 Grice’s theory of conversation and implicatures was interpreted by many (including Grice himself) as a convincing way of accounting for the variety of contextually specific communicative contents while preserving the uniqueness of a sentence’s “literal” meaning, which was identified with truth conditions and regarded as determined by syntax and the conventional meanings of the occurring words, as in formal semantics. The only semantic role context was allowed to play was in determining the content of indexical words (such as ‘I’, ‘now’, ‘here’, etc.) and the effect of context-sensitive structures (such as tense) on a sentence’s truth conditions. However, in about the same years Travis (1975) and Searle (1979, 1980) pointed out that the semantic relevance of context might be much more pervasive, if not universal: intuitively, the same sentence type could have very different truth conditions in different contexts, though no indexical expression or structure appeared to be involved. Take the sentence “There is milk in the fridge”: in the context of morning breakfast it will be considered true if there is a carton of milk in the fridge and false if there is a patch of milk on a tray in the fridge, whereas in the context of cleaning up the kitchen truth conditions are reversed. Examples can be multiplied indefinitely, as indefinitely many factors can turn out to be relevant to the truth or falsity of a sentence as uttered in a particular context. Such variety cannot be plausibly reduced to traditional polysemy such as the polysemy of ‘property’ (meaning quality or real estate), nor can it be described in terms of Gricean implicatures: implicatures are supposed not to affect a sentence’s truth conditions, whereas here it is precisely the sentence’s truth conditions that are seen as varying with context.