Metalanguage
Encyclopedia
Broadly, any metalanguage is language or symbols used when language itself is being discussed or examined. In logic
and linguistics
, a metalanguage is a language used to make statements about statements in another language (the object language
). Expressions in a metalanguage are often distinguished from those in an object language by the use of italics, quotation marks, or writing on a separate line.
'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.”.
It occurs in natural, or informal, languages, as well—such as in English, where adjectives, adverbs, and possessive pronouns constitute an embedded metalanguage; and where nouns, verbs, and, in some instances, adjectives and adverbs, constitute an object language. Thus, the adjective “red” in the phrase “red barn” is part of the embedded metalanguage of English; the noun “barn” is part of the object language. In the phrase “slowly running,” the verb “running” is part of the object language; the adverb “slowly” is part of the embedded metalanguage.
, and very often the metalanguage as well.
) consists of the axiom
s (or axiom schema
ta) and rules of inference that can be used to derive
the theorem
s of the system.
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:
The symbols A and B are not symbols of the object language
, they are metavariables in the metalanguage (in this case, English) that is discussing the object language 
.
whose subject matter is some other theory (a theory about a theory). Statements
made in the metatheory about the theory are called metatheorem
s. A metatheorem is a 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
.
of meanings to the symbols
and word
s of a language.
. This paradigm operates through two distinct, related frameworks.
The major framework views language as a sealed pipeline between people:
1. Language transfers people's thoughts and feelings (mental content) to others
ex: Try to get your thoughts across better.
2. Speakers and writers insert their mental content into words
ex: You have to put each concept into words more carefully.
3. Words are containers
ex: That sentence was filled with emotion.
4. Listeners and writers extract mental content from words
ex: 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:
1. Speakers and writers eject mental content into an external space
ex: Get those ideas out where they can do some good.
2. Mental content is reified (viewed as concrete) in this space
ex: That concept has been floating around for decades.
3. Listeners and writers extract mental content from this space
ex: Let me know if you find any good concepts in the essay.
involves the use of a metalanguage. Backus–Naur Form
, developed in the 1960s by John Backus and Peter Naur, is one of the earliest metalanguages used in computing.
Logic
In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...
and linguistics
Linguistics
Linguistics is the scientific study of human language. Linguistics can be broadly broken into three categories or subfields of study: language form, language meaning, and language in context....
, a metalanguage is a language used to make statements about statements in another language (the object language
Object language
An object language is a language which is the "object" of study in various fields including logic, linguistics, mathematics and theoretical computer science. The language being used to talk about an object language is called a metalanguage...
). Expressions in a metalanguage are often distinguished from those in an object language by the use of italics, quotation marks, or writing on a separate line.
Types of metalanguage
There is a variety of recognized metalanguages, including embedded, ordered, and nested (or, hierarchical).Embedded metalanguage
An embedded metalanguage is a language formally, naturally and firmly fixed in an object language. This idea is found in Douglas HofstadterDouglas Hofstadter
Douglas Richard Hofstadter is an American academic whose research focuses on consciousness, analogy-making, artistic creation, literary translation, and discovery in mathematics and physics...
's book, Gödel, Escher, Bach
Gödel, Escher, Bach
Gödel, Escher, Bach: An Eternal Golden Braid is a book by Douglas Hofstadter, described by his publishing company as "a metaphorical fugue on minds and machines in the spirit of Lewis Carroll"....
, in a discussion of the relationship between formal languages and number theory
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
: “... it is in the nature of any formalization of number theory that its metalanguage is embedded within it.”.
It occurs in natural, or informal, languages, as well—such as in English, where adjectives, adverbs, and possessive pronouns constitute an embedded metalanguage; and where nouns, verbs, and, in some instances, adjectives and adverbs, constitute an object language. Thus, the adjective “red” in the phrase “red barn” is part of the embedded metalanguage of English; the noun “barn” is part of the object language. In the phrase “slowly running,” the verb “running” is part of the object language; the adverb “slowly” is part of the embedded metalanguage.
Ordered metalanguage
An ordered metalanguage is analogous to 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 metalanguage
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 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.Types of expressions in a metalanguage
There are several entities commonly expressed in a metalanguage. In logic usually the object language that the metalanguage is discussing is a formal languageFormal language
A formal language is a set of words—that is, finite strings of letters, symbols, or tokens that are defined in the language. The set from which these letters are taken is the alphabet over which the language is defined. A formal language is often defined by means of a formal grammar...
, and very often the metalanguage as well.
Deductive systems
A deductive system (or, deductive apparatus) of a formal systemFormal system
In formal logic, a formal system consists of a formal language and a set of inference rules, used to derive an expression from one or more other premises that are antecedently supposed or derived . The axioms and rules may be called a deductive apparatus...
) consists of the axiom
Axiom
In traditional logic, an axiom or postulate is a proposition that is not proven or demonstrated but considered either to be self-evident or to define and delimit the realm of analysis. In other words, an axiom is a logical statement that is assumed to be true...
s (or axiom schema
Axiom schema
In mathematical logic, an axiom schema generalizes the notion of axiom.An axiom schema is a formula in the language of an axiomatic system, in which one or more schematic variables appear. These variables, which are metalinguistic constructs, stand for any term or subformula of the system, which...
ta) and rules of inference that can be used to derive
Formal proof
A formal proof or derivation is a finite sequence of sentences each of which is an axiom or follows from the preceding sentences in the sequence by a rule of inference. The last sentence in the sequence is a theorem of a formal system...
the theorem
Theorem
In mathematics, a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems, and previously accepted statements, such as axioms...
s of the system.
Metavariables
A metavariable (or, metalinguistic variable) is a symbolSymbol (formal)
For other uses see Symbol In logic, symbols build literal utility to illustrate ideas. A symbol is an abstraction, tokens of which may be marks or a configuration of marks which form a particular pattern...
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 formulaWell-formed formulaIn mathematical logic, a well-formed formula, shortly wff, often simply formula, is a word which is part of a formal language...
of a formal languageFormal languageA formal language is a set of words—that is, finite strings of letters, symbols, or tokens that are defined in the language. The set from which these letters are taken is the alphabet over which the language is defined. A formal language is often defined by means of a formal grammar...
.
The symbols A and B are not symbols of the object language
, they are metavariables in the metalanguage (in this case, English) that is discussing the object language .Metatheories and metatheorems
A metatheory is a theoryTheory
The English word theory was derived from a technical term in Ancient Greek philosophy. The word theoria, , meant "a looking at, viewing, beholding", and referring to contemplation or speculation, as opposed to action...
whose subject matter is some other theory (a theory about a theory). Statements
Statement (logic)
In logic a statement is either a meaningful declarative sentence that is either true or false, or what is asserted or made by the use of a declarative sentence...
made in the metatheory about the theory are called metatheorem
Metatheorem
In logic, a metatheorem is a statement about a formal system proven 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.- Discussion :A formal...
s. A metatheorem is a true
Truth
Truth has a variety of meanings, such as the state of being in accord with fact or reality. It can also mean having fidelity to an original or to a standard or ideal. In a common usage, it also means constancy or sincerity in action or character...
statement about a formal system
Formal system
In formal logic, a formal system consists of a formal language and a set of inference rules, used to derive an expression from one or more other premises that are antecedently supposed or derived . The axioms and rules may be called a deductive apparatus...
expressed in a metalanguage. Unlike theorems proved within a given formal system, a metatheorem is proved within a metatheory
Metatheory
A metatheory or meta-theory is a theory whose subject matter is some other theory. In other words it is a theory about a theory. Statements made in the metatheory about the theory are called metatheorems....
, and may reference concepts that are present in the metatheory
Metatheory
A metatheory or meta-theory is a theory whose subject matter is some other theory. In other words it is a theory about a theory. Statements made in the metatheory about the theory are called metatheorems....
but not the object theory
Object theory
Object theory is a theory in philosophy and mathematical logic concerning objects and the statements that can be made about objects.- An informal theory :...
.
Interpretations
An interpretation awesome is an assignmentValuation (logic)
In logic and model theory, a valuation can be:*In propositional logic, an assignment of truth values to propositional variables, with a corresponding assignment of truth values to all propositional formulas with those variables....
of meanings to the symbols
Symbol (formal)
For other uses see Symbol In logic, symbols build literal utility to illustrate ideas. A symbol is an abstraction, tokens of which may be marks or a configuration of marks which form a particular pattern...
and word
Word
In language, a word is the smallest free form that may be uttered in isolation with semantic or pragmatic content . This contrasts with a morpheme, which is the smallest unit of meaning but will not necessarily stand on its own...
s of a language.
Role in metaphor
Michael J. Reddy (1979) discovered and has demonstrated that much of the language we use to talk about language is conceptualized and structured by what he refers to as the conduit metaphorConduit metaphor
A Conduit metaphor is a linguistic term referring to a dominant class of figurative expressions used when discussing communication itself...
. This paradigm operates through two distinct, related frameworks.
The major framework views language as a sealed pipeline between people:
1. Language transfers people's thoughts and feelings (mental content) to others
ex: Try to get your thoughts across better.
2. Speakers and writers insert their mental content into words
ex: You have to put each concept into words more carefully.
3. Words are containers
ex: That sentence was filled with emotion.
4. Listeners and writers extract mental content from words
ex: 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:
1. Speakers and writers eject mental content into an external space
ex: Get those ideas out where they can do some good.
2. Mental content is reified (viewed as concrete) in this space
ex: That concept has been floating around for decades.
3. Listeners and writers extract mental content from this space
ex: Let me know if you find any good concepts in the essay.
Role in computing
Computers follow programs, sets of instructions in a clear and simple language. The development of a programming languageProgramming language
A programming language is an artificial language designed to communicate instructions to a machine, particularly a computer. Programming languages can be used to create programs that control the behavior of a machine and/or to express algorithms precisely....
involves the use of a metalanguage. Backus–Naur Form
Backus–Naur form
In computer science, BNF is a notation technique for context-free grammars, often used to describe the syntax of languages used in computing, such as computer programming languages, document formats, instruction sets and communication protocols.It is applied wherever exact descriptions of...
, developed in the 1960s by John Backus and Peter Naur, is one of the earliest metalanguages used in computing.
See also
- Category theoryCategory theoryCategory theory is an area of study in mathematics that examines in an abstract way the properties of particular mathematical concepts, by formalising them as collections of objects and arrows , where these collections satisfy certain basic conditions...
- Conduit metaphorConduit metaphorA Conduit metaphor is a linguistic term referring to a dominant class of figurative expressions used when discussing communication itself...
- Language-oriented programmingLanguage-oriented programmingLanguage oriented programming is a style of computer programming in which, rather than solving problems in general-purpose programming languages, the programmer creates one or more domain-specific languages for the problem first, and solves the problem in those languages...
- Metaethics
- MetafictionMetafictionMetafiction, also known as Romantic irony in the context of Romantic works of literature, is a type of fiction that self-consciously addresses the devices of fiction, exposing the fictional illusion...
- Metagraphy
- Metalinguistic abstractionMetalinguistic abstractionIn computer science, metalinguistic abstraction is the process of solving complex problems by creating a new language or vocabulary to better understand the problem space...
- Metalocutionary actMetalocutionary actIn linguistic pragmatics, the term metalocutionary act is sometimes used for a speech act that is about the conversation itself rather than about its primary substance.- References :...
- MetaphilosophyMetaphilosophyMetaphilosophy, also called philosophy of philosophy, is the study of the nature, aims, and methods of philosophy. The term is derived from Greek word meta μετά and philosophía φιλοσοφία ....
- MetaprogrammingMetaprogrammingMetaprogramming is the writing of computer programs that write or manipulate other programs as their data, or that do part of the work at compile time that would otherwise be done at runtime...
- Natural Semantic MetalanguageNatural semantic metalanguageThe Natural semantic metalanguage is a linguistic theory and a practical, meaning-based approach to linguistic analysis. The theory is based on the conception of Polish professor Andrzej Bogusławski...
- ParalanguageParalanguageParalanguage refers to the non-verbal elements of communication used to modify meaning and convey emotion. Paralanguage may be expressed consciously or unconsciously, and it includes the pitch, volume, and, in some cases, intonation of speech. Sometimes the definition is restricted to...
- Self reference
- Use–mention distinction
Dictionaries
- Audi, R. 1996. The Cambridge Dictionary of Philosophy. Cambridge: Cambridge University PressCambridge University PressCambridge University Press is the publishing business of the University of Cambridge. Granted letters patent by Henry VIII in 1534, it is the world's oldest publishing house, and the second largest university press in the world...
. - Baldick, C. 1996. Oxford Concise Dictionary of Literary Terms. Oxford: Oxford University PressOxford University PressOxford University Press is the largest university press in the world. It is a department of the University of Oxford and is governed by a group of 15 academics appointed by the Vice-Chancellor known as the Delegates of the Press. They are headed by the Secretary to the Delegates, who serves as...
. - Cuddon, J. A.J. A. CuddonJohn Anthony Bowden Cuddon , was an English author, dictionary writer, and school teacher. Known best for his Dictionary of Literary Terms , Cuddon also produced the large Dictionary of Sport and Games, as well as several novels, plays, travel books, and other published works.Cuddon also edited two...
1999. The Penguin Dictionary of Literary Terms and Literary Theory. London: Penguin BooksPenguin BooksPenguin Books is a publisher founded in 1935 by Sir Allen Lane and V.K. Krishna Menon. Penguin revolutionised publishing in the 1930s through its high quality, inexpensive paperbacks, sold through Woolworths and other high street stores for sixpence. Penguin's success demonstrated that large...
. - Honderich, T. 1995. The Oxford Companion to PhilosophyThe Oxford Companion to PhilosophyThe Oxford Companion to Philosophy is a reference work in philosophy edited by Ted Honderich and published by Oxford University Press in 1995. A second edition was published in 2005 and included some 300 new entries. The new edition has over 2,200 entries and 291 contributors in 1,080...
. Oxford: Oxford University PressOxford University PressOxford University Press is the largest university press in the world. It is a department of the University of Oxford and is governed by a group of 15 academics appointed by the Vice-Chancellor known as the Delegates of the Press. They are headed by the Secretary to the Delegates, who serves as...
. - Matthews, P. H. 1997. The Concise Oxford Dictionary of Linguistics. Oxford: Oxford University PressOxford University PressOxford University Press is the largest university press in the world. It is a department of the University of Oxford and is governed by a group of 15 academics appointed by the Vice-Chancellor known as the Delegates of the Press. They are headed by the Secretary to the Delegates, who serves as...
. ISBN 978-0-19-280008-4 - McArthur, T. 1996. The Concise Oxford Companion to the English Language. Oxford: Oxford University PressOxford University PressOxford University Press is the largest university press in the world. It is a department of the University of Oxford and is governed by a group of 15 academics appointed by the Vice-Chancellor known as the Delegates of the Press. They are headed by the Secretary to the Delegates, who serves as...
.
External links
- Metalanguage, Principia CyberneticaPrincipia CyberneticaPrincipia Cybernetica is an international cooperation of scientists in the field of cybernetics and systems science, especially known for their Principia Cybernetica Web website...
- Willard McCarty (submitted 2006) Problematic Metaphors, Humanist Discussion Group, Vol. 20, No. 92.