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).)
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.
Stalnaker holds a combination of views that seem independent to me, but closely connected to him. One is a kind of reductive naturalism about intentionality. On this view, the point of attributing beliefs and desires is to give a high-level characterisation of the subject's behavioural dispositions, their functional architecture and their causal relations to the environment. Another of Stalnaker's views is externalism about mental content. This says that intentional characterisations are relational: even when two subjects are perfect intrinsic and functional duplicates, they may still differ in their beliefs and desires, depending on what objects and properties they are causally related to.
Stalnaker's "Lewis on Intentionality" (AJP 82, 2004) is a very odd paper. The aim of the paper is to show that Lewis's account of intentional content as developed in "Putnam's Paradox" -- global discriptivism with naturalness constraints -- faces various problems and conficts with what Lewis says elsewhere.
The first thing that's odd about this is that in "Putnam's Paradox", Lewis doesn't develop an account of intentional content. Rather, he discusses Putnam's model-theoretic argument and suggests that if one holds something like global descriptivism about linguistic content, adding external naturalness constraints on the interpretation of predicates would be an attractive way to block Putnam's argument for underdetermination.
On page 305 of "Assertion Revisited" (in the latest issue of Phil.Studies), Robert Stalnaker suggests that the information conveyed by an utterance is the diagonal proposition associated with the utterance iff it is unclear in the relevant context which horizontal proposition the utterance expresses:
[T]he relevant maxim is that speakers presume that their addressees understand what they are saying. In terms of the two-dimensional apparatus, this presumption will be satisfied if and only if the propositional concept for the utterance [a function that assigns to every relevant possible context the horizontal proposition expressed by the utterance in that context] is constant, relative to the possible worlds that are compatible with the context. Our problematic example [of saying "Hesperus is Phosphorus" to O'Leary who doesn't yet know that Hesperus is Phosphorus], and all cases of necessary truths that would be informative (in the sense that the addressee does not already know that they are true) will be prima facie counterexamples to this maxim, and so will require reinterpretation [so that what is said is the diagonal, not the horizontal proposition].
Three comments:
Suppose theory 1 says that entity x has certain properties, and theory 2 says that entity y has those properties. If we believe both theories, should we conclude that x=y?
It depends. Sometimes we not only should but must conclude that x=y, for example when theory 1 says that x is the planet Venus and theory 2 says that y is the planet Venus. In other cases, there is little reason to draw the conclusion, as when the theories merely say of x and y respectively that it is some planet or other. In yet other cases, the conclusion can be motivated by methodological considerations. For instance, whoever first realized that Hesperus is Phosphorus probably realized that the identity makes for a simpler overall theory.