Choice and prohibition in non-monotonic contexts

Abstract

Disjunctions in the scope of possibility modals give rise to a conjunctive inference, generally referred to as 'free choice.' For example, Emma can take Spanish or Calculus suggests that Emma can take Spanish and can take Calculus. This inference is not valid on standard semantics for modals in combination with a Boolean semantics for disjunction. Hence free choice has sparked a whole industry of theories in philosophy of language and semantics. This paper investigates free choice in sentences involving a non-monotonic modified numeral, under which we embed a possibility modal scoping over disjunction. One example is Exactly one student can(not) take Spanish or Calculus. As we point out, the presence (or absence) of certain readings of these sentences is a key test for a prominent approach, which analyzes free choice as a kind of scalar implicature. We report on two experiments investigating the readings of such sentences, using an inferential task. Our results are challenging for the implicature approach. We sketch two possible solutions within this approach, either adopting a different recent implicature algorithm, or exploring a different meaning for modified numerals with exactly. Both of them suffer from a variety of problems. We then discuss a third solution, which exploits a recent account of free choice based on homogeneity. This approach can account for our results, in combination with plausible assumptions about homogeneity projection, though it too has open issues with related cases. Regardless of which solution is chosen, non-monotonic contexts turn out to be an important test case for theories of free choice, implicature, and modified numerals.

Free choice and presuppositional exhaustification

“…Applied to ♢∨, ¬♢∨, and similar sentences, 'presuppositional exhaustification' predicts that their default interpretations have an assertive component (roughly, the classical interpretation of the prejacent) and a homogeneity presupposition which projects in standard ways. Those predictions, we then show, support a uniform account of the puzzling behavior of ♢∨, ¬♢∨, and related sentences when embedded under (negative) factives (Marty & Romoli 2020), disjunctions (Romoli & Santorio 2019), and in the scope of universal, existential (Bar-Lev & Fox 2020) and non-monotonic quantifiers (Gotzner et al 2020).…”

“…Gotzner, Romoli & Santorio (2020) present experimental evidence that (77) has a salient reading that entails that one student has FC, while all the other students have double prohibition, as captured in (77a):…”

“…Gotzner et al (2020) argue that the exh IE+II account doesn't generalize well to 'all others FC/double prohibition' readings for arbitrary sentences of the form 'exactly n'. It seems to us that the exh IE+II analysis works in general, but only using analogous stipulations as those criticized above.…”

Logic and conversation: The case of free choice

“…recently discussed byGotzner, Romoli & Santorio (2020), can be derived (as in Goldstein 2019):(48) all-others-dual-prohibition a. Exactly one girl can take Spanish or Calculus.…”