Well I certainly won't defend Chomsky against accusations he is vain or a vicious practictioner of academic politics. But the fact remains: Either you can, or you can't, describe the mechanisms of language using the same tools used in computability.
Before Chomsky, linguistics was groping for various squishy answers that one could argue about indefinitely. He put the basic question on the table: Can you describe what is going on in ways that is rigorous, predictive, and provably universal and equivalent to all other possible notations and system, or not?
OK, I'm not arguing against your point. I have two points: ont is that grammar and syntax are a subset of the important features of human language. Second, Chomsky has used his power to prevent any investigation of language features not covered by his analysis. This is the reason for the "Lysenko" comparison.
Correct me if I'm wrong on this, but my understanding of Chomsky's theory is that deep down, all human languages are equivalent to each other. This would imply the possibility of perfect translation, even by computers. So why, after decades of trying, are computer translations so horrible? And why is it so difficult to translate literature and poetry?
I mentioned in an earlier post that there is a specific genetic defect that supports Chomsky. There are people with a single gene variant who cannot learn the rule for regular verbs. They learn language just fine, but for them, all verbs are irregular and must be explicitely learned. In one way it supports Chomsky, but it also supports theories that assert that human language ability evolved from tiny, incremental variations, and is not simply an engine dropped in, completely developed.