There are multiple definitions of language, not one. As another commenter pointed out, if you make the definition broad enough it loses usefulness.
> it’s anything that can have a grammar,
"Can" have a grammar is not restricting. "Does" is the correct verb, and that hasn't been proved.
> All you need is something that can form a sentence and something that can parse it and the thing going on between them is language.
OK, you've actually drawn out an important point. CAN the fungi form a sentence?
I can encode the 2nd sentence in "War and Peace" into polypeptides, but the polypeptides are still just an encoding of the language I picked (English? Russian?), and it doesn't make exchange of polypeptides by any other organism (even grad students!) a linguistic exercise.
There are multiple definitions of language, not one. As another commenter pointed out, if you make the definition broad enough it loses usefulness.
> it’s anything that can have a grammar,
"Can" have a grammar is not restricting. "Does" is the correct verb, and that hasn't been proved.
> All you need is something that can form a sentence and something that can parse it and the thing going on between them is language.
OK, you've actually drawn out an important point. CAN the fungi form a sentence?
I can encode the 2nd sentence in "War and Peace" into polypeptides, but the polypeptides are still just an encoding of the language I picked (English? Russian?), and it doesn't make exchange of polypeptides by any other organism (even grad students!) a linguistic exercise.