Metalanguage:

In logic and linguistics, a metalanguage is a language used to make statements about statements in another language which is called the object language. It can refer to any terminology or language used to discuss language itself: a written grammar, for example, or a discussion about language use. Very often expressions in a metalanguage are distinguished from those in an object language by the use of italics, quotes or being set apart on a line by themselves.


An embedded metalanguage, as its name suggests, is a language embedded in an object language. It occurs both formally and naturally. This idea is found in Douglas Hofstadter's book, Gödel, Escher, Bach, in his discussion of the relationship between formal languages and number theory: "... it is in the nature of any formalization of number theory that its metalanguage is embedded within it." (pg. 270). It occurs in natural, or informal, languages, as well—such as in English, where adjectives, adverbs, and possessive pronouns constitute an embedded metalanguage; and where nouns, verbs, and, in some instances, adjectives and adverbs, constitute an object language^{[citation needed]}. Thus, the adjective 'red' in the phrase 'red barn' is part of the embedded metalanguage of English, and the noun 'barn' is part of the object language. In the example, 'slowly running', the verb 'running' is part of the object language, and the adverb 'slowly' is part of the metalanguage.

An ordered metalanguage is analogous to ordered logic. An example of an ordered metalanguage would be the construction of one metalanguage to talk about an object language, followed by the creation of another metalanguage to talk about the first metalanguage, and so on.

A nested, or hierarchical, metalanguage is similar to an ordered metalanguage in that each level represents a greater degree of abstraction. However, a nested metalanguage differs from an ordered one, in that each level includes the one below. The paradigmatic example of a nested metalanguage comes from the Linnean taxonomic system in biology. Each level in the system incorporates the one below it. The language used to talk about genus is also used to talk about species; the language that is used to talk about orders is also used to talk about genera; and, so on, up to kingdoms.

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