Raising and resolving issues with scalar modifiers

Abstract

We argue that the superlative modifiers at least and at most quantify over a scale of answers to the current question under discussion (and in this sense, resolve issues), and that they draw attention to the individual possibilities along the scale (and in this sense, raise issues for discussion). The point of departure is a simple analysis on which at least denotes what only presupposes, and at most denotes what only contributes as its ordinary atissue content. This analysis captures the truth conditions, focus-sensitivity, and distribution of superlative modifiers but leaves some pragmatic facts unexplained. We enrich the simple account with unrestricted inquisitive semantics in order to explain the fact that superlative modifiers give rise to ignorance implicatures while comparative modifiers like more and less do not, the fact that superlative modifiers do not give rise to scalar implicatures, and two puzzles concerning the interaction between superlative modifiers and deontic modals. We argue that this proposal provides the most empirically successful published account of superlative modifiers to date.

Superlative Modifiers as Modified Superlatives

“…(It is not clear to me that such a natural connection between superlatives and superlative modifiers would be available under the approach involving expression-alternatives to at least, but this is for future research to determine.) The proposal will deviate from Coppock & Brochhagen's (2013) in restricting superlative modifiers to degree-type arguments, but in principle the analysis should nevertheless be flexible enough to maintain the advantages of the discourse-based approach.…”

“…Coppock & Brochhagen (2013) couch this latter strategy in the framework of inquisitive semantics, where declaratives and interrogatives alike denote sets of ordinary propositions, in the style of Hamblin's treatment of questions. Schematically, this analysis for John read at least three books might be represented as follows:…”

“…Examples in this category include Krifka 1999, Geurts & Nouwen 2007, Büring 2008, and Coppock & Brochhagen 2013. Letting stand for 'is pragmatically stronger than' (following Geurts & Nouwen (2007)), the following is an example lexical entry following that approach (τ is any type, and p is an abbreviation for s,t ):…”

“…The strategy pursued here is to derive the uncertainty/variation from the introduction of alternatives, as under Coppock & Brochhagen's (2013) analysis (henceforth C&B) in Inquisitive Semantics; however, we build on Penka/Solt's insight that the range is related to the comparison class of the superlative. The analysis to be derived is one which gives as a meaning for an at least sentence the set of possibilities that are as strong as or stronger than the prejacent according to the contextually salient pragmatic strength ranking .…”

“…For Coppock & Brochhagen (2013), the ignorance implicature is generated through a generalization of Groenendijk & Roelofsen's (2009) maxim of 'Inquisitive Sincerity', which they call 'Interactive Sincerity'. In slogan form, it says: 'Don't raise an issue that you know how to resolve'-and asserting a sentence whose denotation is a set of propositional alternatives amounts to 'raising an issue '.…”