Kurt Gödel: Perbedaan antara revisi
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'''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]].
Gödel mempublikasikan [[teorema
He also showed that neither the [[axiom of choice]] nor the [[continuum hypothesis]] can be disproved from the accepted [[axiomatic set theory|axioms of set theory]], assuming these axioms are consistent. The former result opened the door for mathematicians to assume the axiom of choice in their proofs. He also made important contributions to [[proof theory]] by clarifying the connections between [[classical logic]], [[intuitionistic logic]], and [[modal logic]].
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Gödel secara otomatis menjadi warganegara Cekoslowakia pada usia 12 tahun, ketika Kekaisaran Austro-Hungaria pecah pada akhir [[Perang Dunia I]]. Menurut teman sekelasnya, Klepetař, sebagaimana penduduk wilayah yang tergolong ''German Sudetenländer'', "Gödel selalu menganggap dirinya orang Austria dan hidup dalam pembuangan di Cekoslowakia".<ref>Dawson 1997, p. 15.</ref> Ia memilih menjadi warganegara [[Austria]] pada usia 23 tahun. Ketika [[Jerman]] [[:en:Anschluss|mencaplok Austria]] pada tahun 1938, Gödel otomatis menjadi warganegara Jerman pada usia 32 tahun. Setelah [[Perang Dunia II]], pada usia 42 tahun, ia menjadi warganegara [[Amerika Serikat]].
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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]].
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=== 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]], tetapi ketika ia ikut suatu seminar yang diorganisir oleh [[Moritz Schlick]] yang mempelajari buku karya [[Bertrand Russell]] ''Introduction to Mathematical Philosophy'', ia menjadi tertarik pada [[logika matematika]]. Menurut Gödel, logika matematika adalah "suatu ilmu pengetahuan sebelum semua yang lain, yang memuat ide-ide dan prinsip-prinsip melandasi semua ilmu pengetahuan."<ref>Gleick, J. (2011) ''[[The Information: A History, a Theory, a Flood]],'' London, Fourth Estate, p181.</ref>
Ketika menghadiri kuliah yang diberikan oleh [[David Hilbert]] di [[Bologna]] mengenai kelengkapan dan konsistensi sistem matematika, jalan hidup Gödel menjadi terfokus. Pada tahun 1928, Hilbert dan [[Wilhelm Ackermann]] menerbitkan ''Grundzüge der theoretischen Logik'' (''[[:en:Principles of Mathematical Logic|Prinsip-prinsip logika matematika]]''), suatu pendahuluan kepada [[:en:first-order logic|logika tingkat pertama]] di mana soal kelengkapan diungkapkan: ''Apakah aksioma-aksioma sistem formal memadai untuk menurunkan setiap pernyataan yang benar dalam semua model sistem itu?''
=== Teorema Ketidaklengkapan ===
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# 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.-->
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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.
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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]]).
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=== 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 saraf 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>
Pada tahun 1933, Gödel pertama kali pergi ke [[Amerika Serikat]], di mana ia bertemu dengan [[Albert Einstein]], yang menjadi sahabat karibnya.<ref>[[Hutchinson Encyclopedia]] (1988), p.518</ref> <!--He delivered an address to the annual meeting of the [[American Mathematical Society]]. During this year, Gödel also developed the ideas of computability and [[Computable function|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.
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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.
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Hubungan mereka ditentang oleh orangtuanya karena Adele adalah seorang penari yang pernah bercerai dan 6 tahun lebih tua usianya dari Gödel.
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<!--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.
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[[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. 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 ===
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.
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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}}
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[[
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 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
|
|
|author2=Olga Coschug Toates
|url = https://archive.org/details/obsessivecompuls00fred
|publisher=Class Publishing
|
|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]].
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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. 18, and indirectly in Wang 1996, p. 112. It's also quoted directly in Dawson 1997, p. 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
November 16 and December 7, 1975, which Wang found hard to classify under the main topics considered elsewhere in the book. </ref>
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== Warisan ==
Sebuah yayasan bernama [[:en:Kurt Gödel Society|Kurt Gödel Society]] didirikan pada tahun 1987 untuk menghormatinya. Merupakan suatu organisasi internasional yang mempromosikan riset dalam bidang logika, filsafat dan sejarah [[matematika]]. [[:en:University of Vienna|University of Vienna]] membuka "Kurt Gödel Research Center for Mathematical Logic". [[:en:Association for Symbolic Logic|Association for Symbolic Logic]] telah mengundang pembicara khusus tahunan sebagai "Kurt Gödel lecturer" sejah tahun 1990.
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Five volumes of Gödel's collected works have been published. The first two include Gödel's publications; the third includes unpublished manuscripts from Gödel's ''Nachlass'', and the final two include correspondence.
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[[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]].
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== 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
* [[: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,
* [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,
* ''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,
** Volume
** Volume
** Volume
** Volume
== 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 pm EST March 13, 2008.
* [[:en:Rebecca Goldstein|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.
* [[:en:John W. Dawson, Jr|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
* [[:en:Torkel Franzén|Torkel Franzén]], 2005. ''Gödel's Theorem: An Incomplete Guide to Its Use and Abuse''. Wellesley, MA: A K Peters.
* [[: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)
* [[:en:J.R. Lucas|J.R. Lucas]], 1970. ''The Freedom of the Will''. Clarendon Press, Oxford.
* [[:en:Ernest Nagel|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.
* [[:en:Ed Regis (author)|Ed Regis]], 1987. ''Who Got Einstein's Office?'' Addison-Wesley Publishing Company, Inc.
* [[: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. 861–868):
== Pranala luar ==
{{Commons category|Kurt Gödel}}
{{Wikiquote}}
* {{MathGenealogy|id=19539}}
* {{ScienceWorldBiography |
* 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}}
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{{Winners of the National Medal of Science|math-stat-comp}}
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