Assertions: Updating the Context Set

In his article “Assertion”, Stalnaker gives a pragmatic account of the function of assertions in language. He states that assertions, when not rejected by other conversational participants, serve to reduce the context set of the conversation. Stalnaker uses the term ‘context set’ to refer to the set of all possible worlds that are compatible with the presuppositions of the speaker. For instance, in a conversation about upcoming weekend plans, the context set cannot include possible worlds where the speaker is talking with the philosopher Kant because such worlds do not accord with the presupposition that Kant is dead. Assertions reduce the context set by taking into account the content represented by the proposition asserted to the existing presuppositions. Increasing the number of things presupposed will necessarily lead to a reduction in the context set because the addition of new presuppositions rules out worlds incompatible with the proposition. For Stalnaker, a proposition is a “representation of the world as being a certain way,” and so determines a set of possible worlds. So another way of thinking about Stalnaker’s account of assertions is that when assertions are made, the intersection of the existing context set and the set of possible worlds represented by the proposition becomes the new context set. I will argue, however, that assertions can also function to broaden the context set. If this is true, then assertions function to update the context set rather than just restricting it, contrary to Stalnaker’s account.

Stalnaker states that he does not offer this account as a sufficient definition of assertion, but rather as one component of an adequate definition. Although he makes some remarks about the reason why assertions cannot be sufficiently defined by this effect alone, he does not mention anything about assertions being able to broaden the context set. It seems to me that such assertions occur regularly, even in “non-nondefective” conversations where the speakers initially presuppose the same things. If assertions can in fact broaden the context, Stalnaker’s account of this particular function of assertions is inadequate.

Suppose two friends are deciding on what type of restaurant to go to. They typically prefer pizza and have only ever been to pizza restaurants. One of them asks, “What pizza place do you want to go to?” On this particular day, however, the other replies, “We might eat somewhere other than a pizza place,” and the other agrees. The initial context set only included worlds where the two are eating at pizza restaurants. It seems that the new context set includes worlds where the two are eating at restaurants that both serve pizza and do not (assuming that the speaker did not mean to rule out possible worlds where the two still went to a pizza restaurant).

But there arises a problem. What is semantically expressed by propositions of the form, “It might be that,” or “It could be that,” turns out to be either necessarily true or necessarily false for all the worlds in the context set. The semantic content of “We might eat somewhere other than a pizza place” is that there is some world Φ in the context set in which the two are not eating at a pizza place. In the existing context set, there either is a world Φ or there isn’t. If Φ does exist in the context set, then for every possible world in the context set, the proposition is true. But in the pizza case, since it was presupposed by both speakers that they would eat at a pizza place, the world Φ is not in the context set. Therefore, the statement “We might eat somewhere other than a pizza place” is necessarily false relative to every possible world in the context set.

This violates the principle that Stalnaker takes to be a necessary for rational communication: a proposition asserted must be true in some but not all of the possible worlds in the context set. This principle seems obvious because otherwise the proposition expressed would not be advancing the conversation in any way since it is either trivially true or trivially false. If we assume that the speaker is rational and intends on engaging in a genuine conversation, it seems wrong to interpret his statement as asserting a proposition that is trivially false. Something else seems to be happening. Thus, the fact that the statement is trivially false triggers a pragmatic, Gricean reinterpretation. The speaker wishes to communicate something other than what is literally asserted by the utterance. Given that the statement is false at all possible worlds in the context set, it seems that the speaker wishes to broaden the context set to include possible worlds in which the two are not eating at a pizza place. I will explain how this is possible.

If the other speaker agrees, the context set is broadened to now include the world(s) Φ where they are not eating at a pizza place. Consequently, what’s true for the worlds in the context set has changed. Now, there are worlds for which it is possible that the two might eat at a non-pizza place. The new context set is the result of the union of the previous context set and the set of possible worlds represented by the asserted proposition. But once the context set is updated to include world Φ, there remains the problem that now the statement is trivially true. One solution to this problem is that what is possible at each of the possible worlds is different. At some set of worlds in the context set, it is possible that they will eat at a pizza place. At some other set of worlds in the context set, it is possible that they will eat at a non-pizza place. I offer this only as a mere gesture towards what an adequate solution may be. For the purposes of this paper, I assume that such a solution is possible. The exact details of that solution are not critical to my argument.

The statement is no longer trivially false because it accords with the principle that the proposition asserted is true in some but not all of the worlds in the context set. The speaker has successfully advanced the conversation by broadening the context set. This claim runs contrary to Stalnaker’s notion that the new context set is the result of the intersection of the existing context set and the set of worlds represented by the proposition asserted. I see no reason why the context set cannot be changed by either the intersection or the union of itself with an asserted proposition, depending on whether the assertion is intended to restrict or broaden the context set, respectively. It seems more accurate to say that conversations are advanced when the context set is updated in some way, rather than only restricted.

Statements of the form “It might be the case that…” or “It could be the case that…” often signal an assertion that broadens the context set. One might argue that such statements are not assertions, but some other linguistic move that functions differently. These sorts of utterances, however, do seem to be assertions. When he says “We might eat somewhere other than a pizza place” he is really asserting the proposition that represents the set of worlds in which the two are eating at a non-pizza restaurant, along with expressing his desire that the other speaker accept this assertion.

Philosophical skeptics often make these statements. If a skeptic utters, “We could be experiencing a dream right now,” he is asserting the proposition that represents the worlds in which the speaker is dreaming. It would be unfair to think that skeptical utterances cannot be assertions; certain types of skeptical utterances, especially philosophical ones, aim expressly to break down certain presuppositions, opening up new possible worlds to consider in the discussion.

To defend this claim of mine, it is important to consider why Stalnaker thinks of assertions as functioning solely to restrict the context set. Stalnaker accounts for assertions in this way because the point of a conversation (or at least, the type of conversation in which assertions are employed) is to locate the actual world that the speakers are in. By restricting the context set and limiting the set of possible worlds as live options, the speakers hope to eventually reach a point where only one possible world remains, that one being the real world. Of course, this is only a brief sketch of what actually happens. Different conversations would require different degrees of certainty; a conversation centered on diagnosing a patient would demand that only a single world be left as a live option, so that the doctors know exactly how to treat him. In a conversation about a sports game between two speakers who don’t particular care about sports, the speakers would be satisfied with a number of possible worlds as live options (“The Celtics won, but the final score was either 98-78 or 99-76”).

Given the goal of locating the actual world within the context set, it very well might be the case that a mistake was made by the speakers and the actual world was ruled out by certain false presuppositions. If, as Stalnaker suggests, the role of assertions is to locate the actual world, then it seems perfectly justified, perhaps even necessary, that assertions also function to broaden the context set in such situations. As mentioned above, Cartesian philosophical skeptics make certain statements to account for the possibility that the world is just an illusion orchestrated by an evil demon. Since they are aiming to uncover a metaphysical truth (attempting to locate the real world within the context set), the skeptics are indeed making assertions.

Perhaps another example will make this point clearer. Consider a murder investigation. Two detectives are examining the crime scene and debating possible suspects given the available evidence. They suspect that either the maid or the wife committed the murder, and so the context set contains the possible worlds where the maid or wife committed the crime. Suddenly one of the detectives receives a phone call from an informant telling him that there is strong evidence implicating the butler. This detective then utters, “The butler could have done it.” It is perfectly reasonable to interpret this statement as asserting the proposition that represents the possible worlds in which the butler committed the murder, thus expanding the context set (because otherwise the assertion would be trivially false, violating one of basic conversational principles regarding assertions). After all, the detectives are there to find out who killed the victim. If evidence arises implicating the butler, it seems logically necessary to expand the context set to include worlds in which the butler is the murderer, if the actual world is to be accurately located.

It is not a justified defense to claim that statements that broaden the context set are not assertions. Statements that broaden the context set have the same purpose that Stalnaker suggests for assertions that reduce the context set — to update the context set in hopes of locating the actual world. If the speaker’s hold a mistaken presupposition and the actual world is not within the current context set, it is necessary to broaden the context set to contain the set possible worlds where the real world might be located. Given that locating the real world is the purpose for making assertions, it is insufficient to account for assertions as only reducing the context set. The essential function of assertions seems to be that they update the context set, both by restricting and by expanding it. 

Works Cited

1. Robert Stalnaker, “Assertion,” Syntax and Semantics, ed. J. Kimball. Vol. 9, 1978 Academic Press (New York), pp. 315-332.