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{{Short description|Language used to describe another language}} {{Other uses|Metalanguage (disambiguation)}} {{Distinguish|metalinguistics}} {{multiple issues| {{context|date=April 2021}} {{More footnotes|date=September 2010}} {{generalize|date=January 2013}} }} In [[logic]] and [[linguistics]], a '''metalanguage''' is a language used to describe another language, often called the ''object language''.<ref>2010. ''Cambridge Advanced Learner's Dictionary''. Cambridge: [[Cambridge University Press]]. Dictionary online. Available from http://dictionary.cambridge.org/dictionary/british/metalanguage Internet. Retrieved 20 November 2010</ref> Expressions in a metalanguage are often distinguished from those in the object language by the use of italics, [[quotation mark]]s, or writing on a separate line.{{citation needed|date=January 2018}} The structure of sentences and phrases in a metalanguage can be described by a [[metasyntax]].<ref>van Wijngaarden, A., et al. "[https://link.springer.com/chapter/10.1007/978-3-642-95279-1_2 Language and metalanguage]." Revised Report on the Algorithmic Language Algol 68. Springer, Berlin, Heidelberg, 1976. 17-35.</ref> 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, including ''embedded'', ''ordered'', and ''nested'' (or ''hierarchical'') metalanguages. === <span class="anchor" id="Embedded metalanguage"></span> Embedded === An ''embedded metalanguage'' is a language formally, naturally and firmly fixed in an object language. This idea is found in [[Douglas Hofstadter]]'s book, ''[[Gödel, Escher, Bach]]'', in a discussion of the relationship between formal languages and [[number theory]]: "... it is in the nature of any formalization of number theory that its metalanguage is embedded within it."<ref>[[Douglas Hofstadter|Hofstadter, Douglas]]. 1980. [[Gödel, Escher, Bach|''Gödel, Escher, Bach: An Eternal Golden Braid'']]. New York: Vintage Books {{isbn|0-14-017997-6}}</ref> It occurs in natural, or informal, languages, as well—such as in English, where words such as ''noun'', ''verb'', or even ''word'' describe features and concepts pertaining to the English language itself. === Ordered === An ''ordered metalanguage'' is analogous to an [[ordered 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 === A ''nested'' (or ''hierarchical'') ''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. The [[paradigmatic]] example of a nested metalanguage comes from the [[Scientific classification|Linnean 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 <math>L_0</math>, the grammar of the language is a discourse in the metalanguage <math>L_1</math>, which is a sublanguage<ref>{{cite book | last =Harris | first =Zellig S. | author-link =Zellig Harris | title =A theory of language and information: A mathematical approach | publisher =Clarendon Press | date =1991 | location =Oxford | pages =[https://archive.org/details/theoryoflanguage00harr/page/272 272]–318 | url =https://archive.org/details/theoryoflanguage00harr | isbn =978-0-19-824224-6 | url-access =registration }}</ref> nested within <math>L_0</math>. * The grammar of <math>L_1</math>, which has the form of a factual description, is a discourse in the meta–metalanguage <math>L_2</math>, which is also a sublanguage of <math>L_0</math>. * The grammar of <math>L_2</math>, which has the form of a theory describing the syntactic structure of such factual descriptions, is stated in the meta–meta–metalanguage <math>L_3</math>, which likewise is a sublanguage of <math>L_0</math>. * The grammar of <math>L_3</math> has the form of a metatheory describing the syntactic structure of theories stated in <math>L_2</math>. * <math>L_4</math> and succeeding metalanguages have the same grammar as <math>L_3</math>, differing only in reference. Since all of these metalanguages are sublanguages of <math>L_0</math>, <math>L_1</math> is a nested metalanguage, but <math>L_2</math> and sequel are ordered metalanguages.<ref>''Ibid''. p. 277.</ref> Since all these metalanguages are sublanguages of <math>L_0</math> 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.<ref>{{cite book | last =Borel | first =Félix Édouard Justin Émile | author-link =Émile Borel | title =Leçons sur la theorie des fonctions | publisher =Gauthier-Villars & Cie. | edition =3 | date =1928 | location =Paris | pages =160 | language =fr }}</ref> == Types of expressions == There are several entities commonly expressed in a metalanguage. In logic usually the object language that the metalanguage is discussing is a [[formal language]], and very often the metalanguage as well. === Deductive systems === {{Main|Deductive system}} A ''deductive system'' (or, ''deductive apparatus'' of a [[formal system]]) consists of the [[axiom]]s (or [[axiom schema]]ta) and [[rules of inference]] that can be used to [[formal proof|derive]] the [[theorem]]s of the system.<ref>{{Hunter 1996|p=7}}</ref> === Metavariables === {{Main|Metavariable (logic)}} A ''metavariable'' (or ''metalinguistic'' or ''metasyntactic'' variable) is a [[symbol (formal)|symbol]] 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: :Let ''A'' and ''B'' be arbitrary [[well-formed formula|formula]]s of a [[formal language]] <math>L</math>. The symbols ''A'' and ''B'' are not symbols of the object language <math>L</math>, they are metavariables in the metalanguage (in this case, English) that is discussing the object language <math>L</math>. === Metatheories and metatheorems === {{Main|Metatheory|Metatheorem}} A ''metatheory'' is a [[theory]] whose subject matter is some other theory (a theory about a theory). [[Statement (logic)|Statements]] made in the metatheory about the theory are called [[metatheorem]]s. A ''metatheorem'' is a [[truth|true]] statement about a [[formal system]] expressed in a metalanguage. Unlike theorems proved within a given formal system, a metatheorem is proved within a [[metatheory]], and may reference concepts that are present in the [[metatheory]] but not the object theory.<ref>[[George Ritzer|Ritzer, George]]. 1991. ''Metatheorizing in Sociology''. New York: Simon Schuster {{isbn|0-669-25008-2}}</ref> === Interpretations === {{Main|Interpretation (logic)}} An ''interpretation'' is an [[Valuation (logic)|assignment]] of meanings to the [[symbol (formal)|symbols]] and [[word]]s 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 the [[conduit metaphor]].<ref>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]]</ref> This paradigm operates through two distinct, related frameworks. The ''major framework'' views language as a sealed pipeline between people: {| class="wikitable" |+ 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 |} The ''minor framework'' views language as an open pipe spilling mental content into the void: {| class="wikitable" |+ 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 a formal language. The development of a [[programming language]] involves the use of a metalanguage. The act of working with metalanguages in programming is known as ''[[metaprogramming]]''. [[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 include [[ML (programming language)|ML]], [[Lisp (programming language)|Lisp]], [[m4 (computer language)|m4]], and [[Yacc]]. == See also == {{div col}} * {{annotated link|Category theory}} * {{annotated link|Formal language}} * {{annotated link|Jakobson's functions of language}} * {{annotated link|Language-oriented programming}} * {{annotated link|Meta-communication}} * {{annotated link|Metaethics}} * {{annotated link|Metafiction}} * {{annotated link|Metagraphy}} * {{annotated link|Metamathematics}} * {{annotated link|Metalinguistic abstraction}} * {{annotated link|Metalinguistic awareness}} * {{annotated link|Metalocutionary act}} * {{annotated link|Metaphilosophy}} * {{annotated link|Natural semantic metalanguage}} * {{annotated link|Nested quotation}} * {{annotated link|Paralanguage}} * {{annotated link|Self-reference}} * {{annotated link|Use–mention distinction}} {{div col end}} == 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]]. *[[J. A. Cuddon|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 == {{Reflist}} ==External links== * [http://pespmc1.vub.ac.be/METALARE.html Metalanguage], ''[[Principia Cybernetica]]''. * [http://lists.village.virginia.edu/lists_archive/Humanist/v20/0091.html Willard McCarty (submitted 2006) Problematic Metaphors], ''Humanist Discussion Group'', Vol. 20, No. 92. {{Mathematical logic}} {{Authority control}} [[Category:Metalogic]] [[Category:Linguistics]] [[Category:Linguistics terminology]] [[Category:Metalanguages]] [[Category:Proof theory]]
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