Metalogic

metalogic

Study of the syntax and the semantics of formal languages and formal systems. It is related to, but does not include, the formal treatment of natural languages (e.g., English, Russian, etc.). Metalogic has led to a great deal of work of a mathematical nature in axiomatic set theory, model theory, and recursion theory (in which functions that are computable in a finite number of steps are studied).

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Metalogic 

the part of logic that deals with the meta-theoretical study of the structure and properties of different logical theories.

Metalogic arose at the end of the 19th and beginning of the 20th century as a result of investigations into the foundations of the deductive sciences (primarily mathematics). As these investigations became more specialized, metalogic divided into two separate branches: syntactics and semantics. The syntactic branch, which deals with the examination of purely structural properties of calculi, includes primarily the theory of (formal) proofs (or metamathematics) and the theory of the definability of concepts. The second branch of metalogic, which divides into a theory of sense and a theory of reference (theory of meaning), constitutes logical semantics. The emergence of an independent theory of algebraic content—the model theory—was a result of A. Tarski’s basic work in logical semantics dealing with the notion of truth in formalized languages.

Metalogic also includes the interesting problem of the relation between extensional and intensional languages, which served as the starting point for the new discipline of pragmatics.

REFERENCES

Tarski, A. Vvedenie v logiku i metodologiiu deduktivnykh nauk. Moscow, 1948. (Translated from English.)
Camap, R. Znachenie i neobkhodimost’. Moscow, 1959. (Translated from English.)
Church, A. Vvedenie v matematicheskuiu logiku, vol. 1. Moscow, 1960. (Translated from English.)
Carnap, R. The Logical Syntax of Language. New York-London, 1937.
Tarski, A. Logic, Semantics, Metamathematics. Oxford, 1956.
Martin, R. Towards a Systematic Pragmatics. Amsterdam, 1959.

IU. A. GASTEV and V. K. FINN