AreMostandMore Than HalfTruth-Conditionally Equivalent?

Abstract

Quantifying determiners most and more than half are standardly assumed to have the same truth-conditional meaning. Much work builds on this assumption in studying how the two quantifiers are mentally encoded and processed (Hackl, 2009; Lidz et al., 2011; Pietroski et al., 2009; Steinert-Threlkeld et al., 2015; Szymanik & Zajenkowski, 2010; Talmina et al., 2017). There is however empirical evidence that most is sometimes interpreted as ‘significantly more than half’ (Ariel, 2003, 2004; Ramotowska et al., 2020; Solt, 2011, 2016). Is this difference between most and more than half a pragmatic effect, or is the standard assumption that the two quantifiers are truth-conditionally equivalent wrong? We report two experiments which demonstrate that most preserves the ‘significantly more than half’ interpretation in negative environments, which we argue to speak in favor of there being a difference between the two quantifiers at the level of truth conditions.

Uncovering the Structure of Semantic Representations Using a Computational Model of Decision‐Making

“…The second consequence is that most is a vague quantifier (cf. Denić & Szymanik, 2022;Solt, 2011Solt, , 2016, while more than half has a sharp meaning boundary. Vagueness can relate to a threshold (Solt, 2015), a cut-off point (e.g., proportion) for which the responses change the truth value.…”

“…Moreover, we considered the effect of vagueness. Following the hypothesis that the meaning of most is vague (Denić & Szymanik, 2022; Solt, 2011), we formulated a hypothesis complementary to the Logical Theories hypothesis. Vagueness hypothesis: Most will have a greater variation in individual thresholds than more than half , meaning that some participants will have a higher threshold for most than more than half , and some participants will have a 50% threshold for both quantifiers.…”

“…We chose these quantifiers because they have drawn much attention from semanticists in recent years (Coppock & Strand, 2019; Hackl, 2009; Kotek, Sudo, & Hackl, 2015; Lidz, Pietroski, Halberda, & Hunter, 2011; Pietroski et al., 2009; Register, Mollica, & Piantadosi, 2020; Solt, 2016). Traditionally, they are treated as truth‐conditionally equivalent; however, the behavioral (e.g., Denić & Szymanik, 2022; Hackl, 2009; Ramotowska, Steinert‐Threlkeld, van Maanen, & Szymanik, 2020) and corpus data (e.g., Solt, 2016) showed a number of differences between them. We show that our modeling strategy and experimental design allow us to disentangle different aspects of meaning, such as semantic representations, vagueness, pragmatics, or processing, usually confounded in experimental and corpus data.…”

“…The long tradition of formal semantics (Barwise & Cooper, 1981;Mostowski, 1957) specifies the meaning of quantifiers in a form of rigid truth conditions. However, some natural language quantifiers such as many and few and also most are vague (Denić & Szymanik, 2022;Solt, 2011Solt, , 2016. Moreover, one study (Yildirim, Degen, Tanenhaus, & Jaeger, 2016) has shown individual differences in meaning representations of quantifiers, namely, that speakers apply many and some to describe different quantities.…”

“…This is often referred to as vagueness of meaning. Vagueness is omnipresent in natural language, for example, in the formation of categories (e.g., Gruenenfelder, 2019; Verheyen & Storms, 2013), meaning of adjectives (see Solt, 2015, for review), and quantifiers (e.g., Denić & Szymanik, 2022; Solt, 2011).…”