Alhassanain(p) Network for Heritage and Islamic Thought

2. Epistemic modals

The traditional view about epistemic ‘might’ and ‘must’ is that they quantify over the possibilities that are compatible with the knowledge or potential knowledge of some contextually specified individual or group. When Alice says to Bert that it might rain, she says that she doesn’t know that it won’t rain, or perhaps that neither she nor Bert knows it, or that she is, or they are, not in a position to know it or to come to know it. The puzzle is that no way of pinning the relevant knowledge state down seems to be able to explain both why we are in a position to make the epistemic ‘might’ claims we seem to be in a position to make, and also why it is often reasonable to disagree with ‘might’ claims made by others. If Alice’s statement were about just her own state of knowledge, then how could Bert disagree with her (as it seems he could)? On the other hand, if Alice’s claim is about what information is available or potentially available to some larger group, then Alice will not be in a position to know what might be true in cases where it seems, intuitively that she is.  Different versions of the traditional view – what von Fintel and Gillies have called “the canon”[8]– try to find a way to pin down the constraints on the relevant informational state that can explain the data.

Seth Yalcin’s account of epistemic modals[9]began with a striking observation that raised a new puzzle. First, he observed that, as one would expect on the canonical view of epistemic modals, there are versions of Moore’s paradox for epistemic modals that parallel Moore’s paradoxes for explicit knowledge claims. Just as one cannot coherently say, “it will rain, but I don’t know that it will,” so one cannot coherently say “it will rain, but it might not.” In the case of explicit knowledge claims, the paradoxical conjunctions are shown not to besemantic contradictions by the fact that they can be coherentlysupposed even if they cannot be asserted.  There is no paradox or incoherence is saying, “Suppose it is will rain, but that I don’t know that it will,” or “if it will rain and I don’t know it, then I will get wet.”  But with epistemic modals, the incoherence persists in the supposition context: “Suppose that it is raining, but that it might not be raining” is just as bad as the simple conjunctive assertion.  So the conflict between ‘is’ and ‘might not’ is deeper than in the familiar cases of Moore’s paradox.[10]The new puzzle shows that  ‘f, but it might be that not-f’ cannot simply mean, ‘f, but not-fis compatible with X’s knowledge’, for any choice of X, since whatever the choice of X, it should be perfectly coherent to suppose thatfis true, but that X does not know it.  But despite this fact, ‘f, but it might be that not-f’ still cannot be a straightforward contradiction, since that would imply that the claim that it might rain entails that it will rain, which is obviously wrong.

Yalcin offers a detailed semantic and pragmatic account of epistemic modals that is designed to solve both the traditional problem about bare epistemic modals, and his new problem about epistemic modals embedded in contexts of supposition, and in propositional attitude ascriptions. I will exploit some of the insights of his account, but will spell out my take on the problem in my own way, which will emphasize the analogy with Lewis’s game of commands and permissions. I follow both Yalcin and Lewis in separating the task of giving a compositional semantics for the relevant modal expressions from the task of explaining the pragmatic role of the resulting semantic value. And I will follow them in doing the semantics in the familiar truth-conditional framework. Despite the truth-conditional form of the semantics, Yalcin describes his account of epistemic modals asexpressivist , and the basis for that description is that the speech act that epistemic modals sentences are used to perform (according to the account) contrasts with the speech act of assertion, which aims to describe the world as being a certain way. Lewis’s account of the speech acts of the master in his language game might be called expressivist for the same reason.

As we saw, what is distinctive about the force of the master’s speech acts in Lewis’s  game is that the content of the command or permission sentence is determined  by theposterior context, rather than theprior context, as is the case with assertions. My proposal is to make the same move in explaining the distinctive force of a statement made with an epistemic modal. In the master/slave game, the relevant feature of the context is the sphere of permissibility.  In the case of epistemic modals, the changing contextual feature will be the context set itself.

As with Lewis’s master/slave game, we start with the static compositional semantics, and as with the semantics for Lewis’s game, the semantics will be close to an orthodox Kripke semantics (at least if we ignore certain complications that we will consider later). Our framework already provides us with a binary relation that is determined by a common-ground context. The context, in this sense, is a set whose elements are possible worlds centered on a time and a sequence of individuals, the participants in the conversation. The conversation is taking place in each of the possible worlds in the context set, at the time, and involving the parties that define the center. So for any worldx in the domain of the common ground, there is a set of worlds that are compatible with what is common ground inx . So this gives us a binary accessibility relation on s-worlds, R, defined as follows:x Ry if and only ify is compatible with what is common ground inx . If we restrict our domain, for the moment, to possible worlds compatible with the common ground of a given conversation, and assume that our context is nondefective in the sense that the parties to the conversation are all making the same presuppositions, then the accessibility relation will be an equivalence relation, and so the logic of the ‘might’s and ‘must’s interpreted by it will have a simple S5 structure. (We will come back later to the question what happens when we interpret an epistemic ‘might’ or a ‘must’ in a possible world outside of the context set).  That is all there is to the semantics. As with Lewis’s game, the innovation comes when we specify the force rule, and we will start, as Lewis’s game does, just with a rule for unembedded modal claims. The proposal is to make the ruleprospective in exactly the sense in which the commands and permissions issued by the master in Lewis’s game are prospective. In saying might-f, one is notasserting thatfis possible, relative to theprior context. Rather, one is proposing to adjust the context (if required) to bring it about that what the sentence says, relative to theposterior context – the context as adjusted – is true. 

In Lewis’s game, one player – the master – had complete authority over the relevant parameter, and so that parameter automatically adjusts in response to her speech acts. But in the assertion game, no one player controls the context set; it is subject to negotiation, and this will lead to complications not found in Lewis’s simple game. The slave does not have the authority to reject the master’s commands or permissions, but epistemic ‘might’ statements, like ordinary assertions, can be rejected.  Since the context set models what is commonly accepted, if one party refuses to rule out a possibility, it must remain in the context set. But parties to a conversation can still disagree about whether they are in a position to rule out a possibility. I will defer the question what happens in cases of disagreement (discussed in a later chapter of the book from which this paper is drawn). Let’s consider for now a standard and unremarkable case where the speech act changes the context, but does not result in disagreement. Alice says “Noam might be in his office,” and Bert responds, “No, I just saw him leaving for lunch.” Alice’s statement was true, relative to theprior context, but we are taking it to be a proposal about the posterior context, a proposal that possibilities compatible with Noam being in his office remain in the context set. Bert rejects the proposal, since he has information sufficient to rule these possibilities out.

If it was already compatible with the prior context that Noam is in his office, why did Alice need to say what she said? In the assertion game, we assume that it is inappropriate to assert what is already accepted, since the assertion would have no effect on the context. This question points to two related ways in which we need to refine the simple picture of the common ground, ways that are independently motivated. First, as Kripke’s discussion of presupposition brought out, there is a difference between information that is general background knowledge and information that is presupposed in an active context. Assertions may be appropriate as reminders, even if they are not really news.[11]Such assertions serve to bring an item of background knowledge into the active context – to make it salient.  Second, both philosophers and linguists have recently emphasized the importance of recognizing the questions that are at issue in a given context[12], and a representation of context needs, not just a space of those possibilities that are compatible with what is presupposed, but also a partition of the possibility space, with the questions at issue being those that distinguish between the cells of the partition. If we add this kind of structure to our representation of the common ground, then there will be two ways in which a ‘might’ statement can change the context. In some cases, it will expand the space of relevant possibilities in the minimal way required to make the ‘might’ statement true, relative to that revised context. But in other cases, the job of the ‘might’ statement will be to refine the “modal resolution” (to use Yalcin’s term) – to add a new distinction between the possibilities. The following example is a clear case of the first kind of change: Bert says, “The butler didn’t do it, so it must have been the gardener”, presupposing that the guilty party was one of the two. Alice replies, “Wait, it might have been the chauffeur – we forgot about him.” To illustrate the second kind of context change. Yalcin uses this example: The speaker says, “it might be raining in Topeka.” It was not previously presupposed that it wasnot raining in Topeka – the issue was not on the table.  The statement neither made nor retracted a claim, but served only to raise the question.

Because of the prospective character of the force rule, the interpretation of those ‘might’ statements that are not compatible with the prior context faces a problem that parallels Lewis’s problem about permission. Without additional structure beyond that required by the static semantics, we don’t have determinate context change rule for the epistemic ‘might’. The kind of structure we need is the same as that required for Lewis’s game: nested spheres of possibility around the basic context set. This is exactly the kind of modal structure that semanticists such as Kratzer and von Fintel have used in their accounts of modality and conditionals.

The problem about embedded commands and permissions that I raised for Lewis’s game also has a parallel in the epistemic case, and the solution is the same. If Alice were to say, “if it rained, the game must have been called off,” or “even if the Yankees lost, they might still win the division,” how is she proposing to adjust the context? Unless we modify the semantics, no adjustment to the basic context will be both minimal and sufficient to make the statement true. But if we interpret the ‘must’ and ‘might’ relative to a derived context, the complex sentence can be a proposal of the right kind: one put forward as true relative to the posterior (basic) context.

This modification gives us a solution to Yalcin’s puzzle about ‘might’ in the scope of a supposition, a solution that is close to (and modeled on) the one that he proposed. Yalcin’s theory, formulated in Lewis’s Context/Index framework, proposed that an information state (represented by a set of possible worlds) be added to the index, and this coordinate will be “shifted” for the interpretation of embedded clauses. If we formulate my suggestion in the this framework, it would add a set of  (multiply-centered) worlds to the index. I don’t agree with Yalcin’s original proposal about the way this coordinate of the index shifts in the scope of propositional attitude ascriptions, for reasons that his later work has brought to light, but I agree with the basic idea, and I think the prospective form of the force rule helps to motivate it.[13]

The move that Lewis made in defining his language game (with the adjustments I proposed) allowed for the combination of a smooth compositional semantics with a force rule that made sense of speech acts that do something different from conveying information. On this kind of account, nonassertive speech acts and assertions have in common that a proposition determined by the semantics is put forward as true. In both cases, the end result of a successful and uncontested speech act is a context in which the content of the speech act is accepted – true in all possible worlds in the context set. The contrast between assertions and the other speech acts is in the means by which this is accomplished.

Neither Lewis nor Yalcin discuss the case of deontic or epistemic modals in the scope of quantifiers, but one advantage of a theory that uses a truth-conditional semantics, even for determining the contents of nonassertive speech acts is that it can give a smooth semantics for such cases. There could be a version of Lewis’s game with many slaves, and in such a game, the master could issue general commands and permissions such as this: “each of you may take a day off on your birthday.” With epistemic modals, we have examples such as this: “Any one of the candidates might be selected.”  (Though with both the Lewis game, and the parallel proposal about epistemic modals, not every quantifier would be suitable for issuing permissions, or for altering the common ground. If the master were to say, “some of you may take a day off on your birthday,” this would have to be interpreted as an assertion. If Alice were to say “several of the candidates might be selected,” this will require (or at least favor) a wide scope reading for the ‘might’ (it might be that several of the candidates are selected), or else a nonepistemic interpretation of the  ‘might’.)

In giving the semantics for the epistemic ‘might’ and ‘must’, we restricted the specification of the accessibility relation to worlds that are compatible with the given context. But what about possible worlds outside of the context set? For example, Alice says that it might rain tomorrow in a context in which it is presupposed that the weather forecaster predicted rain. Now consider a possible worldw in which the weather forecaster did not predict rain (perhaps no prediction was made) and in which it in fact did not rain on the relevant day. Is Alice’s ‘might’ statement true or false in that possible world? Since presupposition and common ground are not factive notions, it could be that Alice’s presuppositions in worldw are the same as they are in the actual world. In fact,w might be the actual world. So we know what the context set is, in worldw , but what is the set that is R related to worldw , where R is the relation that is relevant to determining the truth-value of the epistemic modal sentences in that world? One might be tempted to say that the relevant R is just the relation that holds between a worldw and the worlds that are compatible with what is presupposed inw , and this would be the right thing to say if the modal statement were simply the proposition that something is compatible with what is being presupposed. But there is a subtle difference between a proposition that states somethingabout the context and a proposition that expresses something that is context-dependent.  fis compatible with the common ground if and only if we are presupposing that it might be true, and that is enough to tell us whether the ‘might’ statement is true or false in the worlds compatible with the context, but it leaves open the question, whether the proposition expressed in that context is true or false (or neither) in possible worlds outside the context. So our theory, thus far, remains silent on the question whether the ‘might’s and ‘must’s are true or false (or neither) in worlds outside of the context set. Should this gap be closed, and if so how?

To get a more concrete sense for this kind of question, let’s look at some examples. In many cases, there will be a clear and unproblematic fact of the matter about whether some statement is true or false, even if the statement is made in a context in which a relevant presupposition is in fact false. Suppose I try to call Sam Smith, but dial the wrong number and am in fact talking to someone else. “Is this Sam?” I ask, and because my interlocutor happens by coincidence to have the same first name, he answers “yes”.  Presupposing that I am talking to Sam Smith, I say, “The department voted to offer you the job.” It is clear enough what I have said: I referred, with my use of ‘you’ to my actual interlocutor, and inadvertently said something false about him. But in other cases, the semantics may not provide an answer, or it may be controversial what the answer should be. Suppose my interlocutor and I are presupposing of Jones that he is the unique man drinking a martini and I say “The man drinking a Martini is a philosopher.”[14]Jones is in fact a philosopher, but our presupposition that he is drinking a martini is false – it is Perrier in his martini glass. Russell, Strawson and Donnellan will all agree about the way the assertion affects the context, since they all agree about the truth-value of the statement with the definite description in possible worlds compatible with what is being presupposed in the context. But their analyses of definite descriptions will disagree about the truth-value of the statement in theactual world, which is outside of the context set: Assuming that no unique man in the room is actually drinking a martini, Russell will say the statement is false, Strawson will say that it is neither true or false, and Donnellan (assuming the description is being used referentially) will say that it is true.

On the dynamicpragmatic story, it is a minimal requirement on appropriate speech that one use a sentence that has a truth-valueat least for all the possible worlds compatible with the common-ground context. That is, it is required that the function from possible worlds to truth-values determined by the semantics be a total function, relative to that domain. On the dynamicsemantic story, where the semantic values are context-change potentials, truth-values are determinedonly for possible world in the context set. On the pragmatic theory that separates the determination of content from the force of the speech act, the proposition expressedmay extend beyond the possibilities compatible with what is being presupposed. On this kind of account, some speech acts are more robust: what is asserted may be detached and added to one’s stock of beliefs. In other case, what is said may be more fragile, succeeding in distinguishing between the possibilities compatible with a local context, but not extending much or at all beyond it. The silence of the account we are considering about the relevant information state for interpreting epistemic modals in possible worlds outside the context set implies that sentences with bare epistemic modals will, or at least may, be cases for which the proposition expressed is partial, and so the statement gets no truth-value in the actual world. But in some cases, there may be a natural extension of the relevant parameter to worlds outside the context set.  Consider this extended example.  It is the last day of the baseball season, and the Yankees are one game ahead of the Red Sox. Each team has one game to play, though not with each other. If the Yankees win, or if the Red Sox lose, the Yankees win the division.  But if the Yankees loseand the Red Sox win, they will then be tied, so there will be a playoff game to determine the division champion.  All of this is common ground in the context. Alice says: “The Yankees lost, so the Red Sox still might win the division.” This is true in all of the possible worlds compatible with the (posterior) context. But, let us suppose, Alice was wrong about the Yankees – they in fact won. Alice’s ‘might’ statement was appropriate, and succeeded in changing the context in a determinate way, but was it truein the actual world ?We know that the Red Sox won’t be the division winner, but we have information not available to Alice and her interlocutors. It could have been that one of the interlocutors knew that Alice was mistaken, in which case he would reject both her assertion about the Yankees, and her proposal that possibilities in which the Red Sox win the division remain in the context set. But no one in the conversation had this information. In this case, was Alice in fact wrong – not just about the Yankees game, but about her epistemic ‘might’ statement about the Red Sox?  Now consider the reverse situation: Suppose Alice said, “The Yankees won, so the Red Sox must be out of the running for the division title.” Alice got it wrong in this version of the example too: the Yankees in fact lost.  But alas, the Red Sox also lost (though none of the relevant parties know this), so the Red Soxare in fact out of the running. Is Alice’s statement that theymust be out of the running true in the actual world? Her reasoning was based on a false premise, but is this enough to make it false?  I don’t think these questions have obvious answers. There is some inclination to fill the vacuum left by our theory’s silence by shifting toour context – the context of the theorist giving the example, bringing in the stipulated facts about the story that are used to raise the problem. There is also some inclination to shift to a nonepistemic modality to give an answer. (If the Yankees lost, and the Red Sox game is still undecided, then even if we stipulate that theywill lose, we can say that, as of now, they stillmight win. But if we say this, we are using the ‘might’ in a nonepistemic sense.) Further elaboration of the example, or of the theory, might give reason to assign a truth-value, outside of the context set in such cases, but for some cases, the semantics might resolutely retain its silence.[15]

The semantics will give a definite answer, even outside the context set, in the case where the prejacent of the ‘might’ statement is true in a given world, or when the prejacent of a ‘must’ statement is false. Whatever anyone believes, knows or is presupposing, if the Red Sox actually did win the division in the end, then the statement that they might win was actually true, relative to any context in which that statement was made, or denied. That follows from the reflexivity condition on the relevant accessibility relation, which it seems intuitively clear should hold. And this condition will hold for deontic ‘must’ and ‘may’ as well as for the epistemic modals. Lewis’s little language game used an artificial language, with ‘!’ and ‘¡’ for the command and permission operators, but if Lewis’s commands and permissions were made with ‘must’ and ‘may’, with their normal senses, then a disobedient slave will be a problem, not just for the master, but for the semantics. The master can make it the case, just by her speech act, that the slave is obliged to stay out of her wine cellar, but she cannot make it the case, by her speech act, that the slave does what he is obliged to do.  If either the master or the kibitzer says to the slave, “you must stay out of the wine cellar,” she or he must presuppose that the slave will do what he must do. If one wants to allow for the possibility of the disobedient slave, one must put the command or statement differently – for example, with ‘should’ or ‘ought’ rather than ‘must.’[16]