Modal semantics: Quantificational vs. scalar approaches

From its beginnings, work on the logic and formal semantics of modality has been dominated by two trends: the assumption that modals denote restricted quantifiers over possible worlds, and a near-exclusive focus on the semantics of the modal auxiliaries must, might, may, can, should, ought and a non-representative sample of modal verbs and adjectives (in particular require(d), permitted/permissible, possible, necessary, and obligatory, neglecting modified and comparative forms of these as well as e.g. likely, good, certain, evident, plausible, prefer among many others). 

Although the quantificational approach accounts for many facts about these expressions, I argue that it loses its attraction once we expand our evidential base to include a wider range of verbs and adjectives with modal semantics. In particular, there is far more overt gradability among the modal adjectives and verbs of English than has previously been recognized (and, to a more limited extent, among the auxiliaries). This suggests that an account built around modal degrees organized into scales is more appropriate. Although the most popular theory of modality in linguistics, Kratzer's, takes important steps in this direction, I argue that neither the particular method of ordering worlds and propositions that Kratzer uses nor the substantial quantificational component that remains can withstand scrutiny. What we need, instead, is a theory of modality that takes the scalar apparatus as basic and dispenses with direct quantification over possible worlds altogether. 

I propose a framework of this type, treating modals as operators that relate propositions to points on a scale and compare them to contextually or grammatically controlled threshold values, just as gradable adjectives do in standard accounts. In the particular implementation that I suggest, epistemic modals relate their propositional complement to its probability, while deontic, bouletic, and teleological modals relate their propositional complement to its expected utility. The proposal demonstrates the much greater flexibility that scalar semantics has in how propositions are ordered and how they interact with connectives: several phenomena in addition to gradability that are deeply problematic for standard theories, including Kratzer's, are resolved immediately. Specifically, quantificational theories predict wrongly that all modals should interact in the same way with disjunction, but epistemic and deontic/bouletic/teleological modals diverge sharply in this respects, and quantificational theories make incorrect predictions about both. In addition, deontic, bouletic, and teleological modals display much more fine-grained information-sensitivity than quantificational accounts lead us to expect. These phenomena receive a simple and straightforward account in the scalar semantics that I propose.