David, a lot of the ways that Chomsky has affected linguistics are unproductive . The whole notion that only humans had real “language” and thus, ipso facto, any apparent use of language by nonhumans — signing apes, gray parrots, or dogs that identify words — can’t “really” represent language use stalled “xenolinguistics” for 50 years.
But your analysis of Chomsky’s grammars is simply wrong, the result of at least a couple of severe category errors.
The biggest one, and what appears to be the root cause of the others, is trying to apply Popperian falsifiability and “scientific method” — what Peirce called “adduction” — to test Chomskian grammars. The category error here is that Chomsky’s theory of symbol systems, what’s known as “formal language theory” is not an experimental science at all. It’s mathematics. Chomsky proposes an axiomatic basis for languages as symbol systems, and derives from some basic rules (which came from previous researchers, like Russell, Whitehead, Gödel, Frege, Cantor, and many others) the Chomsky hierarchy of grammars. This hierarchy turns out to be intimately related — technically, mutually reducible –to the other models fo symbol manipulation, which we also call computation.
One of the consequences of this is that Chomsky’s grammars are exhaustive: there is nothing that is recognizably a language that won’t fall into some Chomsky grammar class. (Now, strictly, this depends on the Church-Turing thesis in its broader form, that what can be reasoned can be reasoned by an effective computation. I take this as axiomatic; it’s a legitimate philosophical position, perhaps, to not make that assumption, but if you take that course I’ll promptly challenge you to display a counter-example.) It can no more be falsified than you can falsify the proposition that there exists no integer x such that 4 < x < 5. As with other forms of mathematics, the question isn’t whether it’s falsifiable — hell, Euclidean geometry is obviously falsifiable — but whether it’s useful.
There’s no doubt Chomsky’s formal symbol systems and hierarchy of grammar classes is useful: it’s central to most of mathematical logic, and nearly all of computer science: the HTML we’re using for PJM is described by a Chomsky grammar.
You then make a second category error by trying to then claim there’s a flaw in Chomsky’s grammars because they don’t explain how we then apply “meaning” to those strings. Again, the mathematics there is well-developed; it’s the results that aren’t very satisfying. A language has “meaning” because of a mapping to some other system, called a model, and we certainly can apply that sort of mapping to interpret natural languages.
We run into the problem that we don’t, in some essential sense, know what we mean by “meaning”. Searle’s “Chinese room” demonstrates that — it constructs an example of a symbol system that exhibits all the characteristics we’d see as “understanding meaning” in a natural language, but asserts that because it’s merely a symbol system, it’s not “real understanding”. The problem is that when we look at the brain, we don’t see any signs of anything other than a physical system behaving as a computational system, performing effective computations. So if Searle’s Chinese room can’t “understand”, apparently neither can we.
Here’s the category error is to assert some special sense of “understanding” when we don’t understand “understanding” to start with.
Although he started in linguistics, his real contributions are now really considered part of mathematical logic and computer science. The real point here, which you are on a good path to demonstrating, is that merely because Chomsky has presented effective and useful mathematics that describe languages, doesn’t mean he’s particularly qualified to then have his political opinions taken more seriously.
As a logician and computer scientist myself, I’d be more inclined to believe the opposite.
