‘Maximize Presupposition’ and Gricean Reasoning

Recent semantic research has made increasing use of a principle, ‘Maximize Presupposition’, which requires that under certain circumstances the strongest possible presupposition be marked (Sauerland 2006). This principle is generally taken to be irreducible to standard (neo-) Gricean reasoning because, by definition, the forms that are in competition have the same assertive component (Percus 2006). We suggest, however that (parts of) Maximize Presupposition might be reducible to the theory of scalar implicatures. The analysis is a direct application of Stalnaker 2002: a speaker who asserts a sentence with presupposition p thereby indicates that he believes that it is common ground that p; if the addressee also believes that p, this suffices to make it common ground that p (even if p was not part of the common ground before the speaker's utterance). Thus, even in the absence of any process of accommodation, more information is produced by a sentence S with presupposition p than with an alternative S’ that has the same assertive component but a weaker presupposition. If S and S’ form a scale, one should thus utter S rather than S’ whenever this is possible. 1 Maximize Presupposition Following Heim (1991) and Sauerland (2002, 2003, 2005, 2006), several researchers have recently made use of a principle, Maximize Presupposition, which requires that one choose from a pre-determined set of competitors the Logical Form which marks the strongest presupposition compatible with the common ground (see also Percus 2006; Heim 2005; Schlenker 2003, 2004, 2005). The analysis comes in several varieties (Percus 2006), but for the moment we will assume that Maximize Presupposition has the following properties: (i) The principle is triggered by certain lexical items, which have a pre-determined presuppositional scale. In this respect the analysis resembles the neo-Gricean account of scalar implicatures, which are triggered by lexically determined scales. (ii) Maximize Presupposition only compares Logical Forms whose assertive components are contextually equivalent. Specifically, if C is the common ground, if F and F’ form a ‘presuppositional scale’ and if Maximize Presupposition applies to this scale, {w∈C: F is true in w} = {w∈C: F’ is true in w} (iii) Among the competitors, Maximize Presupposition selects the Logical Form that carries the strongest presupposition compatible with the common ground. The rule is best defined in two steps: a. F carries a stronger presupposition than F’ just in case {w∈W: F is neither true nor false in w} ⊂ {w∈W: F’ is neither true nor false in w}, where W is the set of all possible worlds (⊂ is used for strict inclusion). * I wish to thank the following for helpful remarks and criticisms: Emmanuel Chemla, Paul Egré, Uli Sauerland and Benjamin Spector. Special thanks to Emmanuel Chemla for detailed comments and suggestions. The author gratefully acknowledges the financial support of the American Council of Learned Societies (‘Ryskamp Fellowship’) and of UCLA. 1 However see Chemla 2006a for French data that are problematic for Maximize Presupposition when the scales are taken to be lexically specified. 2 We write trueC for ‘true with respect to the common ground C’; the relativization to C in addition to w is necessary because a formula may result in a presupposition failure due to global properties of the common ground C; we assimilate a common ground to a set of possible worlds, i.e. to what is sometimes called a ‘context set’. 3 This requirement holds of what Percus 2006 calls ‘Maximize Presupposition à la Sauerland’. It doesn’t quite hold of what he calls ‘Maximize Presupposition à la Schlenker’, nor of the proposal that he himself endorses. We come back to this point at the end of this squib.