Halliday & Matthiessen (1999: 426):
Jackendoff and a number of others now prefer the second position [semantic structures as subset of conceptual structures]. It is also shared by e.g. Langacker (1987), representing cognitive semantics from the other US coastline:Meaning is a mental phenomenon that must eventually be described with reference to cognitive processing. I therefore side with Chafe (1970, p. 74-76) by adopting a "conceptual" or "ideational" view of meaning ... I assume it is possible at least in theory (if not yet in practice) to describe in a principled, coherent, and explicit manner the internal structure of such phenomena as thoughts, concepts, perceptions, images and mental experience in general. The term conceptual structure will be applied indiscriminately to any such entity, whether linguistic or nonlinguistic. A semantic structure is then defined as a conceptual structure that functions as the semantic pole of a linguistic expression. Hence semantic structures are regarded as conceptualisations shaped for symbolic purposes according to the dictates of linguistic convention, (pp. 97-8)From our standpoint, this appears as a transcendent interpretation of meaning: we on the other hand prefer an immanent approach to meaning, where "conceptual organisation" is interpreted as meaning that is created by various semiotic systems, among which language is the primary one.