7,129
个编辑
更改
无编辑摘要
'''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 – 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 – 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 [[]] were analyzing the use of logic and [[set theory]] to understand the [[foundations of mathematics]] pioneered by [[Georg Cantor]].
'''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。
'''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。当时其他人，如伯特兰·罗素 Bertrand Russell、阿尔弗雷德·诺斯·怀特黑德 Alfred North Whitehead和大卫·希尔伯特 David Hilbert都在分析逻辑和集合论的使用，以理解乔治·坎托 Georg Cantor开创的数学基础。
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. 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. 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. 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>]]
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. 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>]][[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?
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>]]
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>]][[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>