Modified numerals and maximality

Abstract

In this article, we describe and attempt to solve a puzzle arising from the interpretation of modified numerals like less than five and between two and five. The puzzle is this: such modified numerals seem to mean different things depending on whether they combine with distributive or non-distributive predicates. When they combine with distributive predicates, they intuitively impose a kind of upper bound, whereas when they combine with non-distributive predicates, they do not (they sometimes even impose a lower bound). We propose and explore in detail four solutions to this puzzle, each involving some notion of maximality, but differing in the type of maximality involved ('standard' maximality versus 'informativity-based' maximality) and in the source of maximality (lexically encoded in the meaning of the numeral modifier versus non-lexical). While the full range of data we consider do not conclusively favor one theory over the other three, we do argue that overall the evidence (i) goes against the view that modified numerals lexically encode a 'standard' maximality operator, and (ii) suggests the need for a pragmatic blocking mechanism that filters out readings (logical forms) of sentences that are generated by the grammar but intuitively unavailable.

On “zero” and semantic plurality

“…It is well-known, however, that the requirement of being in a downward entailing environment is at times too lax. In quite a few places in the literature, it is suggested that not only should NPI environments be downward entailing, they should also not be upward entailing (Progovac 1993;Lahiri 1998;Gajewski & Hsieh 2014;Barker 2017). One illustration of this comes from singular definite descriptions.…”

A Link Between Local Enrichment and Scalar Diversity

“… 8 In principle there are analytical possibilities as to how UBELE may arise without the use of alternatives. One possibility is that scalar terms (like, ‘warm’) may be upper-bounded in virtue of the presence of a maximality operation as suggested for the analysis of quantificational expressions with numerals (see Kennedy, 2015 ; Buccola and Spector, 2016 ). The research on numerals suggests there is a strong bias to understand those expressions via something like maximality ( Geurts, 2006 ; Breheny, 2008 ).…”

NPIs, intervention, and collectivity

“…In the remainder of this remark, we present evidence that casts doubt on (5). We provide new arguments that the descriptive condition on NPI licensing, (1), must be environment-based (rather than operator-based), and must reference full sentential alternatives (rather than scalemates), thus replacing (5) (see, e.g., Kadmon & Landman 1993, Lahiri 1998, Homer 2008, Gajewski 2011, Chierchia 2004, 2013, Crnič 2014, 2019a,b, 2020, Buccola & Spector 2016 for further arguments). Specifically, we argue that the acceptability of a sentence instantiating an intervention configuration does not depend simply on the position that the relevant operator occupies in its scale, but rather depends on the logical relation that the pertinent constituent dominating the operator (i.e., the pertinent environment) bears to its alternatives.…”