Epistemic counterparts 5: Coincident roles and shifted beliefs
In the previous post, I have assumed that conversational context somehow determines a unique "suitable role" for each individual under discussion, relative to every epistemic subject. This is an unrealistic assumption.
For example, I believe that Canberra gets cold in winter. But Canberra is known to me as the occupant of many roles. Among other things, I know it as the capital of Australia, as the city in which I lived for most of 2012, and as the destination of my most recent international trip. When I say that I know (or believe) that Canberra gets cold, none of these roles may be particularly salient.
Perhaps you also know that Canberra gets cold in winter. If so, I could truly say that you know (and believe) that Canberra gets cold in winter – even though I have no idea of the ways in which Canberra is known to you. How could the context of my utterance select exactly one of these ways?
Fortunately, the multiplicity of suitable roles doesn't really matter, as long as the roles all coincide.
Remember that (definite) roles are functions from worlds to individuals. Two rules coincide for an epistemic subject iff they yield the same output for each world that is doxastically accessible for the subject.
For example, the roles expressed by 'the capital of Australia' and 'the destination of my most recent trip' coincide for me (in the actual world), because at each of my belief worlds, the capital of Australia is the destination of my most recent trip.
Since the two roles coincide, it doesn't make a difference whether you track Canberra across my belief worlds as the capital of Australia or as the destination of my most recent trip – either way, you end up with the same city at every world.
It's worth having a closer look at why the multiplicity of suitable roles does not matter in cases like this, for the reason brings to light another important issue.
Let CAPITAL and DESTINATION be the two roles just mentioned, and consider the sentence
(*) I believe that Canberra gets cold in winter.
Imagine two contexts. In context 1, the CAPITAL role is selected as the uniquely suitable role. In context 2, the DESTINATION role is selected. On what I called the Quine-Kaplan model, (*) is true in context 1 iff (1) at all my belief worlds, the capital of Australia gets cold, and (2) the capital of Australia is Canberra. In context 2, on the other hand, (*) is true iff (1') at all my belief worlds, the destination of my last trip gets cold, and (2') the destination of my last trip is Canberra.
These conditions are not equivalent. More precisely, they are materially equivalent, but they come apart at other worlds. One might therefore conclude that the choice of role matters for the truth-conditions of (*), although it does not matter for its truth-value.
But this conclusion rests on a false assumption. It assumes, as the letter of the "Quine-Kaplan model" suggests, that we hold fixed the role when we interpret a belief report at different worlds. In reality, when we talk about what someone believes at other worlds or times, we let the relevant roles vary with the worlds or times.
An example:
If Mia had seen Max at the pub, she would have thought he's an idiot, but if she had seen him at the beach, she would have thought he's great.
In the first subsentence, the world of evaluation is shifted to worlds where Mia saw Max at the pub. Here the relevant role by which we track Max across Mia's belief worlds is something like the guy in the pub. When we then shift the world of evaluation to worlds where Mia saw Max at the beach, the relevant role is something like the guy at the beach.
One might respond that this is merely a context switch: the first subsentence makes a different role salient than the second. But this response doesn't work for other cases:
If Mia had seen Max at the pub or at the beach, she would have thought he's an idiot.
No matter how we introduce Max to Mia, she is bound to think that he's an idiot.
Mia has always thought that Max is an idiot.
The upshot is that conversational context does not associate a fixed role with every relevant individual. The role varies with the world and time of evaluation.
My semantics from the previous post accounts for this shiftiness of roles, at least with respect to worlds. (I didn't use time indices, but they are trivial to add).
Recall my definition of counterparthood: an individual i' at a world w' is a counterpart of i at w iff there is a suitable role R for which R(w) = i and R(w') = i'. This makes the role depend on w. If w is a world at which Mia saw Max in the pub, and i is Max, then R might be the guy in the pub. But if w is a world at which Mia instead saw Max at the beach, R can't be the guy in the pub, because this would fail the condition that R(w) = i.
There's a second, less obvious, way in which the operative role can vary from world to world. Suitability depends on two kinds of factors. It depends on transparent features of the relevant utterance context, such as which roles are salient, and which would make the uttered sentence interesting. But it also depends on (often unknown) features of the relevant belief state. In particular, I suggested (in part 2) that suitable roles should be "strong", meaning that they coincide with many other roles in the subject's belief state. So when we look at a subject's belief state across different worlds or times, the domain of suitable roles may vary.
Now return to the problem of multiple roles. We've seen that if two suitable roles for an individual coincide within the worlds that are doxastically accessible for a subject, then it does not matter for the truth-value of relevant belief reports which of these roles we use to track the individual. We can generalise: if the suitable roles for an individual coincide within the worlds that are accessible for a subject at some point of evaluation, then it does not matter for the truth-value of a relevant belief report at this point of evaluation which of the roles we use.
If conversational context does not favour any particular role (for a given individual), so that at many points of evaluation, multiple roles are "suitable", then these roles tend to coincide for the relevant subject at the relevant point of evaluation. And so it doesn't matter for the truth-conditions of a belief report which of the roles we use to define the counterpart relation.
There are exceptions, of course. In Quine's well-known Ortcutt scenario, there are two salient roles under which Ortcutt is known to Ralph. Relative to one role, Ralph believes of Ortcutt that he is a spy; relative to the other, he does not. Conversational context may not render one of these roles salient. If it doesn't, we are stuck with two equally suitable, and non-coincident roles. As Quine pointed out, it really isn't clear whether, in such a context, 'Ralph believes that Ortcutt is a spy' is true or false – or both, or neither. The semantics I have offered can easily be adjusted to deliver each of these four verdicts.