On January 28th, 2025, our six-year student Omri Doron gave an invited talk at the Hebrew University of Jerusalem, entitled “Presupposing multiplicity: another look at the semantics of plural marking”. Abstract can be seen here:
Plural indefinites in argument position give rise to so-called multiplicity inferences, which are neutralized in downward-entailing environments:
(1) a. Mary owns cats. -> Mary owns more than one cat.
b. Mary doesn’t own cats. -> Mary owns zero cats.
Numerous accounts have been proposed to explain this pattern (Sauerland 2003, Spector 2007, Zweig 2009, de Swart and Farkas 2010, Ivlieva 2013, Kriz 2017, a.o.), but all seem to face major empirical or conceptual challenges. I take as a desideratum two puzzling facts, both pointed out by Spector (2007): the projection of multiplicity from non-monotonic environments (2), and the infelicity of negated sentences in certain contexts (3).
(2) Exactly one of my friends owns a cat. ->
a. Exactly one of my friends owns exactly one cat.
b. The rest of my friends own zero cats.
(3) a. Bill likes to dress fancy, but today he’s not wearing a suit.
b. #Bill likes to dress fancy, but today he’s not wearing suits.
I propose a solution to these puzzles based on the argument that multiplicity is the result of a presupposition, present both in the basic examples (1a) and the negated ones (1b): that Mary either has more than one cat or zero cats. I show that this presupposition naturally falls out once we consider a recent proposal on the nature of scalar implicatures (Bassi et al. 2021). Finally, I argue that the same mechanism may be extended to account for the behavior of plural definites as well (homogeneity).