A variable force analysis of positive polarity neg-raising modals

Abstract

I develop a new analysis of “weak necessity” modals should and supposed to that is motivated by novel observations of extra-weak meanings in some environments. I argue that this evidence of weak readings suggests that these modal verbs exhibit a type of variable force. Sentences with weak necessity modals express universal force in positive sentences and existential force under negation. The analysis will build on an analogy with free choice disjunction that assumes a basic weak meaning that strengthens in upward-entailing environments (Fox,2007; Bassi and Bar-Lev, 2016). I hypothesize that the precise distribution of the strengthened readings is governed by the polarity-sensitive nature of the modals (cf. Iatridou and Zeijlstra, 2013; Homer, 2015). In particular, I argue that the polarity sensitivity of the modals is the result of the association of their domains with a covert even (cf. Lahiri, 1995; Crni?c, 2014, 2019 for NPI any). This hypothesis makes intricate predictions about the range of readings that should be observed in various logical environments that I show to be borne out. I also argue that the analysis provides a natural link between neg-raising and weak necessity.