On the role of entailment patterns and scalar implicatures in the processing of numerals

Abstract

There has been much debate, in both the linguistics and the psycholinguistics literature, concerning numbers and the interpretation of number denoting determiners ('numerals'). Such debate concerns, in particular, the nature and distribution of upper-bounded ('at-least') interpretations vs. lowerbounded ('exact') construals. In the present paper we show that the interpretation and processing of numerals are affected by the entailment properties of the context in which they occur. Experiment 1 established off-line preferences using a questionnaire. Experiment 2 investigated the processing issue through an eye tracking experiment using a silent reading task. Our results show that the upperbounded interpretation of numerals occurs more often in an upward entailing context than in a downward entailing context. Reading times of the numeral itself were longer when it was embedded in an upward entailing context than when it was not, indicating that processing resources were required when the context triggered an upper-bounded interpretation. However, reading of a following context that required an upper-bounded interpretation triggered more regressions towards the numeral when it had occurred in a downward entailing context than in an upward entailing one. Such findings show that speakers' interpretation and processing of numerals is systematically affected by the polarity of the sentence in which they occur, and support the hypothesis that the upper-bounded interpretation of numerals is due to a scalar implicature. Keywords numbers; numeral determiners; scalar implicature; polarity; entailment; semantic processing Numerical expressions ('numerals') are known to have (minimally) two interpretations or construals: an 'exact' (or upper bounded) reading and an 'at-least' (or lower bounded) reading (the upper/lower bounded terminology is standard; Horn, 1972). They are exemplified by (1a) and (1b) respectively (and similarly for (2a) and (2b)):(1) a. If I find my wallet, I'll lend you ten dollars.© 2009 Elsevier Inc. All rights reserved.Address correspondence to: Daniele Panizza, Dipartimento di Scienze della Cognizione e della Formazione, Corso Bettini n. 31, 38068 Rovereto (TN), Italy. Telephone: 0039-0464-808668, Fax Number: 0039-0464-808655, daniele.panizza@unitn.it. Publisher's Disclaimer: This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. (2) a. Everyone will lend John ten dollars. NIH Public Accessb. Everyone who lends John ten dollars will never see his money again.The most salient reading of (1a) is an upper bounded one (…, I'll give you exactly ten dollars), while (1b) is more naturally inte...

At least ignorance inferences come at a processing cost: Support from eye movements

“…They found longer reading times at the region of the scalar expression in the implicature-triggering context condition, which they interpreted as an indication of online scalar implicature generation. A similar effect was found by Panizza, Chierchia & Clifton (2009), who tested the interpretation of bare numerals (lower-bounded vs. upper-bounded) with an eyetracking reading task with a similar context manipulation: the context that biased an upper-bounded interpretation (upward entailing context) exhibited a slowdown at the region of the numeral, which the authors take to suggest that the upper-bounded interpretation of numerals is due to the computation of a scalar implicature that happens online and is costly. 2…”

“…We found that the region where the interpretation of the whole modified numeral is completed as well as the one just after cause difficulties to the interpreters and make them slow down in -knowledgeable speaker contexts. After having excluded potential confounding effects of the unroundness of the numbers used in the experimental items, we take the processing cost incurred in these specific regions to be associated with the derivation of an ignorance implicature, similarly to the interpretation of similar findings by studies on scalar implicatures using the same paradigm (Breheny et al 2006;Panizza et al 2009). Our online finding is in line with the neo-Gricean pragmatic accounts that derive ignorance as a scalar implicature, but again at odds with Geurts & Nouwen (2007); Nouwen (2010); Coppock & Brochhagen (2013b); Spychalska (2015), who would predict the opposite effect, assuming that the contradiction between the speaker's epistemic state as encoded in the semantics of at least or signalled by its use and of that revealed by the +knowl-edgeability contexts would cause extra processing cost.…”

What Exactly do Numbers Mean?

“…Some accounts take the form described above: the lower-bounded meaning arises because the lexical item itself lacks an upper bound (Horn, 1972 & 1989; Gadzar, 1979; Levinson, 2000; Winter, 2001). In other theories, the lexical item may have an upper bound but the entire phrase (the determiner phrase or quantifier phrase) generates a mandatory lower-bound meaning as part of semantic composition (Fox & Hackl, 2004; van Rooy & Shulz, 2006; Ionin & Matushansky, 2006; Chierchia, Fox, & Spector, 2008; Barner & Bachrach, 2010; Foppollo, Guasti, & Chierchia, under review; Panizza, Chierchia, & Clifton, 2009). Our data and arguments will speak to both versions of this hypothesis.…”

“…Calculating the scalar implicature (to obtain the SOME BUT NOT ALL and EXACTLY TWO readings) would narrow down the set of people who feel fine, thus resulting in a weaker statement. For this reason, most linguistic theories predict that implicatures are typically cancelled in these contexts (Levinson, 2000; Chierchia, Spector, & Fox, 2008; Noveck, Chierchia, Chevaux, Guelminger, & Sylvestre, 2002; Chierchia, Crain, Guasti, Gualmini, & Meroni, 2001; Panizza et al, 2009). Consistent with this prediction, the most natural reading of (6) is one in which some is lower bounded, allowing us to conclude that even the folks who ate all of their berries felt fine.…”

The neural computation of scalar implicature

“… 5 Panizza, Chierchia, and Clifton Jr. (2009) report an eyetracking-while-reading study that manipulates entailment context. But critically this work focuses on the interpretation of number words (“two” means two and not three).…”