Editing Self-reference

{{short description|Sentence, idea or formula that refers to itself}}
{{For|the use of self-references in Wikipedia articles|Wikipedia:Manual of Style/Self-references to avoid|selfref=yes}}
{{Use dmy dates|date=December 2020}}
<!-- 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 -->
[[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 |access-date=16 May 2015}}</ref>]]

'''Self-reference''' is a concept that involves referring to oneself or one's own attributes, characteristics, or actions. It can occur in [[language]], [[logic]], [[mathematics]], [[philosophy]], and other fields.

In [[natural language|natural]] or [[formal language]]s, self-reference occurs 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, self-reference 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 is studied and has applications in mathematics, philosophy, [[computer programming]], [[second-order cybernetics]], and [[linguistics]], as well as [[self-referential humor|in humor]]. Self-referential statements are sometimes [[paradox]]ical, and can also be considered [[Recursion|recursive]].

==In logic, mathematics and computing ==
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>{{cite book| url = https://plato.stanford.edu/entries/liar-paradox/| title = ''Liar Paradox''| year = 2020| publisher = Metaphysics Research Lab, Stanford University}}</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 [[game theory]], undefined behaviors can occur where two players must model each other's mental states and behaviors, leading to infinite regress.

In [[computer programming]], self-reference occurs in [[Reflection (computer science)|reflection]], where a program can read or modify its own instructions like any other data.<ref>{{cite web|last1=Malenfant|first1=J.|last2=Demers|first2=F-N|title=A Tutorial on Behavioral Reflection and its Implementation|url=http://www2.parc.com/csl/groups/sda/projects/reflection96/docs/malenfant/malenfant.pdf|publisher=PARC|archive-url=https://web.archive.org/web/20170821214626/http://www2.parc.com/csl/groups/sda/projects/reflection96/docs/malenfant/malenfant.pdf|access-date=17 May 2015|archive-date=21 August 2017}}</ref> 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.<ref name="Drucker2008">{{cite book |last=Drucker |first=Thomas |title=Perspectives on the History of Mathematical Logic |url=https://books.google.com/books?id=R70M4zsVgREC&pg=PA110 |date=4 January 2008 |publisher=Springer Science & Business Media |isbn=978-0-8176-4768-1 |page=110}}</ref> '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 (programming language)|ML]]. Using a compiler to compile itself is known as [[bootstrapping (compilers)|bootstrapping]]. [[Self-modifying code]] is possible to write (programs which operate on themselves), both with [[Assembly language|assembler]] and with functional languages such as [[Lisp (programming language)|Lisp]], but is generally discouraged in real-world programming. Computing hardware makes fundamental use of self-reference in [[Flip-flop (electronics)|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 (email client)|PINE]] ('Pine is not Elm'). The [[GNU Hurd]] is named for a pair of mutually self-referential acronyms.

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

==In art==
[[File:高機模様裂-Textile fragment with incomplete repeating pattern of loom, weaver, and drawboy MET DP11389.jpg|thumb|[[Drawloom]], with drawboy above to control the harnesses, woven as a repeating pattern in an early-1800s piece of Japanese silk. The silk illustrates the means by which it was produced.]]
[[File:Paradox.jpg|alt=graffiti art on a wall stating "SORRY ABOUT YOUR WALL"|thumb|A self-referencing work of [[graffiti]] apologizing for its own existence]]
[[File:Eron_biennale_dozza_bologna.jpeg|thumb|Self-referential [[graffiti]]. The painter drawn on a wall erases his own graffiti, and may be erased himself by the next facade cleaner.]]

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 (novel)|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).<ref>{{cite book |last1=Homer |others=Translated by Robert Fagles |title=Iliad |year=1990 |publisher=Penguin Books |isbn=1-101-15281-8 |page=207}}</ref>

Self-reference in art is closely related to the concepts of [[fourth wall|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 (film)|Adaptation]]'', the latter pushing the concept arguably to its breaking point as it attempts to portray its own creation, in a [[Story within a story#Fractal Fiction|dramatized version]] of the [[Droste effect]].

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.

The [[Quran]] includes numerous instances of self-referentiality.<ref>{{cite book |last1=Madigan |first1=David |title=The Qur'ân's Self-Image. Writing and Authority in Islam's Scripture}}</ref><ref>{{cite book |last1=Boisliveau |first1=Anne-Sylvie |title=Le Coran par lui-même}}</ref>

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.<ref name="NöthBishara2007">{{cite book |last1=Nöth |first1=Winfried |last2=Bishara |first2=Nina |title=Self-reference in the Media |url=https://books.google.com/books?id=NBOFIdchEQYC&pg=PA75 |year=2007 |publisher=Walter de Gruyter |isbn=978-3-11-019464-7 |page=75}}</ref> [[M.C. Escher]]'s art also contains many self-referential concepts such as hands drawing themselves.

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

A sentence which inventories its own letters and punctuation marks is called an [[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 [[Liar paradox|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 [[Gödel's Loophole|loophole]] in the [[United States Constitution]] at his citizenship ceremony.

Self-reference occasionally occurs in the [[Broadcast media|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]].

[[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]].<ref>{{cite web| url = http://alt-usage-english.org/humorousrules.html| title = Humorous Rules for Writing |first1=Donna |last1=Richoux |date=June 18, 2002 |website=alt.usage.english }}</ref><ref>{{Cite news |first = William |last= Safire |author-link=William Safire |publication-date=1979-11-04 |title=On Language; The Fumblerules of Grammar |periodical=The New York Times |url=https://www.nytimes.com/1979/11/04/archives/on-language-the-fumblerules-of-grammar.html  |page=SM4 |url-status=live |archive-url=https://web.archive.org/web/20230205052204/https://www.nytimes.com/1979/11/04/archives/on-language-the-fumblerules-of-grammar.html?sq=Fumblerules&scp=1&st=p |archive-date= 2023-02-05}}</ref>

[[Circular definition]] is a type of self-reference in which the definition of a term or concept includes the term or concept itself, either explicitly or implicitly. Circular definitions are considered [[Fallacy|fallacious]] because they only define a term in terms of itself.<ref>{{Cite book |last=Walton |first=Douglas N. |url=https://books.google.com/books?id=5-TWAAAAMAAJ |title=Begging the Question: Circular Reasoning as a Tactic of Argumentation |date=1991 |publisher=Greenwood Press |isbn=978-0-313-27596-8 |language=en}}</ref> This type of self-reference may be useful in [[argumentation]], but can result in a lack of clarity in communication.

The adverb "hereby" is used in a self-referential way, for example in the statement "I hereby declare you husband and wife."<ref>{{cite web| url = https://en.wiktionary.org/wiki/hereby|title=''hereby'' in wiktionary|date=19 June 2023 }}</ref>

==In popular culture==
* [[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"<ref>[[Douglas Hofstadter|Hofstadter, Douglas]]. ''[[Gödel, Escher, Bach: An Eternal Golden Braid]]''. 20th-anniversary ed., 1999, p. 152. {{ISBN|0-465-02656-7}}</ref> 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 [[wiki]]s 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 "[[recursion|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.<ref>{{Cite web |url=https://data.nesfa.org/Recursion/index.htm |work=New England Science Fiction Association |title=Recursive Science Fiction |date= 3 August 2008}}</ref>

==In law==
Several constitutions contain self-referential clauses defining how the constitution itself may be amended.<ref>{{Cite book|last=Hart|first=H. L. A.|url=http://www.oxfordscholarship.com/view/10.1093/acprof:oso/9780198253884.001.0001/acprof-9780198253884|title=Essays in Jurisprudence and Philosophy|date=1983-11-24|publisher=Oxford University Press|isbn=978-0-19-825388-4|pages=170–178|chapter=Self-referring Laws|doi=10.1093/acprof:oso/9780198253884.003.0008}}</ref> An example is [[Article Five of the United States Constitution]].

==See also==<!--***PLEASE NOTE*** Do not post a link to this article, i.e. "Self-reference", in the "See also" section, it will be removed.--->
<!-- Why not? -->
{{columns-list|
* {{annotated link|Autopoesis}}
* {{annotated link|Circular reference}}
* {{annotated link|Droste effect}}

* {{annotated link|Fourth wall}}
* {{annotated link|List of self–referential paradoxes}}
* {{annotated link|Lucid dreaming}} – A dream during which the dreamer is aware that they are dreaming
* {{annotated link|Meta-joke}}
* {{annotated link|Mise en abyme}}
* {{annotated link|Pleonasm#Bilingual tautological expressions|Bilingual tautological expressions}}
* {{annotated link|Recursion}}
* {{annotated link|Recursive acronym}}
* {{annotated link|Quine (computing)}}
* {{annotated link|Strange loop}}
* {{annotated link|this (computer programming)}}
* {{annotated link|Use–mention distinction}}
* {{annotated link|Vertiginous question}}
}}

==References==
{{reflist}}

==Sources==
* Bartlett, Steven J. [James] (Ed.) (1992). ''Reflexivity: A Source-book in Self-reference''. Amsterdam, North-Holland. [http://repub.eur.nl/pub/78707 (PDF). RePub, Erasmus University]
* [[Douglas Hofstadter|Hofstadter, D. R.]] (1980). ''[[Gödel, Escher, Bach: an Eternal Golden Braid]]''. New York, [[Vintage Books]].
* [[Raymond Smullyan|Smullyan, Raymond]] (1994), ''Diagonalization and Self-Reference'', Oxford Science Publications, {{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, {{ISBN|978-1-876949-60-0}}

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[[Category:Self-reference| ]]
[[Category:Grammar]]
[[Category:Theory of computation]]
[[Category:Logic]]
[[Category:Philosophy of language]]