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Remarks on exhaustification and embedded free choice

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Abstract

Some sentences that contain disjunctions imply that their disjunct-alternatives are false, while others imply that they are true. Recent work on scalar implicature has been guided by the behavior of such constructions. In this paper I consider examples in which free choice disjunctions (phrases of the form allowed to A or B) appear in various intensional contexts. I discuss the significance of the findings in light of current views of exhaustification.

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Notes

  1. Aloni (2007) and Goldstein (2019) propose this kind of view for cases like (1); Simons’s (2005) semantic account applies to (1) and (2); and Geurts (2005) attempts to account for all of (1)-(3) with a modal semantics of disjunction. See Meyer (2020) for a recent review.

  2. I assume that it is contradictory for attitude holders to have inconsistent beliefs/desires, and for contextually-determined ordering sources to entail inconsistent propositions.

  3. Ramotowska et al. (2022) report experimental results that suggest otherwise; they find in their experimental setting that participants accept similar disjunctive sentences in scenarios where one of the two disjuncts is required while the other is permitted. I found this report in the final stages of preparing this manuscript, so I cannot give it as much thought as I would like. I return to it in Sect. 6.

  4. See Bar-Lev (2018, §1.5, specifically fn. 55).

  5. The sloppy interpretation of the pronouns in (18) is significant. Crnič (2015), Bar-Lev (2018), and Bar-Lev and Fox (2020) take it that the parallelism domains of the two parts of (18) can only be semantically identical (modulo focus marking) if they contain the (focused) subject quantifiers. If this is so, then semantic identity can only be met if either Exh appears in both parallelism domains (between the quantifier and the possibility modal), or appears in neither.

  6. If we assume that any prejacent ϕ is an alternative of itself (ϕ∈C), then ϕ will always be includable. So strictly speaking there is no need to write ϕ separately in the definition of in (26), but I leave it there to keep things clear.

  7. Del Pinal et al. add the qualification that Pex’s presuppositions are accommodated if they are consistent with the common ground. This detail is not relevant for my purposes, so I ignore it here.

  8. Applying Pex above negation is of course possible, but it does not produce a significantly different result from applying Exh above negation. The exclusions/inclusions in these cases, if there are any, are predicted to be presupposed and (by hypothesis) freely accommodated, which is the same as the result we get from applying Exh. I therefore do not discuss these parses in this section.

  9. Alxatib (2020).

  10. There remains the parse in which Pex appears above only. The resulting inferences in this case are consistent with one another and with the facts, but as the reader may verify, they make only vacuous and therefore infelicitous.

  11. See related suggestions in Simons (2001) and Chemla (2009a).

  12. This has the desirable consequence that FC, unlike other implicatures, is predicted to be an at-issue inference. I suspect that this result can help explain why FC cannot be canceled with in fact continuations (Barker 2010), but I leave the details to another occasion.

  13. The assertion ∃x(◊(Px∨Qx)) and the presupposition ∀x(◊Px↔◊Qx) entail ∃x(◊Px & ◊Qx).

  14. Gazdar (1979) made similar observations about epistemic possibility modals—see his examples (79)-(81), p. 111.

  15. Universal projection is predicted by Schlenker (2008, 2009) for both existential quantifiers and possibility expressions.

  16. Based on Crnič (2015) and Chemla (2009b). Recall the relevance of pronoun binding, summarized in fn. 5.

  17. The alternative ◊◊(p∧q) is left out of C here. Keeping it would produce a stronger exclusion: ¬◊◊(p∧q).

  18. Notice that, if, e.g., believe and want had a dual ◊ as an alternative, we predict that, e.g., ¬believe(ϕ) has ¬◊(ϕ) as an alternative. Depending on what we assume the literal semantics of ¬believe(ϕ) to be, there is a risk that the alternativehood of ¬◊(ϕ) would block the possibility of deriving the strengthened “neg-raising” inference of ¬believe(ϕ). An altogether different possibility—one that does not require believe and want to have a dual—is that it is the very property of “neg-raising” that strengthens the exclusion of, e.g., want(◊p) and want(◊q) to want(¬◊p) and want(¬◊q), and that this keeps the alternatives from being excludable, given want(◊(p∨q)). The problem with this possibility is that it does not predict any kind of distribution in the case of want(p∨q).

  19. Explanation: the prejacent □◊(p∨q) can be rewritten equivalently as □(◊p∨◊q). If the alternative ◊◊q is false, it follows that □¬◊q. From □(◊p∨◊q) and □¬◊q, it follows that □◊p. Therefore the alternative □◊p cannot be consistently negated together with ◊◊q, so neither alternative is innocently excludable. Likewise for □◊q and ◊◊p. These alternatives are all includable, because they are simultaneously consistent with the predicted exclusion of the conjunctive alternative.

  20. I do not know if there are good theoretical reasons why ◊p, ◊q should not be alternatives to □(p∨q), but I also do not know if there are good theoretical reasons why they should be. The issue is related to a more general question that has come up in the literature: should alternative generation permit replacement of multiple items in the prejacent? If the answer is no, then there would be reason to not consider ◊p, ◊q as alternatives of □(p∨q). The issue is complicated, however. I refer interested readers to discussions in Magri (2009), Chemla and Spector (2011), Romoli (2012), Trinh and Haida (2015), and Breheny et al. (2018). See also Gotzner and Romoli (2018), Geurts and Pouscoulous (2009), and Ippolito (2010) for discussions of configurations where a modal/intensional verb embeds a scalar item.

  21. Here the conjunctive alternative ◊(p∧q) has consequences on includability: if ◊(p∧q) were in C, the alternative would be excludable, but its exclusion would block all other alternatives from being includable; ◊p would not be includable because its assertion alongside □q contradicts ¬◊(p∧q) Therefore ◊p does not appear in every subset of C that satisfies (i,ii) from the includability condition. The alternative ◊q is not includable for the same reason (given □p).

  22. □p, □q are not II because they cannot be consistently asserted given the exclusion ¬□(p∧q).

  23. This replicates what Crnič et al. (2015) found for sentences of the form \(\forall x(Px\hspace {-0.015cm}\vee \hspace {-0.02cm}Qx)\).

  24. See Crnič et al. (2015) for a proposal that derives the parallel inferences ∃x(Px) and ∃x(Qx) from \(\forall x(Px\hspace {-0.015cm}\vee \hspace {-0.02cm}Qx)\) from global+embedded exhaustification.

  25. We may add to our existential alternatives the results of replacing some/at least one with the universal quantifier. This gives us ∀x(◊Px), ∀x(◊Qx), \(\forall (\Diamond (P\!\wedge \hspace {-0.015cm}Q))\). These alternatives are excludable, but their exclusion does not lead to the target existential FC inference.

  26. Focusing on the comparison between these two views, it is worth remarking that, on the Pex-based account of FC, it is not strictly necessary to use the notion of inclusion. The reader may verify this by observing that for any propositional argument ϕ and set of alternatives C, is equivalent to recursive application of the exclusion-only to ϕ with intervening accommodation. That is, is equivalent to —here B is the set of alternatives to , generated in the same way as the alternatives to the higher occurrence of on Fox’s account of FC. To the extent that such a theoretical move is possible, the empirical motivation for adding inclusion to exhaustification is weakened. (I thank Guillermo del Pinal for discussion of this point.)

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Acknowledgements

For helpful disussion and feedback, I am grateful to three anonymous NALS reviewers, Luka Crnič, Guillermo Del Pinal, André Eliatamby, Anamaria Fălăuş, Paloma Jeretič, Clemens Mayr, Rick Nouwen, Jacopo Romoli, Philippe Schlenker, Yasutada Sudo, Tomasz Zyglewicz, and the audience at the 27th Sinn und Bedeutung.

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    Sam Alxatib

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Alxatib, S. Remarks on exhaustification and embedded free choice. Nat Lang Semantics 31, 291–314 (2023). https://doi.org/10.1007/s11050-023-09208-x

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