Self-reference

From Free net encyclopedia

Image:Ouroboros.pngA 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).

1 Usage
2 Examples
3 References
4 See also
5 External links

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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 or her work in the context of the work itself. Famous examples include Cervantes's Quixote, 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. The surrealistic painter René Magritte is famous for his self-referential works. Image:MagrittePipe.jpg 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.

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Examples

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 fragment 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, 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 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).
Every rule has exceptions.
All generalizations are false.
74.6% of statistics are completely made up.
The following statement is true. The preceding statement is false.
This statement doesn't contain the letter 'y'.
Is this a question?