We investigate the compositional semantics of vague quantified sentences, focusing on sentences such as “All of the students are tall,” where a non-vague quantifier quantifies into a vague predicate. While much work has been done on vagueness in natural language, including the semantics of vague adjectives, little attention has been paid so far to how vagueness interacts with complex sentences. We present an experiment that gathers data on naïve speakers’ interpretation of such sentences after collecting their judgment on the applicability of the vague predicate for each individual in the restrictor. We then compare how three prominent fuzzy logics – Gödel, product, and Łukasiewicz – predict the acceptability of the quantified sentences. Our results indicate that Gödel logic best matches human behavior. We then prove an equivalence between Gödel logic and a probabilistic form of Williamson’s epistemicism for the sentences we have tested, and discuss how our findings inform the broader debate on the semantics of vagueness, particularly between epistemicism and graded-truth approaches.
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