Self-reference
Self-reference is a concept that involves referring to oneself or one's own attributes, characteristics, or actions. It can occur in language, logic, mathematics, philosophy, and other fields.
For the use of self-references in Wikipedia articles, see Wikipedia:Manual of Style/Self-references to avoid.
In natural or formal languages, self-reference occurs when a sentence, idea 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, self-reference also refers to the ability of a subject to speak of or refer to itself, that is, to have the kind of thought expressed by the first person nominative singular pronoun "I" in English.
Self-reference is studied and has applications in mathematics, philosophy, computer programming, second-order cybernetics, and linguistics, as well as in humor. Self-referential statements are sometimes paradoxical, and can also be considered recursive.
In logic, mathematics and computing[edit]
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 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.[2]
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.[3] 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.[4] '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 biology[edit]
The biology of self-replication is self-referential, as embodied by DNA and RNA replication mechanisms. Models of self-replication are found in Conway's Game of Life and have inspired engineering systems such as the self-replicating 3D printer RepRap.
In language[edit]
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".
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 paradox in the United States Constitution at his citizenship ceremony.
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.
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.[9][10]
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.[11] 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."[12]
In law[edit]
Several constitutions contain self-referential clauses defining how the constitution itself may be amended.[15] An example is Article Five of the United States Constitution.