From http://en.wikipedia.org/wiki/Meta

In linguistics, a grammar is considered as being expressed in a metalanguage, language that operates on a higher level in order to describe properties of the plain language (and not itself).

I wonder if a formal grammar of a formal language is a metalanguage of the formal language?

  • Yes, of course. It's turtles all the way up.
    – jlawler
    Commented Jul 12, 2014 at 22:51
  • Not all grammars are written that way. Some just use terminology to describe the grammar. But a grammar using NSM would be.
    – curiousdannii
    Commented Jul 12, 2014 at 22:53
  • @curiousdannii: I am talking about formal grammars for formal languages. Not natural ones.
    – Tim
    Commented Jul 12, 2014 at 22:56
  • @jlawler: Thanks. What is the "metalanguage" in the quote "a grammar is considered as being expressed in a metalanguage"? It doesn't seem to be the "grammar".
    – Tim
    Commented Jul 12, 2014 at 22:56
  • 1
    Which formal languages are you talking about? Lojban? COBOL? Klingon? Second-order quantified predicate calculus? Legal English? yacc + lex? There are a lot of things that are called "formal languages".
    – jlawler
    Commented Jul 12, 2014 at 23:43

1 Answer 1


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.

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