Weak necessity modals as homogeneous pluralities of worlds

We claim that weak necessity modals like English "should" are referential expressions that denote pluralities of worlds, against the standard analysis, according to which all modal auxiliaries are quantifiers. Weak necessity modals pattern like plural definites when tested for homogeneity effects (Löbner 2000, Križ 2016): they have scopeless readings under negation, they tolerate exceptions in certain discourse contexts, and they exhibit other properties characteristic of homogeneous definite plurals. We also discuss how to extend this analysis to French and Javanese, in which weak necessity modals are built compositionally from strong necessity modals by adding subjunctive morphology.