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'''Kurt Friedrich Gödel''' ({{IPAc-en|ˈ|ɡ|ɜːr|d|əl}};<ref>{{cite Merriam-Webster|Gödel}}</ref> {{IPA-de|ˈkʊɐ̯t ˈɡøːdl̩|lang|Kurt gödel.ogg}}; April 28, 1906&nbsp;– January 14, 1978) was a [[logician]], [[mathematician]], and [[analytic philosopher]]. Considered along with [[Aristotle]] and [[Gottlob Frege]] to be one of the most significant logicians in history, Gödel had an immense effect upon scientific and philosophical thinking in the 20th century, a time when others such as [[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> [[Alfred North Whitehead]],<ref name="Stanford&Son"/> and [[David Hilbert]] were analyzing the use of logic and [[set theory]] to understand the [[foundations of mathematics]] pioneered by [[Georg Cantor]].

'''Kurt Friedrich Gödel''' ({{IPAc-en|ˈ|ɡ|ɜːr|d|əl}};<ref>{{cite Merriam-Webster|Gödel}}</ref> {{IPA-de|ˈkʊɐ̯t ˈɡøːdl̩|lang|Kurt gödel.ogg}}; April 28, 1906&nbsp;– January 14, 1978) was a [[logician]], [[mathematician]], and [[analytic philosopher]]. Considered along with [[Aristotle]] and [[Gottlob Frege]] to be one of the most significant logicians in history, Gödel had an immense effect upon scientific and philosophical thinking in the 20th century, a time when others such as [[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> [[Alfred North Whitehead]],<ref name="Stanford&Son"/> and [[David Hilbert]] were analyzing the use of logic and [[set theory]] to understand the [[foundations of mathematics]] pioneered by [[Georg Cantor]].

Kurt Friedrich Gödel (; ; April 28, 1906&nbsp;– January 14, 1978) was a logician, mathematician, and analytic philosopher. Considered along with Aristotle and Gottlob Frege to be one of the most significant logicians in history, Gödel had an immense effect upon scientific and philosophical thinking in the 20th century, a time when others such as Bertrand Russell, Alfred North Whitehead, Throughout his life, Gödel would remain close to his mother; their correspondence was frequent and wide-ranging. At the time of his birth the city had a German-speaking majority which included his parents. His father was Catholic and his mother was Protestant and the children were raised Protestant. The ancestors of Kurt Gödel were often active in Brünn's cultural life. For example, his grandfather Joseph Gödel was a famous singer of that time and for some years a member of the  (Men's Choral Union of Brünn).

'''库尔特·弗里德里希·哥德尔'''（1906年4月28日至1978年1月14日）是一位逻辑学家、数学家和分析哲学家。与亚里士多德和哥特洛布·弗雷格一起被认为是历史上最重要的逻辑学家之一。<font color="#32CD32">哥德尔在20世纪对这个时代的其他人，如伯特兰·罗素 Bertrand Russell、阿尔弗雷德·诺斯·怀特黑德 Alfred North Whitehead的科学和哲学思想产生了巨大的影响。 </font>哥德尔一生中都与母亲保持着亲密的关系；他们的通信往来频繁而广泛。在他出生时，这个城市大多数人讲德语，其中包括他的父母。他的父亲是天主教徒，母亲是新教徒，孩子们都是新教徒。库尔特哥德尔的祖先经常活跃在布吕恩的文化生活中。例如，他的祖父约瑟夫哥德尔是当时著名的歌唱家，多年来一直是（布吕恩男子合唱团联盟）的成员。

Gödel automatically became a [[Czechoslovakia|Czechoslovak]] citizen at age 12 when the Austro-Hungarian Empire collapsed, following its defeat in the [[World War I]]. (According to his classmate {{lang|cs|Klepetař|italic=no}}, like many residents of the predominantly German {{lang|de|[[Sudetenland|Sudetenländer]]}}, "Gödel considered himself always Austrian and an exile in Czechoslovakia".)<ref>Dawson 1997, p.&nbsp;15.</ref> In February 1929 he was granted release from his Czechoslovakian citizenship and then, in April, granted Austrian citizenship.<ref>{{Cite book|url=https://books.google.com/books?id=5ya4A0w62skC&pg=PA37|title=Collected works|last=Gödel, Kurt|publisher=|others=Feferman, Solomon|year=1986|isbn=0195039645|location=Oxford|pages=37|oclc=12371326}}</ref> When [[Nazi Germany|Germany]] [[Anschluss|annexed Austria]] in 1938, Gödel automatically became a German citizen at age 32. After [[World War II]] (1948), at the age of 42, he became an American citizen.<ref>{{cite web |last1=Balaguer |first1=Mark |title=Kurt Godel |url=https://school.eb.com/levels/high/article/Kurt-G%C3%B6del/37162 |website=Britannica School High |publisher=Encyclopædia Britannica, Inc. |accessdate=3 June 2019}}</ref>

Gödel automatically became a [[Czechoslovakia|Czechoslovak]] citizen at age 12 when the Austro-Hungarian Empire collapsed, following its defeat in the [[World War I]]. (According to his classmate {{lang|cs|Klepetař|italic=no}}, like many residents of the predominantly German {{lang|de|[[Sudetenland|Sudetenländer]]}}, "Gödel considered himself always Austrian and an exile in Czechoslovakia".)<ref>Dawson 1997, p.&nbsp;15.</ref> In February 1929 he was granted release from his Czechoslovakian citizenship and then, in April, granted Austrian citizenship.<ref>{{Cite book|url=https://books.google.com/books?id=5ya4A0w62skC&pg=PA37|title=Collected works|last=Gödel, Kurt|publisher=|others=Feferman, Solomon|year=1986|isbn=0195039645|location=Oxford|pages=37|oclc=12371326}}</ref> When [[Nazi Germany|Germany]] [[Anschluss|annexed Austria]] in 1938, Gödel automatically became a German citizen at age 32. After [[World War II]] (1948), at the age of 42, he became an American citizen.<ref>{{cite web |last1=Balaguer |first1=Mark |title=Kurt Godel |url=https://school.eb.com/levels/high/article/Kurt-G%C3%B6del/37162 |website=Britannica School High |publisher=Encyclopædia Britannica, Inc. |accessdate=3 June 2019}}</ref>

奥匈帝国在一战中战败，12岁时，哥德尔自动成为了[捷克斯洛伐克|捷克斯洛伐克]]公民。（根据他的同学{lang| cs | klepata|italic=no}的说法，和德国人占主导地位的{lang de |[[捷克苏台德区]]}}的许多居民一样，“哥德尔一直认为自己是奥地利人，是捷克斯洛伐克的流亡者。”<ref>Dawson 1997, p.&nbsp;15.</ref>1929年2月，他被授予捷克斯洛伐克国籍，4月获得奥地利国籍。<ref>{{Cite book|url=https://books.google.com/books?id=5ya4A0w62skC&pg=PA37|title=Collected works|last=Gödel, Kurt|publisher=|others=Feferman, Solomon|year=1986|isbn=0195039645|location=Oxford|pages=37|oclc=12371326}}</ref> 1938年[[纳粹德国]][[Anschluss |吞并奥地利]时，哥德尔在32岁时自动成为德国公民。[第二次世界大战]（1948年）之后，42岁的他成为美国公民。<ref>{{cite web |last1=Balaguer |first1=Mark |title=Kurt Godel |url=https://school.eb.com/levels/high/article/Kurt-G%C3%B6del/37162 |website=Britannica School High |publisher=Encyclopædia Britannica, Inc. |accessdate=3 June 2019}}</ref>

奥匈帝国在一战中战败，12岁时，哥德尔自动成为了[捷克斯洛伐克|捷克斯洛伐克]]公民。（根据他的同学{lang| cs | klepata|italic=no}的说法，和德国人占主导地位的{lang de |[[捷克苏台德区]]}}的许多居民一样，“哥德尔一直认为自己是奥地利人，是捷克斯洛伐克的流亡者。”<ref>Dawson 1997, p.&nbsp;15.</ref>1929年2月，他被授予捷克斯洛伐克国籍，4月获得奥地利国籍。<ref>{{Cite book|url=https://books.google.com/books?id=5ya4A0w62skC&pg=PA37|title=Collected works|last=Gödel, Kurt|publisher=|others=Feferman, Solomon|year=1986|isbn=0195039645|location=Oxford|pages=37|oclc=12371326}}</ref> 1938年[[纳粹德国]][[Anschluss |吞并奥地利]时，哥德尔在32岁时自动成为德国公民。[第二次世界大战]（1948年）之后，42岁的他成为美国公民。<ref>{{cite web |last1=Balaguer |first1=Mark |title=Kurt Godel |url=https://school.eb.com/levels/high/article/Kurt-G%C3%B6del/37162 |website=Britannica School High |publisher=Encyclopædia Britannica, Inc. |accessdate=3 June 2019}}</ref>]][[Index.php?title=库尔特·哥德尔 Kurt Gödel#cite%20note-17|<span class="mw-reflink-text">[17]</span>]]

Attending a lecture by David Hilbert in Bologna on completeness and consistency of mathematical systems may have set Gödel's life course. In 1928, Hilbert and Wilhelm Ackermann published  (Principles of Mathematical Logic), an introduction to first-order logic in which the problem of completeness was posed: Are the axioms of a formal system sufficient to derive every statement that is true in all models of the system?

Attending a lecture by David Hilbert in Bologna on completeness and consistency of mathematical systems may have set Gödel's life course. In 1928, Hilbert and Wilhelm Ackermann published  (Principles of Mathematical Logic), an introduction to first-order logic in which the problem of completeness was posed: Are the axioms of a formal system sufficient to derive every statement that is true in all models of the system?

In his family, young Kurt was known as {{lang|de|Herr Warum}} ("Mr. Why") because of his insatiable curiosity. According to his brother Rudolf, at the age of six or seven Kurt suffered from [[rheumatic fever]]; he completely recovered, but for the rest of his life he remained convinced that his heart had suffered permanent damage. Beginning at age four, Gödel suffered from "frequent episodes of poor health", which would continue for his entire life.<ref>{{Cite book |url=http://plato.stanford.edu/archives/win2015/entries/johann-herbart/ |title=Johann Friedrich Herbart |last=Kim |first=Alan |date=2015-01-01 |editor-last=Zalta |editor-first=Edward N. |edition=Winter 2015 }}</ref>

In his family, young Kurt was known as {{lang|de|Herr Warum}} ("Mr. Why") because of his insatiable curiosity. According to his brother Rudolf, at the age of six or seven Kurt suffered from rheumatic fever; he completely recovered, but for the rest of his life he remained convinced that his heart had suffered permanent damage. Beginning at age four, Gödel suffered from "frequent episodes of poor health", which would continue for his entire life.<ref>{{Cite book |url=http://plato.stanford.edu/archives/win2015/entries/johann-herbart/ |title=Johann Friedrich Herbart |last=Kim |first=Alan |date=2015-01-01 |editor-last=Zalta |editor-first=Edward N. |edition=Winter 2015 }}</ref>

在他的家族中，年轻的库尔特因其永不满足的好奇心而被称为{lang | de | Herr Warum}}（“为什么先生”）。据他的兄弟鲁道夫说，库尔特在六七岁的时候患了[风湿热]；他完全康复了，但在他的余生中，他仍然坚信他的心脏受到了永久性的损害。从四岁开始，哥德尔就饱受“频繁发作的健康不佳”之苦，这种情况持续了一生。<ref>{{Cite book |url=http://plato.stanford.edu/archives/win2015/entries/johann-herbart/ |title=Johann Friedrich Herbart |last=Kim |first=Alan |date=2015-01-01 |editor-last=Zalta |editor-first=Edward N. |edition=Winter 2015 }}</ref>

<nowiki>在他的家族中，年轻的库尔特因其永不满足的好奇心而被称为{lang | de | Herr Warum}}（“为什么先生”）。据他的兄弟鲁道夫说，库尔特在六七岁的时候患了[风湿热]；他完全康复了，但在他的余生中，他仍然坚信他的心脏受到了永久性的损害。从四岁开始，哥德尔就饱受“频繁发作的健康不佳”之苦，这种情况持续了一生。</nowiki><ref>{{Cite book |url=http://plato.stanford.edu/archives/win2015/entries/johann-herbart/ |title=Johann Friedrich Herbart |last=Kim |first=Alan |date=2015-01-01 |editor-last=Zalta |editor-first=Edward N. |edition=Winter 2015 }}</ref>

This problem became the topic that Gödel chose for his doctoral work. In 1929, at the age of 23, he completed his doctoral dissertation under Hans Hahn's supervision. In it, he established his eponymous completeness theorem regarding the first-order predicate calculus. He was awarded his doctorate in 1930, and his thesis (accompanied by some additional work) was published by the Vienna Academy of Science.

This problem became the topic that Gödel chose for his doctoral work. In 1929, at the age of 23, he completed his doctoral dissertation under Hans Hahn's supervision. In it, he established his eponymous completeness theorem regarding the first-order predicate calculus. He was awarded his doctorate in 1930, and his thesis (accompanied by some additional work) was published by the Vienna Academy of Science.

Gödel attended the {{lang|de|Evangelische Volksschule}}, a Lutheran school in Brünn from 1912 to 1916, and was enrolled in the {{lang|de|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]].

Gödel attended the {{lang|de|Evangelische Volksschule}}, a Lutheran school in Brünn from 1912 to 1916, and was enrolled in the {{lang|de|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, Goethe's ''Theory of Colours'' and criticisms of Isaac Newton, and the writings of Immanuel Kant.

哥德尔于1912年至1916年就读于布伦的路德教会学校{{lang|de|Evangelische Volksschule}}，1916年至1924年在 {{lang|de|Deutsches Staats-Realgymnasium}}就读，在所有科目中都表现出色，尤其是在数学、语言和宗教方面。尽管库尔特最初擅长语言，但后来他对历史和数学更感兴趣。1920年，他的哥哥鲁道夫（生于1902年）前往[维也纳]]就读于[[维也纳大学]]医学院时，更增加了他对数学的兴趣。在他十几岁的时候，库尔特学习了[[Gabelberger速记]]，[[Johann Wolfgang von Goethe | Goethe]]的“[[色彩理论（书）| Theory of Colours]]”和对[[艾萨克牛顿]]的批评，以及[[康德Immanuel Kant]]的著作。

哥德尔于1912年至1916年就读于布伦的路德教会学校{{lang|de|Evangelische Volksschule}}，1916年至1924年在 {{lang|de|Deutsches Staats-Realgymnasium}}就读，在所有科目中都表现出色，尤其是在数学、语言和宗教方面。尽管库尔特最初擅长语言，但后来他对历史和数学更感兴趣。1920年，他的哥哥鲁道夫（生于1902年）前往[维也纳就读于[[维也纳大学]]医学院时，更增加了他对数学的兴趣。在他十几岁的时候，库尔特学习了[[Gabelberger速记]]，[[Johann Wolfgang von Goethe | Goethe]]的“[[色彩理论（书）| Theory of Colours]]”和对[[艾萨克牛顿]]的批评，以及[[康德Immanuel Kant]]的著作。

===Studying in Vienna在维也纳的学习===

===Studying in Vienna在维也纳的学习===

Gödel earned his [[habilitation]] at Vienna in 1932, and in 1933 he became a {{lang|de|[[Privatdozent]]}} (unpaid lecturer) there. In 1933 [[Adolf Hitler]] came to power in Germany, and over the following years the Nazis rose in influence in Austria, and among Vienna's mathematicians. In June 1936, [[Moritz Schlick]], whose seminar had aroused Gödel's interest in logic, was assassinated by one of his former students, [[Johann Nelböck]].  This triggered "a severe nervous crisis" in Gödel.<ref name=Casti2001>{{Cite book |last1=Casti |first1=John L. |last2=Depauli |first2=Werner |year=2001 |title=Gödel&thinsp;: a life of logic |doi=10.1287/moor.1050.0169 |isbn=978-0-7382-0518-2 |location=Cambridge, Mass. |publisher=Basic Books |journal=Mathematics of Operations Research |volume=31 |page=147 |last3=Koppe |first3=Matthias |last4=Weismantel |first4=Robert |arxiv=math/0410111 |s2cid=9054486 }}. From p.&nbsp;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.<ref>Dawson 1997, pp. 110–12</ref>

Gödel earned his [[habilitation]] at Vienna in 1932, and in 1933 he became a {{lang|de|[[Privatdozent]]}} (unpaid lecturer) there. In 1933 [[Adolf Hitler]] came to power in Germany, and over the following years the Nazis rose in influence in Austria, and among Vienna's mathematicians. In June 1936, [[Moritz Schlick]], whose seminar had aroused Gödel's interest in logic, was assassinated by one of his former students, [[Johann Nelböck]].  This triggered "a severe nervous crisis" in Gödel.<ref name=Casti2001>{{Cite book |last1=Casti |first1=John L. |last2=Depauli |first2=Werner |year=2001 |title=Gödel&thinsp;: a life of logic |doi=10.1287/moor.1050.0169 |isbn=978-0-7382-0518-2 |location=Cambridge, Mass. |publisher=Basic Books |journal=Mathematics of Operations Research |volume=31 |page=147 |last3=Koppe |first3=Matthias |last4=Weismantel |first4=Robert |arxiv=math/0410111 |s2cid=9054486 }}. From p.&nbsp;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.<ref>Dawson 1997, pp. 110–12</ref>

1932年，哥德尔在维也纳为人熟知（获得了[[习惯化]]），1933年他成为了{lang | de |[[Privatdozent]]}}（无薪讲师）。1933年[[阿道夫希特勒]在德国掌权，在接下来的几年里，纳粹在奥地利和维也纳数学家中的影响力不断上升。1936年6月，[[Moritz Schlick]]的研讨会引起了哥德尔对逻辑学的兴趣，他被他的一个前学生[[Johann Nelböck]]暗杀。这在哥德尔引发了“严重的神经危机”。<ref name=Casti2001>{{Cite book |last1=Casti |first1=John L. |last2=Depauli |first2=Werner |year=2001 |title=Gödel&thinsp;: a life of logic |doi=10.1287/moor.1050.0169 |isbn=978-0-7382-0518-2 |location=Cambridge, Mass. |publisher=Basic Books |journal=Mathematics of Operations Research |volume=31 |page=147 |last3=Koppe |first3=Matthias |last4=Weismantel |first4=Robert |arxiv=math/0410111 |s2cid=9054486 }}摘自第80页，其中引用了库尔特的哥哥、医生鲁道夫·哥德尔的话。这句话引述了索尔夫的话：“这是一次严重的刺杀，这是鲁德的一次严重的刺杀。”。鲁道夫在那几年很了解库尔特。</ref>他出现了偏执症状，包括害怕中毒，并在一所治疗神经疾病的疗养院呆了几个月。<ref>Dawson 1997, pp. 110–12</ref>

1932年，哥德尔在维也纳为人熟知（获得了[[习惯化]]），1933年他成为了{lang | de |[[Privatdozent]]}}（无薪讲师）。1933年[[阿道夫希特勒]在德国掌权，在接下来的几年里，纳粹在奥地利和维也纳数学家中的影响力不断上升。1936年6月，[[Moritz Schlick]]的研讨会引起了哥德尔对逻辑学的兴趣，他被他的一个前学生[[Johann Nelböck]]暗杀。这在哥德尔引发了“严重的神经危机”。<ref name="Casti2001">{{Cite book |last1=Casti |first1=John L. |last2=Depauli |first2=Werner |year=2001 |title=Gödel&thinsp;: a life of logic |doi=10.1287/moor.1050.0169 |isbn=978-0-7382-0518-2 |location=Cambridge, Mass. |publisher=Basic Books |journal=Mathematics of Operations Research |volume=31 |page=147 |last3=Koppe |first3=Matthias |last4=Weismantel |first4=Robert |arxiv=math/0410111 |s2cid=9054486 }}摘自第80页，其中引用了库尔特的哥哥、医生鲁道夫·哥德尔的话。这句话引述了索尔夫的话：“这是一次严重的刺杀，这是鲁德的一次严重的刺杀。”。鲁道夫在那几年很了解库尔特。</ref>他出现了偏执症状，包括害怕中毒，并在一所治疗神经疾病的疗养院呆了几个月。<ref>Dawson 1997, pp. 110–12</ref>

Subsequently, he left for another visit to the United States, spending the autumn of 1938 at the IAS and publishing Consistency of the axiom of choice and of the generalized continuum-hypothesis with the axioms of set theory, 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 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.

Subsequently, he left for another visit to the United States, spending the autumn of 1938 at the IAS and publishing Consistency of the axiom of choice and of the generalized continuum-hypothesis with the axioms of set theory, 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 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.

Gödel spent the spring of 1939 at the [[University of Notre Dame]].<ref>{{cite web |url=https://math.nd.edu/assets/13975/logicatndweb.pdf |title=Kurt Gödel at Notre Dame |last=Dawson |first=John W. Jr |date= |page=4 |quote=the Mathematics department at the University of Notre Dame was host ... for a single semester in the spring of 1939 [to] Kurt Gödel }}</ref>

Gödel spent the spring of 1939 at the University of Notre Dame.<ref>{{cite web |url=https://math.nd.edu/assets/13975/logicatndweb.pdf |title=Kurt Gödel at Notre Dame |last=Dawson |first=John W. Jr |date= |page=4 |quote=the Mathematics department at the University of Notre Dame was host ... for a single semester in the spring of 1939 [to] Kurt Gödel }}</ref>]][[Index.php?title=库尔特·哥德尔 Kurt Gödel#cite%20note-31|<span class="mw-reflink-text">[31]</span>]]

1939年春，哥德尔在[[圣母大学]]度过。<ref>{{cite web |url=https://math.nd.edu/assets/13975/logicatndweb.pdf |title=Kurt Gödel at Notre Dame |last=Dawson |first=John W. Jr |date= |page=4 |quote=the Mathematics department at the University of Notre Dame was host ... for a single semester in the spring of 1939 [to] Kurt Gödel }}</ref>

1939年春，哥德尔在圣母大学度过。<ref>{{cite web |url=https://math.nd.edu/assets/13975/logicatndweb.pdf |title=Kurt Gödel at Notre Dame |last=Dawson |first=John W. Jr |date= |page=4 |quote=the Mathematics department at the University of Notre Dame was host ... for a single semester in the spring of 1939 [to] Kurt Gödel }}</ref>

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".

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".

1942年的夏天，哥德尔和他的妻子阿黛尔在缅因州的蓝山海湾顶端的蓝山旅馆度过。哥德尔不仅仅是在度假，而且还有一个非常富有成效的夏季工作。小约翰 · w · 道森(John w. Dawson jr.)利用哥德尔尚未出版的[工作笔记本][卷15]推测，哥德尔在1942年《布鲁希尔》(Blue Hill)一书中发现了选择公理独立于集合论弱化形式——有限型理论的证明。哥德尔的密友王支持这一猜想，指出哥德尔的蓝山笔记本包含了他对这一问题最广泛的论述。

1942年的夏天，哥德尔和他的妻子阿黛尔在缅因州的蓝山海湾顶端的蓝山旅馆度过。哥德尔不仅仅是在度假，而且还有一个非常富有成效的夏季工作。小约翰 · w · 道森(John w. Dawson jr.)利用哥德尔尚未出版的[工作笔记本][卷15]推测，哥德尔在1942年《布鲁希尔》(Blue Hill)一书中发现了选择公理独立于集合论弱化形式——有限型理论的证明。哥德尔的密友王支持这一猜想，指出哥德尔的蓝山笔记本包含了他对这一问题最广泛的论述。

After the [[Anschluss]] on 12 March 1938, Austria had become a part of [[Nazi Germany]].

After the Anschluss on 12 March 1938, Austria had become a part of Nazi Germany.

Germany abolished the title {{lang|de|[[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.

Germany abolished the title {{lang|de|[[Privatdozent]]}}<nowiki>, 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.

在1938年3月12日的[纳粹德国]之后，奥地利成为了[纳粹德国]的一部分。

在1938年3月12日的[纳粹德国]之后，奥地利成为了[纳粹德国]的一部分。

德国废除了{lang | de |[[Privatdozent]]}}的头衔，因此哥德尔不得不根据新秩序申请另一个职位。他以前与维也纳圈子里的犹太成员，特别是与哈恩的交往，对他不利。维也纳大学拒绝了他的申请。

德国废除了{lang | de |Privatdozent}}的头衔，因此哥德尔不得不根据新秩序申请另一个职位。他以前与维也纳圈子里的犹太成员，特别是与哈恩的交往，对他不利。维也纳大学拒绝了他的申请。

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 could allow the U.S. to become a dictatorship. Einstein and Morgenstern were concerned that their friend's unpredictable behavior might jeopardize his application. 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.

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 could allow the U.S. to become a dictatorship. Einstein and Morgenstern were concerned that their friend's unpredictable behavior might jeopardize his application. 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.

哥德尔于1946年成为普林斯顿高等研究院的常任成员。大约在这个时候，他停止了出版，尽管他继续工作。1953年，他成为该研究所的全职教授，1976年成为名誉教授的全职教授。

哥德尔于1946年成为普林斯顿高等研究院的常任成员。大约在这个时候，他停止了出版，尽管他继续工作。1953年，他成为该研究所的全职教授，1976年成为名誉教授的全职教授。

Before the year was up, Gödel and his wife left Vienna for [[Princeton, New Jersey|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 US by train to Princeton. There Gödel accepted a position at the Institute for Advanced Study (IAS), which he had previously visited during 1933–34.<ref>{{Cite web|url=https://www.ias.edu/scholars/godel|title=Kurt Gödel|website=Institute for Advanced Study}}</ref>

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 US by train to Princeton. There Gödel accepted a position at the Institute for Advanced Study (IAS), which he had previously visited during 1933–34.</nowiki><ref>{{Cite web|url=https://www.ias.edu/scholars/godel|title=Kurt Gödel|website=Institute for Advanced Study}}</ref>

在这一年结束之前，哥德尔和他的妻子离开维也纳去了[[普林斯顿，新泽西|普林斯顿]]。为了避免穿越大西洋的困难，哥德尔一家乘坐[[横贯西伯利亚铁路]]到达太平洋，从日本航行到旧金山（他们于1940年3月4日到达旧金山），然后乘火车横渡美国到达普林斯顿。哥德尔在那里接受了高等研究所（IAS）的一个职位，他曾在1933-34年间访问过该研究所。<ref>{{Cite web|url=https://www.ias.edu/scholars/godel|title=Kurt Gödel|website=Institute for Advanced Study}}</ref>

在这一年结束之前，哥德尔和他的妻子离开维也纳去了普林斯顿。为了避免穿越大西洋的困难，哥德尔一家乘坐横贯西伯利亚铁路到达太平洋，从日本航行到旧金山（他们于1940年3月4日到达旧金山），然后乘火车横渡美国到达普林斯顿。哥德尔在那里接受了高等研究所（IAS）的一个职位，他曾在1933-34年间访问过该研究所。<ref>{{Cite web|url=https://www.ias.edu/scholars/godel|title=Kurt Gödel|website=Institute for Advanced Study}}</ref>

During his many years at the Institute, Gödel's interests turned to philosophy and physics. In 1949, he demonstrated the existence of solutions involving closed timelike curves, to Einstein's field equations in general relativity. He is said to have given this elaboration to Einstein as a present for his 70th birthday. His "rotating universes" would allow time travel to the past and caused Einstein to have doubts about his own theory. His solutions are known as the Gödel metric (an exact solution of the Einstein field equation).

During his many years at the Institute, Gödel's interests turned to philosophy and physics. In 1949, he demonstrated the existence of solutions involving closed timelike curves, to Einstein's field equations in general relativity. He is said to have given this elaboration to Einstein as a present for his 70th birthday. His "rotating universes" would allow time travel to the past and caused Einstein to have doubts about his own theory. His solutions are known as the Gödel metric (an exact solution of the Einstein field equation).

哥德尔在研究所的多年时间里，他的兴趣转向了哲学和物理学。1949年，他证明了包含封闭时间型曲线的解的存在性，这些解是爱因斯坦在《广义相对论的场方程。据说他把这个精心设计作为爱因斯坦70岁生日的礼物送给了他。他的“旋转宇宙”将允许时间旅行回到过去，并使爱因斯坦对自己的理论产生怀疑。他的解被称为哥德尔度量(爱因斯坦场方程的精确解)。

哥德尔在研究所的多年时间里，他的兴趣转向了哲学和物理学。1949年，他证明了包含封闭时间型曲线的解的存在性，这些解是爱因斯坦在《广义相对论的场方程。据说他把这个精心设计作为爱因斯坦70岁生日的礼物送给了他。他的“旋转宇宙”将允许时间旅行回到过去，并使爱因斯坦对自己的理论产生怀疑。他的解被称为哥德尔度量(爱因斯坦场方程的精确解)。

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".<ref>Goldstein (2005), p.&nbsp;33.</ref>

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".<ref>Goldstein (2005), p.&nbsp;33.</ref>

阿尔伯特·爱因斯坦也住在普林斯顿大学。爱因斯坦因长期的友谊而闻名于世。他们谈话的性质对研究所的其他成员来说是个谜。经济学家[[Oskar Morgenstern]]叙述说，爱因斯坦在临终时透露，“他自己的工作已经没有多大意义，他来到研究所只是为了。。。有幸和哥德尔一起步行回家”。<ref>Goldstein (2005), p.&nbsp;33.</ref>

阿尔伯特·爱因斯坦也住在普林斯顿大学。爱因斯坦因长期的友谊而闻名于世。他们谈话的性质对研究所的其他成员来说是个谜。经济学家Oskar Morgenstern叙述说，爱因斯坦在临终时透露，“他自己的工作已经没有多大意义，他来到研究所只是为了。。。有幸和哥德尔一起步行回家”。<ref>Goldstein (2005), p.&nbsp;33.</ref>

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. 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 proof of God's existence. This is now known as Gödel's ontological proof.

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. 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 proof of God's existence. This is now known as Gödel's ontological proof.

他研究和欣赏莱布尼茨的作品，但是他开始相信是一个敌对的阴谋导致了莱布尼茨的一些作品被压制。在一定程度上，他研究了康德和胡塞尔。在20世纪70年代早期，哥德尔在他的朋友中间传阅了莱布尼茨版本的关于上帝存在的本体论证明的安瑟伦。这就是现在众所周知的哥德尔的本体论证明。

他研究和欣赏莱布尼茨的作品，但是他开始相信是一个敌对的阴谋导致了莱布尼茨的一些作品被压制。在一定程度上，他研究了康德和胡塞尔。在20世纪70年代早期，哥德尔在他的朋友中间传阅了莱布尼茨版本的关于上帝存在的本体论证明的安瑟伦。这就是现在众所周知的哥德尔的本体论证明。

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 {{lang|de|Heft 15}} [volume 15] of Gödel's still-unpublished {{lang|de|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 (academic)|Hao Wang]] supports this conjecture, noting that Gödel's Blue Hill notebooks contain his most extensive treatment of the problem.

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 {{lang|de|Heft 15}} [volume 15] of Gödel's still-unpublished {{lang|de|Arbeitshefte}}<nowiki> [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.

1942年夏天，哥德尔和他的妻子阿黛尔在海湾顶端的蓝山旅馆度过了一个夏天。哥德尔不仅仅是在度假，而且整个夏天的工作非常富有成效。利用哥德尔尚未出版的{lang| de | Heft 15}[第15卷]（{lang | de | Arbeitshefte}}[工作笔记本]，[约翰W道森小]]推测哥德尔在1942年的《蓝山》中发现了选择公理独立于有限类型理论的一个证明，这是集合论的一种弱化形式。哥德尔的密友[[王浩（学术）|王浩]支持这个猜想，他指出哥德尔的蓝山笔记本包含了他对这个问题最广泛的处理。

1942年夏天，哥德尔和他的妻子阿黛尔在海湾顶端的蓝山旅馆度过了一个夏天。哥德尔不仅仅是在度假，而且整个夏天的工作非常富有成效。利用哥德尔尚未出版的{lang| de | Heft 15}[第15卷]（{lang | de | Arbeitshefte}}[工作笔记本]，[约翰W道森小推测哥德尔在1942年的《蓝山》中发现了选择公理独立于有限类型理论的一个证明，这是集合论的一种弱化形式。哥德尔的密友[[王浩（学术）|王浩]支持这个猜想，他指出哥德尔的蓝山笔记本包含了他对这个问题最广泛的处理。</nowiki>

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 could allow the U.S. to become a dictatorship. Einstein and Morgenstern were concerned that their friend's unpredictable behavior might jeopardize his application. 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.<ref>Dawson 1997, pp. 179–80. 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=https://robert.accettura.com/wp-content/uploads/2010/10/Morgenstern_onGoedelcitizenship.pdf |title=History of the Naturalization of Kurt Gödel |date=September 13, 1971 |author=Oskar Morgenstern |accessdate=April 16, 2019 }}</ref>

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 could allow the U.S. to become a dictatorship. Einstein and Morgenstern were concerned that their friend's unpredictable behavior might jeopardize his application. 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.<ref>Dawson 1997, pp. 179–80. 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=https://robert.accettura.com/wp-content/uploads/2010/10/Morgenstern_onGoedelcitizenship.pdf |title=History of the Naturalization of Kurt Gödel |date=September 13, 1971 |author=Oskar Morgenstern |accessdate=April 16, 2019 }}</ref>

哥德尔是一个坚定的有神论者，在基督教传统中。他认为上帝是个人的。

哥德尔是一个坚定的有神论者，在基督教传统中。他认为上帝是个人的。

[[File:Kurt godel tomb 2004.jpg|right|thumb|200px|Gravestone of Kurt and Adele Gödel in the Princeton, N.J., cemetery]]

[[File:Kurt godel tomb 2004.jpg|right|thumb|200px|Gravestone of Kurt and Adele Gödel in the Princeton, N.J., cemetery|链接=Special:FilePath/Kurt_godel_tomb_2004.jpg]]