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metalanguageany ‘second order’ language used to discuss a language; any set or system of propositions about propositions.
a basic concept in modern logic and theoretical linguistics, used in studying the languages of various mathematical logical calculi, natural languages, and the relations between languages of different “levels” and for determining the relations between the languages under consideration and the object realms that these languages describe.
Metalanguage is a language used to express judgments about another language, the object-language. Metalanguage is employed in the study of the structure of the sign-combinations (expressions) of an object-language, and in the demonstration of theorems about the object-language’s expressive, and perhaps deductive, capacity and about its relation to other languages. Like the object-language, the metalanguage may also be an ordinary (natural) language. The metalanguage may differ from the object-language (for example, in an English-language textbook for Russians, Russian is the metalanguage and English is the object-language), or it may coincide, or partly differ from it, for example, as far as special terminology is concerned. Russian linguistic terminology, for example, is a part of metalanguage for the description of Russian; semantic factors belong to a metalanguage that describes the semantics of natural languages.
The concept of metalanguage was introduced and became extremely productive in connection with the study of formalized languages—calculi constructed within the framework of mathematical logic. In contrast to formalized object-languages, metalanguage—which is used to formulate a metatheory for the study of an object-theory formulated in the object-language—is, as a rule, an ordinary natural language or, more precisely, part of a natural language that has been specially limited so as not to contain any ambiguities, metaphors, metaphysical concepts, or other elements of ordinary language that hinder its function as an instrument of precise scientific research. At the same time, metalanguage itself may be formalized, and, independently of this, may be the object of study of a metametalanguage, and so on, in a series that may conceivably progress ad infinitum.
However, as an instrument in the metatheoretical study of formalized languages that permit versatile and orthodox enough interpretations in the logical sphere, the metalanguage should in no way be “poorer” than its object-language (that is, each expression of the object-language should be “translatable” into the metalanguage); the metalanguage should contain expressions of higher “logical types” than does the object-language. Failure to fulfill these requirements (which inevitably occurs in natural languages if special steps are not taken) leads to semantic paradoxes (antinomies).
REFERENCESTarski, A. Vvedenie v logiku i metodologiiu deduktivnykh nauk. Moscow, 1948. (Translated from English.)
Kleene, S. C. Vvedenie v metamatematiku, Ch. 1. Moscow, 1957. (Translated from English.)
Church, A. Vvedenie v matematicheskuiu logiku, vol. 1. Moscow, 1960. (Introduction.) (Translated from English.)
Curry, H. B. Osnovaniia matematicheskoi logiki, chs. 1–3. Moscow, 1969. (Translated from English.)
IU. A. GASTEV and V. K. FINN