Quantifying presupposition projection

There is a long-standing debate in the literature on how presuppositions project from the scope of quantifiers. Some theories argue for universal projection while others for existential projection, or a combination of both. More recently, some theories have proposed more nuanced, quantifier-specific predictions, where the projected presupposition roughly aligns with the ‘force’ of the quantifier. Previous quantitative studies have helped clarify the empirical landscape, but their results do not fully distinguish between these theories. Building on their methodologies, we conducted two experiments to further investigate presupposition projection in quantificational contexts, focusing on the existence presupposition of definite descriptions, and gender presuppositions of pronouns. Our results show that theories integrating both universal and what we dub ‘intermediate’ projection, in addition to local accommodation, provide the strongest account of the data in both experiments. However, our results also reveal differences between existence and gender presuppositions which are not fully accounted for by existing theories. We suggest that this discrepancy partly arises from the differential availability of local accommodation across presupposition types and explore potential theoretical refinements to address this issue.