Self-reference

The Treachery Of Images (1928-29) by René Magritte depicts a pipe along with text stating "This is not a pipe." Note: This image is an illustration of a self-reference case only if the demonstrative pronoun "ceci ("this") refers not to the idea of a pipe, but to the pipe-image, or to the sentence in which the word, "ceci", occurs. Neither the pipe-image nor the sentence is a functional pipe.

Self-reference occurs in natural or formal languages when a sentence 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 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 by the first person pronoun, the word "I" in English. Self-reference is related to self-reflexivity and apperception.

Self-reference is studied and has applications in mathematics, philosophy, computer programming, and linguistics. Self-referential statements sometimes have paradoxical behavior.

Usage

The Ouroboros, a dragon that continually consumes itself, is used as a symbol for self-reference.

An example of a self-referential situation is the one of autopoiesis, as the logical organization produces itself the physical structure which creates itself.

In metaphysics, self-reference is subjectivity, while "hetero-reference", as it is called (see Niklas Luhmann), is objectivity.^{[citation needed]}

Self-reference also occurs in literature and film when an author refers to his work in the context of the work itself. 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, Luigi Pirandello's Six Characters in Search of an Author, and Federico Fellini's 8½ . This is closely related to the concepts of breaking the fourth wall and meta-reference, which often involve self-reference.

The surrealist painter René Magritte is famous for his self-referential works. His painting The Treachery of Images, shown above, includes words claiming, in French, that it 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 sentence itself.

In computer science, self-reference occurs in reflection, 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 (related to the mathematical recurrence relation), where a code structure refers back to itself during computation.

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.

Words

See also: Appendix:Autological words

A word that describes itself is called an autological word (or autonym). This generally applies to adjectives, for example sesquipedalian, but can also apply to other parts of speech, such as TLA, as a three-letter abbreviation for three-letter abbreviation, and PHP which is a recursive acronym for "PHP: Hypertext Preprocessor".

Mathematics

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

Cognition

See also: Metacognition

Neuroscience research suggests the existence of neuroplasticity, a phenomenon in which thinking processes change the neural circuitry and structure of the brain.^{[citation needed]}

Self-referential sentences

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 paradox.

• "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.)

• "This sentence contains thirty-eight letters."

Linguistics

A reflexive sentence has the same subject and object (e.g., "The man washed himself"). In contrast, a transitive sentence requires the subject and object to be non-identical (e.g., "The man hit John").

Fumblerules

See also: Obfuscation

Fumblerules state rules of good grammar and writing through sentences that violate those very rules. (Examples: "Avoid cliches like the plague" and "Don't use no double negatives".) George L. Trigg and William Safire have made their own lists, but anyone knowledgeable of grammar can do the same.

In popular culture

Main article: Metafiction

• Paul Auster's The New York Trilogy, specifically City Of Glass.
• Mel Brooks' film Spaceballs uses the video release of the movie that the audience is watching to see what will happen in the future.
• Miguel de Cervantes mentions his own work La Galatea and the novel Don Quixote itself in the novel Don Quixote. A character of an apocryphal version of Don Quixote acknowledges that Cervantes' Don Quixote and Sancho Panza are the real ones and not those of the apocryphal text, which implies that the reader is one of the characters of the novel.
• In DC Comics' Legion of the 3 Worlds, The main antagonist, Superboy Prime, is the Clark Kent from a destroyed iteration of the real universe, supremely displeased from how his favourite comic books turned out while journeying in their multiverse (depicted as coexisting with the real one). Eventually, Clark returns to our dimension, where is confronted by his distraught parents and girlfriend, having read the chronicles of his villainous action from the comic books published after his "departure".
• Dave Eggers's A Heartbreaking Work of Staggering Genius has characters referring to their role in the book and references to the book itself. This includes a list of tips to help better enjoy the book (including several tips not to bother reading large sections of the book), and a guide to its symbols and metaphors.
• Michael Ende's The Neverending Story uses self-reference of the book prominently, when a character (Bastian) 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.
• Jostein Gaarder's Sophie's World, in which the titular character realizes she is the character in a book.
• Ain Gordon and David Gordon's Obie Award-winning play The Family Business, in which a character who is a playwright is asked what he is writing. "This," he replies, "I'm writing this."
• Robert A. Heinlein's The Cat Who Walks Through Walls considers the universe, or multiverse, as an author-manipulated object, including the plot of the book itself.
• Abbie Hoffman's Steal This Book
• Douglas Hofstadter's Gödel, Escher, Bach uses self-referencing mathematical (formal language) and English (natural language) sentences, pictures (M.C. Escher's dragon for example), and music (Bach's fugues) to convey the concept and its recursive nature.
• Some Monty Python sketches involves characters consulting or referring to the script to determine what to do next. Their film Monty Python and the Holy Grail is extensively self-referencing, including numerous on-screen references to incidents in "Scene 24"; soundtrack music being repeatedly noticed and silenced by a character; a sotto voce admission that a castle is "only a model", and the like.
• Luigi Pirandello's Six Characters in Search of an Author involves a collection of people that show up at a play rehearsal, claiming to be characters in search of a playwright to help them finish their story. The play plays itself out as a way of (possibly) doing just that.
• The Sesame Street book The Monster at the End of This Book references itself in the title, as well as throughout the story.
• Carly Simon's song "You're So Vain", which contains the lyrics, "You're so vain, you probably think this song is about you."
• In Miguel de Unamuno's novel Niebla ("Fog") the main character, Augusto Pérez, confronts Unamuno himself and has a quarrel with his author and inventor, reproaching Unamuno to have created him.
• Kurt Vonnegut refers to himself as the author in his novel Breakfast of Champions, where he has a conversation with himself about the writing of the novel itself. The character Kilgore Trout also engages in a conversation with the author.
• Several classic Warner Bros. Looney Tunes animated cartoons show characters going into a movie theatre, where they watch a version of the cartoon they're in.
• Robert Anton Wilson's Schrödinger's Cat Trilogy takes place in a universe where the books of the trilogy exist. Indeed, a character named Robert Wilson exists in the third book, and he is aware that he is a character in a book, having read the book and found himself described there.
• The 2006 film Stranger Than Fiction is about a character's knowledge that he is apparently living out a story written by an author, complete with narration which is audible to him. He eventually confronts the author, identifying himself as a character from one of her books.
• James Joyce's Finnegans Wake contains multiple references to itself.

See also

• Catch-22
• Double bind
• Droste effect
• Recursion
• Spiegel im Spiegel

References

Notes

Bibliography

• Hofstadter, D. R. (1980). Gödel, Escher, Bach: an Eternal Golden Braid. New York, Vintage Books.
• Smullyan, Raymond (1994), Diagonalization and Self-Reference, Oxford Science Publications, ISBN 0-19-853450-7

External links

• Self-Referential Story, from the Internet Oracularities #1353
• Self-Referential Aptitude Test, by Jim Propp
• Self-reference and apparent self-reference
• Self-reference jokes
• The Paradox of Self-Amendment: A Study of Logic, Law, Omnipotence, and Change, by Peter Suber (Peter Lang Publishing, 1990). A book-length study of self-reference in law. (The book is OP but the full text is free online.)
• University of Wisconsin-Milwaukee (at archive.org) Self-Reference in ``Self-Reference in `Self-Reference in ...'", a review of a review of a review of ... (archived at WebCite)