Free choice, simplification, and Innocent Inclusion
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Free choice, simplification, and Innocent Inclusion Moshe E. Bar-Lev1
· Danny Fox2
© Springer Nature B.V. 2020
Abstract We propose a modification of the exhaustivity operator from Fox (in: Sauerland and Stateva (eds) Presupposition and implicature in compositional semantics, Palgrave Macmillan, London, pp 71–120, 2007. https://doi.org/10.1057/9780230210752_4) that on top of negating all the Innocently Excludable alternatives affirms all the ‘Innocently Includable’ ones. The main result of supplementing the notion of Innocent Exclusion with that of Innocent Inclusion is that it allows the exhaustivity operator to identify cells in the partition induced by the set of alternatives (assign a truth value to every alternative) whenever possible. We argue for this property of ‘cell identification’ based on the simplification of disjunctive antecedents and the effects on free choice that arise as the result of the introduction of universal quantifiers. We further argue for our proposal based on the interaction of only with free choice disjunction. Keywords Implicature · Exhaustification · Free choice · Simplification of disjunctive antecedents · Innocent Inclusion · Innocent Exclusion
1 Introduction As is well known, a sentence like (1), where an existential modal takes scope above or, gives rise to the free choice (FC) inferences (1a) and (1b) (von Wright 1968; Kamp 1974). It is also well known that these inferences don’t follow from standard
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Moshe E. Bar-Lev [email protected] Danny Fox [email protected]
1
The Hebrew University of Jerusalem, Jerusalem, Israel
2
Massachusetts Institute of Technology, Cambridge, USA
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M. E. Bar-Lev, D. Fox
assumptions about the semantics of allowed and or: (a ∨b) is equivalent to a ∨b rather than the conjunction a ∧ b.1 (1)
Free choice disjunction: Mary is allowed to eat ice cream or cake. a. Mary is allowed to eat ice cream. b. Mary is allowed to eat cake.
(a ∨ b) ⇔ (a ∨ b) a b
Implicature-based accounts of FC (Kratzer and Shimoyama 2002; Fox 2007; Klinedinst 2007; Chemla 2009a; Franke 2011) maintain that the basic meaning of (1) can be stated as (a ∨ b) using standard modal logic and that the FC inferences are explained by enriching the meaning with mechanisms that are independently motivated in the account of scalar implicatures.2 Implicature accounts of FC are motivated both on conceptual grounds—they do not involve altering the meaning of logical words—and on empirical grounds—they correctly predict the behavior of FC disjunction under negation (Alonso-Ovalle 2005). However, there are some lingering problems for such accounts, which will be the focus of this paper. First, when FC disjunction is embedded under only, the FC inferences become part of only’s presupposition (Alxatib 2014). As (2) shows, the inferences project out of a question as though they were presuppositions. At the same time, deriving FC inferences in the scope of only (as an embedded implicature) leads to further problems; specifically, it yields an assertive component which i
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