Intensional anaphora

Abstract

Intensional operators are often treated as quantifiers over possible worlds, parallel to the treatment of determiners as quantifiers over individuals. Individuals introduced in intensional contexts cannot serve as antecedents to later pronouns as easily as those introduced in (merely) quantificational contexts, though. For instance, a quantified sentence like Everyone is eating a cheeseburger may be felicitously followed by an anaphoric statement like They are large, where they refers to the totality of cheeseburgers being eaten. However, as Stone (1999) points out, the quite similar Andrea might be eating a cheeseburger does not support later anaphoric references such as It is large or They are large. Stone (1999), Stone & Hardt (1999), and Brasoveanu (2010) solve this problem by restricting the value of pronouns: in their systems, a pronoun presupposes that its referent(s) exist in the world of evaluation, ruling out anaphora from non-veridical intensional contexts. And yet, we show in this paper (i) cases where such anaphora is disallowed even when the pronoun’s referents clearly exist and (ii) cases where such anaphora is indeed allowed, even though the pronoun’s referents might not exist. We argue instead that intensional anaphora is best captured using a description-based, rather than a value-based account. We propose that a pronoun presupposes that its corresponding antecedent description is instantiated in each world of the context set. For instance, there must be a cheeseburger being eaten by Andrea in every candidate world of the context set in order for It is large to be felicitous after Andrea might be eating a cheeseburger. We implement our proposal via a new logic (building on work by Keshet 2018, Abney & Keshet 2022) that we name Plural Intensional Presuppositional predicate calculus (or PIP). Each PIP formula translates directly into standard first-order predicate calculus with set abstraction, providing a classical foundation for this work.

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