Formal Metalanguage and Formal Theory as Two Aspects of Generative Grammar

As is known, metalanguage is a language by means of which another language is described. The latter is called object-language. One and the same language may play the role of object-language and metalanguage. For example, the Russian language taken as an object of linguistic description is an object-language, the Russian language used for a linguistic description of Russian is a metalanguage. There are non-formal and formal metalanguages. For example, the Russian language used in ordinary grammars of Russian as a means of describing the Russian language is a non-formal metalanguage. Formal metalanguage is an artificial language, defined by deductive rules of construction, and used to describe natural languages. The problem of formal metalanguages for linguistic descriptions is a broad topic which we do not mean to-exhaust. We shall restrict ourselves to clarifying the role of formal metalanguages in constructing generative grammars. Every generative grammar is a formal theory. For example, a generative grammar of Russian is a formal theory of Russian, a generative grammar of English is a formal theory of English. We shall focus our attention on the question of correlation between formal metalanguages and formal linguistic theories understood as generative grammars. Let us take a concrete example: formal metalanguage and formal theory as two aspects of applicative generative grammar. This concrete example will make it possible, we hope, to draw certain general conclusions about the role of formal metalanguages in generative grammar. We shall start with formal metalanguage in applicative generative grammar. We call this metalanguage a universal operator language. The universal operator language is defined by the grammar which is an ordered quadruple