A speaker, in uttering a semantically non-exhaustive answer, can convey that it is intended as an exhaustive answer. E.g.:
(1) Q: Of red, green and blue, which colours does John like?
A: He likes red and green. [exhaustivity: he doesn't like blue]
The conveyed exhaustivity has been traditionally considered a case of Gricean conversational implicature, i.e., as a logical consequence of what is said plus the assumption that the speaker is behaving cooperatively. However, over the last decade, cracks in this parsimonious picture have appeared – mostly as argued by proponents of the ‘grammatical’ approach to exhaustivity – such as cases of exhaustivity without a contextual competence assumption, exhaustivity despite an inactive maxim of Quantity, or ‘embedded’ cases of exhaustivity.
I show that a Gricean theory can quite easily mend these cracks (highlighting that, in fact, the grammatical approach on its own cannot). The crucial insight is that pragmatic reasoning is only as good as the stuff you put into it, i.e., literal meanings. If we adopt a slightly richer-than-usual notion of meaning (which, crucially, in the spirit of Grice, still treats informative content classically), an existing set of maxims from the literature can do the job.
I will use exhaustivity as an example to show that Grice was partially wrong about the cancellability of conversational implicatures.