Abstract
Contextology is the science of the dynamics of the conversational context. Contextology formulates laws governing how the shared information states of interlocutors evolve in response to assertion. More precisely, the contextologist attempts to construct a function which, when provided with just a conversation’s pre-update context and the content of an assertion, delivers that conversation’s post-update context. Most contextologists have assumed that the function governing the evolution of the context is simple: the post-update context is just the pre-update context intersected with the content of the assertion. We argue that this assumption is wrong: not only is it false, it is also incoherent given standard contextological assumptions. Moreover, it is impossible in principle to revise it to correctly describe the dynamics of context. We conclude that there can be no science of Contextology. The laws governing the evolution of the context in response to assertion must make essential reference to the private information states of interlocutors.
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Notes
Another tradition of work, stemming from Kaplan (1977/1989) and Lewis (1981), appeals to a distinct notion of context. Instead of using the word ‘context’ to refer to bodies of information, this tradition uses it to pick out the features of concrete utterance situations which settle the values of various context-sensitive expressions. Our arguments below do not engage with this alternative conception of context.
Note that we use ‘accept’ here to describe the act a speaker performs with respect to a given assertion just in case she does not reject it. The act of rejecting an assertion is understood by contextologists to be a move in the conversational language game which any interlocutor can perform in response to an assertion and which prevents that assertion from updating the context. Thus Stalnaker (2014): “...it is a rule of the assertion game that the addressee has the option of rejecting the assertion, blocking this rule-governed change [to the context]. Rejection is another of the possible rule-governed moves in the game.” Acceptance in this sense should be carefully distinguished from the propositional attitude of acceptance which Stalnaker (2014) uses to define the notion of a conversational context. We use the word ‘accept’ in both ways in what follows; in each case, our intended meaning should be clear from context.
It is worth noting that, while theorists who posit a conversational context often explicitly discuss and endorse (Reduction) and (Public Functionality), (Private Functionality) is usually taken for granted rather than explicitly discussed. The idea expressed in (Private Functionality)—that the way a rational agent’s attitudes evolve in response to new information is determined by her existing information together with the content of the new information—is nevertheless ubiquitous: one encounters it in a wide range of formal theories of belief revision, whether qualitative (as in, for example, Alchourrón et al. (1985)) or probabilistic (as in standard Bayesian approaches). For this reason, we believe that all or nearly all theorists who posit a conversational context would endorse (Private Functionality). Thanks to an anonymous referee for pressing us to clarify this point.
Stalnaker explicates the notion of the information state immediately before an assertion is accepted as follows: “In general, given the assumption that the semantics of the language and the rules of the game are common knowledge among the players, we can conclude that when an assertion is made, it will be a manifest event that an assertion with a particular content was made by the person who made it... The context in which an assertion is evaluated (the point at which the addressee decides whether to accept or reject it) is the context as it is after the assertion has been made and mutually recognized.” (2014, p. 51). We discuss the significance of the information interlocutors gain from observing the manifest events of assertoric utterances in Sect. 5.
More precisely: let c be the context, and let I be the set of information states of the interlocutors of the context. Let \(\sqcup \) be the function introduced by (Reduction), which maps interlocutors’ information states to contexts. Let \(+\) be the function introduced by (Private Functionality), which maps private information states and contents to new private information states. Let \(\cdot [\cdot ]\) be the function introduced by (Public Functionality), which maps contexts and contents to new contexts. Then (Coherence) says that \(c[p] = \sqcup \{i + p \mid i \in I\}\).
Lederman (2018a, 2018b) argue that common attitudes are elusive, and that various phenomena explained by common attitudes can be explained in other ways. Here, it is worth noting that our arguments below can be adapted straightforwardly to apply to other iterated notions of context. For example, consider the proposal that the context is the set of worlds consistent with what the interlocutors all believe that the interlocutors all believe (Lederman (2018b, p. 1095) discusses proposals of this type). Our arguments below can be adapted straightforwardly to apply to this proposal, and others like it.
See for example Stalnaker (2002, p. 704). Stalnaker (2014) models context in terms of common acceptance rather than common belief. Finally, Stalnaker (2002, p. 716) defines the context as whatever is accepted to be commonly believed. Our arguments below also apply to this more complex conception of context, since we can simply assume in our examples that each agent believes a claim if and only if she accepts it. Because our results in what follows are negative, we only need one such context in order to make our argument.
For example, Stalnaker writes, “I assume that one has access to what one accepts [for the purposes of the conversation], which means that one accepts that one accepts that \(\psi \) when one accepts it, and accepts that one does not when one does not” (2014, p. 45). For arguments that these assumptions are too strong in this setting, see Hawthorne and Magidor (2009).
Stalnaker often restricts his attention to contexts that satisfy an extra constraint. These “non-defective” contexts are ones where communication proceeds especially smoothly. Stalnaker (2014) defines the notion of non-defectiveness for contexts such that a context is non-defective just in case every agent in the context believes it is commonly believed that p iff it actually is commonly believed that p. In other words, non-defective contexts are those where no agents are mistaken about the context. Throughout, we confine our attention to non-defective contexts.
Thanks to an anonymous referee for pressing us to clarify this point.
Similarly, here is Stalnaker: “Assume that the speech act of assertion is governed by the following rule: an assertion changes the context by adding the propositional content of the assertion to the common ground” (2014, p. 51). And here is Yalcin: “The effect of successful assertion, on Stalnaker’s view, is to eliminate possibilities incompatible with the proposition asserted from the common ground” (2012, p. 2).
Two other examples: First, asserting a sentence which carries a presupposition can, via a process of accommodation, cause that proposition to become commonly believed. Second, asserting a sentence containing a conventional implicature item like a non-restrictive relative clause can result in the implicated proposition becoming commonly believed. These processes do not involve the essential dynamic effect of assertion, and our arguments do not make reference to them.
Like (Private Functionality), (Naive Private Update) is a principle which is more often assumed than explicitly endorsed by contextologists. It is, however, simple and independently plausible—it corresponds exactly to the Expansion rule in the AGM theory of belief revision (Alchourrón et al., 1985), for example—and we believe many contextologists endorse it. Note, however, that our arguments succeed even on alternative conceptions of private update; see Sect. 6 for discussion. Thanks to an anonymous referee for pressing us to clarify this point.
Strictly speaking, we model an agent’s information at world w with an accessibility relation, not simply a set of worlds. We can derive (Naive Private Update) from a corresponding update procedure on accessibility relations. Suppose that in world w and time t an interlocutor’s belief state is represented by the accessibility relation S (so that her belief state at w at that time is Sw). Suppose that between t and \(t'\) the interlocutor learns that p. Then the agent’s information at \(t'\) can be represented by the accessibility relation \(S' = S \cap \{\langle w', v \rangle \mid w' \ne w \text { or } v \in p \}\).
This example is adapted from van Ditmarsch et al. (2008, p. 82). They use this example to demonstrate a principle that is structurally related to the failure of (Coherence): that the formula \([p]Cq \leftrightarrow (p \rightarrow C[p]q)\) is invalid in Public Announcement Logic. Here, the left-hand side roughly says that q is accepted in the state of common knowledge that results from each agent learning from a public announcement of p, and the right-hand side roughly says that if p then all p worlds consistent with what is commonly known are q worlds. To our knowledge, however, no one in the Public Announcement Logic tradition has appreciated the implications of examples of this kind for formal pragmatics. We regard it as unfortunate that there has not been more dialogue between philosophers working on the foundations of conversation, on the one hand, and logicians in the DEL tradition, on the other. Indeed, we see our arguments against Contextology as attempts to integrate the insights of these two theoretical approaches.
For simplicity, we omit from the diagram the world (z) where both propositions are false, since it is not in the transitive closure of the epistemic accessibility relations of Speaker and Hearer at w.
Our argument holds fixed (Common Reduction) and (Naive Private Update). One could in principle seek to salvage Contextology by constructing the context out of interlocutors’ private information states in a less direct way, or by endorsing a different private update rule, or by abandoning (Reduction) or (Private Functionality) altogether. We find these options unattractive: As long as the context plays its usual theoretical role of representing the information interlocutors take for granted for the purposes of the conversation, it seems to us that in both of our models below, the context must contain at least the worlds we specify prior to being updated and exactly the worlds we specify after being updated—so doing away with (Common Reduction) is no help. Along similar lines, we argue in Sect. 6 that there is no plausible private update rule on which our argument would not succeed. Thus, although (Common Reduction) and (Naive Private Update) are officially premises of our argument, we think the foundational problem arises for a wide variety of possible views about the nature of the context and the dynamics of private information states—though not, perhaps, for all possible views.
An agent \(\Omega \)-believes p iff they believe p, believe that they believe p, and so forth.
Is this modified version of [Coins] suspicious in some way? For example, we have stipulated that Hearer accepts Speaker’s assertion even though he leaves open the possibility that Speaker has not responded correctly to silence. But perhaps there is some general cooperative principle governing conversation which requires us to take for granted (at least for the purposes of conversation) that our fellow interlocutors are responding correctly to their evidence. Or perhaps there is some general cooperative principle governing conversation which secures that updating on an assertion results in it becoming commonly believed that the speaker who produced it was responding correctly to their evidence. The first of these suggestions seeks to dismiss our modified version of [Coins] on the basis that the context as we have described it fails to meet some constraint on what sort of contexts are rationally permissible even before Speaker asserts. The second seeks to dismiss our modified versions of [Coins] on the basis that in cases of rational communication the context will not evolve as we have suggested.
Three points are relevant here. First, nothing about the structure of the case requires that Hearer leaves open the possibility that Speaker does not respond to silence in the correct way. For example, instead of imagining that Hearer leaves open the possibility that Speaker will respond incorrectly to silence, we can imagine that Hearer believes it is possible that Speaker has yet another tiny bell: one wired to ring just in case the first coin comes up heads. However, hearer also believes that if Speaker has this bell, and if the first coin lands tails and the second lands heads, a once-in-a-lifetime intervention by the demon Chort will cause the bell to ring in Speaker’s ear, giving him misleading evidence that the first coin has landed heads and the second coin has landed tails. If Speaker has this extra bell and the first coin comes up heads, on the other hand, its ringing gives Speaker knowledge that the first coin has landed heads and the second tails. In this case, Hearer is sure that Speaker would respond to silence in the correct way, though he is not sure that Speaker will assert truly. And the revised case can be used to demonstrate a violation of (Coherence) in the same way as the original.
What is crucial to the case, then, is the fact that Hearer leaves open the possibility that Speaker asserts falsely even if she is responding correctly to her evidence. Here the second point comes into play: If we require all interlocutors to rule out from the get-go the possibility that speakers might assert falsely, we trivialize the theory of assertion. For then learning that a speaker has asserted p suffices for learning p itself, and the essential effect of assertion is irrelevant to the dynamics of the context. (Even setting this trivialization worry aside, it strikes us as implausible that conversational participants do or should rule out the possibility that their interlocutors will assert falsely.)
For these reasons, we do not think the first strategy of dismissing [Coins] by placing rational constraints on what the context can be like before Speaker asserts is promising. What of the second strategy of building certain extra requirements into the theory of updating? Dialectically, this second strategy is premature: our argument in this section is just that accounting for manifest update does not solve the problem of incoherence for naive update rules. But more importantly (and this is the third point), adding some stipulation to the effect that updating on Speaker’s assertion must involve coming to believe that she responded correctly to her evidence will not solve the problem, since (as we have seen) we can imagine that at world \(u'\) she asserts reasonably and even knowingly. This means that even the imagined strengthened public update rule will not eliminate world \(u'\) from the context.
Still other variants of [Coins] might involve agents who fail to infer anything about another speaker’s evidence from observation of the manifest event of their assertion—thanks to an anonymous referee for emphasizing this point.
When it comes to private information states, cases involving failures of preservation are structurally similar to the paradoxes of introspective belief change familiar from dynamic epistemic logic. See Enqvist and Olsson (2013) for a helpful overview. Our own discussion of these cases differs from extant work in connecting these issues to the theory of context. We discuss the relevance of work in dynamic epistemic logic to our arguments later in this section.
To see why common belief satisfies positive introspection, recall that the common beliefs of two agents at w are found by taking the transitive closure R of the accessibility relations S and H of the two agents at w. Here the key observation is that R is itself a transitive relation. If some proposition p is true throughout the set of worlds Rw accessible from w, then it must also be true throughout the set of worlds \(Rw'\) accessible from any world \(w'\) in Rw, since \(Rw'\) must be a subset of Rw.
In the presence of our assumptions about manifest update, (Introspective Private Update) is at least as strong as the alternative update rule which requires i to update her private information state with p and the proposition that she \(\Omega \)-believes p. For discussion of a similar rule, see Segerberg (2006). See Caie (2019), Gerbrandy and Groeneveld (1997), and van Benthem (2007) for other accounts of updating which imply that whenever an agent updates on p, they subsequently \(\Omega \)-believe p.
We focus on the revised version of [Coins] in this section because, in light of the discussion in Sect. 5, it is more probative than the original version of [Coins]. But it is worth noting that the advanced update rules presented in this section do not escape the problems with the original version of [Coins], either.
All of the private update rules we have canvassed deliver these results.
DEL avoids our results because it has no commitment to (Public Functionality). Rather, DEL explains how each conversational interlocutor’s beliefs change in response to a public announcement; the evolution of the context is parasitic on this underlying change.
This interpretation is also suggested at various points in the text of “Defaults in Update Semantics” (Veltman, 1996). For example, Veltman writes: “I want the information states \(\sigma \) to represent... what the agent regards as his or her knowledge” (p. 260).
For further elaboration of a dynamic treatment of presupposition which faces related problems, see Beaver (2001).
Thanks to an anonymous referee for emphasizing the possibility of Neo-Contextology.
References
Alchourrón, C. E., Gärdenfors, P., & Makinson, D. (1985). On the logic of theory change: Partial meet contraction and revision functions. The Journal of Symbolic Logic, 50, 510–530.
Baltag, A., Moss, L. S., & Solecki, S. (1998). The logic of common knowledge, public announcements, and private suspicions. In I. Gilboa (Ed.), Proceedings of the 7th conference on theoretical aspects of rationality and knowledge (TARK 98) (pp. 43–56).
Barker, C. (2002). The dynamics of vagueness. Linguistics and Philosophy, 25, 1–36.
Beaver, D. I. (2001). Presupposition and assertion in dynamic semantics. CSLI Publications.
Bowker, M. (2019). Saying a bundle: Meaning, intention, and underdetermination. Synthese, 196(10), 4229–4252.
Caie, M. (2019). Doxastic logic. In R. Pettigrew, & J. Weisberg (Eds.), The open handbook of formal epistemology. PhilPapers.
Cariani, F. (2020). Assertion and modality. In S. Goldberg (Ed.), The Oxford handbook of assertion. Oxford University Press.
Egan, A. (2007). Epistemic modals, relativism and assertion. Philosophical Studies, 133, 1–22.
Egan, A. (2018). De Se Pragmatics. Philosophical Perspectives, 32(1), 144–164.
Enqvist, S., & Olsson, E. J. (2013). Segerberg on the paradoxes of introspective belief change. In R. Trypuz (Ed.), Krister Segerberg on logic of actions. Springer.
Gazdar, G. (1981). Speech act assignment. In A. K. Joshi, B. L. Webber, & I. A. Sag (Eds.), Elements of discourse understanding. Cambridge University Press.
Gerbrandy, J., & Groeneveld, W. (1997). Reasoning about information change. Journal of Logic, Language, and Information, 6, 147–169.
Harris, D. W. (2020). We talk to people, not contexts. Philosophical Studies, 177, 2713–2733.
Hawthorne, J., & Magidor, O. (2009). Assertion, context, and epistemic accessibility. Mind, 118, 377–397.
Heim, I. (1992). Presupposition projection and the semantics of attitude verbs. Journal of Semantics, 9, 183–221.
Hintikka, J. (1962). Knowledge and belief. Cornell University Press.
Kaplan, D. (1989). Demonstratives. In J. Almog, J. Perry, & H. Wettstein (Eds.), Themes from Kaplan (pp. 481–564). Oxford University Press.
Karttunen, L. (1974). Presupposition and linguistic context. Theoretical Linguistics, 1, 181–194.
Lederman, H. (2018a). Two paradoxes of common knowledge. Noûs, 52(4), 921–945.
Lederman, H. (2018b). Uncommon knowledge. Mind, 127(508), 1069–1105.
Lewis, D. (1981). Index, context and content. In S. Kanger, & S. Öhman (Eds.), Philosophy and grammar (pp. 79–100). D. Reidel Publishing Company.
Murray, S. E. (2014). Varieties of update. Semantics & Pragmatics, 7(2), 1–53.
Plaza, J. A. (1989). Logics of public communications. In M. L. Emrich, M. S. Pfeifer, M. Hadzikadic, & Z. W. Ras (Eds.), Proceedings of the fourth international symposium on methodologies for intelligent systems (pp. 201–216).
Roberts, C. (2012). Information structure in discourse: Towards an integrated formal theory of pragmatics. Semantics & Pragmatics, 5(6), 1–69.
Segerberg, K. (2006). Moore problems in full dynamic doxastic logic. In J. Malinowski, & A. Pietruszczak (Eds.), Poznan studies in the philosophy of the sciences and the humanities: Essays in logic and ontology (pp. 95–110). Rodopi.
Stalnaker, R. (1973). Presuppositions. Journal of Philosophical Logic, 2, 447–457.
Stalnaker, R. (1974). Pragmatic presuppositions. In his Context and content, Oxford University Press, 1999, pp. 47–62. Originally published in M. K. Munitz, & P. Unger (Eds.), Semantics and philosophy. New York University Press.
Stalnaker, R. (1978). Assertion. In his Context and content, Oxford University Press, 1999, pp. 78–95. Originally published in Syntax and semantics (Vol. 9, pp. 315–332).
Stalnaker, R. (1998). On the representation of context. Journal of Logic, Language, and Information, 7, 3–19.
Stalnaker, R. (1999). Context and content: Essays on intentionality in speech and thought. Oxford University Press.
Stalnaker, R. (2002). Common ground. Linguistics and Philosophy, 25, 701–721.
Stalnaker, R. (2014). Context. Oxford University Press.
Stalnaker, R. (2018). Dynamic pragmatics, static semantics. In D. Fogal, D. W. Harris, & M. Moss (Eds.), New work on speech acts (pp. 384–399). Oxford University Press.
van Benthem, J. (2007). Dynamic logic for belief revision. Journal of Applied Non-Classical Logics, 17(2), 129–155.
van Ditmarsch, H., van der Hoek, W., & Kooi, B. (2008). Dynamic epistemic logic. Springer.
Veltman, F. (1996). Defaults in update semantics. Journal of Philosophical Logic, 25(3), 221–261.
Yalcin, S. (2012). Context probabilism. Lecture Notes in Computer Science, 7218, 12–21.
Yalcin, S. (2018). Expressivism by force. In D. Fogal, D. W. Harris, & M. Moss (Eds.), New work on speech acts (pp. 400–429). Oxford University Press.
Acknowledgements
We are grateful for helpful feedback from Bob Beddor, Kyle Blumberg, Dan Hoek, Ben Holguin, Harvey Lederman, Mandy Simons, and Bob Stalnaker, from the audience at the Philosophy of Language Digital Work-in-Progress Group organized in December 2020 by Lukas Lewerentz and Henry Schiller, and from two anonymous referees for Philosophical Studies.
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Goldstein, S., Kirk-Giannini, C.D. Contextology. Philos Stud 179, 3187–3209 (2022). https://doi.org/10.1007/s11098-022-01820-7
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DOI: https://doi.org/10.1007/s11098-022-01820-7