Self-reference - Definition and Overview

A self-reference occurs when an object 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).

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

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. This is closely related to the concept of breaking the fourth wall.

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 and 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.

Examples

• pentasyllabic (a word which describes itself)
• 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.
• "Yields falsehood when preceded by its quotation," yields falsehood when preceded by its quotation. (This, the original quine, 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 aren't elements of themselves.
• The Examples section of this article refers to itself.
• One word in this sentence is mispelled.

Naturally, this Wikipedia article refers to itself.

See also

• Gödel's incompleteness theorem
• List of self-referential songs
• recursion
• reference work
• Russell's paradox
• Grelling-Nelson paradox
• self-similarity
• use-mention distinction
• meta-reference

References

• Hofstadter, D. R. (1980). Gödel, Escher, Bach: an Eternal Golden Braid. New York, Vintage Books.

External links

• This Is The Title Of This Story, Which Is Also Found Several Times In The Story Itself, by David Moser (http://www.triplette.com/by_david_moser.htm)