Metalanguage: Wikis

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In logic and linguistics, a metalanguage is a language used to make statements about statements in another language which is called the object language. It can refer to any terminology or language used to discuss language itself: a written grammar, for example, or a discussion about language use. Very often expressions in a metalanguage are distinguished from those in an object language by the use of italics, quotes or being set apart on a line by themselves.

Contents

Types of metalanguage

There are a variety of recognized metalanguages, including embedded, ordered, and nested (hierarchical).

An embedded metalanguage, as its name suggests, is a language embedded in an object language. It occurs both formally and naturally. This idea is found in Douglas Hofstadter's book, Gödel, Escher, Bach, in his 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." (pg. 270). 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, and the noun 'barn' is part of the object language. In the example, 'slowly running', the verb 'running' is part of the object language, and the adverb 'slowly' is part of the metalanguage.

An ordered metalanguage is analogous to ordered logic. An example of an ordered metalanguage would be the construction of one metalanguage to talk about an object language, followed by the creation of another metalanguage to talk about the first metalanguage, and so on.

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 talk about genus is also used to talk about species; the language that is used to talk about orders is also used to talk about genera; and, so on, up to kingdoms.

Types of expressions in a metalanguage

There are a few entities which are commonly expressed in a metalanguage. In logic, usually the object language about which the metalanguage is talking is a formal language, and very often the metalanguage is as well.

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Deductive systems

A deductive system (also called a deductive apparatus of a formal system) consists of the axioms (or axiom schemata) and rules of inference that can be used to derive the theorems of the system.[1]

Metalinguistic variables

A metasyntactic variable (also metalinguistic variable) is a 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 formula of a Formal language \mathcal{L}.

The symbols A and B are not symbols of the object language \mathcal{L}, they are metasyntactic variables in the metalanguage (in this case, English) which is talking about the object language \mathcal{L}.

Metatheorems

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.

Metatheories

A metatheory 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.

Interpretations

An interpretation is an assignment of meanings to the symbols and words of a language.

Role in metaphor

Michael Reddy (1979) 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 metaphor, which holds that ideas can be expressed and interpreted through language. It incorporates these three interconnected metaphors:

  • Concepts, thoughts, feelings, meanings, sense and ideas are objects.
  • Words, sentences, and so on are containers (with an inside and an outside) for these objects.
  • Finally, communication is the act of sending and receiving these containers (through a conduit).

Those who speak and expect their meaning to be understood as it was intended are thinking of language as a conduit, perhaps a more faithful one than it truly is: miscommunications and misunderstandings can be attributed to this assumption.

Reddy offers sentences similar to the following as evidence of the prevalence of the conduit metaphor in society:

  1. What is the meaning in his words?
  2. Try to get your thoughts into words.
  3. I couldn't get any meaning out of his words.
  4. I couldn't find any sense in his words.
  5. His words were empty and 'devoid' of feeling.
  6. His promises were hollow.
  7. His ideas were hidden in a dense thicket of sentences.
  8. Like a maggot in a turd he hid within the word.
  9. How do I convey my love in mere words.
  10. How do I get it across to you that I don't want to see you again.
  11. I gave her a call.
  12. I received your call.
  13. I got the message.

Computing

Computers follow programs which are sets of instructions in a clear and simple language. The development of a programming language involves the use of a metalanguage. Backus–Naur Form is one of the earliest metalanguages used in computing and was developed in the 1960s by John Backus and Peter Naur.

See also

References

  • 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.
  • Hofstadter, D. R. (1980). Godel, Escher, Bach: An Eternal Golden Braid. New York, Vintage 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.
  • McArthur, T. (1996). The Concise Oxford Companion to the English Language. Oxford, Oxford University Press.
  • Reddy, Michael J. (1979). "The conduit metaphor: A case of frame conflict in our language about language", in Metaphor and Thought, ed. Andrew Ortony, 2nd edn (Cambridge: Cambridge University Press, 1993): 164-201.
  • Ritzer, G. (1991). Metatheorizing in Sociology.
  1. ^ Hunter, Geoffrey, Metalogic: An Introduction to the Metatheory of Standard First-Order Logic, University of California Pres, 1971

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