That is extremely helpful. It’s almost always hard to jump into an intricate literature, and these comments help clarify a lot.

As far as I can tell, the B is just a device for making the restriction argument of the modal (the domain) explicit in the syntax and truth-conditions. The crucial thing is that B is not an indexical; for the relativist, [[B]]c is invariant, for all c. So I’m having difficulty seeing why you would want to locate the supposed indexicality of the formalization with B.

According to the relativist proposal, we don’t get a domain for the modal to quantify over at the context of utterance; we get it at the point of evaluation (the index). But I think pretty much everyone is happy to allow that there’s nothing strange — and certainly nothing peculiar to the relativist proposal — about this. “Modal bases” (functions from points of evaluation into domains [or things defining domains] of quantification) are the common currency of the modals literature (from Kratzer onward). No one seems to think they make the content of an epistemic modal index-dependent in any way.

Anyway, you seem to be claiming that the content of the sentence “might(B)(p)” at a context c can be gotten just by reading off the right hand of the biconditional. That is, that the speaker of the sentence is saying that p compatible with what she knows. I still can’t tell why you think that.

The reason I was paraphrasing (1a) and (2a) with (1b) and (2b) was not because of the right hand of the biconditional. It was because of the presence of B in might(B)(p) and how B is defined. What role is the B playing?

I realize that the right hand of the biconditional isn’t a good indicator of what proposition is being expressed (I hope that I was aware of this the whole time), but what I don’t get is what B is supposed to be doing. Its restricting the domain, sure. But how does this restriction relate to the content of the proposition expressed? Really, I cannot figure it out beyond my stabs at it with (1b) and (2b).

I think it will make things clearer if we think about relativism as a
proposal for augmenting the index parameter of the semantics (usually
a world-time pair) with something extra: an assessor/judge parameter.
Something like this:

[[might(B)(p)]]c,(w,t,e) = 1 iff there’s a world w’ in [[B]]c,(w,t,e):
[[p]]c,(w,t,e) = 1

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

This is fine, since as far as I can tell the assessor parameter is
behaving pretty much like an extra index in the relativist proposals
I’m aware of. (Note: This isn’t precisely Andy’s view — Andy would
construe B as defining a set of centered worlds, not worlds
simpliciter — but it’s close enough for our purposes.)

Anyway, you seem to be claiming that the content of the sentence
“might(B)(p)” at a context c can be gotten just by reading off the
right hand of the biconditional. That is, that the speaker of the
sentence is saying that p compatible with what she knows. I still
can’t tell why you think that. The assessor parameter (as with the
world and time parameters) just doesn’t get into the assignment of
content at all. Just consider how evaluation of contents at indices
works in more mundane cases:

[[my copy of On the Plurality of Worlds has a shoddy binding]]c,w = 1
iff Nate’s copy of On the Plurality of Worlds has a shoddy binding at
w.

It would be wrong to say that in uttering “my copy of On the Plurality
of Worlds has a shoddy binding” I am claiming that Nate’s copy of On
the Plurality of Worlds has a shoddy binding at the world of
utterance. For one, if it turns out that nate’s copy of on the
plurality of worlds has a shoddy binding at the world of utterance,
then what I say is necessarily true. Clearly, though, it’s only
contingently true. The lesson is this: don’t be misled by the presence
of index parameters in statements of truth-conditions. They’re just
not a part of what sentences are in the business of communicating.

A quick word about the problem of disagreement. Let A utter “might p”
at c at (w,t), and let B utter “cannot p” at a different context d at
(w,t). On the proposal I’ve described, A’s utterance expresses a
function f from world, time, assessor triples to truth-values
(equivalently, the set of world, time, assessor triples that this
function maps to true; call this set “X”). B’s utterance expresses a
function g from world, time, assessor triples to truth-values. Since
[[might(B)(p)]] is context invariant (modulo indexicals, which I’ll
continue to ignore), and assuming that “might” and “cannot” are duals,
g defines a set that is the complement of X with respect to the
universe of indices. So, from a formal point of view, it’s fairly
clear how they’re disagreeing. One is expressing a set of triples that
is just the complement of the other with respect to the universe. But
this in no way rules out that both f(w,t,A) = g(w,t,B) = 1. Both can
be speaking truly, even though B asserts the negation of what A
asserts.

That is really helpful. First, the retractions. Tamina’s proposal is equivalent to Kai and Thony’s. I hadn’t looked at her paper for 6 months or so. I went back today and quickly realized it was equivalent. Since her proposal is equivalent to Andy’s (I think), his must be equivalent to Kai and Thony’s as well.

Second, I now realize what a stupid mistake I was making when thinking about what the content is supposed to be on (e.g.) Tamina’s proposal. I actually think this stupidity is slightly encouraged by the way relativists argue for their view. Perhaps the best way to put the point is by answering your question about why I still don’t see why all of these views aren’t really indexical-relativist views.

So, imagine I utter (1a):

(1a) Nate might be in Ann Arbor.

(1b) is the content of what I say according to (3) combined with (6).

(1b) Nate being in Ann Arbor is compatible with what Errol knows at 3.45 pm in the actual world.

Imagine MvR, being the caring philosophical mentor that he is, knows that you are in fact in Omaha because he went to visit you there today. Moreover, suppose that MvR hears me utter (1a) while watching me on his close circuited television system that he set up around the department. He then utters (2a):

(2a) Nate cannot be in Ann Arbor.

(2b) is the natural paraphrase for (2a) within the current framework:

(2b) Nate being in Ann Arbor is not compatible with what MvR knows at 3.45 pm in the actual world.

But if that is all MvR is saying, then I don’t understand why he and I are supposed to be disagreeing. This seems to me to be the position the indexical-relativist is in with the disagreement cases, not the position the non-indexical relativist should be in.

On the other hand, though, the last sentence cannot be right. Kai and Thony’s proposal does retain content across points of assessment. But I don’t see how such a proposal can give an elegant response to the disagreement cases in the way that MacFarlane and others say it can.

While I’m rambling, let me say that I get in moods where non-indexical relativism seems incoherent. If (3) and (6) are the right way of formulating the view, then it seems to me we’re just adding more context-sensitivity. Jason Stanley articulates these types of worries nicely. See especially the comment thread of this old Thoughts, Arguments, and Rants thread.

If we pretend (as Thony and Kai would like us to) that our intermediate formal language is strictly that of propositional logic, then we can pretend that might(B)(p) contains no indexicals and that what I said in the above post is literally true.

That said, I don’t think what you’ve written here is right. On the standard Kaplanian picture, “content” is determined by evaluating the value the interpretation function [[ ]] assigns to the sentence with respect to the context parameter. But on the view you call “indexical relativism,” [[might(B)(p)]]c is constant. So the Kaplanian content is invariant across points of assessment.

So I take it that you mean something else by “content” — probably truth-conditional content (i.e., the right-half of the biconditional formalizations)? In which case, in order to formalize non-indexical relativism, you’ll want a proposal that makes truth-conditions invariant across points of assessment. But then how are we going to get different truth-values across different points of assessment, if the truth-conditions are invariant across them? I think this begins to make vivid your worry about how we are to go about formalizing non-indexical relativism as a semantic proposal.

These worries are pretty half-baked, and I don’t really expect you to have an answer to them. What I really want to know is what your reasons are for thinking that (7) “is a formalization of indexical relativism.” That should help clear things up for me.

* As a footnote, both Tamina and Andy’s proposals seem to me to be best formalized by the proposal given in Thony and Kai’s paper, Tamina’s pretty clearly so. Why do you think otherwise?