Epistemic Necessity Modality and Presupposition

Necessity modality is semantically characterized by the fact that it is involved in universal quantification. This paper points out some problems that might arise from this: weak necessity modals do not respect the semantics of necessity modals. This is because according to the traditional treatment of the modal, the set of worlds in which the strong necessity modal is assessed is predicted to include the set of worlds in which the weak modal is assessed. To remedy this, this paper argues that strong and weak necessity modals have their own set of worlds which are determined by the respective presupposition triggered by them, and universally quantify over each of their own possible worlds.