue39/features/dawson/ "Gödel and the limits of logic"] by John W Dawson Jr. (June 2006)
* [http://www.ams.org/notices/200604/200604-toc.html Notices of the AMS, April 2006, Volume 53, Number 4] Kurt Gödel Centenary Issue
* [http://www.abc.net.au/rn/scienceshow/stories/2006/1807626.htm Paul Davies and Freeman Dyson discuss Kurt Godel]
* [http://www.edge.org/3rd_culture/goldstein05/goldstein05_index.html "Gödel and the Nature of Mathematical Truth"] Edge: A Talk with Rebecca Goldstein on Kurt Gödel.
* [http://simplycharly.com/godel/gregory_chaitin_interview.htm It's Not All In The Numbers: Gregory Chaitin Explains Gödel's Mathematical Complexities.] {{Webarchive|url=https://web.archive.org/web/20091106003330/http://simplycharly.com/godel/gregory_chaitin_interview.htm |date=2009-11-06 }}
* [http://www.univie.ac.at/bvi/photo-gallery/photo_gallery.htm Gödel photo g.] {{Webarchive|url=https://web.archive.org/web/20090301015757/http://www.univie.ac.at/bvi/photo-gallery/photo_gallery.htm |date=2009-03-01 }}
* {{Find a Grave|25996503}}
* [http://www.nasonline.org/publications/biographical-memoirs/memoir-pdfs/gdel-kurt.pdf National Academy of Sciences Biographical Memoir]
* {{MacTutor Biography|id=Godel}}
{{Notable logicians}}
{{Teori himpunan}}
{{Winners of the National Medal of Science|math-stat-comp}}
 
{{Authority control|VIAF=97851774|LCCN=n/79/7770}}
 
{{Persondata
|NAME=Gödel, Kurt
|ALTERNATIVE NAMES=
|SHORT DESCRIPTION=[[logician]], [[mathematician]], and [[philosophy of mathematics|philosopher of mathematics]]
|DATE OF BIRTH=1906-04-28
|PLACE OF BIRTH=[[Brno]]
|DATE OF DEATH=1978-01-14
|PLACE OF DEATH=[[Princeton, New Jersey|Princeton]], New Jersey
}}
{{DEFAULTSORT:Godel, Kurt}}
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