At least not false, at most possible: between truth and assertibility of superlative quantifiers

Abstract

Generalized Quantifier Theory defines superlative quantifiers at most n and at least n as truth-conditionally equivalent to comparative quantifiers fewer than n+1 and more than n−1. It has been demonstrated, however, that this standard theory cannot account for various linguistic differences between these two types of quantifiers. In this paper I discuss how the distinction between assertibility and truth-conditions can be applied to explain this phenomenon. I draw a parallel between the assertibility of disjunctions and superlative quantifiers, and argue that those assertibility conditions are essentially modal. I use epistemic logic to formalize the assertibility conditions and revisit some of the linguistic puzzles related to superlative quantification.

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

“…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. As to the secondary goal of our study, we found no evidence that the ignorance reading that arises when at least is embedded under a universal modal is due to the wide-scope movement of at least.…”

“…The higher coherence rates in the case of the -knowledgeability contexts as opposed to +knowledgeability contexts go against Geurts & Nouwen's (2007), Nouwen's (2010), Coppock & Brochhagen's (2013b), and Spychalska's (2015) accounts. That is, those accounts by virtue of a semantic encoding -in one way or another -of the epistemic component of at least predict that the target sentence with at least should be judged as more compatible with a preceding -knowledgeability context than with a +knowledgeability context.…”

“…This first finding already invalidates the accounts that assume a clear semantic status for the epistemic effects of superlative modifiers (Geurts & Nouwen 2007;Nouwen 2010) or that pose a maxim/condition on the use of superlative modifiers, requiring that, when a speaker utters them, she has to entertain more than one possibility and should not know which one holds (Coppock & Brochhagen 2013b;Spychalska 2015). 5 All those accounts predict that a sentence with a superlative modifier would be contradictory or infelicitous when uttered by a +knowledgeable speaker, contrary to what the pretest revealed.…”

“…At the other extreme, a clearly semantic account of ignorance, such as Geurts & Nouwen's (2007) and Nouwen's (2010), would be in line with a negative main effect of SPEAKER'S KNOWLEDGEABILITY. The same could hold for hybrid accounts that include a different maxim or condition on the use of at least (Coppock & Brochhagen 2013b;Spychalska 2015), assuming that the violation of such a condition would be costly. The statistical analyses revealed a positive main effect of SPEAKER'S KNOWLEDGE-ABILITY in Region 5 ("seven hours"), which was significant in total reading times (β = .055, SE = .024, p = .033) (see Figure 2), and marginal in re-reading probability (β = .347, SE = .177, p = .050) and in first-pass reading times (β = .043, SE = .025, p = .092).…”

“…Moving to more semantic accounts of ignorance effects, Spychalska (2015), who makes a distinction between truth-and assertibility conditions, takes ignorance to be part of the assertibility conditions of superlative modifiers. While, roughly speaking, at least n is false if the quantity under discussion is smaller than n and true if it is exactly n or greater, the assertibility conditions for at least n require that the speaker considers it possible that the quantity in question is n and considers it possible that it is greater than n. Both the truth-and the assertibility conditions are met in the -knowledgeability contexts, whereas this is not the case for the assertibility conditions in the +knowledgeability contexts.…”