logical form and non-indexical relativism

Although at points the terminology used in the contextualism/relativism literature has been very confusing, recent work by MacFarlane and Weatherson seems to be focusing the terminology a bit. MacFarlane’s paper ‘Non-Indexical Contextualism’ does a really nice job mapping logical space (here, pdf). I’m going to follow Weatherson because it’s going to be easier for my purposes (the details of this are here (pdf), but I’m quoting from here). Weatherson distinguishes between two different ways a view can neglect assessor-sensitivity. That is, they can either accept (T) or (U):

(U) The content of what is said by an utterance is the same relative to any assessor

(T) The truth value of something that is the content of an utterance is the same relative to any assessors

Obviously, there is a view that holds (U) but rejects (T) about some domain . On this view, the content of -propositions is the same relative to any assessor, but the extension of those propositions is relative to assessors. Weatherson labels this view non-indexical relativism.

MacFarlane and Mark Richard have defended non-indexical relativism (see here and here (both pdfs) for MacFarlane and here for Richard). MacFarlane has defended non-indexical relativism about epistemic modals (see the first paper linked in the first sentence above). Non-indexical relativism, he thinks, allows him to solve the problem of disagreement that plagues the indexical contextualist (which is a popular view on the matter). The indexical contextualist accepts both (T) and (U). The problem of disagreement can be seen by considering Ned and Fred (an example similar to this is given by Kratzer somewhere; I cannot remember where). Ned, let’s say, is 15 feet away from a street corner. Fred is 50 feet from the same street corner. A person is approaching the corner. Fred has poor eyesight, and thus cannot see the corner all that well. He utters (1)

(1) That might be Zed.

Since Ned is closer and has better eyesight, he knows that it isn’t Zed. So, he utters (2),

(2) That cannot be Zed.

The indexicalist holds that the content of (1) and (2) is a function of what Ned knows and what Fred knows (obviously I’m assuming some stuff about epistemic modals; hopefully mostly everyone follows what I’m skipping in the interests of time). But since Ned and Fred know differing amounts of information, the indexicalist has it that Ned and Fred aren’t disagreeing. That is, Ned isn’t denying a proposition that Fred is affirming. But, intuitively, he is, and thus they are disagreeing. Nevertheless, it seems as if both Ned and Fred are saying something true. The indexical contextualist gets this result only if she saddles herself with the problem with disagreement.

The non-indexical relativist, however, can solve this problem. Since she’s a non-indexicalist, she can say that Ned and Fred are disagreeing about the same proposition. However, since she is a relativist (i.e. since she denies (T)), she can hold that (1) is true from Fred’s point of assessment and (2) is true from Ned’s point of assessment.

So far, I’ve just sketched some background for what I’m worried about. Kai von Fintel and Thony Gillies have attacked relativism (see here, pdf). They focus on epistemic modals, and they explicitly say that MacFarlane’s view is one they are attacking. They offer up a proposal about the logical form of sentences like (1). So, they hold that the logical form of (1) is (3),

(3) might (B) ()

where is the prejacent (or the proposition being quantified over) and B restricts the quantification. They then give an interpretation of B for the contextualist (i.e. someone who accepts (U)). That interpretation is (4):

(4) [[B]]c ,i = {v : v is compatible with the c-relevant information at i}

where c is the context and i is an world-time index. From (4), we can formalize what it takes for a proposition like (1) to be true,

(5) [[might(B)()]]c ,i =1 if and only if ∃w ∈ [[B]]c ,i: [[]]c ,w,ti =1

So far, so good. They then try to give similar formalizations for the relativist. (6) is how they assign the denotation for B,

(6) [[B]]c ,i,a ={v : v is compatible with what ja knows at ta in wa}

where ja is some judge (or assessor) and ta is the time of assessment and wa is the world where the assessing takes place. They they give (7) as an analogue of (5)

(7) [[might(B)()]]c ,i,a =1 if and only if ∃w ∈ [[B]]c ,i,a : [[]]c ,w,ti ,a = 1

However, thisdoesn’t seem like the correct formalization for non-indexical relativism. Instead, this seems like a formalization of indexical relativism. That’s because (3) and (6) result in points of assessment getting into how content is fixed. Thus, it’s not at all clear that indexical relativism can solve the problem concerning disagreement. Thus, when von Fintel and Gillies attack views that accept (6), they are not attacking MacFarlane. This is a problem considering they think they are attacking MacFarlane.

An interesting question arises, however. How should we formalize non-indexical relativism? As far as I know, Andy Egan’s centered world approach is the only explicit attempt at fixing what the content is supposed to be (I think Tamina Stephenson’s view is like Egan’s, but I’m not entirely sure). Any help with how to do this is greatly appreciated.

By the way, aside from being interested in epistemic modals, I’m also interested in how this all relates to the semantics of ‘ought’. I want to defend non-indexical relativism about ‘ought.’ I’m writing a paper on this right now, and I initially used the von Fintel and Gillies formalizations. But after trying to convert their formalizations about ‘might’ and ‘must’ to ‘ought,’ I realized that they didn’t give correct formalizations for non-indexical relativism.

Update July 7th: Tamina’s view is equivalent to Egan’s. Also, as Nate has pointed out in the comments, Kai and Thony’s relativist is equivalent to Tamina and Egan’s. Finally, and also because of Nate, I should point out that Kai and Thony’s relativist proposal does preserve content across points of assessment. Unfortunately, I’m still puzzled about the dialectic. See my comment below.

~ by Errol Lord on July 5, 2008.