Choice Points for a Modal Theory of Disjunction

Abstract

This paper investigates the prospects for a semantic theory that treats disjunction as a modal operator. Potential motivation for such a theory comes from the way in which modals (and especially, but not exclusively, epistemic modals) embed within disjunctions. After reviewing some of the relevant data, I go on to distinguish a variety of modal theories of disjunction. I analyze these theories by considering pairs of conflicting desiderata, highlighting some of the tradeoffs they must face.

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Notes

  1. 1.

    See, among others, Zimmermann (2000), Geurts (2005), Lin (ms.), Fusco (forthcoming).

  2. 2.

    On the other side of the debate, see Fusco (2014) for a critique of pragmatic accounts.

  3. 3.

    Zimmermann (2000) and Geurts (2005) seek to provide uniform explanations of this phenomenon and of free-choice inferences. They seem to view all these interactions as inextricably linked.

  4. 4.

    There is another kind of analysis of disjunction which could turn out to have much in common with the theories I discuss here. This is the alternative-introducing analysis of Von Stechow (1991), Alonso-Ovalle (2006), Aloni (2007), Roelofsen (unpublished), among others. A detailed analysis of the relationship between these theories and the modal theories I am to discuss will need to take place elsewhere.

  5. 5.

    Though some speakers find it to be less than perfect, they agree that it is much better than “It is likely that Meg is in Portugal or she is in Spain”.

  6. 6.

    The apparent failure of this form of disjunctive syllogism is noted in Klinedinst and Rothschild (2012), who credit the observation to Yalcin, and in Schroeder (2015).

  7. 7.

    Here is a partial illustration of the explanation (Lin’s explanation differs somewhat because his semantics for ‘\(\Diamond \)’ is not the domain semantics of Sect. 2): \(\ulcorner \Diamond \textit{A}\,or \,\Diamond \textit{B} \urcorner \) requires (a) that \(s_{p }\) accept \(\ulcorner \Diamond \textit{A} \urcorner \) and (b) that \(s_{q }\) accept \(\ulcorner \Diamond \textit{B} \urcorner \). Now suppose we also accept that neither \(s_{p }\) nor \(s_{q }\) is empty. It then follows that \(s\) accepts \( \ulcorner \Diamond \textit{A}\quad \& \quad \Diamond \textit{B} \urcorner \).

  8. 8.

    This idea was suggested to me as an option in independent conversations with Daniel Rothschild and Seth Yalcin (p.c.).

  9. 9.

    Another option would be to deny that contingency is to be understood as world-variance. This might fail, for example, on some interpretations of two-dimensional semantics. But it is not clear that two-dimensionalist techniques apply here, so it is not clear how relevant this response is.

  10. 10.

    Schroeder also notes that this problem persists if, instead of the simple framework from Sect. 2, which was based on Yalcin (2007), the semantic framework reflects the more sophisticated approach in Yalcin (2011).

  11. 11.

    Disjunction introduction is valid on informational consequence. It can fail on point consequence if we introduce the right disjunct. Here is a proof of the invalidity: there are \(c, s, w\) with \(\llbracket \Diamond \textit{A} \rrbracket ^{c, s, w}=1\) but \(\llbracket \textit{A}\,or \,\Diamond \textit{A} \rrbracket ^{c, s, w}=0\). For let \(s=\{w,v\}\) with \(\textit{A}\) true at v but not at w.

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Acknowledgments

For conversations and exchanges, I thank Melissa Fusco, Hanti Lin, Sarah Moss, Daniel Rothschild, Paolo Santorio, Seth Yalcin.

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Correspondence to Fabrizio Cariani.

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Cariani, F. Choice Points for a Modal Theory of Disjunction. Topoi 36, 171–181 (2017). https://doi.org/10.1007/s11245-015-9362-z

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Keywords

  • Disjunction
  • Epistemic modals
  • Dynamic semantics
  • Partition semantics
  • Context sensitivity