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Informational dynamics of epistemic possibility modals

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Abstract

We investigate, in a logical setting, the expressivist proposal that assertion primarily functions to express and coordinate doxastic states and that ‘might’ fundamentally expresses lack of belief. We provide a formal model of an agent’s doxastic state and novel assertability conditions for an associated formal language. We thereby prove that an arbitrary assertion (including a complex of ‘might’ and ‘factual’ claims) always succeeds in expressing a well-defined (partial) doxastic state, and propose a fully general and intuitive update operation as a model of an agent coming to accept an arbitrary assertion. Leaving a comprehensive philosophical and linguistic defense for elsewhere, we explore technical aspects of our framework, providing, for instance, a complete logic of assertability and reduction axioms for the novel update operations related to our proposal. Finally, we contrast our work with related proposals in the logic literature.

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Notes

  1. The orthodox semantics belongs to Kratzer (1981, (2012). See also Papafragou (2006).

  2. For more on the case against orthodoxy, see Yalcin (2011) and MacFarlane (2011a).

  3. See von Fintel and Gillies (2011).

  4. See MacFarlane (2011a, (2014). Note that MacFarlane and Yalcin’s views are, arguably, closely related, so the line between the different approaches we outline in the main text is sometimes blurry.

  5. See Yalcin (2007, (2011) for expressivism about epistemic modals. Compare the following to (i) and (ii) in the main text: “[The correct model of might discourse] recommends the idea that in modeling the communicative impact of an epistemic possibility claim, we construe the objective as one of coordination on a certain global property of one’s state of mind—the property of being compatible with a certain proposition—not of one of coordination concerning the way the world is” (Yalcin 2011, p. 310). See also Swanson (2006) and Moss (2013, (2015).

  6. One may elaborate ‘awareness’ in different ways: say, as mere psychological salience, or in dispositional terms. See (Portner 2009, Sect. 4.2.3) for a useful discussion of this general approach, with more comprehensive references to the literature. See Willer (2013) for a precise development of the dispositional approach (though he discourages understanding his framework in terms of the ordinary notion of ‘awareness’). See Ciardelli et al. (2009) for a precise development of the ‘bringing to attention’ view in the context of inquisitive semantics.

  7. The typical expressivist view is that ‘might’ expresses compatibility with the agent’s beliefs. Our own proposal follows if one identifies—as is again typical – ‘compatible with the agent’s beliefs’ with ‘the agent does not disbelieve’. See Yalcin (2011), building on the ideas of Veltman (1996). Note that in Sects. 5 and 6, Yalcin (2011) presents a potential counter-example to the claim that ‘might’ expresses a lack of belief: if an agent does not have Topeka or its state at all in mind, yet it is consistent with the agent’s beliefs that it is raining in Topeka, it is natural to conclude: first, that the agent does not believe that it is not raining in Topeka; and, second, that the agent does not believe that it might be raining in Topeka. This example suggests that the agent’s awareness (or, in Yalcin’s terms, what distinctions the agent’s doxastic state is sensitive to) is indeed one factor in the semantics for ‘might’ locutions, and should not be overlooked by expressivists of our stripe. We largely agree with this assessment, but nevertheless ignore issues of awareness/sensitivity in our treatment, for two reasons. First, since the typical formal tools for handling these issues are compatible with our framework, we can postpone extra levels of complexity for elsewhere. Second, once again, it seems to us that awareness/sensitivity presents issues that are not peculiar to ‘might’ locutions, and so are fruitfully backgrounded when focusing on ‘might’. One might, for instance, claim that the issues that an agent is aware of imposes a certain ‘resolution’ on logical space, and that every belief ascription is relative to such a resolution (cf. Yalcin (2016)). In this case, an expressivist of our stripe can be more precise by saying that ‘might’ expresses a lack of belief relative to the resolution in question.

  8. Our view is easily extended to the more nuanced position that different discourses have different ‘tones’—and so aim to coordinate different kinds of informational attitudes—and that ‘might’ serves to express a lack of whatever attitude is relevant to that discourse (cf. Yalcin, 2007, p. 464). Nevertheless, belief-toned exchanges strike us as the natural candidate for default or normal assertoric discourse.

  9. Cf. Zimmermann (2000), Simons (2005), Ciardelli et al. (2009), and Lin (2013).

  10. Cf. Yalcin (2007), especially page 1005, and the general discussion concerning the robust incompatibility of \(\lnot p\) and \(\lozenge p\).

  11. For instance, this goal is not, in our view, accomplished by the especially well developed theory of epistemic modals presented in Yalcin (2007). However, since our goal in this paper is not to argue that our theory has advantages over any particular rival, we leave such arguments for another time. See Hawke and Steinert-Threlkeld (2015b).

  12. Though see Chapter 6 of Stalnaker (2014) for an outline of a proposal that, in certain key respects, is similar to that which we propose here. In particular, Stalnaker proposes that acceptance of a ‘might’ claim leads to certain possibilities being added to the common ground of the conversation, and that an ordering on worlds be used to model the selection of those possibilities. Willer (2013) provides a precise theory of update in the tradition of dynamic semantics, but explicitly discourages the reader (on page 60) from conflating this with a theory of belief revision.

  13. See, for instance, van Benthem (2011).

  14. \(w \succ v\) means w is strictly more plausible than v. In our notation, b, n, p are all equally plausible.

  15. Conservative revision corresponds in a precise sense to transitively relational partial meet revision and conservative contraction corresponds to transitively relational partial meet contraction. See Hansson (2014), especially Sect. 4, for an overview of these results. See Rott (2009) for a comprehensive list of belief update procedures, including those that appear in this paper.

  16. It is not our goal to here offer an account that does full justice to our ordinary conception of assertion, nor the many facets of the theoretical role that assertion is intended to play in linguistic theorizing. For a more thoroughgoing discussion of assertion, see MacFarlane (2011b). Our immediate goal is to offer a simple and natural account of when a sentence is assertable relative to a particular body of information, predominantly thought of as the belief worlds of a relevant agent.

  17. Our framework of assertability conditions is similar in technical spirit to the expressivist semantics of Lin (2013), a connection we do not detail here. At any rate, the formulation, conceptual underpinnings, dialectical role and technical consequences of the current framework diverge from that of Lin (2013) in significant ways.

  18. See van Benthem (2011) for an overview of this tradition.

  19. See Kratzer (1991) and Lewis (1973).

  20. Note that the result easily generalizes to the case of doxastic state descriptions with more than one abelief.

  21. See Holliday and Icard (2010) for a solution to the similar problem of finding the successful formulas in the case of knowledge and the update operation of public announcement.

  22. Thanks to an anonymous reviewer for identifying this example, and the ensuing worry about our account.

  23. See Hawke and Steinert-Threlkeld (2015b) for more discussion.

  24. We owe thanks to an anonymous referee for suggesting the below proof, which is in the spirit of but more concise than the proof we furnished for review.

  25. See Hawke and Steinert-Threlkeld (2015b).

  26. See Chapter 8 of van Benthem (2011), where it goes by ‘conservative upgrade’.

  27. Ciardelli and Roelofsen (2015) introduce a disjunction with the same semantics as ours and would then have to define \(\lozenge \varphi \) as \(?\left\{ \varphi , \top \right\} \).

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Acknowledgments

The authors wish to thank the following people for providing comments that helped in the development of this paper (of course, any remaining errors or other infelicities in the paper remain the authors’ sole responsibility): the audience at LORI-V, Rob Bassett, Johan van Benthem, Michael Cohen, Cleo Condoravdi, Sophie Dandelet, Tom Donaldson, Melissa Fusco, Lelia Glass, Dave Gottlieb, Thomas icard, David Israel, Lauri Kartunnen, Dan Lassiter, Meica Magnani, Katy Meadows, Prerna Nadathur and Seth Yalcin. Special thanks to our anonymous referees and Alex Kocurek for very detailed comments. Thanks to the organizers of LORI-V and especially to Wen-fang Wang. This paper was developed at the Logical Dynamics Lab at CSLi, Stanford University.

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  1. Philosophy Department, Stanford University, 450 Serra Mall, Stanford, CA, 94305, USA

    Peter Hawke & Shane Steinert-Threlkeld

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Correspondence to Peter Hawke.

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The current paper substantially extends and refines (Hawke and Steinert-Threlkeld 2015a).

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Hawke, P., Steinert-Threlkeld, S. Informational dynamics of epistemic possibility modals. Synthese 195, 4309–4342 (2018). https://doi.org/10.1007/s11229-016-1216-8

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