In his article Mr. Wall says: "So it's rather ironic that my views on Postmodernism were primarily informed by studying linguistics and translation as taught by missionaries, specifically, the Wycliffe Bible Translators. One of the things they hammered home is that there's really no such thing as a primitive human language. By which they mean essentially that all human languages are Turing complete. When you go out to so-called primitive tribes and analyze their languages, you find that structurally they're just about as complex as any other human language. Basically, you can say pretty much anything in any human language, if you work at it long enough. Human languages are Turing complete, as it were."
The former Wycliffe Bible Translator/Summer Institute of Linguistics member Dan Everett reportedly counters this in the New Yorker article. "Everett, once a devotee of Chomskyan linguistics, insists not only that Pirahã is a severe counterexample to the theory of universal grammar but also that it is not an isolated case." This article is fascinating.
My grad school experience is too far in my past to exactly distinguish the nuances between "non-Turing-complete" and "not conforming to Chomsky's universal grammar" -- so have at it discussing the differences. In any case, this article describes a language where it's impossible to describe some common human ideas -- and not through lack of vocabulary, and perhaps not even because of inadequate grammar. Rather, the language betrays a completely different mindset where such ideas may not be relevant to survival.
Dan Everett, former Wycliffe missionary, reached crisis when he found no way to describe the notion of a God or Jesus Christ and their relation to humans to this Amazonian tribe. Mr. Everett decided that if there are people to whom one cannot convey a Christian message, the message must not be universal and cannot be real.