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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Self-reference</span></span>

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<p><b>Self-reference</b> is a concept that involves referring to oneself or one's own attributes, characteristics, or actions. It can occur in <a href="Language" title="Language">language</a>, <a href="Logic" title="Logic">logic</a>, <a href="Mathematics" title="Mathematics">mathematics</a>, <a href="Philosophy" title="Philosophy">philosophy</a>, and other fields.

</p><p>In <a href="Natural_language" title="Natural language">natural</a> or <a href="Formal_language" title="Formal language">formal languages</a>, self-reference occurs when a <a href="Sentence_(linguistics)" title="Sentence (linguistics)">sentence</a>, idea or <a href="Well-formed_formula" title="Well-formed formula">formula</a> refers to itself. The reference may be expressed either directly—through some intermediate sentence or formula—or by means of some <a href="Semantics_encoding" title="Semantics encoding">encoding</a>.

</p><p>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 <a href="I_(pronoun)" title="I (pronoun)">"I"</a> in English.

</p><p>Self-reference is studied and has applications in mathematics, philosophy, <a href="Computer_programming" title="Computer programming">computer programming</a>, <a href="Second-order_cybernetics" title="Second-order cybernetics">second-order cybernetics</a>, and <a href="Linguistics" title="Linguistics">linguistics</a>, as well as <a href="Self-referential_humor" title="Self-referential humor">in humor</a>. Self-referential statements are sometimes <a href="Paradox" title="Paradox">paradoxical</a>, and can also be considered <a href="Recursion" title="Recursion">recursive</a>.

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<div class="mw-heading mw-heading2"><h2 id="In_logic,_mathematics_and_computing">In logic, mathematics and computing</h2></div>

<p>In classical <a href="Philosophy" title="Philosophy">philosophy</a>, <a href="Paradoxes" class="mw-redirect" title="Paradoxes">paradoxes</a> were created by self-referential concepts such as the <a href="Omnipotence_paradox" title="Omnipotence paradox">omnipotence paradox</a> 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 <a href="Epimenides_paradox" title="Epimenides paradox">Epimenides paradox</a>, '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.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>

</p><p>In <a href="Mathematics" title="Mathematics">mathematics</a> and <a href="Computability_theory" title="Computability theory">computability theory</a>, self-reference (also known as <a href="Impredicativity" title="Impredicativity">impredicativity</a>) is the key concept in proving limitations of many systems. <a href="G%C3%B6del's_incompleteness_theorems" title="Gödel's incompleteness theorems">Gödel's theorem</a> uses it to show that no formal <a href="Consistency" title="Consistency">consistent</a> system of mathematics can ever contain all possible mathematical truths, because it cannot prove some truths about its own structure. <a href="The_halting_problem" class="mw-redirect" title="The halting problem">The halting problem</a> 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 <a href="Russell's_paradox" title="Russell's paradox">Russell's paradox</a> and <a href="Berry's_paradox" class="mw-redirect" title="Berry's paradox">Berry's paradox</a>, and ultimately to classical philosophical paradoxes.

</p><p>In <a href="Game_theory" title="Game theory">game theory</a>, undefined behaviors can occur where two players must model each other's mental states and behaviors, leading to infinite regress.

</p><p>In <a href="Computer_programming" title="Computer programming">computer programming</a>, self-reference occurs in <a href="Reflection_(computer_science)" class="mw-redirect" title="Reflection (computer science)">reflection</a>, where a program can read or modify its own instructions like any other data.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> Numerous programming languages support reflection to some extent with varying degrees of expressiveness. Additionally, self-reference is seen in <a href="Recursion" title="Recursion">recursion</a> (related to the mathematical <a href="Recurrence_relation" title="Recurrence relation">recurrence relation</a>) in <a href="Functional_programming" title="Functional programming">functional programming</a>, where a code structure refers back to itself during computation.<sup id="cite_ref-Drucker2008_4-0" class="reference"><a href="#cite_note-Drucker2008-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> 'Taming' self-reference from potentially paradoxical concepts into well-behaved recursions has been one of the great successes of <a href="Computer_science" title="Computer science">computer science</a>, and is now used routinely in, for example, writing <a href="Compilers" class="mw-redirect" title="Compilers">compilers</a> using the 'meta-language' <a href="ML_(programming_language)" title="ML (programming language)">ML</a>. Using a compiler to compile itself is known as <a href="Bootstrapping_(compilers)" title="Bootstrapping (compilers)">bootstrapping</a>. <a href="Self-modifying_code" title="Self-modifying code">Self-modifying code</a> is possible to write (programs which operate on themselves), both with <a href="Assembly_language" title="Assembly language">assembler</a> and with functional languages such as <a href="Lisp_(programming_language)" title="Lisp (programming language)">Lisp</a>, but is generally discouraged in real-world programming. Computing hardware makes fundamental use of self-reference in <a href="Flip-flop_(electronics)" title="Flip-flop (electronics)">flip-flops</a>, 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 <a href="GNU" title="GNU">GNU</a> ('GNU's not Unix') and <a href="Pine_(email_client)" title="Pine (email client)">PINE</a> ('Pine is not Elm'). The <a href="GNU_Hurd" title="GNU Hurd">GNU Hurd</a> is named for a pair of mutually self-referential acronyms.

</p><p><a href="Tupper's_self-referential_formula" title="Tupper's self-referential formula">Tupper's self-referential formula</a> is a mathematical curiosity which plots an image of its own formula.

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<p>Self-reference occurs in <a href="Literature" title="Literature">literature</a> and <a href="Film" title="Film">film</a> when an author refers to his or her own work in the context of the work itself. Examples include <a href="Miguel_de_Cervantes" title="Miguel de Cervantes">Miguel de Cervantes</a>' <i><a href="Don_Quixote" title="Don Quixote">Don Quixote</a></i>, <a href="Shakespeare" class="mw-redirect" title="Shakespeare">Shakespeare</a>'s <i><a href="A_Midsummer_Night's_Dream" title="A Midsummer Night's Dream">A Midsummer Night's Dream</a></i>, <i><a href="The_Tempest" title="The Tempest">The Tempest</a></i> and <i><a href="Twelfth_Night" title="Twelfth Night">Twelfth Night</a></i>, <a href="Denis_Diderot" title="Denis Diderot">Denis Diderot</a>'s <i><a href="Jacques_le_fataliste_et_son_ma%C3%AEtre" class="mw-redirect" title="Jacques le fataliste et son maître">Jacques le fataliste et son maître</a></i>, <a href="Italo_Calvino" title="Italo Calvino">Italo Calvino</a>'s <i><a href="If_on_a_winter's_night_a_traveler" title="If on a winter's night a traveler">If on a winter's night a traveler</a></i>, many stories by <a href="Nikolai_Gogol" title="Nikolai Gogol">Nikolai Gogol</a>, <i><a href="Lost_in_the_Funhouse" title="Lost in the Funhouse">Lost in the Funhouse</a></i> by <a href="John_Barth" title="John Barth">John Barth</a>, <a href="Luigi_Pirandello" title="Luigi Pirandello">Luigi Pirandello</a>'s <i><a href="Six_Characters_in_Search_of_an_Author" title="Six Characters in Search of an Author">Six Characters in Search of an Author</a></i>, <a href="Federico_Fellini" title="Federico Fellini">Federico Fellini</a>'s <i><a href="8%C2%BD" title="8½">8½</a></i> and <a href="Bryan_Forbes" title="Bryan Forbes">Bryan Forbes</a>'s <i><a href="The_L-Shaped_Room" title="The L-Shaped Room">The L-Shaped Room</a></i>. Speculative fiction writer <a href="Samuel_R._Delany" title="Samuel R. Delany">Samuel R. Delany</a> makes use of this in his novels <i><a href="Nova_(novel)" title="Nova (novel)">Nova</a></i> and <i><a href="Dhalgren" title="Dhalgren">Dhalgren</a></i>. In the former, Katin (a space-faring novelist) is wary of a long-standing curse wherein a novelist dies before completing any given work. <i>Nova</i> ends mid-sentence, thus lending credence to the curse and the realization that the novelist is the author of the story; likewise, throughout <i>Dhalgren</i>, 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 <i><a href="Spaceballs" title="Spaceballs">Spaceballs</a></i>, Director <a href="Mel_Brooks" title="Mel Brooks">Mel Brooks</a> 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 <a href="Homer" title="Homer">Homer</a>'s <i><a href="Iliad" title="Iliad">Iliad</a></i>, where <a href="Helen_of_Troy" title="Helen of Troy">Helen of Troy</a> laments: "for generations still unborn/we will live in song" (appearing in the song itself).<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup>

</p><p>Self-reference in art is closely related to the concepts of <a href="Fourth_wall" title="Fourth wall">breaking the fourth wall</a> and <a href="Meta-reference" title="Meta-reference">meta-reference</a>, which often involve self-reference. The short stories of <a href="Jorge_Luis_Borges" title="Jorge Luis Borges">Jorge Luis Borges</a> play with self-reference and related paradoxes in many ways. <a href="Samuel_Beckett" title="Samuel Beckett">Samuel Beckett</a>'s <i><a href="Krapp's_Last_Tape" title="Krapp's Last Tape">Krapp's Last Tape</a></i> 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 <a href="Charlie_Kaufman" title="Charlie Kaufman">Charlie Kaufman</a>'s films <i><a href="Being_John_Malkovich" title="Being John Malkovich">Being John Malkovich</a></i> and <i><a href="Adaptation_(film)" title="Adaptation (film)">Adaptation</a></i>, the latter pushing the concept arguably to its breaking point as it attempts to portray its own creation, in a <a href="Story_within_a_story#Fractal_Fiction" title="Story within a story">dramatized version</a> of the <a href="Droste_effect" title="Droste effect">Droste effect</a>.

</p><p>Various <a href="Creation_myths" class="mw-redirect" title="Creation myths">creation myths</a> invoke self-reference to solve the problem of what created the creator. For example, the <a href="Egyptian_creation_myth" class="mw-redirect" title="Egyptian creation myth">Egyptian creation myth</a> has a god swallowing his own semen to create himself. The <a href="Ouroboros" title="Ouroboros">Ouroboros</a> is a mythical dragon which eats itself.

</p><p>The <a href="Quran" title="Quran">Quran</a> includes numerous instances of self-referentiality.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup>

</p><p>The <a href="Surrealist" class="mw-redirect" title="Surrealist">surrealist</a> painter <a href="Ren%C3%A9_Magritte" title="René Magritte">René Magritte</a> is famous for his self-referential works. His painting <i><a href="The_Treachery_of_Images" title="The Treachery of Images">The Treachery of Images</a></i>, includes the words "this is not a pipe", the truth of which depends entirely on whether the word <i>ceci</i> (in English, "this") refers to the pipe depicted—or to the painting or the word or sentence itself.<sup id="cite_ref-NöthBishara2007_8-0" class="reference"><a href="#cite_note-NöthBishara2007-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> <a href="M.C._Escher" class="mw-redirect" title="M.C. Escher">M.C. Escher</a>'s art also contains many self-referential concepts such as hands drawing themselves.

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<div class="mw-heading mw-heading2"><h2 id="In_language">In language</h2></div>

<p>A word that describes itself is called an <i><a href="Autological_word" title="Autological word">autological word</a></i> (or <i>autonym</i>). This generally applies to adjectives, for example <a href="https://en.wiktionary.org/wiki/sesquipedalian" class="extiw external" title="wikt:sesquipedalian">sesquipedalian</a> (i.e. "sesquipedalian" is a sesquipedalian word), but can also apply to other parts of speech, such as <a href="https://en.wiktionary.org/wiki/TLA" class="extiw external" title="wikt:TLA">TLA</a>, as a three-letter <a href="Abbreviation" title="Abbreviation">abbreviation</a> for "<a href="Three-letter_abbreviation" class="mw-redirect" title="Three-letter abbreviation">three-letter abbreviation</a>".

</p><p>A sentence which inventories its own letters and punctuation marks is called an <a href="Autogram" title="Autogram">autogram</a>.

</p><p>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 <a href="Liar_paradox" title="Liar paradox">paradox</a>. Such sentences can lead to problems, for example, in law, where statements bringing laws into existence can contradict one another or themselves. <a href="Kurt_G%C3%B6del" title="Kurt Gödel">Kurt Gödel</a> claimed to have found such a <a href="G%C3%B6del's_Loophole" title="Gödel's Loophole">loophole</a> in the <a href="United_States_Constitution" class="mw-redirect" title="United States Constitution">United States Constitution</a> at his citizenship ceremony.

</p><p>Self-reference occasionally occurs in the <a href="Broadcast_media" class="mw-redirect" title="Broadcast media">media</a> when it is required to write about itself, for example the <a href="BBC" title="BBC">BBC</a> reporting on job cuts at the BBC. Notable encyclopedias may be required to feature articles about themselves, such as Wikipedia's article on <a href="Wikipedia" title="Wikipedia">Wikipedia</a>.

</p><p><a href="Fumblerules" title="Fumblerules">Fumblerules</a> 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 <a href="William_Safire" title="William Safire">William Safire</a>.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup>

</p><p><a href="Circular_definition" title="Circular definition">Circular definition</a> 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 <a href="Fallacy" title="Fallacy">fallacious</a> because they only define a term in terms of itself.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> This type of self-reference may be useful in <a href="Argumentation" class="mw-redirect" title="Argumentation">argumentation</a>, but can result in a lack of clarity in communication.

</p><p>The adverb "hereby" is used in a self-referential way, for example in the statement "I hereby declare you husband and wife."<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup>

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<div class="mw-heading mw-heading2"><h2 id="In_popular_culture">In popular culture</h2></div>

<ul><li><a href="Douglas_Hofstadter" title="Douglas Hofstadter">Douglas Hofstadter</a>'s books, especially <i><a href="Metamagical_Themas" title="Metamagical Themas">Metamagical Themas</a></i> and <i><a href="G%C3%B6del%2C_Escher%2C_Bach" title="Gödel, Escher, Bach">Gödel, Escher, Bach</a></i>, play with many self-referential concepts and were highly influential in bringing them into mainstream intellectual culture during the 1980s. <a href="Hofstadter's_law" title="Hofstadter's law">Hofstadter's law</a>, which specifies that "It always takes longer than you expect, even when you take into account Hofstadter's Law"<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> 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 <a href="Wiki" title="Wiki">wikis</a> and other technologies. Hofstadter's '<a href="Strange_loop" title="Strange loop">strange loop</a>' <a href="Metaphysics" title="Metaphysics">metaphysics</a> attempts to map <a href="Consciousness" title="Consciousness">consciousness</a> onto self-reference, but is a minority position in <a href="Philosophy_of_mind" title="Philosophy of mind">philosophy of mind</a>.</li>

<li>The subgenre of "<a href="Recursion" title="Recursion">recursive</a> <a href="Science_fiction" title="Science fiction">science fiction</a>" or <a href="Metafiction" title="Metafiction">metafiction</a> is now so extensive that it has fostered a fan-maintained bibliography at the <a href="New_England_Science_Fiction_Association" title="New England Science Fiction Association">New England Science Fiction Association</a>'s website; some of it is about <a href="Science-fiction_fandom" class="mw-redirect" title="Science-fiction fandom">science-fiction fandom</a>, some about science fiction and its authors.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup></li></ul>

<p>Several constitutions contain self-referential clauses defining how the constitution itself may be amended.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> An example is <a href="Article_Five_of_the_United_States_Constitution" title="Article Five of the United States Constitution">Article Five of the United States Constitution</a>.

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<ul><li><a href="Autopoesis" class="mw-redirect" title="Autopoesis">Autopoesis</a> – System capable of producing itself<span style="display:none" class="category-annotation-with-redirected-description">Pages displaying short descriptions of redirect targets</span></li>

<li><a href="Circular_reference" title="Circular reference">Circular reference</a> – Series of references where the last object references the first</li>

<li><a href="Droste_effect" title="Droste effect">Droste effect</a> – Recursive visual effect</li></ul>

<ul><li><a href="Fourth_wall" title="Fourth wall">Fourth wall</a> – Separation of performers and audience</li>

<li><a href="List_of_self%E2%80%93referential_paradoxes" class="mw-redirect" title="List of self–referential paradoxes">List of self–referential paradoxes</a> – List of statements that appear to contradict themselves<span style="display:none" class="category-annotation-with-redirected-description">Pages displaying short descriptions of redirect targets</span></li>

<li><a href="Lucid_dreaming" class="mw-redirect" title="Lucid dreaming">Lucid dreaming</a> – Dream where one is aware that one is dreaming<span style="display:none" class="category-annotation-with-redirected-description">Pages displaying short descriptions of redirect targets</span> – A dream during which the dreamer is aware that they are dreaming</li>

<li><a href="Meta-joke" class="mw-redirect" title="Meta-joke">Meta-joke</a> – Humor that alludes to itself<span style="display:none" class="category-annotation-with-redirected-description">Pages displaying short descriptions of redirect targets</span></li>

<li><a href="Mise_en_abyme" title="Mise en abyme">Mise en abyme</a> – Technique of placing a copy of an image within itself, or a story within a story</li>

<li><a href="Pleonasm#Bilingual_tautological_expressions" title="Pleonasm">Bilingual tautological expressions</a> – Redundancy in linguistic expression</li>

<li><a href="Recursion" title="Recursion">Recursion</a> – Process of repeating items in a self-similar way</li>

<li><a href="Recursive_acronym" title="Recursive acronym">Recursive acronym</a> – Acronym whose expansion includes a copy of itself</li>

<li><a href="Quine_(computing)" title="Quine (computing)">Quine (computing)</a> – Self-replicating program</li>

<li><a href="Strange_loop" title="Strange loop">Strange loop</a> – Cyclic structure that goes through several levels in a hierarchical system</li>

<li><a href="This_(computer_programming)" title="This (computer programming)">this (computer programming)</a> – In programming languages, the object or class the currently running code belongs to</li>

<li><a href="Use%E2%80%93mention_distinction" title="Use–mention distinction">Use–mention distinction</a> – Distinction between using a word and mentioning it</li>

<li><a href="Vertiginous_question" title="Vertiginous question">Vertiginous question</a> – Philosophical argument by Benj Hellie</li></ul></div>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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</style><cite id="CITEREFSoto-AndradeJaramilloGutierrezLetelier" class="citation web cs1">Soto-Andrade, Jorge; Jaramillo, Sebastian; Gutierrez, Claudio; Letelier, Juan-Carlos. <a rel="nofollow" class="external text" href="https://mitpress.mit.edu/sites/default/files/titles/alife/0262297140chap115.pdf">"Ouroboros avatars: A mathematical exploration of Self-reference and Metabolic Closure"</a> <span class="cs1-format">(PDF)</span>. MIT Press<span class="reference-accessdate">. Retrieved <span class="nowrap">16 May</span> 2015</span>.</cite></span>

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<li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><cite class="citation book cs1"><a rel="nofollow" class="external text" href="https://plato.stanford.edu/entries/liar-paradox/"><i></i>Liar Paradox<i></i></a>. Metaphysics Research Lab, Stanford University. 2020.</cite></span>

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<div class="mw-heading mw-heading2"><h2 id="Sources">Sources</h2></div>

<ul><li>Bartlett, Steven J. [James] (Ed.) (1992). <i>Reflexivity: A Source-book in Self-reference</i>. Amsterdam, North-Holland. <a rel="nofollow" class="external text" href="http://repub.eur.nl/pub/78707">(PDF). RePub, Erasmus University</a></li>

<li><a href="Douglas_Hofstadter" title="Douglas Hofstadter">Hofstadter, D. R.</a> (1980). <i><a href="G%C3%B6del%2C_Escher%2C_Bach%3A_an_Eternal_Golden_Braid" class="mw-redirect" title="Gödel, Escher, Bach: an Eternal Golden Braid">Gödel, Escher, Bach: an Eternal Golden Braid</a></i>. New York, <a href="Vintage_Books" title="Vintage Books">Vintage Books</a>.</li>

<li><a href="Raymond_Smullyan" title="Raymond Smullyan">Smullyan, Raymond</a> (1994), <i>Diagonalization and Self-Reference</i>, Oxford Science Publications, <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-19-853450-7</bdi></li>

<li>Crabtree, Jonathan J. (2016), <i>The Lost Logic of Elementary Mathematics and the Haberdasher who Kidnapped Kaizen</i>, Proceedings of the Mathematical Association of Victoria (MAV) Annual Conference, 53, 98–106, <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-1-876949-60-0</bdi></li></ul>

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