Daniel Everett, the guy whose work inspired Wolfe's attack on Chomsky and Darwin, talks about his work and ideas here. The core of Everett's beef with Chomsky is whether or not recursion is central to language.
If there were a finite language, because of the lack of recursion, that wouldn't mean that it wasn't spoken by normal humans, nor would it mean that it wasn't a very rich source of communication. But if you lived in an environment in which culture restricted the topics that you talked about, and not only just your general environmental limitations on the topics you talked about, but if there were a value in the culture that said, don't talk about topics that go beyond, say, immediate experience—in other words, don't talk about anything that you haven't seen or that hasn't been told to you by an eyewitness—this would severely limit what you could talk about. If that's the case, then that language might be finite, but it wouldn't be a poor language; it could be a very rich language. The fact that it's finite doesn't mean it's not a very rich language. And if that's the case, then you would look for evidence that this language lacked recursion.
So in the case of Pirahã, the language I've worked with the longest of the 24 languages I've worked with in the Amazon, for about 30 years, Pirahã doesn't have expressions like "John's brother's house." You can say "John's house," you can say "John's brother," but if you want to say "John's brother's house," you have to say "John has a brother. This brother has a house." They have to say it in separate sentences.
As I look through the structure of the words and the structure of the sentences, it just becomes clear that they don't have recursion. If recursion is what Chomsky and Mark Hauser and Tecumseh Fitch have called "the essential property of language," the essential building block—in fact they've gone so far as to claim that that might be all there really is to human language that makes it different from other kinds of systems—then, the fact that recursion is absent in a language—Pirahã—means that this language is fundamentally different from their predictions.
If you go back to the Pirahã language, and you look at the stories that they tell, you do find recursion. You find that ideas are built inside of other ideas, and one part of the story is subordinate to another part of the story. That's not part of the grammar per se, that's part of the way that they tell their stories. So my idea is that recursion is absolutely essential to the human brain, and it's a part of the fact that humans have larger brains than other species. In fact, one of the papers at the recursion conference was on recursion in other species, and it talked about how when deer look for food in the forest, they often use recursive strategies to map their way across the forest and back, and take little side paths that can be analyzed as recursive paths. So it's not clear, first of all that recursion is unique to humans, and it's certainly not clear that recursion is part of language as opposed to part of the brain's general processing.