LaGraM

Lisa Bylinina (LUCL, Leiden University)

Numeral semantics: quantification, maximization and polarity

During the last several decades, numerals proved to be a rich source of debate in semantics and pragmatics. I will focus on one segment of this debate that centers around the question whether bare numerals are quantifiers, and if yes, of what kind. There is a consensus that numerals are not quantifiers over individuals of the same type as quantificational determiners like ‘every’, ’some’ and so on (type <et,<et,t>>).

One argument against this quantificational analysis is the fact that in different contexts, numerals come with different quantificational force, compare (1) and (2), where the numeral is interpreted existentially and generically, respectively (see Buccola 2017):

(1) Twelve people came to the party.
(2) Twelve people can fit in the lift.

Two main alternatives to the classic quantificational analysis are: 1) a family of in-situ analyses, where numerals have a modificational semantic type or combine with some silent element to get it (Hackl 2000, Ionin and Matushansky 2006, Rothstein 2017); 2) a quantificational analysis, according to which numerals are quantifiers over degrees rather than individuals (Kennedy 2015).

These two classes of theories differ also with respect to which reading of the numeral they consider basic — the ‘at-least’ or the ‘exactly’ reading. Modificational analyses derive ‘exactly’ readings from ‘at-least’ ones, while Kennedy (2015) does the opposite — numerals, according to this analysis, are inherently maximized quantifiers over degrees. I will discuss potential reasons to tease quantification and inherent maximality apart. These reasons will have to do with polarity and NPI licensing conditions as discussed in Gajewski (2011). Finally, I will propose an analysis under which numerals are degree quantifiers that are not lexically maximized, thus producing an ‘at-least’ reading as basic. Maximization will be introduced as an additional step.

The talk is based on joint work with Rick Nouwen and Dominique Blok (Bylinina and Nouwen 2018; Blok, Bylinina and Nouwen 2019).

References
Blok, D., L. Bylinina and R. Nouwen (2019) Splitting Germanic negative indefinites. Ms.
Buccola, B. (2017). Bare numerals, collectivity, and genericity: A new puzzle. Ms.
Bylinina, L. and R. Nouwen (2018). On ‘zero’ and semantic plurality. Glossa: a journal of general linguistics 3(1).
Gajewski, J. R. (2011). Licensing strong NPIs. Natural Language Semantics 19(2), 109–148.
Hackl, M. (2000). Comparative quantifiers. Ph. D. thesis, MIT.
Ionin, T. and O. Matushansky (2006). The composition of complex cardinals. Journal of semantics, 23(4), 315-360.
Kennedy, C. (2015). A "de-Fregean" semantics (and neo-Gricean pragmatics) for modified and unmodified numerals. Semantics and Pragmatics, 8, 10-1.
Rothstein, S. (2017). Semantics for counting and measuring. Cambridge University Press.