Epistemic must, known as a strong necessity modal, conveys a weaker meaning than epistemic would, which suggests that a set of the best ranked worlds for must is a subset of a set of the best ranked worlds for its counterpart, according to Kratzer’s (1997 and 1991) framework for modal semantics. This paper points out that for this reason, Kratzer’s framework would have to predict incorrectly that epistemic must does not universally quantify over best possible worlds. In order to remedy this, the present study proposes, following Stalnaker (1974 and 2002), who argues that presupposition should be treated as the propositional attitude, that a set of presuppositional accessible worlds needs to be considered for the domain of quantification for the two modals, on the basis of the observed fact that what is presupposed by epistemic must is different from what is presupposed by would. Thus, the domain of quantification for the former differs from that for the latter, and hence this will make it possible for epistemic must to involve universal quantification over its own best ranked worlds.
1. Introduction
2. Epistemic would vs. must
3. Kratzer’s Modal Semantics and Epistemic would
4. Presuppositional Difference
5. Presuppositional Accessibility Relations
6. Formalization
7. Epistemic modals and Presupposition Failure
8. Closing Remarks