Modified Numerals, Vagueness, and Scale Granularity

Abstract

A key prerequisite for drawing the quantity implicature from ‘three’ to ‘not more than three’ in e.g. ‘Nigel has three children’ is the assumption that the speaker knows the exact number of Nigel’s children. This led to the assumption that ‘more than n’ constructions generate no implicatures as the comparative quantifier ‘more than’ signals that the speaker lacks sufficient knowledge for making a more precise statement (Krifka 2009). However, experimental results from Cummins et al. (2012) show that scalar implicatures are available from these constructions. For example, the size of the interval defined by the estimated lower and upper bounds for the number of people getting married is much higher for More than 100 people got married today than for More than 110 people got married today, in spite of 100 being smaller than 110. This led some researchers (Cummins et al. 2012; Cummins 2013; Benz 2015) to assume that the estimated most likely true value and distance to the upper bound of a modified numeral n is determined by the roundness level of n (Jansen & Pollmann 2001). However, the experimental study by Hesse & Benz (2020) showed that the most likely value is determined by a fixed 10% rule, and that the distance to the upper bound is determined by the distance to the next rounder number. In this paper we explore the implications of this finding for semantic and pragmatic theory. In particular, we will argue that the interpretation of numerals recruits general cognitive mechanisms that make an analysis of modified numerals along the lines of alternative semantics or a Hornian theory of scalar alternatives unsuitable.