It’s my second post and I’m writing about subjunctive conditionals. Does it follow that if this had been my second post, I would’ve written about subjunctive conditionals?
If you are inclined to answer affirmatively, you’re in good company. The entailment, and the associated inference pattern – and-to-if for the subjunctive – is upheld by many (it’s upheld on Lewis’s account in Counterfactuals for instance). Jonathan Bennett, however, is sceptical and is inclined to reject and-to-if (see his A Philosophical Guide to Conditionals, §§92-93).
You might think that this is a minor issue. After even those who accept and-to-if are likely to think that it’d be odd to assert many of the subjunctives in question. But it’s dialectically significant for the debate about closeness in the Lewis-Stalnaker setting. For rejecting if and-to-if means that a world w could be just as close to another world v as v is to itself. To see this, recall Lewis’s account: a subjunctive conditional is (non-vacuously) true at w just in case some (accessible) AC world is closer to w than any world at which A and not-C. Then consider a world where A&C is true. Since no world is closer to w than w, the counterfactual A>C will be true just in case no A&~C world is as close to w as w is to itself. So if we want to reject and-to-if, we must allow that, in this case, w doesn’t automatically win the competition for closeness. This has a bearing on the question of whether some respects of similarity don’t matter when it comes to ordering worlds in terms of closeness. And this is something that is important for Lewis in connection to the future similarity objection. But Bennett’s thought is that if we allow that some aspects of similarity are irrelevant to determining closeness, then, even though nothing is closer to w than w, other worlds may be as close. In particular, we might have cases where A&C is true at w but A&~C is true at some world v such that v is as close to w as w. In this case, A&C is true at w but A>C is false at w. And in this setting, ‘and-if’ fails.
Onto the main point: though Bennett rejects and-to-if, he accepts the following thesis:
HOME FROM ABROAD If A and C are both true at w, then A>C is true at w iff A>C is true at the closest not-A world.
Bennett gives a two little arguments for this. One attempts to establish it on the assumption to w is deterministic, the other attempts to establish it on the assumption that w is indeterministic. Arguing by cases, Bennett defends HOME FROM ABROAD. Since my worry is with a common element in both, I’ll focus on the easier, first argument.
Here’s his argument. Suppose that A and C are both true in w, and that C is deterministically caused. In this setting, Bennett holds it is safe to conclude that A>C. But now consider w’s closest ~A world – call it v. Since v is w’s closest ~A world, Bennett claims that w should is v’s closet A world. But given that C is also true at v’s closest A world, A>C is true at v. So if A&C is true and C is deterministically caused, then A>C is true at w iff A>C is true at w’s closest not-A world.
This argument looks obviously invalid to me. The critical, and problematic step, is the one form “v is w’s closest not-A world” to “w is v’s closest A world”. Surely we can’t rely on this sort of symmetry. For instance, if the closest not-A world v is really far away from w, then we have no guarantee that the shortest journey from v to an A-world is the journey from v to w. In particular, there may be some world u such that A¬-C is true at u and u is closer to v than w. In this case, A>C will be false at v, even though v is w’s closest not-A world. I really can’t see any way to block this in a non ad hoc manner.
So, unless I’m missing something, Bennett’s argument for HOME FROM ABROAD doesn’t work. That’s bad in context because one of his main motivations for rejecting and-to-if is that it allows him to argue for this “agreeable result” (p.241). (Why it’s agreeable, he doesn’t say).
Contra Bennett, I’m inclined to think that the friend of the Lewis-Stalnaker account has good reason to accept and-to-if. But that’s another story.
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June 22, 2008 at 9:34 pm
Robbie
Heya,
That seems right to me–and “Home from Abroad” seems very odd. Let A=C. Let w be a world where A is true. Then HFA says that A>A is true at w iff ~A>A is true at the closest ~A world to w. But on standard treatments, the former is true at all worlds, and the latter is true (at any world) only when A is impossible. So we have a tension…
One little comment about and-to-if. It follows from modus ponens in a setting where you have conditional excluded middle. (By CEM we have A>CvA>~C. Suppose for reductio ~(A>C). Then by disjunctive syllogism, A>~C. But if we have A&C, then by modus ponens we’d have ~C, and so C&~C. So, by reductio, we have A>C.) So if you have reason to like CEM, you have reason to like and-to-if
June 23, 2008 at 8:25 am
Daniel Nolan
I think you’re right, o mysterious blogger, that Home From Abroad is a bad argument. I’d be interested to hear why the L/S types should like and-to-if. Especially since I’m a L/S type person and I don’t like a-t-i. (Or CEM, fortunately.)
June 23, 2008 at 8:37 am
Daniel Nolan
PS While I think HFA is a bad argument, I think Robbie’s argument against it is mistaken.
He says
Let A=C. Let w be a world where A is true. Then HFA says that A>A is true at w iff ~A>A is true at the closest ~A world to w.
No it doesn’t. It says that A>A is true at w iff A>A is true at the closest ~A world to w. But A>A will be true there!
(Well, I think so on most days, anyway, and for most As on all days – and it certainly will be in the sorts of systems Bennett has in mind.)
It’d be interesting to try to come up with real-life-ish examples where HFA fails. But I’m temporarily out of inspiration.
June 23, 2008 at 10:39 am
Robbie
Doh. That’s right. Transcription error. And then mind error.
June 23, 2008 at 1:48 pm
Robbie
Ok. Suppose that A, B and C are in the running to be England manager. A and B have virtually identical records, and are old drinking buddies of the FA executive, while C is the young up and coming manager with far greater potential, and is far and away the most qualified, keen to take the job etc. The FA try to choose an appointments committee that’ll be able to ignore potential bias and appoint on merit. In the end, C gets appointed.
The following seems true:
“If A weren’t to get the job, C would get it”.
This’ll be so since B-appointing worlds are further away than C appointing worlds — which is secured because the appointments committee is chosen so as to select on merit.
Now consider the (counterfactually closest) world where despite C’s record, A gets appointed. That’s gotta be a world where it’s the drinking-buddy factor that gets A the job, since he’s beaten hollow by C in other ways. I.e. this world deviates from actuality in that the wrong people were put onto the appointments committee by the FA executive.
Of course, B beats C on drinking-buddy stakes too, so at this world, we get:
“If A weren’t to get the job, B would get it”.
What this adds up to is “~A>C” true (and “A&C” true) but “A>(~A>C)” false. And that’s a counterexample to HFA.
June 24, 2008 at 9:58 am
richwoodward
Hey guys,
Nice example Robbie – unfortunately, the F.A don’t always pick on merit
One think I don’t really get is why HFA is supposed to be so attractive. Like I said, Bennett is explicit that his reason for rejecting and-to-if is based on the fact that he can subsequently argue for HFA. But we’re not told why HFA is worth arguing for.
Back to and-to-if. Here is one thought as to why we should give up and-to-if that I can imagine someone giving.
If we reject and-to-if, we’re going to have cases where A&C but not-(A>C). Supposing that not-(A>C) entails the weak ‘might’ counterfactual ‘A might C’ (note that that is weaker than Duality), then that entails A&C but A might C.
One might see an argument for and-to-if knocking about here. Let A be ‘0=0′ and let C be ‘England didn’t qualify for the Euros’. As we know, A&C is true. But it’s natural to think that the weak, might, counterfactual – if 0 has been identical to itself, then it might have been the case that England qualified – is true (at least in certain contexts). But if we have and-to-if, we know (at least, given that A might not-C entails not-(A>C), which is just the contrapositive of the principle I gave earlier), that the weak, might counterfactual is false. So we should give up and-to-if.
I could imagine Benentt giving this argument, especitally since he’s up for Duality (though not as an analysis of might counterfactuals). But as someone who isn’t keen on duality, the question is whether a similar kind of argument can be run on a different account of might-counterfactuals. What would need to be the case is that A>C is consistent with A might not-C. That sounds weird – nay, inconsistent – but if the might counterfactual is understood in epistemic terms, a la Stalnaker, then we might have to countenance such cases.