1. Felicitous underspecification and its limits

Stalnaker seminally proposed three “essential conditions of rational communication” ([1978] Reference Stalnaker1999, 88). Those principles are constraints on what the common ground of a conversation must be given that an assertion has taken place. A common ground, again, is information mutually taken for granted by interlocutors for the purposes of conversation. For the purposes of this paper, I identify a common ground with its context set: the set of maximally specific ways the world might be—i.e., possible worlds—consistent with what the interlocutors mutually take for granted for the purposes of conversation.

One of the principles, called ‘Uniformity,’ is of central concern in what follows.Footnote ² Uniformity holds that any two hypotheses about what the speaker means, consistent with the context set, must lead to the same update on that context set. Here is the principle stated in a bit more detail.

Uniformity allows there to be indeterminacy in the context set as to what the speaker means as long as there is a determinate suggestion as to how the context set may be updated. There is guaranteed to be such a determinate suggestion if Uniformity is satisfied because update-equivalence must hold between the context set and any potential claims the speaker might be making according to the context set.

Uniformity may be equivalently stated as the requirement that every hypothesis about what the speaker means, consistent with the context set, leads to the same update on the context set. These two statements of Uniformity are equivalent because every one of a set of propositions has the same intersection with a given context set just in case every pair of propositions in the set of propositions is update-equivalent on that context set. So, for simplicity, I will talk of sets of propositions being update-equivalent (on context sets).

The cases of felicitous underspecification from the introduction satisfy Uniformity. In Sports Car, the speaker, John, has done enough, but only enough, to make it common ground that he is either saying that the car kind is beautiful, or that the car token of that kind, in front of them, is beautiful. But it is a manifestly plausible mutual assumption that a kind is beautiful just in case its instances are. See figure 1 for an illustration of how Uniformity holds in Sports Car. In Package, the common ground has it that John is either saying that the package arrived, or its contents. But it is a reasonable joint assumption that a package arrives just in case its contents do. In Tablets, the common ground does not settle whether it is this or that particular tablet that John is speaking of, or even the kind, when he says that it is not the one he ordered. But it is plausibly part of the common ground that all the tablet tokens are of the same kind. Thus, one of the tablets is of the wrong kind just in case the others are, as well as the kind itself. In Co-Pilots, the common ground holds that John may be saying either that one co-pilot or the other is in trouble. But it is a plausible assumption that, when a plane is threatening to go down, one of the co-pilots is in trouble just in case the other is.

Figure 1. The solid rectangle represents the common ground. The dotted rectangles represent the different claims the speaker could be making. T represents the worlds where the car token is beautiful ( $ \overline{T} $ where it is not), and K the worlds where the car kind is.

In addition to Uniformity, here are Stalnaker’s two other principles.

The three principles together guarantee that, given an assertion, the context set itself determines that there is a single way of updating that same context set (Uniformity), where that update is a genuine reduction of the context set (Informativeness), and where it is clear for each world in the context, whether it survives that reduction or not (Contentfulness).Footnote ⁴

It should be apparent that the latter two principles are also satisfied in the cases under discussion. In each of the cases it is plausible that any proposition the speaker might be intending to say, given the context set, is one that is not already taken for granted by the interlocutors. So Informativeness is satisfied. And it is also plausible that in each case no proposition the speaker might be intending to say, given the context set, is one that has truth-value gaps. So Contentfulness is satisfied.

So, based on the cases under discussion, I propose that Stalnaker’s three principles are satisfied in all cases of the felicitous underspecification of demonstratives.

Furthermore, I propose that the principles are not satisfied in cases of the infelicitous underspecification of demonstratives. Consider the following Strawson (Reference Strawson1950)-inspired case.

Cluttered Shop: John and Mary are in a cluttered shop, surrounded by bric-à-brac. John utters the following with a vague gesture and no thought about what he means to speak about.

In Cluttered Shop, it is not a reasonable joint assumption that one of the red things in the shop is fine just in case each of the others are. See figure 2 for an illustration of how Uniformity is not satisfied in this case. So my focus remains on the principle Uniformity, which, again, requires that the every hypothesis about what the speaker means that is consistent with the context set leads to the same update on that context set. As I am about to show, Uniformity places a substantial general limit on the possibility of felicitous underspecification, given the way that the principle does not allow aspects of conversational context other than common ground to help make underspecification felicitous.Footnote ⁵

Figure 2. T represents worlds where one certain thing is a fine red one, and $ {T}^{\prime } $ represents worlds where a certain other is. I have assumed here, for the simplicity of the diagram, that there are only two relevant things.

King (Reference King2017, Reference King2021), in contrast, proposes to account for felicitous underspecification by suggesting that contextual goals—interlocutors’s conversational interests—play a role in permitting felicitous underspecification. This appeal to contextual goals may be refined by looking to Roberts’s influential taxonomy of discourse and domain goals (Roberts Reference Roberts, Horn and Ward2005, Reference Roberts2012a, Reference Roberts2012b). Discourse goals provide the topics of conversations, playing a core role in conversation’s function of enabling joint enquiry. Roberts takes discourse goals to be questions under discussion (QUDs). Accordingly, each context has a QUD, which can be either implicit or given explicitly. A QUD—for instance, what is John’s favorite cheese?—structures the joint inquiry endemic to conversation. On the other hand, Domain goals are practical interests of interlocutors that they have agreed to work together to satisfy through their conversation. They are particular things that individuals want out of the world—our “domain.” They also are either implicit or explicit. Suppose, for instance, that John is lost in a foreign city and needs to find the train station, so he strikes up a conversation with a stranger. More examples of both discourse and domain goals are given below, alongside pertinent data.

Underspecific uses of demonstratives are, however, more constrained in their felicity than they would be if either discourse or domain goals played a role in permitting such felicity. Consider first domain goals.

Hammer: A mechanic and his assistant are working together to repair a car. The mechanic gestures vaguely at his table of tools, without looking, and says to his assistant,

This utterance is infelicitous even if the mechanic is at a stage in the repair such that a certain hammer is needed.

The mechanic’s vague demonstration makes it compatible with the common ground that he may be intending to speak about one or the other of the several tools on the table. And given the mechanic and assistant’s coordination on their practical goal, there is a specific tool on the table such that the mechanic needing it is uniquely conducive to that goal. So it seems that domain goals could play a role in narrowing down the hypotheses about what the speaker is intending to say, in this case to, a single one. Yet the utterance in Hammer is infelicitous.Footnote ⁶ And Uniformity is violated: the different hypotheses suggested by the demonstration—that the mechanic needs this or that tool on the table—are not update-equivalent, since it is not a plausible common assumption that the mechanic needs one tool just in case he needs another. Thus, domain goals do not play a role in narrowing down the potential hypotheses about what the speaker is intending to say.

Taking a step back, it is theoretically unclear why domain goals should even be expected to permit felicity. They are simply interests the interlocutors happen to have, and thus not integral to conversation as such. QUDs, on the other hand, as discourse goals do have a more intimate connection to the nature of conversation. Hence, it is more plausible that they may help refine King’s initial appeal to contextual goals. Yet Dickie (Reference Dickie2020) shows, with the following cases, that QUDs do not play that role.

Good Student: John and Mary are professors, and Mary visits John’s graduate seminar. John has previously mentioned to her that even one good student can make a seminar worthwhile, to which she has expressed agreement. The seminar that Mary visits ends up going terribly with much awkward silence and off-topic comments. As the students are leaving, Mary asks John whether this seminar, on the whole, is worthwhile. In response, he gestures toward the corner of the seminar table, where several students sat taking notes the whole time. He utters,

The relevant QUD here is explicit: Is this seminar worthwhile? John’s answer, despite the fact that it is underspecific, provides a clear answer to that question (Yes). Yet the utterance is infelicitous.

Miser: John is complaining to Mary that food has become extremely expensive due to the recession. She responds by accusing John of being a “misery guts” who always thinks everything is overpriced. John retorts as follows, while gesturing toward a shelf behind Mary that contains dozens of knickknacks, but withdraws his arm quickly before she turns to look. He says,

The relevant QUD here, though implicit, is plausibly whether John thinks anything is cheap. And the utterance, despite the fact that it is underspecific, provides a clear answer to that question (No). Yet there is infelicity.Footnote ⁷

In both these cases, Uniformity is violated. In Good Student, John could be speaking of one or the other student (according to the common ground). But it is not a plausible joint assumption that one student is good just in case the other is. In Miser, John could be speaking about one or another kickknack. But it is not a plausible joint assumption that one knickknack is cheap just in case another is.

King’s (Reference King2017) initial appeal to contextual goals is brief and highly schematic, so it is plausibly challenged by Dickie’s cases Good Student and Miser. In his more recent book, however, King (Reference King2021) develops a more detailed proposal. He proposes that underspecification is felicitous when the QUD is answered by either the disjunction or conjunction of all the potential specific interpretations of the utterance. What is crucial for present purposes is that he claims the range of specific interpretations is determined by the speaker’s explicit aim to say something indeterminately about one or another of some collection of objects where that intention must be knowable by an idealized hearer. So, in cases of felicitous underspecification, a speaker must have a special sort of referential intention with the disjunctive content to talk about one or another of some collection of objects, and must make that intention appropriately manifest.Footnote ⁸ He then argues that his account does not predict felicity in Good Student and Miser, since the speaker in such cases does not have an appropriately disjunctive intention, and, even if the speaker did, that intention could not come to be known by an idealized hearer.

King does not provide much argument for why, even if it is assumed in Good Student and Miser that the speaker does have an appropriately disjunctive intention, an idealized hearer could not come to know that the speaker has that intention. King’s insight, though, seems to be that in those cases the speaker is suggesting that he is intending to speak about one of the relevant objects, but at the same time not allowing the addressee to work out which one. But now consider the following modification of Miser.

Modified Miser: John is complaining to Mary that food has become extremely expensive due to the recession. She responds by accusing John of being a “misery guts” who always thinks everything is overpriced. In addition, John has a strange obsession with placing his possessions on various shelves according to their relative cheapness, and he and Mary are aware of this strange miserly obsession. John retorts as follows, while gesturing vaguely toward one of his shelves containing dozens of knickknacks:

Similarly, Good Student could be modified by adding the assumption into the common ground that the students the professor gestures toward are equally good. In both modified cases, given the additional assumption in the common ground, it seems reasonable to suppose that the speaker is intending to say something indeterminately about one or another of the potential referents, and that intention could come to be known by an idealized hearer. Yet infelicity remains.

Admittedly, my intuitions about idealized hearers are murky. Moreover, I do not find the approach of positing sophisticated sorts of intentions to be theoretically illuminating. So, in the next section, I develop my own proposal further without appeal to idealized hearers or special intentions, in order to shed further light on felicitous underspecification. Afterward, in section 3, I show how my developed proposal accounts for the infelicity in the modified Dickie cases just given despite the fact that Uniformity seems to be satisfied in them.

2. Understanding and the commonplace effect

In order to begin developing my proposal further, let me return to Dickie’s original, unmodified cases Good Student and Miser. (I set aside the modifed versions of those case until the next section.) In the previous section, the original, unmodified cases helped establish that the satisfaction of Stalnaker’s principles is necessary and sufficient for felicitous underspecification. Dickie, however, uses her cases to do something very different than provide support for Stalnaker’s principles. She uses the cases in an argument against the traditional Stalnakerian view that assertion is fundamentally about sharing pieces of information. The argument goes as follows. The possibility of felicitous underspecification is mysterious, given that traditional Stalnakerian view, since in such cases there is not a determinate piece of information shared by the speaker. So, she argues, the Stalnakerian proposal is naturally elaborated as holding that assertion is about sharing information determinate enough given our discourse goals. But, as her cases show, that elaboration overgenerates felicity.

Here is an argument for the claim that the possibility of felicitous underspecification challenges the traditional Stalnakerian view that assertion is fundamentally about sharing pieces of information. Recall from the introduction that what is meant by an ‘assertion’ is the claim that the speaker intends to make, and what is said is what the speaker intends to say according to the common ground. The piece of information to be shared, according to the traditional view, should be identified either with what is meant or what is said. But, in cases of felicitous underspecification, there are perfectly successful assertions without there being anything that the common ground entails the speaker means. And there may be nothing that the speaker in fact means. In Sports Car, for instance, it is plausible that the speaker has not settled, in his intentions, whether he is saying of either the car type or token that it is beautiful. But something that can fail to hold in a perfectly successful assertion cannot be the essential effect of assertion. (It might be pointed out that there is a way in which an assertion may be successful without the essential effect holding: the assertion may be understood but not accepted. But, in cases of felicitous underspecification, it may be that the assertion is understood and accepted without there being anything said or meant.)

On the basis of her criticism of the traditional Stalnakerian view of assertion, Dickie and Szabó (Reference Szabó2020), following in her stead, outline alternative pragmatic views. Their proposals are promising, but I do not dwell on them here. As just argued, felicitous underspecification does pose a challenge to the traditional Stalnakerian view of assertion, since in such cases there need not be anything that is said nor even meant. Yet, as argued in the previous section, Stalnaker’s principles are satisfied in cases of felicitous underspecification. And here is an argument for why the principles may be satisfied despite there being nothing that is meant. Crucially, the principles do not require that the common ground be consistent with the truth about what the speaker meant. In general, there should be no requirement that the common ground reflects the truth: it is possible that what the interlocutors take for granted, for the purposes of conversation, does not reflect how things actually are. Hence, the truth about what the speaker meant—which may be that the speaker meant nothing at all—need not be entailed by, or even consistent with, the common ground. Here I am not appealing to any intentions with special content as King does, but instead I am simply observing that it is possible for Stalnaker’s principles to be satisfied while the speaker does not have the intention to make a particular claim.

There is more to be said in filling out the arguments of the previous two paragraphs. I do so in the next section by addressing a couple objections to them. But before that, I get more of my proposal onto the table in the remainder of the present section.

The upshot of the foregoing discussion is that the phenomenon of felicitous underspecification is captured by Stalnaker’s pragmatic principles, yet poses a problem for the traditional background view of assertion meant to motivate those principles. So the foregoing raises the question of how the principles may be motivated otherwise than by the background view that assertion is fundamentally about sharing pieces of information. What I do in the remainder of this section is develop an alternative basis for the principles, then use it to shed further light on how there is understanding in cases of felicitous underspecification.

To begin this task, I dig into how Stalnaker ([1978] Reference Stalnaker1999), in the course of motivating his principles, goes about proposing his background view of the essential effect of assertion. He begins doing so by identifying two ways in which an assertion may influence the common ground.

This first, ‘commonplace’ effect—as he later calls it on the same page—is the effect an assertion has on the common ground in virtue of it being a mutually observed event. The addressee, for instance, need not accept the assertion in order for the commonplace effect to take place. Stalnaker, however, sets aside the commonplace effect, turning instead to the essential effect.

In this latter passage, we find the traditional Stalnakerian view that assertion is fundamentally about sharing pieces of information.

As was just argued, felicitous underspecification challenges that view about the essential effect of assertion, while not challenging the pragmatic principles that it is supposed to motivate. I wish to set aside the question of what exactly the essential effect should instead be taken as. Regarding the essential effect, all that matters in what follows is that it is what takes place when an assertion is understood and accepted by the addressee. I focus instead on the commonplace effect, which, recall, is the effect an assertion has on the common ground preceding the essential effect.

Stalnaker sets aside the commonplace effect in the course of motivating his principles, but that he does so is misleading. His principles are in fact constraints on what the commonplace effect of an assertion must bring about. The principles are requirements that the context set must satisfy, given that an assertion has taken place—which is to say given that the context set has been influenced by the commonplace effect of that assertion. Together, the principles require that the commonplace effect of an assertion bring it about that the context set is consistent with only update-equivalent hypotheses about what the speaker meant (Uniformity), where the determinate update determined by these hypotheses genuinely reduces the context set (Informativeness), and where none of the hypotheses lacks a truth-value in any of the worlds of the context set (Contentfulness). So if the commonplace effect of an assertion brings about the satisfaction of the three principles, then there is a clear way of updating the context set on the basis of that assertion. Thus, according to the principles, the commonplace effect ought to provide the rational basis for what is to happen if the assertion is accepted. And the notion of understanding an assertion corresponds precisely to that which provides the rational basis for its acceptance. Therefore, the principles are requirements for understanding.

As mentioned at the beginning of the previous section, Stalnaker characterizes his principles as “essential conditions of rational communication.” The present considerations unpack that characterization by revealing that the principles are conditions of understanding. So I propose that there is understanding of an assertion just in case the commonplace effect of that assertion brings it about that the context set satisfies the three Stalnakerian principles.

I turn now to finding theoretical motivation for my proposed connection between the principles and understanding.

One approach to theorizing understanding develops Grice’s work on speaker meaning (Grice [1957] Reference Grice1989, [1969] Reference Grice1989), which I have already drawn upon in characterizing what is meant by an assertion. That Gricean tradition elaborates the intentional structure behind a speaker’s communicative act, then holds that understanding consists in the addressee properly identifying certain parts of that structure. King’s (Reference King2021) recent work, discussed at the end of the previous section, can be seen as one way of developing that Gricean tradition to account for cases in which the speaker does not intend to make a particular claim.Footnote ⁹ But part of what is theoretically interesting about cases of felicitous underspecification is the disturbing lack of mental activity on behalf of the interlocutors. So here I characterize a notion of understanding, which supports my proposed connection between understanding the principles, by beginning with another strand of the Gricean tradition, the one beginning with Grice’s ([1975] Reference Grice1989) proposal that conversation is a cooperative enterprise.

An immediate problem for the proposal that conversation is cooperative concerns what the relevant sense of ‘cooperative’ could be. Individuals may converse despite having very different, or even opposed, reasons for doing so. Imagine, for instance, a trial in which the accused takes the stand and is cross-examined by the prosecution, or imagine the vicious back-and-forth of a presidential debate. So ‘cooperative’ must be meant in a weak and perhaps unfamiliar sense. But now consider engagement in joint activity: doing something together. As noted by Bratman (Reference Bratman2014), joint activity always has a joint goal, despite the fact that participants may have ulterior motives. Imagine two roommates lifting a heavy chair together up the stairs to their apartment, each with the hope of using it the most. A joint activity may even be explicitly competitive, as in a game of chess. Thus, what I take to be correct about Grice’s proposal about cooperativity is the claim that conversation is a joint activity, since that claim provides a plausible account of the way in which conversation is cooperative.

If conversation is a joint activity, then it has a joint goal. In specifying that goal, I think an insight behind the first strand of Griceanism, that concerning speaker meaning, is relevant. I propose that the joint goal is that of interlocutors making sense of one another, as fellow intentional agents, in virtue of their actions—the goal of achieving mutual intelligibility. Footnote ¹⁰ So, given the central role of understanding in conversation, I take it that the foregoing provides support for the following, premise 1: there is understanding of an assertion just in case the goal of achieving mutual intelligibility has been enabled on the basis of that assertion.

So far in this paper, the common ground of a conversation has been characterized as the information mutually taken for granted by the interlocutors for the purposes of conversation. But now something can be said to refine that characterization. I propose that the common ground is the background information drawn upon by interlocutors in the joint activity of finding mutual intelligibility. Thus, if the common ground is updated, then the project of achieving mutual intelligibility has been served, since there is thereby more information that the interlocutors may rely on in doing so. Therefore, (i): if there is a clear way of updating the context set on the basis of the commonplace effect of an assertion, then there is a clear way of contributing to the joint activity of making sense of one another on the basis of that assertion. Moreover, I propose that the common ground exhausts the resources that interlocutors have in making sense of one another: since in conversation interlocutors are jointly engaged in achieving mutual intelligibility, the information drawn upon in making sense of one another must be information mutually taken for granted. Therefore, (ii): there being a clear way of contributing to the joint activity of making sense of one another on the basis an assertion requires that there be a clear way of updating the context set on the basis of the commonplace effect of an assertion.

From (i) and (ii) follows premise 2: the goal of achieving mutual intelligibility has been enabled on the basis of an assertion just in case there is a clear way of updating the context set on the basis of the commonplace effect of the assertion. Given premises 1 and 2, the connection between understanding and Stalnaker’s principles is thereby motivated, that there is understanding of an assertion just in case the commonplace effect of that assertion brings it about that the context set satisfies the three Stalnakerian principles.

So I have found theoretical motivation for the proposal that all that is required for understanding an assertion is that the interlocutors’ joint project of making sense of one another is served on the basis of the assertion, for which it is sufficient that the information drawn upon in that joint project provide a determinate way of updating that very same information. Now recall again the notions of what is meant and what is said: what the speaker intends to say and what the common ground entails that the speaker intends to say. These notions stand at opposite extremes on a scale of sociality. What is meant is something private in that it is determined by the speaker’s mental states. But what the speaker has said is fully public in such a way that the speaker is on the hook for having said what they said; that the speaker said what they said can transcend the particular interaction between the speaker and addressee, as the addressee can take it from their interaction with the speaker and share it with others (Camp Reference Camp, Fogal, Harris and Moss2018).Footnote ¹¹ So what is said is social, in a large-scale, collective sense of ‘social.’ In the foregoing, I developed a notion of understanding according to which it is neither private nor social. It is a joint interaction between interlocutors. So it is not entirely up to the speaker, and thus not private. But it is merely a small-scale, interpersonal interaction, which need not give rise to anything public. So, with regard to cases of felicitous underspecification, that is how there may be understanding without anything meant or said.

3. Objections and replies

The previous sections developed and motivated the proposal that the satisfaction of Stalnaker’s priniciples is necessary and sufficient for understanding, including in cases where a use of a demonstrative is underspecified. I turn now to responding to objections raised by various anonymous referees to both the proposal and its motivation. Perhaps the most pressing problems are the modified Dickie cases from the end of section 1, which seem to be counterexamples to the proposal. Before returning to those cases, though, I begin by addressing a couple objections to the motivation for my proposal given in the previous section.

At the beginning of the previous section, I provided an argument to further motivate Dickie’s claim that the possibility of felicitous underspecification challenges the traditional Stalnakerian view that assertion is fundamentally about sharing pieces of information. In that argument, I assumed that the piece of information to be shared (if there is one), according to the traditional view, should be identified with either what is meant or what is said—where, again, what is meant by an assertion is the claim that the speaker intends to make, and what is said is what the speaker intends to say according to the common ground. But that assumption may be questioned, for there are other pieces of information that a Stalnakerian might identify as the one that it is the essential effect of assertion to share such that, crucially, these other pieces of information are present in cases of felicitous underspecification.

First, it might be proposed that the essential effect of assertion is to share the diagonal proposition associated with an utterance. The diagonal proposition associated with an utterance, a notion seminally introduced in Stalnaker ([1978] Reference Stalnaker1999), can be specified without any commitment to a determinate way that context-sensitive expressions contained in the uttered sentence are to be resolved. So, for instance, the diagonal proposition of an utterance of ‘That man is happy’ is the proposition that whoever is being demonstrated is happy, restricted the context set, where the context set may contain worlds that disagree concerning what is being demonstrated.

Here are three problems for the proposal that the essential effect of an assertion is to share its associated diagonal proposition. (i) The essential effect would then be to share a piece of information that entails everything that happens to be assumed by the interlocutors so far in their conversation, which is odd to say the least.Footnote ¹² (ii) The issue then arises of why it is that interlocutors ever care about resolving the reference of context-sensitive expressions such as demonstratives: more specifically, in terms of the present discussion, such a proposal seems to overgenerate felicitous underspecification. (iii) In Stalnaker’s seminal discussion of it, the diagonal proposition is only supposed to become relevant when the principles are violated; in cases of felicitous underspecification, however, the principles are not violated.

In more recent work, Stalnaker (Reference Stalnaker2014) introduces the notion of the superdiagonal proposition associated with an utterance, which is the diagonal proposition not restricted to the context set. But, even if it is proposed that the essential effect of an assertion is to share the superdiagonal, the problems identified in (ii) and (iii) above for the regular diagonal nonetheless apply. Thus, appealing to diagonals is off the table in attempting to save Stalnaker’s traditional view of assertion in light of felicitous underspecification.

Finally, it might be proposed that the essential piece of information to be shared is the unique update on the context set that each of the candidates for what is meant lead to when the three principles are satisfied. But this proposal faces a similar problem as that raised in point (i) above, since the updated context set entails the prior context set.

The points (ii) and (iii) made above—though crucial in addressing the objection just discussed—themselves raise a problem for my proposal that the principles constrain the possibility of felicitous underspecification. In order to explain the judgments of infelicity in the cases of infelicitous underspecification, I have argued that there cannot be understanding of an underspecific use of a demonstrative when the principle Uniformity is not satisfied. But, in cases of infelicitous underspecification, it seems open to the interlocutors to suppose that it is the diagonal proposition that the speaker means, thus bringing it about that the context set entails that the speaker means the diagonal proposition, where that context set does satisfy all the principles. So, it seems that my proposal overgenerates felicitous underspecification.

It is not a satisfactory response to the problem just raised to hold that interlocutors never take the diagonal proposition to be what is meant, for one of Stalnaker’s seminal applications of his framework involves specifying when such ‘diagonalization’ does occur. Stalnaker ([1978] Reference Stalnaker1999) considers, for instance, an utterance of ‘That is either Zsa Zsa Gabor or Elizabeth Anscombe,’ said after the interlocutors hear a voice from another room. Any world w in which the claim that the speaker intends to make is about a particular individual—that is, where that individual is what the speaker is referring to with their use of the demonstrative ‘that’—will be such that the claim that is meant in w is either a necessary truth or a necessary falsehood. If, in w, the claim is about either Gabor or Anscombe, then the claim is a necessary truth. If the claim is about some other particular individual, then it is a necessary falsehood. But then, if the interlocutors suppose that the speaker is intending to make a claim about some particular individual, then not all the principles are satisfied: either the principle Informativeness is violated, or both principles Informativeness and Uniformity are. Similar remarks apply generally, as Stalnaker notes, to identity claims made with directly referential expressions such as demonstratives and proper names. Accordingly, Stalnaker explains how there can be understanding of such utterances despite the fact that his principles seem not to be satisfied by proposing that interlocutors diagonalize: the interlocutors take it to be common ground that the speaker meant the diagonal proposition.

I do not wish to rule out this application of Stalnaker’s framework with the claim that interlocutors never diagonalize. I think, nonetheless, that there is theoretical room to predict that interlocutors diagonalize in response to identity utterances such as the ones discussed in the previous paragraph, but at the same time that that process cannot occur in the cases of infelicitous underspecification I have discussed, such as Cluttered Shop from section 1. I do not attempt here to explain where the difference between the two types of cases lies, though it should be noted that a crucial part of the application to identity-utterances is that, before the process of diagonalization, Informativeness is violated, in addition to Uniformity perhaps being violated. In contrast, only Uniformity is violated in the cases of infelicitous underspecification I have discussed.

Let me now move on to address another objection, this one to another part of the motivation for my proposal given in the previous section. The objection targets the claim that Stalnaker’s principles may be satisfied while there is nothing that is meant.

One implication of Uniformity is that, given the commonplace effect of an assertion, every world w in the resulting context set must be such that there is a unique claim that the speaker means in w. So the principle requires that it be inconsistent with the context set that the speaker means nothing. Thus, given the commonplace effect of an assertion, it must be taken for granted (for the purposes of conversation) by each interlocutor that there is some claim or other the speaker means. So, while it is not required that a common ground reflect the way things actually are, if the principles are satisfied while there is nothing the speaker in fact means, then the speaker takes it for granted that there is something she means, despite the fact that she does not mean anything. Since facts about what a subject intends are accessible to that very subject, there is thus a difficult question as to how it could be that a speaker takes it for granted that there is something she means, despite in fact meaning nothing.

The refinement of the notion of common ground from the previous section—that it is the information taken for granted for the purposes of the joint activity of making sense of one another—answers that difficult question. The answer is that there are strong practical reasons, given the purposes of the joint activity of making sense of one another, for taking it for granted that there is some determinate claim that is meant by an assertion. Consider, by analogy, an example Bratman (Reference Bratman2014) uses to show that there are assumptions that must be taken for granted in an individual’s individual deliberation, regardless of whether one believes them.

This Kantian example alleges that, while one may not believe in free will, there are strong practical reasons for taking it for granted that one has it, for the purposes of individual action. Similarly, I suggest that in working together to make sense of one another as intentional agents, both speaker and addressee typically take it for granted that there is an intelligible answer as to what the speaker is doing in making an utterance: in particular, that there is a unique and determinate claim that the speaker intends to say.

It is thus a crucial aspect of the four cases of felicitous underspecification—those given in the introduction and discussed in section 1—that the background assumptions—the ones permitting update-equivalence to hold between the potential hypotheses concerning what the speaker might mean—are themselves common background assumptions. Consider again the assumption, for instance, that a car model is beautiful just in case its tokens are, or that one co-pilot is in trouble just in case the other is. These are standard, community-wide assumptions, standardly part of common grounds; thus, they are present in the common grounds of those cases without being particularly salient to the interlocutors. Hence, the interlocutors have no reason to think that the speaker is not saying anything, since the most plausible way in such cases that a speaker might be not intending to say anything is if she were attempting to exploit an assumption that guarantees update-equivalence in order to not have to commit to one or another specific interpretation of her assertion. In general, it seems implausible that ordinary speakers always form the communicative intentions required for there to be something in particular the speaker means. Yet it is plausible that interlocutors generally take it for granted that there is some determinate answer regarding what the speaker means to say, and, crucially, there is no reason for interlocutors not to make that assumption in the four cases of felicitous underspecification discussed earlier in this paper.

We are now in a position to see how the modifications of Dickie’s cases from the end of section 1 are not in fact counterexamples to my proposal. In those modifications, an assumption is added to the common ground that establishes update-equivalence among the claims the speaker could be making about each of the potential referents. In the modification of Good Student, where the professor utters ‘She’s really good,’ it is mutually assumed that the students at which the professor vaguely gestures are equally skilled at philosophy. In Modified Miser, it is mutually assumed that the speaker arranges his possessions on shelves according to their relative worth. But both these assumptions are unusual compared to the generic assumptions that permit felicitous underspecification in the first four felicitous cases. Thus, the added assumptions in the modified cases are particularly salient, so it is an open possibility that they are being exploited by the speaker in order to not have to make any particular claim. Hence, the possibility is consistent with the common ground that the speaker is intending to say nothing, in addition to each of the possibilities that the speaker is intending to speak about one of the potential referents. So Uniformity is violated.

As discussed at the end of section 1, King attempts to explain how Dickie’s original cases are not wrongly predicted to be felicitous on his view by claiming that felicitous underspecification requires that the speaker has a certain special intention, with the aim to say something indeterminately about one or another of some set of potential referents, where this intention must also be knowable by an idealized hearer. But, as I argued at the end of section 1, King’s proposal thus falters with the modifications of Dickie’s cases. In contrast, my proposal explains the infelicity in Dickie’s original cases, as well the modified ones, as violations of Uniformity. And a crucial part of how it does so is with the requirement that it be taken for granted, even in cases of felicitous underspecification, that there is some particular claim the speaker is intending to make—a requirement that stands in contrast with King’s approach of positing special intentions.

Finally, I discuss some further cases provided by King (Reference King2021, 31–32, 68–72), which seem to show that a demonstrative may be used felicitously while it is apparent to the interlocutors that the speaker has the special sort of intention he posits.Footnote ¹³ The cases are as follows:

Job Interview: John is interviewed by five women for a job. As he is walking out of the interview room, one of the women says, ‘You’ll get a call from one of us today to tell you if you get the job.’ Mary, who is in the hallway waiting for John, overhears this. As they are walking away, John vaguely gestures towards the interviewers, saying,Footnote ¹⁴

Martial Arts Tournament: John and Mary are at a martial arts tournament. The winner of each of the four brackets will go on to be a semifinalist for the championship. The members of the tournament are currently practicing, each with members of their own bracket. Mary notices that the members of bracket B are all much larger than the members of any of the other brackets. So she gestures vaguely towards bracket B, saying,

iPad Pro: John is at the Apple store looking to buy an iPad Pro. He is greeted by a salesperson, who gives him a floor model to experiment with, while also pointing to the remaining stock of four iPad Pros on the wall. John spends a while with the floor model, then finally says to the salesperson,

I agree that these cases are felicitous, and that the speaker is not intending to say anything about any particular interviewer, member of bracket B, or iPad. Nonetheless, in these cases there is plausibly something the speaker is intending to say, which is also plausibly apparent in the common ground. In Job Interview, it is that whichever interviewer calls John about the job will probably call at the end of the day. In Martial Arts Tournament, it is that whoever wins among bracket B will win the championship. Admittedly, it is a bit harder to give a similar interpretation to the utterance (12) of iPad Pro, yet, to my ear at least, that utterance is significantly more awkward than (10) and (11): it is part of the setup that the speaker has been focusing on the floor model for a while before making the utterance, but it is also presumably common ground that the floor model is not for sale. I think, however, that what is meant by (12) can be most plausibly be glossed as the claim that John is going to buy the iPad he chooses (then take it home).

What I am proposing is that the demonstratives in (10)–(12) are being used as ‘descriptive indexicals,’ similar to the uses of the referential expressions in the following (Nunberg Reference Nunberg1993).

In each case of (13), the referential expression contributes an identifying description to what is said, under the scope of an operator. In (13c), for instance, the relevant reading is not that Obama could have been a Republican, but instead that it could have been that whoever was elected was a Republican; In (13a), the relevant claim is that usually the one about to be executed is given a steak dinner. Similarly, the predictive constructions in (10)—(12) involve a future-oriented modal, which scopes over the descriptions contributed by the demonstratives.Footnote ¹⁵

In sum, I do not think that the possibility of descriptive uses of demonstratives poses a problem for my account of felicitous underspecification. The first-person pronoun ‘I,’ as shown in (13a) and (13b), can be used descriptively, but I assume that it does not have felicitously underspecified uses. Hence, the possibility of descriptive uses and the possibility of felicitous underspecification are importantly different phenomena.

4. Nondemonstrative underspecificity

In this final section, I compare the felicitous underspecification of demonstratives with that which arises for other context-sensitive expressions. The reason for this discussion is twofold. First, King (Reference King2017, Reference King2021) argues that the felicitous underspecification had by demonstratives is the same as that which arises for other context-sensitive expressions. Second, Bowker (Reference Bowker2015, Reference Bowker2019) presents a solution to the so-called ‘problem of incomplete descriptions’—an old problem, which goes back to Strawson (Reference Strawson1950)—that is similar to my proposal regarding the felicitous underspecification of demonstratives. So, in this section, I justify my focus on demonstratives, and explain the difference between my proposal and Bowker’s. My central contention is that there is a significant difference regarding the felicitous underspecification of demonstratives and that of other context-sensitive expressions, including definite descriptions.

The problem of incomplete descriptions pertains to definite descriptions—phrases such as ‘the man.’ The problem may be introduced with the following case from Buchanan and Ostertag (Reference Buchanan and Ostertag2005).Footnote ¹⁶

Famous Professor: John and Mary are waiting for a public lecture to begin by a divisive philosopher. They have never seen the philosopher before, but have a stock of relevant shared information: he is the author of a book called Smells and Tickles, he is the only living philosopher to have claimed to have a solution to the mind–body problem, etc. The professor is late, as usual, but the crowd becomes shocked as a rumour spreads that he has been spotted at the bar down the street. John overhears the people next to him whispering, and says to Mary,

On a simple Russellian treatment of definite descriptions, (14) expresses the proposition that there is a unique professor and that professor is drunk (Russell Reference Russell1905). On a simple Fregean treatment, (14) presupposes that there is a unique professor, and, if that presupposition is met, expresses the proposition that that professor is drunk (Strawson Reference Strawson1950). Both these simple treatments predict that (14) implicates in some way that there is a unique professor (in all of existence). Yet that implication is false and plausibly known to be so by the interlocutors. So both accounts incorrectly predict that (14) is infelicitous.

The standard way of avoiding that incorrect prediction is by appeal to implicit domain restriction (Stanley and Szabó Reference Stanley and Szabó2000). A simple way of capturing implicit domain restriction involves positing a covert variable inside the definite description’s logical form, as follows.

The variable f is assigned a property by a contextually given assignment function, which composes by intersection with the property of professorhood.Footnote ¹⁷ Now, considering for simplicity the Russellianism treatment, (14) expresses the proposition that there is a unique professor with the property assigned to the covert variable, and who, in addition, is drunk. So, with implicit domain restriction, the proposition expressed by (14) may be, for instance, that there is unique professor who John and Mary are waiting to see who is drunk. And here is where the problem of incomplete descriptions arises. There are a number of possible properties that may be assigned to the covert variable in cases such as Famous Professor, each leading to distinct overall propositions. So which proposition is expressed? How is there successful communication? These questions constitute the problem of incomplete descriptions.

Recent commentators on this problem have settled on the following related answers to those questions (Blackburn Reference Blackburn1988, Buchanan and Ostertag Reference Buchanan and Ostertag2005, Buchanan Reference Buchanan2010). First, a use of a definite description as in Famous Professor helps express a range of propositions, where each is generated from some reasonable way of filling in the implicit domain restriction. Second, successful communication is then constituted by the addressee grasping one or another member of that cloud of propositions.

What Bowker adds to the solution provided by those answers is based on the observation that the list of reasonable potential completions of the implicit domain restriction in cases such as Famous Professor constitutes an update-equivalent group of propositions. Consider each of the following.

Bowker assumes that the following claim is part of the common ground in Famous Professor.

Granting Bowker’s assumption, it follows that the propositions expressed by the sentences in (16) are update-equivalent. Accordingly, Bowker proposes that in a case such as this, where the propositions determined by every reasonable completion of the implicit domain restriction of a definite descriptions are update-equivalent, the audience may thereby grasp every such proposition at once by grasping the update to which each member of the clouds leads.

In contrast to my proposal regarding demonstratives, Bowker does not propose that the reasonable completions of a definite description’s implicit domain restriction are given by what the speaker might have meant according to the common ground. He writes that an utterance of an underspecified definite description “leaves open a number of completing properties” for its implicit domain restriction (Reference Bowker2019, 4244), but that notion of leaving-open is left unanalyzed. He also writes that with an utterance of an underspecified definite description, the addressee may be “left to identify a suitable proposition based on the context” (4241). But, even assuming the relevant sense of “context” here is the common ground, it is not specified that the potential completions of the implicit domain restriction are given by the possibilities, consistent with the common ground, concerning what the speaker is intending to say.

More importantly, if an account were to be given of the basis of an utterance’s leaving open of a number of potential completions of a definite description’s implicit domain restriction, that basis should not be identified with that which determines potential referents for demonstratives, for it is not the case with a definite description that understanding requires that the potential completions of the implicit domain restriction together generate a set of update-equivalent propositions. I turn now to discussing King’s work on the underspecification of context-sensitive expressions other than demonstratives. Doing so will allow me to motivate the point just made that the felicitous underspecification of definite descriptions differs from that of demonstratives.

Taking a brief step back, the felicitous underspecification of demonstratives seems exceptional; specificity of reference for demonstratives seems the norm. But definite descriptions seem to be a member of a group of expressions for which underspecification is the rule rather than the exception. Some other expressions in this latter group are universal quantifiers, modals, and gradable adjectives. King, however, discusses the felicitous underspecification of all these other expressions (and more) alongside demonstratives. He labels this entire group of expressions, including demonstratives, ‘supplementives,’ since they are context-sensitive and such that the resolution of their context-sensitivity involves special supplementation from context. (Compare, for instance, how the use of the first-person pronoun ‘I,’ not a supplementive according to King, seems to simply pick out the speaker.) King holds that all supplementives have the same mechanism governing their context sensitivity. So, despite the fact that he notes that felicitous underspecification is less typical for demonstratives than for other supplementives, he nonetheless suggests that the phenomenon is essentially the same among all supplementives.

But in this paper I have focused only on demonstratives, and there is reason to think that what is occurring with demonstratives in underspecification is importantly different from what occurs with other supplementives. Consider, for instance, a simple use of a gradable adjective.

On the standard semantic story, context must supply a degree of wealth, and (18) says John’s wealth exceeds that degree (Kennedy Reference Kennedy2007). Yet it is implausible that felicitous use of such a sentence requires that context supply one particular threshold. Moreover, in cases of felicitous underspecification for gradable adjectives, there is the intuitive feeling that a disjunctive claim is being proposed: in (18), it is that John’s wealth exceeds some—one or another—appropriate threshold. But that disjunctive effect is different than what the account in this paper holds for demonstratives, which is that their felicitous yet underspecific uses bring about update on the conjunction of the possible interpretations.Footnote ¹⁸

A similar disjunctive effect has been claimed for modals (von Fintel and Gillies Reference von Fintel, Gillies, Egan and Weatherson2011), and, as already mentioned, for definite descriptions (Blackburn Reference Blackburn1988, Buchanan and Ostertag Reference Buchanan and Ostertag2005, Buchanan Reference Buchanan2010). The way von Fintel and Gillies (Reference von Fintel, Gillies, Egan and Weatherson2011) unpack the disjunctive effect is that the addressee may understand the utterance by only grasping one or another of the potential determinate propositions expressed, and that the speaker is able to fall back on any one of the potential propositions if pushed by the addressee. But this potential retreat to any of the resolutions differs from what intuitively holds for demonstrative underspecification: the speaker may not protest if the addressee focuses on one or another of the potential referents. In Sports Car, for instance, the addresse could reasonably disagree by either denying that the car token or the kind is beautiful. Consider each of the following responses to (1), ‘That’s a beautiful car.’

King (Reference King2017, 16) makes a similar observation, and notes that with either type of response the speaker would not feel as if the addressee has changed the topic. He uses this observation to motivate the claim that there is genuine felicitous underspecification in Sports Car. What I wish to emphasize here is that the speaker may not, in response to either (19a) or (19b), avoid the criticism, by claiming, for instance, that they really had the other potential referent (type or token) in mind.

The contrast between, on the one hand, what I have called the ‘disjunctive effect’ of context-sensitive expressions other than demonstratives and, on the other, the way that demonstratives are limited in their felicitous underspecification demands further elaboration. I do not provide it here, though see this footnoteFootnote ¹⁹ for an outline of a proposal. What I emphasize is that this contrast throws doubt on King’s claim that all supplementatives have the same mechanisms governing their context sensitivity, and, in particular, the contrast justifies my focus on demonstratives. Moreover, the most forceful considerations King gives in favor of the view that demonstratives behave relevantly like other context-sensitive expressions are based on the cases, from his most recent book (2021), which I discussed at the end of the previous section. Thus, having diagnosed those cases, I hope that the present paper’s focus on demonstratives is sufficiently justified.

Returning finally to Bowker, in order for his proposal to accommodate the disjunctive effect of definite descriptions, the potential completions of a definite description’s implicit domain restrictions should not be taken to be determined by the possibilities consistent with the context set concerning what the speaker means. If, on Bowker’s proposal, the potential completions of a definite description’s implicit domain restriction were so determined, then the proposal would incorrectly predict that understanding of a definite description requires that the potential completions lead to a set of update-equivalent propositions. Bowker’s proposal should instead be taken as outlining a special way in which understanding of a definite description may come about in the case where that set of propositions is update-equivalent: again, the special way is that the addressee identifies each one of the set “at once” by identifying the update. But that proposal, taken properly, is consistent with there being understanding of a definite description when the update-equivalence does not hold, for in such a case the speaker may identify one or another of the candidate propositions. Thus, if Bowker’s proposal is taken properly, it cannot be simply extended to demonstratives to account for their felicitous underspecification. For, as I have argued, the understanding of a demonstrative requires update-equivalence among the relevant set of candidate propositions.