An experimental investigation of implicature and homogeneity approaches to free choice

A sentence containing disjunction in the scope of a possibility modal, such as Angie is allowed to buy the boat or the car, gives rise to the free choice inference that Angie can freely choose between the two. This inference poses a well-known puzzle, in that it is not predicted by a standard treatment of modals and disjunction (e.g., Kamp (Proceedings of the Aristotelian Society 74:57–74, 1974)). To complicate things further, free choice tends to disappear under negation: Angie is not allowed to buy the boat or the car doesn’t merely convey the negation of free choice, but rather the stronger double prohibition reading that Angie cannot buy either one. There are two main approaches to the free choice-double prohibition pattern in the literature. While they both capture the relevant data points, they make a testable, divergent prediction regarding the status of positive and negative sentences in a context in which Angie can only buy one of the two objects, e.g., the boat. In particular, the implicature-based approach (e.g., Fox (Presupposition and implicature in compositional semantics, pp. 71–120, 2007); Klinedinst (Plurality and possibility, PhD diss., UCLA, 2007); Bar-Lev and Fox (Proceedings of SALT 27, pp. 95–115, 2017); Bar-Lev and Fox (Natural Language Semantics 28:175–223, 2020)) predicts that the positive sentence is true in such a context, but associated with a false implicature, while it predicts the negative sentence to be straightforwardly false. The homogeneity-based approach in Goldstein (Semantics & Pragmatics 12:1–53, 2019) predicts both the positive and negative sentences to be equally undefined (see also Aloni (Semantics & Pragmatics 15:5, 2022); Willer (Proceedings of the 21st Amsterdam Colloquium, pp. 511–520, 2017)) for similar predictions). Investigating the contrast between these sentences in such a context therefore provides a clear way to address the debate between implicature and non-implicature accounts of free choice. We present a set of four experiments aiming to do just this, by comparing free choice inferences to regular implicatures, using a ternary judgment task. The results overall present a challenge for the implicature approach. We discuss how the implicature approach could be amended to account for our results, based on a recent proposal by Enguehard and Chemla (Linguistics & Philosophy 44:79–112, 2021) on the distribution of implicatures.