  Lewis’s account is not alone in encountering difficulties with productivity. Most contemporary conventionalist theories encounter similar difficulties, because most such theories, heeding Frege’s context principle (only the context of a sentence do words have meaning), focus attention upon the link between sentences and propositions rather than the link between words and their meanings. One might hope to supplement convention-based accounts with the Chomsky-inspired thesis, advocated by James Higginbotham (1986) and Richard Larson and Gabriel Segal (1995), that speakers have tacit knowledge of a compositional semantic theory. However, as Martin Davies observes (2003), no one seems to have worked out this supplementary strategy in any detail, and it is not obvious how important a role the resulting account would assign to convention, let alone the Gricean communicative mechanism.