According to the Gricean approach to scalar implicatures (SIs for short), SIs are pragmatic inferences that result from a reasoning about the speaker’s communicative intentions. In recent years, an alternative view of SIs (let us call it the ‘grammatical view’ of SIs) has been put forward, according to which they result from the optional presence of a covert so-called exhaustivity operator in the logical form of the relevant sentences and are thus reducible to standard semantic entailment (see Chierchia 2006, Fox 2007, Chierchia, Fox, and Spector in press, a.o, building on earlier grammatical approaches by, e.g., Landman 1998, Chierchia 2004).