metalanguage in formal semantics, a language used to describe another language (the object language). The object language may be either a natural language or a formal language. The goal of a formal semantic theory is to provide an axiomatic or otherwise systematic theory of meaning for the object language. The metalanguage is used to specify the object language’s symbols and formation rules, which determine its grammatical sentences or well-formed formulas, and to assign meanings or interpretations to these sentences or formulas. For example, in an extensional semantics, the metalanguage is used to assign denotations to the singular terms, extensions to the general terms, and truth conditions to sentences. The standard format for assigning truth conditions, as in Tarski’s formulation of his ‘semantical conception of truth,’ is a T-sentence, which takes the form ‘S is true if and only if p.’ Davidson adapted this format to the purposes of his truth-theoretic account of meaning. Examples of T-sentences, with English as the metalanguage, are ‘ ‘La neige est blanche’ is true if and only if snow is white’, where the object langauge is French and the homophonic (Davidson) ”Snow is white’ is true if and only if snow is white’, where the object language is English as well. Although for formal purposes the distinction between metalanguage and object language must be maintained, in practice one can use a langauge to talk about expressions in the very same language. One can, in Carnap’s terms, shift from the material mode to the formal mode, e.g. from ‘Every veterinarian is an animal doctor’ to ‘ ‘Veterinarian’ means ‘animal doctor’.’ This shift is important in discussions of synonymy and of the analytic–synthetic distinction. Carnap’s distinction corresponds to the use–mention distinction. We are speaking in the formal mode – we are mentioning a linguistic expression – when we ascribe a property to a word or other expression type, such as its spelling, pronunciation, meaning, or grammatical category, or when we speak of an expression token as misspelled, mispronounced, or misused. We are speaking in the material mode when we say ‘Reims is hard to find’ but in the formal mode when we say ‘ ‘Reims’ is hard to pronounce.’
See also PHILOSOPHY OF LANGUAGE , TYPE – TOKEN DISTINCTION , USE – MENTION DISTINC – TIO. K.B.