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Metalanguage

From Wikipedia, the free encyclopedia

Language used to describe another language

For other uses, seeMetalanguage (disambiguation).

Not to be confused withmetalinguistics.

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Inlogic andlinguistics, ametalanguage is a language used to describe another language, often called theobject language.^[1] Expressions in a metalanguage are often distinguished from those in the object language by the use of italics,quotation marks, or writing on a separate line.^{[citation needed]} The structure of sentences and phrases in a metalanguage can be described by ametasyntax.^[2] For example, to say that the word "noun" can be used as a noun in a sentence, one could write"noun" is a <noun>.

Types of metalanguage

There are a variety of recognized types of metalanguage, includingembedded,ordered, andnested (orhierarchical) metalanguages.

Embedded

Anembedded metalanguage is a language formally, naturally and firmly fixed in an object language. This idea is found inDouglas Hofstadter's book,Gödel, Escher, Bach, in a discussion of the relationship between formal languages andnumber theory: "... it is in the nature of any formalization of number theory that its metalanguage is embedded within it."^[3]

It occurs in natural, or informal, languages, as well—such as in English, where words such asnoun,verb, or evenword describe features and concepts pertaining to the English language itself.

Ordered

Anordered metalanguage is analogous to anordered logic. An example of an ordered metalanguage is the construction of one metalanguage to discuss an object language, followed by the creation of another metalanguage to discuss the first, etc.

Nested

Anested (orhierarchical)metalanguage is similar to an ordered metalanguage in that each level represents a greater degree of abstraction. However, a nested metalanguage differs from an ordered one in that each level includes the one below.

Theparadigmatic example of a nested metalanguage comes from theLinnean taxonomic system in biology. Each level in the system incorporates the one below it. The language used to discuss genus is also used to discuss species; the one used to discuss orders is also used to discuss genera, etc., up to kingdoms.

In natural language

Natural language combines nested and ordered metalanguages. In a natural language there is an infinite regress of metalanguages, each with more specialized vocabulary and simpler syntax.

Designating the language now as $L_{0}$ , the grammar of the language is a discourse in the metalanguage $L_{1}$ , which is a sublanguage^[4] nested within $L_{0}$ .

The grammar of $L_{1}$ , which has the form of a factual description, is a discourse in the meta–metalanguage $L_{2}$ , which is also a sublanguage of $L_{0}$ .
The grammar of $L_{2}$ , which has the form of a theory describing the syntactic structure of such factual descriptions, is stated in the meta–meta–metalanguage $L_{3}$ , which likewise is a sublanguage of $L_{0}$ .
The grammar of $L_{3}$ has the form of a metatheory describing the syntactic structure of theories stated in $L_{2}$ .
$L_{4}$ and succeeding metalanguages have the same grammar as $L_{3}$ , differing only in reference.

Since all of these metalanguages are sublanguages of $L_{0}$ , $L_{1}$ is a nested metalanguage, but $L_{2}$ and sequel are ordered metalanguages.^[5] Since all these metalanguages are sublanguages of $L_{0}$ they are all embedded languages with respect to the language as a whole.

Metalanguages of formal systems all resolve ultimately to natural language, the 'common parlance' in which mathematicians and logicians converse to define their terms and operations and 'read out' their formulae.^[6]

Types of expressions

There are several entities commonly expressed in a metalanguage. In logic usually the object language that the metalanguage is discussing is aformal language, and very often the metalanguage as well.

Deductive systems

Main article:Deductive system

Adeductive system (or,deductive apparatus of aformal system) consists of theaxioms (oraxiom schemata) andrules of inference that can be used toderive thetheorems of the system.^[7]

Metavariables

Main article:Metavariable (logic)

Ametavariable (ormetalinguistic ormetasyntactic variable) is asymbol or set of symbols in a metalanguage which stands for a symbol or set of symbols in some object language. For instance, in the sentence:

LetA andB be arbitraryformulas of aformal language

L {\displaystyle L}

.

The symbolsA andB are not symbols of the object language $L {\displaystyle L}$ , they are metavariables in the metalanguage (in this case, English) that is discussing the object language $L {\displaystyle L}$ .

Metatheories and metatheorems

Main articles:Metatheory andMetatheorem

Ametatheory is atheory whose subject matter is some other theory (a theory about a theory).Statements made in the metatheory about the theory are calledmetatheorems. Ametatheorem is atrue statement about aformal system expressed in a metalanguage. Unlike theorems proved within a given formal system, a metatheorem is proved within ametatheory, and may reference concepts that are present in themetatheory but not the object theory.^[8]

Interpretations

Main article:Interpretation (logic)

Aninterpretation is anassignment of meanings to thesymbols andwords of a language.

Role in metaphor

Michael J. Reddy (1979) argues that much of the language we use to talk about language is conceptualized and structured by what he refers to as theconduit metaphor.^[9] This paradigm operates through two distinct, related frameworks.

Themajor framework views language as a sealed pipeline between people:

Major framework
Stage	Description	Example
1	Language transfers people's thoughts and feelings (mental content) to others	Try to get your thoughts across better
2	Speakers and writers insert their mental content into words	You have to put each concept into words more carefully
3	Words are containers	That sentence was filled with emotion
4	Listeners and readers extract mental content from words	Let me know if you find any new sensations in the poem

Theminor framework views language as an open pipe spilling mental content into the void:

Minor framework
Stage	Description	Example
1	Speakers and writers eject mental content into an external space	Get those ideas out where they can do some good
2	Mental content is reified (viewed as concrete) in this space	That concept has been floating around for decades
3	Listeners and readers extract mental content from this space	Let me know if you find any good concepts in the essay

Metaprogramming

Computers follow programs, sets of instructions in formal languages. The development of aprogramming language involves the use of a metalanguage. The act of working with metalanguages in programming is known asmetaprogramming.

Backus–Naur form, developed in the 1960s by John Backus and Peter Naur, is one of the earliest metalanguages used in computing. Examples of modern-day programming languages which commonly find use in metaprogramming includeML,Lisp,m4, andYacc.

See also

Category theory – General theory of mathematical structures
Formal language – Sequence of words formed by specific rules
Jakobson's functions of language – Theory of language
Language-oriented programming – Programming paradigm
Meta-communication – Communication about how information is meant to be interpreted
Metaethics – Branch of ethics seeking to understand ethical properties
Metafiction – Genre of fiction about fiction
Metagraphy – Experimental form of visual communicationPages displaying short descriptions of redirect targets
Metamathematics – Study of mathematics itself
Metalinguistic abstraction – Principle in computer science of domain-specific languages for problem solving
Metalinguistic awareness – Ability to consciously reflect on the nature of language
Metalocutionary act – Concept in linguistic pragmatics
Metaphilosophy – Investigation of the nature of philosophy
Natural semantic metalanguage – Linguistic theory of semantic description
Nested quotation – Quotations within quotations
Paralanguage – Communication of additional meaning, nuance, or emotion in speech
Self-reference – Sentence, idea or formula that refers to itself
Use–mention distinction – Distinction between using a word and mentioning it

Dictionaries

Audi, R. 1996.The Cambridge Dictionary of Philosophy. Cambridge:Cambridge University Press.
Baldick, C. 1996.Oxford Concise Dictionary of Literary Terms. Oxford:Oxford University Press.
Cuddon, J. A. 1999.The Penguin Dictionary of Literary Terms and Literary Theory. London:Penguin Books.
Honderich, T. 1995.The Oxford Companion to Philosophy. Oxford:Oxford University Press.
Matthews, P. H. 1997.The Concise Oxford Dictionary of Linguistics. Oxford:Oxford University Press.ISBN 978-0-19-280008-4.
McArthur, T. 1996.The Concise Oxford Companion to the English Language. Oxford:Oxford University Press.

References

^2010.Cambridge Advanced Learner's Dictionary. Cambridge:Cambridge University Press. Dictionary online. Available fromhttp://dictionary.cambridge.org/dictionary/british/metalanguage Internet. Retrieved 20 November 2010
^van Wijngaarden, A., et al. "Language and metalanguage." Revised Report on the Algorithmic Language Algol 68. Springer, Berlin, Heidelberg, 1976. 17-35.
^Hofstadter, Douglas. 1980.Gödel, Escher, Bach: An Eternal Golden Braid. New York: Vintage BooksISBN 0-14-017997-6
^Harris, Zellig S. (1991).A theory of language and information: A mathematical approach. Oxford: Clarendon Press. pp. 272–318.ISBN 978-0-19-824224-6.
^Ibid. p. 277.
^Borel, Félix Édouard Justin Émile (1928).Leçons sur la theorie des fonctions (in French) (3 ed.). Paris: Gauthier-Villars & Cie. p. 160.
^Hunter, Geoffrey (1996) [1971].Metalogic: An Introduction to the Metatheory of Standard First-Order Logic. University of California Press (published 1973). p. 7.ISBN 9780520023567.OCLC 36312727. (accessible to patrons with print disabilities)
^Ritzer, George. 1991.Metatheorizing in Sociology. New York: Simon SchusterISBN 0-669-25008-2
^Reddy, Michael J. 1979. The conduit metaphor: A case of frame conflict in our language about language. In Andrew Ortony (ed.),Metaphor and Thought. Cambridge:Cambridge University Press

External links

Look upmetalanguage in Wiktionary, the free dictionary.

Metalanguage,Principia Cybernetica.
Willard McCarty (submitted 2006) Problematic Metaphors,Humanist Discussion Group, Vol. 20, No. 92.

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