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The fact that renowned theoretical physicists like Poincaré, Boltzmann or Gibbs were not awarded the Nobel Prize is seen as evidence that the Nobel committee had more regard for experimentation than theory.<ref>{{cite journal|last1=Crawford |first1= Elizabeth |title=Nobel: Always the Winners, Never the Losers|journal=[[Science (journal)|Science]]|date=13 November 1998|volume=282|issue=5392|pages=1256–1257|doi=10.1126/science.282.5392.1256|bibcode = 1998Sci...282.1256C |s2cid= 153619456 }}{{dead link|date=July 2016}}</ref><ref>{{cite journal|last1=Nastasi|first1=Pietro|title=A Nobel Prize for Poincaré? |journal=Lettera Matematica|date=16 May 2013|volume=1|issue=1–2|pages=79–82|doi=10.1007/s40329-013-0005-1 |url= |accessdate=|doi-access=free}}</ref> In Poincaré's case, several of those who nominated him pointed out that the greatest problem was to name a specific discovery, invention, or technique.<ref name="gray-biography"/>
 
The fact that renowned theoretical physicists like Poincaré, Boltzmann or Gibbs were not awarded the Nobel Prize is seen as evidence that the Nobel committee had more regard for experimentation than theory.<ref>{{cite journal|last1=Crawford |first1= Elizabeth |title=Nobel: Always the Winners, Never the Losers|journal=[[Science (journal)|Science]]|date=13 November 1998|volume=282|issue=5392|pages=1256–1257|doi=10.1126/science.282.5392.1256|bibcode = 1998Sci...282.1256C |s2cid= 153619456 }}{{dead link|date=July 2016}}</ref><ref>{{cite journal|last1=Nastasi|first1=Pietro|title=A Nobel Prize for Poincaré? |journal=Lettera Matematica|date=16 May 2013|volume=1|issue=1–2|pages=79–82|doi=10.1007/s40329-013-0005-1 |url= |accessdate=|doi-access=free}}</ref> In Poincaré's case, several of those who nominated him pointed out that the greatest problem was to name a specific discovery, invention, or technique.<ref name="gray-biography"/>
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==Philosophy==
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==Philosophy哲学==
    
On algebraic topology:
 
On algebraic topology:
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Poincaré had philosophical views opposite to those of [[Bertrand Russell]] and [[Gottlob Frege]], who believed that mathematics was a branch of [[logic]]. Poincaré strongly disagreed, claiming that [[intuition (knowledge)|intuition]] was the life of mathematics. Poincaré gives an interesting point of view in his book ''[[Science and Hypothesis]]'':
 
Poincaré had philosophical views opposite to those of [[Bertrand Russell]] and [[Gottlob Frege]], who believed that mathematics was a branch of [[logic]]. Poincaré strongly disagreed, claiming that [[intuition (knowledge)|intuition]] was the life of mathematics. Poincaré gives an interesting point of view in his book ''[[Science and Hypothesis]]'':
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庞加莱的哲学观点与[[伯特兰·罗素]]和[[哥特罗布·弗雷格]]相反,他们认为数学是[[逻辑]]的一个分支。庞加莱强烈反对,声称[[直觉(知识)|直觉]]是数学的生命。庞加莱在他的书“[[科学与假设]]”中提出了一个有趣的观点:
    
| url=http://www.maths.ed.ac.uk/~aar/papers/poincare2009.pdf}}. The first systematic study of topology.
 
| url=http://www.maths.ed.ac.uk/~aar/papers/poincare2009.pdf}}. The first systematic study of topology.
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{{quote|text=For a superficial observer, scientific truth is beyond the possibility of doubt; the logic of science is infallible, and if the scientists are sometimes mistaken, this is only from their mistaking its rule.}}
 
{{quote|text=For a superficial observer, scientific truth is beyond the possibility of doubt; the logic of science is infallible, and if the scientists are sometimes mistaken, this is only from their mistaking its rule.}}
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{{quote | text=对于一个肤浅的观察者来说,科学的真理是不容置疑的;科学的逻辑是绝对正确的,如果科学家有时是错误的,这仅仅是因为他们错误地理解了它的规则}}
    
On celestial mechanics:
 
On celestial mechanics:
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Poincaré believed that [[arithmetic]] is [[Analytic/synthetic distinction|synthetic]]. He argued that [[Peano's axioms]] cannot be proven non-circularly with the principle of induction (Murzi, 1998), therefore concluding that arithmetic is ''[[A priori and a posteriori|a priori]]'' synthetic and not analytic. Poincaré then went on to say that mathematics cannot be deduced from logic since it is not analytic. His views were similar to those of [[Immanuel Kant]] (Kolak, 2001, Folina 1992). He strongly opposed Cantorian [[set theory]], objecting to its use of [[Impredicativity|impredicative]] definitions{{Citation needed|date=March 2018}}.
 
Poincaré believed that [[arithmetic]] is [[Analytic/synthetic distinction|synthetic]]. He argued that [[Peano's axioms]] cannot be proven non-circularly with the principle of induction (Murzi, 1998), therefore concluding that arithmetic is ''[[A priori and a posteriori|a priori]]'' synthetic and not analytic. Poincaré then went on to say that mathematics cannot be deduced from logic since it is not analytic. His views were similar to those of [[Immanuel Kant]] (Kolak, 2001, Folina 1992). He strongly opposed Cantorian [[set theory]], objecting to its use of [[Impredicativity|impredicative]] definitions{{Citation needed|date=March 2018}}.
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庞加莱认为[[算术]]是[[分析/合成区别|合成]]。他认为[[皮亚诺的公理]]不能用归纳法原理进行非循环证明(Murzi,1998),因此得出结论认为算术是“综合的而非分析的”。庞加莱接着说,数学不能从逻辑中推导出来,因为它不是分析性的。他的观点与[[Immanuel Kant]]的观点相似(Kolak,2001,Folina 1992)。他强烈反对Cantorian[[set theory]],反对其使用[[不精确性|非指示性]]定义{{Citation needed|date=March 2018}}。
    
However, Poincaré did not share Kantian views in all branches of philosophy and mathematics. For example, in geometry, Poincaré believed that the structure of [[Non-Euclidean geometry|non-Euclidean space]] can be known analytically. Poincaré held that convention plays an important role in physics. His view (and some later, more extreme versions of it) came to be known as "[[conventionalism]]".<ref>Yemima Ben-Menahem, ''Conventionalism: From Poincare to Quine'', Cambridge University Press, 2006, p. 39.</ref> Poincaré believed that [[Newton's first law]] was not empirical but is a conventional framework assumption for mechanics (Gargani, 2012).<ref>{{Citation|author=Gargani Julien|title=Poincaré, le hasard et l'étude des systèmes complexes|publisher=L'Harmattan|year=2012|page=124|url=http://www.editions-harmattan.fr/index.asp?navig=catalogue&obj=livre&no=38754|access-date=5 June 2015|archive-url=https://web.archive.org/web/20160304140554/http://www.editions-harmattan.fr/index.asp?navig=catalogue&obj=livre&no=38754|archive-date=4 March 2016|url-status=dead}}</ref> He also believed that the geometry of physical space is conventional. He considered examples in which either the geometry of the physical fields or gradients of temperature can be changed, either describing a space as non-Euclidean measured by rigid rulers, or as a Euclidean space where the rulers are expanded or shrunk by a variable heat distribution. However, Poincaré thought that we were so accustomed to [[Euclidean geometry]] that we would prefer to change the physical laws to save Euclidean geometry rather than shift to a non-Euclidean physical geometry.<ref>{{Citation|title=Science and Hypothesis|first1=Henri |last1=Poincaré |publisher=Cosimo, Inc. Press|year=2007|isbn=978-1-60206-505-5 |page=50
 
However, Poincaré did not share Kantian views in all branches of philosophy and mathematics. For example, in geometry, Poincaré believed that the structure of [[Non-Euclidean geometry|non-Euclidean space]] can be known analytically. Poincaré held that convention plays an important role in physics. His view (and some later, more extreme versions of it) came to be known as "[[conventionalism]]".<ref>Yemima Ben-Menahem, ''Conventionalism: From Poincare to Quine'', Cambridge University Press, 2006, p. 39.</ref> Poincaré believed that [[Newton's first law]] was not empirical but is a conventional framework assumption for mechanics (Gargani, 2012).<ref>{{Citation|author=Gargani Julien|title=Poincaré, le hasard et l'étude des systèmes complexes|publisher=L'Harmattan|year=2012|page=124|url=http://www.editions-harmattan.fr/index.asp?navig=catalogue&obj=livre&no=38754|access-date=5 June 2015|archive-url=https://web.archive.org/web/20160304140554/http://www.editions-harmattan.fr/index.asp?navig=catalogue&obj=livre&no=38754|archive-date=4 March 2016|url-status=dead}}</ref> He also believed that the geometry of physical space is conventional. He considered examples in which either the geometry of the physical fields or gradients of temperature can be changed, either describing a space as non-Euclidean measured by rigid rulers, or as a Euclidean space where the rulers are expanded or shrunk by a variable heat distribution. However, Poincaré thought that we were so accustomed to [[Euclidean geometry]] that we would prefer to change the physical laws to save Euclidean geometry rather than shift to a non-Euclidean physical geometry.<ref>{{Citation|title=Science and Hypothesis|first1=Henri |last1=Poincaré |publisher=Cosimo, Inc. Press|year=2007|isbn=978-1-60206-505-5 |page=50
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|url=https://books.google.com/books?id=2QXqHaVbkgoC&pg=PA50}}</ref>
 
|url=https://books.google.com/books?id=2QXqHaVbkgoC&pg=PA50}}</ref>
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然而,庞加莱并没有在哲学和数学的所有分支中分享康德的观点。例如,在几何学中,庞加莱认为[[非欧几里德几何|非欧几里德空间]]的结构可以通过分析得到。庞加莱认为传统在物理学中起着重要的作用。他的观点(以及后来一些更极端的版本)被称为“[[传统主义]]”。<ref>Yemima Ben-Menahem, ''Conventionalism: From Poincare to Quine'', Cambridge University Press, 2006, p. 39.</ref>庞加莱认为[[牛顿第一定律]]不是经验性的,而是力学的传统框架假设(Gargani,2012)。.<ref>{{Citation|author=Gargani Julien|title=Poincaré, le hasard et l'étude des systèmes complexes|publisher=L'Harmattan|year=2012|page=124|url=http://www.editions-harmattan.fr/index.asp?navig=catalogue&obj=livre&no=38754|access-date=5 June 2015|archive-url=https://web.archive.org/web/20160304140554/http://www.editions-harmattan.fr/index.asp?navig=catalogue&obj=livre&no=38754|archive-date=4 March 2016|url-status=dead}}</ref>他还认为物理空间的几何学是传统的。他考虑了物理场的几何结构或温度梯度可以改变的例子,要么将一个空间描述为由刚性标尺测量的非欧几里德空间,要么描述为标尺通过可变热分布而膨胀或收缩的欧几里德空间。然而,庞加莱认为我们太习惯了[[欧几里德几何]],我们宁愿改变物理定律来保存欧几里德几何,而不是转向非欧几里德物理几何。<ref>{{Citation|title=Science and Hypothesis|first1=Henri |last1=Poincaré |publisher=Cosimo, Inc. Press|year=2007|isbn=978-1-60206-505-5 |page=50|url=https://books.google.com/books?id=2QXqHaVbkgoC&pg=PA50}}</ref>
    
On the philosophy of mathematics:
 
On the philosophy of mathematics:
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关于数学哲学:
 
关于数学哲学:
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===Free will===
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===Free will自由意志===
    
Poincaré's famous lectures before the Société de Psychologie in Paris (published as ''[[Science and Hypothesis]]'', ''[[The Value of Science]]'', and ''Science and Method'') were cited by [[Jacques Hadamard]] as the source for the idea that creativity and invention consist of two mental stages, first random combinations of possible solutions to a problem, followed by a critical evaluation.<ref>Hadamard, Jacques. ''An Essay on the Psychology of Invention in the Mathematical Field''. Princeton Univ Press (1945)</ref>
 
Poincaré's famous lectures before the Société de Psychologie in Paris (published as ''[[Science and Hypothesis]]'', ''[[The Value of Science]]'', and ''Science and Method'') were cited by [[Jacques Hadamard]] as the source for the idea that creativity and invention consist of two mental stages, first random combinations of possible solutions to a problem, followed by a critical evaluation.<ref>Hadamard, Jacques. ''An Essay on the Psychology of Invention in the Mathematical Field''. Princeton Univ Press (1945)</ref>
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庞加莱在巴黎心理学学会之前的著名演讲(出版为“[[科学与假设]]”、[[科学的价值]]”和“科学与方法”)被[[Jacques Hadamard]]引用为创意和发明由两个心理阶段组成的思想来源,首先是可能的解决方案的随机组合一个问题,然后是一个批判性的评估<ref>Hadamard, Jacques. ''An Essay on the Psychology of Invention in the Mathematical Field''. Princeton Univ Press (1945)</ref>
    
Although he most often spoke of a deterministic universe, Poincaré said that the subconscious generation of new possibilities involves [[Randomness|chance]].
 
Although he most often spoke of a deterministic universe, Poincaré said that the subconscious generation of new possibilities involves [[Randomness|chance]].
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尽管庞加莱经常谈到确定性宇宙,但他说潜意识中新可能性的产生涉及到[随机性|机会]]。
    
<blockquote>
 
<blockquote>
    
It is certain that the combinations which present themselves to the mind in a kind of sudden illumination after a somewhat prolonged period of unconscious work are generally useful and fruitful combinations... all the combinations are formed as a result of the automatic action of the subliminal ego, but those only which are interesting find their way into the field of consciousness... A few only are harmonious, and consequently at once useful and beautiful, and they will be capable of affecting the geometrician's special sensibility I have been speaking of; which, once aroused, will direct our attention upon them, and will thus give them the opportunity of becoming conscious... In the subliminal ego, on the contrary, there reigns what I would call liberty, if one could give this name to the mere absence of discipline and to disorder born of chance.<ref>{{cite book|title =Science and Method|chapter= 3: Mathematical Creation|date= 1914|chapter-url = https://ebooks.adelaide.edu.au/p/poincare/henri/science-and-method/book1.3.html|first = Henri|last =Poincaré }}</ref>
 
It is certain that the combinations which present themselves to the mind in a kind of sudden illumination after a somewhat prolonged period of unconscious work are generally useful and fruitful combinations... all the combinations are formed as a result of the automatic action of the subliminal ego, but those only which are interesting find their way into the field of consciousness... A few only are harmonious, and consequently at once useful and beautiful, and they will be capable of affecting the geometrician's special sensibility I have been speaking of; which, once aroused, will direct our attention upon them, and will thus give them the opportunity of becoming conscious... In the subliminal ego, on the contrary, there reigns what I would call liberty, if one could give this name to the mere absence of discipline and to disorder born of chance.<ref>{{cite book|title =Science and Method|chapter= 3: Mathematical Creation|date= 1914|chapter-url = https://ebooks.adelaide.edu.au/p/poincare/henri/science-and-method/book1.3.html|first = Henri|last =Poincaré }}</ref>
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可以肯定的是,在经过一段长时间的无意识工作之后,以一种突然的光明出现在头脑中的组合通常是有用的和富有成效的组合。。。所有的组合都是潜意识自我自动作用的结果,但是那些有趣的组合却进入了意识领域。。。只有少数人是和谐的,因此同时又是有用的和美丽的,它们将能够影响我所说的几何学家的特殊情感;一旦被唤起,就会把我们的注意力引向它们,从而使它们有机会变得有意识。。。与此相反,在潜意识自我中,存在着我称之为自由的统治,如果一个人可以把这个名字命名为纯粹的缺乏纪律和偶然产生的混乱。<ref>{{cite book|title =Science and Method|chapter= 3: Mathematical Creation|date= 1914|chapter-url = https://ebooks.adelaide.edu.au/p/poincare/henri/science-and-method/book1.3.html|first = Henri|last =Poincaré }}</ref>
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</blockquote>
 
</blockquote>
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Poincaré's two stages—random combinations followed by selection—became the basis for [[Daniel Dennett]]'s two-stage model of free will.<ref>Dennett, Daniel C. 1978. Brainstorms: Philosophical Essays on Mind and Psychology. The MIT Press, p.293</ref>
 
Poincaré's two stages—random combinations followed by selection—became the basis for [[Daniel Dennett]]'s two-stage model of free will.<ref>Dennett, Daniel C. 1978. Brainstorms: Philosophical Essays on Mind and Psychology. The MIT Press, p.293</ref>
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庞加莱的两阶段随机组合和选择成为[[Daniel Dennett]]自由意志两阶段模型的基础。<ref>Dennett, Daniel C. 1978. Brainstorms: Philosophical Essays on Mind and Psychology. The MIT Press, p.293</ref>
    
==Bibliography==
 
==Bibliography==
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