Earlier quoted context omitted.
>They mention a profound difference in the opening paragraph, "Large language models do not depend on symbolic parts of speech or syntactic rules. "Human language models very obviously and evidently do. Honestly do they ? To me, they clearly don't. Grammar is not how language works. It's useful fiction. Language even in humans seems to be a very statistical process.
Yes! As somebody who speaks 2 languages, and sort of reads/understands 2 more, I cannot agree more. Human spoken languages do not follow any grammars. Grammars are just simplified representations of reality that is probabilistic in nature. This is something that Chomsky got very wrong, and the statistical/ML crowd got very right. But still, grammars are a very useful model.
Statistics are just another way to record a grammar, all the way down to the detail of how one talks about bicycles, or the Dirty War in Argentina.
If a grammar is defined as a book that enumerates the rules of a language, then of course language doesn't require following a grammar. If a grammar is defined as a set of rules for communicating reasonably well with another person who knows those same rules, then language follows grammars.