Conceptual structure is not part of language per se--it is part of thought. It is the locus for the understanding of linguistic utterances in context, incorporating pragmatic considerations and "world knowledge"; it is the cognitive structure in terms of which reasoning and planning take place. That is, the hypothesized level of conceptual structure is intended as a theoretical counterpart of what common sense calls "meaning." (p. 123)
Paraphrasing Stebbins, Jackendoff posits that events in the real world (outside our minds) are perceived by our perceptual systems (e.g., sight, hearing), which in turn deliver percepts ("bundled chunks of experience"--Stebbins) to the conceptual structures in our minds. Stebbins notes that "Jackendoff emphasizes that each stage in this cognitive process is physical, that the sequence from external event to our meaning of it is...a natural, material event." Moreover, he quotes Jackendoff as saying in Foundations of Language:
People find sentences (and other entities) meaningful because of something going on in their brains...There is no magic. That is, we seek a thoroughly naturalistic explanation that ultimately can be embedded in our understanding of the physical world. (p. 268, emphasis mine)
I do not profess to be an expert on cognitive linguistics like Jackendoff. Nevertheless, as someone with an interest in the philosophy of science (and a degree in linguistics), I find the position Jackendoff is advocating here to be problematic. To understand why, let us analyze what, given the two quotations presented above, Jackendoff is actually saying about language and cognition. He says in the first quotation that conceptual structures enable us to understand language. In the second quotation, he says that we find sentences (language) meaningful "because of something going on in [our] brains." Bringing these two ideas together, it seems reasonable to assume that Jackendoff believes that conceptual structures exist in our brains. The brain is, of course, a material entity; consequently, anything existing in it must also be material. Therefore, the conceptual structures that we use to assign meaning to language must also be material in nature. However, according to Jackendoff, conceptual structures are "part of thought," and thoughts are not material in nature. Philosophical materialists/naturalists (like Jackendoff, I assume) might respond that thoughts are really the result of electrochemical processes in the brain, but even if electrochemical processes cause thoughts, they are not the same thing as thoughts. The cause of something is not identical with the thing it causes. Thus, if the conceptual structures that interpret language are "part of thought," they cannot be material in nature, so it follows that they cannot exist in the brain, at least in any literal sense. In short, there is a logical problem here.
In other words, in attempting to explain the relationship between language and thought, Jackendoff fails to account for what Einstein (cited in Stebbins) called "the logically unbridgeable gulf which separates the world of sensory experiences [which are caused by physical phenomena] from the world of concepts and propositions." That is to say, there is a sort of "magic" to how the mind processes language, despite what Jackendoff says to the contrary. And what is the ultimate source of this "magic"? Is it blind, purposeless evolution or a purposeful, omnipotent Designer? That is the most important question to answer, I would say.
Image of Ray Jackendoff by Michael Yoshitaka Erlewine, from Wikipedia.org