natural
Nature, in the broadest sense, is the physical world or universe. "Nature" can refer to the phenomena of the physical world, and also to life in general. The study of nature is a large, if not the only, part of science. Although humans are ...
or
formal language
In logic, mathematics, computer science, and linguistics, a formal language consists of words whose letters are taken from an alphabet and are well-formed according to a specific set of rules.
The alphabet of a formal language consists of sy ...
s 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 communications and information processing, code is a system of rules to convert information—such as a letter, word, sound, image, or gesture—into another form, sometimes shortened or secret, for communication through a communication ...
. 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 is studied and has applications in mathematics, philosophy,
computer programming
Computer programming is the process of performing a particular computation (or more generally, accomplishing a specific computing result), usually by designing and building an executable computer program. Programming involves tasks such as anal ...
,
second-order cybernetics
Second-order cybernetics, also known as the cybernetics of cybernetics, is the recursive application of cybernetics to itself and the reflexive practice of cybernetics according to such a critique. It is cybernetics where "the role of the observer ...
, and
linguistics
Linguistics is the science, scientific study of human language. It is called a scientific study because it entails a comprehensive, systematic, objective, and precise analysis of all aspects of language, particularly its nature and structure ...
, as well as in humor. Self-referential statements are sometimes
paradox
A paradox is a logically self-contradictory statement or a statement that runs contrary to one's expectation. It is a statement that, despite apparently valid reasoning from true premises, leads to a seemingly self-contradictory or a logically u ...
ical, and can also be considered
recursive
Recursion (adjective: ''recursive'') occurs when a thing is defined in terms of itself or of its type. Recursion is used in a variety of disciplines ranging from linguistics to logic. The most common application of recursion is in mathematics ...
paradoxes
A paradox is a logically self-contradictory statement or a statement that runs contrary to one's expectation. It is a statement that, despite apparently valid reasoning from true premises, leads to a seemingly self-contradictory or a logically u ...
were created by self-referential concepts such as the
omnipotence paradox
The omnipotence paradox is a family of paradoxes that arise with some understandings of the term ''omnipotent''. The paradox arises, for example, if one assumes that an omnipotent being has no limits and is capable of realizing any outcome, e ...
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
The Epimenides paradox reveals a problem with self-reference in logic. It is named after the Cretan philosopher Epimenides of Knossos (alive circa 600 BC) who is credited with the original statement. A typical description of the problem is giv ...
, '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 mathematics and computability theory, self-reference (also known as
impredicativity
In mathematics, logic and philosophy of mathematics, something that is impredicative is a self-referencing definition. Roughly speaking, a definition is impredicative if it invokes (mentions or quantifies over) the set being defined, or (more com ...
) is the key concept in proving limitations of many systems. Gödel's theorem uses it to show that no formal
consistent
In classical deductive logic, a consistent theory is one that does not lead to a logical contradiction. The lack of contradiction can be defined in either semantic or syntactic terms. The semantic definition states that a theory is consistent ...
system of mathematics can ever contain all possible mathematical truths, because it cannot prove some truths about its own structure.
The halting problem
In computability theory, the halting problem is the problem of determining, from a description of an arbitrary computer program and an input, whether the program will finish running, or continue to run forever. Alan Turing proved in 1936 that 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
Russell's paradox
In mathematical logic, Russell's paradox (also known as Russell's antinomy) is a set-theoretic paradox discovered by the British philosopher and mathematician Bertrand Russell in 1901. Russell's paradox shows that every set theory that contains ...
and
Berry's paradox
The Berry paradox is a self-referential paradox arising from an expression like "The smallest positive integer not definable in under sixty letters" (a phrase with fifty-seven letters).
Bertrand Russell, the first to discuss the paradox in print, ...
, 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
Computer programming is the process of performing a particular computation (or more generally, accomplishing a specific computing result), usually by designing and building an executable computer program. Programming involves tasks such as anal ...
, self-reference occurs in
reflection Reflection or reflexion may refer to:
Science and technology
* Reflection (physics), a common wave phenomenon
** Specular reflection, reflection from a smooth surface
*** Mirror image, a reflection in a mirror or in water
** Signal reflection, in ...
, 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
Recursion (adjective: ''recursive'') occurs when a thing is defined in terms of itself or of its type. Recursion is used in a variety of disciplines ranging from linguistics to logic. The most common application of recursion is in mathemati ...
(related to the mathematical
recurrence relation
In mathematics, a recurrence relation is an equation according to which the nth term of a sequence of numbers is equal to some combination of the previous terms. Often, only k previous terms of the sequence appear in the equation, for a parameter ...
) in
functional programming
In computer science, functional programming is a programming paradigm where programs are constructed by applying and composing functions. It is a declarative programming paradigm in which function definitions are trees of expressions that ...
, 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
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to practical disciplines (includi ...
, and is now used routinely in, for example, writing
compilers
In computing, a compiler is a computer program that translates computer code written in one programming language (the ''source'' language) into another language (the ''target'' language). The name "compiler" is primarily used for programs that ...
using the 'meta-language' ML. Using a compiler to compile itself is known as
bootstrapping
In general, bootstrapping usually refers to a self-starting process that is supposed to continue or grow without external input.
Etymology
Tall boots may have a tab, loop or handle at the top known as a bootstrap, allowing one to use fingers ...
.
Self-modifying code
In computer science, self-modifying code (SMC) is code that alters its own instructions while it is executing – usually to reduce the instruction path length and improve performance or simply to reduce otherwise repetitively similar code, ...
is possible to write (programs which operate on themselves), both with
assembler
Assembler may refer to:
Arts and media
* Nobukazu Takemura, avant-garde electronic musician, stage name Assembler
* Assemblers, a fictional race in the ''Star Wars'' universe
* Assemblers, an alternative name of the superhero group Champions of ...
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
Flip-flops are a type of light sandal, typically worn as a form of casual footwear. They consist of a flat sole held loosely on the foot by a Y-shaped strap known as a toe thong that passes between the first and second toes and around both side ...
, 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 () is an extensive collection of free software (383 packages as of January 2022), which can be used as an operating system or can be used in parts with other operating systems. The use of the completed GNU tools led to the family of operat ...
('GNU's not Unix') and
PINE
A pine is any conifer tree or shrub in the genus ''Pinus'' () of the family Pinaceae. ''Pinus'' is the sole genus in the subfamily Pinoideae. The World Flora Online created by the Royal Botanic Gardens, Kew and Missouri Botanical Garden accepts ...
('Pine is not Elm'). The
GNU Hurd
GNU Hurd is a collection of microkernel servers written as part of GNU, for the GNU Mach microkernel. It has been under development since 1990 by the GNU Project of the Free Software Foundation, designed as a replacement for the Unix kernel, and ...
is named for a pair of mutually self-referential acronyms.
Tupper's self-referential formula
Tupper's self-referential formula is a formula that visually represents itself when graphed at a specific location in the (''x'', ''y'') plane.
History
The formula was defined by Jeff Tupper and appears as an example in Tupper's 2001 SIGGRAP ...
is a mathematical curiosity which plots an image of its own formula.
In biology
The biology of
self-replication
Self-replication is any behavior of a dynamical system that yields construction of an identical or similar copy of itself. Biological cells, given suitable environments, reproduce by cell division. During cell division, DNA is replicated and c ...
is self-referential, as embodied by DNA and RNA replication mechanisms. Models of self-replication are found in
Conway's Game of Life
The Game of Life, also known simply as Life, is a cellular automaton devised by the British mathematician John Horton Conway in 1970. It is a zero-player game, meaning that its evolution is determined by its initial state, requiring no furthe ...
and have inspired engineering systems such as the self-replicating 3D printer
RepRap
The RepRap project started in England in 2005 as a University of Bath initiative to develop a low-cost 3D printer that can print most of its own components, but it is now made up of hundreds of collaborators worldwide. RepRap is short for rep''li ...
.
In art
Self-reference occurs in
literature
Literature is any collection of written work, but it is also used more narrowly for writings specifically considered to be an art form, especially prose fiction, drama, and poetry. In recent centuries, the definition has expanded to include ...
and film when an author refers to his or her own work in the context of the work itself. Examples include
Miguel de Cervantes
Miguel de Cervantes Saavedra (; 29 September 1547 (assumed) – 22 April 1616 NS) was an Early Modern Spanish writer widely regarded as the greatest writer in the Spanish language and one of the world's pre-eminent novelists. He is best kno ...
' ''
Don Quixote
is a Spanish epic novel by Miguel de Cervantes. Originally published in two parts, in 1605 and 1615, its full title is ''The Ingenious Gentleman Don Quixote of La Mancha'' or, in Spanish, (changing in Part 2 to ). A founding work of West ...
'',
Shakespeare
William Shakespeare ( 26 April 1564 – 23 April 1616) was an English playwright, poet and actor. He is widely regarded as the greatest writer in the English language and the world's pre-eminent dramatist. He is often called England's natio ...
Twelfth Night
''Twelfth Night'', or ''What You Will'' is a romantic comedy by William Shakespeare, believed to have been written around 1601–1602 as a Twelfth Night's entertainment for the close of the Christmas season. The play centres on the twins Vi ...
'',
Denis Diderot
Denis Diderot (; ; 5 October 171331 July 1784) was a French philosopher, art critic, and writer, best known for serving as co-founder, chief editor, and contributor to the '' Encyclopédie'' along with Jean le Rond d'Alembert. He was a promi ...
's ''
Jacques le fataliste et son maître
''Jacques the Fatalist and his Master'' (french: Jacques le fataliste et son maître) is a novel by Denis Diderot, written during the period 1765–1780. The first French edition was published posthumously in 1796, but it was known earlier in Germ ...
'',
Italo Calvino
Italo Calvino (, also , ;. RAI (circa 1970), retrieved 25 October 2012. 15 October 1923 – 19 September 1985) was an Italian writer and journalist. His best known works include the '' Our Ancestors'' trilogy (1952–1959), the ''Cosmicomi ...
's ''
If on a winter's night a traveler
''If on a winter's night a traveler'' ( it, Se una notte d'inverno un viaggiatore) is a 1979 novel by the Italian writer Italo Calvino. The postmodernist narrative, in the form of a frame story, is about the reader trying to read a book called ...
Lost in the Funhouse
''Lost in the Funhouse'' (1968) is a short story collection by American author John Barth. The postmodern stories are extremely self-conscious and self-reflexive and are considered to exemplify metafiction.
Though Barth's reputation rests mainly ...
'' by
John Barth
John Simmons Barth (; born May 27, 1930) is an American writer who is best known for his postmodern and metafictional fiction. His most highly regarded and influential works were published in the 1960s, and include ''The Sot-Weed Factor'', a sa ...
,
Luigi Pirandello
Luigi Pirandello (; 28 June 1867 – 10 December 1936) was an Italian dramatist, novelist, poet, and short story writer whose greatest contributions were his plays. He was awarded the 1934 Nobel Prize in Literature for "his almost magical power ...
's ''
Six Characters in Search of an Author
''Six Characters in Search of an Author'' ( it, Sei personaggi in cerca d'autore, link=no ) is an Italian play by Luigi Pirandello, written and first performed in 1921. An absurdist fiction, absurdist metatheatrical, metatheatric play about th ...
8½
' (Italian title: , ) is a 1963 surrealist comedy-drama film directed and co-written (with Tullio Pinelli, Ennio Flaiano and Brunello Rondi) by Italian filmmaker Federico Fellini. The metafictional narrative centers on Guido Anselmi, played by M ...
'' and
Bryan Forbes
Bryan Forbes CBE (; born John Theobald Clarke; 22 July 1926 – 8 May 2013) was an English film director, screenwriter, film producer, actor and novelist described as a "Renaissance man"Falk Q. . BAFTA. 17 October 2007. Retrieved 9 May 2013 and ...
's ''
The L-Shaped Room
''The L-Shaped Room'' is a 1962 British film directed by Bryan Forbes, based on the 1960 novel of the same name by Lynne Reid Banks. It tells the story of Jane Fosset ( Leslie Caron), a young French woman, unmarried and pregnant, who moves in ...
''. Speculative fiction writer
Samuel R. Delany
Samuel R. "Chip" Delany (, ) (born April 1, 1942), is an American author and literary critic. His work includes fiction (especially science fiction), memoir, criticism, and essays (on science fiction, literature, sexuality, and society). His ...
Dhalgren
''Dhalgren'' is a 1975 science fiction novel by American writer Samuel R. Delany. It features an extended trip to and through Bellona, a fictional city in the American Midwest cut off from the rest of the world by an unknown catastrophe.
Plot ...
''. 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
''Dhalgren'' is a 1975 science fiction novel by American writer Samuel R. Delany. It features an extended trip to and through Bellona, a fictional city in the American Midwest cut off from the rest of the world by an unknown catastrophe.
Plot ...
, 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
Mel Brooks (born Melvin James Kaminsky; June 28, 1926) is an American actor, comedian and filmmaker. With a career spanning over seven decades, he is known as a writer and director of a variety of successful broad farces and parodies. He began ...
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
Homer (; grc, Ὅμηρος , ''Hómēros'') (born ) was a Greek poet who is credited as the author of the ''Iliad'' and the ''Odyssey'', two epic poems that are foundational works of ancient Greek literature. Homer is considered one of the ...
's ''
Iliad
The ''Iliad'' (; grc, Ἰλιάς, Iliás, ; "a poem about Ilium") is one of two major ancient Greek epic poems attributed to Homer. It is one of the oldest extant works of literature still widely read by modern audiences. As with the '' Odys ...
'', where Helen of Troy laments: "for generations still unborn/we will live in song" (appearing in the song itself).
Self-reference in art is closely related to the concepts of breaking the fourth wall and
meta-reference
Meta-reference is a special type of self-reference that can occur in all media or media artifacts, for instance literature, film, painting, TV series, comic strips, or video games. It includes all references to, or comments on, a specific medium, ...
, which often involve self-reference. The short stories of
Jorge Luis Borges
Jorge Francisco Isidoro Luis Borges Acevedo (; ; 24 August 1899 – 14 June 1986) was an Argentine short-story writer, essayist, poet and translator, as well as a key figure in Spanish-language and international literature. His best-known b ...
play with self-reference and related paradoxes in many ways. Samuel Beckett's ''
Krapp's Last Tape
''Krapp's Last Tape'' is a 1958 one-act play, in English, by Samuel Beckett. With a cast of one man, it was written for Northern Irish actor Patrick Magee and first titled "Magee monologue". It was inspired by Beckett's experience of listenin ...
'' 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
Charles Stuart Kaufman (; born November 19, 1958) is an American filmmaker and novelist. He wrote the films '' Being John Malkovich'' (1999), '' Adaptation'' (2002), and '' Eternal Sunshine of the Spotless Mind'' (2004). He made his directorial ...
's films ''
Being John Malkovich
''Being John Malkovich'' is a 1999 American fantasy comedy film directed by Spike Jonze and written by Charlie Kaufman, both making their feature film debut. The film stars John Cusack, Cameron Diaz, and Catherine Keener, with 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.
Various
creation myths
A creation myth (or cosmogonic myth) is a symbolic narrative of how the world began and how people first came to inhabit it., "Creation myths are symbolic stories describing how the universe and its inhabitants came to be. Creation myths develop ...
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
The ouroboros or uroboros () is an ancient symbol depicting a serpent or dragon eating its own tail. The ouroboros entered Western tradition via ancient Egyptian iconography and the Greek magical tradition. It was adopted as a symbol in Gnost ...
is a mythical dragon which eats itself.
The
Quran
The Quran (, ; Standard Arabic: , Quranic Arabic: , , 'the recitation'), also romanized Qur'an or Koran, is the central religious text of Islam, believed by Muslims to be a revelation from God. It is organized in 114 chapters (pl.: , s ...
includes numerous instances of self-referentiality.
The
surrealist
Surrealism is a cultural movement that developed in Europe in the aftermath of World War I in which artists depicted unnerving, illogical scenes and developed techniques to allow the unconscious mind to express itself. Its aim was, according to ...
painter
René Magritte
René François Ghislain Magritte (; 21 November 1898 – 15 August 1967) was a Belgian surrealist artist known for his depictions of familiar objects in unfamiliar, unexpected contexts, which often provoked questions about the nature and bound ...
is famous for his self-referential works. His painting ''
The Treachery of Images
''The Treachery of Images'' (french: La Trahison des Images, link=no) is a 1929 painting by Belgian surrealist painter René Magritte. It is also known as ''This Is Not a Pipe'' and ''The Wind and the Song''. Magritte painted it when he was 30 ye ...
'', 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
Maurits Cornelis Escher (; 17 June 1898 – 27 March 1972) was a Dutch graphic artist who made Mathematics and art, mathematically inspired woodcuts, lithography, lithographs, and mezzotints.
Despite wide popular interest, Escher was for ...
'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
An autological word (also called homological word) is a word that expresses a property that it also possesses (e.g., "word" is a word, "noun" is a noun, "English" is an English word, " pentasyllabic" has five syllables, and "writable" is writab ...
'' (or ''
autonym
Autonym may refer to:
* Autonym, the name used by a person to refer to themselves or their language; see Exonym and endonym
* Autonym (botany), an automatically created infrageneric or infraspecific name
See also
* Nominotypical subspecies, in zo ...
''). This generally applies to adjectives, for example
ames
Ames may refer to:
Places United States
* Ames, Arkansas, a place in Arkansas
* Ames, Colorado
* Ames, Illinois
* Ames, Indiana
* Ames, Iowa, the most populous city bearing this name
* Ames, Kansas
* Ames, Nebraska
* Ames, New York
* Ames, Ok ...
Vintage Books
Vintage Books is a trade paperback publishing imprint of Penguin Random House originally established by Alfred A. Knopf in 1954. The company was purchased by Random House in April 1960, and a British division was set up in 1990. After Random ...
.
* 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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