questions about relativism and contextualism about epistemic modals

All of these are minor questions, probably stemming more from ignorance than any sort of insight. Let me stress I’m not trying to push any sort of objection — my puzzlement here is genuine.

Q1: Where’s the asymmetry in disagreement cases?

Relativism about the semantics of epistemic modal sentences (e.g., sentences with the logical form might φ) is partly motivated by its ability to handle the intuition of disagreement in, e.g., eavesdropping cases. The relativist is able to fix on a single proposition on which disagreement in such cases can focus, while the contextualist, it’s claimed, is not.

Stealing from Kai von Fintel and Thony Gillies’ Phil. Review paper “CIA Leaks” (p. 80), consider a relativist proposal that looks something like this (c is the context of utterance, i is the index of evaluation — for now, a world, time pair — and a is a point of assessment).

[[might(B)(φ)]]^c,i,a = 1 iff ∃w’ ε [[B]]^c,i,a: [[φ]]^{c,<w’,t_i>,a} = 1

[[B]]^c,i,a = {w: w is compatible with what is known at a}

So the common item of disagreement according to this kind of relativist will be a function from points of assessment and indices to truth-values — intuitively, I guess, a disagreement about what points of assessment are best or correct.

My question is this: what blocks the contextualist from adapting this line to his own view? Borrowing again from von Fintel and Gillies (p. 78), let’s understand a generic contextualist proposal as follows.

[[might(B)(φ)]]^c,i = 1 iff ∃w’ ε [[B]]^c,i: [[φ]]^c,<w’,t_i> = 1

[[B]]^c,i = {w: w is compatible with the relevant information at c}

Why can’t the contextualist just say that the common item of disagreement is a two-place function from contexts and indices to truth-values? Intuitively this might amount to a disagreement about what contexts are associated with correct functions from indices to truth-values. (But maybe this is philosophically unsatisfying for some reason that I can’t yet see. Perhaps, for example, the relativist proposal can somehow get us a disagreement in what is said. It is, I’ll admit, hard to see how the contextualist proposal would do this.)

Q2: Where do points of assessment fit into the semantics?

The second question is related to the first. Many relativists talk as if they have located a single proposition about which disagreement can occur, but whose truth-value varies with respect to different points of assessment. But the schematic relativist proposal outlined above doesn’t seem to track with this. If a function from contexts and indices to truth-values (what the contextualist proposal can get us) doesn’t count as a proposition, then why should the relativist’s function from points of assessment and indices to truth-values?

I have a sketch of an answer in mind, though I hope people will let me know if it’s obviously inadequate. Contra Kai and Thony (I think), I think maybe it’s natural to understand some relativist proposals as suggestions for augmenting the index of evaluation with an extra point of assessment parameter, but not as suggestions for adding a third, independent point of assessment parameter into the semantics. Andy Egan, for example, takes an epistemic modal claim to express a centered-worlds proposition, i.e., a something that has a truth-value relative to a world-time-individual triple. So maybe we should understand his proposal along these lines (e is an individual).

[[might(B)(φ)]]^c,<w,t,e> = 1 iff ∃<w’,t’,e’> ε [[B]]^c,<w,t,e>: [[φ]]^{c,<w’,t’,e’>} = 1

[[B]]^c,<w,t,e> = {<w’,t’,e’>: it is compatible with what e knows (perhaps in w at t) that her location is given by <w’,t’,e’>}

Alternatively, if we want to limit the role that centered worlds play in our semantics for such sentences, we could go in for a relativist proposal along the following lines:

[[might(B)(φ)]]^c,<w,t,e> = 1 iff ∃w’ ε [[B]]^c,<w,t,e>: [[φ]]^c,<w’,t,e> = 1

[[B]]^c,<w,t,e> = {w’: w’ is compatible with what e knows (perhaps in w at t)}

According to Egan, either kind of view will still be relativist since “it says that some of our utterances have contents which can, for two individuals x and y, simultaneously determine different truth-values relative to x and y, even though x and y are worldmates [and possibly timemates too].”

For what it’s worth: (1) Tamina Stephenson’s basic proposal (which is usually classified as a relativist view) is essentially the same as the first proposal sketched here; (2) either sort of relativism will, I think, have an easier time getting the right results in cases where epistemic modals are embedded under tense and attitude operators. Briefly, handling such cases will involve shifting parameters in the index with respect to which [[B]] is interpreted, as Stephenson does in her work.

Q3: The logical form of epistemic modality claims

I’m slightly bothered by the presence of an unpronounced B element in the statement of a relativist semantics, though I’m not sure if I really should be. Using the simpler version of the relativist semantics sketched above, interpreting B with respect to the world, time, and individual responsible for the utterance yields this:

{w: w is compatible with what is known by the utterer (perhaps at the world and time of utterance)}.

Now, it is part of the relativist position that the utterer is not claiming that there is a world in the set of possibilities compatible with what she knows where the prejacent φ is true. Indeed, the relativist needs to deny this, lest her view become simply a radically subjectivized version of contextualism. But in order to deny this, the relativist will, I think, need to claim that B doesn’t receive its “final,” propositional interpretation from the semantics at the context of utterance, which is to say that B only receives its final, propositional interpretation when the semantic content of the utterance is evaluated with respect to a centered world.

But what will stop the semantics from assigning B its propositional interpretation? That’s to say, what kind of syntactic object is B such that the semantics doesn’t directly assign B a propositional meaning, but rather assigns it a function from centered-worlds to sets of possibilities? Maybe a special kind of pro-form. It’s hard for me to say, but I do think someone should try.

Alternatively, we can just avoid the syntactic issues by removing B from the logical form of the epistemic modal claim, while keeping the semantics pretty much as before:

[[might(φ)]]^c,<w,t,e> = 1 iff ∃w’ ε B_w,t,e: [[φ]]^c,<w’,t,e> = 1

B_w,t,e = {w’: w’ is compatible with what e knows (perhaps in w at t)}

I guess this is what I’d regard as my favored statement of a relativist position about epistemic modals, for all the reasons sketched in this post. What do you think?