Previous work on graded modality: Lewis and Kratzer

This chapter begins the discussion of graded modality with a review of two influential previous accounts. Lewis’ qualitative theory of comparative goodness begins with an ordinal scale – like those discussed in chapter 2, but composed of propositions rather than individuals. Measurement-theoretic considerations reveal that Lewis’ semantics is inadequate on several fronts, including the interpretation of quantitative comparisons (much better than) and a problematic ‘maximax’ feature that Lewis himself identifies. Kratzer’s proposal – a modification of Lewis’ which extends the account to non-gradable modals and graded epistemics – is presented, along with a compositional implementation using tools developed in ch.2. This theory shares the problems of Lewis’ theory, and adds additional problems due to unified treatment of epistemic and deontic modals. While this unification is methodologically attractive, it is also empirically problematic because epistemic and deontic comparatives generate radically different validities in cases involving disjunction and subset reasoning.