How obligatory irrelevance, symmetric alternatives, and dense scales conspire: The case of modified numerals and ignorance

Abstract

Buccola & Haida (2019) explore the consequences of a semantic-pragmatic theory in which relevance is closed under speaker belief. A primary consequence of this closure condition, they show, is that the Maxim of Quantity commits speakers to expressing their epistemic state about every relevant proposition. We argue that this commitment, dubbed Strong Epistemic Transparency, explains the contrast in ignorance inferences exhibited by non-strict comparative expressions like at least vs. strict ones like more than (hence the class A/B distinction of Nouwen 2010). We also discuss how our analysis might be extended to account for the observations of Cummins, Sauerland & Solt (2012) and Enguehard (2018) that the modifier more than does not block scalar inferences of round numerals.

Scalar diversity and ignorance inferences: An experimental study on 'at least' as a modifier of numerals vs. adjectives

“…5 Spector (2015), on the other hand, derives SpI effects of at least in grammar as Quantity implicatures and captures their robustness via the application of an obligatory exhaustification operation above the speaker belief operator that propositions are prefixed with (as in Meyer 2013). Buccola & Haida (2020) offer a similar account, where ignorance effects are derived in grammar as entailments across the board and are additionally derived via a pragmatic route when there is a how many Question under Discussion (QuD; see also Cremers et al 2021).…”

“…There has been an extensive theoretical investigation of at least as a numeral modifier (at least n) and the SpI inference it triggers (Geurts & Nouwen 2007;Kennedy 2015;Nouwen 2010;Coppock & Brochhagen 2013a;Cohen & Krifka 2014;Schwarz 2016;Buccola & Haida 2020;Cremers, Coppock, Dotlačil & Roelofsen 2021;a.m.o.). Nouwen (2010) provides crosslinguistic evidence of the robustness with which this inference is triggered by superlative numeral modifiers and their counterparts in a large number of languages (so-called Class B modifiers in Nouwen 2010).…”

Ignorance implicatures of modified numerals

“…There has been a lot of work on modified numerals recently both within the neo-Gricean approach to implicatures (Nouwen 2015;Kennedy 2015;Alrenga 2018) and within the grammatical approach (Mayr 2013;Schwarz 2016b;Enguehard 2018;Buccola and Haida 2020;Mihoc 2019).…”

Modified Numerals

“…Another strategy, suggested for instance in Coppock and Brochhagen (2013) and pursued in Buccola and Haida (2017), is to interpret at most numerals in situ, and to capitalize on the fact that possibility modals trigger so-called free-choice inferences. Buccola and Haida's (2017) proposal is fairly complex, and cannot be presented here due to lack of space.…”

“…Another strategy, suggested for instance in Coppock and Brochhagen (2013) and pursued in Buccola and Haida (2017), is to interpret at most numerals in situ, and to capitalize on the fact that possibility modals trigger so-called free-choice inferences. Buccola and Haida's (2017) proposal is fairly complex, and cannot be presented here due to lack of space. What I will do is present the general intuition behind the proposal, without keeping to the letter of their proposalthis wil be sufficient to show the limitations of that sort of account (which are fully discussed and acknowledged by Buccola and Haida 2017) Very informally, the first step of the proposal is rooted in the observation that, under a standard semantics for at most n, where it is synonymous (when applied to discrete objects) with fewer than (n+1), the meaning of (32) can be represented as follows (where the symbol 3 now represents any possibility modal).…”