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What is the John Doe or John Smith of language names for when a linguist is making an example?

We’ve all seen

Suppose that in language  . . .

and

Imagine a language . . .

and in another post, I saw

a language Gwambomambo which lacks the word . . .

Is there a more common way to refer to a dummy language without using a plausible-sounding name as the last example does?

Lucas
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    I think what I see is "imagine a language L"... or "a language L1"... – melissa_boiko Jun 25 '19 at 15:45
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    Well, if you go that far, you're already talking about math and not linguistics. There's no reason to invent or imagine a language with certain properties if you can't find one that actually does; if you did imagine it and needed to name it, a good name might be one that preserves the properties you imagined it with, like "English without be" or "SOV French". – jlawler Jun 26 '19 at 15:16
  • I think it's a good question. L1 and L2 sound fine to me. –  Jul 03 '19 at 03:24
  • @jlawler I remembered one actual source, Chomsky’s Syntactic Structures: “[…] a general theory of linguistic structure in which such notions as “phoneme in L”, “phrase in L” […] are defined for an arbitrary language L”. – melissa_boiko Jul 10 '19 at 13:06
  • Like I said, math. The actual linguistic phenomena are waved away as already defined, and then the serious work of abstraction begins. – jlawler Jul 10 '19 at 14:44

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