Speaker: Nina Haslinger (MIT)
Title: Strengthening under quantifiers: Gap projection rules vs. supervaluationism
Time: Wednesday, April 9th, 1pm – 2pm
Location: 32-D461
Abstract: In line with the goal of moving to a more informal, interactive format for the LFRG, this will not be a talk presenting results, but an attempt to start a discussion and figure out the theoretical options in an ongoing debate together.
I want to look at a recent line of work on strengthened meanings under quantifiers, which makes use of the idea that exhaustification results in trivalent meanings that follow a Strong Kleene projection pattern, and explore an alternative account of some of the basic data motivating this approach, based on a supervaluation principle.
The core data points I am interested in involve embedded strengthening of *some* to a ‘not all’ interpretation in sentences like (i)/(ii) (e.g. Chemla & Spector 2011). At first sight, an LF along the lines of (iii) with a standard bivalent exhaustifier is problematic for at least two reasons. First, without further stipulations it leads us to expect strengthening under negative quantifiers (‘no student’) as well, but such readings are marginal. Second, with a non-monotonic embedding environment such as (ii), it seems possible to get embedded strengthening in the UE (‘at least two’) component without also strengthening the DE (‘at most two’) component (Bassi et al. 2021, Gotzner & Benz 2022).
(i) Every student did some of the reading.
possible reading: ‘Every student did some, but not all of the reading.’
(ii) Exactly two students did some of the reading.
possible reading: ‘There are two students who did some, but not all of the reading, and it is not the case that there are three students who did some of the reading.’
(iii) {every student / exactly two students} [1 [exh [[some of the reading] [2 [t_1 did t_2]]] ]]
One currently popular account of this pattern (Bassi et al. 2021) makes use of the idea that exh triggers presuppositions that project following a Strong Kleene pattern (cf. George 2008, Fox 2013). An analogous puzzle arises for homogeneity effects triggered by definite plurals, as in (iv)-(vi), whose projection pattern has been studied experimentally in Kri & Chemla (2015) and Romoli et al. (2024). Motivated by these similarities, the presuppositional exhaustification account has been extended to definite plurals (Guerrini & Wehbe to appear, Paillé 2023).
(iv) Every boy opened the presents.
(v) Exactly two boys opened the presents.
(vi) No boy opened the presents.
For the plural case, Kri & Spector 2021 have developed an alternative account that relies on a supervaluation principle applying to a set of ‘candidate meanings’ that involve stronger and weaker interpretations of the plural. One reason why this account is conceptually attractive is that, since the truth-value gap comes about ‘after’ composition, there is no need to specify gap projection rules. There are also subtle empirical differences from the Strong Kleene pattern (Kri & Chemla 2015) that seem to favor this approach.
However, since their approach does not make use of exh, it does not lead us to expect an analogy with scalar strengthening as in (i)/(ii). I will discuss a way of extending this approach to exhaustification, so that the core projection facts motivating the presuppositional exhaustification approach are derived without using trivalent meanings in the composition. This provides the background for us to discuss the empirical pros and cons of both approaches, and potential ways of combining their core insights.