Monday, February 13, 2012

Knowledge, stakes, and closure

I've been sitting in on, and enjoying, Carrie Jenkins's grad seminar in epistemology. Today, one of our grad students, Kousaku Yui, brought up a pretty interesting suggestion in response to Jason Stanley's stakes-relative approach to knowledge. I didn't recognize the point as one that I've seen discussed before -- if there is a literature on it, I'd be very interested to see it.

The worry is this. Jason thinks that when the stakes are high, it's harder to know. But stakes aren't just a feature of an individual at a time; stakes are high for certain propositions when the truth or falsehood of those propositions make a big difference. It's possible to be such that the stakes for p are high, but the stakes for q are low. For example, it may be very important to Hannah and her wife Sarah whether the bank is open tomorrow, but not at all important to them whether it will rain tomorrow. In such a case, they would need to meet more exacting 'standards' in order to know about the bank than they would to know about the rain. That's a little bit counterintuitive, but only in the way that pragmatic encroachment is generally a little bit counterintuitive.

But here's what might be a deeper problem. Suppose someone is in a situation like the one just mentioned -- the stakes for p are high, but the stakes for q are low -- but where the subject knows that if q, then p. If so, then it's easy to know q, but hard to know p; but it looks like anyone who knows q could easily infer p. Closure plus the possibility of a case with this structure looks like they entail that the stakes-sensitive view can't be right.

Do we have to say such cases are possible? I don't see anything that forces us to, but certain cases are very naturally described in that way. Suppose Hannah and Sarah have an important bill, as per the standard high-stakes bank case; it's very important to them whether the bank will be open on Saturday. Suppose also that they have a friend Franklin who is a bank teller, and they have some small interest in whether he will be at the bank on Saturday. Here, however, the stakes are low -- nothing much hangs on whether they're correct about Franklin's location on Saturday. Assume that they have a good enough position for arbitrary strong knowledge standards for the proposition that Franklin will be at the bank only if it is open. So we have:

  • p: The bank is open Saturday

  • q: Franklin is at the bank Saturday

  • The stakes for p are high

  • The stakes for q are low

  • Everyone knows that if q, then p.

If Hannah and Sarah have a middling epistemic position with respect to q, then it looks like they're in a position to know q, but not to know p. But this violates closure.

Might Jason say that in such a case, the high stakes for p force the stakes up for q as well? He might, but it seems like a pretty strange thing to say. Intuitively, it doesn't matter to them much at all whether Franklin is at work on Saturday. Their bill situation has nothing to do with Franklin. Maybe we can wrap our heads around the idea that the bill makes it harder to know that the bank is open -- but can it really make it harder to know where their friends are?


  1. Masashi Kasaki2/13/2012 11:47:00 AM

    Hi Jonathan,

    I didn't mention this in class, but yes, this kind of problem is brought up by at least two, as far as I know:

    Robert J. Howell (2005). A Puzzle for Pragmatism. American Philosophical Quarterly 42 (2):131-136.
    Gillian K. Russell & John M. Doris (2008). Knowledge by Indifference. Australasian Journal of Philosophy 86 (3):429 – 437.

    I think whether this is a problem for SSI depends on what stakes are and/or how stakes affect knowledge. Of course, SSiists differ as to what answer they give to these questions. For example, on Stanley's view (p. 92, his 2005), "a proposition is a serious practical question for a subject, if there are alternatives to that proposition that the subject ought rationally to consider in decision making."

    Then, the relevant question about your case is not so much whether lows stakes on q affect knowledge of q as whether, given high stakes on p, Hannah and Sarah ought rationally to consider that the bank may have changed its hours recently (and so Franklin is not there), in deciding what to do with Franklin, i.e., in deciding what to do on the assumption that q is right. Stanley would give an affirmative answer to the latter question.

  2. What about claiming that when the stakes are high and it's harder to know 'p' it's also harder to know that 'if q, then p'?

  3. Thanks, Masashi.

    I don't know that Howell paper -- I'll check it out. I do know the Gillian and Doris paper, though. After reviewing it this morning, I didn't find discussion of the sort of cases I'm talking about here. They talk a lot about how surprising features influence knowledge, but they don't appear to discuss the kind of closure puzzle I have in mind.

  4. Gabriele,

    One can say that, but I don't think it's very plausible that it will be able to resolve the puzzle in a plausible way. We can stipulate an arbitrarily strong epistemic position with respect to the conditional.

  5. Elliot Svensson2/14/2012 05:08:00 AM

    Hey Jonathan,

    I think there might be a relevant analogy to this question in the field of structural engineering.

    People always want to know whether their structure will be strong enough the way it's built. For something like a woodshed or a wheelchair access ramp, people are happy to overbuild, since the additional material cost is low. It's different when you're building a bridge.

    When it's expensive to overbuild, people start asking how sure you are that a structure is strong enough. Typical statistical estimates are for 95% certainty, but this needs to be higher where people’s lives may be in danger. You may increase cost and bring this up to 99.99%, or 99.9999%. The science tells us that if you need ≥100% certainty, the cost will become infinite.

    So with cranes and bridges, people spend the money to be really sure that the structure is strong enough. Yet they could always be spending more.

  6. Masashi Kasaki2/14/2012 07:44:00 AM

    The Howell paper does discuss the closure puzzle you brought up in this post. You're right that the Gillian and Doris paper does not. I was taking your problem to be more general: something like, if propositions are different with regard to how much is at stakes on them (or the same proposition differs in stakes over time), there may be some puzzling or unintuitive cases in which S knows one but not the other. I apologize for the confusion.

  7. Jonathan:

    I don't think we can "stipulate an arbitrarily strong epistemic position with respect to the conditional". After all the point of contention is whether or not knowledge depends at least in part on how high the stakes are and, if the stakes for p are high and the ones for q are low, then the stakes wrt that conditional are high.

    Moreover, it doesn't seem to be implausible to say that, if the stakes are high, it's harder to know that, if Franklin is at the bank on Sat, then the bank is open. After all, there might be all sort of reasons why he had to go there even if it's closed.

  8. Hi Jonathan,

    For what it's worth, at the end of Evidence, Pragmatics, and Justification, Matt and I have a proof that being "rational to act as if p" is closed under entailment. That is, if you're rational to act as if p, and rational to act as if (p-->q), then you're rational to act as if q. Of course, if we're right, then if you know that p and you know that (p-->q), then you'll know that q. So, whenever the requirements of that particular closure principle are satisfied (that is, you know that p and you know that p-->q), you'll be rational to act as if q.


  9. Jonathan, suppose one accepts the principle:

    KA: If you know that p, then what you're rational to do is the same as what it is rational to do given p.

    and suppose that the truth of the consequent is a matter of whether the act with the highest expected utility (what you are rational to do) is the same whether or not one conditionalizes on p. If they aren't the same, you don't know, or so says the principle KA.

    In light of KA, we can ask about your last case: do Hannah and Sarah know q? Well, conditionalizing on q, since the epistemic standards they meet for *if q, then p* are enough for probability 1 (or very close to it), the probability of p will be 1 as well (or very close to it). But if this probability is 1, the act with the highest expected utility is *coming back to the bank tomorrow*. However, not conditionalizing on q, the act with the highest expected utility is *waiting in line today*. Since the act with the highest expected utility conditionalizing on q is not the same as the act with the highest expected utility using one's actual probability function, Hannah and Sarah don't know q. So, this wouldn't be a counterexample to closure if the knowledge-action principle KA is true.

  10. Hi Matt, hi Jeremy,

    Thanks for your comments. I think that looks pretty much right, but I'm not sure it makes me feel any better. Part of what was motivating me in my post was that it seems somewhat bizarre that the high stakes with respect to the check should make it harder to know where one's friend is. You've argued that this result is implied by the principles you use to motivate encroachment; this suggests choosing the closure-embracing horn of the dilemma, but it still strikes me as somewhat counterintuitive. (I tend towards a contextualist approach that embraces encroachment, like the one you gesture at in your book -- I think that'd smooth a lot of this over.)


    You're right of course that there are possible versions of the case where there's a relevant possibility in which the friend is at the closed bank. But I think my case works just the same if we stipulate that such possibilities are arbitrarily remote.