Self-reference is a concept that involves referring to oneself or one's own attributes, characteristics, or actions. It can occur inlanguage,logic,mathematics,philosophy, and other fields.
Innatural orformal languages, self-reference occurs when asentence, idea orformula refers to itself. The reference may be expressed either directly—through some intermediate sentence or formula—or by means of someencoding.
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" in English.
Self-reference is studied and has applications in mathematics, philosophy,computer programming,second-order cybernetics, andlinguistics, as well asin humor. Self-referential statements are sometimesparadoxical, and can also be consideredrecursive.
Indirect self-reference describes an objectreferring to itself indirectly. For example, the "this sentence is false." contains a direct self-reference, in which the phrase "this sentence" refers directly to the sentence as a whole. An indirectly self-referential sentence would replace the phrase "this sentence" with an indirect reference; an expression that effectively still referred to the sentence, but did not use the pronoun "this."[2]
Indirect self-reference can be defined rigorously in terms of cycles in a graph of reference relationships.[3]
An example of this is thepostcard paradox, in which a sentence refers to another sentence which in turn references the original one.[2]
Indirect self-reference was studied in great depth byW. V. Quine and occupies a central place in the proof ofGödel's incompleteness theorem.[4]
In classicalphilosophy,paradoxes were created by self-referential concepts such as theomnipotence 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. TheEpimenides 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.[5]
Inmathematics andcomputability theory, self-reference (also known asimpredicativity) is the key concept in proving limitations of many systems.Gödel's theorem uses it to show that no formalconsistent 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 asRussell's paradox andBerry's paradox, and ultimately to classical philosophical paradoxes.
Ingame theory, undefined behaviors can occur where two players must model each other's mental states and behaviors, leading to infinite regress.
Incomputer programming, self-reference occurs inreflection, where a program can read or modify its own instructions like any other data.[6] Numerous programming languages support reflection to some extent with varying degrees of expressiveness. Additionally, self-reference is seen inrecursion (related to the mathematicalrecurrence relation) infunctional programming, where a code structure refers back to itself during computation.[7] 'Taming' self-reference from potentially paradoxical concepts into well-behaved recursions has been one of the great successes ofcomputer science, and is now used routinely in, for example, writingcompilers using the 'meta-language'ML. Using a compiler to compile itself is known asbootstrapping.Self-modifying code is possible to write (programs which operate on themselves), both withassembler and with functional languages such asLisp, but is generally discouraged in real-world programming. Computing hardware makes fundamental use of self-reference inflip-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 asGNU ('GNU's not Unix') andPINE ('Pine is not Elm'). TheGNU 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.
Self-reference in art is closely related to the concepts ofbreaking the fourth wall andmeta-reference, which often involve self-reference.
Self-reference occurs inliterature andfilm when an author refers to his or her own work in the context of the work itself. Examples includeMiguel de Cervantes'Don Quixote,Shakespeare'sA Midsummer Night's Dream,The Tempest andTwelfth Night,Denis Diderot'sJacques le fataliste et son maître,Italo Calvino'sIf on a winter's night a traveler, many stories byNikolai Gogol,Lost in the Funhouse byJohn Barth,Luigi Pirandello'sSix Characters in Search of an Author,Federico Fellini's8½ andBryan Forbes'sThe L-Shaped Room.
Speculative fiction writerSamuel R. Delany makes use of this in his novelsNova andDhalgren. 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, throughoutDhalgren, 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 filmSpaceballs, DirectorMel 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 inHomer'sIliad, whereHelen of Troy laments: "for generations still unborn/we will live in song" (appearing in the song itself).[8]
The short stories ofJorge Luis Borges play with self-reference and related paradoxes in many ways.Samuel Beckett'sKrapp'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 therubber reality movement, notably inCharlie Kaufman's filmsBeing John Malkovich andAdaptation, the latter pushing the concept arguably to its breaking point as it attempts to portray its own creation, in adramatized version of theDroste effect.
Thesurrealist painterRené Magritte is famous for his self-referential works. His paintingThe Treachery of Images, includes the words "this is not a pipe", the truth of which depends entirely on whether the wordceci (in English, "this") refers to the pipe depicted—or to the painting or the word or sentence itself.[9]M.C. Escher's art also contains many self-referential concepts such as hands drawing themselves.
Self-reference occasionally occurs in themedia when it is required to write about itself, for example theBBC reporting on job cuts at the BBC. Notable encyclopedias may be required to feature articles about themselves, such as Wikipedia's article onWikipedia.
Variouscreation myths invoke self-reference to solve the problem of what created the creator. For example, theEgyptian creation myth has a god swallowing his own semen to create himself. TheOuroboros is a mythical dragon which eats itself.
TheQuran includes numerous instances of self-referentiality.[12][13]
A word that describes itself is called anautological word (orautonym). This generally applies to adjectives, for examplesesquipedalian (i.e. "sesquipedalian" is a sesquipedalian word), but can also apply to other parts of speech, such asTLA, as a three-letterabbreviation for "three-letter abbreviation".
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 consideredfallacious because they only define a term in terms of itself.[14] This type of self-reference may be useful inargumentation, 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."[15]
A sentence which inventories its own letters and punctuation marks is called anautogram.
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-referentialparadox. 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 aloophole in theUnited States Constitution at his citizenship ceremony.
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 byWilliam Safire.[16][17]
Several constitutions contain self-referential clauses defining how the constitution itself may be amended.[18] An example isArticle Five of the United States Constitution.[19]
