So according to the authors of a paper in Nature:
It suggests rather that language is part of not a specialised module distinct from the rest of cognition, but more part of broad human cognitive skills.
The paper is Evolved structure of language shows lineage-specific trends in word-order universals. They found that the various grammatical rules governing the proper order of different words in a sentence changed over time, and crucially that there were no fixed associations between them: no correlations such that when one rule changed, another rule had to change at the same time.
This, they say, is inconsistent with the currently dominant linguistic theory of "language universals" fixed by the structure of the human brain/mind. One of the authors has written an excellent explanation here and languagelog has a nice discussion here.
Yet I'm not convinced that "broad human cognitive skills" can explain language. I'm not qualified to comment on the details of this study, but, I do know that the average 7 year old kid has effortlessly learned how to use at least one language, with the appropriate grammar, syntax, and a vocabulary of thousands of words.
On the other hand, take my phone. My phone can't do that. It can, just about, take my voice and convert it into text. It gets it right most of the time. It has absolutely no idea what those words mean. All it can do is send them to Google and search for them.
Speaking of Google, Google Translate is what you get when roomfuls of computers try to "do language". It's useful, it's cool, and it gets it more-or-less right most of the time. But the output it produces is stilted, often ungrammatical, and generally sounds nothing like a native speaker would ever produce.
Let me repeat myself:
On the other hand,takemy phone.My phoneisthatyou can notdoit.Itjustconverts thetexttovoicecantakeme.Most ofthe timeitgetsto the right.Whatisthe meaningofthe wordthathasabsolutely no idea.Thatitcan, Google,is tosendthemtofindthem.SpeakingofGoogle, Googletranslatoryou useyour computer'sroomfulssaid, "dolanguage"andattempt to,areobtained.It'scool,thengreat, butitismore or lessright, getsmost of the time.However,the outputit generatesisoftenexaggeratedungrammaticalIt sounds morelikea native speakerso fargeneratedin general.
That's my last paragraph Google Translated to Japanese and right back. Hmm.
On the other hand my phone can perform millions of arithmetical operations per second. The 7 year old probably takes a minute or two of hard effort to multiply two digits together. So who's got more "general cognitive ability"?
To say that language is a manifestation of human "general" or "broad" cognition is to say that human general cognition is better at learning languages than it is at doing arithmetic: which rather begs the question of how "general" it is.
This doesn't mean that language is a special module of the brain, or that there are "language universals" beyond the fact that they're all languages, though that seems like a pretty big one. But it would take very, very strong evidence to make me doubt that the existence of language is somehow built into the human brain.
Dunn M, Greenhill SJ, Levinson SC, & Gray RD (2011). Evolved structure of language shows lineage-specific trends in word-order universals. Nature PMID: 21490599