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| | 在此期间，阿尔伯特·爱因斯坦 Albert Einstein也住在普林斯顿。哥德尔和爱因斯坦建立了深厚的友谊，众所周知，他们经常一起长途跋涉往返于高等研究院。他们谈话的性质对其他研究所成员来说是个谜。经济学家Oskar Morgenstern回忆说，在爱因斯坦生命的最后时刻，他坦言“自己的工作不再有意义，他来到研究所只是为了……有幸与哥德尔一起步行回家”。<ref>Goldstein (2005), p. 33.</ref> | | 在此期间，阿尔伯特·爱因斯坦 Albert Einstein也住在普林斯顿。哥德尔和爱因斯坦建立了深厚的友谊，众所周知，他们经常一起长途跋涉往返于高等研究院。他们谈话的性质对其他研究所成员来说是个谜。经济学家Oskar Morgenstern回忆说，在爱因斯坦生命的最后时刻，他坦言“自己的工作不再有意义，他来到研究所只是为了……有幸与哥德尔一起步行回家”。<ref>Goldstein (2005), p. 33.</ref> |
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| − | 1942年的夏天，哥德尔和他的妻子Adele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。John w. Dawson jr.利用哥德尔尚未出版的工作笔记本中的卷15推测哥德尔发现了选择公理独立于有限类型理论（集合论的弱化形式）的证明， 1942 年在蓝山时。哥德尔的密友Hao Wang支持这个猜想，并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。
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| | + | 1942年的夏天，哥德尔和他的妻子Adele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。John w. Dawson jr.利用哥德尔尚未出版的工作笔记本中的卷15推测哥德尔发现了选择公理独立于有限类型理论（集合论的弱化形式）的证明， 1942年在蓝山时。哥德尔的密友Hao Wang支持这个猜想，并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。 |
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| − | 1947年12月5日，爱因斯坦和摩根斯坦陪同哥德尔参加了他的美国公民身份考试，他们在考试中充当了见证人。哥德尔曾向他们透露，他发现美国宪法存在不一致之处，这可能使美国成为一个独裁国家。爱因斯坦和摩根斯坦担心他们的朋友不可预测的行为可能会危及他的申请。法官原来是菲利普 · 福曼，他认识爱因斯坦，并在爱因斯坦自己的公民听证会上主持了宣誓。一切都很顺利，直到 Forman 碰巧问哥德尔，他是否认为像纳粹政权一样的独裁会在美国发生，然后哥德尔开始向 Forman 解释他的发现。福尔曼明白发生了什么事，打断了哥德尔的话，把听证会转移到其他问题和例行结论上。
| + | 1947年12月5日，爱因斯坦和摩根斯坦陪同哥德尔参加了他的美国公民身份考试，他们在考试中充当了见证人。哥德尔曾向他们透露，他发现美国宪法存在不一致之处，这可能使美国成为一个独裁国家。爱因斯坦和摩根斯坦担心他们的朋友不可预测的行为可能会危及他的申请。法官是Phillip Forman，他认识爱因斯坦，并在爱因斯坦自己的公民听证会上主持了宣誓。一切都很顺利，直到 Forman 碰巧问哥德尔，他是否认为像纳粹政权一样的独裁会在美国发生，然后哥德尔开始向 Forman 解释他的发现。Forman明白发生了什么事，打断了哥德尔的话，把听证会转移到其他问题和例行结论上。<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 |access-date=April 16, 2019 }}</ref> |
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| | + | 1946年，哥德尔成为普林斯顿高等研究院的永久成员。大约在这个时候，他停止了出版，但他继续工作。他于1953年成为该研究所的正教授，并于 1976 年成为名誉教授。<ref>{{cite web |url=https://www.ias.edu/people/godel |title=Kurt Gödel – Institute for Advanced Study |access-date=December 1, 2015 }}</ref> |
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| − | His predicament intensified when the German army found him fit for conscription. World War II started in September 1939.
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| − | 当德军发现他适合应征入伍后，他的困境更加严重。第二次世界大战始于1939年9月。
| + | 在研究所任职期间，哥德尔的兴趣转向哲学和物理学。1949年，他展示了涉及解的存在性封闭类时曲线，对爱因斯坦场方程的广义相对论。<ref>{{cite journal |last=Gödel |first=Kurt |title=An Example of a New Type of Cosmological Solutions of Einstein's Field Equations of Gravitation |journal=[[Rev. Mod. Phys.]] |volume=21 |issue=447 |pages=447–450 |date=July 1, 1949 |doi=10.1103/RevModPhys.21.447 |bibcode=1949RvMP...21..447G |doi-access=free }}</ref>据说，他将这一阐述作为礼物送给爱因斯坦 70 岁生日。<ref>{{cite news |url=http://www.tagesspiegel.de/magazin/wissen/Albert-Einstein-Kurt-Goedel;art304,2454513 |title=Das Genie & der Wahnsinn |work=[[Der Tagesspiegel]] |date=January 13, 2008 |language=de }}</ref>他的“旋转宇宙”将允许时间旅行到过去，并导致爱因斯坦对他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）。 |
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| − | Gödel became a permanent member of the Institute for Advanced Study at Princeton in 1946. Around this time he stopped publishing, though he continued to work. He became a full professor at the Institute in 1953 and an emeritus professor in 1976.
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| − | 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。
| + | 他研究并钦佩戈特弗里德·莱布尼茨 Gottfried Leibniz的作品，但开始相信敌对的阴谋导致Leibniz的一些作品被压制。<ref>{{cite book |first=John W., Jr. |last=Dawson |url=https://books.google.com/books?id=gA8SucCU1AYC&q=godel+leibniz&pg=PA166 |title=Logical Dilemmas: The Life and Work of Kurt Gödel. |publisher=A K Peters |year=2005 |page=166 |isbn=9781568812564 }}</ref>他在较小程度上研究了Immanuel Kant和Edmund Husserl。在 1970 年代初期，哥德尔在他的朋友中传播了Leibniz版本的坎特伯雷安塞姆 Anselm of Canterbury关于上帝存在的本体论证明。这现在被称为“哥德尔本体论证明 Gödel's ontological proof”。 |
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| − | 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>
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| − | 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>
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| − | 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).
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| − | 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)。
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| − | 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. 33.</ref>
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| − | 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. 33.</ref>
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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. 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.
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| − | 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。
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| − | 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.
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| − | 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>
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| − | 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>
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| − | 1947年12月5日，爱因斯坦和摩根斯坦陪同哥德尔参加了他的[[美国国籍]]考试，在那里他们充当了证人。哥德尔向他们透露，他发现了[[美国宪法]中的一个不一致之处，这可能会使美国成为一个独裁政权。爱因斯坦和摩根斯坦担心他们朋友不可预测的行为可能会危及他的应用。法官原来是[[Phillip Forman]]，他认识爱因斯坦，并在爱因斯坦自己的公民听证会上主持了宣誓仪式。一切都很顺利，直到福尔曼碰巧问哥德尔，他是否认为美国会发生类似[纳粹政权]的独裁统治，然后戈德尔开始向福尔曼解释他的发现。福尔曼明白发生了什么，切断了哥德尔的话，把听证会转移到其他问题和常规结论上。<ref>道森1997，第179-80页。哥德尔公民听证会的故事在许多版本中重复出现。道森的叙述是最仔细研究过的，但在摩根斯坦的笔录被重新发现之前就写好了。大多数其他的说法似乎是基于道森，道听途说或猜测。<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>
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| − | Gödel was awarded (with Julian Schwinger) the first Albert Einstein Award in 1951, and was also awarded the National Medal of Science, in 1974. Gödel was elected a Foreign Member of the Royal Society (ForMemRS) in 1968. The Gödel Prize, an annual prize for outstanding papers in the area of theoretical computer science, is named after him.
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| − | 哥德尔于1951年被授予(与朱利安·施温格一起)第一个阿尔伯特·爱因斯坦奖勋章，并于1974年获得美国国家科学奖章勋章。1968年，哥德尔被选为英国皇家学会的外籍会员。哥德尔奖是一年一度的理论计算机科学领域杰出论文奖，以他的名字命名。
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| − | Gödel became a permanent member of the Institute for Advanced Study at Princeton in 1946. Around this time he stopped publishing, though he continued to work. He became a full professor at the Institute in 1953 and an emeritus professor in 1976.<ref>{{cite web |url=https://www.ias.edu/people/godel |title=Kurt Gödel – Institute for Advanced Study |accessdate=December 1, 2015 }}</ref>
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| − | 1946年，哥德尔成为普林斯顿高级研究所的常任理事国。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正式教授，1976年成为名誉教授。<ref>{{cite web |url=https://www.ias.edu/people/godel |title=Kurt Gödel – Institute for Advanced Study |accessdate=December 1, 2015 }}</ref>
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| − | Gravestone of Kurt and Adele Gödel in the Princeton, N.J., cemetery
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| − | 新泽西州普林斯顿公墓的库尔特和阿黛尔 · 哥德尔墓碑
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| − | 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 curve]]s, to [[Einstein's field equations]] in [[general relativity]].<ref>{{cite journal |last=Gödel |first=Kurt |title=An Example of a New Type of Cosmological Solutions of Einstein's Field Equations of Gravitation |journal=[[Rev. Mod. Phys.]] |volume=21 |issue=447 |pages=447–450 |date=July 1, 1949 |doi=10.1103/RevModPhys.21.447 |bibcode=1949RvMP...21..447G |doi-access=free }}</ref> He is said to have given this elaboration to Einstein as a present for his 70th birthday.<ref>{{cite news |url=http://www.tagesspiegel.de/magazin/wissen/Albert-Einstein-Kurt-Goedel;art304,2454513 |title=Das Genie & der Wahnsinn |work=[[Der Tagesspiegel]] |date=January 13, 2008 |language=de }}</ref> 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]]).
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| − | 在学院的多年里，哥德尔的兴趣转向了哲学和物理学。1949年，他证明了在[[广义相对论]]中，涉及[[封闭的类时间曲线]]的解的存在性。<ref>{{cite journal |last=Gödel |first=Kurt |title=An Example of a New Type of Cosmological Solutions of Einstein's Field Equations of Gravitation |journal=[[Rev. Mod. Phys.]] |volume=21 |issue=447 |pages=447–450 |date=July 1, 1949 |doi=10.1103/RevModPhys.21.447 |bibcode=1949RvMP...21..447G |doi-access=free }}</ref> 据说他把这一精髓送给爱因斯坦作为70岁生日礼物。<ref>{{cite news |url=http://www.tagesspiegel.de/magazin/wissen/Albert-Einstein-Kurt-Goedel;art304,2454513 |title=Das Genie & der Wahnsinn |work=[[Der Tagesspiegel]] |date=January 13, 2008 |language=de }}</ref> 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[[Gödel metric]]（爱因斯坦场方程的精确解）。
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| − | Later in his life, Gödel suffered periods of mental instability and illness. Following the assassination of his close friend Moritz Schlick, Gödel had an obsessive fear of being poisoned; he would eat only food that his wife, Adele, prepared for him. Late in 1977, she was hospitalized for six months and could subsequently no longer prepare her husband's food. In her absence, he refused to eat, eventually starving to death. He weighed when he died. His death certificate reported that he died of "malnutrition and inanition caused by personality disturbance" in Princeton Hospital on January 14, 1978. He was buried in Princeton Cemetery. Adele's death followed in 1981.
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| − | 后来，哥德尔经历了一段精神不稳定和疾病的时期。在他的密友 Moritz Schlick 被暗杀后，哥德尔对中毒有着强迫性的恐惧; 他只吃他的妻子阿黛尔为他准备的食物。1977年底，她住院6个月，随后不能再为丈夫准备食物。在她不在的时候，他拒绝进食，最终饿死。他死的时候称了体重。他的死亡证明显示他于1978年1月14日在普林斯顿医院死于“人格障碍引起的营养不良和缺乏意识”。他被埋葬在普林斯顿公墓。阿黛尔于1981年去世。
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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>{{cite book |first=John W., Jr. |last=Dawson |url=https://books.google.com/books?id=gA8SucCU1AYC&q=godel+leibniz&pg=PA166 |title=Logical Dilemmas: The Life and Work of Kurt Gödel. |publisher=A K Peters |year=2005 |page=166 |isbn=9781568812564 }}</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]].
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| − | 他研究和钦佩[[戈特弗里德·莱布尼兹]的作品，但后来认为，敌对阴谋使莱布尼兹的一些作品遭到压制。<ref>{{cite book |first=John W., Jr. |last=Dawson |url=https://books.google.com/books?id=gA8SucCU1AYC&q=godel+leibniz&pg=PA166 |title=Logical Dilemmas: The Life and Work of Kurt Gödel. |publisher=A K Peters |year=2005 |page=166 |isbn=9781568812564 }}</ref> 在较小程度上，他研究了[[伊曼纽尔·康德]]和[[埃德蒙·胡塞尔]]。20世纪70年代初，哥德尔在他的朋友中传播了一本莱布尼茨对神的存在的解释。这现在被称为[[哥德尔的本体论证明]]。
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| | ==Awards and honours奖励与荣誉== | | ==Awards and honours奖励与荣誉== |