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.
Similar content being viewed by others
Notes
On the other side of the debate, see Fusco (2014) for a critique of pragmatic accounts.
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 This is the alternative-introducing analysis of Von Stechow (1991), Alonso-Ovalle (2006), Aloni (2007), Roelofsen (unpublished), among others.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.
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”.
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 \( \ulcorner \Diamond \textit{A}\quad \& \quad \Diamond \textit{B} \urcorner \).
This idea was suggested to me as an option in independent conversations with Daniel Rothschild and Seth Yalcin (p.c.).
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.
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.
References
Aloni M (2007) Free choice, modals and imperatives. Nat Lang Semant 15:65–94
Alonso-Ovalle L (2006) Disjunction in alternative semantics. Ph.D. thesis, UMass Amherst
Dorr C, Hawthorne J (forthcoming) Embedding epistemic modals. Mind 1–47 (electronic version)
Fox D (2007) Free choice and the theory of scalar implicatures. In: Sauerland U, Stateva P (eds) Presupposition and implicature in compositional semantics, pp 71–120
Fusco M (2014) Free choice permission and the counterfactuals of pragmatics. Linguist Philos 37(4):275–290
Fusco M (forthcoming) Deontic modals and the semantics of choice. Philos Impr
Geurts B (2005) Entertaining alternatives: disjunctions as modals. Nat Lang Semant 13
Klinedinst N, Rothschild D (2012) Connectives without truth tables. Nat Lang Semant 20(2):137–175
Kolodny N, MacFarlane J (2010) Ifs and oughts. J Philos 107(3):115–143
Kratzer A, Shimoyama J (2002) Indeterminate phrases: the view from Japanese. In: Otsu Y (ed) The proceedings of the third Tokyo conference on psycholinguistics, pp 1–25 (Hituzi Syobo)
Lin H (ms.) When ‘or’ meets ‘might’: towards acceptability-conditional semantics. Manuscript, University of California, Davis
MacFarlane J (2011) Epistemic modals are assessment sensitive. In: Egan A, Weatherson B (eds) Epistemic modality. Oxford University Press, Oxford, pp 144–178
MacFarlane J (2014) Assessment sensitivity. Oxford University Press, Oxford
Moss S (2015) On the semantics and pragmatics of epistemic vocabulary. Semant Pragmat 8(5):1–81
Roberts C (1989) Modal subordination and pronominal anaphora in discourse. Linguist Philos 12(6):683–721
Roelofsen F (unpublished) Two alternatives for disjunction. Manuscript, University of Amsterdam
Rothschild D (2012) Expressing credences. Proc Aristot Soc 112:99–114
Schroeder M (2015) Attitudes and epistemics. In: Expressing our attitudes. Oxford University Press, Oxford, pp 225–256
Silk A (2014) Why ‘ought’ detaches: or, why you ought to get with my friends (if you want to be my lover). Philos Impr 14(7):1–16
Veltman F (1996) Defaults in update semantics. J Philos Log 25:221–261
Von Stechow A (1991) Focusing and backgrounding operators. In: Abraham W (ed) Discourse particles: descriptive and theoretical investigations on the logical, syntactic and pragmatic properties of discourse particles in German, vol 6, pp 37–84 (Benjamins)
Willer M (2013) Dynamics of epistemic modality. Philos Rev 122:45–92
Yalcin S (2007) Epistemic modals. Mind 116(4):983–1027
Yalcin S (2011) Nonfactualism about epistemic modality. In: Egan A, Weatherson B (eds) Epistemic modality. Oxford University Press, Oxford
Yalcin S (2012) A counterexample to modus tollens. J Philos Log 41:1001–1024
Zimmermann TE (2000) Free choice disjunction and epistemic possibility. Nat Lang Semant 8:255–290
Acknowledgments
For conversations and exchanges, I thank Melissa Fusco, Hanti Lin, Sarah Moss, Daniel Rothschild, Paolo Santorio, Seth Yalcin.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Cariani, F. Choice Points for a Modal Theory of Disjunction. Topoi 36, 171–181 (2017). https://doi.org/10.1007/s11245-015-9362-z
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11245-015-9362-z