“自指”的版本间的差异

2021年1月20日 (三) 15:59的版本

此词条暂由水流心不竞初译，翻译字数共1339。已由三奇同学完成第一次审校。

在自然语言或形式语言formal language中，当一个句子、想法或公式指向自己时，就会出现自指现象 Self-reference。（自指的英文Self-reference中，reference有“参照”的意思。）参照可以直接通过一些中间句或公式来表达，也可以通过一些编码来表达。在哲学中，它也指一个主体谈论或指称自己的能力，也就是说，具有第一人称主格单数代词“我”在英语中所表达的那种思想。

自指Self-reference经常在数学，哲学，计算机编程和语言学中被研究和应用。自指陈述有时是自相矛盾的，也可以被认为是递归的。

自指在逻辑、数学和计算中的体现

In classical philosophy, paradoxes were created by self-referential concepts such as the omnipotence paradox of asking if it was possible for a being to exist so powerful that it could create a stone that it could not lift. The Epimenides paradox, 'All Cretans are liars' when uttered by an ancient Greek Cretan was one of the first recorded versions. Contemporary philosophy sometimes employs the same technique to demonstrate that a supposed concept is meaningless or ill-defined. In classical philosophy, paradoxes were created by self-referential concepts such as the omnipotence paradox of asking if it was possible for a being to exist so powerful that it could create a stone that it could not lift. The Epimenides paradox, 'All Cretans are liars' when uttered by an ancient Greek Cretan was one of the first recorded versions. Contemporary philosophy sometimes employs the same technique to demonstrate that a supposed concept is meaningless or ill-defined.

在古典哲学中，悖论Paradoxes是由自指概念创造出来的，比如全能悖论：是否有一个足够强大的存在，可以创造出一个祂自己也举不起的石块？还有埃庇米尼得斯悖论。这一悖论有许多不同的表述形式，古希腊克里特岛人说的“所有克里特岛人都是骗子”是有记载的最早版本之一。当代哲学有时使用同样的技巧来证明一个假定的概念是没有意义的或者定义不明确的。^[2]

In mathematics and computability theory, self-reference (also known as Impredicativity) is the key concept in proving limitations of many systems. Gödel's theorem uses it to show that no formal consistent system of mathematics can ever contain all possible mathematical truths, because it cannot prove some truths about its own structure. The halting problem equivalent, in computation theory, shows that there is always some task that a computer cannot perform, namely reasoning about itself. These proofs relate to a long tradition of mathematical paradoxes such as Russell's paradox and Berry's paradox, and ultimately to classical philosophical paradoxes.

在数学和可计算性理论中，自指(也被称为不确定性)是证明许多系统局限性的关键概念。哥德尔定理Gödel's theorem用它来表明，没有一个形式上一致的数学系统可以包含所有可能的数学真理，因为它不能证明某些关于它自身结构的真理。在计算理论中，哥德尔定理的等价表述是停机问题，这一问题表明计算机不能完成关于自身的推理。这些证明关系到数学悖论的悠久传统，如罗素悖论和贝瑞悖论，并最终关系到经典哲学悖论。

In game theory, undefined behaviors can occur where two players must model each other's mental states and behaviors, leading to infinite regress.

在博弈论中，当博弈双方必须模拟对方的心理状态和行为时，就会出现不确定的行为，导致无穷回归。

In computer programming, self-reference occurs in reflection, where a program can read or modify its own instructions like any other data.^[3] Numerous programming languages support reflection to some extent with varying degrees of expressiveness. Additionally, self-reference is seen in recursion (related to the mathematical recurrence relation) in functional programming, where a code structure refers back to itself during computation.^[4] 'Taming' self-reference from potentially paradoxical concepts into well-behaved recursions has been one of the great successes of computer science, and is now used routinely in, for example, writing compilers using the 'meta-language' ML. Using a compiler to compile itself is known as bootstrapping. Self-modifying code is possible to write (programs which operate on themselves), both with assembler and with functional languages such as Lisp, but is generally discouraged in real-world programming. Computing hardware makes fundamental use of self-reference in flip-flops, the basic units of digital memory, which convert potentially paradoxical logical self-relations into memory by expanding their terms over time. Thinking in terms of self-reference is a pervasive part of programmer culture, with many programs and acronyms named self-referentially as a form of humor, such as GNU ('Gnu's not Unix') and PINE ('Pine is not Elm'). The GNU Hurd is named for a pair of mutually self-referential acronyms.

In computer programming, self-reference occurs in reflection, where a program can read or modify its own instructions like any other data. Numerous programming languages support reflection to some extent with varying degrees of expressiveness. Additionally, self-reference is seen in recursion (related to the mathematical recurrence relation) in functional programming, where a code structure refers back to itself during computation. 'Taming' self-reference from potentially paradoxical concepts into well-behaved recursions has been one of the great successes of computer science, and is now used routinely in, for example, writing compilers using the 'meta-language' ML. Using a compiler to compile itself is known as bootstrapping. Self-modifying code is possible to write (programs which operate on themselves), both with assembler and with functional languages such as Lisp, but is generally discouraged in real-world programming. Computing hardware makes fundamental use of self-reference in flip-flops, the basic units of digital memory, which convert potentially paradoxical logical self-relations into memory by expanding their terms over time. Thinking in terms of self-reference is a pervasive part of programmer culture, with many programs and acronyms named self-referentially as a form of humor, such as GNU ('Gnu's not Unix') and PINE ('Pine is not Elm'). The GNU Hurd is named for a pair of mutually self-referential acronyms.

在计算机程序设计中，自指发生在反馈中，程序可以像读取或修改其他数据一样读取或修改自己的指令。许多编程语言在某种程度上支持反射，具有不同程度的表达能力。此外，在函数式编程中的递归(与数学递归关系式相关)中可以看到自引用，其中代码结构在计算过程中反向引用自身。把自指从潜在的矛盾概念“驯服”到良好的行为递归一直是计算机科学的伟大成功之一，现在经常被 “元语言”机器学习用于编写编译器。使用编译器编译其自身被称为自举。无论是使用汇编语言还是使用Lisp 之类的函数式语言，编写程序自修改程序都是可能的，但在实际编程中通常不提倡这样做。计算器硬件使用了触发器中的自指，触发器是数字存储器的基本单位，它随时间推移扩展条件，存储潜在的逻辑自相关矛盾。自指思维在程序员文化中普遍存在，许多程序和首字母缩略词都是以自指的方式命名，这是一种幽默的形式，比如 GNU (“ GNU 不是 Unix”)和 PINE (“ PINE 不是 Elm”)。GNU Hurd 是以一对相互自我参照的缩写命名的。

Tupper's self-referential formula is a mathematical curiosity which plots an image of its own formula.

塔珀自指公式是一种数学上的奇思妙想，它的图像与其公式本身的样子几乎是一样的。

In biology 生物学

The biology of self-replication is self-referential, as embodied by DNA and RNA replication mechanisms. Models of self-replication are found in Conway's Game of Life and have inspired engineering systems such as the self-replicating 3D printer RepRap .

自指在生物学中表现为自我复制，正如 DNA 和 RNA 复制机制所体现的那样。《康威的生命游戏》中有自我复制的模型，这些模型启发制造了工程系统，比如自我复制的3D打印机 RepRap。

In art 艺术

Self-reference occurs in literature and film when an author refers to his or her own work in the context of the work itself. Examples include Miguel de Cervantes' Don Quixote, Shakespeare's A Midsummer Night's Dream, The Tempest and Twelfth Night, Denis Diderot's Jacques le fataliste et son maître, Italo Calvino's If on a winter's night a traveler, many stories by Nikolai Gogol, Lost in the Funhouse by John Barth, Luigi Pirandello's Six Characters in Search of an Author, Federico Fellini's 8½ and Bryan Forbes's The L-Shaped Room. Speculative fiction writer Samuel R. Delany makes use of this in his novels Nova and Dhalgren. In the former, Katin (a space-faring novelist) is wary of a long-standing curse wherein a novelist dies before completing any given work. Nova ends mid-sentence, thus lending credence to the curse and the realization that the novelist is the author of the story; likewise, throughout Dhalgren, Delany has a protagonist simply named The Kid (or Kidd, in some sections), whose life and work are mirror images of themselves and of the novel itself. In the sci-fi spoof film Spaceballs, Director Mel Brooks includes a scene wherein the evil characters are viewing a VHS copy of their own story, which shows them watching themselves “watching themselves”, ad infinitum. Perhaps the earliest example is in Homer's Iliad, where Helen of Troy laments: "for generations still unborn/we will live in song" (appearing in the song itself).^[5]

Self-reference occurs in literature and film when an author refers to his or her own work in the context of the work itself. Examples include Miguel de Cervantes' Don Quixote, Shakespeare's A Midsummer Night's Dream, The Tempest and Twelfth Night, Denis Diderot's Jacques le fataliste et son maître, Italo Calvino's If on a winter's night a traveler, many stories by Nikolai Gogol, Lost in the Funhouse by John Barth, Luigi Pirandello's Six Characters in Search of an Author, Federico Fellini's 8½ and Bryan Forbes's The L-Shaped Room. Speculative fiction writer Samuel R. Delany makes use of this in his novels Nova and Dhalgren. In the former, Katin (a space-faring novelist) is wary of a long-standing curse wherein a novelist dies before completing any given work. Nova ends mid-sentence, thus lending credence to the curse and the realization that the novelist is the author of the story; likewise, throughout Dhalgren, Delany has a protagonist simply named The Kid (or Kidd, in some sections), whose life and work are mirror images of themselves and of the novel itself. In the sci-fi spoof film Spaceballs, Director Mel Brooks includes a scene wherein the evil characters are viewing a VHS copy of their own story, which shows them watching themselves “watching themselves”, ad infinitum. Perhaps the earliest example is in Homer's Iliad, where Helen of Troy laments: "for generations still unborn/we will live in song" (appearing in the song itself).

自指在文学与电影中同样存在，譬如，一个作者可能在作品本身的背景下提到他自己的作品。例子包括米格尔·德·塞万提斯的《堂吉诃德》，莎士比亚的《仲夏夜之梦》，《暴风雨》和《第十二夜》，丹尼斯·狄德罗Denis Diderot 的《宿命论者雅克和他的主人》，意大利卡尔维诺Italo Calvino 的《如果在冬夜，一个旅人》，尼古拉·戈戈Nikolai Gogol 的许多故事，约翰·巴特John Barth 的《游乐园里的迷失》，路伊吉·皮兰德娄的《寻找作家的六个人物》，费德里柯·费里尼的《八部半》和布莱恩·福布斯Bryan Forbes 的《陋室红颜》。推理小说作家塞谬尔·迪兰尼在他的小说《新星》和《代尔格林》中使用了这一点。在前者中，卡廷(一个航天小说家)担心一个长期存在的诅咒，即小说家会在完成任何给定的作品之前死去。诺瓦结束了中间的句子，因此增加了诅咒的可信度，并使读者意识到小说家是故事的作者; 同样地，在《代尔格林》一书中，德拉尼有一个名为Kid(或Kidd，在某些部分)的主角，这个主角的生活就是小说本身的镜像。在科幻恶搞电影《太空漫步》中，导演梅尔 · 布鲁克斯(Mel Brooks)拍摄了一个场景，反派们正在观看自己故事的 VHS 拷贝，这个场景展示了他们无限地观看自己的“观看自己”。也许最早的例子是在伊利亚特Homer’s Iliad，特洛伊的海伦哀叹道: “为了尚未出生的后代/我们将生活在歌曲中”(出现在歌曲中)。

Self-reference in art is closely related to the concepts of breaking the fourth wall and meta-reference, which often involve self-reference. The short stories of Jorge Luis Borges play with self-reference and related paradoxes in many ways. Samuel Beckett's Krapp's Last Tape consists entirely of the protagonist listening to and making recordings of himself, mostly about other recordings. During the 1990s and 2000s filmic self-reference was a popular part of the rubber reality movement, notably in Charlie Kaufman's films Being John Malkovich and Adaptation, the latter pushing the concept arguably to its breaking point as it attempts to portray its own creation, in a dramatized version of the Droste effect.

Self-reference in art is closely related to the concepts of breaking the fourth wall and meta-reference, which often involve self-reference. The short stories of Jorge Luis Borges play with self-reference and related paradoxes in many ways. Samuel Beckett's Krapp's Last Tape consists entirely of the protagonist listening to and making recordings of himself, mostly about other recordings. During the 1990s and 2000s filmic self-reference was a popular part of the rubber reality movement, notably in Charlie Kaufman's films Being John Malkovich and Adaptation, the latter pushing the concept arguably to its breaking point as it attempts to portray its own creation, in a dramatized version of the Droste effect.

艺术中的自指与打破第四道墙和元参考的概念密切相关。豪尔赫·路易斯·博尔赫斯的短篇小说在许多方面玩弄着自指和相关的悖论。塞缪尔 · 贝克特的话剧《克拉普的最后碟带》完全由主人公自己听录音组成，大部分是关于其他录音的。在20世纪90年代和21世纪初，电影自指是橡胶现实运动的一个流行部分，特别是在查理考夫曼的电影《成为约翰·马尔科维奇》和改编作品中，后者可以说是把这一概念推动到了临近崩溃的边缘，因为它试图在一个德罗斯特效应剧本化的版本里描绘自己的创作。

Various creation myths invoke self-reference to solve the problem of what created the creator. For example, the Egyptian creation myth has a god swallowing his own semen to create himself. The Ouroboros is a mythical dragon which eats itself.

各种创世神话援引自指来解决是什么创造了创造者的问题。例如，埃及创世神话中有一个神吞下自己的精液来创造自己。衔尾蛇是一种神话中的会吃自己的龙。

The Quran includes numerous instances of self-referentiality.^[6]^[7]

The Quran includes numerous instances of self-referentiality.

《古兰经》中有许多自指的例子。^[8]^[9]

The surrealist painter René Magritte is famous for his self-referential works. His painting The Treachery of Images, includes the words "this is not a pipe", the truth of which depends entirely on whether the word ceci (in English, "this") refers to the pipe depicted—or to the painting or the word or sentence itself.^[10] M.C. Escher's art also contains many self-referential concepts such as hands drawing themselves.

The surrealist painter René Magritte is famous for his self-referential works. His painting The Treachery of Images, includes the words "this is not a pipe", the truth of which depends entirely on whether the word ceci (in English, "this") refers to the pipe depicted—or to the painting or the word or sentence itself. M.C. Escher's art also contains many self-referential concepts such as hands drawing themselves.

超现实主义画家勒内 · 马格利特以自指著称。其真实性完全取决于单词 ceci (英语中的“ this”)是指画作所描绘的烟斗，还是指画作本身，抑或“ceci”这个单词，或者是指这个句子本身。他的画作《形象的叛逆》有“这不是烟斗”的字样，M.c.埃舍尔的艺术也包含了许多自指的概念，比如他的手绘作品。

In language 语言学

A word that describes itself is called an autological word (or autonym). This generally applies to adjectives, for example sesquipedalian (i.e. "sesquipedalian" is a sesquipedalian word), but can also apply to other parts of speech, such as TLA, as a three-letter abbreviation for "three-letter abbreviation".

A word that describes itself is called an autological word (or autonym). This generally applies to adjectives, for example sesquipedalian (i.e. "sesquipedalian" is a sesquipedalian word), but can also apply to other parts of speech, such as TLA, as a three-letter abbreviation for "three-letter abbreviation".

一个描述自己的词叫做自动词(或自动词)。这通常适用于形容词，例如例如英文中“多音节”一词sesquipedalian (即“ sesquipedalian”是一个多音节的的单词) ，但也可以用于其他词类，如 TLA，作为“三个字母缩写”的三个字母的缩写。

A sentence which inventories its own letters and punctuation marks is called an autogram.

一个有自己的字母和句读的句子叫做自拍像autogram。

There is a special case of meta-sentence in which the content of the sentence in the metalanguage and the content of the sentence in the object language are the same. Such a sentence is referring to itself. However some meta-sentences of this type can lead to paradoxes. "This is a sentence." can be considered to be a self-referential meta-sentence which is obviously true. However "This sentence is false" is a meta-sentence which leads to a self-referential paradox. Such sentences can lead to problems, for example, in law, where statements bringing laws into existence can contradict one another or themselves. Kurt Gödel claimed to have found such a paradox in the US constitution at his citizenship ceremony.

元语句中的句子内容与宾语中的句子内容相同是元语句的一种特殊情况。这样的句子指的是它自己。然而，这种类型的元语句也可能导致悖论。“这是一个句子。”可以认为是一个自指的元语句，这显然是正确的。然而，“这句话是假的”是一个元句子，它导致了一个自指悖论。这样的句子可能会导致问题，例如，在法律中，元语句使法条的陈述可能会相互矛盾或自相矛盾。库尔特•哥德尔(Kurt Gödel)在他的公民身份仪式上宣称，他在美国宪法中发现了这样一个悖论。

Self-reference occasionally occurs in the media when it is required to write about itself, for example the BBC reporting on job cuts at the BBC. Notable encyclopedias may be required to feature articles about themselves, such as Wikipedia's article on Wikipedia.

自指偶尔会在传媒中出现，比如媒体报道自己的时候，例如BBC 对BBC裁员的报道著名的百科全书可能被要求提供关于他们自己的文章，比如维基百科上的文章。

Fumblerules are a list of rules of good grammar and writing, demonstrated through sentences that violate those very rules, such as "Avoid cliches like the plague" and "Don't use no double negatives". The term was coined in a published list of such rules by William Safire.^[11]^[12]

Fumblerules are a list of rules of good grammar and writing, demonstrated through sentences that violate those very rules, such as "Avoid cliches like the plague" and "Don't use no double negatives". The term was coined in a published list of such rules by William Safire.

失球规则Fumblerules是一系列好的语法和写作规则，描述这些规则的句子本身违反了这些规则，比如“避免像瘟疫一样的陈词滥调”和“不要使用没有双重否定”。这个术语是威廉 · 萨菲尔在一份她发表的规则列表中创造出来的。

In popular culture在流行文化中

Douglas Hofstadter's books, especially Metamagical Themas and Gödel, Escher, Bach, play with many self-referential concepts and were highly influential in bringing them into mainstream intellectual culture during the 1980s. Hofstadter's law, which specifies that "It always takes longer than you expect, even when you take into account Hofstadter's Law"^[13] is an example of a self-referencing adage. Hofstadter also suggested the concept of a 'Reviews of this book', a book containing only reviews of itself, which has since been implemented using wikis and other technologies. Hofstadter's 'strange loop' metaphysics attempts to map consciousness onto self-reference, but is a minority position in philosophy of mind.

侯世达的书，特别是“超魔法主题”和“哥德尔埃舍尔巴赫” 使用了许多自指概念，这些书籍在20世纪80年代成功地将“自指”概念引入主流知识文化。Hofstadter定律，“做一件事情所用的时间总是比你预期的要长，即使考虑到候世达定律 “^[14] 是一个自指格言的例子。候世达Hofstadter还提出了“这本书的评论”的概念，即一本“只包含对自己的评论”的书，这本书已经使用wiki和其他技术实现。候世达的“奇怪的循环”形而上学试图将意识映射到自指上，但这在心灵哲学中是少数人的立场。

The subgenre of "recursive science fiction" or metafiction is now so extensive that it has fostered a fan-maintained bibliography at the New England Science Fiction Association's website; some of it is about science-fiction fandom, some about science fiction and its authors.^[15]

“递归科幻”或元小说的子类型现在非常流行，以至于在新英格兰科幻小说协会的网站上培育了一个粉丝维护的书目；其中一些有关于科幻迷，一些有关于科幻小说及其作者的文章。^[16]

References 参考文献

↑ Soto-Andrade, Jorge; Jaramillo, Sebastian; Gutierrez, Claudio; Letelier, Juan-Carlos. "Ouroboros avatars: A mathematical exploration of Self-reference and Metabolic Closure" (PDF). MIT Press. Retrieved 16 May 2015.
↑ Liar Paradox
↑ Malenfant, J.; Demers, F-N. "A Tutorial on Behavioral Reflection and its Implementation" (PDF). PARC. Retrieved 17 May 2015.
↑ Drucker, Thomas (4 January 2008). Perspectives on the History of Mathematical Logic. Springer Science & Business Media. p. 110. ISBN 978-0-8176-4768-1. https://books.google.com/books?id=R70M4zsVgREC&pg=PA110.
↑ Homer (1990). Iliad. Translated by Robert Fagles. Penguin Books. p. 207. ISBN 1-101-15281-8.
↑ Madigan, David. The Qur'ân's Self-Image. Writing and Authority in Islam's Scripture.
↑ Boisliveau, Anne-Sylvie. Le Coran par lui-même.
↑ Madigan, David. The Qur'ân's Self-Image. Writing and Authority in Islam's Scripture.
↑ Boisliveau, Anne-Sylvie. Le Coran par lui-même.
↑ Nöth, Winfried; Bishara, Nina (2007). Self-reference in the Media. Walter de Gruyter. p. 75. ISBN 978-3-11-019464-7. https://books.google.com/books?id=NBOFIdchEQYC&pg=PA75.
↑ alt.usage.english.org's Humorous Rules for Writing
↑ Safire, William (1979-11-04). "On Language; The Fumblerules of Grammar". New York Times. p. SM4.

↑ Hofstadter, Douglas. Gödel, Escher, Bach: An Eternal Golden Braid. 20th-anniversary ed., 1999, p. 152.

↑ "Recursive Science Fiction" New England Science Fiction Association website, last updated 3 August 2008
↑ "Recursive Science Fiction" New England Science Fiction Association website, last updated 3 August 2008

Sources资料库

Bartlett, Steven J. [James] (Ed.) (1992). Reflexivity: A Source-book in Self-reference. Amsterdam, North-Holland. (PDF). RePub, Erasmus University

Bartlett，Steven J.【詹姆斯】（编辑）（1992年）。”自反性：自引用“”中的源帐簿。阿姆斯特丹，北荷兰。[1]

Hofstadter, D. R. (1980). Gödel, Escher, Bach: an Eternal Golden Braid. New York, Vintage Books.

[Douglas Hofstadter | Hofstadter，D.R.]]（1980年）。哥德尔埃舍尔巴赫:一条永恒的金色辫子。纽约，Vintage Books。

Smullyan, Raymond (1994), Diagonalization and Self-Reference, Oxford Science Publications,

雷蒙德·斯莫利安，雷蒙德（1994），“对角化和自我参照”，牛津科学出版物，{ISBN.0-19-853450-7}

Crabtree, Jonathan J. (2016), The Lost Logic of Elementary Mathematics and the Haberdasher who Kidnapped Kaizen, Proceedings of the Mathematical Association of Victoria (MAV) Annual Conference, 53, 98-106,

Crabtree，Jonathan J.（2016年），“丢失的初等数学逻辑和绑架Kaizen的Haberdasher”，《维多利亚数学协会（MAV）年会论文集》，53，98-106，{ISBN | 978-1-876949-60-0}

Category:Grammar

分类: 语法

Category:Theory of computation

类别: 计算理论

Category:Logic

分类: 逻辑

Category:Philosophy of language

范畴: 语言哲学

This page was moved from wikipedia:en:Self-reference. Its edit history can be viewed at 自指/edithistory

此页摘自维基百科：英语：自指。其编辑历史可在自指/编辑历史记录处查看

[1] Soto-Andrade, Jorge; Jaramillo, Sebastian; Gutierrez, Claudio; Letelier, Juan-Carlos. "Ouroboros avatars: A mathematical exploration of Self-reference and Metabolic Closure" (PDF). MIT Press. Retrieved 16 May 2015.

[2] Liar Paradox

[3] Malenfant, J.; Demers, F-N. "A Tutorial on Behavioral Reflection and its Implementation" (PDF). PARC. Retrieved 17 May 2015.

[Drucker2008-4] Drucker, Thomas (4 January 2008). Perspectives on the History of Mathematical Logic. Springer Science & Business Media. p. 110. ISBN 978-0-8176-4768-1. https://books.google.com/books?id=R70M4zsVgREC&pg=PA110.

[5] Homer (1990). Iliad. Translated by Robert Fagles. Penguin Books. p. 207. ISBN 1-101-15281-8.

[6] Madigan, David. The Qur'ân's Self-Image. Writing and Authority in Islam's Scripture.

[7] Boisliveau, Anne-Sylvie. Le Coran par lui-même.

[8] Madigan, David. The Qur'ân's Self-Image. Writing and Authority in Islam's Scripture.

[9] Boisliveau, Anne-Sylvie. Le Coran par lui-même.

[N.C3.B6thBishara2007-10] Nöth, Winfried; Bishara, Nina (2007). Self-reference in the Media. Walter de Gruyter. p. 75. ISBN 978-3-11-019464-7. https://books.google.com/books?id=NBOFIdchEQYC&pg=PA75.

[11] t.usage.english.org's Humorous Rules for Writing

[12] Safire, William (1979-11-04). "On Language; The Fumblerules of Grammar". New York Times. p. SM4.

[13] Hofstadter, Douglas. Gödel, Escher, Bach: An Eternal Golden Braid. 20th-anniversary ed., 1999, p. 152.
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[14] Hofstadter, Douglas. Gödel, Escher, Bach: An Eternal Golden Braid. 20th-anniversary ed., 1999, p. 152.
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[15] "Recursive Science Fiction" New England Science Fiction Association website, last updated 3 August 2008

[16] "Recursive Science Fiction" New England Science Fiction Association website, last updated 3 August 2008

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@@ 第2行： / 第2行： @@
 已由三奇同学完成第一次审校。
-{{short description|A sentence, idea or formula that refers to itself}}
+[[Image:ouroboros.png|thumb|古代的符号[[衔尾蛇，一条吞噬自己尾巴的蛇，表示自指]].<ref>{{cite web |last1=Soto-Andrade |first1=Jorge |last2=Jaramillo |first2=Sebastian |last3=Gutierrez |first3=Claudio |last4=Letelier |first4=Juan-Carlos |title=Ouroboros avatars: A mathematical exploration of Self-reference and Metabolic Closure |url=https://mitpress.mit.edu/sites/default/files/titles/alife/0262297140chap115.pdf |publisher=MIT Press |accessdate=16 May 2015}}</ref>]]
-{{简述〉<font color="#ff8000">一个指向自己的概念或公式 </font>}}
-{{Selfref|For the self-reference template on Wikipedia, see [[Template:Selfref]].}}
-{{自指|有关Wikipedia上的自引用模板，请参见[[模板：自指]].}}
-{{Use dmy dates|date=July 2012}}
-{{使用dmy日期|日期=2012年7月}}
+在自然语言或<font color='ff8800'>形式语言formal language</font>中，当一个句子、想法或公式指向自己时，就会出现<font color='ff8800'>自指现象 Self-reference</font>。（自指的英文Self-reference中，reference有“参照”的意思。）参照可以直接通过一些中间句或公式来表达，也可以通过一些编码来表达。在哲学中，它也指一个主体谈论或指称自己的能力，也就是说，具有第一人称主格单数代词“我”在英语中所表达的那种思想。
-<!-- Note to anyone who is thinking of making this article self referential: Please do not do this, see the note at top of the recursion article for why -->
-<!-- Note to anyone who is thinking of making this article self referential: Please do not do this, see the note at top of the recursion article for why -->
+<font color='ff8800'>自指Self-reference</font>经常在数学，哲学，计算机编程和语言学中被研究和应用。自指陈述有时是自相矛盾的，也可以被认为是递归的。
-< ! ——注意：任何人都请不要试图让本文自述，详细原因请参阅递归文章顶部的注释 -- >
-[[Image:ouroboros.png|thumb|The ancient symbol [[Ouroboros]], a dragon that continually consumes itself, denotes self-reference.<ref>{{cite web |last1=Soto-Andrade |first1=Jorge |last2=Jaramillo |first2=Sebastian |last3=Gutierrez |first3=Claudio |last4=Letelier |first4=Juan-Carlos |title=Ouroboros avatars: A mathematical exploration of Self-reference and Metabolic Closure |url=https://mitpress.mit.edu/sites/default/files/titles/alife/0262297140chap115.pdf |publisher=MIT Press |accessdate=16 May 2015}}</ref>]]
-The ancient symbol [[Ouroboros, a dragon that continually consumes itself, denotes self-reference.]]
+==自指在逻辑、数学和计算中的体现 ==
-古代的符号[[衔尾蛇，一条吞噬自己尾巴的蛇，表示自指]]
-'''Self-reference''' occurs in [[natural language|natural]] or [[formal language]]s when a [[Sentence (linguistics)|sentence]], idea or [[Well-formed formula|formula]] refers to itself. The reference may be expressed either directly—through some intermediate sentence or formula—or by means of some [[Semantics encoding|encoding]]. In [[philosophy]], it also refers to the ability of a subject to speak of or refer to itself, that is, to have the kind of thought expressed by the first person nominative singular pronoun [[I (pronoun)|"I"]] in English.
-Self-reference occurs in natural or formal languages when a sentence, idea or formula refers to itself. The reference may be expressed either directly—through some intermediate sentence or formula—or by means of some encoding. In philosophy, it also refers to the ability of a subject to speak of or refer to itself, that is, to have the kind of thought expressed by the first person nominative singular pronoun "I" in English.
-在自然语言或<font color='ff8800'>形式语言formal language</font>中，当一个句子、想法或公式指向自己时，就会出现<font color='ff8800'>自指现象Self-reference</font>。（自指的英文Self-reference中，reference有“参照”的意思。）参照可以直接通过一些中间句或公式来表达，也可以通过一些编码来表达。在哲学中，它也指一个主语谈论或指称自己的能力，也就是说，具有第一人称主格单数代词“我”在英语中所表达的那种思想。
-Self-reference is studied and has applications in [[mathematics]], [[philosophy]], [[computer programming]], and [[linguistics]]. Self-referential statements are sometimes [[paradox]]ical, and can also be considered [[Recursion|recursive]].
-Self-reference is studied and has applications in mathematics, philosophy, computer programming, and linguistics. Self-referential statements are sometimes paradoxical, and can also be considered recursive.
-<font color='ff8800'>自指Self-reference</font>研究和应用在数学，哲学，计算机编程和语言学中。自指陈述有时是矛盾的，也可以被认为是递归的。
-==In logic, mathematics and computing 逻辑、数学和计算==
-In classical [[philosophy]], [[paradoxes]] were created by self-referential concepts such as the [[omnipotence paradox]] of asking if it was possible for a being to exist so powerful that it could create a stone that it could not lift. The [[Epimenides paradox]], 'All Cretans are liars' when uttered by an ancient Greek Cretan was one of the first recorded versions. Contemporary philosophy sometimes employs the same technique to demonstrate that a supposed concept is meaningless or ill-defined.<ref>[https://plato.stanford.edu/entries/liar-paradox/ ''Liar Paradox'']</ref>
+In classical [[philosophy]], [[paradoxes]] were created by self-referential concepts such as the [[omnipotence paradox]] of asking if it was possible for a being to exist so powerful that it could create a stone that it could not lift. The [[Epimenides paradox]], 'All Cretans are liars' when uttered by an ancient Greek Cretan was one of the first recorded versions. Contemporary philosophy sometimes employs the same technique to demonstrate that a supposed concept is meaningless or ill-defined.
 In classical philosophy, paradoxes were created by self-referential concepts such as the omnipotence paradox of asking if it was possible for a being to exist so powerful that it could create a stone that it could not lift. The Epimenides paradox, 'All Cretans are liars' when uttered by an ancient Greek Cretan was one of the first recorded versions. Contemporary philosophy sometimes employs the same technique to demonstrate that a supposed concept is meaningless or ill-defined.
-在古典哲学中，<font color="#ff8000"> 悖论Paradoxes</font>是由<font color='ff8800'>自指</font>概念创造出来的，比如<font color="#ff8000">全能悖论：是否有一个足够强大的存在，可以创造出一个祂自己也举不起的石块？ </font><font color="#ff8000">还有埃庇米尼得斯悖论。这一悖论有许多不同的表述形式，古希腊克里特岛人说的“所有克里特岛人都是骗子”是有记载的最早版本之一。 </font>当代哲学有时使用同样的技巧来证明一个假定的概念是没有意义的或者定义不明确的。
+在古典哲学中，<font color="#ff8000"> 悖论Paradoxes</font>是由<font color='ff8800'>自指</font>概念创造出来的，比如<font color="#ff8000">全能悖论：是否有一个足够强大的存在，可以创造出一个祂自己也举不起的石块？ </font><font color="#ff8000">还有埃庇米尼得斯悖论。这一悖论有许多不同的表述形式，古希腊克里特岛人说的“所有克里特岛人都是骗子”是有记载的最早版本之一。 </font>当代哲学有时使用同样的技巧来证明一个假定的概念是没有意义的或者定义不明确的。<ref>[https://plato.stanford.edu/entries/liar-paradox/ ''Liar Paradox'']</ref>
-In [[mathematics]] and [[computability theory]], self-reference (also known as [[Impredicativity]]) is the key concept in proving limitations of many systems. [[Gödel's incompleteness theorems|Gödel's theorem]] uses it to show that no formal [[Consistency|consistent]] system of mathematics can ever contain all possible mathematical truths, because it cannot prove some truths about its own structure. [[The halting problem]] equivalent, in computation theory, shows that there is always some task that a computer cannot perform, namely reasoning about itself. These proofs relate to a long tradition of mathematical paradoxes such as [[Russell's paradox]] and [[Berry's paradox]], and ultimately to classical philosophical paradoxes.
 In mathematics and computability theory, self-reference (also known as Impredicativity) is the key concept in proving limitations of many systems. Gödel's theorem uses it to show that no formal consistent system of mathematics can ever contain all possible mathematical truths, because it cannot prove some truths about its own structure. The halting problem equivalent, in computation theory, shows that there is always some task that a computer cannot perform, namely reasoning about itself. These proofs relate to a long tradition of mathematical paradoxes such as Russell's paradox and Berry's paradox, and ultimately to classical philosophical paradoxes.
-在数学和可计算性理论中，<font color='ff8800'>自指</font>(也被称为<font color='ff8800'>不确定性</font>)是证明许多系统局限性的关键概念。<font color='ff8800'>哥德尔定理Gödel's theorem</font>用它来表明，没有一个形式上一致的数学系统可以包含所有可能的数学真理，因为它不能证明某些关于它自身结构的真理。<font color="#ff8000"> 在计算理论中，哥德尔定理的等价表述是停机问题，这一问题表明计算机不能完成关于自身的推理。</font>这些证明关系到数学悖论的悠久传统，如<font color='ff8800'>罗素悖论</font>和<font color='ff8800'>贝瑞悖论</font>，并最终关系到经典哲学悖论。
+在数学和[[可计算性理论]]中，<font color='ff8800'>自指</font>(也被称为<font color='ff8800'>不确定性</font>)是证明许多系统局限性的关键概念。<font color='ff8800'>哥德尔定理Gödel's theorem</font>用它来表明，没有一个形式上一致的数学系统可以包含所有可能的数学真理，因为它不能证明某些关于它自身结构的真理。<font color="#ff8000"> 在计算理论中，哥德尔定理的等价表述是停机问题，这一问题表明计算机不能完成关于自身的推理。</font>这些证明关系到数学悖论的悠久传统，如<font color='ff8800'>罗素悖论</font>和<font color='ff8800'>贝瑞悖论</font>，并最终关系到经典哲学悖论。