In logic, mathematics and computing In classical
philosophy,
paradoxes were created by self-referential concepts such as the
omnipotence paradox of asking if it was possible for a being to exist that was so powerful that it could create a stone that it could not lift. The
Epimenides paradox, 'All Cretans are liars' when uttered by an ancient Greek Cretan was one of the first recorded versions. Contemporary philosophy sometimes employs the same technique to demonstrate that a supposed concept is meaningless or ill-defined. In
mathematics and
computability theory, self-reference (also known as
impredicativity) is the key concept in proving limitations of many systems.
Gödel's theorem uses it to show that no formal
consistent system of mathematics can ever contain all possible mathematical truths, because it cannot prove some truths about its own structure.
The halting problem equivalent, in computation theory, shows that there is always some task that a computer cannot perform, namely reasoning about itself. These proofs relate to a long tradition of mathematical paradoxes such as
Russell's paradox and
Berry's paradox, and ultimately to classical philosophical paradoxes. In
game theory, undefined behaviors can occur where two players must model each other's mental states and behaviors, leading to infinite regress. In
computer programming, self-reference occurs in
reflection, where a program can read or modify its own instructions like any other 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) in
functional programming, where a code structure refers back to itself during computation. 'Taming' self-reference from potentially paradoxical concepts into well-behaved recursions has been one of the great successes of
computer science, and is now used routinely in, for example, writing
compilers using the 'meta-language'
ML. Using a compiler to compile itself is known as
bootstrapping.
Self-modifying code is possible to write (programs which operate on themselves), both with
assembler and with functional languages such as
Lisp, but is generally discouraged in real-world programming. Computing hardware makes fundamental use of self-reference in
flip-flops, the basic units of digital memory, which convert potentially paradoxical logical self-relations into memory by expanding their terms over time. Thinking in terms of self-reference is a pervasive part of programmer culture, with many programs and acronyms named self-referentially as a form of humor, such as
GNU ('GNU's not Unix') and
PINE ('Pine is not Elm'). The
GNU Hurd is named for a pair of mutually self-referential acronyms.
Tupper's self-referential formula is a mathematical curiosity which plots an image of its own formula.
In the arts Self-reference in art is closely related to the concepts of
breaking the fourth wall and
meta-reference, which often involve self-reference.
In literature and film , with drawboy above to control the harnesses, woven as a repeating pattern in an early-1800s piece of Japanese silk. The silk illustrates the means by which it was produced. apologizing for its own existence . The painter drawn on a wall erases his own graffiti, and may be erased himself by the next facade cleaner. Self-reference occurs in
literature and
film when an author refers to his or her own work in the context of the work itself. Examples include
Miguel de Cervantes'
Don Quixote,
Shakespeare's ''
A Midsummer Night's Dream, The Tempest and Twelfth Night'',
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,
Federico Fellini's
8½ and
Bryan Forbes's
The L-Shaped Room. Speculative fiction writer
Samuel R. Delany makes use of this in his novels
Nova and
Dhalgren. In the former, Katin (a space-faring novelist) is wary of a long-standing curse wherein a novelist dies before completing any given work.
Nova ends mid-sentence, thus lending credence to the curse and the realization that the novelist is the author of the story; likewise, throughout
Dhalgren, Delany has a protagonist simply named The Kid (or Kidd, in some sections), whose life and work are mirror images of themselves and of the novel itself. In the sci-fi spoof film
Spaceballs, Director
Mel Brooks includes a scene wherein the evil characters are viewing a VHS copy of their own story, which shows them watching themselves "watching themselves", ad infinitum. Perhaps the earliest example is in
Homer's
Iliad, where
Helen of Troy laments: "for generations still unborn/we will live in song" (appearing in the song itself). The short stories of
Jorge Luis Borges play with self-reference and related paradoxes in many ways.
Samuel Beckett's ''
Krapp's Last Tape'' consists entirely of the protagonist listening to and making recordings of himself, mostly about other recordings. During the 1990s and 2000s filmic self-reference was a popular part of the
rubber reality movement, notably in
Charlie Kaufman's films
Being John Malkovich and
Adaptation, the latter pushing the concept arguably to its breaking point as it attempts to portray its own creation, in a
dramatized version of the
Droste effect.
In art The
surrealist painter
René Magritte is famous for his self-referential works. His painting
The Treachery of Images, includes the words "this 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 word or sentence itself.
M.C. Escher's art also contains many self-referential concepts such as hands drawing themselves.
In popular culture •
Douglas Hofstadter's books, especially
Metamagical Themas and
Gödel, Escher, Bach, play with many self-referential concepts and were highly influential in bringing them into mainstream intellectual culture during the 1980s.
Hofstadter's law, which specifies that "It always takes longer than you expect, even when you take into account Hofstadter's Law" is an example of a self-referencing adage. Hofstadter also suggested the concept of a 'Reviews of this book', a book containing only reviews of itself, which has since been implemented using
wikis and other technologies. Hofstadter's '
strange loop'
metaphysics attempts to map
consciousness onto self-reference, but is a minority position in
philosophy of mind. • The subgenre of "
recursive science fiction" or
metafiction is now so extensive that it has fostered a fan-maintained bibliography at the
New England Science Fiction Association's website; some of it is about
science-fiction fandom, some about science fiction and its authors.
In media Self-reference occasionally occurs in the
media when it is required to write about itself, for example the
BBC reporting on job cuts at the BBC. Notable encyclopedias may be required to feature articles about themselves, such as Wikipedia's article on
Wikipedia.
In mythology and religion Various
creation myths invoke self-reference to solve the problem of what created the creator. For example, the
Egyptian creation myth has a god swallowing his own semen to create himself. The
Ouroboros is a mythical dragon which eats itself. The
Quran includes numerous instances of self-referentiality.
In language Words A word that describes itself is called an
autological word (or
autonym). This generally applies to adjectives, for example
sesquipedalian (i.e. "sesquipedalian" is a sesquipedalian word), but can also apply to other parts of speech, such as
TLA, as a three-letter
abbreviation for "
three-letter abbreviation".
Circular definition is a type of self-reference in which the definition of a term or concept includes the term or concept itself, either explicitly or implicitly. Circular definitions are considered
fallacious because they only define a term in terms of itself. This type of self-reference may be useful in
argumentation, but can result in a lack of clarity in communication. The adverb "hereby" is used in a self-referential way, for example in the statement "I hereby declare you husband and wife."
Sentences A sentence which inventories its own letters and punctuation marks is called an
autogram. There is a special case of meta-sentence in which the content of the sentence in the metalanguage and the content of the sentence in the object language are the same. Such a sentence is referring to itself. However some meta-sentences of this type can lead to paradoxes. "This is a sentence." can be considered to be a self-referential meta-sentence which is obviously true. However "This sentence is false" is a meta-sentence which leads to a self-referential
paradox. Such sentences can lead to problems, for example, in law, where statements bringing laws into existence can contradict one another or themselves.
Kurt Gödel claimed to have found such a
loophole in the
United States Constitution at his citizenship ceremony.
Fumblerules are a list of rules of good grammar and writing, demonstrated through sentences that violate those very rules, such as "Avoid cliches like the plague" and "Don't use no double negatives". The term was coined in a published list of such rules by
William Safire.
In law Several constitutions contain self-referential clauses defining how the constitution itself may be amended. An example is
Article Five of the United States Constitution. ==See also== ==References==