Variable Force Modality in English Infinitival Relatives: A Matter of Degree

Abstract English infinitival relative clauses exhibit variable force deontic modality, with the restriction that whereas a weak necessity (should-like) reading is always available, a possibility (can/could-like) reading is available only under weak quantifiers. I propose: weak necessity modals have a degree semantics, whereby combination with a silent positive morpheme yields weak necessity; existential closure of the degree variable yields possibility; and existential closure is available only under weak quantifiers because only they are interpreted within VP. The account supports the view that modality is scalar, that deontic possibility and (weak) necessity occupy the same scale, and that existential closure is structurally constrained.