Semantics circle: Homogeneity and exhaustification under embedding: Against the dichotomy between basic and strengthened meanings

Abstract

Much recent work in plural semantics has focused on the closely related properties of homogeneity (a gap between the semantic contributions an expression makes in UE and DE contexts, illustrated in (1)) and imprecision, a form of context-dependency driven by an implicit QUD.

(1)

(i) Ann read the papers. (= Ann read all/almost all of the papers)

(ii) Ann didn’t read the papers. (= Ann read none/almost none of the papers)

Experimental work has shown that the projection behavior of these two phenomena under embedding operators depends to some extent on the polarity of the embedding environment.  As shown by Augurzky et al. 2023, (2-ii) is less sensitive to QUD manipulations than (2-i). Further, Križ & Chemla 2015 show that in a trivalent truth-value judgment paradigm, sentences with a plural in a DE environment, as in (2-ii), are more likely to be judged “completely false” in a gap scenario than their UE counterparts, such as (2-i). These asymmetric patterns parallel the behavior of embedded exhaustification (see e.g. Chemla & Spector 2011). 

(2)

(i) Every boy opened his presents.

(ii) No boy opened his presents.

(iii) Not every boy opened his presents.

This parallel has motivated analyses of homogeneity and non-maximality in terms of grammaticalized exhaustification, using either a bivalent exh operator that is blocked in DE contexts (Bar-Lev 2021) or presuppositional exhaustification (Paillé 2022, 2023, del Pinal et al. 2023, Guerrini & Wehbe 2024).  However, variants of the exh approach that explicitly aim to account for the semantic asymmetries between (2-i) and (2-ii) face three puzzles: a) the fact that the negation asymmetries are not clear-cut, with some speakers accessing non-maximal construals under negation; b) the projection behavior of homogeneity gaps under non-monotonic operators like “exactly two” (Križ & Chemla 2015) and c) the observation that “not every” as in (2-iii) patterns with “every” rather than “no” (Augurzky et al. 2023). The bivalent exh approach needs to be supplemented with extra stipulations to account for a) and b) (see Bar-Lev 2021); the presuppositional exh approach solves puzzle b) but does not account for a) and c).

I argue that puzzles a) and c) reflect a problematic assumption underlying current analyses of exh: their reliance on a grammaticalized dichotomy between “basic meaning” and alternatives.  To illustrate the problem abstractly, let us assume a presuppositional exh theory and consider a sentence S[exh phi] containing [exh phi] as a subconstituent. Then S[exh phi] cannot be true at any context-world pair at which the sentence S[phi] obtained by removing the embedded exh is false. In effect, whereas particular alternatives of phi can be eliminated based on considerations of relevance (“alternative pruning”; see e.g. Bar-Lev 2021) so that the corresponding strengthened meanings are ignored, the basic meaning of phi can never be ignored.  

To develop an alternative view of strengthening that does not have this problem, I take Križ & Spector’s (2021) supervaluationist approach to homogeneity as my starting point. On this theory, imprecise expressions such as definite plurals introduce a set of alternative meanings; at the sentence level, only those alternatives are retained that are relevant to the QUD without being overinformative. This framework does not run into problems a) and c) since none of the alternatives is designated as “basic”, but does not derive any polarity effects. I propose to supplement this theory with a new constraint that filters out certain relevant alternatives. Intuitively, the option of locally strengthening an imprecise expression can be ignored if it leads to a weakening of the overall truth conditions: Given two alternative meanings A and B of an imprecise sentence S, B is blocked if it is globally weaker than A, but involves a locally stronger construal of some imprecise subexpression than A.  While stipulative in nature, this constraint turns out to have independent applications to otherwise puzzling imprecision phenomena outside the plural domain, such as round degree expressions under negation (cf. Solt & Waldon 2019 on numerals) and total/partial predication (Feinmann 2022, Haslinger & Paillé 2023).

The resulting system derives properties a)-c) without having to introduce two distinct sources of imprecision in plural semantics as in Bar-Lev (2021) or two distinct ways of weakening the effect of exh as in Guerrini & Wehbe (2024). But since Križ & Spector (2021) only discuss definite plurals, not standard cases of implicature, the question arises how the analogous embedding patterns of homogeneity and implicatures can be captured. I conclude the talk by sketching a new treatment of exh and implicatures in the supervaluationist setting from which the parallels with homogeneity fall out.