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ЛОГИЧЕСКИЙ СИНТАКСИС

Logical Syntax

  1. Set of rules governing the construction and transformation of the expressions of a calculus.

  2. Branch of metalogic concerned with studying the structure and properties of uninterpreted calculi. The main problems arising from the syntactical examination of logical calculi are the problems of non-contradiction, completeness (see Non-Contradiction and also Axiomatic Theory, Completeness of), independence (see Axiomatic System, Independence of), decision (see Decision Problem), and provability. The problem of provability is to find the algorithm which provides the proof for any demonstrable. Logical Syntax thus includes the theory of proof.

The concept of Logical Syntax was introduced by Wittgenstein in 1919, although the problems of Logical Syntax had been considered by many representatives of mathematical logic by the end of the 19th century (Frege, Russell, Hilbert, Gödel, Church, Kleene, and others). Carnap gave a systematic exposition of the problems and concepts of Logical Syntax in The Logical Syntax of Language (1934), which shows the fertility of the syntactical investigation of the languages that formalize the various branches of the natural sciences (see Formalized Language).