Contents › Section 7: Theory, terminology and disciplinary question › answer 9 of 39
Is a formal grammar of a formal language a formal language?
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Your question is confused. You confuse a grammar (an entity) with its expression (a language). So by very definition, the grammar of any language (formal or informal) is expressed in a metalanguage.
However, the difference between "formal" and natural languages is that a grammar of a natural language is always expressed in a metalanguage which is a part of natural language in the broadest possible sense (point made strongly by Gadamer in his Hermeneutics). In this, the Wikipedia quote is not very accurate because metalanguage can very easily be applied to itself.
However, a grammar of a formal language is more likely to be expressed by a different order language. Even a simple A -> B contains a symbol not of that language. However, this all depends on a metaphor of thinking about formal languages as language, in the first place. It's very useful but needn't be taken to extremes.
© Dominik Lukeš. Licensed under CC BY-SA 3.0. Originally published on Linguistics Stack Exchange, attributed there to Dominik Lukes (profile).