9 Oct 2025

Nina Haslinger (Leibniz-Zentrum Allgemeine Sprachwissenschaft – ZAS)

Morphosemantic primitives in universal quantification

(joint work with Alain Noindonmon Hien, Emil Eva Rosina, Viola Schmitt and Valerie Wurm)

The quantifier systems of natural languages encode distinctions that have no counterpart in classical first-order logic, such as the distinction between what I’ll call "distributive" universal quantifiers (English *every*, *each*) and "maximizing" universal quantifiers (English *all*). Distributive universal quantifiers systematically disallow collective and cumulative interpretations wrt. their nuclear scope, whereas maximizing ones permit them to a limited extent and seem to have the effect of picking out a maximal element with respect to a part-whole relation. The standard view has been that this reflects two distinct primitive quantifier meanings, in line with the distinct lexicalizations generally found in European languages.

In this talk, we argue based on data from Keenan & Paperno (2012, 2017) and new data from Mabia languages that the standard view fails to derive a number of typological facts. First, some languages use the same form for distributive and maximizing universal quantifiers, with the choice of interpretation seemingly determined by properties of the complement, such as number and definiteness (cf. Gil 1995, Winter 2001, Fassi Fehri 2020). Second, in languages with distinct distributive and maximizing forms, the same properties of the complement correlate with the choice between quantifier forms in a non-arbitrary way that does not reduce to syntactic agreement and does not have a straightforward account on a standard theory with two lexical primitives. Third, distributive forms are often internally complex and formally related to the numeral *one*.

We propose an alternative account in which there is a single primitive for universal quantification, which contributes either maximization or distributivity depending on the algebraic properties of the restrictor predicate it combines with. "Distributive" forms like English *every* and *each* are analyzed as portmanteau forms that jointly realize the quantifier itself and elements that add a non-overlap or atomicity presupposition concerning the restrictor predicate. We implement this idea within a spanning approach to lexicalization in which portmanteau forms are not exceptional, but reflect the default mechanism for exponents that realize more than one feature. The resulting system derives the correlation between form choice and semantic properties of the restrictor predicate and also allows us to make sense of apparent mismatches between distributivity and complement number, e.g. uses of maximizing forms with definite singular complements to express roughly the meaning of *whole*, and uses of distributive forms with degree-interval expressions as in *every ten minutes*.

This talk is based on our recent NLLT paper, but in some places analytical choices will be made that deviate slightly from the "official" proposal adopted in the paper.