[groovy2shoes]

In formal language theory, '[formal] language' and '[formal] grammar' are well-defined mathematical terms, and it's indeed appropriate to say that a grammar defines language in that context.

Similarly, the 'language of languages' is also appropriate given that BNF is defined with a grammar, and is used to specify grammars.

Furthermore, formal grammars were originally invented for purposes of exploring natural languages.

Sorry if you didn't enjoy the article, but there's nothing wrong with it in the context of formal language theory :)