Stalnaker on self-location
Here are some notes on Stalnaker's account of self-locating beliefs, in chapter 3 of Our Knowledge of the Internal World. I find the discussion there slightly intransparent, so I'll start with a presentation of what I take to be Stalnaker's account, but in my own words. This will lead to a few objections further down.
We start with extreme haecceitism. Every material object and every moment in time has, in addition to its normal, qualitative properties also a non-qualitative property, its 'haecceity', that distinguishes it from everything else. My haecceity belongs to me with metaphysical necessity, and could not belong to anyone else. Moreover, it is my only (non-trivial) essential property. (This is the 'extreme' part in extreme haecceitism.) In this world, I am a human being, but in other worlds, I am a cockatoo, or a poached egg. My haecceity is freely combinable with any qualitative property.
Every qualitative way a world might be thus divides into infinitely many complete ways a world might be, depending on the distribution of haecceities. In particular, for any individual x in our world and any time t, there is a world qualitatively just like ours, except that x has been replaced with a qualitatively identical individual that shares my haecceity H, and t with a time that shares the haecceity of the present time N.
Finally, we assume that every thinker has infallible a priori knowledge of their own haecceity, and of the haecceity of the present time. By this I mean that if a thinker has a particular haecceity, then they cannot fail to be absolutely certain that this is their haecceity. Likewise for the haecceity of the present time. This may sound odd, but remember that haecceities are non-qualitative and freely combinable with qualitative properties. Our haecceitistic knowledge therefore tells us nothing qualitative about the world at all, nor about ourselves.
The benefit of our haecceitistic knowledge is that it puts us in a position to locate ourselves in any complete description of the world. The description has to be complete, not merely qualitatively complete. Someone could know all qualitative truths and still not know which of the many people in the world they are, and which of the many times is now. However, once not only the qualitative truths are given, but also the non-qualitative truths -- once it is given that the guy on the tallest mountain has haecceity H, etc. --, I cannot fail to know who I am.
On this account, self-locating information is haecceitistic information. It is information about the whereabouts of particular haecceities, in my case H and N, of which I know a priori that they indicate me and the present time.
Let's compare all this with Lewis's centered-worlds account. According to Lewis, the object of beliefs are qualitative ways things might be for an individual at a time. When Stalnaker says that my beliefs rule out any world where the H individual has (qualitative) property P at the N time, Lewis says that my beliefs rule out any centered world where the individual at the center has P. In the other direction, if in Lewis's model I self-ascribe property P, then in Stalnaker's model, my belief reduces the open possibilities to worlds where the individual with H at N has P.
The mapping is many-one: each of the centered worlds in my Lewisian belief space corresponds to infinitely many uncentered worlds in my Stalnaker belief space, differing in the distribution of haecceities other than H and N. Whether this makes a real difference depends on the extent to which I have knowledge of any haecceities apart from H and N. This question will occupy us for a while.
To understand what I'm asking, consider the haecceity T of the time one hour ago. According to Stalnaker it is impossible for me not to be certain that the present time has haecceity N. Is it likewise impossible for me not to know that the time an hour ago had T? There are possible worlds where T is instantiated tomorrow, while some other property T' is instantiated an hour ago. The question is whether I can somehow rule out alternatives like this.
Stalnaker thinks I can, but it is instructive to consider what happens if the answer is no.
Suppose, then, that the only haecceities revealed to us are our own and that of the present time. Belief states in Stalnaker's model then correspond one-one with belief states in Lewis's model. (There is even a one-one map between the belief contents, as we can single out the believer and the time of the believing from the Stalnaker content as the bearers of the only haecceities about which anything is ruled out.)
Think of my belief space as determined in two steps. First we characterize all qualitative ways the world might be for all I believe. Then we say, for each of these ways, where I myself might be if the world is like this. If there are several points where I might be, we duplicate the relevant world and assign marks to different centers within the duplicates. Lewis does this by replacing the worlds with something like world-time-individual triples. Stalnaker does it by introducing haecceitistic differences into the worlds and marking the relevant point by the non-qualitative properties H and N.
The main difference between the two accounts is that Stalnaker uses different markers for different believers at different times. H and N are the markers for my place now. In your belief space, a different property G is used instead of H, and a different time haecceity T instead of N. It is therefore impossible for two subjects (or the same subject at different times) to have exactly the same beliefs (unless the subjects have no opinions about their place in the world).
Stalnaker approves of this result because he wants to maintain that you and I express different beliefs when we both say "I was born in New Jersey"; your belief concerns the location of G, mine the location of H. By contrast, Lewis would want to treat our beliefs as the same. We can reconstrue this sense of sameness in Stalnaker's framework. Call two belief contents qualitatively identical if they differ at most by permutation of haecceities. Lewisian contents can then be regarded as equivalence classes of qualitatively identical Stalnaker contents.
To reconstrue Stalnaker contents in Lewis's framework, we could replace every centered world c in a subject's belief space with a triple of c, the subject and the time of the believing. A triple <c,i,t> is true at an uncentered world w iff c is true at the point where i is a t in w. For example, when you and I simultaneously belief that it is raining, all triples <c,you,now> in your belief space contain a centered world c where it is raining, and so do all triples <c,I,now> in my belief space. We share the belief that it is raining because both our belief sets are subsets of the class of triples <c,i,now> with rain at c. (This shows that extreme haecceitism isn't essential to Stalnaker's account: we can have essentially the same model without any haecceitism at all, though at the cost of replacing the worlds in belief space by something that looks less worldly.)
As I said, Stalnaker wants to individuate content his way, rather than Lewis's way, because it makes for simple comparisons of beliefs. It also makes for a simple theory of communication: when I sincerely utter "I was born in New Jersey", and you hear and trust what I say, then the belief you acquire has the same content as the belief I express. Stalnaker also wants to hold onto conditioning as the only rule of rational belief update, which gets implausible if belief contents can change their truth value over time.
Unfortunately, none of these targets can be met if the only haecceities revealed to us are our own and that of the present time. My belief that I was born in New Jersey rules out all (uncentered) worlds where the individual with haecceity H was born elsewhere. Whatever belief you acquire when I tell you that I was born in New Jersey, it cannot have this content unless you know that I have haecceity H. If you don't, the belief you acquire will be that whoever talks to the person with haecceity G was born in New Jersey. And this is something I cannot know, unless I know that your haecceity is G.
Or consider how my beliefs change over time. My present belief rules out that it is raining in Canberra at the time with haecceity N. If tomorrow I can have no beliefs about N because I am no longer acquainted with it, then my beliefs cannot have changed by conditioning. My credence in rain at N goes down even though I receive no relevant information about N.
Stalnaker rejects the assumption that we cannot know the haecceities of strangers. This is illustrated on page 66, where Daniel tells Lingens that he is Lingens: speaker and hearer, Stalnaker explains, both rule out worlds where this person, the person with haecceity L, is not Rudolph Lingens. Daniels must therefore have knowledge of Lingens's haecceity.
This is where Stalnaker's account becomes externalist. How can Daniels rule out a world qualitatively just like ours but where Lingens's haecceity has been swapped with, say, Ernst Mach's? How can he know that the person he is confronting instantiates haecceity L rather than M, seeing as he has no haecceity detector? Wouldn't everything appear to him just the same in this alternative situation? Stalnaker's answer is that Daniels can indeed rule out those situations despite the fact that everything would seem exactly the same for him if they obtained. Daniels can rule them out merely by actually confronting L. Beliefs are attributed from the outside, and we, the attributers, are free to draw on facts that leave no trace in Daniels's phenomenology.
How far extends our haecceitistic knowledge? Suppose it is unlimited: if we can think of an object at all, we cannot fail to know its haecceity. Daniels knows not only the haecceity of the person he is talking to, but also the haecceity of this person's father, the haecceity of the first child born in the 21st century, and the haecceity of whoever invented the zip. That is, he can exclude any world where the inventor of the zip has any haecceity other than J, his actual haecceity.
Daniels's beliefs will then almost certainly be inconsistent. Perhaps he believes that the inventor of the zip was Hungerian, but also that the American who filed US patent 504,038 was not Hungerian. Since these persons both have haecceity J, he then believes both that the bearer of J was Hungarian and that he was not Hungerian. In even more cases, Daniels will have different degrees of belief in the very same proposition. We can no longer model Daniels's beliefs with a single space of possible worlds. The whole framework breaks down.
Daniels also violates conditioning. Today, he believes that the brightest point in the evening sky is a star; tomorrow he learns that the brightest point in the morning sky is a planet; but he does not revise his earlier belief, despite the fact that its content (that the bearer of V is a star) contradicts the new information.
Stalnaker has to steer very carefully between sparse haecceitistic knowledge and abundant haecceitistic knowledge. If we have too little haecceitistic knowledge, his account doesn't work. If we have too much, it doesn't work either.
So let's have a look at what he says. From what I can tell, Stalnaker imposes two restrictions on the attribution of haecceitistic knowledge. The first bans attribution of inconsistent beliefs in cases where someone is ignorant of relevant identities or non-identities (a very common situation, since every proposition is a priori equivalent to an identity proposition). For example, when Ernst Mach doesn't recognise himself in the mirror and believes that that guy is a vagrant, while at the same time not believing that he himself is a vagrant, we should not, according to Stalnaker, say that he believes of the haecceity M that it is instantiated by a vagrant. What Mach believes is merely that whatever haecceity is located over there is instantiated by a vagrant.
The second restriction is not made explicit, but it shows up in Stalnaker's treatment of Sleeping Beauty. On Stalnaker's account, Sleeping Beauty cannot on Sunday rule out any possibilities concerning the haecceity of the following day, which I will call M (not to be confused with Ernst Mach's haecceity). She knows the haecceity S of the present day (Sunday), and she knows that whatever day follows the day with S is a Monday, but she does not know of the day with M that it is a Monday. For all she knows, M could be instantiated on Tuesday, while Monday instantiates M'. Only when she awakens on Monday and becomes acquainted with M (as the haecceity of today) can she rule out some of those possibilities, viz. possibilities where M is located on a Tuesday and the coin landed heads. Conditioning then leads her to thirding.
Why can Daniels rule out possibilities concerning L under the guise of "you", but Beauty cannot (on Sunday) rule out possibilities concerning M under the guise of "tomorrow"? What's the relevant difference? Unlike in Mach's case, attribution of haecceitistic knowledge to Beauty would not lead to inconsistent beliefs; it would only lead to halfing. There must be some other principle restricting attributions of haecceitistic knowledge. Perhaps it matters that there is a causal connection from Lingens to Daniels, but not from Monday to Beauty? Stalnaker doesn't explain. On p.110, he even suggests that the only precondition for attributing haecceitistic knowledge is the existence of a contextually dominant 'cognitive connection' between thinker and object, however indirect and weak.
Whatever the unstated principle is, it breaks many trans-time comparisons of belief: yesterday, I said "it will rain tomorrow"; today, I say "it is raining today". According to Stalnaker, my utterances express different beliefs, for only my present belief is about N, whereas yesterday's belief was descriptively about whatever day would follow the time it was then. I'm tempted to say that the second restriction on haecceitistic knowledge is an epicycle Stalnaker introduced ad hoc to please the community of thirders, without realising its drawbacks.
The issue about trans-time comparisons shows that Stalnaker can't fully avoid the problems with sparse haecceitistic knowledge. These problems are essentially independent of whatever restriction is imposed. If my attribution of F-ness to x sometimes singles out x not by his haecceity but by his relation to me (to H and N), then my belief will have a different content from your attribution of F-ness to x, unless you (bizarrly) also happen to single out x by his relation to H and N (to my haecceity and my time). When I tell you that x is F, the belief I express will then be different from the belief you acquire.
Stalnaker also can't entirely avoid the problems with abundant haecceitistic knowledge. For these problems arise not only from inconsistent full beliefs, but also from the more common case of incompatible probabilities in the same proposition. How can Daniels be more certain that this point is a star than that that point is a star? How can he increase his credence in that stuff being water by bringing it into the lab and finding that it is H2O? If in all such cases we have to withdraw our haecceitistic belief attribution and return to descriptive beliefs, we run straight into the other set of problems.
There is no space between Skylla and Charybdis. Stalnaker's theories of agreement, communication and belief revision work neither with sparse nor with abundant haecceitistic knowledge, and there is no safe ground in between. Any attempt to escape the one set of problems drives us into the other. Sometimes, of course, neither problem may show up, as when we deal with completely uncentered information. Then it does no harm to pretend that Stalnaker's theories are correct. But if we want something more general, we should look for something better. I think it is possible to give fully general and satisfactory theories of agreement, communication and belief revision from the centered-worlds perspective, though admittedly those theories are slightly more complex than Stalnaker's.
There are further job descriptions for beliefs and desires, e.g. in decision theory. Here, too, I think the centered-worlds view is preferable, even though Stalnaker's will get it right in many easy cases. Here is how: for Stalnaker, rational action is not just a matter of what is believed and desired, but also of who does the believing and desiring. It is rational for individual x to choose action A iff worlds where x does A have higher expected utility than worlds where x does anything else. (Again, this wouldn't work if people could be ignorant of who they are.) This is why we should act differently when we both believe that you are being attacked by a bear, and even if we share all our beliefs and desires.
Since nobody will have read this far anyway, I'll spend a few more words on how my discussion relates to the way Stalnaker presents things.
Stalnaker introduces 'belief states' as pairs of a world-time-individual triple -- the subject who does the believing together with the time and world of the believing -- and a class of such triples, representing the possibilities left open by the subject's beliefs. The primary content of a belief state (the 'belief worlds') is therefore centered. However, we'll see that the centers actually do very little, as they can't vary.
Stalnaker stipulates that a subject's belief worlds never contain more than one centered world from the same uncentered world. It follows that it is impossible to know exactly what world one inhabits without also knowing who one is and what time it is. This means that there must be an objective feature of the world of which I know for certain that it indicates my presence. This feature, Stalnaker explains, is a haecceity. It can only be picked out by demonstration, or by a demonstratively introduced name. A purely qualitative, demonstrative-free description of the world is therefore always incomplete.
Since I cannot fail to know that I have haecceity H, and that the present time has haecceity N, any triple in my belief space must have me (the bearer of H) and the present time (the bearer of N) as coordinates. The only thing that can vary is the world. This is illustrated by Stalnaker's discussion of Lewis's two gods. Four belief worlds are in play here. The belief worlds of god A consist of a world W where he is on the tallest mountain and another world V where he is on the coldest mountain. The open possibilities are <W,T,A> and <V,T,A>. For god B, the open possibilities are <W,T,B> and <V,T,B>. If A and B were to find out where they are by receiving uncentered information excluding V, A would be left with <W,T,A> and B with <W,T,B>. If <W,T,B> had ever been a possibility for god A -- as it was for god B --, he would still not know where he is (and we would have a violation of the uniqueness stipulation).
Since the individual and time coordinates in a subject's belief worlds are fixed, belief states can be characterised uniquely by stating who does the believing, and when, and what uncentered worlds are left open. Thus it is "possible to describe belief states unambiguously by ascribing propositional belief" (p.55). We do have to say who does the believing in order to see in the uncentered content where the subject locates herself. After learning where they are, god A and god B both believe { W }, but they locate themselves at different points. Once we add that it is god A who believes { W }, we can tell where he locates himself: wherever A is in W. (Remember that he can't possibly be mistaken about whether he is A.) According to Stalnaker, "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 the subject takes it to be with the subject who has the beliefs" (p.53).
On the other hand, if we start out with the belief world triples, we can easily recover subject and time of the believing from the second and third element of all the triples. "The roles of the centers", Stalnaker explains, "is to link the believer, and time of belief, to the possible worlds that are the way the believer takes the world to be at that time, and to represent where, in those worlds, he takes himself to be" (p.54). I don't really understand why belief states in the formal model contain both the actual subject and belief time and the complete triples, so that the uncentered content is linked to the believer and the belief time twice over. Just to make sure, I suppose.