Sunday, November 29, 2009

Wide-Scope: use sparingly or use something else?

Zimmerman (1996: 118) says that you shouldn't try to represent conditional obligation in terms of a material conditional where the 'ought' operator takes wide-scope. At first I thought I got it, but now I'm not so sure.

(1) You should vote Obama but if you don't you shouldn't vote at all.

Let A: Vote Obama.
Let B: Vote for no one.

Letting the arrow stand for the material conditional, the idea is that we model conditional obligation (e.g., (1)) as follows:

(2) O(~A --> B)

Here's the problem with that. Suppose O(A). O(A) entails O(AvB), which entails O(~A-->B).

Now, let C: Vote for Romney. Suppose O(A). O(A) entails O(AvC), which entails:

(3) O(~A-->C).

At first I thought that his problem with (2) was that (2) was too weak and that there's got to be more to conditional obligation than (2). That still seems right, but now I'm worried. I could be wrong, but doesn't (1) entail?

(4) O(A).

Doesn't (4) entail (2) and (3)? Doesn't it seem that (1) is incompatible with (3)?

I've been traveling all afternoon and evening, reading Zimmerman on the plane and then driving back to Austin from San Antonio. It is now 1:14 AM and I've just stepped in the door (can't sleep), so there's a non-zero chance that I'm just missing something obvious, but I can't tell whether the problem is that (2) is false or that it's just too weak. What do we have to give up to block the inference from (4) to (2)? He doesn't deny that O(A) entails O(AvB). (His solution to Ross' paradox is the one that I'd offer and it doesn't require denying that inference.)

Maybe the idea is that (1) is compatible with (2) and (3)? Maybe that's right, and maybe the problem is just that (2) is too weak to capture the conditional obligation stated in (1). (AvB) and (AvC) are logically equivalent to (~A --> B) and (~A --> C) respectively and to ~(~A & ~B) and ~(~A & ~C). Just as there's no deontically superior world accessible to this one where you neither A nor B on the assumption that the best accessible world is an A-world, there's no deontically superior world accessible to this one where you neither A nor C on the assumption that the best accssible world is an A-world.

So, maybe the idea is that (1)-(4) are all true and that's consistent with the denial of:

(5) You should vote Obama but if you don't you should vote for Romney.

Why not? If there's more to (1) than (2), then there's more to (5) than (3) and that extra stuff is what we can use to capture the intuition that there's something wrong with (3) that really is the intuition that (5) can't be true if (1) is.


Gabriele Contessa said...

Hi Clayton,

I'm even more tired than you were when writing the post (look at the time of my comment!) so I maybe making a mistake but shouldn't (1) be analyzed as (5) O(A) & ~A ->O(B)?

(Btw, isn't there a clear sense in which O(A) does not imply o(AvB)? I have an obligation to feed my daughters' fish (they never do it themselves and the guy is starving) but I don't seem to have an obligation to do that or torture the neighbour's cat, do I?)

Clayton said...

Hey Gabriele,

Looking at (5), I guess I have this worry. It seems I can't A and B, so it can't be that I ought to (A&B). But, suppose:

(6) I don't A.

It seems to follow from (5) and (6) that I ought to A and I ought to B. I guess you could block the inference to I ought to (A&B) by denying agglomeration or you could deny OIC. (I have mixed feelings about both.) I like Zimmerman's suggestion that there are subsidiary obligations and that's what we're talking about when we talk about not voting rather than voting for Romney.

I think one way to deal with your example of the fish & torture is to say something like this. It's true that you ought to (feed the fish or torture the guy). It is, however, misleading to assert this because you should assert the strongest thing you know, which is that you ought to feed the fish. To speak otherwise is to imply either that you don't know where your obligation is or that either is an acceptable way of meeting your obligation. But, neither of those things is true. That should go some distance towards capturing the intuition that there's something wrong with O(feed v torture). To argue that that's got to be right, I think Zimmerman would say that you are free to make the disjunction true, free to make it false, and there's some accessible world where you do both that is more valuable than any of the accessible worlds in which you do neither (holding all else fixed, I guess).

4:07 and I can't get to sleep. Back to a paper that I'm writing which is getting better and better as time passes.

Clayton said...

Oh, but you were right that O(A) should have been part of the formalization of (1).

Gabriele Contessa said...

I'm inclined to reject OIC (I think I ought to save the people in the trolley's way and not kill the guy on the side track even if it's impossible for me to do both, it's just bad moral luck!) but in any case if you believe OIC isn't it the case that your obligation to vote for Obama disappears once it becomes impossible for you to vote for Obama?

I think you are right about O(feed v torture) especially considering that I'm assuming O(~torture).

nate said...

I must be missing something, but I've been working a lot on conditional obligation, so I'll post anyway.

"Doesn't it seem that (1) is incompatible with (3)?"

Are you inclined to say that? I'm not. I take (1)'s right conjunct to mean that all the best ~A-worlds are B-worlds (which entails that all the best ~A-worlds are ~C-worlds). I take (3) to mean that all the best worlds satisfy (AvC). These are only incompatible if some of the best worlds are C-worlds. But that's ruled out by (1)'s left conjunct.

Here's how I would state the problem for WSO: (4) doesn't seem to entail either conditional obligation all by itself, but the WSO analysis of conditional obligation says it does. That's a problem: the conjunction of "if you don't vote, you shouldn't vote at all" and "if you don't vote, you should vote for Romney" is a contradiction.

nate said...

In reply to Gabriele (and to engage in a little axe-grinding), I think it's poor methodology (although unfortunately very prevalent; see most of the extensive Ross Paradox literature!) to let your intuitions about natural language deontic modals (which have strange and subtle interactions with natural language disjunctions) influence your intuitions about what inferences ought to be licensed in a regimented deontic logic.

The Ross Paradox is explained by the fact that most people hear "You oughta A or B" as permitting both A and B, and requiring at least one. You need the bare modal operators of standard deontic logic (with their usual closure properties) to represent the meaning of this sort of free choice requirement: O(AvB) & P(A) & P(B).

Clayton said...

Hey Nate,

Well, my axe grinding friend, I was initiall inclined towards thinking (1) and (3) were incompatible, but as I was writing I was realizing that the appearance of incompatibility was to read (3) as if it were the proper characterization of a conditional obligation, which it isn't. So, I think that (3) is harmless but seemed not to be because I was reading (3) as something like 'If you don't vote for O, you should vote for R'. But, speaking for myself and Gabriele, I think we were both pretty tired when I wrote this and he responded.

On other matters, I'd love to know what you thought was worth reading on conditional obligation. I have a crazy project on the back burner about OIC and O-implies-can-know-O that I can't do much with until I read up on conditional obligation. All I have is the Zimmerman and the McKinsey paper he references.

Gabriele Contessa said...

You are right on both scores, Nate. (That should teach me a lesson about early morning blogging! ;-)) Anyway, thanks for trying to defend my philosophical honor, Clayton! ;-)

nate said...

My focus is pretty much on the formal semantics, so my recommendations will reflect that.

That said, I'd tend to recommend stuff that makes use of the Lewis/Kratzer semantics for conditionals. Lewis "Semantic Analyses for Dyadic Deontic Logic". Loewer and Belzer "Dyadic Deontic Detachment". van Fraassen's stuff from the 1970s ("The Logic of Conditional Obligation") is good. More recently, Niko Kolodny and John MacFarlane's "Ifs and Oughts" is technically state-of-the-art and surveys a lot of the views on conditional obligation out there. I wrote a paper riffing on Kolodny and MacFarlane, on the relationship between an agent's information and her conditional obligations ("What We Know and What to Do"), which you can find on my webpage, but which is also way too formal and probably a slog.