Resolving the Vagueness of Quantifiers With Explicit Expectations.

Abstract

Vague quantifiers like many, few, and several may vary considerably with respect to the quantity they denote. Depending on the context, many may indicate different quantities in "many students" versus "many cups of coffee." The vagueness and context sensitivity of such quantifiers pose a challenge for semantic theories that aim to formally characterize quantifier meaning. We address this challenge by extending and experimentally testing a Bayesian model proposed by Schöller and Franke (2017), which represents quantifiers as cumulative density thresholds over probability distributions of expected values. We hypothesized that each quantifier has a stable semantic threshold, with contextual variability arising from differences in expected value distributions. To test this, we conducted two experiments: one eliciting contextual expectations, and another collecting cardinality judgments for quantified utterances. We then fit five hierarchical Bayesian models and used model comparison (via WAIC and DIC) to evaluate whether thresholds generalize across contexts. Our results reveal conflicting evidence. While estimated thresholds are highly overlapping across contexts-suggesting some stability-models with individualized thresholds consistently outperform the context-stable alternative. Moreover, semantically motivated bounds do appear more stable than pragmatically motivated ones, as expected.