Epistemic Counterparts 3: Possible-worlds models
Recall the guiding idea: A de re report 'S believes that x is F' is true iff there is a suitable role R such that (1) S believes that whatever plays R is F, and (2) in fact, x plays R.
I said that these truth-conditions naturally emerge if we treat 'believes' as a modal, quantifying over a set of accessible worlds. So I am going to assume that for any relevant subject in any relevant situation there is a set of "doxastically accessible" worlds which somehow characterise what the subject believes. I want to say a few words to clarify this assumption.
Possible-worlds models are widely used in modal logic and formal semantics. There are different conceptions about what such models are supposed to achieve.
On a minimal understanding, the goal of model-theoretic semantics is merely to provide an interpretation of the vocabulary that correctly predicts certain facts about entailment, validity, synonymy and other such relations.
Possible-world models can do this, but they can do more.
When we give a semantics for modal sentences in terms of possible worlds, we effectively specify a translation from a modal language into an extensional language with quantifiers over worlds. Both of these languages are languages we understand. We are familiar with talk about times and possible worlds. And we are familiar with modal talk. So we can check that the proposed translation preserves truth-conditions. For example, we can see that 'hydrangeas can grow here' means more or less the same as 'there is a world at which hydrangeas grow here that matches the actual world in certain contextually relevant facts such as regional climate and soil conditions'.
So possible-worlds models don't just systematise facts about entailment and validity; they can also formalise intelligible and intuitive truth-conditions for the target sentences.
A third feature of possible-worlds models is that they may track how our language faculty computes or represents the meaning of the target sentences. There are pervasive similarities between quantificational and modal constructions in natural language, suggesting that their processing involves common linguistic mechanisms. To give just one example, the puzzling phenomenon of "free choice" arises both for modal and for quantificational constructions; the main attempts at explaining the phenomenon all assume that the relevant modals are quantifiers over possible worlds. So the quantificational analysis promises to explain otherwise puzzling facts about how we understand modal expressions.
A fourth idea that is often associated with possible-worlds semantics is that it may reveal the metaphysical grounds of modal sentences. Perhaps what makes it true that hydrangeas can grow here is that there is an accessible worlds at which hydrangeas grow here. On this view, the extensional possible-worlds language is closer to fundamental metaphysical reality than the modal language.
An extreme version of this view holds that possible worlds are part of fundamental ontology, and facts about other worlds ultimately ground modal facts about the actual world. For most kinds of modality, this is highly implausible.
But I like a more moderate version of the view. Here, what grounds the relevant modal facts are facts about the actual world; but to express what it takes for a modal fact to be true, it proves useful to introduce a an accessibility relation between possible worlds as a middle step.
To illustrate, let's take the case of belief.
We will translate belief statements into statements about doxastically accessible worlds. It would be crazy to think that what a person believes, here at our world, is ultimately grounded in facts about other worlds. But it's not crazy to think that the answer to the "problem of intentionality" – the problem of spelling out the metaphysical grounds of intentional states – might go via a doxastic accessibility relation.
I like a broadly functionalist account of intentionality. What makes it the case that an agent is in a given intentional state is that they are in a state with the right functional profile. (For present purposes, we can remain neutral on whether that profile involves only physical states or whether it also involves irreducibly non-physical states of phenomenal consciousness.)
If we take ordinary belief reports to transparently express intentional states, a full account would have to specify the characteristic functional profile of believing that S, for every sentences S.
There was some excitement about this project in the 1970s and 80s. Perhaps, it was thought, our brain stores individual beliefs in an internal language, whose words get their meaning by causal connections to things in the environment. This would explain, it was conjectured, why causal acquaintance is required for singular thought.
On closer inspection (as we saw in the last post), causal acquaintance is neither necessary nor sufficient for singular thought, by our ordinary practice of belief ascriptions. Moreover, to account for the context-dependence of belief reports, we would have to specify a family of functional roles for each belief, with a parameter that is set by conversational context.
Perhaps this can be done. But I think it is fair to say that nobody has done it, and the prospects don't look good.
By contrast, suppose we model a belief state in terms of an accessibility relation to possible worlds, without assuming a simple correspondence between ordinary attitude reports and belief states. Intuitively, we assume that a belief state represents the world as being a certain way; a world is accessible iff it is that way. We then have to associate a functional profile with states of that kind. This task looks more feasible to me (in principle, of course, not in practice). Lewis 1974 outlines the key steps.
This is how a semantics in terms of doxastic accessibility may translate belief sentences into sentences that bring us closer to the relevant metaphysical grounds.
In part 1 of this series, I mentioned the doctrine of "doxastic descriptivism", according to which ordinary people are not belief-related to singular propositions involving ordinary objects. This wasn't the best way of putting it. The hypothesis is rather that at the more fundamental level of doxastic accessibility, ordinary belief states are not singular with respect to ordinary objects. That is, we almost never find that throughout an agent's doxastically accessible worlds, one and the same ordinary object x has the same ordinary property P. Why not? Because such belief states would have very unusual functional profiles.