Self-reference

The Treachery Of Images (1928-29) by René Magritte depicts a pipe along with text stating "This is not a pipe."

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

Usage

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

An example of a self-referential situation is the one of autopoiesis, as the logical organization produces itself the physical structure which creates 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.

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".

See: Appendix:Autological words.

Mathematics

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

Sentences

• "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)

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.

Literature

Main article: Metafiction

• The Monster at the End of This Book references itself in the title, as well as throughout the story.
• Steal This Book by Abbie Hoffman
• The New York Trilogy, specifically City Of Glass, by Paul Auster.
• The Cat Who Walks Through Walls by Robert A. Heinlein considers the universe (multiverse) as an author-manipulated object including the plot in the book itself.
• Sophie's World by Jostein Gaarder, in which the titular character realizes she is the character of a book.
• The Neverending Story by Michael Ende uses self-reference of the book prominently, when a character (Atreyu) of a story within the story (also called 'Neverending Story') finds a book called the same, and it is the same book the reader is reading.
• A Heartbreaking Work of Staggering Genius by Dave Eggers has characters referring to their role in the book and references to the book itself. This includes a list of tips to help better enjoy the book (including several tips not to bother reading large sections of the book), and a guide to its symbols and metaphors.
• Six Characters in Search of an Author by Luigi Pirandello involves a collection of people that show up at a play rehearsal, claiming to be characters in search of a playwright to help them finish their story. The play plays itself out as a way of (possibly) doing just that.
• "You're So Vain", a song by Carly Simon which contains the lyrics, "You're so vain, you probably think this song is about you."
• The main antagonist in the comic Legion of the 3 Worlds, Superboy Prime, is the Clark Kent from a destroyed iteration of the real universe, supremely displeased from how his favourite comic books turned out while journeying in their multiverse (depicted as coexisting with the real one). Eventually, Clark returns to our dimension, where is confronted by his distraught parents and girlfriend, having read the chronicles of his villainous action from the comic books published after his "departure".

See also

• Autological word
• Circular reference
• Diagonal lemma
• Feedback
• Gödel's incompleteness theorem
• Grelling–Nelson paradox
• Indirect self-reference
• Meta-reference

• Object of the mind
• Philosophy of philosophy
• Pseudohistory
• Recursion
• Reference work
• Russell's paradox
• Self-coup
• Self-insertion

• Self-refuting idea
• Self-relocation
• Self-replication
• Self-similarity
• Shepard tone
• Use–mention distinction
• Virtuous circle and vicious circle

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

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)