Self-reference

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The Ouroboros, a snake which consumes itself, is a symbol for self-reference.

Self-reference is a phenomenon in natural or formal languages consisting in a sentence or formula referring to itself directly, through some intermediate sentence or formula, or by means of some encoding.^[1] In philosophy, it also refers to the ability of a subject to speak of or refer to themself: to have the kind of thought expressed in English by "I".

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. Self-referential statements can lead to paradoxes (but see antinomy for limits on the significance of these).

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 when an author refers to his work in the context of the work itself. Famous examples include Cervantes's 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. This is closely related to the concept of breaking the fourth wall or meta-reference (which often involve self-reference).

"The Treachery Of Images" (1928-9) by René Magritte depicts a pipe along with text meaning, "This is not a pipe."

Self-reference is also employed in tautology and in licensed terminology. 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. The Lisp programming language is especially designed to exploit recursion. Object oriented languages use special keywords to refer to the current instance of an object like this in Java, PHP, or C++ or Me in Visual Basic.

Examples

Many of the following examples appear in Douglas Hofstadter's Gödel, Escher, Bach: an Eternal Golden Braid or Metamagical Themas.

Sentences

• This statement is short.
• I am not the subject of this sentence.
• "I" is the subject of this sentence.
• Which question is also its own answer?
• This sentence contains thirty-eight letters.
• This sentence has threee erors.
• This sentence no verb.
• This sentence has, and therefore contains, two verbs.
• "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 leading 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)
• The Examples section of this article refers to itself.
• This sentence exemplifies cacozelia (using rare/foreign words to appear learned).
• Is this a question?
• Thit sentence is not self-referential because 'thit' is not a word.
• If the meanings of "true" and "false" were switched, then this sentence wouldn't be false.
• Click here
• Backwards written is sentence this.
• This sentence is an example of self-reference.

Poetry

• "" by Ishmael Reed - "the hunger of this poem is legendary, it has taken in many victims"

Other

• Self-enumerating pangrams

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
• Encyclopedia contributors. (2007). "Self-reference". Encyclopedia. Retrieved on 2007-03-10.

See also

External links

• 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.)
• This Is The Title Of This Story, Which Is Also Found Several Times In The Story Itself, by David Moser.
• This is Not the Title of This Essay: A Playful Look at Attempts to Solve the Problems of Paradox and Self-Reference, by Tim Maly
• Self-Referential Aptitude Test, by Jim Propp
• Self-reference and apparent self-reference
• "Elegancelessness" A collection of self-references by Paul Niquette
• Parody site Uncyclopedia's self-reference have some good examples of self-reference.

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