If it rains

This appears to be a problem for pure epistemic accounts of indicative conditionals (a la Weatherson and Chalmers), on which "if A then B" is true iff the [epistemically] closest worlds verifying A also verify B.

The match cannot be played if it rains; either it has to be postponed or canceled. Which of these will happen is regulated by the rule book, but nobody has looked up the relevant passages so far. All we know is that exactly one of these two conditionals is in the rule book, and therefore true, and the other false:

1) if it rains, the match will be postponed.
2) if it rains, the match will be canceled.

Going to the epistemically closest worlds where it rains, I find some where the match is postponed and others where it is canceled. So both conditionals come out either false or indeterminate. But we want one of them to be true and the other false. (And we want their disjunction to be true, but one could possibly get that by tinkering with "or".)


Update: Here's a version for impure epistemic accounts a la Nolan.

Same setting as before, except that we also truly believe (from different sources) that a) it won't rain, and that b) the match will not be canceled. To evaluate "if it rains, the match will be canceled", we should now look at the world w such that i) it rains at w, ii) those of our actually true beliefs compatible with (i) are also true at w, and iii) among the worlds satifying (i) and (ii), w is closest to the actual world by the similarity standards for counterfactuals. Since we truly believe that the match will not be canceled, (ii) will presumably rule out all worlds where it rains and the match will be canceled. So on this account, "if it rains, the match will be canceled" is false. But in fact, it may well be true, if that's what the rule book says.

The background worry here is that conditionals can be true independent of what anyone believes or knows; so any analysis that builds doxastic or epistemic clauses into the truth conditions seems wrong. Suppose it is a law of nature that if it rains the match will be canceled (or take a suitable other example). What does this law say? Does it say that the epistemically closest worlds where it rains the match will be canceled? It seems not. The law doesn't make any claim about epistemic states.

Comments

# on 13 February 2007, 12:48

The rule book which nobody has checked yet is reminiscent of the unopened ship's logbook that Hacking uses to argue that epistemic modals are sensitive to more than the actual knowledge of the members of a relevant group, suggesting some notion of "available evidence". What's true for epistemic modals should of course also be true of epistemic conditionals if they exist. In the case of epistemic modals, this is rather extensively discussed on the literature: Hacking, I. (1967). "Possibility," Philosophical Review 76: 143-168. Teller, P. (1972). "Epistemic possibility," Philosophia 2: 203-320. DeRose, K. (1991). "Epistemic possibilities," Philosophical Review 100: 581-605.

# on 13 February 2007, 15:14

(Minor point: shouldn't the putative counterexample to Nolan say that we *know* (a) and (b), not merely truly believe them? He's got an impure epistemic theory, after all, not an impure doxastic theory.)

In the version of this stuff I favour, indicatives with antecedents that are incompatible with knowledge (either my knowledge, or common knowledge of conversational participants) will be vacuously true. Basically, the space of worlds over which the indicative is defined is ordered just like the counterfactual metric, except that worlds we know not to obtain are "missing".

That leads to some issues in other places (I'm not sure it's wise to frame this epistemically rather than doxastically, for example), but it at least gets the examples you mention right, I think. In the first case, because the counterfactual similarity ordering kicks in. In the second case, because of the vacuous truth of the conditional.

(NB: of course, it'll also make the 2nd indicative you mention vacuously true. But most people in this debate need a mechanism to explain away the unassertability of vacuously true conditionals).

Do you reckon there's a reformulation of the problem for a proposal along these lines?

# on 15 February 2007, 13:35

Thanks Kai! JC Bjerring also showed me a similar case in Lycan's book "Real Conditionals".

Robbie, the background worry that conditionals can occur in laws of nature etc. that are independent of anyone's knowledge still remains. In this respect, conditionals seems different from epistemic modals.

And as you say, I would complain that "(even) if it rains, the match will not be canceled" doesn't seem true given that it's a law that if it rains the match will be canceled.

I take it your proposal is basically Brian Weatherson's 2001 account together with Daniel's condition (iii) for ties?

I haven't really thought this through. One worry I have about this kind of approach is that it subscribes to some of the most counterintuitive results of the truth-functional account, e.g. that if Hume was born in London, then Hume was born in Scotland. (Assuming we know he wasn't born in London.) Another is that when I'm in the grip of sceptical considerations, it doesn't seem to me that all non-strict indicative conditionals suddenly turn indeterminate (Brian) or fall together with the corresponding counterfactuals (you).

Also, suppose we have considerable evidence that Kennedy was shot, but it doesn't quite amount to knowledge; moreover, we know this, i.e. we know that our (well supported and moderately strong) belief that Kennedy was shot isn't knowledge. Then on your account, we should judge "if Oswald didn't shoot Kennedy, somebody else did" as definitely false. For by the counterfactual similarity metrics, worlds where somebody else shoots Kennedy are rather far away, and our knowledge doesn't rule out the closer worlds where nobody shoots Kennedy.

# on 17 February 2007, 20:09

Hi Wo,

On the last point: exactly those belief/non-knowledge Oswald/Kennedy cases, are the basis for my concerns about formulating this theory in epistemic terms (though I'm prepared to consider an epistemic version for purposes of easier comparison with Brian and Daniel). What I really want to do is to replace "worlds not known to obtain" by "live conversational possibilities". You then get some interesting interactions between conversational dynamics and conditionals.

As Daniel pointed out to me, if presupposition is understood non-factively (as per normal), you seem to get some weird results unless you make some apparently ad hoc adjustments. E.g. modus ponens fails. Bad stuff (unless you're Lycan)! So we've got a dilemma between counterintuitive results of doing things epistemically, and really bad results of appealing to a non-factive attitude. There's other combinations to try, of course.

On comparison to earlier accounts: yup, the similarity metric is equivalent to cross-breeding Daniel's and Brian's (and Stalnaker's), plus changing the appeal to epistemic attitudes to appeal to some other kind of attitudes. Plus some other minor stuff.

On the "paradoxes of material implication" type stuff: cases get a bit rarer when you shift from an epistemic setting to something like a presuppositional one. And there are reasons to think that we do want vacuous truth at some stage: I think that's the moral to take from Gibbard cases. Actually, it's not so much "paradoxes of material implication" that trouble me with the material conditional account (I'm sort of happy with Geachian responses to those). I just don't think that implicatures alone make a material conditional analysis defensible (not clear what they say about indicative-conditional versions of Sobel sequences etc.)

On the issue on laws of nature. I like the general point. But why not this as a fall-back position: laws of nature should be formulated with material conditionals? I mean, we might talk about laws of nature using indicative conditionals, but isn't it exactly the sort of area where you might expect regimentation to be needed in order to state precisely what the laws of nature are?

Interesting questions arise about the practice of formulating laws on English, certainly. Here's something that would be nice if true: if we could argue that you wouldn't turn truths to falsities by substituting indicative conditionals for the material conditionals that "really" occur in formulating a law of nature. And maybe your examples put pressure on that sort of "safety result". Will have to think about them a bit more.

# trackback from on 17 February 2007, 08:02

Here is a suggestion for a pure doxastic account of indicative conditionals: ‘If A, then C‘ is true iff the most probable world which verifies A also verifies C. By representing degrees of beliefs or credences by a set of possible worlds,...

wo's weblog: If it rains. Un problema para las teorías sobre los condicionales basadas en condiciones doxásticas o epistémicas.

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