Ascriptions of belief and other doxastic propositional attitudes are commonly interpreted as quantifying over a set of possible worlds constituting doxastic alternatives for the belief experiencer. Katz (2000, 2003, 2008) has argued that belief predicates and other stative attitude predicates, along with stative predicates generally, lack a Davidsonian event argument and therefore do not report on any eventuality (event or state). Hacquard (2010), in contrast, assumes that all attitude ascriptions describe an event corresponding to the mental state of the attitude experiencer. The present investigation suggests that the strengths of doxastic predicates can be modeled by generalized quantifiers over the doxastic alternative set, permitting us to formulate and test predictions based on standard interactions of these quantifiers with negation when these ascriptions are negated. This provides a middle ground between Katz and Hacquard, whereby some belief ascriptions are interpreted as nothing more than a quantified condition over a doxastic alternative set, while others attribute a Davidsonian belief state to the experiencer. In the latter case, the condition involving quantification over doxastic alternatives is an essential content condition which serves to individuate the eventuality described by the belief report, and to identify it across possible worlds.

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