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Suppose I have a formal system consisting of a formal grammar and deductive rules. To "describe" the formal grammar and deductive rules, I require some sort of metalanguage.

My question is, how does one describe "describe" in a rigorous sense? What does it mean for a language to describe another.

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    The minute you start describing some language phenomenon, that is already metalanguage. It just means language used to describe some natural language and its forms/processes, etc. So, grammar is a type of metalanguage and so are the various formal grammars (generativist, structuralist, Chomskyan, etc.) that are metalanguage explanations. Semiology is another. They all have their own metalanguage vocabulary.
    – Lambie
    Commented Apr 3 at 22:12
  • @Lambie This I understand, but I am specifically talking about logical formal languages. I'm looking for a logical definition using rigorous terms. Should I ask this instead on the logic stack exchange?
    – JayZenvia
    Commented Apr 3 at 22:16
  • Isn't a deductive method a formal method? The grammar and deductions you use are a metalanguage. There's formal logic, yes. But I never heard of a logical formal language unless it's some kind of math something. It's important to distinguish natural language from others (machine, etc.).
    – Lambie
    Commented Apr 3 at 22:20
  • @Lambie I'm not talking about natural language. I'm talking about the math something. I take it I'm in the wrong place? Can you direct me to where I should be? Thank you.
    – JayZenvia
    Commented Apr 3 at 22:23

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