An alternatives account of 'most’ and 'more than half’

Abstract

While 'most' and 'more than half' are generally assumed to be truth-conditionally equivalent, the former is usually interpreted as conveying greater proportions than the latter. Previous work has attempted to explain this difference in terms of pragmatic strengthening or variation in meanings. In this paper, we propose a novel explanation that keeps the truth-conditions equivalence. We argue that the difference in typical sets between the two expressions emerges as a result of two previously independently motivated mechanisms. First, the two expressions have different sets of pragmatic alternatives. Second, listeners tend to minimize the expected distance between their representation of the world and the speaker's observation. We support this explanation with a computational model of usage in the Rational Speech Act framework. Moreover, we report the results of a quantifier production experiment. We find that the difference in typical proportions associated with the two expressions can be explained by our account.

AreMostandMore Than HalfTruth-Conditionally Equivalent?

“…The second account assumes that most and more than half are truth-conditionally equivalent, but that most is subject to scalar implicatures leading to pragmatic strengthening. We also note that in parallel to the present work, another version of the scalar implicature proposal for the differences in the observed thresholds between most and more than half has been put forward by Carcassi and Szymanik (2021).…”

“…logically stronger) alternative utterances a sentence may activate (Grice, 1975;Horn, 1972, a.o.). There may be various versions of the SI account for the differences in thresholds between most and more than half which may differ in the implicature computing mechanism and/or postulated alternative utterances; for concreteness, we develop one version of the SI account (see Carcassi and Szymanik (2021) for another). More specifically, it will be outlined how the fact that the threshold of most is higher than the threshold of more than half could be accounted for as a higher-order SI (cf.…”

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

“…The empirical data (Kotek et al, 2015;Solt, 2016) showed that most is used and verified differently than more than half. These patterns of results have been explained in multiple ways (Carcassi & Szymanik, 2021;Hackl, 2009;Pietroski et al, 2009;Solt, 2016). None of these explanations, however, considered the difference in truth conditions between most and more than half.…”

“…For example, a corpus study (Solt, 2016) showed that most is not suitable to use in some contexts when the proportion is close to 50% (e.g., “ Most of the American population is female” vs. “ More than half of the American population is female”; Solt, 2016, p. 67). Furthermore, Carcassi and Szymanik (2021) support a pragmatic explanation by embedding it into the computational framework of the Rational Speech Act (Frank & Goodman, 2012).…”

“…Human language is an exceptionally complex phenomenon. The meaning of words and sentences has been studied from a variety of perspectives, ranging from formal semantics descriptions through computational simulations to experimental semantics (e.g., Carcassi & Szymanik, 2021; Deschamps, Agmon, Loewenstein, & Grodzinsky, 2015; Frank & Goodman, 2012; Hackl, 2009; Katsos et al., 2016; Pietroski, Lidz, Hunter, & Halberda, 2009). Formal semantics analyzes linguistic meaning at an abstract level and studies the logical form and composition of meanings.…”