Jonathan - I like a very similar contextualism about counterfactuals (I can send you a paper setting it out if you’re interested) but hadn’t thought about using the same context set of possibilities for both epistemic contextualism and counterfactual contextualism. That’s a really interesting idea that I’ll have to think more about. My proposal for fixing the context set for counterfactual contextualism involves salient and true chancy theories (or chancy models of theories); if this works out then maybe it could also help to characterise the context set for epistemic contextualism.

My version of the view is motivated primarily by low-chance possibilities - in particular the badness of claims like ‘if I were to drop the plate, it would smash, but there’s a non-zero chance of it not smashing when dropped’. That comes out true on accounts like Robbie’s and Lewis’. And if you also like the duality of might-would counterfactuals, then you also get bad consequences like ‘it’s not the case that, if this plate were dropped, it might hover, even though there’s a non-zero chance of it hovering when dropped.’ That seems to violate plausible connections between objective chance and epistemic modals.

Robbie - here’s a rough kind of reason for thinking that at least some lottery cases and counterfactuals should be given a uniform treatment:

Suppose I’m intending to perform a million coin flips, and am wondering whether p is true: (call this context A)

p - The coin will not land heads every time.

Suppose now I’m undecided about performing the flips, and am wondering about whether q is true: (call this context B)

q - If I flip this coin a million times, it will not land heads every time.

I suggest it’s plausible that p in context A and q in context B should stand and fall together. q is basically just the claim that p is true under the supposition that we’re in context A. So our theory should assign the same truth-values to p in context A as it does to q in context B.

Now suppose I’m intending not to perform a million coin flips, and am wondering whether r is true: (call this context C)

r - If I were to flip this coin a million times, it would not land heads every time.

It seems to me that r at context C, like q at context B, says something about what the appropriate attitude to take to p in context A is. The only difference between q in context B and r in context C is that context C includes an intention not to flip, which (for whatever reason) causes us to use a subjunctive rather than an indicative grammatical form to express ourselves in. But I think what’s said by q in B and by r in C is essentially the same - they amount to endorsing p in context A.

I’m told by people who ought to know that there’s a fair amount of evidence from linguistics that ‘will’ and ‘would’ are closely related, differing primarily in tense. This would also seem to support the view (which I find anyway very intuitive) that p,q, and r stand and fall together.

I think this gives us reason to assign p in A, q in B, and r in C the same truth-value. But this has the consequence that, even prior to a run of flips which does in fact turn out all heads, p is false in the mouth of the budding flipper. That’s anathema to a lot of people, who take it to be obvious that while true in some worlds, p is unknowable in any world (at contexts like A, that is).

This is a risky strategy. Because of the pressure to treat p, q, and r in the same way, and because we’re treating p as obeying LEM, we might be driven to the conclusion that LEM also holds for q and r, and hence to CEM. The picture you end up with is the Stalnakerian one where there is exactly one closest world at every context.

So it looks like we either
1) Go for the Stalnakerian picture.
2) Treat p, q, and r in an artificially different way from one another.
3) Deny LEM for sentences like p.

My preference is actually for 3), though I think this won’t be a very popular option.

(This wouldn’t involve abandoning bivalence for future contingents, by the way - we can still make perfectly good sense of bivalent future contingent sentences which obey LEM, for example. All 3) amounts to is a thesis about the behaviour of the modal ‘will’.)

(And by the way, I’d be more than happy to sign up for the Bennett epistemic principles - they follow from the contextualist semantics for counterfactuals that I like, plus the principal principle, plus a conception of knowledge as credence 1.)

Anyway, I’m interested to hear your thoughts…

My turn to apologise for very slow reply! Just on the first part of 10. There’s something similar to the modus ponens argument in Dylan Dodd’s Synthese paper objecting to the general Lewisian ideas the PPR paper works within. Here’s how I’ve been thinking of it.

Consider defenders of strong centering (which includes me, because of CEM+weak centering, and includes Lewis, weirdly—it fits *very* badly with his views on “might” counterfactuals). For these guys, once you’re certain of the antecedent of a counterfactual, your credence in the counterfactual is then fixed by your credences in the consequent. Indeed, you’ll believe it exactly to the extent you believe the consequent.

So much is neutral territory. Where views diverge, for strong centering folks, is over the truth values of counterfactuals in non-antecedent worlds. This is where disagreements over the shape of the closeness ordering kick in. In the limit, when I’m certain the antecedent is false, I’m able to be certain that “if fair coin were flipped a billion times, then it wouldn’t land all-heads” is true. When I give some credence to the antecedent, those nasty antecedent+not-consequent detract from it somewhat.

In short, in situations where I don’t know the negation of the antecedent, the lottery-like character of the setup comes in *anyway*—because in (epistemically possible) antecedent worlds the truth value of the counterfactual turns on the actual (chancy) outcome. So something like this tempts me: when we *know* the antecedent is false, it’s feasible to *know* that the counterfactual is true. When we come to believe the antecedent, clearly we don’t know it’s negation, and so it’s truth at epistemic possibilities turns lottery-like. Whether we can know it becomes lottery-problematic.

On the other hand, for Bennett’s hypothetical knower, the situation is always lottery-like, since ex hypothesi they’re in a world where the antecedent obtains, and the question is whether they know the outcome.

I’m inclined to deny, therefore (at least for the highly probabilistic counterfactuals) that knowledge of these particular counterfactuals survives learning that the antecedent is true. Of course, this is more drawing out the consequences of my theory, rather than motivating them! But I’d be interested to figure out whether you think that’s enough, or whether I owe something more illuminating…

Good question, though, whether I want to sign up for Bennett’s Hypothesis. I’m not sure, to be honest. I haven’t been thinking in those terms. Certainly, I don’t see any clear counterexamples. I sort of suspect I might be committed to it by the stories of knowledge and counterfactuals in my PPR paper, although I couldn’t quite prove it in the two minutes I just spent with my whiteboard. So call me attracted but uncertain, I guess.

In this comment, I’ll just develop the suggestion that if you deny my agglomeration principle, the conjunction is bad enough. That’s not just because the conjunction is counterintuitive; I think there are theoretical pressures against accepting it.

You think that it’s false that flips1>K(tail1) — that if we were to flip coin 1 a billion times, one could know coin 1 would land tails at least once. I think it’s very hard to think that without also thinking it’s false that K(flips1>tail1). Argument: suppose I know the counterfactual. Then suppose I come to learn that the antecedent is true. This, I’d think, shouldn’t prevent me from continuing to know the counterfactual. Then, by modus ponens, I could come to know tail1. I’m not sure if you’ll agree with me this far. But I think that if flips1>K(tail1) is false, then so must K(flips1>tail1) be.

So we don’t know flip1>tail1. But what should be our attitude to flip1>tail1? If you’re a CEM guy, presumably, should think it’s very likely, though not certain. (If you’re Lewis, you might just think it’s false. Or you might play around with quasi-miracles.) And of course, we should take the same attitude towards flip2>tail2, etc.

What about the conjunction? Your view is that it is true. That’s just a view about metaphysics, not about what attitudes anybody ought to have; but of course, in holding a view, you commit yourself to a certain attitude’s being appropriate toward it. It’s not a good situation to have the view that p and also the view that the rational credence in p is very low. But I worry that this is the view that you may now be committed to. For, plausibly, the rational credence in the conjunction (flip1>tail1 & flip2>tail2 & … & flipn>tailn) is arbitrarily low for a sufficiently large n. The only extra assumption we need to get this result from what we had already is that the probability of each counterfactual is independent from each other. It’s hard to think clearly about these questions, but I think that this is intuitively very plausible — what this coin would do if flipped does not depend probabilistically on what this other coin would do if flipped.

(Suppose we tried to deny the needed independence; the only plausible way I can see to do that is to say that we’re certain that each counterfactual has the same truth value. This might be plausible in the case where we’re certain that none of the coins are going to be flipped — everything is metaphysically symmetric in those cases. But it is not at all plausible if we’re uncertain about whether there will be flippings. If we think some of the coins might be flipped, then we must think there’s a nonzero chance that some coins, but not all, will land heads a billion times.)

More thoughts — and responses to your questions — to follow soon.

@Jonathan6. Let me think this through. First, on the lottery case, you like a certain kind of contextualist quantifier treatment. Now if we apply that to the relevant cases, we’ll get that ideal agent can’t know that the result of coin flips won’t be all-heads (in the relevant context); but that the ideal agent can know that the mug will fall (in the relevant context). (Feel free to insert quotes or whatever to avoid any use/mention problems in that statement). Marry that with the treatment of the counterfactual that I like, and you get the result I favour, right? So if I believed you on the right way to think about lotteries, but stuck to my guns on conditionals, the situation would be very much like the one I describe… wouldn’t it?

Of course there’s the issue about why we don’t give a uniform solution to the two issues. I should read your paper on that! But I guess I don’t really see any prima facie tension between giving different solutions (it’s a bit like what I feel about people like Field who want a uniform solution to the Liar and the Sorites. It’s an interesting idea, and worth working out. But the two phenomena are intuitively pretty different, and it wouldn’t surprise me, or feel unprincipled, if the ultimate accounts are very different).

There’s a different kind of uniformity characteristic of my favoured account of counterfactuals: if you believe the Lewis analysis from Time’s arrow is roughly right for the non-chancy case, mine is (roughly) what you get if you reinterpret what it is for a world to “fit” with the laws in the way we anyway need to to get a Humean best system account theory of chancy laws (this is the Elga stuff). So to me it seems utterly unsurprising that we end up with the sort of closeness conditions for chancy counterfactuals I talk about. And that already solves (at least some of) Hajek’s worries, without the need to appeal to context dependence.

One question that is interesting is whether your theory sustains close enough connections between the relevant class of worlds for counterfactuals and epistemic modals to make the connection I’m discussing in the paper plausible. Would you sign up for (or find attractive) the Bennettian principles I discuss?