Self-reference

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The Ouroboros, a dragon that bites its tail, is a symbol for self-reference.
The Ouroboros, a dragon that bites its tail, 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).

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[edit] 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 surrealistic painter René Magritte is famous for his self-referential works.

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

"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. 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. 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.

[edit] Examples

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

[edit] Mathematics

[edit] Sentences

  • This statement is short.
  • I am not the subject of this sentence.
  • "I" is the subject of this sentence.
  • This sentence is both the subject and the object 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 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)
  • The Examples section of this article refers to itself.
  • This sentence exemplifies cacozelia (using rare/foreign words to appear learned).
  • Is this a question?
  • Please repeat this sentence once.
  • 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.
  • This sentence is unfinished, and therefore
  • "Is not the title of a book, so far as I know" is not the title of a book, so far as I know.

[edit] Poetry

  • "beware: do not read this poem" by Ishmael Reed - "the hunger of this poem is legendary, it has taken in many victims"

[edit] Other

[edit] References

[edit] See also

[edit] External links

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