For the Wikipedia guideline, please see Wikipedia:Avoid self-references.

The Ouroboros, a dragon that bites its tail, is a symbol for self-reference. The Ouroboros (Greek grc Ουροβόρος from grc ουροβόρος όφις "tail-devouring snake" also spelled Ourorboros, Oroborus, Uroboros

Self-reference is a phenomenon in natural or formal languages consisting of a sentence or formula referring to itself directly, or through some intermediate sentence or formula, or by means of some encoding. In the Philosophy of language, a natural language (or ordinary language) is a Language that is spoken or written in phonemic-alphabetic or phonemically-related A formal language is a set of words, ie finite strings of letters, or symbols. In Linguistics, a sentence is a grammatical unit of one or more words bearing minimal syntactic relation to the words that precede or follow it often preceded and followed In Mathematics and in the Sciences a formula (plural formulae, formulæ or formulas) is a concise way of expressing information A semantics encoding is a "translation" between Formal languages For programmers the most familiar form of encoding is the compilation of a programming language In philosophy, it also refers to the ability of a subject to speak of or refer to himself, herself, or itself: to have the kind of thought expressed in English by the word "I". Philosophy is the study of general problems concerning matters such as existence knowledge truth beauty justice validity mind and language I (aɪ is the first-person, singular Personal pronoun ( subject case) in Modern English.

Self-reference is possible when there are two logical levels, a level and a meta-level. It is most commonly used in mathematics, philosophy, computer programming, and linguistics. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and Philosophy is the study of general problems concerning matters such as existence knowledge truth beauty justice validity mind and language Linguistics is the scientific study of Language, encompassing a number of sub-fields Self-referential statements can lead to paradoxes (but see Antinomy for limits on the significance of these). A paradox is a true statement or group of statements that leads to a Contradiction or a situation which defies intuition; or inversely Antinomia redirects here For the Brachiopod Genus, see Antinomia (brachiopod.

Usage

An example of a self-referential situation is the one of autopoiesis, as the logical organization produces itself the physical structure which creates itself. Autopoiesis literally means "auto (self-creation" (from the Greek: auto αυτό for self- and poiesis ποίησις for creation or production

In metaphysics, self-reference is subjectivity, while "hetero-reference", as it is called (see Niklas Luhmann), is objectivity. Metaphysics is the branch of Philosophy investigating principles of reality transcending those of any particular science Subjectivity refers to a subject's perspective particularly feelings beliefs and desires Niklas Luhmann ( December 8, 1927 - November 6, 1998) was a German Sociologist, administration expert and a prominent

Self-reference also occurs in literature when an author refers to his work in the context of the work itself. Literature is the Art of written works Literally translated the word means "acquaintance with letters" (from Latin littera letter Famous examples include Cervantes's Don Quixote, 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, and Luigi Pirandello's Six Characters in Search of an Author. Miguel de Cervantes Saavedra ( in modern Spanish; September 29, 1547 &ndash April 22, 1616) was a Spanish Novelist es '''''Don Quixote''''' (, see spelling and pronunciation below fully titled es '''''El ingenioso hidalgo Don Quijote de la Mancha''''' ("The Ingenious Hidalgo Don Denis Diderot ( October 5, 1713 – July 31, 1784) was a French Philosopher and writer Jacques the Fatalist and his Master (Jacques le fataliste et son maître is a Novel by Denis Diderot, written in the late 1760s—1778 and published in Italo Calvino ( October 15, 1923 &ndash September 19, 1985) (ˈiːtalo kalˈviːno was an Italian journalist and writer of short If on a winter's night a traveler ( Se una notte d'inverno un viaggiatore) is a Novel published in 1979 by Italo Calvino. Nikolai Vasilievich Gogol (Никола́й Васи́льевич Го́голь Nikolai Vasilevich Gogol;; Микола Васильович Гоголь Lost in the Funhouse is a collection of loosely connected Short stories that was originally published by John Barth in 1968. John Simmons Barth (born May 27 1930 is an American novelist and short-story writer known for the postmodernist and metafictive quality of his work Luigi Pirandello ( June 28, 1867 — December 10, 1936) was an Italian Dramatist Novelist, and short Six Characters in Search of an Author ( Sei personaggi in cerca d'autore) is the most famous and celebrated play by the Italian writer Luigi Pirandello. This is closely related to the concepts of breaking the fourth wall and meta-reference, which often involve self-reference. The fourth wall is the imaginary wall at the front of the stage in a Proscenium Theater, through which the audience sees the action in the world of the play Meta-reference, a Meta-fiction technique is a situation in a work of fiction whereby Fictional characters display an awareness that they are in such a work such

The surrealistic painter René Magritte is famous for his self-referential works. Surrealism is a cultural movement that began in the early-1920s and is best known for the visual artworks and writings of the group members René François Ghislain Magritte ( 21 November 1898 - 15 August 1967) was a Belgian Surrealist artist

The Treachery Of Images (1928-29) by René Magritte depicts a pipe along with text stating "This is not a pipe. The Treachery of Images ( La trahison des images 1928&ndash29 is a series of paintings by Belgian Surrealist painter René Magritte René François Ghislain Magritte ( 21 November 1898 - 15 August 1967) was a Belgian Surrealist artist "

His painting The Treachery of Images, shown at right, includes words claiming, in French, it is not a pipe, the truth of which depend entirely on what the word "ceci" (in English, "this") is taken to refer to. The Treachery of Images ( La trahison des images 1928&ndash29 is a series of paintings by Belgian Surrealist painter René Magritte Is it the pipe depicted—or is it the painting, or even the sentence itself?

Self-reference is also employed in tautology and in licensed terminology. In Rhetoric, a tautology is an unnecessary (and usually unintentional repetition of meaning using different words that effectively say the same thing twice (often originally When a word defines itself (e. g. , "Machine: any objects put together mechanically"), the result is a tautology. Such self-references can be quite complex, include full propositions rather than simple words, and produce arguments and terms that require license (accepting them as proof of themselves).

Self-reference in computer science is seen in the concept of recursion, where a program unit relies on instances of itself to perform a computation. Computer science (or computing science) is the study and the Science of the theoretical foundations of Information and Computation and their Recursion, in Mathematics and Computer science, is a method of defining functions in which the function being defined is applied within its own definition The Lisp programming language is especially designed to exploit recursion. Lisp (or LISP) is a family of Computer Programming languages with a long history and a distinctive fully parenthesized syntax Many object oriented languages use special keywords to refer to the current instance of an object: this in C++, Java, and PHP; self in Smalltalk and Objective C; and Me in Visual Basic, although some, like Python, do this differently. In many Object-oriented Programming languages, this (or self) is a keyword which can be used in Instance methods to refer to the object on which C++ (" C Plus Plus " ˌsiːˌplʌsˈplʌs is a general-purpose Programming language. PHP is a computer Scripting language. Originally designed for producing Dynamic web pages it has evolved to include a Command line interface capability Smalltalk is an object-oriented, dynamically typed, reflective programming language. Objective-C is a reflective, object-oriented Programming language which adds Smalltalk -style messaging to C. Visual Basic ( VB) is the third-generation event-driven programming language and associated development environment (IDE from Python is a general-purpose High-level programming language. Its design philosophy emphasizes programmer productivity and code readability

Examples

Many of the following examples appear in Douglas Hofstadter's Gödel, Escher, Bach: an Eternal Golden Braid Metamagical Themas, or I Am a Strange Loop. Douglas Richard Hofstadter (born February 15 1945 in New York New York) is an American academic whose research focuses on consciousness thinking and creativity Gödel Escher Bach an Eternal Golden Braid (commonly GEB) is a Pulitzer Prize -winning book by Douglas Hofstadter, described Metamagical Themas is an eclectic collection of articles written for Scientific American during the early 1980s by Douglas Hofstadter, and published I Am a Strange Loop is a 2007 book by Douglas Hofstadter, examining in depth the concept of a Strange loop originally developed in his 1979

Mathematics

• Tupper's self-referential formula
• Loop (graph theory)

Sentences

• "Yields falsehood when preceded by its quotation" yields falsehood when preceded by its quotation. (This is a version of the liar paradox, an example of indirect self-reference through a quine, which leads to a paradox. Tupper's self-referential formula is a self-referential Formula defined by Jeff Tupper that when graphed in two dimensions can visually reproduce the formula itself In Graph theory, a loop (also called a self-loop) is an edge that connects a vertex to itself Quine's paradox is a Paradox concerning truth values attributed to W In Philosophy and Logic, the liar paradox, known to the ancients as the pseudomenon, encompasses Paradoxical statements such as "This Indirect self-reference describes an object referring to itself indirectly. In Computing, a quine is a program, a form of metaprogram, that produces its complete Source code as its only output A paradox is a true statement or group of statements that leads to a Contradiction or a situation which defies intuition; or inversely )

• Russell's paradox: The set of all sets which are not elements of themselves (which includes, and therefore does not, and therefore does include itself)

The Fumblerules

Fumblerules state rules of good grammar and writing through sentences that violate those very rules. Part of the Foundations of mathematics, Russell's paradox (also known as Russell's antinomy) discovered by Bertrand Russell in 1901 showed that the Fumblerules are humorous Rules for Writing, collected from teachers of English grammar George L. Trigg and William Safire have made their own lists, but anyone knowledgeable on grammar can do the same.

Literature

Main article: Metafiction

• "beware: do not read this poem" by Ishmael Reed - "the hunger of this poem is legendary, it has taken in many victims"
• The Monster at the End of This Book references itself in the title, as well as throughout the story. Metafiction is a literary term for a type of Fiction that systematically and self-consciously addresses the devices of fiction including the relationship between fiction and Ishmael Scott Reed ( February 22, 1938) is an American Poet, essayist and novelist The Monster at the End of This Book Starring Lovable Furry Old Grover is a post-modern children's book based on the television series Sesame Street and
• Steal This Book by Abbie Hoffman
• The Cat Who Walks Through Walls by Robert A. Heinlein considers the universe (multiverse) as an author-manipulated object including the plot in the book itself. Steal This Book is a book written by Abbie Hoffman in 1970 and published in 1971 The Cat Who Walks Through Walls is a Science fiction Novel by Robert A Robert Anson Heinlein (July 7 1907 – May 8 1988 was an American Novelist and Science fiction Writer. The multiverse (or meta-universe) is the hypothetical set of multiple possible Universes (including our universe that together comprise all of Reality.
• Sophie's World by Jostein Gaarder, in which the titular character realizes she is the character of a book. Sophie's World ( Sofies verden in the original Norwegian) is a Novel by Jostein Gaarder, published in 1991 Jostein Gaarder (born August 8 1952 in Oslo) is a Norwegian Intellectual and author of several Novels short stories
• The Neverending Story by Michael Ende uses self-reference of the book prominently, when a character (Atreyu) of a story within the story (also called 'Neverending Story') finds a book called the same, and it is the same book the reader is reading. The Neverending Story (Die unendliche Geschichte is a German fantasy novel by Michael Ende, first published in 1979. Michael Andreas Helmuth Ende ( November 12, 1929 - August 28, 1995) was a German writer of fantasy and Children's

Other

• Self-enumerating pangrams
• Article 52 of the Irish Constitution has prohibited publication of Article 52 in official texts since 1938 despite continuing to have the force of law. A pangram ( Greek: pan gramma, "every letter" or holoalphabetic sentence, is a sentence using every letter of the Alphabet at least The Constitution of Ireland (Bunreacht na hÉireann came into force on 29 December 1937 after having been passed by a national plebiscite the previous July
• RFC 2119 dictates the use of key words describing requirement levels — such as "must", "should" and "may" — in RFCs. In Computer network Engineering, a Request for Comments (RFC is a Memorandum published by the Internet Engineering Task Force (IETF describing The abstract of the RFC states that the key words are to be interpreted as described in the RFC.
• Don't Download This Song by "Weird Al" Yankovic
• Steal This Album! by System of a Down
• Steal This Album by The Coup
• referring to oneself in third person narrative
• TLA, as an acronym for Three-letter acronym

References

• Hofstadter, D. R. (1980). " Don't Download This Song " is the first single from "Weird Al" Yankovic 's 12th studio album Straight Outta Lynwood. Alfred Matthew "Weird Al" Yankovic (ˈjæŋkəvɪk born October 23 1959 is a Grammy Award winning American singer Musician, actor satirist Steal This Album! is the third album by System of a Down. Produced by Rick Rubin and Daron Malakian, Steal This Album! was recorded System of a Down (commonly referred to as System or abbreviated as SOAD) is an Armenian American rock band formed in 1994 in Steal This Album is the third album by Oakland hip hop duo The Coup, released four years after their second album Genocide & Juice The Coup is a Political hip hop group based in Oakland California. The third-person narrative is a Narrative mode applying the third person. A three-letter acronym, three-letter abbreviation, or TLA is an Acronym, Abbreviation, Alphabetism or Initialism consisting Douglas Richard Hofstadter (born February 15 1945 in New York New York) is an American academic whose research focuses on consciousness thinking and creativity Gödel, Escher, Bach: an Eternal Golden Braid. Gödel Escher Bach an Eternal Golden Braid (commonly GEB) is a Pulitzer Prize -winning book by Douglas Hofstadter, described New York, Vintage Books.
• Raymond Smullyan (1994), Diagonalization and Self-Reference, Oxford Science Publications, ISBN 0-19-853450-7

See also

External links

• The Paradox of Self-Amendment: A Study of Logic, Law, Omnipotence, and Change, by Peter Suber (Peter Lang Publishing, 1990). Raymond Merrill Smullyan (born 1919 is an American Mathematician, Logician, Philosopher, and magician. Year 1994 ( MCMXCIV) was a Common year starting on Saturday (link will display full 1994 Gregorian calendar) A circular reference, sometimes referred to as a run-around is a series of References where the last object references the first thus causing the whole series of references In Mathematical logic, the diagonal lemma or fixed point theorem establishes the existence of Self-referential sentences in formal theories of In Mathematical logic, Gödel's incompleteness theorems, proved by Kurt Gödel in 1931 are two Theorems stating inherent limitations of all but the most The Grelling–Nelson paradox is a Semantic Self-referential Paradox formulated in 1908 by Kurt Grelling and Leonard Nelson and Indirect self-reference describes an object referring to itself indirectly. Meta-reference, a Meta-fiction technique is a situation in a work of fiction whereby Fictional characters display an awareness that they are in such a work such An object of the mind is an object which exists in the Imagination, but can only be represented or modeled in the Real world. Optical feedback is the optical equivalent of Acoustic feedback. Recursion, in Mathematics and Computer science, is a method of defining functions in which the function being defined is applied within its own definition This article is about a kind of publication Reference work may also refer to the work that librarians perform at a Library reference desk. Part of the Foundations of mathematics, Russell's paradox (also known as Russell's antinomy) discovered by Bertrand Russell in 1901 showed that the A self-coup or autocoup is a form of Coup d'état that occurs when a country's leader dissolves or renders powerless the national Legislature and assumes extraordinary In Mathematics, a self-similar object is exactly or approximately similar to a part of itself (i Self-refuting ideas are ideas or statements whose falsehood is a Logical consequence of the act or situation of holding them to be true The use–mention distinction (sometimes referred to as the words-as-words distinction) is the distinction between using a word (or phrase and mentioning Self-insertion is a literary device in which the real author of a work of fiction appears as a character within that fiction either overtly or in disguise A book-length study of self-reference in law. (The book is OP but the full text is free online. )
• Self-Referential Aptitude Test, by Jim Propp
• Self-reference and apparent self-reference
• "Elegancelessness" A collection of self-references by Paul Niquette
• Self-Referential Story, from the Internet Oracularities #1353
• Self-reference jokes
• Self-Reference in ``Self-Reference in `Self-Reference in ...'", a review of a review of a review of . The Internet Oracle (historically known as The Usenet Oracle) is an effort at collective humor in a pseudo-Socratic question-and-answer format . .