Can anyone give a steelman version of Chomsky's anti-statistics colorless green ideas sleep furiously argument? The more I think about it, the more absurd it seems.
Here's my take on Chomsky's argument:
Naively, this seems plausible enough. But consider the following mirror-image argument, about physics:
The mirror image argument seems patently absurd, but it follows the exact same line of reasoning.
The passage seems silly. It is easy to make statistical models that contradict Chomsky's claim. But I think he means something else, that whether a sentence is grammatical, while not a binary, admits sharply discrete levels. The concept of grammar cuts human understanding of language at its joint and statistical understanding is largely on the other side. At least, that is the claim; I think introspection is difficult and usually turns statistical understanding into an illusion of discreteness.
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