Self-reference

From Wikinfo

The Ouroboros, a dragon that bites its tail, can be used as a symbol for self-reference.

A self-reference occurs when a statement refers to itself. 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. Self-referential statements can lead to paradoxes (but see antinomy for limits on the significance of these).

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 also occurs in literature when an author refers to his or her work in the context of the work itself. Famous examples include Denis Diderot's Jacques the Fatalist and Luigi Pirandello's Six Characters in Search of an Author.

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

Usage

An example of a self-reference situation is the one of autopoiesis, as the logical organisation produces itself the physical structure which create itself.

In metaphysics, self-reference is subjectivity, while "hetero-reference", as it is called (see Niklas Luhmann), is objectivity.

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 surrealistic 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 as if they were 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.

• If an article (See this article as an example) has a link to itself, the link is sometimes called a self-link. Sometimes this is done on purpose for technical reasons.

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".

• pentasyllabic (a word which describes itself)

See: Appendix:Autological words.

Sentences

• This statement is short.
• "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.)
• 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)

Mathematics

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

Linguistics

A reflexive sentence has the same subject and object (e.g., "The man washed himself"). In contrast, a transitive sentence requires both a direct subject and one or more objects ( e.g., "The man hit John").

The Fumblerules

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 on grammar can do the same.

Related articles

External links

• Self-Referential Story, from the Internet Oracularities #1353
• Elegancelessness A collection of self-references by Paul Niquette
• 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)

References

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