Metalogic

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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

References in periodicals archive ?
Having said that, I maintain that "Being-qua-Being" is the "none-of-these" part of the above meta-logic and a most direct Surdetermination ("Surholding") of Reality, in the subsequent vicinity of the most neutral "non-non-A" determination of Existence whose universal object is a "Qualon", that is [O]bject = (Surject, Prefect, Abject, Subject, Object)--again, see the work on "Surjective Monism" for the peculiar new-contented glossary of these terms.
The central issue is whether Frege has a meta-theory and meta-logic of logic or whether he follows the concept sometimes called 'logic as language', which takes logic not as a formal systems besides language, but as a partial regimentation of language for specific scientific (mostly mathematical) purposes.
The reader has to have advanced background knowledge and understanding in meta-logic and semantics.