自指

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The ancient symbol Ouroboros, a dragon that continually consumes itself, denotes self-reference.

The ancient symbol Ouroboros, a dragon that continually consumes itself, denotes self-reference.

古代的符号衔尾蛇，一条连续吞噬自己的龙，表示自我参照

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.

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.

在自然语言或形式语言中，当一个句子、想法或公式指向自己时，就会出现自指现象。指称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 paradoxical, and can also be considered 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.

自我参照是研究和应用在数学，哲学，计算机编程和语言学。自我参照的陈述有时是矛盾的，也可以被认为是递归的。

In logic, mathematics and computing

在逻辑，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.

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，悖论是由自我参照的概念创造出来的，比如全能悖论问是否存在一个如此强大的存在，以至于它可以创造一块无法举起的石头。埃庇米尼得斯悖论，古希腊克里岛人说的“所有克里岛人都是骗子”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所谓的概念是没有意义的或者定义不明确的。

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.

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，自我参照(也被称为不确定性)是证明许多系统局限性的关键概念。格德尔定理用它来表明，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，因为它不能证明关于它自己的结构的一些真理。计算理论中的停机问题等价表明，总有一些计算机无法完成的任务，即关于自身的推理。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.

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，不确定的行为可能发生在双方必须模仿彼此的心理状态和行为的情况下，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. 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.

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，自引用发生在反射中，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(与数学递回关系式相关)中可以看到自引用，其中代码结构在计算过程中回溯到自身。“驯服”自我参照从潜在的矛盾概念到良好的行为递归一直是计算机科学的伟大成功之一，并且现在经常被用于，例如，使用“元语言”机器学习编译器。使用编译器自行编译被称为引导。无论是使用汇编语言还是使用诸如 Lisp 之类的函数式语言，编写程序自修改程序都是可能的，但在实际编程中一般不提倡这样做。计算硬件在触发器中基本利用了自参考，触发器是数字存储器的基本单元，它通过随时间推移扩展词项，将潜在的矛盾逻辑自我关系转换为存储器。自我引用思维是程序员文化中一个普遍存在的部分，许多程序和首字母缩略词都以自我引用的方式命名为一种幽默形式，比如 GNU (“ GNU 不是 Unix”)和 PINE (“ PINE 不是 Elm”)。Gnu Hurd 是以一对相互参照的首字母缩写命名的。

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

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

塔珀的自我参照公式是一种数学上的奇思妙想，它用自己的公式描绘出一幅图像。

In biology

在生物学上

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 .

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 .

自我复制的生物学是自我参照的，正如 DNA 和 RNA 复制机制所体现的那样。在 Conway 的《生命的游戏》中可以找到自我复制的模型，这些模型启发了工程系统，比如自我复制的3 d 打印机 RepRap。

In art

在艺术上

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 Cervantes's 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).

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 Cervantes's 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).

自我参照发生在文学和电影中，当一个作者提到他或她自己的作品在作品本身的背景下。比如塞万提斯的《堂吉诃德》 ，莎士比亚的《仲夏夜之梦》 ，《暴风雨》和《第十二夜》 ，Denis Diderot 的《 Jacques le fataliste et son ma tre 》 ，Italo Calvino 的《 If on a winter’ s Night a traveler 》 ，Nikolai Gogol 的许多故事，John Barth 的《迷失在游乐场》 ，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《81年2月》和 Bryan Forbes 的《陋室红颜》。推想小说作家塞谬尔·迪兰尼在他的小说《 Nova 》和《 Dhalgren 》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，即小说家在完成任何给定的作品之前死去。同样，在整个 Dhalgren，德拉尼的主人公只是简单地命名为孩子(或基德，在某些部分) ，他的生活和工作就是他们自己和小说本身的镜像。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，邪恶的角色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 Homer’s Iliad，特洛伊的海伦哀叹道: “为了未出生的后代 / 我们将生活在歌曲中”(出现在歌曲本身中)。

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.

艺术中的自我参照与打破第四道墙和元参照的概念密切相关，这些概念往往涉及自我参照。豪尔赫·路易斯·博尔赫斯的短篇小说在许多方面玩弄着自我参照和相关的悖论。塞缪尔 · 贝克特的《最后的磁带》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，电影自我参照是橡胶现实运动的一个流行部分，尤其是在查理 · 考夫曼的电影《傀儡人生和改编，后者可以说把这个概念推到了崩溃的边缘，因为它试图描绘自己的创造，在一个剧本化版本的德罗斯特效应。

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.

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我参照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.

The Quran includes numerous instances of self-referentiality.

《古兰经》中有许多自我指称的例子。

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.

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.

超现实主义画家任 · 马格里特以自我参照著称。他的画作《形象的叛逆有“这不是烟斗”的字样，其真实性完全取决于单词 ceci (英语中的“ this”)是指所描绘的烟斗，还是指画作或单词或句子本身。主持人。埃舍尔的艺术也包含了许多自我参照的概念，比如手绘本身。

In language

用语言

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 sesquipedalian (即。“ sesquipedalian”是一个倍半音的单词) ，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.

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

一个由自己的字母和句读组成的句子叫做“ 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.

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.

元语言中的句子内容与宾语中的句子内容相同是元语言句子的一种特殊情况。这样的句子指的是它自己。然而，这种类型的元句子可能会导致悖论。“这是一个句子。”可以认为是一个自指的元句，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，使法律存在的陈述可能会相互矛盾或自相矛盾。库尔特 · 德尔声称在他的入籍仪式上发现了美国宪法中的这样一个悖论。

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.

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.

当媒体被要求写自己的时候，自我引用偶尔会出现，例如 BBC 对裁员的报道。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.

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.

拙劣是一系列好的语法和写作规则，通过违反这些规则的句子展现出来，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 · 萨菲尔在一份已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" 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.

• 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.

See also

参见

! -- 请注意不要发布本文的链接，即。“自我引用” ，在“请参阅”部分，它将被删除

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References

参考资料

Sources

资料来源

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

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

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

  
  

  • 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,

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