At least et al: The semantic of scalar modifiers

Abstract

On the naive account of scalar modifiers like more than and at least, At least three girls snored is synonymous with More than two girls snored, and both sentences mean that the number of snoring girls exceeded two (the same, mutatis mutandis, for sentences with at most and less/fewer than). We show that this is false and propose an alternative theory, according to which superlative modifiers (at least/most) are quite different from comparative ones (more/less/fewer than). Whereas the naive theory is basically right about comparative modifiers, it is wrong about superlative modifiers, which we claim have a MODAL meaning: an utterance of At least three girls snored conveys two things: first, that it is CERTAIN that there was a group of three snoring girls, and second, that more than four girls MAY have snored. We argue that this analysis explains various facts that are problematic for the naive view, which have to do with specificity, distributional differences between superlative and comparative modifiers, differential patterns of inference licensed by these expressions, and the way they interact with various operators, like modals and negation.* 2.1. PUZZLE #1: SPECIFICITY. If the naive view on comparative and superlative quantifiers were correct, 3a and 3b should be equivalent. (3) a. I will invite at most two people, namely Jack and Jill. b. ?I will invite fewer than three people, namely Jack and Jill. Yet, there are clear differences. First, for most speakers 3b is markedly less felicitous than 3a is. Second, while 3a does not entail that anyone will be invited, it follows from 3b that the number of people to be invited equals two (that is to say, the invitees will be Jack and Jill). Similarly, while 4a is perfectly acceptable, and allows for the possibility that more than two people will be invited, 4b is less felicitous and rules out that possibility (cf. Kadmon 1992, Corblin 2007). (4) a. I will invite at least two people, namely Jack and Jill. b. ?I will invite more than one person, namely Jack and Jill. These contrasts already suggest rather strongly that superlative and comparative quantifiers are not interdefinable. But how do they arise? Our suggestion is that the namely riders in the (a) and (b) sentences are licensed in entirely different ways (assuming that the latter sentences are acceptable at all). The superlative quantifiers in the (a) sentences contain an existential expression that admits of a specific construal, viz. 'two people'. Thus interpreted, the phrase conveys that there is a particular pair of persons the speaker has in mind, and the namely rider identifies this pair as Jack and Jill. If this analysis is correct as far as it goes, it does not extend to the (b) sentences, if only because the phrases three people and one person are of the wrong cardinality. Furthermore, it is clear that an indefinite embedded in a comparative quantifier never admits of a specific construal. (5) *I will invite more/fewer than two people, namely Jack and Jill. If the namely riders in 3b and 4b are not li...

Superlative Modifiers as Modified Superlatives

“…As Geurts & Nouwen (2007) These judgments appear quite clear and consistent across all superlative modifiers; I conclude that the inferences should be attributed to at, not to at least and at most specifically.…”

“…As Geurts & Nouwen (2007) observed, the superlative modifiers at least and at most are intriguingly different from the comparative modifiers more than and less than. For example, at least is felt to be an odd choice in the following example for a speaker who knows how many sides a hexagon has, while more than is not problematic in the same way (Nouwen 2010): (1) a.…”

“…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 semantics and pragmatics of directional numeral modifiers

“…Hackl 2000; Geurts & Nouwen 2007;Büring 2008;Nouwen 2010;Cohen & Krifka 2010, 2014Coppock & Brochhagen 2013;Kennedy 2015), no attention has been paid thus far to the bounds these expressions set. In this section I show that this is an area where directional numeral modifiers differ fundamentally from their non-directional counterparts.…”

The Interpretation of the German Specificity Markers Bestimmt and Gewiss

“…The internal structure of the quantificational DP then must be such that more/less than is applied to three CDs by Madonna, such that the structure is [more/less than [three [CDs by Madonna]] rather than the usually assumed generalized quantifier structure [[more/less than [three]] [CDs by Madonna]]. See also Krifka (1999) or Geurts and Nouwen (2007) for proposals of at least or more than and other comparative operators along these lines and Endriss (2009) for discussion. Concerning indefinites modified by gewiss in (2-g) and (3-g), judgements show a strong tendency towards unacceptability.…”