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Simplifying with Free Choice

Abstract

This paper offers a unified semantic explanation of two observations that prove to be problematic for classical analyses of modals, conditionals, and disjunctions: (1) the fact that disjunctions scoping under possibility modals give rise to the free choice effect and (2) the fact that counterfactuals license simplification of disjunctive antecedents. It shows that the data are well explained by a dynamic semantic analysis of modals and conditionals that uses ideas from the inquisitive semantic tradition in its treatment of disjunction. The analysis explains why embedding a disjunctive possibility under negation reverts disjunction to its classical behavior, is general enough to predict less studied simplification patterns, and also makes progress toward a unified perspective on the distinction between informative, inquisitive, and attentive content.

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Notes

  1. Kamp’s (1973, 1978) discussion of the free choice effect is seminal, though the label goes back to von Wright (1968).

  2. Pragmatic treatments of the free choice effect include Alonso-Ovalle (2006), Fox (2007), Franke (2011), Klinedinst (2007), Kratzer and Shimoyama (2002), and Schulz (2005). Semantic approaches include Aher (2012), Aloni (2007), Barker (2010), Fusco (2015a, b), Geurts (2005), Simons (2005), Starr (2016), Zimmermann (2000). Simplification has also received some attention in the literature: Franke (2011), Klinedinst (2009), and van Rooij (2010) offer pragmatic explanations for why counterfactuals should simplify in a variably strict analysis, while Alonso-Ovalle (2009) and van Rooij (2006) propose semantic approaches.

  3. Recent processing and acquisition studies suggest significant differences between free choice effects and scalar implicatures (see Chemla and Bott 2014 and Tieu et al. 2016, respectively), but of course this does not prove that free choice cannot be a pragmatic affair.

  4. As I will discuss more explicitly in Sect. 4.2, not all counterfactuals with negated conjunctions as antecedents seem to simplify, but I take this to be part of the explanandum rather than showing that there is nothing to be explained here in the first place. Nute’s (1980) original example moves from ‘If Nixon and Agnew had not both resigned, Ford would never have become president’ to ‘If Nixon had not resigned, Ford would never have become president’ and ‘If Agnew had not resigned, Ford would never have become president.’ One may worry that the appeal of Nute’s example stems from our knowledge of the historical facts, however, and so it is preferable to choose are more arbitrary case such as (6).

  5. The appeal to acceptance and rejection inducing update procedures owes inspiration to Aher (2012) and to Groenendijk and Roelofsen (2015), who think of acceptance and rejection as static relations between inquisitive states and sentences. The idea that free choice effects are to be explained in terms of the inquisitiveness of disjunction is also prominent in Aloni (2007), Ciardelli et al. (2009), and Roelofsen (2013). Its implementation here has the important consequence of offering a straightforward explanation of why disjunctive possibilities embedded under negation behave in a classical fashion.

  6. Bringing presuppositions into the picture also raises the question of how they project and a proper answer requires minor modifications to some of our original update rules. For instance, in order to predict that presuppositions project out of the possibility operator one would need to say that \(\sigma [\Diamond \phi]^{+}_{s} \tau \) holds just in case \(\tau = \{w \in \sigma :\langle {\mathtt{info}}(s), \underline{\bot}\rangle \notin [\phi]^{+}_{s}\}\) and, moreover, \(\exists \nu . \sigma [\phi]^{+}_{s} \nu \). Likewise for the negative entry: \(\sigma [\Diamond \phi]^{-}_{s} \tau \) holds just in case and, moreover, \(\exists \nu . \sigma [\phi]^{-}_{s} \nu \). I set these additional complexities, which would also affect the update rules to disjunction, aside to streamline the notation and since getting all the facts about presupposition projection right goes beyond the scope of this investigation.

  7. I appeal here to the ‘standard recipe’ for deriving quantity implicatures. See, for instance, Geurts (2014) and references therein.

  8. Fusco (2015a) suggests that it is the very availability of the sluice in (12b) which shows that the disjunction takes scope over the modal in (12a).

  9. Thanks to an anonymous reviewer for the 20th Amsterdam Colloquium for drawing my attention to this case.

  10. The claim that implicatures may cancel presuppositions is empirically well-attested, though the former are not always given priority over the latter in case of a conflict. See Beaver (2010) and references therein for detailed discussion.

  11. On the other hand, the fact that not all existential quantifiers need to receive a test semantics may account for Klinedinst’s (2007) observation that singular existentials do not behave like free choice items.

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Acknowledgements

Thanks to audiences at the University of Chicago, the 20th Amsterdam Colloquium, and the 2nd UC Berkeley Meaning Science Workshop (organized by Seth Yalcin). Special thanks to Martin Aher, Fabrizio Cariani, Lucas Champollion, Ivano Ciardelli, Melissa Fusco, Daniel Lassiter, Matt Mandelkern, Patrick Munoz, Paul Portner, Paolo Santorio, Floris Roelofsen, Will Starr, and two anonymous reviewers for Topoi for extensive and very helpful comments and discussion.

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Willer, M. Simplifying with Free Choice. Topoi 37, 379–392 (2018). https://doi.org/10.1007/s11245-016-9437-5

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Keywords

  • Free choice
  • Simplification of disjunctive antecedents
  • Modals
  • Conditionals
  • Dynamic semantics
  • Inquisitive semantics