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I haven't read anything of Chompsky's, except his politic essays now and then, so I can comment on syntax or his analysis of lanugage.
Sure it makes sense to study language through linguistically derived concepts. It sounds like that's what linguistics does---independent of other areas of study.
But I take it that Kenneally wants to step out of that box and start looking at language differntly. So there is a dilemma. How much of say the background of anthropological study of language does a linguist want to incorporate? Psychology is another field that has a similar dilemma. They have their theories of learning and development, derived from their own kind of empirical work. They were forced early on to start dealing with the brain as a biological entity and there is a kind of dissonance between say psychology and psychiatry...
CG