Stalnaker on self-location II

In 2008, I wrote a post on Stalnaker on self-location, in which I attributed a certain position to Stalnaker and raised some objections. But the position isn't actually Stalnaker's. (It might be closer to Chisholm's). So here is another attempt at figuring out Stalnaker's view. (I'm mostly drawing on chapter 3 of Our Knowledge of the internal world (2008), chapter 5 of Context (2014), and a forthcoming paper called "Modeling a perspective on the world" (2015).)

One can approach the topic of belief from different angles. Lewis's starting point is a certain kind of formal epistemology and Bayesian decision theory. Others start from ordinary-language belief reports, asking for example about the semantics of sentences like "Lingens believes that he is Gustav Lauben". Relatedly, assuming that utterances express beliefs, one can ask about the content of the belief expressed by Lingens when he says "I am Lauben". Lewis always emphasized that his account is at best very indirectly related to questions like these: "the connection of belief sentences with belief as characterised by doxastic alternatives is complicated and multifarious" (Plurality, p.34).

Stalnaker lies somewhere in between these two extremes. He argues that an account of self-locating attitudes should begin not with the semantics of 'believe' and indexicals, but with an account of self-locating thought (2014: 108f.). However, what he seeks is an account of what is asserted in utterances and attributed in belief reports -- hence his emphasis on "question (2)" in (2008): "what is the content ascribed when one ascribes a particular belief?" (2008: 54).

Let's begin with a simple example. Lingens sincerely utters 'I am sad'. Lingens believes that he is sad. What is the content we thereby ascribe to Lingens? Is it an essentially centred content, something like the property of being sad? Or is it an uncentred content, perhaps the proposition that Lingens is sad?

Stalnaker holds that the content ascribed in belief reports and expressed in assertions is always uncentred. The belief Lingens expresses when he says 'I am sad' has as its content the set of (uncentred) worlds in which Lingens is sad.

The supposed advantage of this view is that it allows for simple models of communication, belief update, and agreement. The belief Lingens expresses is the same as the belief his addressee acquires. If tomorrow Lingens believes that he was sad yesterday he has retained today's belief that he is sad today. If I believe that I am not sad, my belief does not disagree with Lingens's belief that he is sad.

In (2008) and (2014), Stalnaker seems to suggest that the Lewisian picture gets all these facts wrong and thus "provide[s] no resources for representing the relations between informational states across time and across persons, and so no resources for clarifying the dynamics of knowledge and belief, or the communication of information between different subjects" (2008: 64). That is not true. One can nicely account for communication, update, and relations between belief states in the Lewisian framework. In fact, I would argue that the Lewisian account of these matters is simpler, more general, and more powerful than Stalnaker's account (which, among other things, requires difficult feats of "calibration"). But let's set aside these points. Our goal is to understand Stalnaker's positive view.

As I said, according to Stalnaker, what is asserted or ascribed in belief reports is always uncentred. Lingens's belief that he is sad has as its content the set of worlds in which Lingens is sad. But what if Lingens doesn't know that he is Lingens? If he believes that he is Gustav Lauben, we can't usefully model the content of his beliefs by the set of worlds in which Lingens is Lauben. After all, Lingens may be perfectly aware of the fact that Rudolf Lingens and Gustav Lauben are different people. One might say that Lingens does believe that Lingens is Lauben, under a particular "guise". But Stalnaker wants to give a pure possible-worlds account of belief, without "guises" or "files" or "modes of presentation" (for good reasons, I think).

It is not too hard to a find a suitable possible-worlds content. If Lingens utters 'I am sad' and believes that he is Lauben, then the worlds compatible with Lingens's belief state are worlds in which (a) Gustav Lauben is producing his sentence 'I am sad', and (b) Gustav Lauben is sad. So the belief Lingens here expresses by 'I am sad' is not the belief that Lingens is sad, but the belief that the person producing the token sentence 'I am sad' is sad. (According to Stalnaker, this kind of "reinterpretation" or "diagonalisation" is necessary whenever agents are uncertain or mistaken about identities; the basic phenomenon is not about self-location.)

It is important that the reinterpreted, diagonalised content is still uncentred content (unlike the diagonalisation of Kaplanian characters). What Lingens expresses is not the set of centred worlds in which someone sad utters 'I am sad'. Rather, it is the set of uncentred worlds in which someone sad produces this particular utterance of 'I am sad'. The belief content involves the actual utterance.

What shows up here is another, and arguably deeper, disagreement between Stalnaker and Lewis: Lewis's contents are purely qualitative ("descriptive"), while Stalnaker's are "haecceitistic", defined in terms of actual objects in the subject's environment.

This also allows Stalnaker to explain away cases of intra-world ignorance, where an agent's beliefs are compatible with several locations within the same uncentred world. Consider Sleeping Beauty who awakens on Monday, knowing that if a certain coin landed tails then she has an indistinguishable waking experience on Tuesday. One might think that Beauty's ignorance about whether it is Monday can't be understood as ignorance about the world as a whole: even if she knew all facts about the world from a God's eye perspective, she still couldn't tell whether her present awakening is the one on Monday or the one on Tuesday. If we were to tell her that it is Monday, she would then come to learn something that can't be captured by a set of uncentred worlds. On Stalnaker's account, this never happens. So he must represent Beauty's ignorance as ignorance about the world as a whole. As above, her ignorance could be represented as ignorance about the location of a particular token sentence or thought. Even if she has qualitatively indistinguishable thoughts on Monday and Tuesday, her thoughts are numerically distinct. If Beauty can have beliefs directly involving a particular thought, we can distinguish worlds where this thought occurs on Monday and worlds where it occurs on Tuesday.

(Recall that we began with the question, what content is ascribed by a particular belief ascription? So, what is the content ascribed by 'Beauty believes that it is Monday'? On Stalnaker's account, the content is something like the set of worlds in which a certain token thought occurs on Monday -- despite the fact that the belief ascription doesn't mention any thought tokens and actually seems compatible with the assumption that Beauty doesn't have any occurrent thoughts on Monday at all. So it looks as if for Stalnaker, too, the connection of belief sentences with belief as characterised by doxastic alternatives is complicated and multifarious.)

Now comes the puzzling part of Stalnaker's account.

Stalnaker actually agrees with Lewis that one cannot fully capture an agent's belief state by a set of uncentred possible worlds, since that would leave out where the agent locates herself within any given world. To fully capture a belief state, he says, we have to add centres to the worlds compatible with the agent's beliefs. Thus we model belief by an accessibility relation between centred worlds: (w',t',a') is accessible from (w,t,a) iff the agent a at world w at time t cannot rule out being a' at t' at w'. The set of centred worlds accessible for a given agent (at a time at a world) Stalnaker calls the agent's belief set.

Superficially, that looks exactly like Lewis's account. Indeed, Stalnaker's motivation for adding the centres often sounds just like Lewis's: "you cannot infer from an objective description [of the world] where you are in the world, and what time is now" (2008: 52). "I cannot infer from a purely objective description of the world that I am at the east end [of the parking lot]. ... Of course, my objective description may tell me that Bob Stalnaker is at the east end ... on Monday afternoon, but it is only because I know that I am Bob Stalnaker, and that it is Monday afternoon, that I can use this information" (2014: 116f.). Two agents might have the same uncentred beliefs about the world but locate themselves at different places or times, and that is genuine difference in belief (2015: 2).

So one might think that Stalnaker's (new) position on self-location is the same as Lewis's, except that Stalnaker adds a certain story about assertion and belief reports: that the beliefs ascribed in belief reports and expressed in assertions are always uncentred. Recall that Lewis's view is not really a view about assertion and attitude reports, and the view certainly allows for uncentred beliefs. So from this perspective, Stalnaker's account looks more like an extension than an alternative to Lewis's.

However, Stalnaker holds on to his ban on intra-world ignorance -- as he must to maintain his account of belief reports and assertion -- and that dramatically alters the situation. If we just focus on belief reports and assertion, the ban on intra-world ignorance doesn't look like a big deal, since (i) scenarios of intra-world ignorance seem a little artificial and far-fetched, and (ii) the externalist, haecceitistic account of belief seems to offer a natural way of handling those scenarios. But notice what happens to the Lewisian picture once we add the ban.

We can factorize the information captured by a set S of centred worlds into two parts. First, there is objective information O about the world, as represented by the worlds w for which some centre (w,t,a) is in S. Second, there is purely indexical information I, represented by the set of centred worlds (w,t,a) such that either w is not in O or (w,t,a) is in S. O contains no indexical information, I contains no objective information; together, I and O determine S. (Intuitively, I is the set of "material conditionals" with an uncentred world w in O as antecedent and a corresponding centred world (w,t,a) in S as consequent. Such a conditional is true at (w',t',a') iff either ~(w'=w) or (t,a)=(t',a').)

The ban on intra-world ignorance makes the indexical component I trivial in that a given uncentred world is never compatible with multiple possibilities concerning the agent's own location. On the supposition that the objective world is a certain way, an agent is always certain about who and when and where they are. Hence one can never acquire purely indexical information, nor can there be any uncertainty about purely indexical matters.

To illustrate, imagine two ideally rational agents A and B who start out with no information at all and then acquire more and more information until they become omniscient about everything, including their own location. At the end, their belief sets are { (w,t,A) } and { (w,t,B) }. Was (w,t,B) ever a live possibility for agent A? No: that would contradict the ban on intra-world ignorance. The agents' belief sets were disjoint from the start. Even at the beginning of their inquiry, agent A already knew if the objective world is like this -- w -- then there is only one possibility about herself: she must be A at t. The reason is not (as I thought in the old blog post) that we model A as having innate and infallible access to her own haecceity and to the haecceity of the present time. As Stalnaker makes clear in (2015), if A doesn't yet know whether she is A or B, then her belief set includes points (w',t',B) centred on B. These points are never live possibilities for B.

From a Lewisian perspective, this looks very mysterious. Why is (w',t',B) a priori possible for A but not for B? How can B have innate knowledge, prior to any empirical evidence, that she is not B at t' at w', while the same hypothesis is a live possibility for A?

The answer is that we must drop the Lewisian perspective. For Stalnaker, centred worlds do not represent ways things might be; they are not possibilities. The purely indexical component of an agent's belief state does not represent information. If (w,t,a) is in your belief set, that is not because w is a way the world might be by your lights, t is a time where you might be (compatible with w), and a is an agent you might be (compatible with t and a). Rather, (w,t,a) is in your belief set because (i) w is a way the world might be by your lights, and (ii) if the world is like that, then you are at (t,a). The latter is not really a matter of belief. It is not something on which you could have one opinion rather than another, on which you could be undecided, or about which you could gain information.

"The role of the centers", Stalnaker says, "is to link the believer, and the time of belief, to the possible worlds that are the way that the believer takes the world to be at the time, and to represent where, in those worlds, he takes himself to be" (2008: 54, similarly 2014: 113, 2015: 3). The role of centres is not to capture further (more fine-grained) information that a set of uncentred worlds would leave out. "Using more fine-grained contents of belief does not help us to represent these links, and it is not necessary to use more fine-grained contents once we have added the structure to represent the links" (2014: 113).

So, when Stalnaker accepts that we need centred worlds to fully represent an agent's belief state, this is not because he accepts that agents have genuine self-locating information (or knowledge, or ignorance) that goes beyond objective information (knowledge, ignorance) about the world. All information, knowledge, and ignorance is about the objective world.

OK. But then why does Stalnaker say that "you cannot infer from an objective description [of the world] where you are in the world, and what time is now" (2008: 52)? Why does he say that he can only infer from the objective description that he is at the east end of the parking lot "because I know that I am Bob Stalnaker, and that it is Monday afternoon" (2014: 117)? That surely suggests that the objective description lacks information, that once the objective description is given, it is a further question -- a genuine open matter -- who and when and where we are. On Stalnaker's actual account, you can infer from an objective description of the world where you are in the world, because any question about where you are is in fact a question about the objective world. ("[B]elief about where one is in the world is always also belief about what world one is in" (2008: 55).)

So Stalnaker should not have said these things. His account has no room for non-trivial, genuinely self-locating ignorance or information.

Then why do we need the centres? Supposedly their role is to "link" the agent's (uncentred) belief worlds with the situation in which the belief takes place. But what is that role? What does the theory look like that postulates that role? Stalnaker doesn't say. He does say that "the lesson we should learn from the phenomenon of self-locating belief is that we cannot give an adequate representation of a state of belief without connecting the world as subject takes it to be with the subject who has the belief" (2008: 53). But what is the phenomenon he has in mind?

For Stalnaker, we do not need centred worlds to model Lingens's ignorance when he doesn't know who he is, or to model the information he acquires when he learns that he is Lingens. Let's say that belief is a relation between a subject (at a world and a time) and a set of uncentred worlds, without centres. According to Stalnaker, Lingens is initially belief-related to worlds in which certain thought tokens are tokened by Gustav Lauben. When he learns that he is Lingens, he comes to rule out those worlds. For Stalnaker, that is what it is for Lingens to come to know that he is Lingens. What is missing in this model?

Well, one thing that's missing is a plausible story about the connection between belief and rational action. In standard decision theory, a rational agent's choices in a decision situation are (generally) determined by their beliefs and desires. If two agents have the same beliefs and desires and the same options, they should make the same choices. But if beliefs and desires are uncentred this seems false. You and I both want to meet. We both know that in order for us to meet, I need to turn left and you need to turn right. We have the same uncentred beliefs and desires. But I turn left and you turn right.

Is this where Stalnaker's "links" will help? Maybe. But Stalnaker barely mentions the problem about action, and never explains how the links are meant to solve it. If the links do the job then we still need to revise standard decision theory: our choices are not determined by our beliefs and desires, but also by certain links between the belief worlds and the choice situation (whether or not we know about those links). Moreover, Lewis's more fine-grained, centred contents elegantly solve the present problem, without any Stalnakerian links, and without any revisions to decision theory. So it would hardly be true, as Stalnaker claims, that one cannot adequately account for "the phenomenon of self-location" in Lewis's way, without the added links.

I suppose we can grant that there is a role for Stalnakerian links here, although the precise job description remains a little obscure. Intuitively, there are differences in belief that go beyond differences in uncentred content -- as witnessed for example by the fact that people with the same uncentred beliefs and desires should often make very different choices. Moreover, these differences are intuitively differences in where the agents locate themselves within the relevant worlds. By introducing his centres, Stalnaker can to some extent respect these intuitions (although not the intuition that an objective description of the world would always leave something out).

There is another job description. I said that Stalnaker barely mentions the problem about action. By contrast, he spends a long time -- both in (2008) and (2014) -- discussing iterated belief reports and beliefs expressed by assertions about beliefs. Here the centres really do figure as "links", so presumably that is the main phenomenon for which Stalnaker thinks they are needed.

Consider the following scenario from (2014). While talking to Bob, John (Perry) comes to believe that Bob believes that he (John) is Fred Dretske. How would we model this in the classical Hintikka framework? We might say that the worlds doxastically accessible for John are worlds in which John is talking to Bob, and that the worlds accessible for Bob from those worlds are worlds in which Bob is talking to Fred Dretske. In the Lewisian framework, we might instead say that John's doxastic alternatives talk to someone whose doxastic alternatives talk to Fred Dretske. Either account leaves something out if we are interested in our actual practice of attitude reports. For while it is true that John believes that Bob believes that whoever he (Bob) is talking to is Fred Dretske, it is also true that John believes that Bob believes that he (John) is Fred Dretske. Accordingly, John might say "Bob believes that I am Fred Dretske", and that would be true. How can we explain that?

This is one of the phenomena that convinced Lewis that there is no simple connection between attitude reports and doxastic alternatives. But Stalnaker wants a simple connection, because his starting point is the very question what content is ascribed by particular attitude reports.

Stalnaker's model goes as follows. Like the Lewisian model, belief is represented by an accessibility relation between centred worlds. Ignoring times for now, a centred world is a pair of a world and an agent. John's belief state relates (@, John) to various pairs (w, John). In those worlds w, John is talking to Bob. Moreover, for all those w, (w, Bob) is belief-related to further pairs (w', Bob) such that Bob is talking to Fred Dretske in w'. That's how John believes that Bob believes that he (Bob) is talking to Dretske. Now if John wants to express what Bob believes about him (John), he needs to locate himself in Bob's belief worlds -- even though these worlds are incompatible with his own belief worlds. There are two natural ways for John to locate himself in Bob's belief worlds: either as John or as the conversational partner of Bob, i.e. as Dretske. According to Stalnaker, both are acceptable. The first choice makes it OK for John to say "Bob doesn't know that he is talking to me", the second makes it OK to say "Bob believes that I am Dretske". John's indexical 'I' picks out wherever John locates himself in a world, even inside iterated attitude reports.

Here the centres seem to play some role, by linking people from one world with people in other people's belief worlds. But it is not clear that we couldn't tell essentially the same story without the centres. Consider what John takes to be Bob's belief worlds: worlds in which Bob talks to Dretske. The question is why in a certain context John can describe those worlds as worlds in which "I am Fred Dretske", and not as worlds in which "John Perry is Fred Dretske". Evidently, the belief context shifts the reference of 'I'. How so? Well, perhaps there is a contextually salient reading of 'I' on which its intension picks out whoever Bob is talking to. In John's own belief worlds, that is John Perry. In what John takes to be Bob's belief worlds, it is Fred Dretske. Isn't that more or less the same account? Instead of considering where John locates himself in various worlds, we directly talk about the reference of 'I' in those worlds.

It's also not clear to me that the phenomenon at issue here is about self-location in particular, rather than about iterated de re attitude reports in general. As an onlooker, I could say "Bob believes that John is Dretske", but also "Bob doesn't believe that John is Dretske"; in the first case, 'John' refers to whoever Bob is talking to, in the second, it refers to John. Isn't that a very similar phenomenon? But here it has nothing to do with self-location.

So what's the overall verdict? Compared to Lewis's, Stalnaker's epistemology strikes me as cumbersome and unintuitive. For example, we have to assume that even agents without any information have no intra-world ignorance: supposing that the objective world is a certain way, they always know exactly where they are. That seems plain wrong, and here Stalnaker's externalism and haecceitism don't help. To be sure, agents without any information are "science fiction", as Stalnaker might say. But the fiction is central to (attractive versions of) Bayesian epistemology and confirmation theory.

But arguably Stalnaker's focus is not on epistemology in a Lewisian sense. Stalnaker primarily wants to capture the contents ascribed in believe reports and expressed in assertions. He assumes without argument that there are such contents, and that their study will lead to a theoretically useful epistemology. I am less optimistic about this procedure. At some point, a complete epistemological theory must have something to say about attitude reports and assertions, but it is not obvious that we can simply read off a useful notion of belief content from ordinary language belief reports and intuitions about assertions. Even setting these matters aside, Stalnaker's reasons for banning genuinely self-locating contents seem weak.

(I haven't yet mentioned one reason, presented in (2014: 117f.) as a decisive argument that "one must take doxastic and alternatives to be different possible worlds, even in fanciful cases". Stalnaker claims that this is required to give a proper account of belief and knowledge in action. "Suppose I know that I will be in a similar situation ... both Monday and Tuesday .... On each day, I must make a decision .... In deciding what to do, I am making it true that this is what I do in all of the possible situations that are epistemically possible for me. ... But it would distort the deliberative situation to think that on Tuesday (or Monday) I was deciding what to do on the other day." Right. But why is that supposed to be an argument against intra-world ignorance? Stalnaker seems to imagine that a Lewisian account would have four relevant centred worlds before the decision: Monday & Left Tuesday & Left, Monday & Right, Tuesday & Right. Deciding Left would then rule out Monday & Right and Tuesday & Right, leaving me certain that I choose Left on both days. That is indeed inadequate. But that's clearly not the right way to model the situation. By hypothesis, I know that there are two choice points, one today and one either yesterday or tomorrow. So the relevant possibilities are On Monday Left & On Tuesday Left & Today Monday, On Monday Left & On Tuesday Left & Today Tuesday, ..., On Monday Right & On Tuesday Right & Today Tuesday. After deciding Left, we are left with On Monday Left & On Tuesday Left & Today Monday, On Monday Left & On Tuesday Right & Today Monday, On Monday Left & On Tuesday Left & Today Tuesday, On Monday Right & On Tuesday Left & Today Tuesday. I am not deciding what to do on the other day.)


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